Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 366 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 |
|---|---|---|
| 2. #65804 | C2 | semidirect |
| 3. #65369 | C2 | semidirect |
| 4. #65360 | C2 | semidirect |
| 5. #65324 | C2 | semidirect |
| 6. #65297 | C2 | semidirect |
| 7. #65296 | C2 | semidirect |
| 8. #65215 | C2 | semidirect |
| 191. C5 | #3235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| #65804 | 2 |
| #65369 | 2 |
| #65360 | 2 |
| #65324 | 2 |
| #65297 | 2 |
| #65296 | 2 |
| #65215 | 2 |
| #3235 | 5 |