Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10604083 | C2 | semidirect |
| 3. #10598650 | C2 | semidirect |
| 4. C16×#170 | C2 | semidirect |
| 5. #10598623 | C2 | semidirect |
| 30. Dic40 | C8 | semidirect |
| 31. #3932 | C8 | semidirect |
| 32. D80 | C8 | semidirect |
| 133. C5 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604083 | 2 |
| #10600150 | 2 |
| #10598650 | 2 |
| C16×#170 | 2 |
| #10598623 | 2 |
| #12046 | 5 |