Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #10602820 | C2 | semidirect |
| 5. #10598188 | C2 | semidirect |
| 19. #64768 | C4 | semidirect |
| 20. #64762 | C4 | semidirect |
| 252. C5 | #12975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615009 | 2 |
| C5×#1884 | 2 |
| #10602820 | 2 |
| #10602613 | 2 |
| #10598188 | 2 |
| #12975 | 5 |