Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4070 conjugacy classes of subgroups; only the 456 normal subgroups are shown.
This group has 4070 conjugacy classes of subgroups — too many to draw. Only its 456 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. C22×#4003 | C2 | semidirect |
| 3. #10604983 | C2 | direct (N × H) |
| 12. C2×#4003 | C22 | semidirect |
| 143. C2×C5 | #1780 | semidirect |
| 167. C5 | C2×#1780 | semidirect |
| 180. C2 | #10604983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#713 | 2 |
| C22×#4003 | 2 |
| #10604983 | 2 |
| C2×#1780 | 5 |