Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
388 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10604020 | C2 | semidirect |
| 4. #10603859 | C2 | semidirect |
| 6. #10598592 | C2 | semidirect |
| 7. #10598531 | C2 | semidirect |
| 139. C5×Q8 | #108 | semidirect |
| 277. Q8 | #3996 | semidirect |
| 310. C5 | #8899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617206 | 2 |
| #10604441 | 2 |
| #10604020 | 2 |
| #10603859 | 2 |
| #10599022 | 2 |
| #10598592 | 2 |
| #10598531 | 2 |
| #8899 | 5 |