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• The study proposed a method to predict the complex subharmonic vibrations. • Local subharmonic vibrations of order-1/3 and −1/5 were obtained accurately. • Local "full tree" and "half tree" of subharmonic vibrations were predicted. • Strange vibrations in the real turbo-engine testings were explained. • Experiments were conducted for comparing with the theoretical predictions. In real turbomachinery testing, we always confront strange high order vibrations which scatter a few points or draw some local lines in the experimental bifurcation diagrams. Such vibrations maybe ignored due to the lack of experiences and knowledge while they can be important in design and operation due to the nonsmooth jumping and instability. This paper proposes a new method for predicting the complex high order subharmonic vibrations for a nonlinear rotor system with light rub. The nonlinearity is induced by the contact of the bristles and the rotor. A continuous nonlinear rotor system is established based on the geometric and bending force diagrams. We discretize the complex orbits and built implicit mappings between the adjacent nodes. A directional eigenfunctional matrix is constructed which maps each nodes and passes the perturbation along the orbits for semi-analytical prediction of the high order subharmonic vibrations. Stability criterion is defined. Numerical bifurcation diagrams and harmonic contours are presented for quick glance of the global subahrmonic vibrations. Two local subharmonic vibrations of odd orders are succesfuly predicted. Local high order subharmonic vibrations of "full tree" and "half tree" are predicted and achieved accurately. An experimental platform is established to compare the semi-analytical predictions with experimental results. The research delivers a new perspective for predicting and computing the high order subharmonic vibrations in nonlinear rotor system. [Display omitted] [ABSTRACT FROM AUTHOR]