Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 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. C2×#4016 | C2 | semidirect |
| 3. #65353 | C2 | semidirect |
| 4. #65345 | C2 | semidirect |
| 5. #65333 | C2 | semidirect |
| 6. #65332 | C2 | semidirect |
| 9. #65311 | C2 | semidirect |
| 10. #65298 | C2 | semidirect |
| 11. #65214 | C2 | semidirect |
| 227. C5 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#529 | 2 |
| C2×#4016 | 2 |
| #65353 | 2 |
| #65345 | 2 |
| #65333 | 2 |
| #65332 | 2 |
| #65323 | 2 |
| #65322 | 2 |
| #65311 | 2 |
| #65298 | 2 |
| #65214 | 2 |
| #3232 | 5 |