  We examine the properties of dark matter halos within a rich galaxy cluster
using a high resolution simulation that captures the cosmological context of a
cold dark matter universe. The mass and force resolution permit the resolution
of 150 halos with circular velocities larger than 80 kms within the cluster's
virial radius of 2 Mpc. This enables an unprecedented study of the statistical
properties of a large sample of dark matter halos evolving in a dense
environment. The cumulative fraction of mass attached to these halos varies
from 0% at 200 kpc, to 13% at the virial radius. Even at this resolution the
overmerging problem persists; halos that pass within 200 kpc of the cluster
center are tidally disrupted. Additional substructure is lost at earlier epochs
within the massive progenitor halos. The median ratio of apocentric to
pericentric radii is 6:1; the orbital distribution is close to isotropic,
circular orbits are rare, radial orbits are common. The orbits of halos are
unbiased with respect to both position within the cluster and with the orbits
of the smooth dark matter background and no velocity bias is detected. The
tidal radii of surviving halos are generally well-fit using the simple analytic
prediction applied to their orbital pericenters. Halos within clusters have
higher concentrations than those in the field. Within the cluster, halo density
profiles can be modified by tidal forces and individual encounters with other
halos that cause significant mass loss - ``galaxy harassment''. Mergers between
halos do not occur inside the clusters virial radius.
