Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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. #65379 | C2 | semidirect |
| 4. C8×Dic10 | C2 | semidirect |
| 5. #64767 | C2 | semidirect |
| 7. #64678 | C2 | semidirect |
| 140. C5 | #1682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#486 | 2 |
| #65379 | 2 |
| #65364 | 2 |
| C8×Dic10 | 2 |
| #64767 | 2 |
| #64764 | 2 |
| #64678 | 2 |
| #1682 | 5 |