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. #65166 | C2 | semidirect |
| 7. #65165 | C2 | semidirect |
| 8. #65088 | C2 | semidirect |
| 9. #65086 | 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×#484 | 2 |
| #65332 | 2 |
| #65259 | 2 |
| #65166 | 2 |
| #65165 | 2 |
| #65088 | 2 |
| #65086 | 2 |
| #65010 | 2 |
| #65008 | 2 |
| #3236 | 5 |