Large eddy simulation (LES) is used to investigate the structure of the laminar horseshoe vortex (HV) system and the dynamics of the necklace vortices as they fold around the base of a circular cylinder mounted on the flat bed of an open channel for Reynolds numbers defined with the cylinder diameter, D, smaller than 4460. The study concentrates on the analysis of the structure of the HV system in the periodic breakaway sub-regime, which is characterized by the formation of three main necklace vortices. Over one oscillation cycle of the previously observed breakaway sub-regime, the corner vortex and the primary vortex merge (amalgamate) and a developing vortex separates from the incoming laminar boundary layer (BL) to become the new primary vortex. Results show that while the classical breakaway sub-regime, in which one amalgamation event occurs per oscillation cycle, is present when the nondimensional displacement thickness of the incoming BL at the location of the cylinder is relatively large (δ*/D > 0.1), a new type of breakaway sub-regime is present for low values of δ*/D. This sub-regime, which we call the double-breakaway sub-regime, is characterized by the occurrence of two amalgamation events over one full oscillation cycle. LES results show that when the HV system is in one of the breakaway sub-regimes, the interactions between the highly coherent necklace vortices and the eddies shed inside the separated shear layers (SSLs) are very strong. For the relatively shallow flow conditions considered in this study (H/D ≅ 1, H is the channel depth), at times, the disturbances induced by the legs of the necklace vortices do not allow the SSLs on the two sides of the cylinder to interact in a way that allows the vorticity redistribution mechanism to lead to the formation of a new wake roller. As a result, the shedding of large-scale rollers in the turbulent wake is suppressed for relatively large periods of time. Simulation results show that the wake structure changes randomly between time intervals when large-scale rollers are forming and are convected in the wake (von Karman regime), and time intervals when the rollers do not form. When the wake is in the von Karman regime, the shedding frequency of the rollers is close to that observed for flow past infinitely long cylinders.