Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1306 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 232 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 |
|---|---|---|
| 2. #10617473 | C2 | semidirect |
| 3. #10604916 | C2 | semidirect |
| 4. #10604915 | C2 | semidirect |
| 17. #65759 | C22 | semidirect |
| 19. #65757 | C22 | semidirect |
| 21. C4×#704 | C22 | semidirect |
| 23. #64921 | C22 | semidirect |
| 66. #4002 | C23 | semidirect |
| 336. C5 | #17666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4082 | 2 |
| #10617473 | 2 |
| #10604916 | 2 |
| #10604915 | 2 |
| #17666 | 5 |