| 1 | C3×C72×D5×C13 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C72×C13×AGL(1,𝔽5) | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C3×C5×C72×C13 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C3×C4×C72×C13 | — | 5 | 1 | no | maximal, Hall |
| 5 | C72×D5×C13 | C2×C3 | 1 | 1 | yes | characteristic |
| 6 | C3×C7×C13×AGL(1,𝔽5) | C7 | 1 | 8 | yes | maximal, direct product factor |
| 7 | C2×C3×C72×C13 | — | 5 | 1 | no | — |
| 8 | C5×C72×C13 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C3×C72×AGL(1,𝔽5) | C13 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 10 | C3×C7×D5×C13 | C2×C7 | 1 | 8 | yes | — |
| 11 | C4×C72×C13 | — | 5 | 1 | no | Hall |
| 12 | C3×C72×C13 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 13 | C7×C13×AGL(1,𝔽5) | C3×C7 | 1 | 8 | yes | direct product factor |
| 14 | C3×C72×D5 | C2×C13 | 1 | 1 | yes | characteristic |
| 15 | C3×C5×C7×C13 | C4×C7 | 1 | 8 | yes | complemented |
| 16 | C2×C72×C13 | — | 5 | 1 | no | — |
| 17 | C3×C4×C7×C13 | — | 5 | 8 | no | — |
| 18 | C72×AGL(1,𝔽5) | C3×C13 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 19 | C7×D5×C13 | C2×C3×C7 | 1 | 8 | yes | — |
| 20 | C3×C13×AGL(1,𝔽5) | C72 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 21 | C3×C5×C72 | C4×C13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 22 | C72×C13 | C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 23 | C3×C4×C72 | — | 5 | 1 | no | Hall |
| 24 | C2×C3×C7×C13 | — | 5 | 8 | no | — |
| 25 | C72×D5 | C2×C3×C13 | 1 | 1 | yes | characteristic |
| 26 | C5×C7×C13 | C3×C4×C7 | 1 | 8 | yes | complemented |
| 27 | C3×C7×AGL(1,𝔽5) | C7×C13 | 1 | 8 | yes | direct product factor |
| 28 | C3×D5×C13 | C2×C72 | 1 | 1 | yes | characteristic |
| 29 | C4×C7×C13 | — | 5 | 8 | no | — |
| 30 | C2×C3×C72 | — | 5 | 1 | no | — |
| 31 | C3×C7×C13 | C7×AGL(1,𝔽5) | 1 | 8 | yes | direct product factor |
| 32 | C13×AGL(1,𝔽5) | C3×C72 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 33 | C5×C72 | C3×C4×C13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 34 | C3×C7×D5 | C2×C7×C13 | 1 | 8 | yes | — |
| 35 | C4×C72 | — | 5 | 1 | no | Hall |
| 36 | C3×C5×C13 | C4×C72 | 1 | 1 | yes | characteristic, complemented, Hall |
| 37 | C2×C7×C13 | — | 5 | 8 | no | — |
| 38 | C3×C4×C13 | — | 5 | 1 | no | Hall |
| 39 | C3×C72 | C13×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 40 | C7×AGL(1,𝔽5) | C3×C7×C13 | 1 | 8 | yes | direct product factor |
| 41 | D5×C13 | C2×C3×C72 | 1 | 1 | yes | characteristic |
| 42 | C3×C5×C7 | C4×C7×C13 | 1 | 8 | yes | complemented |
| 43 | C2×C72 | — | 5 | 1 | no | — |
| 44 | C7×C13 | C3×C7×AGL(1,𝔽5) | 1 | 8 | yes | direct product factor |
| 45 | C3×C4×C7 | — | 5 | 8 | no | — |
| 46 | C2×C3×C13 | — | 5 | 1 | no | — |
| 47 | C7×D5 | C2×C3×C7×C13 | 1 | 8 | yes | — |
| 48 | C5×C13 | C3×C4×C72 | 1 | 1 | yes | characteristic, complemented, Hall |
| 49 | C3×AGL(1,𝔽5) | C72×C13 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 50 | C4×C13 | — | 5 | 1 | no | Hall |
| 51 | C72 | C3×C13×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 52 | C2×C3×C7 | — | 5 | 8 | no | — |
| 53 | C3×C13 | C72×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 54 | C5×C7 | C3×C4×C7×C13 | 1 | 8 | yes | complemented |
| 55 | C3×D5 | C2×C72×C13 | 1 | 1 | yes | characteristic |
| 56 | C4×C7 | — | 5 | 8 | no | — |
| 57 | C2×C13 | — | 5 | 1 | no | — |
| 58 | C3×C7 | C7×C13×AGL(1,𝔽5) | 1 | 8 | yes | direct product factor |
| 59 | AGL(1,𝔽5) | C3×C72×C13 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 60 | C3×C5 | C4×C72×C13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 61 | C2×C7 | — | 5 | 8 | no | — |
| 62 | C13 | C3×C72×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 63 | C3×C4 | — | 5 | 1 | no | Hall |
| 64 | D5 | C2×C3×C72×C13 | 1 | 1 | yes | characteristic |
| 65 | C7 | C3×C7×C13×AGL(1,𝔽5) | 1 | 8 | yes | direct product factor |
| 66 | C2×C3 | — | 5 | 1 | no | — |
| 67 | C5 | C3×C4×C72×C13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 68 | C4 | — | 5 | 1 | no | Sylow |
| 69 | C3 | C72×C13×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 70 | C2 | — | 5 | 1 | no | — |
Finite Group Databasebeta