Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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×#358 | C2 | semidirect |
| 4. #64784 | C2 | semidirect |
| 6. #64724 | C2 | semidirect |
| 7. #64710 | C2 | semidirect |
| 42. #358 | D5 | semidirect |
| 115. C5 | #2237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65477 | 2 |
| #65169 | 2 |
| C5×#358 | 2 |
| #64784 | 2 |
| #64727 | 2 |
| #64724 | 2 |
| #64710 | 2 |
| #2237 | 5 |