Here are the number of regiments (not division) for the main countries. I have added the date when known
FRANCE. Total : Infantry: 223, Cavalry: 77
Infantry :
- Light infantry : 32 (1804)
- Line infantry : 112 (1806, 135 (1813).
No grenadier regiment, as grenadier were mixed in line infantry regiment.
Cavalry :
- Cuirassier : 12 (1806) 14 (1809)
- Carabiniers : 2
- Dragoon : 30
- Chasseurs : 15
- Chevau-léger lancer : 6 (created in 1811)
- Hussars : 10 (1806), 12(1810)
Guard infantry (number changed a lot during the war):
- Grenadiers : up to 50 in 1813!
- Chasseurs : up to 20
Guard cavalry:
- Horse grenadier : 2
- Chasseur : 1
- Chevaux leger lancer : 2 (3 in 1812 only )
- Dragoon : 1
- Scout : 3
ENGLAND. Total : Infantry : 107, Cavalry : 34
Infantry :
- Guard : 3
- Line : 96 ( 7 highlanders)
- Lignt infantry : 6 (1 highlanders)
- Riflemen : 2
Cavalry :
- Hussar : 0, 4(1811, created from light dragoon)
- Light dragoon : 19, 15 (1811)
- Life guard : 2
- Horse guard : 1
- Dragoon guard : 7
- Dragoon : 5
Austria had until 1809 64 infantry regiments. 5 were Wallon, 1 Italian, 1 Croat, 12 Hungarian and the others German.
Austria also had 17 bounder regiment, and 1 chasseur corps.
In 1812, Austria had 8 Cuirassiers regiments, 12 Hussar regiment 3 Ulhan regiments, 6 dragoon regiments, and 6 Chevauxleger.
In 1805, Russia had 13 Grenadiers regiments, 83 musketeers regiments and 26 chasseurs regiments.
Russian cavalry had 6 Cuirassiers regiments, 30 Dragoon regiments, 8 hussars regiments, 2 horse regiment (ulhan).
In 1812, there were 12 ulhan regiments, with the converion of 7 dragoon regiment to ulhan. 8 other Dragoon regiments were converted into chasseurs à cheval.
The Russian Imperial Guard had in 1811:
- 3 heavy infantry regiment
- 3 chasseur regiment
- 2 cuirassier regiments (a third un 1813)
- 1 hussar regiment
- 1 cossack regiment
- 1 ulhan regiment
-1 dragoon regiment
- 1 chasseur a cheval regiment (1814)
Russia also had 10 cossacks regiments
To finish, here are the russian names of cavalry (but I don't speak Russian, so I hope it's correct)
- cuirassier = kyrasi
- dragoon = dragounski
- hussar = gousari
- horse = konni
- chasseurs à cheval = konno iégurski
PRUSSIA total : Infantry : 60, Cavalry : 19 to 35
Infantry
- total 60 (no details, sorry)
Cavalry, 1792-1807
- Cuirassiers : 13
- Dragoon : 12
- Hussar : 10
Cavalry,1808-1812
- Cuirassiers : 4
- Dragoon: 6
- Hussars : 7
- Ulhan : 2
Cavalry, 1813-1815
- Guard : 4
- Cuirassiers : 4
- Dragoon : 8
- Hussars : 12
- Ulhan : 4
SPAIN :
Infantry :
- Line regiment : 35
- Light regiment : 12
Cavalry :
- Dragoon : 8
- Line : 13
POLAND (Grand Duchy of Warsaw)
Infantry
- 22 regiments
Cavalry :
- Chasseur : 3
- Hussar : 2
- Cuirassiers : 1
- Ulhan : 14
BAVARIA
Infantry :
- line : 11
- light : 6
Cavalry :
- Dragoon : 2 (0 from 1807)
- Chevau-leger : 4 (6 from 1807)
- Hussar : 2 (from 1813)
- Ulhan : 1 (from 1813)