Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
558 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 147 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×C5×M32 | C2 | semidirect |
| 3. #10602764 | C2 | semidirect |
| 4. C2×#64729 | C2 | semidirect |
| 5. #10598297 | C2 | semidirect |
| 14. #65404 | C4 | semidirect |
| 43. C2×C5×C16 | D4 | semidirect |
| 50. C22×M32 | D5 | semidirect |
| 159. C2×C16 | C22⋊D5 | semidirect |
| 262. C5 | #13061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×M32 | 2 |
| C2×#65404 | 2 |
| #10602764 | 2 |
| C2×#64729 | 2 |
| #10598297 | 2 |
| #13061 | 5 |