Degrees of irreducible representations of quotient group are contained in degrees of irreducible representations of group

Statement
Suppose $$G$$ is a finite group, $$H$$ is a normal subgroup of $$G$$, and $$K = G/H$$ is the quotient group. Then, the multiset of degrees of irreducible representations of the group $$K$$ (over a splitting field for $$K$$) is a sub-multiset of the multiset of degrees of irreducible representations of the group $$G$$.

Facts used

 * 1) uses::Irreducible representation of quotient group composed with quotient map gives irreducible representation of group