In order to explain phase diagrams independent of field-orientation, which is now evident in UPt3, we present a scenario based on a superconducting (SC) class belonging to the one-dimensional representation (1D-REP) with odd-parity. The preexisting antiferromagnetic order (AF) lifts the spin space degeneracy of the pairing function to split T(c), which is contrasted with the orbital degeneracy lifting mechanism in the previous 2D-REP scenario. A non-trivial coupling of the two orderings, SC and AF is derived and a GL theory is developed to examine the successive phase transitions. We calculate several quantities, including the upper and lower critical fields, specific heat jumps and derive the phase diagrams under applied fields. It is demonstrated that the present 1D-REP scenario is more consistent with various experiments on UPt3 than the previous 2D-REP one. We emphasize that the 1D-REP scenario is the only choice remained within the symmetry breaking framework, which is able to consistently explain the experiments.