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tokens: In this paper, we have used the E-MOSAICS simulations to quantify the stellar masses and accretion redshifts of five satellite galaxies that have been accreted by the Milky Way, as well as several other of their properties. These satellites are Kraken (previously referred to as the progenitor of the ‘low-energy GCs’ by Massari et al. 2019 ), Gaia -Enceladus, the progenitor of the Helmi streams, Sequoia, and Sagittarius. They likely represent the most massive objects that the Milky Way accreted since z = 4. We predict their properties by training an artificial neural network on the E-MOSAICS simulations, which follow the co-formation and co-evolution of galaxies and their GC populations. This network relates the ages, metallicities, and orbital properties of a group of GCs that formed in a common satellite progenitor to the properties of that progenitor. The conclusions of this work are as follows: The neural network is capable of predicting the stellar masses and accretion redshifts of the satellite progenitors to high precision, with a validation score of and a scatter of and around the true values, respectively. Omitting the GC age–metallicity information leads to considerably worse constraints on both quantities. Additionally, the accretion redshifts strongly rely on the GC orbital information (Fig. 1 ). Modulo a small number of changes, we adopt the proposed GC membership of the satellite progenitors from Massari et al. ( 2019 , see our Table 1 ). The five groups of GCs associated with the different satellite progenitors show clear differences in apocentre–eccentricity space and age–metallicity space. By comparing the orbital properties of GCs to those of fossil streams from Bonaca Kruijssen ( 2020 ), we find that the streams have similar orbital properties as the GCs associated with Kraken, Gaia -Enceladus, the progenitor of the Helmi streams, and Sagittarius. The Fimbulthul stream falls in between the orbital properties spanned by the GCs associated with Kraken and Gaia -Enceladus, suggesting that it may be the relic of a GC that formed in either of these two satellites. In age–metallicity space, the Kraken GCs have the highest metallicities at a given age, closely followed by the Gaia -Enceladus GCs, suggesting that these two galaxies were the most massive at any moment in time, with Kraken having a slightly higher mass (Figs 2 and 3 ). By applying the neural network to the Galactic GCs associated with the five satellite progenitors, we find that the satellites span a relatively narrow stellar mass range at the time of accretion, of M ⋆ = (0.6–4.6) × 10 8 M ⊙ . The top end of this range is occupied by Kraken, Gaia -Enceladus, and Sagittarius, with the latter two being the most massive. This differs from the stellar masses at any given moment in time, because the accretion redshifts of these satellites differ. By accreting later, Sagittarius was able to attain a higher mass, despite initially being considerably less massive than