Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×C5×#131 | C2 | semidirect |
| 3. #66161 | C2 | semidirect |
| 4. #65422 | C2 | semidirect |
| 5. #65409 | C2 | semidirect |
| 6. #65402 | C2 | semidirect |
| 7. C2×#3948 | C2 | semidirect |
| 10. #4150 | C4 | semidirect |
| 39. #709 | C2×C4 | semidirect |
| 44. C2×Dic10 | C2×C4 | semidirect |
| 56. C2×#131 | D5 | semidirect |
| 170. C5 | #2898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4150 | 2 |
| C2×C5×#131 | 2 |
| #66161 | 2 |
| #65422 | 2 |
| #65409 | 2 |
| #65402 | 2 |
| C2×#3948 | 2 |
| #2898 | 5 |