Finite Group Databasebeta

← D₈×C₁₉ #64535

Subgroups — D₈×C₁₉ #64535

Order 304.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₉	C₂	1	2	yes	maximal, complemented
2	C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉	—	2	2	no	—
4	C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₁₉	—	4	2	no	—
6	C₂×C₁₉	D₄	1	1	yes	characteristic
7	C₁₉	D₈	1	1	yes	characteristic, direct product factor, Sylow
8	D₈	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	D₄	C₂×C₁₉	1	2	yes	complemented
10	C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
11	C₂²	—	2	2	no	—
12	C₄	C₂²×C₁₉	1	1	yes	characteristic
13	C₂	—	4	2	no	—
14	C₂	D₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₁₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. D₄×C₁₉	C₂	semidirect
2. C₈×C₁₉	C₂	semidirect
7. C₁₉	D₈	direct (N × H)
8. D₈	C₁₉	direct (N × H)
9. D₄	C₂×C₁₉	semidirect
10. C₈	C₂×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₁₉	2
C₈×C₁₉	2
D₈	19