We analyse complementary Hubble Space Telescope and Subaru data for the globular cluster NGC 2419. We make a detailed analysis of the horizontal branch (HB), which is composed of two main groups of stars: the luminous blue HB stars, which extend by evolution into the RR Lyrae and red HB region, and a fainter, extremely blue population. We examine the possible models for the latter group and conclude that a plausible explanation is that they correspond to a significant (˜30 per cent) extreme second generation with a strong helium enhancement (Y˜ 0.4). We also show that the colour dispersion of the red giant branch is consistent with this hypothesis, while the main-sequence data are compatible with it, although the large observational error blurs the possible underlying splitting. While it is common to find an even larger (50-80) percentage of second generation in a globular cluster, the presence of a substantial and extreme fraction of these stars in NGC 2419 might be surprising, as the cluster is at present well inside the radius beyond which the Galactic tidal field would be dominant. If a similar situation had been present in the first stages of the cluster life, then the cluster would have retained its initial mass and the percentage of second-generation stars would have been quite small (up to ˜10 per cent). Such a large fraction of extreme second-generation stars implies that the system must have been initially much more massive and in different dynamical conditions from what it is today. We discuss this issue in the light of existing models of the formation of multiple populations in globular clusters.