Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. C5×#487 | C2 | semidirect |
| 4. #65382 | C2 | semidirect |
| 5. #65370 | C2 | semidirect |
| 7. #65086 | C2 | semidirect |
| 9. #64970 | C2 | semidirect |
| 73. #487 | D5 | semidirect |
| 194. C5 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| D5×C4⋊Q8 | 2 |
| C5×#487 | 2 |
| #65382 | 2 |
| #65370 | 2 |
| #65091 | 2 |
| #65086 | 2 |
| C4×#676 | 2 |
| #64970 | 2 |
| #3139 | 5 |