Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 2. #65804 | C2 | semidirect |
| 3. #65353 | C2 | semidirect |
| 4. #65345 | C2 | semidirect |
| 5. #65334 | C2 | semidirect |
| 7. #65310 | C2 | semidirect |
| 8. #65309 | C2 | semidirect |
| 9. #65297 | C2 | semidirect |
| 10. #65296 | C2 | semidirect |
| 11. #65214 | C2 | semidirect |
| 234. C5 | #3233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#529 | 2 |
| #65804 | 2 |
| #65353 | 2 |
| #65345 | 2 |
| #65334 | 2 |
| #65324 | 2 |
| #65310 | 2 |
| #65309 | 2 |
| #65297 | 2 |
| #65296 | 2 |
| #65214 | 2 |
| #3233 | 5 |