Many icosahedral viruses undergo large-scale conformational transitions between icosahedrally symmetric conformations during their life cycles. However, whether icosahedral symmetry is maintained along the transition pathways for this process is unknown. By employing a simplified and directed structure-based potential we compute an ensemble of transition pathways for the maturation transition of bacteriophage HK97. We observe localized symmetry-breaking events, but find that the large-scale displacements are dominated by icosahedrally symmetric deformation modes. We find that all pathways obey a common mechanism characterized by formation of pentameric contacts early in the transition.