20F05 Generators, relations, and presentations
20F06 Cancellation theory; application of van Kampen diagrams [See also 57M05]
20F10 Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]
20F12 Commutator calculus
20F14 Derived series, central series, and generalizations
20F16 Solvable groups, supersolvable groups [See also 20D10]
20F17 Formations of groups, Fitting classes [See also 20D10]
20F18 Nilpotent groups [See also 20D15]
20F19 Generalizations of solvable and nilpotent groups
20F22 Other classes of groups defined by subgroup chains
20F24 FC-groups and their generalizations
20F28 Automorphism groups of groups [See also 20E36]
20F29 Representations of groups as automorphism groups of algebraic systems 
20F34 Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
20F36 Braid groups; Artin groups
20F38 Other groups related to topology or analysis
20F40 Associated Lie structures
20F45 Engel conditions
20F50 Periodic groups; locally finite groups
20F55 Reflection and Coxeter groups [See also 22E40, 51F15]
20F60 Ordered groups [See mainly 06F15]
20F65 Geometric group theory [See also 05C25, 20E08, 57Mxx]
20F67 Hyperbolic groups and nonpositively curved groups
20F69 Asymptotic properties of groups
20F99 None of the above, but in this section