Terwilliger proposed a method for studying commutative association schemes by introducing a non-commutative, semi-simple C-algebra, whose structure reflects the combinatorial nature of the corresponding scheme, and applied the method to the P and Q polynomial schemes. In this paper, we continue the initial investigation of Bannai and Munemasa of the Terwilliger algebras of group association schemes. In particular, we determine the structure of the Terwilliger algebras of the group schemes of S ₅ and A ₅.