Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1170 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 312 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. #10604224 | C2 | semidirect |
| 4. #10603777 | C2 | semidirect |
| 9. #65756 | C4 | semidirect |
| 11. C2×#4002 | C22 | semidirect |
| 12. C2×C4×#170 | C22 | semidirect |
| 18. #64918 | C22 | semidirect |
| 217. C5 | #20529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65756 | 2 |
| #10605781 | 2 |
| #10604224 | 2 |
| #10603777 | 2 |
| #20529 | 5 |