query: Non-normal subgroup of prime order
positive_passages.docid: 157819
positive_passages.text: Every group of order $56$ has a proper non - trivial normal subgroup?
negative_passages.docid: 15341
negative_passages.text: Non-abelian finite group in which more than half of the elements have order $2$
negative_passages.docid: 7973
negative_passages.text: Groups of order $pq$ have a proper normal subgroup
negative_passages.docid: 86025
negative_passages.text: Nonabelian semidirect products of order $pq$?
negative_passages.docid: 44152
negative_passages.text: If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
negative_passages.docid: 19352
negative_passages.text: Normal subgroup of index m contains every element of order n where m and n are relatively prime
negative_passages.docid: 48273
negative_passages.text: If a maximal subgroup is normal, it has prime index
negative_passages.docid: 48393
negative_passages.text: Abelian groups of order n.
negative_passages.docid: 23885
negative_passages.text: Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
negative_passages.docid: 35602
negative_passages.text: If a subgroup has smallest prime index, then it is normal
negative_passages.docid: 66877
negative_passages.text: Showing groups of order $p^{k}(p+1)$ are not simple, p prime
negative_passages.docid: 70001
negative_passages.text: Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
negative_passages.docid: 102622
negative_passages.text: K is a subgroup of G. Show that K is not a normal subgroup
negative_passages.docid: 139611
negative_passages.text: Can a normal subgroup of a finite nonabelian group be nonabelian?
negative_passages.docid: 108309
negative_passages.text: An example of a non-abelian group of order $p^3$
negative_passages.docid: 39938
negative_passages.text: Subgroups of a cyclic group and their order.
negative_passages.docid: 8066
negative_passages.text: Sort-of-simple non-Hopfian groups