Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
236 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 151. C5 | #1830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65850 | 2 |
| C2×#3956 | 2 |
| C5×#344 | 2 |
| #64779 | 2 |
| #64776 | 2 |
| #64753 | 2 |
| #1830 | 5 |