Subpronormal subgroup

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

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

such that each $$H_i$$ is a pronormal subgroup of $$H_{i+1}$$.

Stronger properties

 * Weaker than::Pronormal subgroup
 * Weaker than::Subnormal subgroup
 * Weaker than::Subabnormal subgroup
 * Weaker than::Submaximal subgroup
 * Weaker than::Subgroup of finite index