Subgroups — C₂²×C₁₃×D₁₉ #14520366

Order 1976.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×D₁₉	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₁₃×C₁₉	C₂²	1	3	yes	complemented
4	C₁₃×D₁₉	C₂²	1	4	yes	direct product factor
5	C₁₃×C₁₉	C₂³	1	1	yes	characteristic, complemented, Hall
6	C₂²×D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₁₃	—	19	1	no	maximal, Hall
8	C₂²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
9	C₂×D₁₉	C₂×C₁₃	1	6	yes	direct product factor
10	C₂²×C₁₃	—	19	6	no	—
11	C₂²×C₁₃	D₁₉	1	1	yes	characteristic, direct product factor
12	C₂×C₁₉	C₂²×C₁₃	1	3	yes	complemented
13	D₁₉	C₂²×C₁₃	1	4	yes	direct product factor
14	C₂×C₁₃	—	19	4	no	—
15	C₂×C₁₃	C₂×D₁₉	1	3	yes	direct product factor
16	C₁₉	C₂³×C₁₃	1	1	yes	characteristic, complemented, Sylow
17	C₁₃	C₂²×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂³	—	19	1	no	Sylow
19	C₂²	—	19	6	no	—
20	C₂²	C₁₃×D₁₉	1	1	yes	characteristic, direct product factor
21	C₂	—	19	4	no	—
22	C₂	C₂×C₁₃×D₁₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₃	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂³×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₁₃

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.