  There has been substantial work studying consensus problems for which there
is a single common final state, although there are many real-world complex
networks for which the complete consensus may be undesirable. More recently,
the concept of group consensus whereby subsets of nodes are chosen to reach a
common final state distinct from others has been developed, but the methods
tend to be independent of the underlying network topology. Here, an alternative
type of group consensus is achieved for which nodes that are symmetric achieve
a common final state. The dynamic behavior may be distinct between nodes that
are not symmetric. We show how group consensus for heterogeneous linear agents
can be achieved via a simple coupling protocol that exploits the topology of
the network. We see that group consensus is possible on both stable and
unstable trajectories. We observe and characterize the phenomenon of isolated
group consensus, where one or more clusters may achieve group consensus while
the other clusters do not.
