Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
434 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10600927 | C2 | semidirect |
| 5. #10600834 | C2 | semidirect |
| 6. #10598192 | C2 | semidirect |
| 7. #10598188 | C2 | semidirect |
| 10. C23×#168 | C4 | semidirect |
| 16. #65496 | C4 | semidirect |
| 22. #65288 | C4 | semidirect |
| 24. #65286 | C4 | semidirect |
| 386. C5 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614647 | 2 |
| C5×#2120 | 2 |
| #10602509 | 2 |
| #10600927 | 2 |
| #10600834 | 2 |
| #10598192 | 2 |
| #10598188 | 2 |
| #12805 | 5 |