The process $e^+e^-\to\omega\eta\pi^0$ is studied in the energy range $1.45-2.00$ GeV using data with an integrated luminosity of 33 pb$^{-1}$ accumulated by the SND detector at the $e^+e^-$ collider VEPP-2000. The $e^+e^-\to\omega\eta\pi^0$ cross section is measured for the first time. The cross section has a threshold near 1.75 GeV. Its value is about 2 nb in the energy range $1.8-2.0$ GeV. The dominant intermediate state for the process $e^+e^- \to \omega\eta\pi^0$ is found to be $\omega a_0(980)$.
The energy interval, integrated luminosity ($L$), number of selected events ($N$), estimated number of background events ($N_{bkg}$), detection efficiency for $e^+e^-\to\omega\eta\pi^0\to 7\gamma$ events ($\epsilon$), radiative correction ($\delta+1$), and $e^+e^-\to\omega\eta\pi^0$ Born cross section ($\sigma$). The shown cross-section errors are statistical. The systematic error is 4.2%. The 90% confidence level upper limits are listed for the first two energy intervals.
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