Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
514 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×C4×C5×C16 | C2 | semidirect |
| 3. C2×#64723 | C2 | semidirect |
| 5. #10600559 | C2 | semidirect |
| 16. #64985 | C4 | semidirect |
| 53. C2×C4×C16 | D5 | semidirect |
| 246. C5 | #13204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64985 | 2 |
| C2×C4×C5×C16 | 2 |
| C2×#64723 | 2 |
| C2×#64729 | 2 |
| #10600559 | 2 |
| #13204 | 5 |