Subgroups — C₃⋊(C₃⋊(C₁₉⋊#1042)) #30685907

Order 17100.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#1042)	—	3	4	no	maximal
3	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	—	5	1	no	maximal
5	C₃⋊Dic₂₈₅	—	5	1	no	maximal
6	C₃×C₅×D₅×C₁₉	D₃	1	4	yes	—
7	C₁₉⋊#1042	—	9	1	no	Hall
8	C₂×C₃²×C₅×C₁₉	—	5	1	no	—
9	C₃²×D₅×C₁₉	D₅	1	1	yes	characteristic
10	C₃×C₅²×C₁₉	Dic₃	1	4	yes	complemented
11	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	4	no	—
12	Dic₂₈₅	—	15	4	no	—
13	C₅×D₅×C₁₉	C₃⋊D₃	1	1	yes	characteristic
14	C₃⋊(C₃⋊#1042)	—	19	1	no	maximal, Hall
15	C₃²×C₅×C₁₉	—	4	1	no	—
16	C₃²×C₅×C₁₉	Dic₅	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
18	C₃⋊Dic₅₇	—	25	1	no	Hall
19	C₂×C₃×C₅×C₁₉	—	5	4	no	—
20	C₃×D₅×C₁₉	D₁₅	1	4	yes	—
21	C₅²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
22	C₃²×C₅×D₅	D₁₉	1	1	yes	characteristic
23	C₁₉⋊AGL(1,𝔽₅)	—	45	1	no	—
24	Dic₉₅	—	45	1	no	—
25	C₂×C₃²×C₁₉	—	5	1	no	—
26	C₃⋊#1042	—	57	4	no	—
27	C₃×C₅×C₁₉	—	4	4	no	—
28	C₃×C₅×C₁₉	Dic₁₅	1	4	yes	complemented
29	C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	1	4	yes	complemented
30	Dic₅₇	—	75	4	no	—
31	C₃²×C₅²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅×C₁₉	—	5	1	no	—
33	D₅×C₁₉	C₃⋊D₁₅	1	1	yes	characteristic
34	C₃⋊ΓL(1,𝔽₁₆)	—	95	1	no	—
35	C₃⋊Dic₁₅	—	95	1	no	—
36	C₃²×C₁₉	#1042	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×D₅	D₅₇	1	4	yes	—
38	C₂×C₃×C₁₉	—	5	4	no	—
39	#1042	—	171	1	no	Hall
40	C₅×C₁₉	—	4	1	no	—
41	C₅×C₁₉	C₃⋊Dic₁₅	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
43	C₂×C₃²×C₅	—	5	1	no	—
44	C₃²×D₅	D₉₅	1	1	yes	characteristic
45	Dic₁₉	—	225	1	no	Hall
46	C₃×C₅²	Dic₅₇	1	4	yes	complemented
47	ΓL(1,𝔽₁₆)	—	285	4	no	—
48	Dic₁₅	—	285	4	no	—
49	C₃×C₁₉	C₃⋊#1042	1	4	yes	complemented
50	C₅×D₅	C₃⋊D₅₇	1	1	yes	characteristic
51	C₃²×C₅	—	4	1	no	—
52	C₃²×C₅	Dic₉₅	1	1	yes	characteristic, complemented
53	C₃²×C₅	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
54	C₂×C₁₉	—	5	1	no	—
55	C₃⋊Dic₃	—	475	1	no	Hall
56	C₂×C₃×C₅	—	5	4	no	—
57	C₃×D₅	D₂₈₅	1	4	yes	—
58	C₅²	C₃⋊Dic₅₇	1	1	yes	characteristic, complemented, Sylow
59	AGL(1,𝔽₅)	—	855	1	no	—
60	Dic₅	—	855	1	no	—
61	C₁₉	C₃⋊(C₃⋊#1042)	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₃²	—	5	1	no	—
63	C₃×C₅	—	4	4	no	—
64	C₃×C₅	Dic₂₈₅	1	4	yes	complemented
65	C₃×C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	1	4	yes	complemented
66	Dic₃	—	1425	4	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	C₃⋊D₂₈₅	1	1	yes	characteristic
69	C₃²	C₁₉⋊#1042	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	5	4	no	—
71	C₅	—	4	1	no	—
72	C₅	C₃⋊Dic₂₈₅	1	1	yes	characteristic, complemented
73	C₅	C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	1	1	yes	characteristic, complemented
74	C₄	—	4275	1	no	Sylow
75	C₃	C₃⋊(C₁₉⋊#1042)	1	4	yes	complemented
76	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₉	C₄
prime radical, cosocle	C₃²×C₅×D₅×C₁₉	C₂
LCS	G ▷ C₃²×C₅²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₁₉	C₄	semidirect
10. C₃×C₅²×C₁₉	Dic₃	semidirect
16. C₃²×C₅×C₁₉	Dic₅	semidirect
17. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
21. C₅²×C₁₉	C₃⋊Dic₃	semidirect
28. C₃×C₅×C₁₉	Dic₁₅	semidirect
29. C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	semidirect
31. C₃²×C₅²	Dic₁₉	semidirect
36. C₃²×C₁₉	#1042	semidirect
41. C₅×C₁₉	C₃⋊Dic₁₅	semidirect
42. C₅×C₁₉	C₃⋊ΓL(1,𝔽₁₆)	semidirect
46. C₃×C₅²	Dic₅₇	semidirect
49. C₃×C₁₉	C₃⋊#1042	semidirect
52. C₃²×C₅	Dic₉₅	semidirect
53. C₃²×C₅	C₁₉⋊AGL(1,𝔽₅)	semidirect
58. C₅²	C₃⋊Dic₅₇	semidirect
61. C₁₉	C₃⋊(C₃⋊#1042)	semidirect
64. C₃×C₅	Dic₂₈₅	semidirect
65. C₃×C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	semidirect
69. C₃²	C₁₉⋊#1042	semidirect
72. C₅	C₃⋊Dic₂₈₅	semidirect
73. C₅	C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	semidirect
75. C₃	C₃⋊(C₁₉⋊#1042)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₅×C₁₉	2
C₃⋊(C₁₉⋊#1042)	3
C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	5
C₃⋊Dic₂₈₅	5
C₃⋊(C₃⋊#1042)	19

Subgroups — C3⋊(C3⋊(C19⋊#1042)) #30685907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊(C₁₉⋊#1042)) #30685907