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Class I CR manifolds have initial G-structure a certain 4-dimensionalsubgroup of GL_3(C). Class II CR manifolds have initial G-structure a certain10-dimensional subgroup of GL_4(C). Class III-1 CR manifolds have initialG-structure a certain 10-dimensional subgroup of GL_5(C). Class III-2 CRmanifolds have initial G-structure a certain 18-dimensional subgroup ofGL_5(C). Class IV-1 CR manifolds have initial G-structure a certain13-dimensional subgroup of GL_5(C). Class IV-2 CR manifolds have initialG-structure a certain 10-dimensional subgroup of GL_5(C).

Equivalences of 5-dimensional CR-manifolds IV: Six ambiguity matrix groups (Initial G-structures)