| 1 | #14579184 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q16×D79 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14579107 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14579106 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14579104 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14579100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | Q32×C79 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11929625 | — | 2 | 1 | no | — |
| 9 | Q8×D79 | — | 2 | 1 | no | — |
| 10 | Dic316 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11929614 | — | 2 | 1 | no | — |
| 12 | #11929611 | — | 2 | 1 | no | — |
| 13 | D632 | C22 | 1 | 1 | yes | characteristic |
| 14 | C8×D79 | C22 | 1 | 1 | yes | characteristic |
| 15 | C79⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 16 | Q16×C79 | C22 | 1 | 1 | yes | characteristic |
| 17 | Q16×C79 | C22 | 1 | 1 | yes | characteristic |
| 18 | C16×C79 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×C79 | — | 2 | 1 | no | — |
| 20 | Q8×C79 | — | 2 | 1 | no | — |
| 21 | D316 | — | 2 | 1 | no | — |
| 22 | D316 | — | 4 | 1 | no | — |
| 23 | C4×D79 | — | 4 | 1 | no | — |
| 24 | C4×D79 | — | 4 | 1 | no | — |
| 25 | C4×D79 | D4 | 1 | 1 | yes | characteristic |
| 26 | Dic158 | — | 2 | 1 | no | — |
| 27 | Dic158 | — | 4 | 1 | no | — |
| 28 | C8×C79 | C23 | 1 | 1 | yes | characteristic |
| 29 | C79⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×D79 | — | 4 | 1 | no | — |
| 31 | C2×D79 | D8 | 1 | 1 | yes | characteristic |
| 32 | C4×C79 | — | 4 | 1 | no | — |
| 33 | C4×C79 | — | 4 | 1 | no | — |
| 34 | C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 35 | Dic79 | — | 4 | 1 | no | — |
| 36 | Dic79 | D8 | 1 | 1 | yes | characteristic |
| 37 | C2×C79 | C2×D8 | 1 | 1 | yes | characteristic |
| 38 | D79 | — | 2 | 1 | no | — |
| 39 | D79 | — | 8 | 1 | no | — |
| 40 | C79 | #510 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 41 | #510 | — | 79 | 1 | no | maximal, Sylow |
| 42 | #135 | — | 79 | 1 | no | — |
| 43 | C2×Q16 | — | 79 | 1 | no | — |
| 44 | Q32 | — | 79 | 1 | no | — |
| 45 | Q32 | D79 | 1 | 1 | yes | characteristic, complemented |
| 46 | SD32 | — | 79 | 1 | no | — |
| 47 | SD32 | — | 79 | 1 | no | — |
| 48 | M32 | — | 79 | 1 | no | — |
| 49 | #41 | — | 158 | 1 | no | — |
| 50 | C2×Q8 | — | 158 | 1 | no | — |
| 51 | Q16 | — | 79 | 1 | no | — |
| 52 | Q16 | — | 158 | 1 | no | — |
| 53 | Q16 | C2×D79 | 1 | 1 | yes | characteristic |
| 54 | Q16 | C2×D79 | 1 | 1 | yes | characteristic |
| 55 | SD16 | — | 158 | 1 | no | — |
| 56 | D8 | — | 79 | 1 | no | — |
| 57 | C2×C8 | — | 79 | 1 | no | — |
| 58 | C16 | — | 79 | 1 | no | — |
| 59 | C16 | C2×D79 | 1 | 1 | yes | characteristic |
| 60 | Q8 | — | 2 | 1 | no | — |
| 61 | Q8 | — | 2 | 1 | no | — |
| 62 | Q8 | — | 316 | 1 | no | — |
| 63 | Q8 | — | 158 | 1 | no | — |
| 64 | D4 | — | 316 | 1 | no | — |
| 65 | D4 | — | 158 | 1 | no | — |
| 66 | C2×C4 | — | 316 | 1 | no | — |
| 67 | C2×C4 | — | 316 | 1 | no | — |
| 68 | C2×C4 | — | 79 | 1 | no | — |
| 69 | C8 | — | 79 | 1 | no | — |
| 70 | C8 | C22×D79 | 1 | 1 | yes | characteristic |
| 71 | C22 | — | 316 | 1 | no | — |
| 72 | C22 | — | 79 | 1 | no | — |
| 73 | C4 | — | 4 | 1 | no | — |
| 74 | C4 | — | 4 | 1 | no | — |
| 75 | C4 | — | 316 | 1 | no | — |
| 76 | C4 | — | 79 | 1 | no | — |
| 77 | C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 78 | C2 | — | 632 | 1 | no | — |
| 79 | C2 | — | 158 | 1 | no | — |
| 80 | C2 | D8×D79 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta