Half the fandom thinks Gabriel herself is the perfect Audience Surrogate, enjoy the Boke and Tsukkomi Routine between her and Vignette, and thinks she does actually care about her friends in her own way. The other half, however, think she's just a Jerkass with no redeeming qualities and a leech toward other characters such as Vignette or the Angel Coffee owner. Fans who like Satanichia especially don't think too highly of her, since they consider her to be a jerk to Satanichia for no reason.
Raphiel's Troll antics rub some the wrong way, as many don't think she has any deeper dimensions to her character beyond screwing with the others For the Lulz. Others, however, consider her to be a walking Funny Moment, and do think she shows qualities beyond trolling. Just like Gabriel, a lot of her hate comes from the Satanichia fans, as she's Raphiel's most frequent target.
Finally Satanichia. While she might be popular overall, she also has quite a few vocal detractors who are simply tired of her idiocy and complete inability to improve in any way.
Draco in Leather Pants: Far less serious than most, but there's a large section of the fanbase, sometimes referred to as the "Satanichia-Did-Nothing-Wrong Brigade", that paint Satanichia as a pitiful woobie who's constantly bullied and abused by her False Friends. While some of their grievances are justified, she's still a Know-Nothing Know-It-All who brings much of her treatment on herself, plus she's an idiot to the point that she can't take a hint.
Epileptic Trees: Why are the parents of the girls shown so similar to each other outwardly? In particular, the parents of Satanichia differ only in the shade of red hair, and the parents of Vignette have a similar phenotype. Are they relatives? Moreover, we are not shown the parents of Raphiel, but her butler looks like her older sister.
Fandom Rivalry: A minor one with Himouto! Umaru-chan due to both shows having a lazy otaku shut-in as The Protagonist. Umaru fans argue that Gabriel Dropout follows a cliched Four-Girl Ensemble genre that has been done to death while Umaru offers a more unique experience. Gabriel fans cite that Gabriel is a far more likable character than Umaru, stating that Umaru is an awful person and the show tries to pass her annoying behavior off as jokes, as opposed to Gabriel who doesn't pretend to be someone she isn't and is actually a Jerk with a Heart of Gold along with the show offering more versatility through its ensemble cast. Ironically, both anime adaptations were by Studio Doga Kobo and were made by the exact same Production Posse.
Glasses-sensei has been popularly nicknamed "Agent 47" due to his resemblance to the character.
"Kanade Tachibana" for Raphiel, being another highschool angel with silver hair and golden eyes. Rather ironically so, though, due to their vastly different personalities.
Fanon: Everyone in the main cast is gay, no exceptions. Also, some fans have taken a liking to the idea that Vigne always counts Gabriels to go to sleep (although she's only shown to be doing it once). Some fanartists have taken a liking to portray Raphiel as being a fan of BDSM (yes, Satanachia is the passive one). Portraying Vigne and/or Gabriel as covert perverts towards each other is also another popular idea in the fandom (especially fanart).
Fountain of Memes: Satanichia and Raphiel are the most famous characters of this manga among anime fandom because of the former's stupid behavior and the latter' trollish antics.
I'm Satanichia McDowell! Explanation Extremely pompous and theatrical speech of Satanichia from the first episode, with the help of which she was first introduced as a character. Even her pronunciation of her own family name sounds silly.
Poor Satanichia.../Please don't bully Satanichia Explanation Because of Satanichia's popularity among fans of the show, many commentators began to evaluate the scenes with Raphiel as bullying episodes.
Praise the Pantsu!note Gabriel's Teleportation Misfire causing only her panties to get teleported to her classroom desk where they float down in a divine light and all of the boys start praying in thanks to God
Merry Christmas... Merry Christmas! MERRY! CHRISTMAS!!! Explanation During the Christmas Episode, when even Vignette had enough of Satanichia's antics and snaps, she starts shouting this like a Madness Mantra. In context, it's actually pretty chilling rather than funny.
Holy censor barsnote The Gag Censor made from Rays from Heaven that covers Gabriel up whenever she is in a state of undress
In the name of the Dark Lord, Amen.note A particularly liberal translation of "Itadakimasu" in the anime, known around sub circles for being such an outlandish choice and so on the nose (said by Vignette, probably the most angellic character in the series), it wraps around to pure Narm.
I want season 2 for this shipExplanation As there has been so far only one season for the anime, a ton of people wish there was another (partially due to shipping reasons)
A lot of Satanichia's fans, of which there are many, will claim that Raphiel deliberately targets Satanichia and enjoys making her life a living hell, sometimes even going so far as to characterize her as an abuser or someone who gets off on her bullying. However, in canon Raphiel is The Gadfly who simply pranks people to get a few laughs, and Satanichia is only the target of most of said pranks because she's the only one stupid enough to keep falling for them.
The same case could be made for Gabriel, who is often portrayed as being an unapologetic and ungrateful jerk to everyone, and particularly nasty to Satanichia for no reason at all. However, while Gabriel is pretty rude in canon she is usually called out for it, and does have some Pet the Dog moments along the way. Her particular dislike of Satanichia is because she has deliberately tried to fight Gabriel more than once, and continually refuses the latter's occasional nice gestures thanks to a misguided sense of pride.
Unintentionally Sympathetic: Gabriel has this. She is a jerk to Satanichia, but in multiple occasions Satanichia started those fights and she has been shown to threaten Gabriel's life, such as using a gun on her and unleashing a slime beast that put everyone in danger. Gabriel has also shown some Pet the Dog moments towards Satanichia, who just slaps them away.
Ship-to-Ship Combat: There is some between the Gabriel/Vigne shippers and Gabriel/Satania shippers, but it tends to remain mostly peaceful.
The Woobie: If you perceive what is happening around Satanichia too seriously, you can start to consider her a victim of bullying. However, given her behavior, in half the cases this trope will be averted.
Woolseyism: In episode 7, Vignette uses the common Japanese phrase "Itadakimasu!" when she's about to eat. The Crunchyroll subs translate it as "Through the Dark Lord. Amen."