TheU B(6)⊗U F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU B(6)⊗U F(20) related to theU B(5) andO B(6) limits of sdIBM (U B(6)) are analysed. Broadly speaking,U B(6)⊗U F(20) admitsU BF(5)⊗U s F (4), SpinBF(5)⊗U k F (5) andU BF(5)⊗U s F (2) limits withU B(5) core and SpinBF(6),O BF(5)⊗U s F (4), SpinBF(6)⊗U k F (5) andO BF(6)⊗U s F (2) limits withO B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU B(5) andO B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU B(6)⊗U F(20) symmetry limits are briefly discussed.