Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
438 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10604340 | C2 | semidirect |
| 5. #10604277 | C2 | semidirect |
| 6. #10598794 | C2 | semidirect |
| 7. #10598788 | C2 | semidirect |
| 372. C5 | #9356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617551 | 2 |
| #10610601 | 2 |
| #10605003 | 2 |
| #10604340 | 2 |
| #10604277 | 2 |
| #10598794 | 2 |
| #10598788 | 2 |
| #9356 | 5 |