Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10602476 | C2 | semidirect |
| 3. #10602466 | C2 | semidirect |
| 4. #10600744 | C2 | semidirect |
| 5. #10598170 | C2 | semidirect |
| 284. C5 | #10557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3186 | 2 |
| #10602476 | 2 |
| #10602466 | 2 |
| #10600744 | 2 |
| #10598170 | 2 |
| #10557 | 5 |