Finite Group Databasebeta

← C₁₉×D₄₂₇ #30633997

Subgroups — C₁₉×D₄₂₇ #30633997

Order 16226.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₆₁	—	7	1	no	maximal, Hall
3	C₁₉×C₆₁	D₇	1	1	yes	characteristic, complemented, Hall
4	D₄₂₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₆₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	D₇×C₁₉	—	61	1	no	maximal, Hall
7	C₇×C₁₉	D₆₁	1	1	yes	characteristic, complemented, Hall
8	D₆₁	—	7	1	no	Hall
9	C₆₁	D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₉	—	427	1	no	Hall
11	C₁₉	D₄₂₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₇	—	61	1	no	Hall
13	C₇	C₁₉×D₆₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	427	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₄₂₇
commutator, cosocle, hypocenter	C₇×C₆₁	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₆₁	C₂
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₆₁	C₂	semidirect
3. C₁₉×C₆₁	D₇	semidirect
4. D₄₂₇	C₁₉	direct (N × H)
5. C₇×C₆₁	C₂×C₁₉	semidirect
7. C₇×C₁₉	D₆₁	semidirect
9. C₆₁	D₇×C₁₉	semidirect
11. C₁₉	D₄₂₇	direct (N × H)
13. C₇	C₁₉×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₉×C₆₁	2
C₁₉×D₆₁	7
D₄₂₇	19
D₇×C₁₉	61