Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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. #65804 | C2 | semidirect |
| 3. C5×#431 | C2 | semidirect |
| 4. #65134 | C2 | semidirect |
| 5. #65022 | C2 | semidirect |
| 6. #64988 | C2 | semidirect |
| 7. #64983 | C2 | semidirect |
| 8. #64982 | C2 | semidirect |
| 9. #64970 | C2 | semidirect |
| 76. #431 | D5 | semidirect |
| 203. C5 | #3210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65811 | 2 |
| #65804 | 2 |
| C5×#431 | 2 |
| #65134 | 2 |
| #65022 | 2 |
| #64988 | 2 |
| #64983 | 2 |
| #64982 | 2 |
| #64970 | 2 |
| #3210 | 5 |