International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 
International Tables for Crystallography (2016). Vol. A, ch. 3.6, p. 863
Section 3.6.4. Comparison of OG and BNS magnetic group type symbols^{a}Department of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA 
There are other notations for magnetic group type symbols than the notations of Opechowski & Guccione (1965) and Belov, Neronova & Smirnova (1957): for example for the threedimensional magnetic group 55.10.450 P_{2c}b′a′m the Shubnikov notation is (Koptsik, 1966; Shubnikov & Koptsik, 1974) or (Ozerov, 1969a,b) (see also Zamorzaev, 1976). There are also the variations of the Opechowski & Guccione notation put forward by Grimmer (2009, 2010). We shall limit ourselves here to a detailed comparison of the Opechowski & Guccione and Belov, Neronova & Smirnova notations.
For all group types in the reduced magnetic superfamily of , the Opechowski & Guccione (1965) magnetic group type symbols (OG symbols) are based on the symbol of the group . Belov, Neronova & Smirnova (1957) also base their symbols (BNS symbols) on the symbol of the group , but only for magnetic groups of the type , and . For magnetic groups , where is an equiclass subgroup of , the BNS symbol is based on the symbol of the group , the nonprimed subgroup of index 2. A magnetic group can be written as , where is a translation of not in . The BNS symbol for a magnetic group of the type is the symbol for the group type with a subindex inserted on the symbol for the translational subgroup of to denote the translation .
Example
The representative threedimensional space group has a translational subgroup generated by the three translations {1∣1, 0, 0}, {1∣0, 1, 0} and {1∣0, 0, 1} and the standard set of coset representativesThe threedimensional magnetic space group 25.10.165 = has a subgroup with a translational subgroup generated by the three translations {1∣1, 0, 0}, {1∣0, 1, 0} and {1∣0, 0, 2}, = {1∣0, 0, 1}′, and a set of coset representativesThe OG magnetic group type symbol is, see Section 3.6.2.2.4, P_{2c}m′m′2, i.e. based on the symbol for the group type = . The BNS symbol is P_{c}cc2, i.e. based on the symbol for the subgroup of , with a subindex `c' attached to `P' to denote the translation = {1∣0, 0, 1}′ in = .
A sidebyside comparison of OG magnetic group type symbols and BNS symbols is given in Litvin (2013). As the OG and BNS symbols are the same for magnetic groups , and , BNS symbols are explicitly listed only for groups of type . Examples of this comparison are given in Table 3.6.4.1.

References
Belov, N. V., Neronova, N. N. & Smirnova, T. S. (1957). 1651 Shubnikov groups. Sov. Phys. Crystallogr. 1, 487–488. See also (1955) Trudy Inst. Krist. Acad. SSSR, 11, 33–67 (in Russian), English translation in Shubnikov, A. V, Belov, N. V. & others (1964). Colored Symmetry. London: Pergamon Press.Grimmer, H. (2009). Comments on tables of magnetic space groups. Acta Cryst. A65, 145–155.
Grimmer, H. (2010). Opechowski–Guccionelike symbols labelling magnetic space groups independent of tabulated (0, 0, 0)+ sets. Acta Cryst. A66, 284–291.
Koptsik, V. A. (1966). Shubnikov Groups. Handbook on the Symmetry and Physical Properties of Crystal Structures. Izd. MGU (in Russian). English translation of text: Kopecky, J. & Loopstra, B. O. (1971). Fysica Memo 175. Stichting, Reactor Centrum Nederland.
Litvin, D. B. (2013). Magnetic Group Tables, 1, 2 and 3Dimensional Magnetic Subperiodic Groups and Space Groups. Chester: International Union of Crystallography. Freely available from http://www.iucr.org/publ/978–0–9553602–2–0 .
Opechowski, W. & Guccione, R. (1965). Magnetic symmetry. In Magnetism, edited by G. T. Rado & H. Suhl, Vol. 2A, ch. 3. New York: Academic Press.
Ozerov, R. P. (1969a). The design of tables of Shubnikov space groups of dichroic symmetry. Kristallografiya, 14, 393–403.
Ozerov, R. P. (1969b). The design of tables of Shubnikov space groups of dichroic symmetry. Sov. Phys. Crystallogr. 14, 323–332.
Shubnikov, A. V. & Koptsik, V. A. (1974). Symmetry in Science and Art. New York: Plenum Press.
Zamorzaev, A. M. (1976). The Theory of Simple and Multiple Antisymmetry. Kishinev: Shtiintsa. (In Russian.)