Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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. #65684 | C2 | semidirect |
| 3. C4×#700 | C2 | semidirect |
| 4. #64927 | C2 | semidirect |
| 5. #64921 | C2 | semidirect |
| 20. #4002 | C22 | semidirect |
| 21. #4002 | C22 | semidirect |
| 179. C5 | #1527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#124 | 2 |
| #65684 | 2 |
| C4×#700 | 2 |
| #64927 | 2 |
| #64921 | 2 |
| #1527 | 5 |