Use a minipage for the tabular. However, your tabuloar is too wide and, of course, you shouldn't use too many lines. Without it it makes it more readable:

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath,amsthm,amsfonts,latexsym,amscd,amssymb,mathrsfs,hyperref,textcomp,booktabs}
\hypersetup{colorlinks}
\begin{document}

\begin{table}[ht]
\centering
\begin{minipage}{\linewidth}
\begin{tabular}{|p{0.9cm}|p{1.6cm}|p{1.6cm}|p{4cm}|p{4.5cm}|}
\hline
Order&amp;Group $G$&amp;Gap Id&amp;Presentation&amp;$\Gamma_d(G)$\footnote{We shall exclude the cases $d=1,|G|$, since $\Gamma_1(G)=K_1=\Gamma_{|G|}(G)$}\\ \hline
1&amp;$C_1$&amp;1(1)&amp;$\langle a;a^1\rangle$&amp;$\Gamma_1(C_1)=K_1$ \\ \hline
2&amp;$C_2$&amp;2(1)&amp;$\langle a;a^2\rangle$&amp;$\Gamma_1(C_2)=\Gamma_2(C_2)=K_1$ \\ \hline
3&amp;$C_3$&amp;3(1)&amp;$\langle a;a^3\rangle$&amp;$\Gamma_1(C_3)=\Gamma_3(C_3)=K_1$ \\ \hline
4&amp;$C_4$&amp;4(1)&amp;$\langle a;a^4\rangle$&amp;$\Gamma_1(C_4)=\Gamma_2(C_4)=\Gamma_4(C_4)=K_1$\\ \cline{2-5}
&amp;$C_2\times C_2$&amp;2(2)&amp;$\langle a,b;a^2,b^2,aba^{-1}b^{-1}\rangle$&amp;$\Gamma_1(G)=\Gamma_4(G)=K_1,\Gamma_2(G)=K_3$\\ \hline
5.&amp;$C_5$&amp;5(1)&amp;$\langle a;a^5\rangle$&amp;$\Gamma_1(C_5)=\Gamma_5(C_5)=K_1$\\ \hline
\end{tabular}
\end{minipage}
\caption{Abelian groups}
\end{table}

\begin{table}[ht]
\begin{minipage}{\linewidth}
\def\arraystretch{1.4}\tabcolsep=2pt\small\centering
\begin{tabular}{@{} l l l l l @{}}\toprule
Order&amp;Group $G$&amp;Gap Id&amp;Presentation&amp;$\Gamma_d(G)$\footnote{We shall exclude the cases $d=1,|G|$, since $\Gamma_1(G)=K_1=\Gamma_{|G|}(G)$}\\ \midrule
1&amp;$C_1$&amp;1(1)&amp;$\langle a;a^1\rangle$&amp;$\Gamma_1(C_1)=K_1$ \\
2&amp;$C_2$&amp;2(1)&amp;$\langle a;a^2\rangle$&amp;$\Gamma_1(C_2)=\Gamma_2(C_2)=K_1$ \\ 
3&amp;$C_3$&amp;3(1)&amp;$\langle a;a^3\rangle$&amp;$\Gamma_1(C_3)=\Gamma_3(C_3)=K_1$ \\ 
4&amp;$C_4$&amp;4(1)&amp;$\langle a;a^4\rangle$&amp;$\Gamma_1(C_4)=\Gamma_2(C_4)=\Gamma_4(C_4)=K_1$\\ 
&amp;$C_2\times C_2$&amp;2(2)&amp;$\langle a,b;a^2,b^2,aba^{-1}b^{-1}\rangle$&amp;$\Gamma_1(G)=\Gamma_4(G)=K_1,\Gamma_2(G)=K_3$\\ 
5.&amp;$C_5$&amp;5(1)&amp;$\langle a;a^5\rangle$&amp;$\Gamma_1(C_5)=\Gamma_5(C_5)=K_1$\\ \bottomrule
\end{tabular}
\end{minipage}
\caption{Abelian groups}
\end{table}

\end{document}




Footnote in booktabs package
I think the title says it all. Let's say you're mastering a game without the benefit of miniatures, maps, or any kind of physical representation of the environment. How would you keep track of details like line-of-sight, ranged attack viability, and all the other small nuances which go with creating a "believable-enough" environment in which your PCs live and thrive?

(I admit that @LoganMacRae, who is my own DM, is an inspiration for this question. He does this with panache, and in my one-off, I feel like I have some mighty big shoes to fill!)
