Epistasis is a phenomenon in which a phenotype outcome is determined by the interaction of genetic variation at two or more loci and it cannot be attributed to the additive combination of effects corresponding to the individual loci. Although it has been more than 100 years since William Bateson introduced this concept, it still is a topic under active research. Locating epistatic interactions is a computationally expensive challenge that involves analyzing an exponentially growing number of combinations. Authors in this field have resorted to a multitude of hardware architectures in order to speed up the search, but little to no attention has been paid to the vector instructions that current CPUs include in their instruction sets. This work extends an existing third-order exhaustive algorithm to support the search of epistasis interactions of any order and discusses multiple SIMD implementations of the different functions that compose the search using Intel AVX Intrinsics. Results using the GCC and the Intel compiler show that the 512-bit explicit vector implementation proposed here performs the best out of all of the other implementations evaluated. The proposed 512-bit vectorization accelerates the original implementation of the algorithm by an average factor of 7 and 12, for GCC and the Intel Compiler, respectively, in the scenarios tested.