Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
658 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 111 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×C5×#328 | C2 | semidirect |
| 5. #10600216 | C2 | semidirect |
| 7. #10598165 | C2 | semidirect |
| 80. C2×#328 | D5 | semidirect |
| 414. C5 | #9971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614555 | 2 |
| C2×#65332 | 2 |
| C2×#65025 | 2 |
| C2×C5×#328 | 2 |
| #10600216 | 2 |
| C2×#64671 | 2 |
| #10598165 | 2 |
| #9971 | 5 |