Groups 1-2 (except hydrogen) and 13-18 are termed main group elements.
Groups 3-11 are termed transition elements. Transition elements are those whose atoms have an incomplete d-subshell or whose cations have an incomplete d-subshell.
Main group elements in the first two rows of the table are called typical elements.
The first row of the f-block elements are called lanthanoids (or, less desirably, lanthanides. The second row of the f-block elements are called actanoids (or, less desirably, actanides.
The following names for specific groups in the periodic table are in common use: