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Subnormal-to-normal and normal-to-characteristicSubnormal-to-normal subgroup
Subnormal subgroup
Normal subgroup
Intermediately subnormal-to-normal subgroup
Normal-to-characteristic subgroup
Characteristic subgroup
Intermediately normal-to-characteristic subgroup
Pronormal subgroup
Weakly pronormal subgroup
Paranormal subgroup
Polynormal subgroup
Image-closed intermediately subnormal-to-normal subgroup
2-subnormal subgroup
Subgroup with self-normalizing normalizer
Subgroup with abnormal normalizer
Subgroup with weakly abnormal normalizer
Isomorph-free subgroup
Isomorph-containing subgroup
Isomorph-conjugate subgroup
Automorph-conjugate subgroup
Intermediately characteristic subgroup
Intermediately isomorph-conjugate subgroup
Intermediately automorph-conjugate subgroup
Procharacteristic subgroup
Weakly procharacteristic subgroup
Intermediately procharacteristic subgroup
Paracharacteristic subgroup
Polycharacteristic subgroup
Intermediately paracharacteristic subgroup
Ntermediately polycharacteristic subgroup
Weakly characteristic subgroup
Intermediately weakly characteristic subgroup
Sylow subgroup
Hall subgroup
Contranormal subgroup
Self-normalizing subgroup
Weakly abnormal subgroup
Abnormal subgroup