Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 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×#494 | C2 | semidirect |
| 2. C2×#3961 | C2 | semidirect |
| 5. #64681 | C2 | semidirect |
| 36. #494 | D5 | semidirect |
| 101. C5 | #2251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#494 | 2 |
| C2×#3961 | 2 |
| C2×#3960 | 2 |
| #64985 | 2 |
| #64681 | 2 |
| #2251 | 5 |