Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 2. #10602209 | C2 | semidirect |
| 3. C2×#64669 | C2 | semidirect |
| 4. C5×C22⋊C32 | C2 | semidirect |
| 5. #10598087 | C2 | semidirect |
| 9. C2×Dic40 | C22 | semidirect |
| 13. C2×C5×C32 | C22 | semidirect |
| 14. #64724 | C22 | semidirect |
| 40. C22⋊C32 | D5 | semidirect |
| 70. C2×C32 | C2×D5 | semidirect |
| 112. C22×C5 | SD64 | semidirect |
| 168. C5 | #13664 | semidirect |
| 175. C22 | #64669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D80 | 2 |
| #10602209 | 2 |
| C2×#64669 | 2 |
| C5×C22⋊C32 | 2 |
| #10598087 | 2 |
| #13664 | 5 |