The design patterns can't really be assigned to one letter of the SOLID acronym. Design patterns actually help you (or at least they are supposed to!) design your software in a way that respects all five points of the SOLID principles. The principles are some sort of guideline you should keep in mind while doing object-oriented programming even if you are not using a design pattern.
With that said, there are indeed categories for design patterns. For example, the gang of four patterns fell into the categories creational, structural and behavioral.