Subgroups — C₂²×D₁₉ #3894

Order 152.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₉	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₁₉	C₂²	1	3	yes	complemented
4	D₁₉	C₂²	1	4	yes	direct product factor
5	C₁₉	C₂³	1	1	yes	characteristic, complemented, Sylow
6	C₂³	—	19	1	no	maximal, Sylow
7	C₂²	—	19	6	no	—
8	C₂²	D₁₉	1	1	yes	characteristic, direct product factor
9	C₂	—	19	4	no	—
10	C₂	C₂×D₁₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²

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

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