# Relationship between Kleene Star of a subset of regular language and the regular language

If $$L(R_1) \subseteq L(R_2) \subseteq L(R_3)$$ then $$L(R_1)^* \subseteq L(R_2)^* \subseteq L(R_3)^*$$. Does this also imply that $$L(R_1)^* \subseteq L(R_3)$$?