Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #66031 | C2 | semidirect |
| 3. C5×#499 | C2 | semidirect |
| 4. #65358 | C2 | semidirect |
| 5. #65356 | C2 | semidirect |
| 6. #65178 | C2 | semidirect |
| 7. #65175 | C2 | semidirect |
| 8. #65153 | C2 | semidirect |
| 9. #65141 | C2 | semidirect |
| 10. #64982 | C2 | semidirect |
| 11. #64978 | C2 | semidirect |
| 71. #499 | D5 | semidirect |
| 198. C5 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66032 | 2 |
| #66031 | 2 |
| C5×#499 | 2 |
| #65358 | 2 |
| #65356 | 2 |
| #65178 | 2 |
| #65175 | 2 |
| #65153 | 2 |
| #65141 | 2 |
| #64982 | 2 |
| #64978 | 2 |
| #3174 | 5 |