Finite Group Databasebeta

← C₁₉×D₇₁⋊C₇ #34038523

Subgroups — C₁₉×D₇₁⋊C₇ #34038523

Order 18886.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₇₁⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₇₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
4	D₇₁⋊C₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇₁⋊C₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₁₉	—	71	1	no	maximal, Hall
7	D₇₁	C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₉	—	71	1	no	Hall
9	C₇₁	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₉	—	71	1	no	Hall
11	C₁₉	D₇₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇	—	71	1	no	Hall
13	C₇	—	71	1	no	Sylow
14	C₂	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₇₁⋊C₇
commutator, cosocle, hypocenter	C₇₁	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₇₁	C₂×C₇
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₇₁⋊C₇	C₂	semidirect
2. C₁₉×D₇₁	C₇	semidirect
3. C₁₉×C₇₁	C₂×C₇	semidirect
4. D₇₁⋊C₇	C₁₉	direct (N × H)
5. C₇₁⋊C₇	C₂×C₁₉	semidirect
7. D₇₁	C₇×C₁₉	semidirect
9. C₇₁	C₂×C₇×C₁₉	semidirect
11. C₁₉	D₇₁⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×C₇₁⋊C₇	2
C₁₉×D₇₁	7
D₇₁⋊C₇	19
C₂×C₇×C₁₉	71