Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #64692 | C2 | direct (N × H) |
| 6. C23×Dic5 | C4 | semidirect |
| 9. C2×C22⋊Dic5 | C4 | semidirect |
| 12. #4081 | C4 | semidirect |
| 36. C22×Dic5 | C2×C4 | semidirect |
| 42. C22⋊Dic5 | C2×C4 | semidirect |
| 150. C2×C5 | #352 | semidirect |
| 181. C5 | C2×#352 | semidirect |
| 209. C2 | #64692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4081 | 2 |
| C2×C5×#99 | 2 |
| C2×#3965 | 2 |
| #64692 | 2 |
| C2×#352 | 5 |