| 1 | C2×C5×C9×ΓL(1,𝔽32) | C2 | 1 | 3 | yes | maximal, direct product factor |
| 2 | C22×C3×C5×ΓL(1,𝔽32) | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×C9×ΓL(1,𝔽32) | C22 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 4 | C22×C9×ΓL(1,𝔽32) | C5 | 1 | 5 | yes | maximal, direct product factor |
| 5 | C22×C5×C9×C31 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×C3×C5×ΓL(1,𝔽32) | C2×C3 | 1 | 3 | yes | — |
| 7 | C22×C5×ΓL(1,𝔽32) | C9 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 8 | C2×C9×ΓL(1,𝔽32) | C2×C5 | 1 | 15 | yes | direct product factor |
| 9 | C2×C5×C9×C31 | C2×C5 | 1 | 3 | yes | complemented |
| 10 | C3×C5×ΓL(1,𝔽32) | C22×C3 | 1 | 1 | yes | characteristic |
| 11 | C22×C3×C5×C31 | C3×C5 | 1 | 1 | yes | characteristic |
| 12 | C22×C3×ΓL(1,𝔽32) | C3×C5 | 1 | 5 | yes | — |
| 13 | C2×C5×ΓL(1,𝔽32) | C2×C9 | 1 | 3 | yes | direct product factor |
| 14 | C5×C9×C31 | C22×C5 | 1 | 1 | yes | characteristic, complemented |
| 15 | C9×ΓL(1,𝔽32) | C22×C5 | 1 | 5 | yes | direct product factor |
| 16 | C22×C9×C31 | C52 | 1 | 1 | yes | characteristic, complemented, Hall |
| 17 | C2×C3×C5×C31 | C2×C3×C5 | 1 | 3 | yes | — |
| 18 | C2×C3×ΓL(1,𝔽32) | C2×C3×C5 | 1 | 15 | yes | — |
| 19 | C22×C52×C9 | — | 31 | 1 | no | maximal, Hall |
| 20 | C5×ΓL(1,𝔽32) | C22×C9 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 21 | C22×C5×C31 | C5×C9 | 1 | 1 | yes | characteristic, complemented |
| 22 | C22×ΓL(1,𝔽32) | C5×C9 | 1 | 5 | yes | direct product factor |
| 23 | C2×C9×C31 | C2×C52 | 1 | 3 | yes | complemented |
| 24 | C3×C5×C31 | C22×C3×C5 | 1 | 1 | yes | characteristic |
| 25 | C3×ΓL(1,𝔽32) | C22×C3×C5 | 1 | 5 | yes | — |
| 26 | C2×C52×C9 | — | 31 | 3 | no | — |
| 27 | C22×C3×C31 | C3×C52 | 1 | 1 | yes | characteristic |
| 28 | C2×C5×C31 | C2×C5×C9 | 1 | 3 | yes | complemented |
| 29 | C2×ΓL(1,𝔽32) | C2×C5×C9 | 1 | 15 | yes | direct product factor |
| 30 | C22×C3×C52 | — | 31 | 1 | no | — |
| 31 | C9×C31 | C22×C52 | 1 | 1 | yes | characteristic, complemented, Hall |
| 32 | C52×C9 | — | 31 | 1 | no | Hall |
| 33 | C2×C3×C31 | C2×C3×C52 | 1 | 3 | yes | — |
| 34 | C22×C5×C9 | — | 31 | 5 | no | — |
| 35 | C22×C5×C9 | ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 36 | C5×C31 | C22×C5×C9 | 1 | 1 | yes | characteristic, complemented |
| 37 | ΓL(1,𝔽32) | C22×C5×C9 | 1 | 5 | yes | direct product factor |
| 38 | C2×C3×C52 | — | 31 | 3 | no | — |
| 39 | C22×C31 | C52×C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 40 | C22×C52 | — | 31 | 1 | no | Hall |
| 41 | C3×C31 | C22×C3×C52 | 1 | 1 | yes | characteristic |
| 42 | C2×C5×C9 | — | 31 | 15 | no | — |
| 43 | C2×C5×C9 | C2×ΓL(1,𝔽32) | 1 | 3 | yes | direct product factor |
| 44 | C3×C52 | — | 31 | 1 | no | — |
| 45 | C2×C31 | C2×C52×C9 | 1 | 3 | yes | complemented |
| 46 | C22×C3×C5 | — | 31 | 5 | no | — |
| 47 | C22×C3×C5 | C3×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic |
| 48 | C2×C52 | — | 31 | 3 | no | — |
| 49 | C5×C9 | — | 31 | 5 | no | — |
| 50 | C5×C9 | C22×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 51 | C22×C9 | C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 52 | C31 | C22×C52×C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 53 | C2×C3×C5 | — | 31 | 15 | no | — |
| 54 | C2×C3×C5 | C2×C3×ΓL(1,𝔽32) | 1 | 3 | yes | — |
| 55 | C52 | — | 31 | 1 | no | Sylow |
| 56 | C22×C5 | — | 31 | 5 | no | — |
| 57 | C22×C5 | C9×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 58 | C2×C9 | C2×C5×ΓL(1,𝔽32) | 1 | 3 | yes | direct product factor |
| 59 | C3×C5 | — | 31 | 5 | no | — |
| 60 | C3×C5 | C22×C3×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic |
| 61 | C22×C3 | C3×C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic |
| 62 | C2×C5 | — | 31 | 15 | no | — |
| 63 | C2×C5 | C2×C9×ΓL(1,𝔽32) | 1 | 3 | yes | direct product factor |
| 64 | C9 | C22×C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 65 | C2×C3 | C2×C3×C5×ΓL(1,𝔽32) | 1 | 3 | yes | — |
| 66 | C5 | — | 31 | 5 | no | — |
| 67 | C5 | C22×C9×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 68 | C22 | C5×C9×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 69 | C3 | C22×C3×C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic |
| 70 | C2 | C2×C5×C9×ΓL(1,𝔽32) | 1 | 3 | yes | direct product factor |
Finite Group Databasebeta