Is an allegation in an accusatory pleading necessarily included in a lesser crime?

"[A]n offense expressly alleged in an accusatory pleading may necessarily include one or more lesser offenses." (People v. Birks (1998) 19 Cal.4th 108, 117.) "A defendant may be convicted of an uncharged crime if, but only if, the uncharged crime is necessarily included in the charged crime. [Citations.] The reason for this rule is settled. ' "This reasoning rests upon a constitutional basis: 'Due process of law requires that an accused be advised of the charges against him in order that he may have a reasonable opportunity to prepare and present his defense and not be taken by surprise by evidence offered at his trial.' [Citation.]" ' [Citation.] The required notice is provided as to any charged offense and any lesser offense that is necessarily committed when the charged offense is committed. [Citation.]" (People v. Reed (2006) 38 Cal.4th 1224, 1227.)

The trial court has a sua sponte duty to instruct on lesser included offenses when the evidence raises a question whether all of the elements of the charged offense were present. (People v. Breverman (1998) 19 Cal.4th 142, 154, 162; People v. Eid (2014) 59 Cal.4th 650, 656.) "[A] lesser offense is necessarily included in a greater offense if either the statutory elements of the greater offense, or the facts actually alleged in the accusatory pleading, include all the elements of the lesser offense, such that the greater cannot be committed without also committing the lesser. [Citations.]" (People v. Birks, supra, 19 Cal.4th at pp. 117-118, fn. omitted.)