Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 147. C5 | #1636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65904 | 2 |
| C5×#477 | 2 |
| #65380 | 2 |
| #65370 | 2 |
| Q8⋊#168 | 2 |
| #64706 | 2 |
| #64704 | 2 |
| #1636 | 5 |