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We have shown that, in determining the biomolecule-crystal symmetry, the occupation of low-site-symmetry Wyckoff positions is crucial, which contrasts with the overwhelming majority of nonmolecular, inorganic crystals where atoms mainly reside in high-symmetry Wyckoff positions. We consider the general relation between the symmetry of an isolated molecule and the possible symmetries of biomolecular crystals it can generate. We reveal that the improper symmetry operations (inversion and mirror symmetries) are prohibited in the chirally pure biomolecular crystals. Next, we show that the low (C1) symmetry of large biological molecules substantially decreases the space in a crystal where the molecules can reside. The space "forbidden" for molecule centers is found to be in the R vicinity of the higher-symmetry Wyckoff positions on symmetry lines, where R is the molecule characteristic size. The remaining free space and hence the probability for the structure to exist are shown to be drastically increased when replacing any rotation axis by a screw one. Based on the proposed model, we have explained the peculiar distribution of biomolecular crystals over the space groups, which can be obtained from biomolecule-crystal databases.