Subgroups — C₅×#19096457 #37566708

Order 24345.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₅₄₁	C₃	1	1	yes	maximal, characteristic
2	#19096457	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₅₄₁	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅₄₁	C₃×C₅	1	1	yes	characteristic
5	C₅₄₁	C₅×C₉	1	1	yes	characteristic, complemented, Sylow
6	C₅×C₉	—	541	1	no	maximal, Hall
7	C₃×C₅	C₅₄₁⋊C₃	1	1	yes	characteristic
8	C₉	—	541	1	no	Sylow
9	C₅	#19096457	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₅×C₅₄₁⋊C₃	1	1	yes	characteristic

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.