Of course not. Please do.
Here is the best map I could find in the Internet on short notice.
The precise date is indeterminate and unimportant; as of 1490s, all the dated polities still and/or already existed. The Crimean Khanate is obvious, the purple state to its immediate northeast is the Great Horde, northeast of
that is the Khanate of Kazan, the Astrakhan Khanate is the blue state to the southeast, the orange polity is the Nogai Horde, the green state east of that is the Kazakh Khanate and blue to the northeast is the Khanate of Sibir - or, more accurately for until 1495, the Khanate of Tyumen.
Not shown, and rightly so, is the
Qasim Khanate, which was formed after the Khan of Kazan defeated the Grand Prince of Moscow in 1445, and among other conditions had Vasily II give over a region to his (the Khan's) son Qasim and his noble retainers. They eventually fit in relatively well with the rest of Muscovite feudals, having technically become the Grand Prince's vassals, and
technically became a faction/social group of their own, though it's too small to actually add so it might be considered one of the stronger local boyardom groups or alternatively be counted as part of the Court, being reasonably close to it. Regardless, they are mostly important since they are indisputable Genghisids and as such make a neat political card to play against the other Khanates (and played they were, historically).
Without going into too much detail, the Golden Horde (or, rather, Ulus Juchi, so called after the founder of the Genghisid branch that was to rule those western regions in perpetuity as khans) had declined profoundly over the course of the 14th and early 15th centuries due to the Black Death, dynastic struggles and, perhaps most importantly, deterioration of the social structures ironed out by Genghis Khan: to wit, the general socio-economic stratification, the weakening of ethnic and social ties between different tribes (partly because they had intermixed with different local populations), the increasing independence and decreasing loyalty of the military aristocracy and the gradual revival of/shift towards sedentary life, especially in the regions of future Crimean and Kazan Khanates. The attempts to revitalise the failing polity by bringing in the more nomadic Turkic tribes from the east only made the aforementioned dynastic struggles worse, and as they got worse, the military hierarchy became more ambitious and reckless. Mamai was one of the most successful non-Genghisid generals to try and seize power, but his power was nonetheless weak and uncertain, and collapsed soon after the Battle of Kulikovo; Tokhtamysh, one of the more distant Genghisids, killed Mamai, took power for himself and generally shored things up for a while with some local successes, but then was utterly defeated by a Mr. Timur, and things kept going downhill from there.
Tokhtamysh was finished off by one of his emirs and generals, Edigu, who had by then already de facto achieved independence and sovereignty over what would become the
Nogai Horde. He wasn't a Genghisid either, and yet he too went on to try and dominate Ulus Juchi; he succeeded up to a point, as khan-maker and the power behind the throne, but ultimately he got overthrown and then killed too; the Nogai Horde lived on under his successors, though, never reclaiming its political significance but remaining a nuisance to whoever it could reach (not just its immediate neighbours) thanks to its relative retention of nomadic military vitality which was expressed through incessant slave raids (mostly for trade, but also for domestic use) and similar. The Nogai Horde is notable for retaining little or no ideological ties with the old Ulus Juchi (indeed being traditionally fiercely opposed to the Genghisids), for being much more Turkic than Mongolic in general and for being relatively primitive, tribal and nomadic. The mirzas, who in this case are the tribal nobility, would be by far the predominant faction. Currently led by Abbas-biy (biy is the title, presumably similar to beg).
Anyway, things back in the Golden Horde only got more chaotic as Genghisids from different branches fought to fill the vacuum of power left by Edigu, and what remained of the Ulus' unity deteriorated further. In the 1420s, the main struggle went on between Baraq Khan from the east and Ulugh Muhammed Khan from the west; the two kept chasing each other away from the capital, Sarai, until after yet another defeat Baraq Khan got killed for good by an eastern Genghisid (more specifically, Shaybanid) bej, Abu'l-Khayr Khan, in 1427. Abu'l-Khayr Khan went on to found the "Uzbek Khanate", defeating nearby enemies and expanding his realm pretty far, but alienated the tribal nobility by fortifying his power at the expense of theirs. After having been defeated by the invading Oirats in 1456, Abu'l-Khayr quickly began losing what he had gained, and in 1465 the discontent Kazakhs successfully broke away, led by the two sons of Baraq Khan who had now created the
Kazakh Khanate (the Uzbek Shaybanids obviously recovered towards the end of the century, though). Anyway, the Kazakh Khanate gradually settled down and expanded in the eastern parts of the Ulus Juchi, fought with the Shaybanid leftovers and also the Nogai Khanate. Though led by Genghisids and otherwise rather more civilised, the Kazakh Khanate too was a nomadic tribal confederacy (with local tribal rulers called "sultans") if a more centralised one (comparable with late 9th/early 10th century Kievan Rus). In 1490 it was ruled by Buryndyk Khan.
