Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
794 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#4081 | C2 | semidirect |
| 3. #65532 | C2 | direct (N × H) |
| 4. C2×#3966 | C2 | semidirect |
| 10. C23×Dic5 | C22 | semidirect |
| 12. C2×C22⋊Dic5 | C22 | semidirect |
| 14. #4081 | C22 | semidirect |
| 16. #3966 | C22 | semidirect |
| 36. C22×Dic5 | C23 | semidirect |
| 39. C22⋊Dic5 | C23 | semidirect |
| 120. C2×C5 | #458 | semidirect |
| 145. C5 | C2×#458 | semidirect |
| 163. C2 | #65532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×H(5,𝔽2) | 2 |
| C2×#4081 | 2 |
| #65532 | 2 |
| C2×#3966 | 2 |
| C2×#458 | 5 |