Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 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 |
|---|---|---|
| 3. #65383 | C2 | semidirect |
| 4. #65380 | C2 | semidirect |
| 5. #65358 | C2 | semidirect |
| 6. #65354 | C2 | semidirect |
| 178. C5 | #3237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#533 | 2 |
| #65804 | 2 |
| #65383 | 2 |
| #65380 | 2 |
| #65358 | 2 |
| #65354 | 2 |
| #65285 | 2 |
| #65215 | 2 |
| #3237 | 5 |