In a series of recent articles, the problem of individuality in quantum theory was addressed from a radical position: there are neither individuals nor quasi-individuals in the quantum ontology; the quantum world is populated by quantum properties that form bundles which, nevertheless, do not acquire the features necessary to be characterized by the ontological category of individual. The aim of the present article is to relate this view with the symmetries of quantum theories. First, we will argue that, although quantum systems are non-individual bundles, the group of symmetry of non-relativistic quantum mechanics, the Galilei group, introduces in the bundle the difference between essential and contingent properties. Under certain conditions, those essential properties generate the illusion of the presence of an individual. Nevertheless, this is not the case when the behavior of the bundle is considered in its relation with other bundles, for instance, when statistical reasoning is involved. Second, we will extrapolate this idea to other quantum theories. For instance, in relativistic quantum mechanics and in quantum field theory, the space-time symmetry represented by the Poincaré group and the gauge symmetries also define the essential properties of the non-individual bundles, which are precisely the properties that define the different kinds of the so-called fundamental “particles”.