Finite Group Databasebeta

← C₂×D₁₉×C₄₂₁ #44544606

Subgroups — C₂×D₁₉×C₄₂₁ #44544606

Order 31996.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₉×C₄₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₁₉×C₄₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₄₂₁	—	19	1	no	maximal, Hall
5	C₂×C₄₂₁	—	19	2	no	—
6	C₂×C₄₂₁	D₁₉	1	1	yes	characteristic, direct product factor
7	C₄₂₁	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×D₁₉	C₄₂₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₉	C₂×C₄₂₁	1	1	yes	characteristic, complemented
10	D₁₉	C₂×C₄₂₁	1	2	yes	direct product factor
11	C₁₉	C₂²×C₄₂₁	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	19	1	no	Sylow
13	C₂	—	19	2	no	—
14	C₂	D₁₉×C₄₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₂₁	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₄₂₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₄₂₁	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₄₂₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×C₄₂₁	C₂	semidirect
2. D₁₉×C₄₂₁	C₂	direct (N × H)
3. C₁₉×C₄₂₁	C₂²	semidirect
6. C₂×C₄₂₁	D₁₉	direct (N × H)
7. C₄₂₁	C₂×D₁₉	direct (N × H)
8. C₂×D₁₉	C₄₂₁	direct (N × H)
9. C₂×C₁₉	C₂×C₄₂₁	semidirect
10. D₁₉	C₂×C₄₂₁	direct (N × H)
11. C₁₉	C₂²×C₄₂₁	semidirect
14. C₂	D₁₉×C₄₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×C₄₂₁	2
D₁₉×C₄₂₁	2
C₂²×C₄₂₁	19
C₂×D₁₉	421