Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 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 |
|---|---|---|
| 9. #65225 | C4 | semidirect |
| 10. C2×C4×#168 | C4 | semidirect |
| 12. C5×#355 | C4 | semidirect |
| 14. #64761 | C4 | semidirect |
| 81. #355 | Dic5 | semidirect |
| 220. C5 | #7502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#355 | 2 |
| C2×#64761 | 2 |
| #10602518 | 2 |
| #7502 | 5 |