Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 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 |
|---|---|---|
| 2. C2×#3961 | C2 | semidirect |
| 5. C5×#358 | C2 | semidirect |
| 6. #64723 | C2 | semidirect |
| 7. #64710 | C2 | semidirect |
| 47. #358 | D5 | semidirect |
| 127. C5 | #2219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65477 | 2 |
| C2×#3961 | 2 |
| C2×#3930 | 2 |
| #65176 | 2 |
| C5×#358 | 2 |
| #64723 | 2 |
| #64710 | 2 |
| #2219 | 5 |