Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#106 | C2 | semidirect |
| 3. C2×#3946 | C2 | semidirect |
| 5. #65274 | C2 | semidirect |
| 7. #64749 | C2 | semidirect |
| 54. C2×#106 | D5 | semidirect |
| 207. C5 | #2065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#106 | 2 |
| C2×#3953 | 2 |
| C2×#3946 | 2 |
| #65277 | 2 |
| #65274 | 2 |
| C2×#3941 | 2 |
| #64749 | 2 |
| #2065 | 5 |