Subgroups — C₁₉⋊D₅₅₁ #35230239

Order 20938.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₅₁	—	19	20	no	maximal
3	C₁₉⋊D₁₉	—	29	1	no	maximal, Hall
4	C₁₉×C₂₉	D₁₉	1	20	yes	complemented
5	C₁₉²	D₂₉	1	1	yes	characteristic, complemented, Sylow
6	D₂₉	—	361	1	no	Hall
7	D₁₉	—	551	20	no	—
8	C₂₉	C₁₉⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
9	C₁₉	D₅₅₁	1	20	yes	complemented
10	C₂	—	10469	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉²×C₂₉	C₂
LCS	G ▷ C₁₉²×C₂₉
UCS	C₁

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.