\section{Classification of Groups of Order Up to 15}

\begin{theorem}[Classification of Groups of Order 8 (Cayley, 1859)]
	Up to isomorphism, there are only five groups of order 8: $\Z_8$, $\Z_4 \oplus \Z_2$, $\Z_2 \oplus \Z_2 \oplus \Z_2$, $D_4$, and the quaternions.
\end{theorem}