Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
702 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 235 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. C5×#1726 | C2 | semidirect |
| 4. #10600627 | C2 | semidirect |
| 5. C8×#683 | C2 | semidirect |
| 7. #10600231 | C2 | semidirect |
| 55. #1726 | D5 | semidirect |
| 215. C5 | #21668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605151 | 2 |
| C5×#1726 | 2 |
| #10600628 | 2 |
| #10600627 | 2 |
| C8×#683 | 2 |
| C8×#685 | 2 |
| #10600231 | 2 |
| #21668 | 5 |