Notation for subgroup properties

Notations for subgroup properties

 * $$\le, \ge$$ denotes the tautology subgroup property, viz $$H \le G$$ or $$G \ge H$$ 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 $$H char G$$ 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 $$G$$.
 * $$\le_{\max}, \ge_{\max}$$ denotes the subgroup property of being a maximal subgroup, viz $$H \le_{\max} G, H \ge_{\max} H$$ iff $$H$$ is a maximal subgroup of $$G$$