Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
642 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 236 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 |
|---|---|---|
| 1. #10617404 | C2 | semidirect |
| 3. #10604751 | C2 | semidirect |
| 4. C2×#64898 | C2 | semidirect |
| 5. #10604741 | C2 | semidirect |
| 6. #10604084 | C2 | semidirect |
| 7. #10604083 | C2 | semidirect |
| 14. #65725 | C22 | semidirect |
| 21. #64898 | C22 | semidirect |
| 22. #64898 | C22 | semidirect |
| 23. #64889 | C22 | semidirect |
| 24. #64886 | C22 | semidirect |
| 25. #64885 | C22 | semidirect |
| 228. C5 | #33442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617404 | 2 |
| #10610988 | 2 |
| #10604751 | 2 |
| C2×#64898 | 2 |
| #10604741 | 2 |
| #10604084 | 2 |
| #10604083 | 2 |
| #33442 | 5 |