  Let $G$ be a group. We define the coprime graph of subgroups of $G$, denoted
by $\mathcal P(G)$, is a graph whose vertex set is the set of all proper
subgroups of $G$, and two distinct vertices are adjacent if and only if the
order of the corresponding subgroups are coprime. In this paper, we study some
connections between algebraic properties of a group and graph theoretic
properties of its coprime graph.
