Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1382 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 240 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×#4005 | C2 | semidirect |
| 3. C2×#64923 | C2 | direct (N × H) |
| 13. C2×#4005 | C22 | semidirect |
| 14. #64923 | C22 | direct (N × H) |
| 41. #4005 | C23 | semidirect |
| 157. C22×C5 | #355 | semidirect |
| 207. C2×C5 | C2×#355 | semidirect |
| 240. C5 | C22×#355 | semidirect |
| 247. C22 | #64923 | direct (N × H) |
| 259. C2 | C2×#64923 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4082 | 2 |
| C22×#4005 | 2 |
| C2×#64923 | 2 |
| C22×#355 | 5 |