Samples of the [Hg1 - xCx]-Ba2CuOy system [(Hg,C)-1201] with stoichiometries within the range 0.00≤x≤1.00 were synthesized by a highpressure, high-temperature technique. The sample with x = 0.00 [HgBa2CuO4+δ] was non-superconducting with lattice parameters a = 3.8676(2) Å, c = 9.470(1) Å. At low ranges of substitution (0.10≤x≤0.30), the predominant phase was found to be Hg-1201 with identical lattice parameters to those found for x = 0.00. At x = 0.40 the Hg-1201 phase coexists in similar proportions with the phase of mixed [Hg1 - x,Cx]-1201 stoichiometry. At x = 0.50, this second phase with lattice parameters a = 3.9271(3) Å, c = 8.676(2) Å is predominant and only traces of the Hg-1201 phase were found. At x = 0.75 the [Hg1 - x,Cx]-1201 phase found for x = 0.50 coexists with the CO3Ba2CuOy phase, which is the extreme of the substitution range. This latter was predominant at x = 1.00 with lattice parameters a = 4.0044(3) Å, c = 7.909(1) Å, but at higher pressure than the previous substitutions. This system is constituted of three main phases, HgBa2CuO4 + δ, Hg1 - xCxBa2CuOy (x ≈ 0.50) and CO3Ba2CuOy, which appear in different proportions according to the percentage of substitution and the applied synthesis pressure.