Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10598019 | C2 | semidirect |
| 7. C22×Dic20 | C4 | semidirect |
| 12. #65405 | C4 | semidirect |
| 15. C2×#3950 | C4 | semidirect |
| 270. C5 | #11887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65405 | 2 |
| C2×C5×C22⋊C16 | 2 |
| #10602764 | 2 |
| #10598019 | 2 |
| #11887 | 5 |