Predictions of the concordance cosmological model (CCM) of the structures in the environment of large spiral galaxies are compared with observed properties of Local Group galaxies. Five new, most probably irreconcilable problems are uncovered: 1) A wide variety of published CCM models consistently predict some form of relation between dark-matter-mass and luminosity for the Milky Way (MW) satellite galaxies, but none is observed. 2) The mass function of luminous sub-haloes predicted by the CCM contains too few satellites with dark matter (DM) mass ≈107 M⊙ within their innermost 300 pc than in the case of the MW satellites. 3) The Local Group galaxies and data from extragalactic surveys indicate there is a correlation between bulge-mass and the number of luminous satellites that is not predicted by the CCM. 4) The 13 new ultra-faint MW satellites define a disc-of-satellites (DoS) that is virtually identical to the DoS previously found for the 11 classical MW satellites, implying that most of the 24 MW satellites are correlated in phase-space. 5) The occurrence of two MW-type DM halo masses hosting MW-like galaxies is unlikely in the CCM. However, the properties of the Local Group galaxies provide information leading to a solution of the above problems. The DoS and bulge-satellite correlation suggest that dissipational events forming bulges are related to the processes forming phase-space correlated satellite populations. These events are well known to occur since in galaxy encounters energy and angular momentum are expelled in the form of tidal tails, which can fragment to form populations of tidal-dwarf galaxies (TDGs) and associated star clusters. If Local Group satellite galaxies are to be interpreted as TDGs then the substructure predictions of the CCM are internally in conflict. All findings thus suggest that the CCM does not account for the Local Group observations and that therefore existing as well as new viable alternatives have to be further explored. These are discussed and natural solutions for the above problems emerge.