Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
726 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 184 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. #10617371 | C2 | semidirect |
| 3. #10604650 | C2 | semidirect |
| 4. #10604065 | C2 | semidirect |
| 5. #10603817 | C2 | semidirect |
| 6. #10603806 | C2 | semidirect |
| 247. C5 | #17981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617371 | 2 |
| #10613664 | 2 |
| #10604650 | 2 |
| #10604065 | 2 |
| #10603817 | 2 |
| #10603806 | 2 |
| #17981 | 5 |