Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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×#3969 | C2 | semidirect |
| 3. #65521 | C2 | semidirect |
| 4. #65266 | C2 | semidirect |
| 5. #64750 | C2 | semidirect |
| 37. C4×Dic5 | D4 | semidirect |
| 148. C5 | #2040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#537 | 2 |
| C2×#3969 | 2 |
| #65521 | 2 |
| #65266 | 2 |
| #64750 | 2 |
| #2040 | 5 |