Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. #65382 | C4 | semidirect |
| 13. #65381 | C4 | semidirect |
| 111. C2×#168 | Q16 | semidirect |
| 288. C5 | #9290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615101 | 2 |
| #10615060 | 2 |
| C5×#1518 | 2 |
| #10601573 | 2 |
| #10600348 | 2 |
| #10598231 | 2 |
| #10598122 | 2 |
| #9290 | 5 |