Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#65395 | C2 | semidirect |
| 3. #10602871 | C2 | semidirect |
| 4. #10602756 | C2 | semidirect |
| 5. #10601873 | C2 | semidirect |
| 6. #10601863 | C2 | semidirect |
| 7. #10601442 | C2 | semidirect |
| 22. #64784 | C22 | semidirect |
| 23. #64782 | C22 | semidirect |
| 25. #64710 | C22 | semidirect |
| 26. #64709 | C22 | semidirect |
| 265. C5 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3050 | 2 |
| C2×#65395 | 2 |
| #10602871 | 2 |
| #10602756 | 2 |
| #10601873 | 2 |
| #10601863 | 2 |
| #10601442 | 2 |
| #33647 | 5 |