# 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 $G$.
• $char$ 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 $G$