Alice And Her True Friends

Alice has $N$ friends but she believes that not all her friends are true friends. She considers her $i^{th}$ friend as a true friend only if $i$ is composite. Some of Alice's friends know each other. If $A$ knows $B$, then $B$ knows $A$. Also If $A$ knows $B$ and $B$ knows $C$ then $A$ knows $C$. Alice wants to know what is the size of the largest group of her friends who know each other such t