Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 1. C5×#532 | C2 | semidirect |
| 2. #65811 | C2 | semidirect |
| 3. #65527 | C2 | semidirect |
| 4. #65374 | C2 | semidirect |
| 5. #65370 | C2 | semidirect |
| 6. #65362 | C2 | semidirect |
| 7. #65359 | C2 | semidirect |
| 8. #65346 | C2 | semidirect |
| 9. #65214 | C2 | semidirect |
| 70. #532 | D5 | semidirect |
| 216. C5 | #3207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| #65811 | 2 |
| #65527 | 2 |
| #65374 | 2 |
| #65370 | 2 |
| #65362 | 2 |
| #65359 | 2 |
| #65346 | 2 |
| #65214 | 2 |
| #3207 | 5 |