Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #66055 | C2 | semidirect |
| 3. C5×#487 | C2 | semidirect |
| 4. #65383 | C2 | semidirect |
| 7. #65081 | C2 | semidirect |
| 8. #65080 | C2 | semidirect |
| 11. C8×Dic10 | C2 | semidirect |
| 78. #487 | D5 | semidirect |
| 107. Dic10 | SD16 | semidirect |
| 217. C5 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66061 | 2 |
| #66055 | 2 |
| C5×#487 | 2 |
| #65383 | 2 |
| #65372 | 2 |
| #65107 | 2 |
| #65081 | 2 |
| #65080 | 2 |
| #65077 | 2 |
| C4×#677 | 2 |
| C8×Dic10 | 2 |
| #3359 | 5 |