Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1114 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 340 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. #10617530 | C2 | semidirect |
| 3. C2×#65791 | C2 | semidirect |
| 4. #10604745 | C2 | semidirect |
| 5. C2×#64898 | C2 | semidirect |
| 15. C2×#3998 | C22 | semidirect |
| 16. C2×#3998 | C22 | semidirect |
| 17. C22×#674 | C22 | semidirect |
| 18. #64898 | C22 | semidirect |
| 19. #64898 | C22 | semidirect |
| 215. C5 | #33340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619067 | 2 |
| #10617530 | 2 |
| C2×#65791 | 2 |
| #10604745 | 2 |
| C2×#64898 | 2 |
| #33340 | 5 |