Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 3. C5×#366 | C2 | semidirect |
| 5. #64723 | C2 | semidirect |
| 6. #64712 | C2 | semidirect |
| 7. #64709 | C2 | semidirect |
| 40. #366 | D5 | semidirect |
| 117. C5 | #2236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65176 | 2 |
| D5×#107 | 2 |
| C5×#366 | 2 |
| #64727 | 2 |
| #64723 | 2 |
| #64712 | 2 |
| #64709 | 2 |
| #2236 | 5 |