Transfer condition is subordination-closed

Property-theoretic statement
The subgroup metaproperty called the transfer condition satisfies the subgroup metametaproperty of being subordination-closed.

Statement with symbols
Suppose $$p$$ is a subgroup property satisfying the transfer condition. Then, the subordination of $$p$$ also satisfies the transfer condition.

Examples

 * The subordination of the property of being a normal subgroup is the property of being a subnormal subgroup. Thus, the fact that normality satisfies transfer condition implies that subnormality satisfies transfer condition.