Techniques are disclosed relating to routing circuitry configured to perform permute operations for operands of threads in a single-instruction multiple-data group. In some embodiments, an apparatus includes hierarchical operand routing circuitry configured to route operands between a set of single-instruction multiple-data (SIMD) pipelines based on a permute instruction. In some embodiments, the routing circuitry includes a first level and a second level. The first level may include a set of multiple crossbar circuits each configured to receive operands from a respective subset of the pipelines and output one or more of the received operands on multiple output lines based on the permute instruction, where the crossbar circuits support full permutation within a respective subset. A second level may be configured to select an operand from a previous level for each of the pipelines, and may select from among only a portion of output operands from the previous level to provide an operand for a respective pipeline.