Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
692 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
|---|---|---|
| 6. #65272 | C2 | direct (N × H) |
| 123. C2×C5 | #398 | semidirect |
| 153. C5 | C2×#398 | semidirect |
| 169. C2 | #65272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C4⋊C4 | 2 |
| C22×C4⋊Dic5 | 2 |
| C22×#683 | 2 |
| C2×#3963 | 2 |
| #65272 | 2 |
| C2×#398 | 5 |