  We present a classification of the possible regular, spherically symmetric
solutions of the Einstein-Yang-Mills system which is based on a bundle
theoretical analysis for arbitrary gauge groups. It is shown that such solitons
must be of magnetic type, at least if the magnetic Yang-Mills charge vanishes.
Explicit expressions for the Chern-Simons numbers of these selfgravitating
Yang-Mills solitons are derived, which involve only properties of irreducible
root systems and some information about the asymptotics of the solutions. It
turns out, as an example, that the Chern-Simons numbers are always
half-integers or integers for the gauge groups $SU(n)$. Possible physical
implications of these results, which are based on analogies with the unstable
sphaleron solution of the electroweak theory, are briefly indicated.
