- second: from 1933 to 1939 the german army went from minor defense force to the worlds most powerfull fighting force in only six years, 30 Panzer Divisions, 70 Motorized Divisions, 140 Infantry Divisions
Actually in September 1939 Germany had fewer divisions than 240 (from your count: 30 + 70 + 140 = 240), but still it was a considerable amount:
I. Against Poland (designated for the invasion of Poland):
- 7 Panzer divisions - 1., 2., 3., 4., 5., 10., "Kempf"
- 4 Leichte divisions (also armored - like Panzer divisions - but most of them had different organization and fewer tanks) - 1., 2., 3., 4.
- 4 Motorized divisions - 2., 13., 20., 29.
- 3 Mountain divisions - 1., 2., 3.
- 45 1/3 Infantry divisions - 1., 3., 4., 7., 8., 10., 11., 12., 14., 17., 18., 19., 21., 22. Luftlande [1/3], 23., 24., 27., 28., 30., 31., 32., 44., 45., 46., 50., "Eberhard" (60.), 56., 57., 61., 62., 68., 73., 206., 207., 208., 213., 217., 218., 221., 228., 239., 252., 257., 258., "Netze" (301.), "Brand" (311.)
- one Flieger division (it was actually part of Luftwaffe - but its "ground" component consisted of 2 regiments of Fallschirmjägers) - 7.
- 1. Cavalry Brigade & Brigade "Konigsberg (= 2 brigades = +/- equivalent of one more division)
II. Against the West (designated to defend the border with France, Belgium, Holland & Luxemburg) and those left inside the Reich:
- 46 2/3 Infantry divisions - 5., 6., 9., 13., 15., 16., 22. Luftlande [2/3], 25., 26., 33., 34., 35., 36., 52., 58., 69., 71., "Tier" (72.) 75., 76., 78., 79., 86., 87., 14. Landwehr (205.), 209., 211., 212., 214., 215., 216., 223., 225., 227., 231., 246., 251., 253., 254., 255., 256., 260., 262., 263., 267., 268., 269.
Total: ca. 112 divisions
Of course when France declared war on 3 September, some of those in the West (especially those with numbers 200+) were still not fully mobilized.
Aditionally there were many smaller significant independent units (regiments, battalions) which would count as equivalent of several further divisions. Below I will list only more significant of those units and only those used against Poland (and I will not list independent, non-divisional artillery units - which were very numerous, there were dozens of such artillery battalions, vast majority of them motorized, usually subordinated to Corps level, sometimes to Army level):
Against Poland:
- one SA Brigade - 6. SA-Brigade
- 2 strengthened SS Motorized regiments - "Germania", "Leibstandarte"
- one strengthened SS Motorized battalion - "Heimwehr-Danzig"
- one SS Engineer battalion - "Dresden"
- 2 independent tank battalions - I./Pz.Rgt.10, I./Pz.Rgt.23
- 2 independent recon battalions - Aufkl.Lehr.Abt., Aufkl.Abt.1
- one so called Kampfgruppe "Medem"
- 3 independent Festung regiments - 128., 138., 148.
- one independent Landwehr infantry regiment - 183.
- 22 independent Grenzwacht (Border Guard) regiments - 1., 2., 3., 11., 12., 13., 21., 23., 31., 32., 41., 42., 58., 68., 78., 88., 98., 108., 118., 121., 122., 123.
And many other non-divisional units (for example those mentioned motorized artillery battalions, assigned to various Corps and Armies).
Grenzwacht regiments, despite all having "regiment" in their names, were units of extremely various strength (for example out of those at the Polish border, listed above, the weakest was ca. 800 men strong and the strongest was ca. 4400 men strong).
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Several (at least 8) new divisions were formed during September & October 1939:
- between 17 & 21 September 93., 94., 95., 96., 98. Infantry divisions were formed
- on 15 October 526. Infantry division was formed (from Grenzschutz-Ab.-Kom.9)
- on 24 October 430. Infantry division was formed (from Landesschützen battalions)
- SS "Totenkopf" division was formed in October
Also 1. Cavalry Brigade was expanded into Cavalry Division in October.
Then further divisions were formed in November & December 1939, etc., etc.
Conversion of Leichte divisions into Panzer ones also started in October (in case of 1. Leichte-Division it was in fact just enough to rename it to "Panzer", as it was already as strong as Panzer divisions and organized in the same way during the invasion of Poland).
On the other hand Pz.Div. "Kempf" was disbanded in October, its tanks (Panzer-Regiment 7.) went to Leichte divisions (now converted to Panzer divisions), while its infantry - together with independent SS Motorized regiments - went to newly formed SS divisions.