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Alternative proofs that $A_5$ is simple

Are there/Why aren't there any simple groups with orders like this?

Sylow $p$-subgroups of $SO_3(\mathbb{F}_p)$

Direct products inside finite simple groups

How the square model of Fano 3-space, a.k.a. $PG(3, 2)$, embeds in the MOG?

How to get the “$N_G(H)\subseteq N^y$” here?

Maximal subgroups of ${\rm PSL}(2,8)$

Let $G$ be a group of order $1365$. Prove $G$ is not simple.

Composition Series in a finite group

Show that $SL(3,2)$ is simple

$G$ finite simple group with more than $n/p^2$ conjugacy classes then every $p$-Sylow are abelian

Number of $5$-Sylows of a simple group of order $660$.

Let $n=p^mr$ where $p$ is prime and $r\in\mathbb{Z_{>1}}$ such that $p\nmid r$. If $G$ is a simple group of order $n$ then $p^m\mid(r-1)!$

Prove that the given simple group can be generated by two elements.

Order of elements not in any Sylow $2$-subgroup

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