  The WASA-at-COSY experiment has collected $3\times10^{7}$ events with
$\eta$-mesons produced via the reaction $pd\rightarrow{^{3}\textrm{He}}\eta$ at
$\textrm{T} = 1.0 \textrm{GeV}$. Using this data set, we evaluate the branching
ratios of the decays $\eta\to\pi^{+}\pi^{-}\gamma$, $\eta\to e^{+}e^{-}\gamma$,
$\eta\to\pi^{+}\pi^{-}e^{+}e^{-}$ and $\eta\to e^{+}e^{-}e^{+}e^{-}$. The
branching ratios are normalized to the $\eta\rightarrow\pi^{+}\pi^{-}\pi^{0}$
decay. In addition an upper limit on a $CP$-violating asymmetry in
$\eta\rightarrow \pi^{+}\pi^{-}e^{+}e^{-}$ is extracted.
