Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 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. #66066 | C2 | semidirect |
| 3. C5×#498 | C2 | semidirect |
| 4. #65380 | C2 | semidirect |
| 5. #65376 | C2 | semidirect |
| 6. #65156 | C2 | semidirect |
| 7. #65155 | C2 | semidirect |
| 8. #65153 | C2 | semidirect |
| 9. #65149 | C2 | semidirect |
| 10. C4×#677 | C2 | semidirect |
| 11. C8×D20 | C2 | semidirect |
| 76. #498 | D5 | semidirect |
| 218. C5 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66068 | 2 |
| #66066 | 2 |
| C5×#498 | 2 |
| #65380 | 2 |
| #65376 | 2 |
| #65156 | 2 |
| #65155 | 2 |
| #65153 | 2 |
| #65149 | 2 |
| C4×#677 | 2 |
| C8×D20 | 2 |
| #3340 | 5 |