Mutation testing is an effective, yet costly, testing approach, as it requires generating and running large numbers of faulty programs, called mutants. Mutation testing also suffers from a fundamental problem, which is having a large percentage of equivalent mutants. These are mutants that produce the same output as the original program, and therefore, cannot be detected. Higher-order mutation is a promising approach that can produce hard-to-detect faulty programs called subtle mutants, with a low percentage of equivalent mutants. Subtle higher-order mutants contribute a small set of the large space of mutants which grows even larger as the order of mutation becomes higher. In this paper, we developed a genetic algorithm for finding subtle higher-order mutants. The proposed approach uses a new mechanism in the crossover phase and uses five selection techniques to select mutants that go to the next generation in the genetic algorithm. We implemented a tool, called GaSubtle that automates the process of creating subtle mutants. We evaluated the proposed approach by using 10 subject programs. Our evaluation shows that the proposed crossover generates more subtle mutants than the technique used in a previous genetic algorithm with less execution time. Results vary on the selection strategies, suggesting a dependency relation with the tested code.