\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document} \begin{tikzpicture}
    \node[label=above:finite groups] 
        (grp) {\( \circ \)};
    \node[label=left:simple groups] 
        (simp) [below left=of grp] {\( \circ \)};
    \node[label=right:solvable groups] 
        (solv) [below right=of grp] {\( \circ \)};
    \node[label=right:nilpotent groups] 
        (nilp) [below right=of solv] {\( \circ \)};
    \node[label=right:\( p \)-groups] 
        (p-gp) [below right =of nilp] {\( \circ \)};
    \node[label=left:abelian groups] 
        (ab) [below left =of nilp] {\( \circ \)};
    \node[label=right:elementary abelian \( p \)-groups] 
        (elem) [below left =of p-gp] {\( \circ \)};
    \node[label=left:cyclic groups] 
        (cyc) [below left =of ab] {\( \circ \)};
    \node[label=right:the trivial group] 
        (triv) [below right =of cyc] {\( \circ \)};

    \tikzset{every node/.style={fill=white, scale=.8}} 
    \path
        (grp)  edge node {\( A_5 \)} (solv)
	(grp)  edge node {\( S_5 \)} (simp)
	(solv) edge node {\( S_3 \)} (nilp)
	(nilp) edge node {\( C_3 \times Q_8 \)} (p-gp)
	(nilp) edge node {\( Q_8 \)} (ab)
	(ab)   edge node {\( C_3 \times V_4 \)} (cyc)
	(ab)   edge node {\( C_4 \)} (elem)
	(p-gp) edge node {\( Q_8 \)} (elem)
	(elem) edge node {\( V_4 \)} (triv)
	(cyc)  edge node {\( C_6 \)} (triv)
	;
\end{tikzpicture} \end{document}