The authors investigate torsion subgroups of the normalized unit group \(V(\mathbb ZG)\) of the integral group ring \(\mathbb ZG\) of a finite group \(G\). For specific subgroups \(W\) they study the Gruenberg-Kegel graph \(\pi(W)\) of \(W\). Recall that the vertices of this graph are the primes dividing the order of a torsion element of the group \(W\) and that two different vertices \(p\) and \(q\) are connected by an edge if and only if there is an element in \(W\) of order \(pq\). It is well known that the vertices of \(G\) and \(V(\mathbb ZG)\) are the same. Hence the Gruenberg-Kegel graphs of \(G\) and \(V(\mathbb ZG)\) can only differ when the latter has more edges than the former. Recall that a subgroup \(U\) of a finite group \(G\) is said to be isolated if for each non-trivial element \(u\in U\) the centralizer \(C_G(u)\) is contained in \(U\) and if for each \(g\in G\) the intersection \(U\cap U^g\) is trivial or coincides with \(U\). It is known that a finite group \(G\) has an isolated subgroup if and only if \(\pi(G)\) is disconnected [\textit{K. W. Gruenberg} and \textit{K. W. Roggenkamp}, Proc. Lond. Math. Soc., III. Ser. 31, 149-166 (1975; Zbl 0313.20004)] and this is the case if and only if its augmentation ideal decomposes [\textit{J. S. Williams}, J. Algebra 69, 487-513 (1981; Zbl 0471.20013)]. It is shown that the central elements of an isolated subgroup of \(U\) of a group basis \(H\) of \(\mathbb ZG\) are the normalized units of its centralizer ring \(C_{\mathbb ZG}(U)\). Moreover, \(\pi(N_{V(\mathbb ZG)}(U))=\pi(N_H(U))\). If \(G\) has elementary Abelian Sylow \(2\)-subgroups of order at most \(8\), each finite \(2\)-subgroup of \(V(\mathbb ZG)\) is rationally conjugate to a subgroup of \(G\). Finally, torsion subgroups of \(V(\mathbb ZG)\) are considered in the case \(G\) is a minimal simple group. It follows that if \(G\) is a simple group which admits a non-trivial partition for each prime \(p\) the \(p\)-rank of a torsion subgroup of \(V(\mathbb ZG)\) is bounded by that one of \(G\).