Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #65471 | C2 | semidirect |
| 7. #65164 | C2 | semidirect |
| 8. #65083 | C2 | semidirect |
| 9. #65082 | C2 | semidirect |
| 86. C2×Dic5 | Q16 | semidirect |
| 187. C5 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65956 | 2 |
| C5×#467 | 2 |
| #65471 | 2 |
| #65405 | 2 |
| C2×#3946 | 2 |
| #65340 | 2 |
| #65164 | 2 |
| #65083 | 2 |
| #65082 | 2 |
| #3249 | 5 |