Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 6. #65146 | C2 | semidirect |
| 7. #65145 | C2 | semidirect |
| 8. #65086 | C2 | semidirect |
| 9. #65085 | C2 | semidirect |
| 222. C5 | #3236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65956 | 2 |
| C2×#4036 | 2 |
| C5×#483 | 2 |
| #65333 | 2 |
| #65260 | 2 |
| #65146 | 2 |
| #65145 | 2 |
| #65086 | 2 |
| #65085 | 2 |
| #65011 | 2 |
| #65008 | 2 |
| #3236 | 5 |