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A satellite galaxy is a small galaxy, often a dwarf galaxy, orbiting a larger galaxy. Most of the galaxies of the Local Group are satellites of the Milky Way or Andromeda (M31). Some of the 80 or so known satellites of the Milky Way:
Among Andromeda's satellites:
The exact number of satellite galaxies of the Milky Way and Andromeda are unclear as they are still being discovered, there is often discussion as to whether something constitutes a galaxy versus a globular cluster, and knowing whether it is orbiting depends upon its velocity, and such velocity-determination is non-trivial and undergoes corrections over time. Satellites in the Local Group are still being discovered and dwarf galaxies are often even more challenging to identify in more distant groups and clusters.
The term galaxy subgroup (e.g., a subset of a galaxy group) can be used to designate a galaxy plus its satellites, e.g., the Milky Way subgroup. The term hypergalaxy (a term which I suspect is rarely used) refers to a galaxy group consisting of a major spiral galaxy and its satellites.