Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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. #65124 | C2 | semidirect |
| 3. D5×C4⋊C8 | C2 | semidirect |
| 4. C5×#331 | C2 | semidirect |
| 5. #64764 | C2 | semidirect |
| 6. #64701 | C2 | semidirect |
| 7. #64701 | C2 | semidirect |
| 55. #331 | D5 | semidirect |
| 169. C5 | #1551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66050 | 2 |
| #65124 | 2 |
| D5×C4⋊C8 | 2 |
| C5×#331 | 2 |
| #64764 | 2 |
| #64701 | 2 |
| #1551 | 5 |