Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. C5×#2226 | C2 | semidirect |
| 2. #10602152 | C2 | semidirect |
| 4. D8×#168 | C2 | semidirect |
| 5. #10598293 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10598045 | C2 | semidirect |
| 46. #2226 | D5 | semidirect |
| 60. C5×D8 | SD16 | semidirect |
| 165. D8 | #688 | semidirect |
| 209. C5 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2226 | 2 |
| #10602152 | 2 |
| #10601682 | 2 |
| D8×#168 | 2 |
| #10598293 | 2 |
| #10598051 | 2 |
| #10598045 | 2 |
| #12418 | 5 |