Subgroups — C₁₉⋊#11927413 #37550813

Order 23180.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₃₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉⋊#6923	—	5	1	no	maximal, Hall
4	C₁₉×D₆₁	—	5	1	no	—
5	#11927413	—	19	1	no	maximal, Hall
6	C₁₉×C₆₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₃₀₅	D₁₉	1	1	yes	characteristic
8	C₁₉⋊AGL(1,𝔽₅)	—	61	1	no	maximal, Hall
9	C₅×C₆₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	#6923	—	95	1	no	Hall
11	D₅×C₁₉	—	61	1	no	—
12	D₆₁	—	5	1	no	—
13	C₅×C₁₉	#6923	1	1	yes	characteristic, complemented, Hall
14	Dic₁₉	—	305	1	no	Hall
15	C₆₁	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	—	305	1	no	—
17	AGL(1,𝔽₅)	—	1159	1	no	Hall
18	C₁₉	#11927413	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	61	1	no	—
20	C₅	C₁₉⋊#6923	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5795	1	no	Sylow
22	C₂	—	305	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉×C₆₁	C₄
prime radical, cosocle	C₁₉×D₃₀₅	C₂
LCS	G ▷ C₅×C₁₉×C₆₁
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.