Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 107. Dic10 | Q16 | semidirect |
| 214. C5 | #3395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66055 | 2 |
| #65901 | 2 |
| C5×#462 | 2 |
| #65471 | 2 |
| #65470 | 2 |
| #65381 | 2 |
| C4×#689 | 2 |
| #65138 | 2 |
| #65119 | 2 |
| #65082 | 2 |
| #65079 | 2 |
| #3395 | 5 |