| 1 | C22×C3×C5×ΓL(1,𝔽32) | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×A4×ΓL(1,𝔽32) | C3 | 1 | 3 | yes | maximal, direct product factor |
| 3 | C32×C5×ΓL(1,𝔽32) | — | 4 | 1 | no | maximal, Hall |
| 4 | C3×C5×A4×C31 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×A4×ΓL(1,𝔽32) | C5 | 1 | 5 | yes | maximal, direct product factor |
| 6 | C2×C3×C5×ΓL(1,𝔽32) | — | 3 | 1 | no | — |
| 7 | C22×C5×ΓL(1,𝔽32) | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C3×C5×ΓL(1,𝔽32) | — | 4 | 3 | no | — |
| 9 | C3×C5×ΓL(1,𝔽32) | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 10 | C22×C3×C5×C31 | C3×C5 | 1 | 1 | yes | characteristic, complemented |
| 11 | C5×A4×C31 | C3×C5 | 1 | 3 | yes | complemented |
| 12 | C22×C3×ΓL(1,𝔽32) | C3×C5 | 1 | 5 | yes | complemented |
| 13 | A4×ΓL(1,𝔽32) | C3×C5 | 1 | 15 | yes | direct product factor |
| 14 | C2×C5×ΓL(1,𝔽32) | — | 3 | 1 | no | — |
| 15 | C32×C5×C31 | — | 4 | 1 | no | — |
| 16 | C32×ΓL(1,𝔽32) | — | 4 | 5 | no | — |
| 17 | C3×A4×C31 | C52 | 1 | 1 | yes | characteristic, complemented, Hall |
| 18 | C2×C3×C5×C31 | — | 3 | 1 | no | — |
| 19 | C2×C3×ΓL(1,𝔽32) | — | 3 | 5 | no | — |
| 20 | C3×C52×A4 | — | 31 | 1 | no | maximal, Hall |
| 21 | C5×ΓL(1,𝔽32) | C3×A4 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 22 | C22×C5×C31 | C32×C5 | 1 | 1 | yes | characteristic, complemented |
| 23 | C22×ΓL(1,𝔽32) | C32×C5 | 1 | 5 | yes | complemented |
| 24 | C3×C5×C31 | — | 4 | 3 | no | — |
| 25 | C3×C5×C31 | C5×A4 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×ΓL(1,𝔽32) | — | 4 | 15 | no | — |
| 27 | C3×ΓL(1,𝔽32) | C5×A4 | 1 | 5 | yes | direct product factor |
| 28 | C22×C3×C31 | C3×C52 | 1 | 1 | yes | characteristic, complemented |
| 29 | A4×C31 | C3×C52 | 1 | 3 | yes | complemented |
| 30 | C2×C5×C31 | — | 3 | 1 | no | — |
| 31 | C2×ΓL(1,𝔽32) | — | 3 | 5 | no | — |
| 32 | C22×C3×C52 | — | 31 | 1 | no | — |
| 33 | C52×A4 | — | 31 | 3 | no | — |
| 34 | C32×C31 | — | 4 | 1 | no | Hall |
| 35 | C32×C52 | — | 124 | 1 | no | Hall |
| 36 | C2×C3×C31 | — | 3 | 1 | no | — |
| 37 | C3×C5×A4 | — | 31 | 5 | no | — |
| 38 | C3×C5×A4 | ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 39 | C5×C31 | C3×C5×A4 | 1 | 1 | yes | characteristic, complemented |
| 40 | ΓL(1,𝔽32) | C3×C5×A4 | 1 | 5 | yes | direct product factor |
| 41 | C2×C3×C52 | — | 93 | 1 | no | — |
| 42 | C22×C31 | C32×C52 | 1 | 1 | yes | characteristic, complemented, Hall |
| 43 | C22×C52 | — | 31 | 1 | no | Hall |
| 44 | C3×C31 | — | 4 | 3 | no | — |
| 45 | C3×C31 | C52×A4 | 1 | 1 | yes | characteristic, complemented |
| 46 | C3×C52 | — | 31 | 1 | no | — |
| 47 | C3×C52 | — | 124 | 3 | no | — |
| 48 | C2×C31 | — | 3 | 1 | no | — |
| 49 | C22×C3×C5 | — | 31 | 5 | no | — |
| 50 | C22×C3×C5 | C3×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented |
| 51 | C5×A4 | — | 31 | 15 | no | — |
| 52 | C5×A4 | C3×ΓL(1,𝔽32) | 1 | 3 | yes | direct product factor |
| 53 | C2×C52 | — | 93 | 1 | no | — |
| 54 | C32×C5 | — | 4 | 1 | no | — |
| 55 | C32×C5 | — | 124 | 5 | no | — |
| 56 | C3×A4 | C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 57 | C31 | C3×C52×A4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 58 | C2×C3×C5 | — | 3 | 1 | no | — |
| 59 | C2×C3×C5 | — | 93 | 5 | no | — |
| 60 | C52 | — | 31 | 1 | no | Sylow |
| 61 | C22×C5 | — | 31 | 5 | no | — |
| 62 | C22×C5 | C32×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented |
| 63 | C3×C5 | — | 4 | 3 | no | — |
| 64 | C3×C5 | — | 31 | 5 | no | — |
| 65 | C3×C5 | — | 124 | 15 | no | — |
| 66 | C3×C5 | A4×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 67 | C22×C3 | C3×C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented |
| 68 | A4 | C3×C5×ΓL(1,𝔽32) | 1 | 3 | yes | direct product factor |
| 69 | C2×C5 | — | 3 | 1 | no | — |
| 70 | C2×C5 | — | 93 | 5 | no | — |
| 71 | C32 | — | 4 | 1 | no | Sylow |
| 72 | C2×C3 | — | 3 | 1 | no | — |
| 73 | C5 | — | 31 | 5 | no | — |
| 74 | C5 | C3×A4×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 75 | C22 | C32×C5×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 76 | C3 | — | 4 | 3 | no | — |
| 77 | C3 | C5×A4×ΓL(1,𝔽32) | 1 | 1 | yes | characteristic, direct product factor |
| 78 | C2 | — | 3 | 1 | no | — |
Finite Group Databasebeta