| 1 | C2×C3×C5×ΓL(1,𝔽32) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | ΓL(1,𝔽32)⋊Dic5 | — | 3 | 1 | no | maximal, Hall |
| 3 | C3×C5×ΓL(1,𝔽32) | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | Dic465 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3⋊(Dic31⋊C5) | — | 5 | 1 | no | maximal |
| 6 | C2×C5×ΓL(1,𝔽32) | D3 | 1 | 1 | yes | characteristic |
| 7 | C2×C3×C5×C31 | C2×C5 | 1 | 1 | yes | characteristic |
| 8 | C2×C3×ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 9 | C2×C3×ΓL(1,𝔽32) | D5 | 1 | 1 | yes | characteristic |
| 10 | C5×ΓL(1,𝔽32) | Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 11 | Dic155 | — | 3 | 1 | no | — |
| 12 | Dic31⋊C5 | — | 15 | 1 | no | — |
| 13 | C3×C5×C31 | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 14 | C3×ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 15 | C3×ΓL(1,𝔽32) | Dic5 | 1 | 1 | yes | characteristic, complemented |
| 16 | Dic93 | — | 5 | 1 | no | Hall |
| 17 | C2×C5×C31 | C5×D3 | 1 | 1 | yes | characteristic |
| 18 | C2×ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 19 | C2×ΓL(1,𝔽32) | D15 | 1 | 1 | yes | characteristic |
| 20 | C5×Dic15 | — | 31 | 1 | no | maximal, Hall |
| 21 | C2×C3×C31 | C5×D5 | 1 | 1 | yes | characteristic |
| 22 | C5×C31 | C5×Dic3 | 1 | 1 | yes | characteristic, complemented |
| 23 | ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 24 | ΓL(1,𝔽32) | Dic15 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×C3×C52 | — | 31 | 1 | no | — |
| 26 | Dic31 | — | 15 | 1 | no | Hall |
| 27 | C5×Dic5 | — | 93 | 1 | no | Hall |
| 28 | C3×C31 | C5×Dic5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 29 | C3×C52 | — | 31 | 1 | no | Hall |
| 30 | C2×C31 | C5×D15 | 1 | 1 | yes | characteristic |
| 31 | Dic15 | — | 31 | 1 | no | — |
| 32 | C5×Dic3 | — | 155 | 1 | no | — |
| 33 | C2×C52 | — | 31 | 1 | no | — |
| 34 | C31 | C5×Dic15 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 35 | C2×C3×C5 | — | 31 | 1 | no | — |
| 36 | C2×C3×C5 | — | 62 | 2 | no | — |
| 37 | C2×C3×C5 | D31⋊C5 | 1 | 1 | yes | characteristic |
| 38 | C52 | — | 31 | 1 | no | Sylow |
| 39 | C4×C5 | — | 465 | 1 | no | — |
| 40 | Dic5 | — | 93 | 1 | no | — |
| 41 | C3×C5 | — | 31 | 1 | no | — |
| 42 | C3×C5 | — | 62 | 2 | no | — |
| 43 | C3×C5 | Dic31⋊C5 | 1 | 1 | yes | characteristic, complemented |
| 44 | Dic3 | — | 155 | 1 | no | Hall |
| 45 | C2×C5 | — | 31 | 1 | no | — |
| 46 | C2×C5 | — | 62 | 2 | no | — |
| 47 | C2×C5 | C3⋊(D31⋊C5) | 1 | 1 | yes | characteristic |
| 48 | C2×C3 | C5⋊(D31⋊C5) | 1 | 1 | yes | characteristic |
| 49 | C5 | — | 31 | 1 | no | — |
| 50 | C5 | — | 62 | 2 | no | — |
| 51 | C5 | C3⋊(Dic31⋊C5) | 1 | 1 | yes | characteristic, complemented |
| 52 | C4 | — | 465 | 1 | no | Sylow |
| 53 | C3 | ΓL(1,𝔽32)⋊Dic5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 54 | C2 | C3⋊(C5⋊(D31⋊C5)) | 1 | 1 | yes | characteristic |
Finite Group Databasebeta