Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
242 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 81 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. #65215 | C2 | semidirect |
| 3. #65214 | C2 | semidirect |
| 4. #64767 | C2 | semidirect |
| 5. #64764 | C2 | semidirect |
| 141. C5 | #1553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| #65215 | 2 |
| #65214 | 2 |
| #64767 | 2 |
| #64764 | 2 |
| #1553 | 5 |