Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
538 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 1. #10617363 | C2 | semidirect |
| 3. #10604620 | C2 | semidirect |
| 4. #10604604 | C2 | semidirect |
| 5. #10604593 | C2 | semidirect |
| 6. #10598531 | C2 | semidirect |
| 7. #10598530 | C2 | semidirect |
| 21. C5×#493 | C4 | semidirect |
| 24. #65359 | C4 | semidirect |
| 25. #65359 | C4 | semidirect |
| 27. #64971 | C4 | semidirect |
| 124. #700 | D8 | semidirect |
| 147. #493 | AGL(1,𝔽5) | semidirect |
| 400. C5 | #9053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617363 | 2 |
| #10613506 | 2 |
| #10604620 | 2 |
| #10604604 | 2 |
| #10604593 | 2 |
| #10598531 | 2 |
| #10598530 | 2 |
| #9053 | 5 |