We explore 4d gauge-Yukawa theories with weakly coupled UV fixed points. Using Majorana fermions, new families of theories with perturbatively exact asymptotic safety are identified. We find that these families are equivalent in the large-N limit, forming a triality of asymptotically safe models. Moreover, an additional duality of asymptotically free gauge-Yukawa theories is found. The mechanisms behind these new large-N equivalence classes are uncovered, connecting various SU, SO and Sp gauge theories with matter.