In this paper TU-cooperative games are considered from the linear programming point of view. Using the linear programming approach for construction of subcore and grand subcore, which are multiple selectors of the core, we represent them in analytical forms. The investigation of subcore's properties illustrates the possibility to obtain more simple conditions to check whether an arbitrary one point solution lies in the core and subcore. Two solution concepts for cooperative games in characteristic-function form, the nucleolus and Shapley value, are studied in their relationship to the grand subcore in symmetrical n-person TU-cooperative games. Under additional restrictions for the structure of optimal solutions’ set of considered linear programming problem sufficient conditions have been obtained for the nucleolus to be a selector of the grand subcore.