Group of order 35 must have a normal subgroup of order 5 or 7 or both without using Sylow’s theorems
8746
Groups of order $pq$ without using Sylow theorems
157841
Existence of a non-abelian group of order $p^n$.
41231
Subgroups of (Z,+) of order n
47731
Intersection of all $p$-Sylow subgroups is normal
58251
To show every sylow p-subgroup is normal in G
141458
How many subgroups or order 8 an abelian Group of order 72 can have
129830
A group with no proper non-trivial subgroups
50157
order of a sylow p-subgroup
42096
Direct product of Sylow subgroups
89508
Existence of normal subgroups for a group of order $36$
142938
Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
129937
How to prove that $A_5$ has no subgroup of order 30?
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
15630
Normal subgroup of prime order is characteristic
15526
Question on groups of order $pq$
28181
Sylow subgroups of $S_3$ and $S_4$