Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10604710 | C2 | semidirect |
| 3. #10604698 | C2 | semidirect |
| 4. #10598608 | C2 | semidirect |
| 5. #10598607 | C2 | semidirect |
| 270. C5 | #11665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610896 | 2 |
| #10604710 | 2 |
| #10604698 | 2 |
| #10598608 | 2 |
| #10598607 | 2 |
| #11665 | 5 |