Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
438 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10602799 | C2 | semidirect |
| 3. #10602756 | C2 | semidirect |
| 4. #10600678 | C2 | semidirect |
| 5. #10600677 | C2 | semidirect |
| 52. C2×#672 | D4 | semidirect |
| 257. C5 | #13200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2929 | 2 |
| #10602799 | 2 |
| #10602756 | 2 |
| #10600678 | 2 |
| #10600677 | 2 |
| #13200 | 5 |