Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2022 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 400 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. C22×#4004 | C2 | semidirect |
| 3. C2×#64925 | C2 | direct (N × H) |
| 13. C2×#4004 | C22 | semidirect |
| 14. #64925 | C22 | direct (N × H) |
| 40. #4004 | C23 | semidirect |
| 144. C22×C5 | #331 | semidirect |
| 190. C2×C5 | C2×#331 | semidirect |
| 222. C5 | C22×#331 | semidirect |
| 229. C22 | #64925 | direct (N × H) |
| 240. C2 | C2×#64925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4086 | 2 |
| C22×#4004 | 2 |
| C2×#64925 | 2 |
| C22×#331 | 5 |