Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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×#4015 | C2 | semidirect |
| 3. C5×#432 | C2 | semidirect |
| 4. #65140 | C2 | semidirect |
| 5. #65135 | C2 | semidirect |
| 7. #65011 | C2 | semidirect |
| 8. #65003 | C2 | semidirect |
| 9. #64991 | C2 | semidirect |
| 76. #432 | D5 | semidirect |
| 202. C5 | #3239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65813 | 2 |
| C2×#4015 | 2 |
| C5×#432 | 2 |
| #65140 | 2 |
| #65135 | 2 |
| #65024 | 2 |
| #65011 | 2 |
| #65003 | 2 |
| #64991 | 2 |
| #3239 | 5 |