Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
412 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10604295 | C2 | semidirect |
| 5. #10604275 | C2 | semidirect |
| 6. #10598566 | C2 | semidirect |
| 7. #10598558 | C2 | semidirect |
| 365. C5 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617234 | 2 |
| #10613042 | 2 |
| #10604476 | 2 |
| #10604295 | 2 |
| #10604275 | 2 |
| #10598566 | 2 |
| #10598558 | 2 |
| #9531 | 5 |