Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
542 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 3. #10598777 | C2 | semidirect |
| 45. C22×Dic5 | C16 | semidirect |
| 188. C5 | #12844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×Dic5 | 2 |
| C2×C22⋊#674 | 2 |
| #10598777 | 2 |
| #12844 | 5 |