Finite Group Databasebeta

← C₂×C₁₉×D₂₁₁ #30630980

Subgroups — C₂×C₁₉×D₂₁₁ #30630980

Order 16036.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₂₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₁₉×C₂₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₂₁₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₁₁	C₂×C₁₉	1	1	yes	characteristic, complemented
6	D₂₁₁	C₂×C₁₉	1	2	yes	direct product factor
7	C₂₁₁	C₂²×C₁₉	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₁₉	—	211	1	no	maximal, Hall
9	C₂×C₁₉	—	211	2	no	—
10	C₂×C₁₉	D₂₁₁	1	1	yes	characteristic, direct product factor
11	C₁₉	C₂×D₂₁₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²	—	211	1	no	Sylow
13	C₂	—	211	2	no	—
14	C₂	C₁₉×D₂₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₂₁₁
commutator, cosocle, hypocenter	C₂₁₁	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₂₁₁	C₂
LCS	G ▷ C₂₁₁
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×C₂₁₁	C₂	semidirect
2. C₁₉×D₂₁₁	C₂	direct (N × H)
3. C₁₉×C₂₁₁	C₂²	semidirect
4. C₂×D₂₁₁	C₁₉	direct (N × H)
5. C₂×C₂₁₁	C₂×C₁₉	semidirect
6. D₂₁₁	C₂×C₁₉	direct (N × H)
7. C₂₁₁	C₂²×C₁₉	semidirect
10. C₂×C₁₉	D₂₁₁	direct (N × H)
11. C₁₉	C₂×D₂₁₁	direct (N × H)
14. C₂	C₁₉×D₂₁₁	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×C₂₁₁	2
C₁₉×D₂₁₁	2
C₂×D₂₁₁	19
C₂²×C₁₉	211