| 1 | C2×C25×#3862 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×Dic175 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C25×#3862 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | #15668737 | — | 5 | 1 | no | maximal |
| 5 | C2×C72×C25 | C2×C3 | 1 | 1 | yes | characteristic |
| 6 | ΓL(1,𝔽8)⋊Dic25 | — | 7 | 1 | no | maximal |
| 7 | ΓL(1,𝔽8)×Dic25 | — | 7 | 1 | no | maximal |
| 8 | C2×C5×#3862 | D5 | 1 | 1 | yes | characteristic |
| 9 | C72×C25 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | C2×ΓL(1,𝔽8)×C25 | — | 7 | 1 | no | — |
| 11 | C2×ΓL(1,𝔽8)×C25 | — | 7 | 1 | no | — |
| 12 | C7×Dic35 | — | 5 | 1 | no | — |
| 13 | C5×#3862 | Dic5 | 1 | 1 | yes | characteristic |
| 14 | Dic175 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 15 | C7×Dic25 | — | 7 | 1 | no | — |
| 16 | #10596872 | — | 25 | 1 | no | Hall |
| 17 | ΓL(1,𝔽8)×C25 | — | 7 | 1 | no | — |
| 18 | ΓL(1,𝔽8)×C25 | — | 7 | 1 | no | — |
| 19 | C2×C5×C72 | C3×D5 | 1 | 1 | yes | characteristic |
| 20 | ΓL(1,𝔽8)⋊Dic5 | — | 35 | 1 | no | — |
| 21 | Dic5×ΓL(1,𝔽8) | — | 35 | 1 | no | — |
| 22 | C2×C7×C25 | — | 6 | 1 | no | — |
| 23 | C2×C7×C25 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 24 | C2×C7×C25 | C2×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 25 | C3×Dic25 | — | 49 | 1 | no | Hall |
| 26 | C2×#3862 | D25 | 1 | 1 | yes | characteristic |
| 27 | C5×C72 | C3×Dic5 | 1 | 1 | yes | characteristic |
| 28 | C2×C5×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 29 | C2×C5×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 30 | C7×Dic7 | — | 25 | 1 | no | Hall |
| 31 | C7×C25 | — | 6 | 1 | no | — |
| 32 | C7×C25 | ΓL(1,𝔽8)⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | C7×C25 | C4×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×C3×C25 | — | 49 | 1 | no | — |
| 35 | #3862 | Dic25 | 1 | 1 | yes | characteristic, complemented, Hall |
| 36 | Dic35 | — | 5 | 1 | no | — |
| 37 | C7×Dic5 | — | 35 | 1 | no | — |
| 38 | C5×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 39 | C5×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 40 | Dic25 | — | 7 | 1 | no | Hall |
| 41 | C2×C72 | C3×D25 | 1 | 1 | yes | characteristic |
| 42 | C4×ΓL(1,𝔽8) | — | 175 | 1 | no | — |
| 43 | ΓL(1,𝔽8)⋊C4 | — | 175 | 1 | no | — |
| 44 | C3×C25 | — | 49 | 1 | no | Hall |
| 45 | C2×C5×C7 | — | 6 | 1 | no | — |
| 46 | C2×C5×C7 | D5×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 47 | C2×C5×C7 | C5⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 48 | C3×Dic5 | — | 245 | 1 | no | — |
| 49 | C2×C25 | #64422 | 1 | 1 | yes | characteristic |
| 50 | C72 | C3×Dic25 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 51 | C2×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 52 | C2×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 53 | C5×C7 | — | 6 | 1 | no | — |
| 54 | C5×C7 | Dic5×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 55 | C5×C7 | ΓL(1,𝔽8)⋊Dic5 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×C5 | — | 49 | 1 | no | — |
| 57 | C4×C7 | — | 175 | 1 | no | — |
| 58 | Dic7 | — | 25 | 1 | no | — |
| 59 | C25 | #10596872 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 60 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 61 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 62 | Dic5 | — | 35 | 1 | no | — |
| 63 | C3×C5 | — | 49 | 1 | no | — |
| 64 | C2×C7 | — | 6 | 1 | no | — |
| 65 | C2×C7 | ΓL(1,𝔽8)×D25 | 1 | 1 | yes | characteristic |
| 66 | C2×C7 | ΓL(1,𝔽8)⋊D25 | 1 | 1 | yes | characteristic |
| 67 | C3×C4 | — | 1225 | 1 | no | Hall |
| 68 | C2×C5 | C5⋊#64422 | 1 | 1 | yes | characteristic |
| 69 | C7 | — | 6 | 1 | no | — |
| 70 | C7 | ΓL(1,𝔽8)×Dic25 | 1 | 1 | yes | characteristic, complemented |
| 71 | C7 | ΓL(1,𝔽8)⋊Dic25 | 1 | 1 | yes | characteristic, complemented |
| 72 | C2×C3 | — | 49 | 1 | no | — |
| 73 | C5 | #15668737 | 1 | 1 | yes | characteristic |
| 74 | C4 | — | 175 | 1 | no | Sylow |
| 75 | C3 | — | 49 | 1 | no | Sylow |
| 76 | C2 | C25⋊#64422 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta