Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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. C5×#467 | C2 | semidirect |
| 3. #65475 | C2 | semidirect |
| 4. #65405 | C2 | semidirect |
| 6. #65341 | C2 | semidirect |
| 7. #65177 | C2 | semidirect |
| 8. #65103 | C2 | semidirect |
| 9. #65097 | C2 | semidirect |
| 74. #467 | D5 | semidirect |
| 206. C5 | #3202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65962 | 2 |
| C5×#467 | 2 |
| #65475 | 2 |
| #65405 | 2 |
| #65399 | 2 |
| #65341 | 2 |
| #65177 | 2 |
| #65103 | 2 |
| #65097 | 2 |
| #3202 | 5 |