Photosystem II (PSII) is a light-driven protein, involved in the primary reactions of photosynthesis. In plant photosynthetic membranes PSII forms large multisubunit supercomplexes, containing a dimeric core and up to four light-harvesting complexes (LHCs), which act as antenna proteins. Here we solved a three-dimensional (3D) structure of the C$_2$S$_2$M$_2$ supercomplex from $Arabidopsis\ thaliana$ using cryo-transmission electron microscopy (cryo-EM) and single-particle analysis at an overall resolution of 5.3 Å. Using a combination of homology modelling and restrained refinement against the cryo-EM map, it was possible to model atomic structures for all antenna complexes and almost all core subunits. We located all 35 chlorophylls of the core region based on the cyanobacterial PSII structure, whose positioning is highly conserved, as well as all the chlorophylls of the LHCII S and M trimers. A total of 13 and 9 chlorophylls were identified in CP26 and CP24, respectively. Energy flow from LHC complexes to the PSII reaction centre is proposed to follow preferential pathways: CP26 and CP29 directly transfer to the core using several routes for efficient transfer; the S trimer is directly connected to CP43 and the M trimer can efficiently transfer energy to the core through CP29 and the S trimer.