Subgroups — #49152103

Order 37278.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32916115	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₉×C₁₀₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₉×C₁₀₉	C₂×C₃	1	1	yes	characteristic
4	D₁₉×C₁₀₉	C₉	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₁₀₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₂×#11758279	—	19	1	no	maximal, Hall
7	#11758279	—	19	1	no	Hall
8	C₂×C₃×C₁₀₉	—	19	1	no	—
9	#4294⋊C₂	—	109	1	no	maximal, Hall
10	C₃×C₁₀₉	D₁₉⋊C₃	1	1	yes	characteristic
11	C₂×C₁₀₉	—	19	1	no	Hall
12	#4294	—	109	1	no	Hall
13	C₃×D₁₉	C₁₀₉⋊C₃	1	1	yes	characteristic
14	C₁₀₉	#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₉	C₂×C₁₀₉⋊C₃	1	1	yes	characteristic
16	D₁₉	#11758279	1	1	yes	characteristic, complemented, Hall
17	C₁₉	C₂×#11758279	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	2071	1	no	Hall
19	C₉	—	2071	1	no	Sylow
20	C₂×C₃	—	19	1	no	—
21	C₃	#27159095	1	1	yes	characteristic
22	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#27159095
commutator, hypocenter	C₁₉×C₁₀₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₉×C₁₀₉	C₂×C₃
prime radical	C₃×D₁₉×C₁₀₉	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.