We explore the interrelationships between the galaxy group halo mass and various observable group properties. We propose a simple scenario that describes the evolution of the central galaxies and their host dark matter halos. Star formation quenching is one key process in this scenario, which leads to the different assembly histories of blue groups (group with a blue central) and red groups (group with a red central). For blue groups, both the central galaxy and the halo continue to grow their mass. For red groups, the central galaxy has been quenched and its stellar mass remains about constant, while its halo continues to grow by merging smaller halos. From this simple scenario, we speculate about the driving properties that should strongly correlate with the group halo mass. We then apply the machine learning algorithm the Random Forest (RF) regressor to blue groups and red groups separately in the semianalytical model L-GALAXIES to explore these nonlinear multicorrelations and to verify the scenario as proposed above. Remarkably, the results given by the RF regressor are fully consistent with the prediction from our simple scenario and hence provide strong support for it. As a consequence, the group halo mass can be more accurately determined from observable galaxy properties by the RF regressor with a 50% reduction in error. A halo mass more accurately determined in this way also enables more accurate investigations on the galaxy-halo connection and other important related issues, including galactic conformity and the effect of halo assembly bias on galaxy assembly.