Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. #65937 | C2 | semidirect |
| 3. #65442 | C2 | semidirect |
| 4. #65426 | C2 | semidirect |
| 5. #65408 | C2 | semidirect |
| 6. #65330 | C2 | semidirect |
| 7. #65143 | C2 | semidirect |
| 8. #65056 | C2 | semidirect |
| 9. #65050 | C2 | semidirect |
| 188. C5 | #3263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65937 | 2 |
| C5×#469 | 2 |
| #65442 | 2 |
| #65426 | 2 |
| #65408 | 2 |
| #65330 | 2 |
| #65143 | 2 |
| #65056 | 2 |
| #65050 | 2 |
| #3263 | 5 |