Background: Observation of asymmetric fission of $^{180}\mathrm{Hg}$ has led to intensive theoretical and experimental studies of fission of neutron-deficient nuclei in the lead region.Purpose: The study of asymmetric and symmetric fission modes of $^{180,190}\mathrm{Hg}$ and $^{184,192,202}\mathrm{Pb}$ nuclei.Methods: Mass-energy distributions of fission fragments of $^{180,190}\mathrm{Hg}$ and $^{184}\mathrm{Pb}$ formed in the $^{36}\mathrm{Ar}+^{144,154}\mathrm{Sm}$ and $^{40}\mathrm{Ca}+^{144}\mathrm{Sm}$ reactions, respectively, at energies near the Coulomb barrier have been measured using the double-arm time-of-flight spectrometer CORSET and compared with previously measured $^{192,202}\mathrm{Pb}$ isotopes produced in the $^{48}\mathrm{Ca}+^{144,154}\mathrm{Sm}$ reactions. The mass distributions for $^{180,190}\mathrm{Hg}$ and $^{184,192,202}\mathrm{Pb}$ together with old data for $^{187}\mathrm{Ir}, ^{195}\mathrm{Au}, ^{198}\mathrm{Hg}, ^{201}\mathrm{Tl}, ^{205,207}\mathrm{Bi}, ^{210}\mathrm{Po}$, and $^{213}\mathrm{At}$ [J. Nucl. Phys. 53, 1225 (1991)] have been decomposed into symmetric and asymmetric fission modes. The total kinetic-energy distributions for different fission fragment mass regions have been analyzed for $^{180,190}\mathrm{Hg}$ and $^{184}\mathrm{Pb}$.Results: The stabilization role of proton numbers at $Z\ensuremath{\approx}36$, 38, $Z\ensuremath{\approx}45$, 46, and $Z=28/50$ in asymmetric fission of excited preactinide nuclei has been observed. The high ($\ensuremath{\approx}145\text{\ensuremath{-}}\mathrm{MeV}$) and the low ($\ensuremath{\approx}128\text{\ensuremath{-}}\mathrm{MeV}$) energy components have been found in the total kinetic-energy distributions of $^{180,190}\mathrm{Hg}$ fission fragments corresponding to the fragments with proton numbers near $Z\ensuremath{\approx}46$ and $Z\ensuremath{\approx}36$, respectively. In the case of fission of $^{184}\mathrm{Pb}$ only the low-energy component ($\ensuremath{\approx}135\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$) for the fragments with masses corresponding to the proton numbers $Z\ensuremath{\approx}36$ and 46 has been found.Conclusions: The studied properties of asymmetric fission of $^{180,190}\mathrm{Hg}$ and $^{184,192,202}\mathrm{Pb}$ nuclei point out the existence of well deformed proton shell at $Z\ensuremath{\approx}36$ and less deformed proton shell at $Z\ensuremath{\approx}46$.
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