Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
624 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 1. #10617366 | C2 | semidirect |
| 3. #10604794 | C2 | semidirect |
| 4. #10604793 | C2 | semidirect |
| 5. #10604607 | C2 | semidirect |
| 6. #10603821 | C2 | semidirect |
| 7. #10603811 | C2 | semidirect |
| 264. C5 | #17989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617366 | 2 |
| #10613506 | 2 |
| #10604794 | 2 |
| #10604793 | 2 |
| #10604607 | 2 |
| #10603821 | 2 |
| #10603811 | 2 |
| #17989 | 5 |