| 1 | #16838466 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C13×#64422 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #16838454 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D7×D91 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 5 | C13×#3862 | C22 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C7⋊D91 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 7 | C7×D91 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | C7×C13×D7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×ΓL(1,𝔽8)⋊D13 | — | 7 | 1 | no | maximal |
| 10 | D13×AGL(1,𝔽7) | — | 7 | 1 | no | maximal |
| 11 | C72×C13 | C22×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 12 | #64422⋊C2 | — | 13 | 1 | no | maximal, Hall |
| 13 | C2×C13×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 14 | ΓL(1,𝔽8)⋊D13 | — | 7 | 1 | no | — |
| 15 | ΓL(1,𝔽8)⋊D13 | — | 7 | 1 | no | — |
| 16 | ΓL(1,𝔽8)⋊D13 | — | 7 | 1 | no | — |
| 17 | C13×AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 18 | ΓL(1,𝔽8)×D13 | — | 7 | 1 | no | — |
| 19 | C2×D91 | — | 7 | 1 | no | — |
| 20 | D7×D13 | — | 7 | 1 | no | — |
| 21 | #64425 | — | 13 | 1 | no | — |
| 22 | #64422 | — | 13 | 1 | no | — |
| 23 | #64422 | D13 | 1 | 1 | yes | characteristic, complemented |
| 24 | C13×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 25 | C13×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 26 | D72 | — | 13 | 1 | no | Hall |
| 27 | C2×C7×C13 | — | 7 | 1 | no | — |
| 28 | D91 | — | 7 | 1 | no | — |
| 29 | D91 | — | 7 | 1 | no | — |
| 30 | D91 | — | 42 | 1 | no | — |
| 31 | D91 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 32 | C7×D13 | — | 7 | 1 | no | — |
| 33 | C13×D7 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×C3×D13 | — | 49 | 1 | no | Hall |
| 35 | #3862 | C2×D13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 36 | C7⋊D7 | — | 13 | 1 | no | — |
| 37 | C7×D7 | — | 13 | 1 | no | — |
| 38 | C7×D7 | C3×D13 | 1 | 1 | yes | characteristic, complemented |
| 39 | C7×C13 | — | 6 | 1 | no | — |
| 40 | C7×C13 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 41 | C7×C13 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 42 | C2×AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 43 | C2×AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 44 | C2×C3×C13 | — | 49 | 1 | no | — |
| 45 | C3×D13 | — | 49 | 1 | no | — |
| 46 | C3×D13 | — | 49 | 1 | no | — |
| 47 | C2×D13 | — | 49 | 1 | no | Hall |
| 48 | C72 | C2×C3×D13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 49 | C2×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 50 | C2×ΓL(1,𝔽8) | — | 91 | 1 | no | — |
| 51 | AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 52 | AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 53 | AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 54 | AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 55 | C3×C13 | — | 49 | 1 | no | Hall |
| 56 | C2×D7 | — | 91 | 1 | no | — |
| 57 | C2×D7 | — | 91 | 1 | no | — |
| 58 | C2×C13 | — | 7 | 1 | no | — |
| 59 | D13 | — | 7 | 1 | no | — |
| 60 | D13 | — | 49 | 1 | no | — |
| 61 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 62 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 63 | C2×C7 | — | 7 | 1 | no | — |
| 64 | C2×C7 | — | 91 | 1 | no | — |
| 65 | D7 | — | 13 | 1 | no | — |
| 66 | D7 | — | 546 | 1 | no | — |
| 67 | D7 | — | 91 | 1 | no | — |
| 68 | D7 | — | 91 | 1 | no | — |
| 69 | D7 | ΓL(1,𝔽8)⋊D13 | 1 | 1 | yes | characteristic, complemented |
| 70 | C13 | #64422⋊C2 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 71 | C22×C3 | — | 637 | 1 | no | Hall |
| 72 | C7 | — | 6 | 1 | no | — |
| 73 | C7 | D13×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 74 | C7 | C2×ΓL(1,𝔽8)⋊D13 | 1 | 1 | yes | characteristic, complemented |
| 75 | C2×C3 | — | 49 | 1 | no | — |
| 76 | C2×C3 | — | 637 | 1 | no | — |
| 77 | C2×C3 | — | 637 | 1 | no | — |
| 78 | C22 | — | 637 | 1 | no | Sylow |
| 79 | C3 | — | 49 | 1 | no | Sylow |
| 80 | C2 | — | 7 | 1 | no | — |
| 81 | C2 | — | 91 | 1 | no | — |
| 82 | C2 | — | 637 | 1 | no | — |
Finite Group Databasebeta