Galois points on singular plane quartic curves

We study the structure of function fields of plane curves following our method developed in [K. Miura, H. Yoshihara, Field theory for function fields of plane quartic curves, J. Algebra 226 (2000) 283–294]. Especially, we study Galois points on singular plane quartic curves and determine the number of Galois points on them. Furthermore, we give concrete defining equations when the curve has a Galois point.