query: $A_5$ is the only subgroup of $S_5$ of order 60
positive_passages.docid: 1996
positive_passages.text: $A_n$ is the only subgroup of $S_n$ of index $2$.
negative_passages.docid: 51747
negative_passages.text: Showing that the intersection of all subgroups of order $n$ is normal
negative_passages.docid: 37913
negative_passages.text: Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
negative_passages.docid: 12667
negative_passages.text: How many subgroups of order $n$ does $D_n$ have?
negative_passages.docid: 156909
negative_passages.text: $\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
negative_passages.docid: 84658
negative_passages.text: What is the number of distinct subgroups of the automorphism group of $\mathbf{F}_{3^{100}}$?
negative_passages.docid: 933
negative_passages.text: How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
negative_passages.docid: 103829
negative_passages.text: Find the subgroups of A4
negative_passages.docid: 157819
negative_passages.text: Every group of order $56$ has a proper non - trivial normal subgroup?
negative_passages.docid: 99694
negative_passages.text: Number of subgroups of $S_4$
negative_passages.docid: 75590
negative_passages.text: How many normal subgroups does a non-abelian group $G$ of order $ 21$
negative_passages.docid: 54195
negative_passages.text: Do groups of prime order have one subgroup?
negative_passages.docid: 51352
negative_passages.text: Subgroups of a finite abelian group
negative_passages.docid: 108250
negative_passages.text: A group of order $595$ has a normal Sylow 17-subgroup.
negative_passages.docid: 58863
negative_passages.text: Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
negative_passages.docid: 92899
negative_passages.text: $G$ is non abelian simple group of order $<100$ then $G\cong A_5$
negative_passages.docid: 129830
negative_passages.text: A group with no proper non-trivial subgroups