Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #10600765 | C2 | semidirect |
| 5. C2×#64672 | C2 | semidirect |
| 6. #10598179 | C2 | semidirect |
| 7. #10598104 | C2 | semidirect |
| 18. #65339 | C4 | semidirect |
| 19. #65332 | C4 | semidirect |
| 21. #65329 | C4 | semidirect |
| 22. #65322 | C4 | semidirect |
| 428. C5 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614665 | 2 |
| #10614651 | 2 |
| C5×#1504 | 2 |
| #10600765 | 2 |
| C2×#64672 | 2 |
| #10598179 | 2 |
| #10598104 | 2 |
| #9263 | 5 |