Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1134 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 280 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 |
|---|---|---|
| 4. C2×#64910 | C2 | direct (N × H) |
| 20. #64910 | C22 | direct (N × H) |
| 179. C22×C5 | #362 | semidirect |
| 232. C2×C5 | C2×#362 | semidirect |
| 264. C5 | C22×#362 | semidirect |
| 269. C22 | #64910 | direct (N × H) |
| 279. C2 | C2×#64910 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×Q16 | 2 |
| C22×#3995 | 2 |
| C22×#3990 | 2 |
| C2×#64910 | 2 |
| C22×#362 | 5 |