Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 15. C2×#689 | C4 | semidirect |
| 187. C5 | #1979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#689 | 2 |
| C5×#419 | 2 |
| C2×#3968 | 2 |
| C2×#3956 | 2 |
| C2×#3954 | 2 |
| #65293 | 2 |
| #65286 | 2 |
| #1979 | 5 |