Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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. #10610768 | C2 | semidirect |
| 5. #10600286 | C2 | semidirect |
| 6. #10600264 | C2 | semidirect |
| 7. #10598197 | C2 | semidirect |
| 362. C5 | #10195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614900 | 2 |
| #10614890 | 2 |
| #10610768 | 2 |
| C5×#1982 | 2 |
| #10600286 | 2 |
| #10600264 | 2 |
| #10598197 | 2 |
| #10195 | 5 |