WordNet sense 1 (upright in position or posture):

erect

WordNet sense 2 (in a vertical position; not sloping):

upright, unsloped

WordNet sense 3 (exactly vertical):

plumb

WordNet sense 4 (at right angles to the plane of the horizon or a base line):

perpendicular

WordNet sense 5 (classified according to various criteria into successive levels or layers):

hierarchic, hierarchical, hierarchal