Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1754 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 1754 conjugacy classes of subgroups — too many to draw. Only its 264 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 |
|---|---|---|
| 2. C2×#65757 | C2 | semidirect |
| 3. #10604898 | C2 | semidirect |
| 4. #10604329 | C2 | semidirect |
| 15. C2×#4004 | C22 | semidirect |
| 16. C2×#4003 | C22 | semidirect |
| 17. C2×#4002 | C22 | semidirect |
| 251. C5 | #21790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4039 | 2 |
| C2×#65757 | 2 |
| #10604898 | 2 |
| #10604329 | 2 |
| #21790 | 5 |