Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×#681 | C2 | semidirect |
| 3. C5×#380 | C2 | semidirect |
| 4. C2×#3941 | C2 | semidirect |
| 5. #64749 | C2 | semidirect |
| 12. #4076 | C4 | semidirect |
| 46. C2×#168 | D4 | semidirect |
| 50. #380 | D5 | semidirect |
| 180. C5 | #1895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4076 | 2 |
| C22×#681 | 2 |
| C5×#380 | 2 |
| C2×#3941 | 2 |
| #64749 | 2 |
| #1895 | 5 |