Symmetry widely exists in many complex and real-world networks, with flower networks and sunflower networks being two richly symmetric networks and having many practical applications due to their special structures. The number of subtrees (the subtree number index) is closely related to the reliable network design. Using a generating function, structural analysis techniques, and auxiliary structure introduction, this paper presents the subtree generating functions of flower networks Fln,m(n≥3,m≥2) and sunflower networks Sfn,m(n≥3,m≥2) and, thus, solves the computation of subtree number indices of Fln,m(n≥3,m≥2) and Sfn,m(n≥3,m≥2). The results provide a fundamental and efficient method for exploring novel features of symmetric complex cyclic networks from the structural subtree number index perspective. For instance, we conclude that under some parameter constraints, the flower networks are more reliable than sunflower networks.