Saying Yishtabach immediately after Az Yashir:
One is to recite Yishtabach immediately after Az Yashir, without making any interval in-between. This applies even on Shabbos and Yom Tov. Thus, in the event that the Chazan is not yet up to Yishtabach, as commonly occurs on Shabbos and Yom Tov in which the Chazan recites from Shochan Ad with Chazanus, the individual is not to wait for the Chazan, and is to recite Yishtabach right away [if he has already reached the paragraph of Yishtabach].
Waiting for a Minyan: In the event that a Minyan is not yet available, and one must wait until the arrival of the tenth man, the individuals are not to wait prior to Yistabach but are rather to recite Yishtabach and then wait for the Minyan to arrive. This however is with exception to the Chazan as will be explained next.
The Chazan: In the event that a Minyan is not yet available, the Chazan is to wait between Az Yashir and Yishtabach until the arrival of the tenth man. He is to wait silently, without saying anything, until the tenth man arrives, upon which he is to say Yishtabach and Kaddish. The Chazan may wait [between Az Yashir and Yishtabach] even for a period of thirty minutes which is the amount of time it takes to complete the entire Pesukei Dezimra, from Baruch Sheamar until the end of Yishtabach.
 M”A 53/4; M”B 53/9; Aruch Hashulchan 53/4; Ketzos Hashulchan 18/10; Darkei Chaim Veshalom 131
 The reason: Seemingly this is because Yishtabach is the after blessing of Pesukei Dezimra and it hence must be approximated to the Psalms of Pesukei Dezimra. Alternatively, this is based on Kabbala and is done in order to unify Hashems name of Shakaiy. [See Shalmei Tzibur]
 However prior to reaching Yishtabach, such as by Shochen Ad, one may wait for the Chazan, and so is the custom.
 Aruch Hashulchan ibid
 Ketzos Hashulchan ibid
 Admur 53/3; Rama 53/3; M”A 53/5; Maharil Tefila 7
 Admur ibid; M”A ibid; Maharam Mintz 8
 Admur ibid