Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
724 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 89 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×#65339 | C2 | semidirect |
| 4. #10602484 | C2 | semidirect |
| 6. #10600783 | C2 | semidirect |
| 7. #10598179 | C2 | semidirect |
| 400. C5 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3193 | 2 |
| C2×#65339 | 2 |
| C2×#65329 | 2 |
| #10602484 | 2 |
| #10602469 | 2 |
| #10600783 | 2 |
| #10598179 | 2 |
| #9989 | 5 |