Measurements of the branching fractions of $eta_cto K^+K^-pi^0$, $K^0_S K^{pm}pi^{mp}$,$2(pi^+pi^-pi^0)$, and $p bar{p}$

Using data samples collected with the BESIII detector at center-of-mass energies $sqrt{s} = 4.23, 4.26, 4.36,$ and $4.42$~rm{GeV}, we measure the branching fractions of $eta_cto K^+K^-pi^0$, $K^0_S K^{pm}pi^{mp}$, $2(pi^+pi^-pi^0)$, and $p bar{p}$, via the process $e^+e^-topi^+pi^-h_c$, $h_ctogammaeta_c$. The corresponding results are $(1.15pm0.12pm0.10)%$, $(2.60pm0.21pm0.20)%$, $(15.2pm1.8pm1.7)%$, and $(0.120pm0.026pm0.015)%$, respectively. Here the first uncertainties are statistical, and the second ones systematic. Additionally, the charged track multiplicity of $eta_c$ decays is measured for the first time.