Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. #66062 | C2 | semidirect |
| 3. C5×#497 | C2 | semidirect |
| 4. #65476 | C2 | semidirect |
| 5. #65471 | C2 | semidirect |
| 6. #65462 | C2 | semidirect |
| 7. #65452 | C2 | semidirect |
| 8. #65375 | C2 | semidirect |
| 9. #65344 | C2 | semidirect |
| 10. #65003 | C2 | semidirect |
| 11. #64994 | C2 | semidirect |
| 88. #497 | 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 |
|---|---|
| #66062 | 2 |
| #66002 | 2 |
| C5×#497 | 2 |
| #65476 | 2 |
| #65471 | 2 |
| #65462 | 2 |
| #65452 | 2 |
| #65375 | 2 |
| #65344 | 2 |
| #65003 | 2 |
| #64994 | 2 |
| #3216 | 5 |