Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
198 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C5×#493 | C2 | semidirect |
| 2. C2×#3959 | C2 | semidirect |
| 3. C2×#3958 | C2 | semidirect |
| 4. #64985 | C2 | semidirect |
| 5. #64681 | C2 | semidirect |
| 32. #672 | D4 | semidirect |
| 36. #493 | D5 | semidirect |
| 105. C5 | #2250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#493 | 2 |
| C2×#3959 | 2 |
| C2×#3958 | 2 |
| #64985 | 2 |
| #64681 | 2 |
| #2250 | 5 |