If $H$ is a closed subgroup of a Lie Group $G$, and $p:P\to B$ a principal G-bundle. How to show that $q:P\to P/H$ is a principal $H$-bundle?

Question

Let $G$ be a Lie group and $H$ a closed subgroup of $G$. Suppose we are given a principal $G$-bundle $p:P\to B$, how to show that the quotient $q:P\to P/H$ is a principal $H$-bundle? Where $P/H$ denotes orbit space of $P$ under the right action of $H$.

I have no clue how to construct the trivialization charts.