Notation for subgroup properties

This is a notation page: it lists some important notation

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 $G$ .
$c h a r$ denotes the subgroup property of being a characteristic subgroup, viz $H c h a r G$ 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 $G$