Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
298 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 12. #64762 | C4 | semidirect |
| 14. #64760 | C4 | semidirect |
| 219. C5 | #7487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1885 | 2 |
| C2×#64762 | 2 |
| C2×#64760 | 2 |
| #7487 | 5 |