A group of conformal symmetry in E2\{O} is a group of conformal transformations of the plane E2\{O} (H.S.M. Coxeter, 1969; A.M. Zamorzaev, E.I. Galyarski, A.F. Palistrant, 1978) at least one of which is not a similarity transformation. According to the relationships: C20 Ì C21, C20 = C210, any discussion on the conformal symmetry groups in E2\{O} can be reduced to the analysis of the two categories of conformal symmetry groups - C21 and C2.