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**Drexel28** I assume that you mean no non-trivial proper subgroups. The answer is yes $\displaystyle \mathbb{Z}_2$ but in the spirit of your question...no. If $\displaystyle G$ is a finite group and $\displaystyle |G|=2m$ where $\displaystyle m>0$ then a simple application of Cauchy's theorem says that $\displaystyle G$ must have an element of order $\displaystyle 2$. More generally, Sylow's first theorem implies that if $\displaystyle G$ is a finite group and $\displaystyle p^m\mid |G|$ with $\displaystyle p$ prime then $\displaystyle G$ must contain a subgroup of order $\displaystyle p$. From this it's easy to see that the only groups you mention have order $\displaystyle 1$ or $\displaystyle p$ where $\displaystyle p$ is prime.