Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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×#3959 | C2 | semidirect |
| 3. #65405 | C2 | semidirect |
| 4. #64782 | C2 | semidirect |
| 5. C22⋊#672 | C2 | semidirect |
| 12. C2×Dic20 | C22 | semidirect |
| 14. #3950 | C22 | semidirect |
| 16. C2×#672 | C22 | semidirect |
| 76. C22×C5 | SD32 | semidirect |
| 124. C5 | #2187 | semidirect |
| 131. C22 | #3959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D8 | 2 |
| C2×#3959 | 2 |
| #65405 | 2 |
| #64782 | 2 |
| C22⋊#672 | 2 |
| #2187 | 5 |