Subgroups — C₁₉⋊#14274232 #49136299

Order 36252.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₉×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₉×C₅₃	—	6	2	no	—
4	Dic₁₀₀₇	—	9	1	no	maximal, Hall
5	C₃×C₁₉×C₅₃	—	2	2	no	—
6	C₂×C₁₉×C₅₃	—	9	1	no	—
7	#14274232	—	19	1	no	maximal, Hall
8	C₁₉×C₅₃	#157	1	1	yes	characteristic, complemented, Hall
9	C₃⋊D₃×C₅₃	D₁₉	1	1	yes	characteristic
10	C₁₉⋊#157	—	53	1	no	maximal, Hall
11	C₃²×C₅₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
12	C₃⋊D₃×C₁₉	D₅₃	1	1	yes	characteristic
13	D₃×C₅₃	—	6	2	no	—
14	Dic₅₃	—	171	1	no	Hall
15	C₃²×C₁₉	Dic₅₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅₃	—	2	2	no	—
17	D₃×C₁₉	—	6	2	no	—
18	C₂×C₅₃	—	9	1	no	—
19	Dic₁₉	—	477	1	no	Hall
20	C₃×C₁₉	—	2	2	no	—
21	C₅₃	C₁₉⋊#157	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₉	—	9	1	no	—
23	#157	—	1007	1	no	Hall
24	C₁₉	#14274232	1	1	yes	characteristic, complemented, Sylow
25	C₃⋊D₃	D₁₀₀₇	1	1	yes	characteristic
26	C₃²	Dic₁₀₀₇	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	9063	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₉×C₅₃	C₄
prime radical, cosocle	C₃⋊D₃×C₁₉×C₅₃	C₂
LCS	G ▷ C₃²×C₁₉×C₅₃
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.