| 1 | C2×C3×C31×C52⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C52×Dic3×C31 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C4×C31×C52⋊C3 | — | 3 | 1 | no | maximal |
| 4 | C3×C31×C52⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C2×C31×C52⋊C3 | — | 2 | 1 | no | — |
| 6 | C2×C31×C52⋊C3 | D3 | 1 | 1 | yes | characteristic |
| 7 | C2×C3×C52×C31 | C2×C3 | 1 | 1 | yes | characteristic |
| 8 | C4×C52×C31 | — | 3 | 1 | no | Hall |
| 9 | C31×C52⋊C3 | — | 2 | 1 | no | — |
| 10 | C31×C52⋊C3 | Dic3 | 1 | 1 | yes | characteristic, direct product factor |
| 11 | C3×C52×C31 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C5×Dic3×C31 | — | 3 | 2 | no | — |
| 13 | C2×C52×C31 | C3×D3 | 1 | 1 | yes | characteristic |
| 14 | C3×Dic3×C31 | — | 25 | 1 | no | maximal, Hall |
| 15 | C2×C3×C5×C31 | — | 3 | 2 | no | — |
| 16 | Dic3×C52⋊C3 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 17 | C52×C31 | C3×Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 18 | C4×C5×C31 | — | 9 | 2 | no | — |
| 19 | C2×C32×C31 | — | 25 | 1 | no | — |
| 20 | C3×C5×C31 | — | 3 | 2 | no | — |
| 21 | C2×C3×C52⋊C3 | C2×C31 | 1 | 1 | yes | characteristic |
| 22 | C3×C4×C31 | — | 75 | 1 | no | — |
| 23 | Dic3×C31 | C52⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 24 | C2×C5×C31 | — | 3 | 2 | no | — |
| 25 | C52×Dic3 | C3×C31 | 1 | 1 | yes | characteristic, complemented |
| 26 | C4×C52⋊C3 | — | 3 | 1 | no | — |
| 27 | C32×C31 | — | 25 | 1 | no | Hall |
| 28 | C3×C52⋊C3 | C4×C31 | 1 | 1 | yes | characteristic, complemented, Hall |
| 29 | C2×C3×C31 | — | 25 | 1 | no | — |
| 30 | C2×C3×C31 | — | 50 | 1 | no | — |
| 31 | C2×C3×C31 | C2×C52⋊C3 | 1 | 1 | yes | characteristic |
| 32 | C5×C31 | — | 3 | 2 | no | — |
| 33 | C2×C3×C52 | C2×C3×C31 | 1 | 1 | yes | characteristic |
| 34 | C2×C52⋊C3 | — | 2 | 1 | no | — |
| 35 | C2×C52⋊C3 | D3×C31 | 1 | 1 | yes | characteristic |
| 36 | C4×C31 | — | 3 | 1 | no | Hall |
| 37 | C4×C52 | — | 3 | 1 | no | Hall |
| 38 | C3×C31 | — | 25 | 1 | no | — |
| 39 | C3×C31 | — | 50 | 1 | no | — |
| 40 | C3×C31 | C4×C52⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×C52 | C3×C4×C31 | 1 | 1 | yes | characteristic, complemented |
| 42 | C52⋊C3 | — | 2 | 1 | no | — |
| 43 | C52⋊C3 | Dic3×C31 | 1 | 1 | yes | characteristic, direct product factor |
| 44 | C2×C31 | D3×C52⋊C3 | 1 | 1 | yes | characteristic |
| 45 | C5×Dic3 | — | 3 | 2 | no | — |
| 46 | C2×C52 | C3×D3×C31 | 1 | 1 | yes | characteristic |
| 47 | C3×Dic3 | — | 25 | 1 | no | Hall |
| 48 | C31 | Dic3×C52⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 49 | C2×C3×C5 | — | 3 | 2 | no | — |
| 50 | C52 | C3×Dic3×C31 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 51 | C4×C5 | — | 9 | 2 | no | — |
| 52 | C2×C32 | — | 25 | 1 | no | — |
| 53 | C3×C5 | — | 3 | 2 | no | — |
| 54 | C3×C4 | — | 75 | 1 | no | — |
| 55 | Dic3 | C31×C52⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 56 | C2×C5 | — | 3 | 2 | no | — |
| 57 | C32 | — | 25 | 1 | no | Sylow |
| 58 | C2×C3 | — | 25 | 1 | no | — |
| 59 | C2×C3 | — | 50 | 1 | no | — |
| 60 | C2×C3 | C2×C31×C52⋊C3 | 1 | 1 | yes | characteristic |
| 61 | C5 | — | 3 | 2 | no | — |
| 62 | C4 | — | 3 | 1 | no | Sylow |
| 63 | C3 | — | 25 | 1 | no | — |
| 64 | C3 | — | 50 | 1 | no | — |
| 65 | C3 | C4×C31×C52⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 66 | C2 | D3×C31×C52⋊C3 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta