## 1 Introduction  
The current state of knowledge about galaxies, their clusters and the universe itself has made significant progress. There exist various theoretical models describing galaxy formation and their structures, each with different predictions on galaxy orientations in structures, distributions of galactic angular momentum, and collinearity between the location of the brightest galaxy and the major axis of the structure. To verify these expectations and the validity of a particular model, observations are compared with theoretical predictions. This means that the study of galaxy angular momentum distributions is a simple but very important test for the correctness of various models of galaxy formation and their structures [1; 2; 3]. In the commonly accepted \(\Lambda\)CDM cosmological model, one considers the universe to be spatially flat, isotropic and homogeneous in an appropriately large scale. According to the model, structures are formed from primordial, adiabatic, self-scaling Gaussian fluctuations [4; 5; 6; 7]. These assumptions underpin the hierarchical clustering model. Variants that take into account non-Gaussian initial fluctuations are also successfully developed [7]. The analysis of galaxies and their clusters should provide evidence confirming the postulated origins of structures in the universe, and one of such forms is the study of the orientation of galaxies. These analyses assume that normals to the galaxies' planes are their rotation axes, which is especially true for spiral galaxies. The analysis of the distribution position angles of the galaxy major axes, as well as two angles describing the spatial orientation of the galaxy plane, give information about the orientation of galaxies in space and galaxy angular momenta. The investigations described provide a standard method for testing models of galaxy formation because these models predict different outcomes regarding the orientation of galaxies within structures, the distribution of galactic spins, and the alignment between the brightest galaxy and the major axis of the structure [3; 8; 9; 10; 11; 12; 13; 14]. It is not too difficult to analyze the orientation of galaxies in space, and as a result, the distribution of the angular momenta for the luminous matter. Unfortunately in the real universe, luminous galaxies and their structures are surrounded by dark matter halos. These halos are often much more extended and massive than the luminous component of the structures. Unfortunately, dark matter is invisible, and as an result, the direct observation of dark matter halos and their angular momentum is much more complicated. However, as we obBy observing the correlations between luminous and dark matter (sub)structures, we can conclude that there is a dependence between dark matter halos and luminous matter (real galaxies) in terms of the direction of the angular momentum (see for example [15; 16]). The results of [PERSON] et al. (2018) and [PERSON] et al. (2018) [17; 18], based on Horizon-AGN simulations, also show a similar dependence. This allowed for a conclusion that the analysis of angular momentum of luminous matter gives us information about the angular momentum of the total structure as well. As result, the analysis of the angular momentum of \"real\" (luminous) galaxies and their structures is still important as a test of structure formation. The problem of analyzing the alignment of galaxies with different structural scales is very important. This problem, as well as the alignment of galaxies in the larger group, was analyzed many times, both theoretically (see for example [19; 20]) and observationally, for example, by [PERSON] (1976) [21]. The most significant finding is that there is no conclusive evidence supporting the alignment of galaxies in groups and poor clusters of galaxies, whereas ample evidence exists for rich clusters of galaxies. Furthermore, the alignment of galaxies increases with the richness of the structures [7; 9; 22].