Subgroups — C₁₉⋊(C₂₃⋊#157) #30628645

Order 15732.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₉×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₉×C₂₃	—	6	2	no	—
4	Dic₄₃₇	—	9	1	no	maximal, Hall
5	C₃×C₁₉×C₂₃	—	2	2	no	—
6	C₂×C₁₉×C₂₃	—	9	1	no	—
7	C₂₃⋊#157	—	19	1	no	maximal, Hall
8	C₁₉⋊#157	—	23	1	no	maximal, Hall
9	C₁₉×C₂₃	#157	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₃×C₂₃	D₁₉	1	1	yes	characteristic
11	C₃⋊D₃×C₁₉	D₂₃	1	1	yes	characteristic
12	C₃²×C₂₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₁₉	Dic₂₃	1	1	yes	characteristic, complemented, Hall
14	D₃×C₂₃	—	6	2	no	—
15	D₃×C₁₉	—	6	2	no	—
16	Dic₂₃	—	171	1	no	Hall
17	Dic₁₉	—	207	1	no	Hall
18	C₃×C₂₃	—	2	2	no	—
19	C₃×C₁₉	—	2	2	no	—
20	C₂×C₂₃	—	9	1	no	—
21	C₂×C₁₉	—	9	1	no	—
22	#157	—	437	1	no	Hall
23	C₂₃	C₁₉⋊#157	1	1	yes	characteristic, complemented, Sylow
24	C₁₉	C₂₃⋊#157	1	1	yes	characteristic, complemented, Sylow
25	C₃⋊D₃	D₄₃₇	1	1	yes	characteristic
26	C₃²	Dic₄₃₇	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	3933	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×C₂₃	C₄
prime radical, cosocle	C₃⋊D₃×C₁₉×C₂₃	C₂
LCS	G ▷ C₃²×C₁₉×C₂₃
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.