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×C5×#137 | C2 | semidirect |
| 2. #66161 | C2 | semidirect |
| 4. #66150 | C2 | semidirect |
| 5. C2×#3967 | C2 | semidirect |
| 6. #65474 | C2 | semidirect |
| 7. #65471 | C2 | semidirect |
| 8. #65454 | C2 | semidirect |
| 9. #65451 | C2 | semidirect |
| 10. #65422 | C2 | semidirect |
| 11. #65408 | C2 | semidirect |
| 88. C2×#137 | 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×C5×#137 | 2 |
| #66161 | 2 |
| C2×#4096 | 2 |
| #66150 | 2 |
| C2×#3967 | 2 |
| #65474 | 2 |
| #65471 | 2 |
| #65454 | 2 |
| #65451 | 2 |
| #65422 | 2 |
| #65408 | 2 |
| #3046 | 5 |