Is this is a misprint? I was given a question which said that $H\leq K \leq G$ meant that $C_G(K)\leq C_G(H) $.
This doesnt seem right though, my gut is telling me it should say that K is a subgroup of H instead.( ofcourse the gut can never be trusted in such things).
So is this a misprint ? ( I want to work it out myself I just don't want to spend hours on a proof that may have been posed incorrectly ) 

Smaller group means weaker conditoin:
$$x\in C_G(K)\implies \forall y\in K\colon xy=yx\implies \forall y\in H\colon xy=yx\implies x\in C_G(H).$$
