query: Looking for a counter example - Normal subgroups
positive_passages.docid: 23533
positive_passages.text: All subgroups normal $\implies$ abelian group
negative_passages.docid: 91874
negative_passages.text: Existence of finite indexed normal subgroup for a given finite indexed subgroup.
negative_passages.docid: 51747
negative_passages.text: Showing that the intersection of all subgroups of order $n$ is normal
negative_passages.docid: 152904
negative_passages.text: Groups with Same Number Of Elements and Subgroups
negative_passages.docid: 27703
negative_passages.text: an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
negative_passages.docid: 80381
negative_passages.text: Groups with "few" subgroups
negative_passages.docid: 14666
negative_passages.text: What are the non-trivial normal subgroups of $O(3)$?
negative_passages.docid: 135701
negative_passages.text: An example of a group such that $G \cong G \times G$
negative_passages.docid: 58076
negative_passages.text: Subgroup generated by a set
negative_passages.docid: 44165
negative_passages.text: the image of normal subgroups
negative_passages.docid: 14255
negative_passages.text: Commutator subgroup and cyclic normal subgroup
negative_passages.docid: 5024
negative_passages.text: Why do we define quotient groups for normal subgroups only?
negative_passages.docid: 132704
negative_passages.text: If G is not commutative, then is there always a subgroup that is not a normal subgroup?
negative_passages.docid: 133272
negative_passages.text: Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
negative_passages.docid: 123610
negative_passages.text: How to show that the commutator subgroup is a normal subgroup
negative_passages.docid: 141043
negative_passages.text: $H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
negative_passages.docid: 35401
negative_passages.text: Examples of finite groups that are not a semidirect product