Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C22×Dic40 | C2 | semidirect |
| 4. C2×#64712 | C2 | semidirect |
| 5. C5×#1380 | C2 | semidirect |
| 51. #1380 | D5 | semidirect |
| 104. C22×D5 | Q32 | semidirect |
| 240. C5 | #13306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic40 | 2 |
| C2×#65176 | 2 |
| C2×#64727 | 2 |
| C2×#64712 | 2 |
| C5×#1380 | 2 |
| #13306 | 5 |