Fifteen, huh?
The ones I know of are:
Normal
Fire
Water
Grass
Electric
Ice
Rock
Ground
Poison
Bug
Flying
Fighting
Ghost
Dark
Psychic
Steel
Dragon
Fairy
Then there's also Stellar for Terapagos' Tera type, Which isn't really a type and only adds one offensive property to a pokemon's regular typing.
and the Legend plate which technically does all of them but only one at a time, and only works with the Multitype ability
If I had to guess, You'd be missing Steel, Dark, and Fairy.
//Which are the three types introduced in gen 2 (steel, dark) and 6 (fairy)
Sara was impressed to hear what the other pokemon had to say. Clearly they were knowledgeable, even in information that they didn’t know. “Eeehhh, close. Orpheus, the Lord of Shadows, is still very much with us. Not that I’ve ever seen him but…”
“Sara.” Odysseus’ tail was thrown down between the two. He turned to her, his voice a hushed growl. “Stop talking about that. You know we’re not supposed to talk about that.” Whatever playfulness that was there prior was now gone from Odysseus’ eyes, only a stern glare remained. His voice dropped even lower, to a whisper that was only heard between them, as he spoke further with her.
Sara decided not to comment any further.