Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
322 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 113 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. C5×#477 | C2 | semidirect |
| 4. #65380 | C2 | semidirect |
| 5. #65309 | C2 | semidirect |
| 7. #65165 | C2 | semidirect |
| 8. #65140 | C2 | semidirect |
| 11. #65086 | C2 | semidirect |
| 86. #477 | D5 | semidirect |
| 229. C5 | #3237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| #65912 | 2 |
| C5×#477 | 2 |
| #65380 | 2 |
| #65309 | 2 |
| #65177 | 2 |
| #65165 | 2 |
| #65140 | 2 |
| #65124 | 2 |
| #65104 | 2 |
| #65086 | 2 |
| #3237 | 5 |