Subgroups — C₁₉⋊#11744634 #30685556

Order 17100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#1044)	—	3	1	no	maximal
3	C₁₉×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
5	C₁₉⋊#1044	—	9	1	no	Hall
6	C₃×C₅²×C₁₉	Dic₃	1	1	yes	characteristic
7	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	1	no	—
8	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	1	no	—
9	C₁₉×C₅⋊D₅	D₉	1	1	yes	characteristic
10	#11744634	—	19	1	no	maximal, Hall
11	Dic₁₇₁	—	25	1	no	maximal, Hall
12	C₃×D₅×C₁₉	—	30	1	no	—
13	C₃×D₅×C₁₉	—	30	1	no	—
14	C₅²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
15	(C₅⋊D₅)⋊C₉	D₁₉	1	1	yes	characteristic
16	C₁₉⋊AGL(1,𝔽₅)	—	45	1	no	—
17	C₁₉⋊AGL(1,𝔽₅)	—	45	1	no	—
18	C₂×C₉×C₁₉	—	25	1	no	—
19	C₃⋊#1044	—	57	1	no	—
20	C₃×C₅×C₁₉	—	6	1	no	—
21	C₃×C₅×C₁₉	—	6	1	no	—
22	Dic₅₇	—	75	1	no	—
23	C₅²⋊C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
24	D₅×C₁₉	—	15	1	no	—
25	D₅×C₁₉	—	30	1	no	—
26	C₉×C₁₉	—	100	1	no	Hall
27	C₃×C₅⋊D₅	D₅₇	1	1	yes	characteristic
28	C₂×C₃×C₁₉	—	25	1	no	—
29	#1044	—	171	1	no	Hall
30	C₅×C₁₉	—	3	1	no	—
31	C₅×C₁₉	—	6	1	no	—
32	Dic₁₉	—	225	1	no	Hall
33	C₃×C₅²	Dic₅₇	1	1	yes	characteristic
34	ΓL(1,𝔽₁₆)	—	285	1	no	—
35	ΓL(1,𝔽₁₆)	—	285	1	no	—
36	C₃×C₁₉	#64480	1	1	yes	characteristic
37	C₅⋊D₅	D₁₇₁	1	1	yes	characteristic
38	C₂×C₁₉	—	25	1	no	—
39	Dic₉	—	475	1	no	Hall
40	C₃×D₅	—	30	1	no	—
41	C₃×D₅	—	30	1	no	—
42	C₅²	Dic₁₇₁	1	1	yes	characteristic, complemented, Sylow
43	AGL(1,𝔽₅)	—	855	1	no	—
44	AGL(1,𝔽₅)	—	855	1	no	—
45	C₁₉	#11744634	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	25	1	no	—
47	C₃×C₅	—	6	1	no	—
48	C₃×C₅	—	6	1	no	—
49	Dic₃	—	1425	1	no	—
50	D₅	—	15	1	no	—
51	D₅	—	15	1	no	—
52	C₉	—	100	1	no	Sylow
53	C₂×C₃	—	25	1	no	—
54	C₅	—	3	1	no	—
55	C₅	—	3	1	no	—
56	C₄	—	4275	1	no	Sylow
57	C₃	C₁₉⋊#64480	1	1	yes	characteristic
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₁₉×C₅²⋊C₉	C₄
Frattini	C₃	C₁₉⋊#64480
Fitting, socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₅⋊D₅	D₃
cosocle	C₁₉×(C₅⋊D₅)⋊C₉	C₂
LCS	G ▷ C₁₉×C₅²⋊C₉
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₁₉×C₅²⋊C₉	C₄	semidirect
14. C₅²×C₁₉	Dic₉	semidirect
23. C₅²⋊C₉	Dic₁₉	semidirect
42. C₅²	Dic₁₇₁	semidirect
45. C₁₉	#11744634	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×(C₅⋊D₅)⋊C₉	2
C₃⋊(C₁₉⋊#1044)	3
#11744634	19
Dic₁₇₁	25

Subgroups — C19⋊#11744634 #30685556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#11744634 #30685556