Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
488 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 139 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. C22×C5×M32 | C2 | semidirect |
| 3. #10602756 | C2 | semidirect |
| 4. C2×#64728 | C2 | semidirect |
| 5. #10598296 | C2 | semidirect |
| 45. C2×C5×C16 | D4 | semidirect |
| 54. C22×M32 | D5 | semidirect |
| 166. C2×C16 | C22⋊D5 | semidirect |
| 258. C5 | #12984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×M32 | 2 |
| #10615465 | 2 |
| #10602756 | 2 |
| C2×#64728 | 2 |
| #10598296 | 2 |
| #12984 | 5 |