Subgroups — C₁₃²×D₁₉⋊C₃ #34064191

Order 19266.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₉⋊C₃	C₁₃	1	14	yes	maximal, direct product factor
5	C₂×C₃×C₁₃²	—	19	1	no	maximal, Hall
6	C₁₃×C₁₉⋊C₃	C₂×C₁₃	1	14	yes	complemented
7	C₃×C₁₃²	—	19	1	no	Hall
8	C₁₃×D₁₉	C₃×C₁₃	1	14	yes	complemented
9	C₂×C₁₃²	—	19	1	no	Hall
10	C₁₃×C₁₉	C₂×C₃×C₁₃	1	14	yes	complemented
11	C₁₃²	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₁₉⋊C₃	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₃	—	19	14	no	—
14	C₁₉⋊C₃	C₂×C₁₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₃	—	19	14	no	—
16	D₁₉	C₃×C₁₃²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃	—	19	14	no	—
18	C₁₉	C₂×C₃×C₁₃²	1	1	yes	characteristic, complemented, Sylow
19	C₁₃	C₁₃×D₁₉⋊C₃	1	14	yes	direct product factor
20	C₂×C₃	—	19	1	no	Hall
21	C₃	—	19	1	no	Sylow
22	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃²	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃×C₁₃²
Frattini	C₁	G
Fitting, socle	C₁₃²×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₁₃²

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.