Subabnormal subgroup

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed subabnormal if there exists an ascending chain:

$$H = H_0 \le H_1 \le \ldots \le H_n = G$$

such that each $$H_i$$ is an abnormal subgroup of $$G$$.

Stronger properties

 * Abnormal subgroup

Weaker properties

 * Contranormal subgroup
 * Subpronormal subgroup