The randomized group-greedy method and its customized method for large-scale sensor selection problems are proposed. The randomized greedy sensor selection algorithm is applied straightforwardly to the group-greedy method, and a customized method is also considered. In the customized method, a part of the compressed sensor candidates is selected using the common greedy method or other low-cost methods. This strategy compensates for the deterioration of the solution due to compressed sensor candidates. The proposed methods are implemented based on the D- and E-optimal design of experiments, and numerical experiments are conducted using randomly generated sensor candidate matrices with potential sensor locations of 10,000--1,000,000. The proposed method can provide better optimization results than those obtained by the original group-greedy method when a similar computational cost is spent as for the original group-greedy method. This is because the group size for the group-greedy method can be increased as a result of the compressed sensor candidates by the randomized algorithm. Similar results were also obtained in the real dataset. The proposed method is effective for the E-optimality criterion, in which the objective function that the optimization by the common greedy method is difficult due to the absence of submodularity of the objective function. The idea of the present method can improve the performance of all optimizations using a greedy algorithm.