Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. C5×#427 | C2 | semidirect |
| 5. C2×#3948 | C2 | semidirect |
| 6. #65293 | C2 | semidirect |
| 7. #65284 | C2 | semidirect |
| 8. #65177 | C2 | semidirect |
| 9. #65173 | C2 | semidirect |
| 10. #65156 | C2 | semidirect |
| 11. #65151 | C2 | semidirect |
| 85. #427 | D5 | semidirect |
| 230. C5 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65860 | 2 |
| #65857 | 2 |
| C5×#427 | 2 |
| #65399 | 2 |
| C2×#3948 | 2 |
| #65293 | 2 |
| #65284 | 2 |
| #65177 | 2 |
| #65173 | 2 |
| #65156 | 2 |
| #65151 | 2 |
| #3097 | 5 |