Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #66055 | C2 | semidirect |
| 4. #65383 | C2 | semidirect |
| 6. #65057 | C2 | semidirect |
| 7. #65056 | C2 | semidirect |
| 8. #65055 | C2 | semidirect |
| 9. #65047 | C2 | semidirect |
| 10. C4×Dic20 | C2 | semidirect |
| 11. C8×Dic10 | C2 | semidirect |
| 215. C5 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66055 | 2 |
| #66047 | 2 |
| C5×#486 | 2 |
| #65383 | 2 |
| #65364 | 2 |
| #65057 | 2 |
| #65056 | 2 |
| #65055 | 2 |
| #65047 | 2 |
| C4×Dic20 | 2 |
| C8×Dic10 | 2 |
| #3365 | 5 |