Here's the current situation regarding the Local Group. As of early 2019, the Local Group had more than 100 known members.
The following galaxies ARE members of the Local Group:
Sagittarius Dwarf Spheroidal (discovered in 1994; a satellite galaxy of the Milky Way)
Sagittarius Dwarf Irregular Galaxy (NOT a satellite of any galaxy)
Leo I (discovered in 1950; a satellite galaxy of the Milky Way)
Leo II (discovered in 1950; a satellite galaxy of the Milky Way)
Leo A (NOT a satellite of any galaxy)
Sextans Dwarf Spheroidal (discovered on February 8, 1990; a satellite galaxy of the Milky Way)
The following galaxies are NOT members of the Local Group but instead belong to the NGC 3109 Association:
Sextans A
Sextans B
Leo P (discovered in 2012)
References:
Magnificent Universe by Ken Croswell, pages 190-191.
"The Faintest Dwarf Galaxies" by Joshua Simon, Annual Reviews, 2019, in press. Table 1 lists 54 of the 57 known satellite galaxies of the Milky Way (it omits the two most massive, the Large and Small Magellanic Clouds, and also the most recent discovery, Antlia 2).
"The Observed Properties of Dwarf Galaxies in and Around the Local Group" by Alan McConnachie, The Astronomical Journal, 144, 4 (2012). Table 1 gives the boundary between Local Group members and those beyond.
Sky and Telescope, October 2018, cover story.
The Alchemy of the Heavens by Ken Croswell. Pages vii-ix tell the story of the discovery of the Sextans dwarf that orbits the Milky Way.