Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10598034 | C2 | semidirect |
| 6. C2×#4016 | C4 | semidirect |
| 13. #65345 | C4 | semidirect |
| 15. C4×#681 | C4 | semidirect |
| 241. C5 | #13604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615015 | 2 |
| C5×#2126 | 2 |
| #10602613 | 2 |
| #10598034 | 2 |
| #13604 | 5 |