| 1 | C32×C52×C72 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C3⋊(C5⋊(C5⋊(C7⋊D7))) | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 3 | C3×C5⋊(C5⋊(C7⋊D7)) | — | 3 | 1 | no | maximal |
| 4 | C3×C3⋊(C5⋊(C7⋊D7)) | — | 5 | 6 | no | maximal |
| 5 | C3×C52×C72 | — | 2 | 1 | no | — |
| 6 | C3×C52×C72 | D3 | 1 | 1 | yes | characteristic, complemented |
| 7 | C3×C52×C72 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | C3×C3⋊(C5⋊D35) | — | 7 | 8 | no | maximal |
| 9 | C5⋊(C5⋊(C7⋊D7)) | — | 3 | 1 | no | Hall |
| 10 | C32×C5×C72 | D5 | 1 | 6 | yes | complemented |
| 11 | C32×C52×C7 | D7 | 1 | 8 | yes | complemented |
| 12 | C3⋊(C5⋊(C7⋊D7)) | — | 5 | 6 | no | — |
| 13 | C3×C5⋊(C7⋊D7) | — | 15 | 6 | no | — |
| 14 | C52×C72 | C3×D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 15 | C3⋊(C5⋊D35) | — | 7 | 8 | no | — |
| 16 | C3×C5⋊D35 | — | 21 | 8 | no | — |
| 17 | C3×C3⋊(C7⋊D7) | — | 25 | 1 | no | Hall |
| 18 | C3×C5×C72 | — | 2 | 6 | no | — |
| 19 | C3×C5×C72 | C3×D5 | 1 | 6 | yes | complemented |
| 20 | C3×C5×C72 | D15 | 1 | 6 | yes | complemented |
| 21 | C3×D105 | — | 35 | 48 | no | — |
| 22 | C3×C52×C7 | — | 2 | 8 | no | — |
| 23 | C3×C52×C7 | C3×D7 | 1 | 8 | yes | complemented |
| 24 | C3×C52×C7 | D21 | 1 | 8 | yes | complemented |
| 25 | C5⋊(C7⋊D7) | — | 15 | 6 | no | — |
| 26 | C3×C3⋊(C5⋊D5) | — | 49 | 1 | no | Hall |
| 27 | C32×C72 | C5⋊D5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 28 | C5⋊D35 | — | 21 | 8 | no | — |
| 29 | C32×C5×C7 | D35 | 1 | 48 | yes | complemented |
| 30 | C3⋊(C7⋊D7) | — | 25 | 1 | no | — |
| 31 | C3×C7⋊D7 | — | 75 | 1 | no | — |
| 32 | C5×C72 | C3×D15 | 1 | 6 | yes | complemented |
| 33 | C32×C52 | C7⋊D7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 34 | D105 | — | 35 | 48 | no | — |
| 35 | C3×D35 | — | 105 | 48 | no | — |
| 36 | C52×C7 | C3×D21 | 1 | 8 | yes | complemented |
| 37 | C3⋊(C5⋊D5) | — | 49 | 1 | no | — |
| 38 | C3×C5⋊D5 | — | 147 | 1 | no | — |
| 39 | C3×C72 | — | 2 | 1 | no | — |
| 40 | C3×C72 | C3×C5⋊D5 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×C72 | C3⋊(C5⋊D5) | 1 | 1 | yes | characteristic, complemented |
| 42 | C3×D21 | — | 175 | 8 | no | — |
| 43 | C3×C5×C7 | — | 2 | 48 | no | — |
| 44 | C3×C5×C7 | C3×D35 | 1 | 48 | yes | complemented |
| 45 | C3×C5×C7 | D105 | 1 | 48 | yes | complemented |
| 46 | C7⋊D7 | — | 75 | 1 | no | Hall |
| 47 | C3×D15 | — | 245 | 6 | no | — |
| 48 | C3×C52 | — | 2 | 1 | no | — |
| 49 | C3×C52 | C3×C7⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 50 | C3×C52 | C3⋊(C7⋊D7) | 1 | 1 | yes | characteristic, complemented |
| 51 | D35 | — | 105 | 48 | no | — |
| 52 | C32×C7 | C5⋊D35 | 1 | 8 | yes | complemented |
| 53 | C5⋊D5 | — | 147 | 1 | no | Hall |
| 54 | C72 | C3×C3⋊(C5⋊D5) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 55 | C32×C5 | C5⋊(C7⋊D7) | 1 | 6 | yes | complemented |
| 56 | D21 | — | 175 | 8 | no | — |
| 57 | C3×D7 | — | 525 | 8 | no | — |
| 58 | C5×C7 | C3×D105 | 1 | 48 | yes | complemented |
| 59 | D15 | — | 245 | 6 | no | — |
| 60 | C3×D5 | — | 735 | 6 | no | — |
| 61 | C52 | C3×C3⋊(C7⋊D7) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 62 | C3×C7 | — | 2 | 8 | no | — |
| 63 | C3×C7 | C3×C5⋊D35 | 1 | 8 | yes | complemented |
| 64 | C3×C7 | C3⋊(C5⋊D35) | 1 | 8 | yes | complemented |
| 65 | C3×D3 | — | 1225 | 1 | no | Hall |
| 66 | C3×C5 | — | 2 | 6 | no | — |
| 67 | C3×C5 | C3×C5⋊(C7⋊D7) | 1 | 6 | yes | complemented |
| 68 | C3×C5 | C3⋊(C5⋊(C7⋊D7)) | 1 | 6 | yes | complemented |
| 69 | D7 | — | 525 | 8 | no | — |
| 70 | D5 | — | 735 | 6 | no | — |
| 71 | C32 | C5⋊(C5⋊(C7⋊D7)) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 72 | C7 | C3×C3⋊(C5⋊D35) | 1 | 8 | yes | complemented |
| 73 | C2×C3 | — | 3675 | 1 | no | — |
| 74 | D3 | — | 1225 | 1 | no | — |
| 75 | C5 | C3×C3⋊(C5⋊(C7⋊D7)) | 1 | 6 | yes | complemented |
| 76 | C3 | — | 2 | 1 | no | — |
| 77 | C3 | C3×C5⋊(C5⋊(C7⋊D7)) | 1 | 1 | yes | characteristic, complemented |
| 78 | C3 | C3⋊(C5⋊(C5⋊(C7⋊D7))) | 1 | 1 | yes | characteristic, direct product factor |
| 79 | C2 | — | 3675 | 1 | no | Sylow |
Finite Group Databasebeta