There are 5 major classifications of Fungi.
1. Chytridsm: “They produce gametes and diploid zoospores that swim with the help of a single flagellum. Its reproductive cycle includes both asexual and sexual phases”
2. Zygomycota: “Sexual reproduction starts when conditions become unfavorable. Two opposing mating strains (type + and type –) must be in close proximity for gametangia from the hyphae to be produced and fuse, leading to karyogamy. ”
3. Ascomycota: “Sexual reproduction starts with the development of special hyphae from either one of two types of mating strains (Figure).”
4. Basidiomycota: “ The basidia, which are the reproductive organs of these fungi, are often contained within the familiar mushroom, commonly seen in fields after rain, on the supermarket shelves, and growing on your lawn (Figure 6).”
5. Deuteromycota: “ do not display a sexual phase—Since they do not possess the sexual structures that are used to classify other fungi, they are less well described in comparison to other divisions.”
This source was really helpful, if you need more info. :
https://courses.lumenlearning.com/biology2xmaster/chapter/classification-of-fungi/
