His most important contribution to science was his systematic classification of minerals based on their chemical compositions and crystal structures.

[1] In 1883, Groth compiled a monumental five-volume collection entitled Chemische Kristallographie, which contained crystalline morphology and physical property data on thousands of substances.

The German physicist Leonhard Sohncke (1842–1897) had previously derived the 65 chiral space groups (i.e. those lacking an inversion center, mirror planes, or improper axes of rotation that invert the handedness of a crystal).

The mathematical descriptions of the complete set of 230 space groups, including their symmetry elements, were thereafter derived independently by Schönflies, Fedorov, and Barlow.

Finally, in 1922, Ralph Walter Graystone Wyckoff (1897–1994) authored The Analytical Expression of the Results of the Theory of Space Groups, a book which contained, among other things, tables with the positional coordinates, both general and special, permitted by the symmetry elements.