Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. #10603917 | C2 | semidirect |
| 4. #10603916 | C2 | semidirect |
| 6. #10598561 | C2 | semidirect |
| 7. #10598561 | C2 | semidirect |
| 173. C22×D5 | #108 | semidirect |
| 394. C5 | #8859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617090 | 2 |
| #10604320 | 2 |
| #10603917 | 2 |
| #10603916 | 2 |
| #10598936 | 2 |
| #10598561 | 2 |
| #8859 | 5 |