| 1 | C5×C3⋊D3×ΓL(1,𝔽32) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C32×C5×ΓL(1,𝔽32) | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | C5×C31⋊#157 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | ΓL(1,𝔽32)⋊#157 | C5 | 1 | 5 | yes | maximal, direct product factor |
| 5 | C5×D3×ΓL(1,𝔽32) | — | 6 | 2 | no | — |
| 6 | C5×Dic31⋊C5 | — | 9 | 1 | no | maximal, Hall |
| 7 | C5×C3⋊D3×C31 | C2×C5 | 1 | 1 | yes | characteristic |
| 8 | C3⋊D3×ΓL(1,𝔽32) | C2×C5 | 1 | 5 | yes | — |
| 9 | C3×C5×ΓL(1,𝔽32) | — | 2 | 2 | no | — |
| 10 | C2×C5×ΓL(1,𝔽32) | — | 9 | 1 | no | — |
| 11 | C32×C5×C31 | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 12 | C32×ΓL(1,𝔽32) | C4×C5 | 1 | 5 | yes | complemented |
| 13 | C31⋊#157 | C52 | 1 | 1 | yes | characteristic, complemented, Hall |
| 14 | C5×D3×C31 | — | 6 | 2 | no | — |
| 15 | D3×ΓL(1,𝔽32) | — | 6 | 10 | no | — |
| 16 | C52×#157 | — | 31 | 1 | no | maximal, Hall |
| 17 | C5×ΓL(1,𝔽32) | #157 | 1 | 1 | yes | characteristic, complemented, Hall |
| 18 | C5×Dic31 | — | 9 | 1 | no | — |
| 19 | Dic31⋊C5 | — | 9 | 5 | no | — |
| 20 | C3⋊D3×C31 | C2×C52 | 1 | 1 | yes | characteristic |
| 21 | C3×C5×C31 | — | 2 | 2 | no | — |
| 22 | C3×ΓL(1,𝔽32) | — | 2 | 10 | no | — |
| 23 | C52×C3⋊D3 | — | 31 | 1 | no | — |
| 24 | C2×C5×C31 | — | 9 | 1 | no | — |
| 25 | C2×ΓL(1,𝔽32) | — | 9 | 5 | no | — |
| 26 | C32×C31 | C4×C52 | 1 | 1 | yes | characteristic, complemented, Hall |
| 27 | C32×C52 | — | 31 | 1 | no | Hall |
| 28 | D3×C31 | — | 6 | 2 | no | — |
| 29 | C5×#157 | — | 31 | 5 | no | — |
| 30 | C5×#157 | — | 31 | 1 | no | — |
| 31 | C5×C31 | C5×#157 | 1 | 1 | yes | characteristic, complemented |
| 32 | ΓL(1,𝔽32) | C5×#157 | 1 | 5 | yes | complemented |
| 33 | C52×D3 | — | 186 | 2 | no | — |
| 34 | Dic31 | — | 9 | 1 | no | Hall |
| 35 | C4×C52 | — | 279 | 1 | no | Hall |
| 36 | C3×C31 | — | 2 | 2 | no | — |
| 37 | C5×C3⋊D3 | — | 31 | 5 | no | — |
| 38 | C5×C3⋊D3 | D31⋊C5 | 1 | 1 | yes | characteristic |
| 39 | C3×C52 | — | 62 | 2 | no | — |
| 40 | C2×C31 | — | 9 | 1 | no | — |
| 41 | C2×C52 | — | 279 | 1 | no | — |
| 42 | C32×C5 | — | 31 | 5 | no | — |
| 43 | C32×C5 | Dic31⋊C5 | 1 | 1 | yes | characteristic, complemented |
| 44 | #157 | — | 31 | 1 | no | Hall |
| 45 | C31 | C52×#157 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 46 | C5×D3 | — | 6 | 2 | no | — |
| 47 | C5×D3 | — | 186 | 10 | no | — |
| 48 | C52 | — | 31 | 1 | no | Sylow |
| 49 | C4×C5 | — | 279 | 1 | no | — |
| 50 | C4×C5 | — | 279 | 5 | no | — |
| 51 | C3⋊D3 | C5×D31⋊C5 | 1 | 1 | yes | characteristic |
| 52 | C3×C5 | — | 2 | 2 | no | — |
| 53 | C3×C5 | — | 62 | 10 | no | — |
| 54 | C2×C5 | — | 9 | 1 | no | — |
| 55 | C2×C5 | — | 279 | 5 | no | — |
| 56 | C32 | C5×Dic31⋊C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 57 | D3 | — | 6 | 2 | no | — |
| 58 | C5 | — | 31 | 5 | no | — |
| 59 | C5 | ΓL(1,𝔽32)⋊#157 | 1 | 1 | yes | characteristic, direct product factor |
| 60 | C4 | — | 279 | 1 | no | Sylow |
| 61 | C3 | — | 2 | 2 | no | — |
| 62 | C2 | — | 9 | 1 | no | — |
Finite Group Databasebeta