>>1133451These are (H5...H9) are suburban trains, operated by the state railways (MÁV). There are much more lines like those, but the others start from the main railway stations, while these five lines are also a bit more integrated in BKK (schedules are not edited by MÁV, but by BKK), and have their own starting points.
This somehow fucked up system is caused by a bit difficult status: these lines were created and owned by a whole different company (BHÉV) since more than a hundred years ago, and only from this year, and for a short time eariler (from 1951 until 1958) were operated by MÁV. Except that part, until 1968 these were BHÉV lines, in 1968, BHÉV merged into BKV (so the system became a part of BKV, although this was a train system), from 2013(?) the whole BKV operation came under the supervisin of the newly created BKK, and in 2016, BKK/BKV gave the system to MÁV.