Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
650 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 171 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×Q32 | C2 | semidirect |
| 4. #10602854 | C2 | semidirect |
| 5. #10602298 | C2 | semidirect |
| 6. #10602297 | C2 | semidirect |
| 7. #10602197 | C2 | semidirect |
| 56. C22×Q32 | D5 | semidirect |
| 233. C5 | #33608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Q32 | 2 |
| #10615618 | 2 |
| C2×#65190 | 2 |
| #10602854 | 2 |
| #10602298 | 2 |
| #10602297 | 2 |
| #10602197 | 2 |
| #33608 | 5 |