| 1 | C2×C5×ΓL(1,𝔽32)⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×Dic5×ΓL(1,𝔽32) | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×ΓL(1,𝔽32)⋊C9 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | Dic5×C31⋊C9 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C4×ΓL(1,𝔽32)⋊C9 | — | 5 | 1 | no | maximal |
| 6 | C2×C3×C5×ΓL(1,𝔽32) | C2×C3 | 1 | 1 | yes | characteristic |
| 7 | Dic5×ΓL(1,𝔽32) | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C2×C5×C31⋊C9 | C2×C5 | 1 | 1 | yes | characteristic |
| 9 | C2×ΓL(1,𝔽32)⋊C9 | — | 2 | 2 | no | — |
| 10 | C2×ΓL(1,𝔽32)⋊C9 | D5 | 1 | 1 | yes | characteristic |
| 11 | C3×C5×ΓL(1,𝔽32) | C3×C4 | 1 | 1 | yes | characteristic |
| 12 | C3×Dic5×C31 | C3×C5 | 1 | 1 | yes | characteristic |
| 13 | C3×C4×ΓL(1,𝔽32) | — | 5 | 1 | no | — |
| 14 | C2×C5×ΓL(1,𝔽32) | C2×C9 | 1 | 1 | yes | characteristic |
| 15 | C5×C31⋊C9 | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 16 | ΓL(1,𝔽32)⋊C9 | — | 2 | 2 | no | — |
| 17 | ΓL(1,𝔽32)⋊C9 | Dic5 | 1 | 1 | yes | characteristic, direct product factor |
| 18 | C4×C31⋊C9 | — | 5 | 1 | no | Hall |
| 19 | C2×C3×C5×C31 | C2×C3×C5 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 21 | C2×C3×ΓL(1,𝔽32) | C3×D5 | 1 | 1 | yes | characteristic |
| 22 | C5×C9×Dic5 | — | 31 | 1 | no | maximal, Hall |
| 23 | C5×ΓL(1,𝔽32) | C4×C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 24 | Dic5×C31 | C5×C9 | 1 | 1 | yes | characteristic, complemented |
| 25 | C4×ΓL(1,𝔽32) | — | 5 | 1 | no | — |
| 26 | C2×C31⋊C9 | C5×D5 | 1 | 1 | yes | characteristic |
| 27 | C3×C5×C31 | C3×C4×C5 | 1 | 1 | yes | characteristic |
| 28 | C3×ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 29 | C3×ΓL(1,𝔽32) | C3×Dic5 | 1 | 1 | yes | characteristic |
| 30 | C2×C52×C9 | — | 31 | 1 | no | — |
| 31 | C3×C4×C31 | — | 5 | 1 | no | — |
| 32 | C2×C5×C31 | C2×C5×C9 | 1 | 1 | yes | characteristic |
| 33 | C2×ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 34 | C2×ΓL(1,𝔽32) | C9×D5 | 1 | 1 | yes | characteristic |
| 35 | C3×C5×Dic5 | — | 31 | 1 | no | — |
| 36 | C31⋊C9 | C5×Dic5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 37 | C52×C9 | — | 31 | 1 | no | Hall |
| 38 | C2×C3×C31 | C3×C5×D5 | 1 | 1 | yes | characteristic |
| 39 | C4×C5×C9 | — | 155 | 1 | no | — |
| 40 | C9×Dic5 | — | 31 | 1 | no | — |
| 41 | C5×C31 | C4×C5×C9 | 1 | 1 | yes | characteristic, complemented |
| 42 | ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 43 | ΓL(1,𝔽32) | C9×Dic5 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×C3×C52 | — | 31 | 1 | no | — |
| 45 | C4×C31 | — | 5 | 1 | no | Hall |
| 46 | C5×Dic5 | — | 31 | 1 | no | Hall |
| 47 | C3×C31 | C3×C5×Dic5 | 1 | 1 | yes | characteristic |
| 48 | C2×C5×C9 | — | 31 | 1 | no | — |
| 49 | C2×C5×C9 | — | 31 | 1 | no | — |
| 50 | C2×C5×C9 | — | 62 | 2 | no | — |
| 51 | C3×C52 | — | 31 | 1 | no | — |
| 52 | C2×C31 | C5×C9×D5 | 1 | 1 | yes | characteristic |
| 53 | C3×C4×C5 | — | 155 | 1 | no | — |
| 54 | C3×Dic5 | (C31⋊C3)⋊C5 | 1 | 1 | yes | characteristic |
| 55 | C2×C52 | — | 31 | 1 | no | — |
| 56 | C5×C9 | — | 31 | 1 | no | — |
| 57 | C5×C9 | — | 31 | 1 | no | — |
| 58 | C5×C9 | — | 62 | 2 | no | — |
| 59 | C4×C9 | — | 155 | 1 | no | Hall |
| 60 | C31 | C5×C9×Dic5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 61 | C2×C3×C5 | — | 31 | 1 | no | — |
| 62 | C2×C3×C5 | — | 62 | 2 | no | — |
| 63 | C2×C3×C5 | C2×(C31⋊C3)⋊C5 | 1 | 1 | yes | characteristic |
| 64 | C52 | — | 31 | 1 | no | Sylow |
| 65 | C4×C5 | — | 155 | 1 | no | — |
| 66 | Dic5 | ΓL(1,𝔽32)⋊C9 | 1 | 1 | yes | characteristic, direct product factor |
| 67 | C2×C9 | — | 31 | 1 | no | — |
| 68 | C3×C5 | — | 31 | 1 | no | — |
| 69 | C3×C5 | — | 62 | 2 | no | — |
| 70 | C3×C5 | C4×(C31⋊C3)⋊C5 | 1 | 1 | yes | characteristic |
| 71 | C3×C4 | — | 5 | 1 | no | — |
| 72 | C2×C5 | — | 31 | 1 | no | — |
| 73 | C2×C5 | — | 62 | 2 | no | — |
| 74 | C2×C5 | C2×ΓL(1,𝔽32)⋊C9 | 1 | 1 | yes | characteristic |
| 75 | C9 | — | 31 | 1 | no | Sylow |
| 76 | C2×C3 | D5×(C31⋊C3)⋊C5 | 1 | 1 | yes | characteristic |
| 77 | C5 | — | 31 | 1 | no | — |
| 78 | C5 | — | 62 | 2 | no | — |
| 79 | C5 | C4×ΓL(1,𝔽32)⋊C9 | 1 | 1 | yes | characteristic, complemented |
| 80 | C4 | — | 5 | 1 | no | Sylow |
| 81 | C3 | Dic5×(C31⋊C3)⋊C5 | 1 | 1 | yes | characteristic |
| 82 | C2 | D5×ΓL(1,𝔽32)⋊C9 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta