Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1182 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 256 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 |
|---|---|---|
| 3. #10604972 | C2 | direct (N × H) |
| 4. C2×#64931 | C2 | semidirect |
| 20. #64931 | C22 | semidirect |
| 246. C2×C5 | #1558 | semidirect |
| 280. C5 | C2×#1558 | semidirect |
| 296. C2 | #10604972 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4090 | 2 |
| C2×#65757 | 2 |
| #10604972 | 2 |
| C2×#64931 | 2 |
| C2×#1558 | 5 |