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Given a three-dimensional Riemannian manifold with boundary and a finite group of orientation-preserving isometries of this manifold, we prove that the equivariant index of a free boundary minimal surface obtained via an equivariant min-max procedure à la Simon-Smith with n-parameters is bounded above by n. Contents 1. Introduction 1 2. Basic notation 5 3. Equivariant spectrum 5 4. Free boundary minimal surfaces with bounded equivariant index 8 5. Outline of the proof of regularity and genus bound 10 6. Deformation theorem 15 7. Proof of the main theorem 18 8. Equivariant index of some families of (free boundary) minimal surfaces 20 Appendix A. Spectrum of elliptic operators with Robin boundary conditions 21 Appendix B. Bumpyness is G-generic 22 References 24

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