  We present a comprehensive analysis of the emerging order and chaos and
enduring symmetries, accompanying a generic (high-barrier) first-order quantum
phase transition (QPT). The interacting boson model Hamiltonian employed,
describes a QPT between spherical and deformed shapes, associated with its U(5)
and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic
dynamics reveals a rich but simply-divided phase space structure with a
H\'enon-Heiles type of chaotic dynamics ascribed to the spherical minimum and a
robustly regular dynamics ascribed to the deformed minimum. The simple pattern
of mixed but well-separated dynamics persists in the coexistence region and
traces the crossing of the two minima in the Landau potential. A quantum
analysis discloses a number of regular low-energy U(5)-like multiplets in the
spherical region, and regular SU(3)-like rotational bands extending to high
energies and angular momenta, in the deformed region. These two kinds of
regular subsets of states retain their identity amidst a complicated
environment of other states and both occur in the coexistence region. A
symmetry analysis of their wave functions shows that they are associated with
partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS),
respectively. The pattern of mixed but well-separated dynamics and the PDS or
QDS characterization of the remaining regularity, appear to be robust
throughout the QPT. Effects of kinetic collective rotational terms, which may
disrupt this simple pattern, are considered.
