Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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×#432 | C2 | semidirect |
| 4. #65138 | C2 | semidirect |
| 5. #65137 | C2 | semidirect |
| 6. #65022 | C2 | semidirect |
| 7. #65004 | C2 | semidirect |
| 8. #65003 | C2 | semidirect |
| 72. #432 | D5 | semidirect |
| 197. C5 | #3216 | 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×#432 | 2 |
| #65138 | 2 |
| #65137 | 2 |
| #65022 | 2 |
| #65004 | 2 |
| #65003 | 2 |
| #3216 | 5 |