Augury
Augury is perceiving signs and tells. If Augury is Basic, mages will be a hyper-aware bunch. Expertise might look like Holmes-ian deduction or prophecy. This subject might allow for perceiving supernatural influences as appropriate.
Arcanomechanics
This subject allows for machines that run on magic and machines that manipulate magic. It might look futuristic or steampunk, depending on your preferences. Glowing crystals optional. If this subject is Basic, your society is likely industrialized in a magic way.
Biokinesis
This subject is about healing, strengthening and weakening the body. Advanced uses might include the creation of hybrids and chimeras. If Biokinesis is Basic, mages likely make a point of honing their bodies and are unusually long-lived.
Cantrips
Cantrips are everyday useful magic, like making light, cleaning things, animating a knife to chop the vegetables, stopping things from falling or throwing stuff around. It might include simple healing spells, if not provided by other subjects.
Combat Magic
Depending on your setting, this subject might include some of the following it your own making:
Basic offensive and defensive spells, if other subjects don't provide them.
Use of magely weapons and dueling.
Fighting certain foes or monsters.
Field tactics or artillery spells.
If your world is very combative, you might choose several elements as single subjects.
Divination
This subjects teaches information gathering with certain magic tools. Determine the kinds of tools and results for your world, e.g.:
Tarot cards and tea leaves for vague metaphors.
Various instruments for arcane measurements.
Laptops for looking at faraway places.
Elements
Choose whether there is a fixed list of magic elements or anything goes. Mages will have affinities for one, sometimes a few elements. They can bend, move and maybe create their elements. If Elements are Basic other magic will likely have elemental associations.
Enchanting
This subject enchants objects with magic. It might require inscribing runes, special materials or procedures. The most basic trick is making a thing better at what it usually does, but flying carpets are a classic. If Enchanting is Basic, other magic likely requires implements.
Faith
This subject, though believers likely wouldn't call it that, relies on certain higher entities for certain protective and restorative effects. If Faith is Basic, your mages are clergy.
Gating
This subject teaches teleports, portals, extra-dimensional spaces and similar craziness. Low level uses might include bags that are bigger on the inside or farsight. If Gating is Basic, mage society is likely delocalized.
Illusions
This subject might be about flamboyant circus tricks or hiding in shadows depending on the outlook of your mages. It might extend to manipulating memories, entering dreams or similar effects. If Illusions are Basic, mages might philosophize a lot about reality and perceptions.
Mentalism
This subject may provide any or all of the following: Perfect recollection, fast learning, commanding the weak of mind, mental communication.
Necromancy
This subject might include any or all of the following: Talking to the spirits of the dead, channeling the ancestors, creating zombies, manipulating souls, bringing the dead back to life, healing injuries and illness, firing negative energy or poison.
Potions
Imbibing or smearing a thing with a magic elixir can provide various transformative and magic effects for a little while. Determine what a typical mage uses in terms of tools and ingredients. If Potions is Basic other magic will likely require consumables.
Raw Magic
Formless, raw or unstructured magic is either less efficient or harder to control than other magic, and therefore probably requires lots of training and meditation. It allows for sensing and dispelling other magic and is harder to counter itself. Powerful uses might allow for supercharging other spells.
Shifting
Shifting is the art of taking on another form. If Shifting is Basic, a mage likely only has a single alternate form or series of forms. Advanced usage is more flexible. Shifters likely heal faster and can use abilities of their alternate forms without transformation, like having a dog's sense of smell in human form.
Spellforms
This subject teaches the theory behind structured magic. It might be helpful in devising or adapting new spells, understanding foreign magic systems, or programming spells with triggers and conditions. If Spellforms is Basic, other magic likely has linguistic or mathematical elements.
*ology
There is at least one kind of supernatural creature in the world, like angels, spirits, demons, fairies, or cryptids. This subject teaches their kinds and rules, and ways to guard against them. It might include their language, making contracts, taming them, or using their body parts as appropriate.