Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #65140 | C2 | semidirect |
| 5. #65139 | C2 | semidirect |
| 7. #64992 | C2 | semidirect |
| 8. #64991 | C2 | semidirect |
| 178. C5 | #3237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65804 | 2 |
| C5×#432 | 2 |
| #65140 | 2 |
| #65139 | 2 |
| #65012 | 2 |
| #64992 | 2 |
| #64991 | 2 |
| #3237 | 5 |