Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#4055 | C2 | semidirect |
| 3. #65860 | C2 | semidirect |
| 4. #65857 | C2 | semidirect |
| 5. C5×#424 | C2 | semidirect |
| 6. #65422 | C2 | semidirect |
| 7. C2×#3948 | C2 | semidirect |
| 8. #65138 | C2 | semidirect |
| 9. #65134 | C2 | semidirect |
| 10. #65133 | C2 | semidirect |
| 11. #65130 | C2 | semidirect |
| 96. #424 | D5 | semidirect |
| 267. C5 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4055 | 2 |
| C2×#4050 | 2 |
| #65860 | 2 |
| #65857 | 2 |
| C5×#424 | 2 |
| #65422 | 2 |
| C2×#3948 | 2 |
| #65138 | 2 |
| #65134 | 2 |
| #65133 | 2 |
| #65130 | 2 |
| #3046 | 5 |