Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
388 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 388 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. #10598030 | C2 | semidirect |
| 6. #65804 | C4 | semidirect |
| 11. #65360 | C4 | semidirect |
| 15. C4×#681 | C4 | semidirect |
| 35. #4016 | C2×C4 | semidirect |
| 46. #3935 | C2×C4 | semidirect |
| 269. C5 | #13595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614890 | 2 |
| C2×C5×#353 | 2 |
| C2×#64765 | 2 |
| #10598030 | 2 |
| #13595 | 5 |