The recently introduced Dependent Type Higher-Order Logic (DHOL) offers an interesting compromise between expressiveness and automated support. It sacrifices the decidability of the type system in order to greatly extend expressiveness over standard HOL, while maintaining strong automatic theorem proving support via a correct and complete transformation to HOL. In this paper, we leverage this design to extend DHOL with refined types and quotient types. These two features are commonly requested by practitioners but are rarely provided by automated theorem provers, since they require inherently undecidable typing, making them very hard to reverse to a decidable type system. However, since DHOL already handles the hard work, adding them is not only feasible but also elegant and straightforward. Specifically, we add refined types and quotient types as special cases of subtypes, which avoids expensive changes in representation by replacing the relevant canonical inclusion or projection maps with identity maps. We present proofs of correctness and completeness, along with the syntax, semantics, and transformation to HOL for the extended language.