query: The no. of subgroups which are not normal
positive_passages.docid: 151029
positive_passages.text: The number of non normal subgroups of a group cannot be $1$?
negative_passages.docid: 23941
negative_passages.text: Normal Subgroups that Intersect Trivially
negative_passages.docid: 43651
negative_passages.text: Normal subgroups and factor groups
negative_passages.docid: 80381
negative_passages.text: Groups with "few" subgroups
negative_passages.docid: 122353
negative_passages.text: Status of the classification of non-finitely generated abelian groups.
negative_passages.docid: 91772
negative_passages.text: Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
negative_passages.docid: 8066
negative_passages.text: Sort-of-simple non-Hopfian groups
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?
negative_passages.docid: 149578
negative_passages.text: Subgroups of $(\mathbb Z_n,+)$
negative_passages.docid: 67272
negative_passages.text: Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
negative_passages.docid: 89508
negative_passages.text: Existence of normal subgroups for a group of order $36$
negative_passages.docid: 137691
negative_passages.text: What are the self-normalizing subgroups of $S_n$?
negative_passages.docid: 116786
negative_passages.text: normal subgroups of Alternating group
negative_passages.docid: 99114
negative_passages.text: Subgroups of index 3 are normal
negative_passages.docid: 103423
negative_passages.text: Normal subgroup where G has order prime
negative_passages.docid: 124732
negative_passages.text: Finding a nonempty subset that is not a subgroup
negative_passages.docid: 113925
negative_passages.text: Normal Subgroup Counterexample