To study the structure and stability of the isotopes ${}^{295–304}120$, the self-consistent Hartree-Fock-Bogoliubov calculations are performed using the Skyrme-SLy4 energy-density functional and a zero-range pairing interaction, regularized to avoid divergences. The ground-state deformation evolves from prolate to oblate near $N=174$, with shape coexistence, before the oblate deformation vanishes at $N=182$. The fission barriers increase by a few MeV driven by enhanced shell effects near the $N=184$ and $Z=120$ shell closures. The energy of the rotational $2^{+}$ state reaches a minimum near $N=170$, then it rises as deformation decreases. For consistency, $\alpha$-decays into ground and excited states are analyzed within the preformed cluster model using the nucleus-nucleus potential derived from the same energy-density functional, combining Wentzel-Kramers-Brillouin penetrability and assault frequency. Predicted half-lives range from ms for ${}^{300,302}120$ and ${}^{296,298}\mathrm{Og}$ to an order of ${10}^2\mathrm{s}$ for ${}^{292}\mathrm{Fl}$, with a significant population the $2^{+}$ state in the daughter nuclei of ${}^{296}120, {}^{292,294}\mathrm{Og}, {}^{288,294}\mathrm{Lv}$, and ${}^{286}\mathrm{Fl}$.

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• Alpha decay
• Collective levels
• Energy levels
• Nuclear shapes and moments
• Nuclear structure & decays
• A ≥ 220