Exceptional equivalences in N = 2 supersymmetric Yang-Mills theory

We find low-energy equivalences between N = 2 supersymmetric gauge theories with different simple gauge groups with and without matter. We give a construction of equivalences based on subgroups and find all examples with maximal simple subgroups. This is used to solve some theories with exceptional gauge groups G2 and F4. We are also able to solve an E6 theory on a codimension one submanifold of its moduli space.