Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. C4×#3968 | C2 | semidirect |
| 4. #10598135 | C2 | semidirect |
| 16. #64762 | C4 | semidirect |
| 42. #3968 | C2×C4 | semidirect |
| 249. C5 | #12632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2326 | 2 |
| C2×#64762 | 2 |
| C4×#3968 | 2 |
| #10598135 | 2 |
| #12632 | 5 |