Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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×#65332 | C2 | semidirect |
| 4. C2×#64758 | C2 | semidirect |
| 6. #10600215 | C2 | semidirect |
| 7. #10598104 | C2 | semidirect |
| 414. C5 | #9971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2639 | 2 |
| C2×#65332 | 2 |
| C2×#65322 | 2 |
| C2×#64758 | 2 |
| C2×#64757 | 2 |
| #10600215 | 2 |
| #10598104 | 2 |
| #9971 | 5 |