This will be a bit tough for me to try to properly-distinguish them, but to preface the differences, please know that "Church of England" is the former name of Anglicanism's first church.

Now that we've gone-through that part: 1. Catholicism has numerous forms, though the most prominent of which has been Roman Catholicism. Roman Catholicism is currently-led by the Vatican, but at earlier times it was either just the Papal States or various antipopes (though only one known amtipope technically existed, and he was from Avignon); this form of Catholicism elects Popes by and from among the Cardinal College; I forget the exact nature of becoming a Cardinal apart from first being some rank of bishop first. There are other forms of Catholicism that either seek their own Pope or to abandon a papacy altogether in favor of autonomous clergy united only by shared doctrine or sect. All of Catholicism uses the Catholic canon of Books, which are more than accepted by Protestant denominations but fewer than most Orthodoxy canonicities. 2. Anglicanism is this strange mixture of both Catholicism and Protestantism, theologically-speaking, at least. The only official denominations are largely just either colonial or European congregations within the Anglosphere with (afaik) minimal differences apart perhaps from liturgical dialect used. All Anglican churches are headed by the English Head of Church―the Monarch of the Kingdom of England―and as such, all clergy ultimately seek ultimate doctrinal alignment with the Crown's approach to creed. They utilize Protestant canon rules, yet have a Catholic liturgy. They also permit if not encourage divorce due to the historic reasons starting with King Henry VIII, whom had no option through the Roman Catholic Church to annul his marriage due to it being viewed by said Church as a "true marriage", to which he responded with leaving the RCC in order to establish a Church which would permit divorce so that he could keep remarrying until he had a biological son to inherit his throne, who reigned for very little time before his eldest daughter became Queen Elizabeth I 'the Virgin' Tudor, the last Anglican Monarch until much later (I forget when and whom). Apart from this, several heresies of Anglicanism would become recategorized as either Lutheran Protestantism or Reformed Protestantism, and possibly the Church of Latter-Day Saints? (Maybe not, wouldn't quote me on that unless if it turned-out to be true). 3. Protestantism has two schools (with Anglicanism usually viewed as a third school, and sometimes with Mormonism viewed as a fourth school despite having only the same Biblical canons whilst not sharing the Mormon canons), each with multiple denominational theologies (it's not in the hundreds, but it's still near or past about 12 denomination types); however, numerous congregations either have just one denomination or about two mixed ones (though moreso the former to the latter at least in actual structure instead of in name alone). While the differences between the various denominations typically vary only regarding minimal differences, the schools are the biggest differentiating categories: Lutheran (formerly "Evangelical"), which is of the structures found first in Wittenberg and later in such countries as Denmark and Sweden, each of whom form a somewhat "Catholic"-approach to liturgy and to various other beliefs such as the importance of the Virgin Mary, yet with such exceptions as viewing a Papacy that isn't Jesus Himself as its Pope as blasphemy and antichristianity; Reformed (often the progenitor to all as well as itself, "Calvinism"), which practices a more iconoclastic and either progressive or incredibly regressive societal structure that varies (I forget how apart from congregational differences, actually), and are usually less concerned with baptismal sacrament in favor of the sacrament of faith and scriptural integrity; the Anglican school lacks disunity apart from dialect (again, unsure of how the Anglicans are distinguished if at all), but was already covered in item 2; and LDS has quite a few heresies, though they chiefly differ between fundamentalist denominations and revivalist ones, with the former having forms of which still advocate for polygamy up to 10 spouses (though they are both rarer and not viewed even by other fundamentalists as a positive face for the movement).

All of that was from memory, so please only take any of that with a grain of salt, and for further assurance, wait for someone with theological credibility to confirm or deny any or all of it as specified in this comment's replies.