Which finite groups $G$ do not embed in any symmetric group $S_n$ with $n < \lvert G \rvert$?
117965
Does there exist some sort of classification of incompressible groups?
129120
Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
102912
Subgroups of finitely generated groups are not necessarily finitely generated
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
50762
If $S_n$ has cyclic subgroups of these orders or not?
44942
A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
142421
Conjugacy Classes in Finite Groups
79055
Orders of a symmetric group
80381
Groups with "few" subgroups
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
99309
Groups of order $n^2$ that have no subgroup of order $n$
80849
There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
8746
Groups of order $pq$ without using Sylow theorems
21568
Maximal order of an element in a symmetric group
99999
A question on identifying normal subgroups of $S_4$