Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
204 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 67 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×C32 | C2 | semidirect |
| 2. #10602209 | C2 | semidirect |
| 4. C2×#64669 | C2 | semidirect |
| 5. #10598088 | C2 | semidirect |
| 6. #10598087 | C2 | semidirect |
| 7. #10598083 | C2 | semidirect |
| 40. C5×C32 | D4 | semidirect |
| 42. C22×C32 | D5 | semidirect |
| 116. C32 | C22⋊D5 | semidirect |
| 119. C22×C5 | SD64 | semidirect |
| 172. C5 | #13696 | semidirect |
| 178. C22 | #64669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C32 | 2 |
| #10602209 | 2 |
| #10602206 | 2 |
| C2×#64669 | 2 |
| #10598088 | 2 |
| #10598087 | 2 |
| #10598083 | 2 |
| #13696 | 5 |