Subgroups — (C₁₉⋊C₃)⋊#10587739 #44530326

Order 31236.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×D₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#10587739	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉⋊C₃×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×D₁₃₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₁₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#10587739	—	19	1	no	maximal, Hall
7	C₃×D₁₃₇	—	19	1	no	—
8	#10587739	—	19	1	no	Hall
9	C₃×C₁₃₇	—	19	1	no	Hall
10	D₁₃₇	D₁₉⋊C₃	1	1	yes	characteristic
11	(C₁₉⋊C₃)⋊C₄	—	137	1	no	maximal, Hall
12	C₁₃₇	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₉⋊C₃	—	137	1	no	—
14	Dic₁₉	—	137	1	no	Hall
15	C₁₉⋊C₃	#10587739	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₉	—	137	1	no	—
17	C₁₉	C₃×#10587739	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2603	1	no	Hall
19	C₂×C₃	—	2603	1	no	—
20	C₄	—	2603	1	no	Sylow
21	C₃	—	19	1	no	Sylow
22	C₂	—	137	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₉×C₁₃₇	C₃×C₄
prime radical	C₁₉⋊C₃×D₁₃₇	C₂
cosocle	C₁₉×D₁₃₇	C₂×C₃
LCS	G ▷ C₁₉×C₁₃₇
UCS	C₁

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.