Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
884 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 190 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. #10617425 | C2 | semidirect |
| 3. #10604801 | C2 | semidirect |
| 4. #10604618 | C2 | semidirect |
| 5. #10603851 | C2 | semidirect |
| 16. C5×#493 | C4 | semidirect |
| 17. #65444 | C4 | semidirect |
| 18. #65365 | C4 | semidirect |
| 19. #64988 | C4 | semidirect |
| 44. #3996 | D4 | semidirect |
| 45. #3995 | D4 | semidirect |
| 97. #493 | AGL(1,𝔽5) | semidirect |
| 232. C5 | #23196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617425 | 2 |
| #10613513 | 2 |
| #10604801 | 2 |
| #10604618 | 2 |
| #10603851 | 2 |
| #23196 | 5 |