Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
236 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 75 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. #10599859 | C2 | semidirect |
| 4. #10598052 | C2 | semidirect |
| 5. #10597991 | C2 | semidirect |
| 73. C5×D4 | Q32 | semidirect |
| 144. D4 | Dic40 | semidirect |
| 157. C5 | #12431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C16 | 2 |
| #10601643 | 2 |
| #10599859 | 2 |
| #10598052 | 2 |
| #10597991 | 2 |
| #12431 | 5 |