Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 390 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. #65912 | C2 | semidirect |
| 3. C5×#462 | C2 | semidirect |
| 4. #65479 | C2 | semidirect |
| 5. #65476 | C2 | semidirect |
| 6. #65379 | C2 | semidirect |
| 7. #65316 | C2 | semidirect |
| 8. #65137 | C2 | semidirect |
| 9. #65124 | C2 | semidirect |
| 10. #65099 | C2 | semidirect |
| 11. #65084 | C2 | semidirect |
| 90. #462 | D5 | semidirect |
| 256. C5 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66059 | 2 |
| #65912 | 2 |
| C5×#462 | 2 |
| #65479 | 2 |
| #65476 | 2 |
| #65379 | 2 |
| #65316 | 2 |
| #65137 | 2 |
| #65124 | 2 |
| #65099 | 2 |
| #65084 | 2 |
| #3216 | 5 |