Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. C5×#2163 | C2 | semidirect |
| 3. #10600555 | C2 | semidirect |
| 4. #10598019 | C2 | semidirect |
| 12. C4×Dic20 | C4 | semidirect |
| 14. #64985 | C4 | semidirect |
| 15. C4×D40 | C4 | semidirect |
| 17. #64972 | C4 | semidirect |
| 56. #2163 | D5 | semidirect |
| 269. C5 | #11860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610200 | 2 |
| C5×#2163 | 2 |
| #10600555 | 2 |
| #10598019 | 2 |
| #10598017 | 2 |
| #11860 | 5 |