Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
294 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 41 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. #64745 | C2 | semidirect |
| 14. C24×C5 | C8 | semidirect |
| 77. C24 | #168 | semidirect |
| 115. C5 | #1316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#379 | 2 |
| #64745 | 2 |
| #1316 | 5 |