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We present a mathematical model of lophotrichous bacteria, motivated by Pseudomonas putida, which swim through fluid by rotating a cluster of multiple flagella extended from near one pole of the cell body. Although the flagella rotate individually, they are typically bundled together, enabling the bacterium to exhibit three primary modes of motility: push, pull, and wrapping. One key determinant of these modes is the coordination between motor torque and rotational direction of motors. The computational variations in this coordination reveal a wide spectrum of dynamical motion regimes, which are modulated by hydrodynamic interactions between flagellar filaments. These dynamic modes can be categorized into two groups based on the collective behavior of flagella, i.e., bundled and unbundled configurations. For some of these configurations, experimental examples from fluorescence microscopy recordings of swimming P. putida cells are also presented. Furthermore, we analyze the characteristics of stable bundles, such as push and pull, and investigate the dependence of swimming behaviors on the elastic properties of the flagella.