Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10604795 | C2 | semidirect |
| 2. D8×#170 | C2 | semidirect |
| 4. #10598801 | C2 | semidirect |
| 5. #10598801 | C2 | semidirect |
| 6. #10598645 | C2 | semidirect |
| 7. #170⋊C16 | C2 | semidirect |
| 66. C5×D8 | M16 | semidirect |
| 111. #170 | D16 | semidirect |
| 157. D8 | #704 | semidirect |
| 203. C5 | #12069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604795 | 2 |
| D8×#170 | 2 |
| Dic5×D16 | 2 |
| #10598801 | 2 |
| #10598645 | 2 |
| #170⋊C16 | 2 |
| #12069 | 5 |