| 1 | C7×#713 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×C7⋊AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10587931 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C7⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 5 | C5×C7×Q8 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C7×D20 | — | 2 | 1 | no | — |
| 7 | C7×D20 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C4×C7×D5 | — | 2 | 1 | no | — |
| 9 | C4×C7×D5 | C22 | 1 | 1 | yes | characteristic |
| 10 | C7⋊#170 | — | 2 | 1 | no | — |
| 11 | #6411 | — | 5 | 1 | no | maximal, Hall |
| 12 | #4010 | — | 7 | 1 | no | maximal, Hall |
| 13 | C2×C7×D5 | — | 2 | 1 | no | — |
| 14 | C2×C7×D5 | D4 | 1 | 1 | yes | characteristic |
| 15 | C7⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 16 | C4×C5×C7 | — | 2 | 1 | no | — |
| 17 | C4×C5×C7 | C2×C4 | 1 | 1 | yes | characteristic |
| 18 | C7×Dic5 | D4 | 1 | 1 | yes | characteristic |
| 19 | C7×#41 | — | 5 | 1 | no | — |
| 20 | C4×Dic7 | — | 5 | 1 | no | — |
| 21 | #1136 | — | 5 | 1 | no | — |
| 22 | #713 | D7 | 1 | 1 | yes | characteristic |
| 23 | C4×AGL(1,𝔽5) | — | 7 | 1 | no | — |
| 24 | #700 | — | 7 | 1 | no | — |
| 25 | C2×C5×C7 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 26 | C7×D5 | — | 2 | 1 | no | — |
| 27 | C7×D5 | — | 4 | 1 | no | — |
| 28 | C7×Q8 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 29 | C7×D4 | — | 5 | 1 | no | — |
| 30 | C7×D4 | — | 10 | 1 | no | — |
| 31 | C2×C4×C7 | — | 5 | 1 | no | — |
| 32 | C2×C4×C7 | — | 10 | 1 | no | — |
| 33 | C2×Dic7 | — | 10 | 1 | no | — |
| 34 | C7⋊C8 | — | 10 | 1 | no | — |
| 35 | C2×AGL(1,𝔽5) | — | 14 | 1 | no | — |
| 36 | C5×Q8 | Dic7 | 1 | 1 | yes | characteristic, complemented |
| 37 | D20 | — | 2 | 1 | no | — |
| 38 | D20 | Dic7 | 1 | 1 | yes | characteristic, complemented |
| 39 | C4×D5 | — | 2 | 1 | no | — |
| 40 | C4×D5 | C2×D7 | 1 | 1 | yes | characteristic |
| 41 | #170 | — | 14 | 1 | no | — |
| 42 | C5×C7 | #104 | 1 | 1 | yes | characteristic, complemented, Hall |
| 43 | #104 | — | 35 | 1 | no | Sylow |
| 44 | C22×C7 | — | 5 | 1 | no | — |
| 45 | C22×C7 | — | 10 | 1 | no | — |
| 46 | C4×C7 | — | 2 | 1 | no | — |
| 47 | C4×C7 | — | 5 | 1 | no | — |
| 48 | C4×C7 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 49 | Dic7 | — | 10 | 2 | no | — |
| 50 | C2×D5 | — | 2 | 1 | no | — |
| 51 | C2×D5 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 52 | AGL(1,𝔽5) | — | 14 | 2 | no | — |
| 53 | C4×C5 | — | 2 | 1 | no | — |
| 54 | C4×C5 | C2×Dic7 | 1 | 1 | yes | characteristic |
| 55 | Dic5 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 56 | #41 | — | 5 | 1 | no | — |
| 57 | M16 | — | 35 | 1 | no | — |
| 58 | C42 | — | 35 | 1 | no | — |
| 59 | C2×C7 | — | 10 | 1 | no | — |
| 60 | C2×C7 | — | 20 | 1 | no | — |
| 61 | C2×C7 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 62 | C2×C5 | C22⋊Dic7 | 1 | 1 | yes | characteristic |
| 63 | D5 | — | 2 | 1 | no | — |
| 64 | D5 | — | 4 | 1 | no | — |
| 65 | Q8 | C7⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 66 | D4 | — | 5 | 1 | no | — |
| 67 | D4 | — | 10 | 1 | no | — |
| 68 | C2×C4 | — | 5 | 1 | no | — |
| 69 | C2×C4 | — | 10 | 1 | no | — |
| 70 | C2×C4 | — | 70 | 1 | no | — |
| 71 | C8 | — | 70 | 1 | no | — |
| 72 | C7 | #4010 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 73 | C5 | #6411 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 74 | C22 | — | 5 | 1 | no | — |
| 75 | C22 | — | 10 | 1 | no | — |
| 76 | C4 | — | 2 | 1 | no | — |
| 77 | C4 | — | 5 | 1 | no | — |
| 78 | C4 | — | 70 | 2 | no | — |
| 79 | C4 | C2×C7⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 80 | C2 | — | 10 | 1 | no | — |
| 81 | C2 | — | 20 | 1 | no | — |
| 82 | C2 | C22⋊(C7⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic |
Finite Group Databasebeta