Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10604727 | C2 | semidirect |
| 3. #10604713 | C2 | semidirect |
| 4. #10598803 | C2 | semidirect |
| 5. C22×C5×D8 | C4 | semidirect |
| 12. #65448 | C4 | semidirect |
| 16. #65395 | C4 | semidirect |
| 18. #64895 | C22 | semidirect |
| 19. #64891 | C22 | semidirect |
| 99. C22×D8 | AGL(1,𝔽5) | semidirect |
| 276. C5 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615567 | 2 |
| #10604727 | 2 |
| #10604713 | 2 |
| #10598803 | 2 |
| #11868 | 5 |