Proving that the intersection of Sylow p-subgroups is normal?
47731
Intersection of all $p$-Sylow subgroups is normal
35602
If a subgroup has smallest prime index, then it is normal
15630
Normal subgroup of prime order is characteristic
75568
Subgroup of index $2$ is Normal
115204
Show that SO(n) is a normal subgroup of O(n)
6134
Some Subgroup of Dihedral Group is Normal
20386
Any subgroup of index $p$ in a $p$-group is normal.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
42096
Direct product of Sylow subgroups
58251
To show every sylow p-subgroup is normal in G
23941
Normal Subgroups that Intersect Trivially
54911
The preimage of a normal subgroup under a group homomorphism is normal
61235
Sylow $p$-subgroup of a direct product is product of Sylow $p$-subgroups of factors
2174
Proving that HK is a subgroup when K is normal
103423
Normal subgroup where G has order prime
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
51747
Showing that the intersection of all subgroups of order $n$ is normal