| 1 | C31×C3⋊(C3⋊(C5⋊D5)) | C2 | 1 | 2 | yes | maximal, direct product factor |
| 2 | C2×C32×C52×C31 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C31×C3⋊(C5⋊D5) | — | 3 | 4 | no | maximal |
| 4 | C32×C52×C31 | C22 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C2×C31×C3⋊D15 | — | 5 | 6 | no | maximal |
| 6 | C31×C3⋊(C5⋊D5) | — | 3 | 8 | no | — |
| 7 | C2×C3×C52×C31 | D3 | 1 | 4 | yes | complemented |
| 8 | C2×C31×C5⋊D5 | — | 9 | 1 | no | Hall |
| 9 | C31×C3⋊D15 | — | 5 | 12 | no | — |
| 10 | C2×C32×C5×C31 | D5 | 1 | 6 | yes | complemented |
| 11 | C3×C52×C31 | C2×D3 | 1 | 4 | yes | complemented |
| 12 | C2×D15×C31 | — | 15 | 24 | no | — |
| 13 | C2×C52×C31 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 14 | C31×C5⋊D5 | — | 9 | 2 | no | — |
| 15 | C32×C5×C31 | C2×D5 | 1 | 6 | yes | complemented |
| 16 | C2×C3⋊D3×C31 | — | 25 | 1 | no | Hall |
| 17 | C2×C3×C5×C31 | D15 | 1 | 24 | yes | complemented |
| 18 | D15×C31 | — | 15 | 48 | no | — |
| 19 | C2×C3⋊(C3⋊(C5⋊D5)) | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 20 | C52×C31 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 21 | C2×D5×C31 | — | 45 | 6 | no | — |
| 22 | C2×C32×C31 | C5⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3⋊D3×C31 | — | 25 | 2 | no | — |
| 24 | C3×C5×C31 | C2×D15 | 1 | 24 | yes | complemented |
| 25 | C2×C32×C52 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3⋊(C3⋊(C5⋊D5)) | C2×C31 | 1 | 2 | yes | direct product factor |
| 27 | C2×D3×C31 | — | 75 | 4 | no | — |
| 28 | C2×C5×C31 | C3⋊D15 | 1 | 6 | yes | complemented |
| 29 | D5×C31 | — | 45 | 12 | no | — |
| 30 | C2×C3⋊(C5⋊D5) | — | 3 | 4 | no | — |
| 31 | C32×C31 | C2×C5⋊D5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 32 | C32×C52 | C22×C31 | 1 | 1 | yes | characteristic, complemented, Hall |
| 33 | C2×C3×C31 | C3⋊(C5⋊D5) | 1 | 4 | yes | complemented |
| 34 | D3×C31 | — | 75 | 8 | no | — |
| 35 | C2×C3⋊D15 | — | 5 | 6 | no | — |
| 36 | C5×C31 | C2×C3⋊D15 | 1 | 6 | yes | complemented |
| 37 | C2×C3×C52 | D3×C31 | 1 | 4 | yes | complemented |
| 38 | C3⋊(C5⋊D5) | — | 3 | 8 | no | — |
| 39 | C22×C31 | — | 225 | 1 | no | Hall |
| 40 | C2×C5⋊D5 | — | 9 | 1 | no | Hall |
| 41 | C3×C31 | C2×C3⋊(C5⋊D5) | 1 | 4 | yes | complemented |
| 42 | C2×C32×C5 | D5×C31 | 1 | 6 | yes | complemented |
| 43 | C3⋊D15 | — | 5 | 12 | no | — |
| 44 | C3×C52 | C2×D3×C31 | 1 | 4 | yes | complemented |
| 45 | C2×C31 | — | 225 | 2 | no | — |
| 46 | C2×C31 | C3⋊(C3⋊(C5⋊D5)) | 1 | 1 | yes | characteristic, direct product factor |
| 47 | C2×D15 | — | 15 | 24 | no | — |
| 48 | C2×C52 | C3⋊D3×C31 | 1 | 1 | yes | characteristic, complemented |
| 49 | C5⋊D5 | — | 9 | 2 | no | — |
| 50 | C32×C5 | C2×D5×C31 | 1 | 6 | yes | complemented |
| 51 | C2×C3⋊D3 | — | 25 | 1 | no | Hall |
| 52 | C31 | C2×C3⋊(C3⋊(C5⋊D5)) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 53 | C2×C3×C5 | D15×C31 | 1 | 24 | yes | complemented |
| 54 | D15 | — | 15 | 48 | no | — |
| 55 | C52 | C2×C3⋊D3×C31 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 56 | C2×D5 | — | 45 | 6 | no | — |
| 57 | C2×C32 | C31×C5⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 58 | C3⋊D3 | — | 25 | 2 | no | — |
| 59 | C3×C5 | C2×D15×C31 | 1 | 24 | yes | complemented |
| 60 | C2×D3 | — | 75 | 4 | no | — |
| 61 | C2×C5 | C31×C3⋊D15 | 1 | 6 | yes | complemented |
| 62 | D5 | — | 45 | 12 | no | — |
| 63 | C32 | C2×C31×C5⋊D5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 64 | C2×C3 | C31×C3⋊(C5⋊D5) | 1 | 4 | yes | complemented |
| 65 | D3 | — | 75 | 8 | no | — |
| 66 | C5 | C2×C31×C3⋊D15 | 1 | 6 | yes | complemented |
| 67 | C22 | — | 225 | 1 | no | Sylow |
| 68 | C3 | C2×C31×C3⋊(C5⋊D5) | 1 | 4 | yes | complemented |
| 69 | C2 | — | 225 | 2 | no | — |
| 70 | C2 | C31×C3⋊(C3⋊(C5⋊D5)) | 1 | 1 | yes | characteristic, direct product factor |
Finite Group Databasebeta