Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
356 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. #65918 | C2 | semidirect |
| 2. C5×#446 | C2 | semidirect |
| 3. #65138 | C2 | semidirect |
| 4. #65134 | C2 | semidirect |
| 6. #65004 | C2 | semidirect |
| 7. #64999 | C2 | semidirect |
| 8. C4×Dic20 | C2 | semidirect |
| 72. #446 | D5 | semidirect |
| 187. C5 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65918 | 2 |
| C5×#446 | 2 |
| #65138 | 2 |
| #65134 | 2 |
| #65133 | 2 |
| #65004 | 2 |
| #64999 | 2 |
| C4×Dic20 | 2 |
| #64985 | 2 |
| #3402 | 5 |