Fix some $n\times n$ symmetric positive definite matrix $A$. Consider the following matrix product,
$$B = AC$$
where $C$ is an arbitrary $n\times n$ matrix. Given $A$, I would like to know if there are known necessary and sufficient conditions on all square matrices $C$ such that the resulting matrix $B$ is also symmetric positive definite? I am more interested in knowing (if possible) necessary conditions.
I am only concerned with real matrices.