Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. #65904 | C2 | semidirect |
| 3. C5×#446 | C2 | semidirect |
| 4. #65138 | C2 | semidirect |
| 6. #65134 | C2 | semidirect |
| 7. #65130 | C2 | semidirect |
| 8. #65004 | C2 | semidirect |
| 9. #64999 | C2 | semidirect |
| 10. C4×Dic20 | C2 | semidirect |
| 85. #446 | D5 | semidirect |
| 223. C5 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65919 | 2 |
| #65904 | 2 |
| C5×#446 | 2 |
| #65138 | 2 |
| #65137 | 2 |
| #65134 | 2 |
| #65130 | 2 |
| #65004 | 2 |
| #64999 | 2 |
| C4×Dic20 | 2 |
| #64982 | 2 |
| #3400 | 5 |