Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
432 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 19. C5×#500 | C4 | semidirect |
| 20. #65382 | C4 | semidirect |
| 21. #65382 | C4 | semidirect |
| 24. #64988 | C4 | semidirect |
| 102. #700 | Q16 | semidirect |
| 131. #500 | AGL(1,𝔽5) | semidirect |
| 334. C5 | #9056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617377 | 2 |
| #10613665 | 2 |
| #10604679 | 2 |
| #10604645 | 2 |
| #10604622 | 2 |
| #10598531 | 2 |
| #10598530 | 2 |
| #9056 | 5 |