Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 366 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 |
|---|---|---|
| 2. #66022 | C2 | semidirect |
| 3. C5×#490 | C2 | semidirect |
| 4. #65360 | C2 | semidirect |
| 5. #65354 | C2 | semidirect |
| 6. #65073 | C2 | semidirect |
| 7. #65068 | C2 | semidirect |
| 8. #65050 | C2 | semidirect |
| 9. #65048 | C2 | semidirect |
| 10. #64994 | C2 | semidirect |
| 11. #64991 | C2 | semidirect |
| 85. #490 | D5 | semidirect |
| 233. C5 | #3235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66050 | 2 |
| #66022 | 2 |
| C5×#490 | 2 |
| #65360 | 2 |
| #65354 | 2 |
| #65073 | 2 |
| #65068 | 2 |
| #65050 | 2 |
| #65048 | 2 |
| #64994 | 2 |
| #64991 | 2 |
| #3235 | 5 |