Finite Group Databasebeta

← C₁₉⋊(C₁₉⋊#595) #37589484

Subgroups — C₁₉⋊(C₁₉⋊#595) #37589484

Order 24548.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉²×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₉²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉⋊Dic₁₉	—	17	1	no	maximal, Hall
4	C₁₉⋊#595	—	19	20	no	maximal
5	C₂×C₁₉²	—	17	1	no	—
6	C₁₉×D₁₇	D₁₉	1	20	yes	—
7	C₁₉²	#595	1	1	yes	characteristic, complemented, Sylow
8	C₁₇×C₁₉	Dic₁₉	1	20	yes	complemented
9	Dic₁₉	—	323	20	no	—
10	#595	—	361	1	no	Hall
11	C₂×C₁₉	—	17	20	no	—
12	D₁₇	C₁₉⋊D₁₉	1	1	yes	characteristic
13	C₁₉	C₁₉⋊#595	1	20	yes	complemented
14	C₁₇	C₁₉⋊Dic₁₉	1	1	yes	characteristic, complemented, Sylow
15	C₄	—	6137	1	no	Sylow
16	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇×C₁₉²	C₄
prime radical, cosocle	C₁₉²×D₁₇	C₂
LCS	G ▷ C₁₇×C₁₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₇×C₁₉²	C₄	semidirect
7. C₁₉²	#595	semidirect
8. C₁₇×C₁₉	Dic₁₉	semidirect
13. C₁₉	C₁₉⋊#595	semidirect
14. C₁₇	C₁₉⋊Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉²×D₁₇	2
C₁₉⋊Dic₁₉	17
C₁₉⋊#595	19