# Finding Intermediate Subgroups

## TL;DR

This paper presents a practical method for identifying all intermediate subgroups between two given subgroups in a group, leveraging existing tools for conjugacy, cosets, and maximal subgroups, when the number of such subgroups is manageable.

## Contribution

It introduces a new approach for computing the lattice of intermediate subgroups, extending existing subgroup analysis techniques.

## Key findings

- Effective in cases with a manageable number of intermediate subgroups
- Utilizes conjugacy, double cosets, and maximal subgroup computations
- Facilitates subgroup lattice determination in group theory

## Abstract

This article describes a practical approach for determining the lattice of subgroups U < V < G between given subgroups U and G, provided the total number of such subgroups is not too large. It builds on existing functionality for element conjugacy, double cosets and maximal subgroups.