For any $n$, there are at most two simple groups of order $n$?
104112
Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
118022
Show that a group of order $180$ is not simple.
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
151025
If G is a group of order n=35, then it is cyclic
113840
Does converse of Lagrange's theorem hold for a group of order 21?
28266
For $n\geq 3$ there exist $x,y\in S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$.
121142
Take $G$ to be a group of order $600$. Prove that for any element a in $G$ there exist a $b$ in $G$ such that $a = b^7$
79055
Orders of a symmetric group
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
88344
Order of a group and subsequent subgroups
68201
Cyclic group of order $n$
129568
How many different groups of order $15$ there are?
76732
Number of non-isomorphic groups of order 21
142718
How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once?
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
157841
Existence of a non-abelian group of order $p^n$.