Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 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. #65529 | C2 | semidirect |
| 3. #64765 | C2 | semidirect |
| 5. C22×C5×D4 | C4 | semidirect |
| 7. C5×#124 | C4 | semidirect |
| 10. C5×#117 | C4 | semidirect |
| 13. #3966 | C22 | semidirect |
| 56. C22×D4 | Dic5 | semidirect |
| 58. #124 | Dic5 | semidirect |
| 62. #117 | Dic5 | semidirect |
| 120. C5 | #2128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#535 | 2 |
| #65529 | 2 |
| #64765 | 2 |
| #2128 | 5 |