Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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. C5×#424 | C2 | semidirect |
| 3. #65402 | C2 | semidirect |
| 4. #65295 | C2 | semidirect |
| 5. #64777 | C2 | semidirect |
| 42. #424 | D5 | semidirect |
| 133. C5 | #2053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66082 | 2 |
| C5×#424 | 2 |
| #65402 | 2 |
| #65295 | 2 |
| #64777 | 2 |
| #2053 | 5 |