Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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. #65411 | C2 | semidirect |
| 5. C2×#3947 | C2 | semidirect |
| 6. C5×#341 | C2 | semidirect |
| 7. #64775 | C2 | semidirect |
| 16. #4053 | C4 | semidirect |
| 19. #3957 | C4 | semidirect |
| 20. #3953 | C4 | semidirect |
| 21. #3948 | C4 | semidirect |
| 61. #341 | D5 | semidirect |
| 178. C5 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4053 | 2 |
| C2×#3957 | 2 |
| #65411 | 2 |
| #65402 | 2 |
| C2×#3947 | 2 |
| C5×#341 | 2 |
| #64775 | 2 |
| #1765 | 5 |