Minor planets in comet-like orbits similar to HTCs that never come close enough to the Sun to outgas are called centaurs.
HTCs are named after the first discovered member, and the first discovered periodic comet, Halley's Comet, which orbits the Sun in about 75 years, and passing as far as the orbit of Neptune.
Most of the comets that have a period between 20 and 200 years (making them HTCs based on the classical definition) are actually officially classified as either Jupiter-family comets (JFCs) or Chiron-type comets (CTCs), based on their Jupiter Tisserand's parameter (TJupiter).
CTCs, on the other hand, are officially defined by (TJupiter > 3; a > aJupiter).
This list contains only Halley-type comets which are not numbered yet because they have been observed only once.