Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10603842 | C2 | semidirect |
| 5. #10603811 | C2 | semidirect |
| 6. #10598598 | C2 | semidirect |
| 7. #10598596 | C2 | semidirect |
| 15. C5×C8×D4 | C4 | semidirect |
| 17. #65301 | C4 | semidirect |
| 18. #65127 | C4 | semidirect |
| 22. C8×D20 | C4 | semidirect |
| 24. #64925 | C4 | semidirect |
| 29. #64873 | C4 | semidirect |
| 142. C8×D4 | AGL(1,𝔽5) | semidirect |
| 371. C5 | #8253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611153 | 2 |
| #10604408 | 2 |
| #10604389 | 2 |
| #10603842 | 2 |
| #10603811 | 2 |
| #10598598 | 2 |
| #10598596 | 2 |
| #8253 | 5 |