Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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×#4034 | C2 | semidirect |
| 3. C5×#481 | C2 | semidirect |
| 4. #65323 | C2 | semidirect |
| 5. #65257 | C2 | semidirect |
| 6. #65159 | C2 | semidirect |
| 7. #65144 | C2 | semidirect |
| 8. #65050 | C2 | semidirect |
| 9. #65049 | C2 | semidirect |
| 10. #65024 | C2 | semidirect |
| 11. #65007 | C2 | semidirect |
| 88. #481 | D5 | semidirect |
| 248. C5 | #3227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65930 | 2 |
| C2×#4034 | 2 |
| C5×#481 | 2 |
| #65323 | 2 |
| #65257 | 2 |
| #65159 | 2 |
| #65144 | 2 |
| #65050 | 2 |
| #65049 | 2 |
| #65024 | 2 |
| #65007 | 2 |
| #3227 | 5 |