Finite Group Databasebeta

← C₂×C₅×D₁₉ #67416

Subgroups — C₂×C₅×D₁₉ #67416

Order 380.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₅×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₉	C₂×C₅	1	2	yes	direct product factor
7	C₂²×C₅	—	19	1	no	maximal, Hall
8	C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₅	—	19	2	no	—
10	C₂×C₅	D₁₉	1	1	yes	characteristic, direct product factor
11	C₅	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²	—	19	1	no	Sylow
13	C₂	—	19	2	no	—
14	C₂	C₅×D₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₉	C₂	semidirect
2. C₅×D₁₉	C₂	direct (N × H)
3. C₅×C₁₉	C₂²	semidirect
4. C₂×D₁₉	C₅	direct (N × H)
5. C₂×C₁₉	C₂×C₅	semidirect
6. D₁₉	C₂×C₅	direct (N × H)
8. C₁₉	C₂²×C₅	semidirect
10. C₂×C₅	D₁₉	direct (N × H)
11. C₅	C₂×D₁₉	direct (N × H)
14. C₂	C₅×D₁₉	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×C₅×C₁₉	2
C₅×D₁₉	2
C₂×D₁₉	5
C₂²×C₅	19