The behavior of a dc superconducting quantum interference device (SQUID), based on dirty-point contacts between a single-band and three-band superconductor with broken time-reversal symmetry, is investigated. Using previously obtained results for Josephson effects in such systems, new features in characteristics of a dc SQUID are revealed. It is shown that in the case of a BTRS (broken time-reversal symmetry) three-band superconductor for the applied external magnetic flux, which is divisible by the half-integer flux, strong degeneracy of ground states of a dc SQUID has taken place. This can lead to the appearance of possible multi-hysteresis loops on a dependence of a total flux in the dc SQUID from the externally applied flux. The number of these loops depends on the position of ground states of a three-band superconductor. Also it is found that dependencies of a critical current on applied magnetic flux can have complicated multi-periodic forms, which differ from strictly periodic characteristics for conventional dc SQUIDs and Fraunhofer patterns for Josephson contacts in the external magnetic field.