Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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. #65368 | C2 | semidirect |
| 3. #65138 | C2 | semidirect |
| 5. C5×#332 | C2 | semidirect |
| 6. #64704 | C2 | semidirect |
| 53. #332 | D5 | semidirect |
| 158. C5 | #1652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66066 | 2 |
| #65368 | 2 |
| #65138 | 2 |
| #65135 | 2 |
| C5×#332 | 2 |
| #64704 | 2 |
| #64703 | 2 |
| #1652 | 5 |