Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. C2×#4036 | C2 | semidirect |
| 3. C5×#480 | C2 | semidirect |
| 4. #65323 | C2 | semidirect |
| 5. #65256 | C2 | semidirect |
| 6. #65180 | C2 | semidirect |
| 7. #65165 | C2 | semidirect |
| 8. #65053 | C2 | semidirect |
| 9. #65052 | C2 | semidirect |
| 10. #65024 | C2 | semidirect |
| 11. #65008 | C2 | semidirect |
| 87. #480 | D5 | semidirect |
| 242. C5 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65930 | 2 |
| C2×#4036 | 2 |
| C5×#480 | 2 |
| #65323 | 2 |
| #65256 | 2 |
| #65180 | 2 |
| #65165 | 2 |
| #65053 | 2 |
| #65052 | 2 |
| #65024 | 2 |
| #65008 | 2 |
| #3234 | 5 |