  We solve the following algorithmic problems using TC0 circuits, or in
logspace and quasilinear time, uniformly in the class of nilpotent groups with
bounded nilpotency class and rank: subgroup conjugacy, computing the normalizer
and isolator of a subgroup, coset intersection, and computing the torsion
subgroup. Additionally, if any input words are provided in compressed form as
straight-line programs or in Mal'cev coordinates the algorithms run in quartic
time.
