Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #10610841 | C2 | semidirect |
| 5. #10598309 | C2 | semidirect |
| 6. #10598305 | C2 | semidirect |
| 7. #10598212 | C2 | semidirect |
| 31. C2×C5×Q16 | Q8 | semidirect |
| 33. C2×C5×D8 | Q8 | semidirect |
| 165. C2×Q16 | Dic10 | semidirect |
| 167. C2×D8 | Dic10 | semidirect |
| 291. C5 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610841 | 2 |
| C2×C5×#360 | 2 |
| #10602879 | 2 |
| #10602869 | 2 |
| #10598309 | 2 |
| #10598305 | 2 |
| #10598212 | 2 |
| #13374 | 5 |