Subgroups — C₅₃×#67063 #34038249

Order 18868.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₅₃×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#67063	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₅₃	—	89	1	no	maximal, Hall
5	D₈₉	C₂×C₅₃	1	1	yes	characteristic
6	C₂×C₅₃	—	89	1	no	—
7	C₈₉	C₄×C₅₃	1	1	yes	characteristic, complemented, Sylow
8	C₅₃	#67063	1	1	yes	characteristic, direct product factor, Sylow
9	C₄	—	89	1	no	Sylow
10	C₂	—	89	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.