Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
540 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 111 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×#64762 | C2 | semidirect |
| 3. #10602430 | C2 | semidirect |
| 4. C4×#3968 | C2 | semidirect |
| 49. #3968 | D4 | semidirect |
| 209. C4×C5 | #355 | semidirect |
| 298. C5 | #13226 | semidirect |
| 320. C4 | #64762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2548 | 2 |
| C2×#64762 | 2 |
| #10602430 | 2 |
| C4×#3968 | 2 |
| #13226 | 5 |