Before going back to the west: the
Khanate of Sibir was apparently founded, as a practically autonomous component of the Ulus Juchi, way back in the 13th century and since then was ruled by non-Genghisid Taibugids. Back in his better days, Abu'l-Khayr Khan subjugated the area, and since his death the Taibugids had to contend with a branch of the Shaybanids, neither being able to completely defeat the other (so presumably both deserve to be factions if such are needed). Regardless, for now (as of 1490) the Shaybanid Ibak Khan won and consolidated his power somewhat, also allying with Muscovy.
Anyway, Ulugh Muhammed became the closest there was to a khan of the Ulus Juchi, but even then he only ruled the western parts of the Ulus, and very shakily at that. In particular, the
Khanate of Crimea now broke away completely under the Genghisid Haci I Devlet Giray, supported by the Lithuanians. He and his immediate successors worked hard to consolidate the Khanate into a strong state, to defend its independence and to actively meddle in the affairs of the rest of the Steppe to this effect, also allying with Muscovy against common enemies. Anyway, by the 1470s dynastic strife and the growing power of the (classically feudal) beys began to affect the otherwise well-off Khanate, and after the Ottomans established a foothold in Crimea by seizing the Genoese colonies, they were able to get involved in those intrigues, overthrowing and then restoring Mengli I Giray (who is still in power as of 1490). The Khanate (as opposed to former Genoese territories) retained a great deal of de facto autonomy, though the khan now had to be Porte-approved, and there was some measure of oversight. It continued to carry out a very active and ambitious foreign policy in the steppe as well, aiming, like so many before it, to reclaim supreme power over the Ulus Juchi (which is something to consider whether you keep it within the Ottoman Empire or not, and a nice possible source of intrigue if you do).
As for Ulugh Muhammed, after failing to assert himself in Crimea, he decided to focus on establishing his power base in the north. His new base of operations was Kazan', which he seized from what were up to now vassal Volga Bulgar rulers; he consistently tried to reassert predominance over Muscovy, and had some successes, including the aforementioned Qasim Khanate, but after his death in 1445 the
Khanate of Kazan entered a relative decline, losing what little control over the Ulus it still had. Regardless, for a while the Khanate of Kazan continued to fight against Muscovy, but the tide was turning, and besides Kazan too was plagued by dynastic and feudal strife; a pro-Russian noble party eventually prevaield with some military help, and in 1487 Ilham Khan was overthrown and his young half-brother Muhammad Amin was elevated and began paying tribute; still, there was very little at all keeping Kazan from cutting all ties with Muscovy and reclaiming full independence whenever it wanted, except for practical considerations and faction politics. Kazan is perhaps the most advanced khanate as such, with a revived urban culture and economy, and is interesting from the viewpoint of factions, with urban Bulgar nobility, a weaker-than-usual but still present feudal nobility, strongly anti-Russian Nogai palace guard, a sizable population of free commoners (free like Chinese peasants were free, anyway) and reasonably influential Muslim clergy.
The remnants of the post-Ulugh Muhammed Ulus Juchi along with the cities of Sarai and Astrakhan passed to Kuchuk Muhammed, to whom Ulugh Muhammed had all but abandoned those regions earlier. Kuchuk's children fought over this inheritance; the younger, Akmat, ended up winning, but his defeated elder brother Mahmud fled south and established the rival
Astrakhan Khanate, which mostly sat on the defensive throughout its history, coming under attacks from all directions due to lucrative trade routes and wealth in general, eventually submitting de jure but not de facto to the Great Horde. Astrakhan was also reasonably advanced, but with a much stronger feudal and dynastic nobility and weaker khans overall.
As for Akhmat, he had created the
Great Horde (the Ulus Remnant, pretty much) and made an honest effort to reforge the Ulus Juchi; his initial apparent successes had caused several ordinarily hostile khanates to ally with each other and with Muscovy, and after the failed 1480 campaign he was attacked by the Khan of Sibir and by the Nogai, and ended up being killed within 1481. The Great Horde (led by Murtasa Khan as of 1490) insisted on continuing to exist for a while more, but was continually attacked by Sibir and Crimea in particular, the two khanates being eager both to keep the sons of Akhmat from reuniting the Ulus Juchi and to seize Sarai and so hopefully reunite the Ulus Juchi by themselves. The state was remarkably militarised and very true to the traditions of the good old Ulus Juchi in this regard and others, with a strong military aristocracy alongside the remaining and increasingly unhappy tribal one.
Basically, just about everyone needs a tribal (or feudal in Crimea and Astrakhan) nobility, a dynastic faction (or two as in Sibir), and probably retainers because every early feudal ruler had a small army of military retainers who also constituted a special political party.
That good enough for you?
