Context. Understanding baryonic physics at the galaxy-group level is a prerequisite for cosmological studies of the large-scale structure. One poorly understood aspect of galaxy groups is related to the properties of their hot intragroup medium. The well-studied X-ray groups have strong cool cores by which they were selected, so expanding the selection of groups is currently an important avenue in uncovering the diversity within the galaxy group population. Aims. We present a new all-sky catalogue of X-ray-detected groups (AXES-2MRS) based on the identification of large X-ray sources found in the ROSAT All-Sky Survey (RASS) with the Two Micron Redshift Survey (2MRS) Bayesian Group Catalogue. We studied the basic properties of these galaxy groups to gain insights into the effect of different group selections on the properties. Methods. In addition to X-ray luminosity from shallow survey data of RASS, we obtained detailed X-ray properties of the groups by matching the AXES-2MRS catalogue to archival X-ray observations by XMM-Newton and complemented this by adding the published XMM-Newton results on galaxy clusters in our catalogue. We analysed temperature and density to the lowest overdensity accessible by the data, obtaining hydrostatic mass estimates at a uniform overdensity of 10 000 times the critical, M10 000, and comparing them to the velocity dispersions of the groups. We explored the relationship between X-ray and optical properties of AXES-2MRS groups through the σv−LX, σv−kT, kT−LX, σv−M, and c200−LX scaling relations. Results. We find a large spread in the central mass ( M10 000), measured by XMM-Newton, to virial mass (M200), inferred by the velocity dispersion, ratios for galaxy groups. This can either indicate that large non-thermal pressure of galaxy groups affects our X-ray mass measurements or the effect of a diversity of halo concentrations on the X-ray properties of galaxy groups. Previous catalogues based on detecting the peak of the X-ray emission preferentially sample the high-concentration groups. In contrast, our new catalogue uncovered many low-concentration groups, completely revising our understanding of X-ray groups.