It is hard to know what to call the people who entered the capitol and its grounds without biasing the answer by the selection of terms. I am going to call them "intruders" because I must call them something to make an answer.
If police or other authorized people actually invited the intruders in, then some otherwise possible charges go away, at least for those so invited. But the videos and other news coverage I have seen do not appear to include any such invitation. Some do include police or security shouting at intruders to "stop" or "stay out". Some show intruders breaking doors or windows to gain access, and others coming in through such broken openings. I don't see how anyone who entered in such a way could plausibly argue that s/he was invited in.
Documenting exactly who said and did what during the hours that the intrusion lasted, would be a huge effort. I doubt it will ever be fully accomplished. But it seems clear that many laws were violated by at least some of the intruders, both Federal laws and DC laws.
These might include:
Criminal tresspass
DC Code § 22–3302 Unlawful entry on property. Penalty: fine and up to 6 months imprisonment
DC Code § 22–3211 Theft. Penalty: Up to 10 years, depending on circumstances and value of property. Up to 180 days for 2nd degree. See § 22–3212.
DC code § 22–404 Assault or threatened assault in a menacing manner Penalty: fine and up to 180 days; up to 3 years if "serious bodily injury to another" results (defined as requiring prompt hospital treatment)
DC Code § 22–405.01 Resisting arrest. Penalty: fine and up to 6 months.
[DC code 18 DCMR 2000.2] Failure to obey police officer. Penalty: fine up to $1,000.
DC code § 22–2101 Felony murder, for those who can be proved to have engaged in robbery, housebreaking or any of the other listed felonies (most of which would not apply).
18 U.S. Code § 1752 "Restricted building or grounds" Possible penalty: fine or imprisonment for not more than 10 years for those using or carrying firearms or dangerous weapons, up to 1 year otherwise. Several subsections of this were probably violated by many of the intruders.
18 U.S. Code § 1361 "depredation against any property of the United States". Penalty: Fine plus up to 10 years if value over $1,000, up to 1 year if under $1,000.
18 U.S. Code § 2112 Robbing personal property of the United States. Penalty: up to 15 years. Some intruders were seen in videos carrying off fixtures and property from the capitol.
18 U.S. Code § 930 - Possession of firearms and dangerous weapons in Federal facilities. Penalty: fine and up to 1 year; up to 5 years if there is intent to use the weapon to commit a crime. Some intruders are seen carrying guns.
40 U.S. Code § 5104 Restricts various activities on the Capitol grounds including: "A person may not step or climb on, remove, or in any way injure any statue, seat, wall, fountain, or other erection or architectural feature, or any tree, shrub, plant, or turf, in the Grounds." and "may not carry on or have readily accessible to any individual on the Grounds or in any of the Capitol Buildings a firearm, a dangerous weapon, explosives, or an incendiary device". Also, "may not knowingly, with force and violence, enter or remain on the floor of either House of Congress." also a person may not "parade, stand, or move in processions or assemblages in the Grounds; or display in the Grounds a flag, banner, or device designed or adapted to bring into public notice a party, organization, or movement." without authorization.
18 U.S. Code § 231 A person who transports a firearm for use in a civil disorder, or obstructs a law enforcement officer in the course of a civil disorder. Penalty: Fine and up to five years.
18 U.S. Code § 2384 - Seditious conspiracy. Discussed at length in the lawfare blog article Penalty: fine and up to 20 years.
Which, if any, of the above laws might actually be charged against one or another intruder there is no way to know yet, and there way well be other provisions which would apply that I have not thought of or found.