Subgroups — C₂²×C₁₉×C₁₀₉⋊C₃ #38733192

Order 24852.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₁₀₉⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₉×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₁₀₉⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₉×C₁₀₉	C₂×C₃	1	3	yes	complemented
5	C₁₉×C₁₀₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₁₀₉⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₀₉⋊C₃	C₂×C₁₉	1	3	yes	direct product factor
8	C₂²×C₁₀₉	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
9	C₁₀₉⋊C₃	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₃×C₁₉	—	109	1	no	maximal, Hall
11	C₂×C₁₀₉	C₂×C₃×C₁₉	1	3	yes	complemented
12	C₂×C₃×C₁₉	—	109	3	no	—
13	C₁₀₉	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₁₉	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₉	—	109	1	no	Hall
16	C₂×C₁₉	C₂×C₁₀₉⋊C₃	1	3	yes	direct product factor
17	C₁₉	C₂²×C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃	—	109	1	no	Hall
19	C₂×C₃	—	109	3	no	—
20	C₂²	C₁₉×C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	109	1	no	Sylow
22	C₂	C₂×C₁₉×C₁₀₉⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₉	C₁₀₉⋊C₃
commutator, cosocle, hypocenter	C₁₀₉	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₁₉×C₁₀₉	C₃
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₁₉

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.