Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 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. #65370 | C2 | semidirect |
| 4. #65370 | C2 | semidirect |
| 5. #65368 | C2 | semidirect |
| 6. #65367 | C2 | semidirect |
| 8. #65311 | C2 | semidirect |
| 186. C5 | #3231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#533 | 2 |
| #65804 | 2 |
| #65370 | 2 |
| #65368 | 2 |
| #65367 | 2 |
| #65334 | 2 |
| #65311 | 2 |
| #65214 | 2 |
| #3231 | 5 |