A theorem of Boutot asserts that direct summands of rational singularities stay rational. In this talk, I'll explain a refinement of this statement for klt singularities, motivated by an analogous result in positive characteristic that says direct summands of strongly F-regular singularities are also strongly F-regular. As an application, we recover a recent result of Braun, Greb, Langlois and Moraga that reductive quotient singularities are of klt type.