Subgroups — C₃×#27159096 #49152167

Order 37278.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#20261879	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#27159096	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₉×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
5	#20261879	C₂×C₃	1	3	yes	complemented
6	D₁₉×C₁₀₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₁₉×C₁₀₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₁₀₉⋊C₃	—	19	1	no	maximal, Hall
9	C₃×C₁₀₉⋊C₃	—	19	1	no	Hall
10	C₂×C₃×C₁₀₉	—	19	1	no	—
11	C₂×C₁₀₉⋊C₃	—	19	3	no	—
12	C₃×D₁₉⋊C₃	—	109	1	no	maximal, Hall
13	C₃×C₁₀₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
14	C₁₀₉⋊C₃	—	19	3	no	—
15	C₂×C₁₀₉	—	19	1	no	Hall
16	C₃×C₁₉⋊C₃	—	109	1	no	Hall
17	C₃×D₁₉	C₁₀₉⋊C₃	1	1	yes	characteristic, complemented
18	D₁₉⋊C₃	—	109	3	no	—
19	C₁₀₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₁₉	C₂×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented
21	C₁₉⋊C₃	—	109	3	no	—
22	D₁₉	C₃×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₁₉	C₂×C₃×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²	—	2071	1	no	Hall
25	C₃²	—	2071	1	no	Sylow
26	C₂×C₃	—	19	1	no	—
27	C₂×C₃	—	2071	3	no	—
28	C₃	—	2071	3	no	—
29	C₃	#27159096	1	1	yes	characteristic, direct product factor
30	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#27159096
commutator, cosocle, hypocenter	C₁₉×C₁₀₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₀₉	C₂×C₃
LCS	G ▷ C₁₉×C₁₀₉
UCS	C₁ ◁ C₃

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.