Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 2. C2×#4016 | C2 | semidirect |
| 3. C5×#431 | C2 | semidirect |
| 4. #65136 | C2 | semidirect |
| 5. #65118 | C2 | semidirect |
| 8. #65011 | C2 | semidirect |
| 9. #65010 | C2 | semidirect |
| 10. #64986 | C2 | semidirect |
| 11. #64972 | C2 | semidirect |
| 89. #431 | D5 | semidirect |
| 227. C5 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65813 | 2 |
| C2×#4016 | 2 |
| C5×#431 | 2 |
| #65136 | 2 |
| #65118 | 2 |
| #65025 | 2 |
| #65024 | 2 |
| #65011 | 2 |
| #65010 | 2 |
| #64986 | 2 |
| #64972 | 2 |
| #3232 | 5 |