  The $^{80}$Ge structure was investigated in a high-statistics $\beta$-decay
experiment of $^{80}$Ga using the GRIFFIN spectrometer at TRIUMF-ISAC through
$\gamma$, $\beta$-$e$, $e$-$\gamma$ and $\gamma$-$\gamma$ spectroscopy. No
evidence was found for the recently reported 0$_2^{+}$ 639-keV level suggested
as evidence for low-energy shape coexistence in $^{80}$Ge. Large-scale shell
model calculations performed in $^{78,80,82}$Ge place the $0^{+}_{2}$ level in
$^{80}$Ge at 2\,MeV. The new experimental evidence combined with shell model
predictions indicate that low-energy shape coexistence is not present in
$^{80}$Ge.
