Notation for subgroup properties

This is a notation page: it lists some important notation

Notations for subgroup properties

• $\leq ,\geq$ denotes the tautology subgroup property, viz $H\leq G$ or $G\geq H$ means that $H$ is a subgroup of $G$ (with no further restrictions)
• $\triangleleft ,\triangleright$ denotes the subgroup property of being a normal subgroup, viz $H\triangleleft G$ or $G\triangleright H$ means that $H$ is a normal subgroup of $G$.
• $char$ denotes the subgroup property of being a characteristic subgroup, viz $HcharG$ means that $H$ is a characteristic subgroup of $G$.
• $\triangleleft \triangleleft ,\triangleright \triangleright$ denotes the subgroup property of being a subnormal subgroup, viz $H\triangleleft \triangleleft G$ or $G\triangleright \triangleright H$ means that $H$ is a subnormal subgroup of $G$.
• $\leq _{\max },\geq _{\max }$ denotes the subgroup property of being a maximal subgroup, viz $H\leq _{\max }G,H\geq _{\max }H$ iff $H$ is a maximal subgroup of $G$