Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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. C5×#432 | C2 | semidirect |
| 4. #65136 | C2 | semidirect |
| 5. #65118 | C2 | semidirect |
| 7. #65012 | C2 | semidirect |
| 8. #65003 | C2 | semidirect |
| 9. #65003 | C2 | semidirect |
| 10. #64991 | C2 | semidirect |
| 11. #64991 | C2 | semidirect |
| 89. #432 | D5 | semidirect |
| 227. C5 | #3240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65813 | 2 |
| #65804 | 2 |
| C5×#432 | 2 |
| #65136 | 2 |
| #65118 | 2 |
| #65026 | 2 |
| #65012 | 2 |
| #65003 | 2 |
| #64991 | 2 |
| #3240 | 5 |