What is permissible for the Imam to do during the prayer

It was narrated that Abu Qatadah said:

"I saw the Messenger of Allah ﷺleading the people in prayer, carrying Umamah bint Abi Al-As on his shoulder. When he bowed he put her down and when he stood up from prostration he picked her up again."

أَخْبَرَنَا قُتَيْبَةُ، قَالَ حَدَّثَنَا سُفْيَانُ، عَنْ عُثْمَانَ بْنِ أَبِي سُلَيْمَانَ، عَنْ عَامِرِ بْنِ عَبْدِ اللَّهِ بْنِ الزُّبَيْرِ، عَنْ عَمْرِو بْنِ سُلَيْمٍ الزُّرَقِيِّ، عَنْ أَبِي قَتَادَةَ، قَالَ رَأَيْتُ رَسُولَ اللَّهِ ﷺ يَؤُمُّ النَّاسَ وَهُوَ حَامِلٌ أُمَامَةَ بِنْتَ أَبِي الْعَاصِ عَلَى عَاتِقِهِ فَإِذَا رَكَعَ وَضَعَهَا وَإِذَا رَفَعَ مِنْ سُجُودِهِ أَعَادَهَا .