  We have performed the largest ever particle simulation of a Milky Way-sized
dark matter halo, and present the most comprehensive convergence study for an
individual dark matter halo carried out thus far. We have also simulated a
sample of 6 ultra-highly resolved Milky-way sized halos, allowing us to
estimate the halo-to-halo scatter in substructure statistics. In our largest
simulation, we resolve nearly 300,000 gravitationally bound subhalos within the
virialized region of the halo. Simulations of the same object differing in mass
resolution by factors up to 1800 accurately reproduce the largest subhalos with
the same mass, maximum circular velocity and position, and yield good
convergence for the abundance and internal properties of dark matter
substructures. We detect up to four generations of subhalos within subhalos,
but contrary to recent claims, we find less substructure in subhalos than in
the main halo when regions of equal mean overdensity are compared. The overall
substructure mass fraction is much lower in subhalos than in the main halo.
Extrapolating the main halo's subhalo mass spectrum down to an Earth mass, we
predict the mass fraction in substructure to be well below 3% within 100 kpc,
and to be below 0.1% within the Solar Circle. The inner density profiles of
subhalos show no sign of converging to a fixed asymptotic slope and are well
fit by gently curving profiles of Einasto form. The mean concentrations of
isolated halos are accurately described by the fitting formula of Neto et al.
down to maximum circular velocities of 1.5 km/s, an extrapolation over some 5
orders of magnitude in mass. However, at equal maximum circular velocity,
subhalos are more concentrated than field halos, with a characteristic density
that is typically ~2.6 times larger and increases towards the halo centre.
