Notation for subgroup properties

Notations for subgroup properties

• $\leq$ denotes the tautology subgroup property, viz $H\leq G$ means that $H$ is a subgroup of $G$ (with no further restrictions)
• $\triangleleft$ denotes the subgroup property of being a normal subgroup, viz $H\triangleleft G$ 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 $G$.
• $\triangleleft \triangleleft$ denotes the subgroup property of being a subnormal subgroup, viz $H\triangleleft \triangleleft G$ means that $H$ is a subnormal subgroup of $G$.