Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 14. C5×C8×Q8 | C4 | semidirect |
| 15. #65313 | C4 | semidirect |
| 18. #65120 | C4 | semidirect |
| 23. C8×Dic10 | C4 | semidirect |
| 24. #64931 | C4 | semidirect |
| 29. #64873 | C4 | semidirect |
| 131. C8×Q8 | AGL(1,𝔽5) | semidirect |
| 321. C5 | #8254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611648 | 2 |
| #10604443 | 2 |
| #10604424 | 2 |
| #10603842 | 2 |
| #10603811 | 2 |
| #10598598 | 2 |
| #10598596 | 2 |
| #8254 | 5 |