Subgroups — C₃⋊(C₃⋊(C₁₉⋊#1044)) #30685905

Order 17100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#1044)	—	3	4	no	maximal
3	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	—	5	2	no	maximal
5	C₃×C₁₉×C₅⋊D₅	D₃	1	4	yes	—
6	C₁₉⋊#1044	—	9	1	no	Hall
7	C₃²×D₅×C₁₉	—	5	2	no	—
8	C₃²×D₅×C₁₉	—	10	2	no	—
9	C₃×C₅²×C₁₉	Dic₃	1	4	yes	complemented
10	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	8	no	—
11	C₁₉×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
12	C₃⋊(C₃⋊#1044)	—	19	1	no	maximal, Hall
13	C₃²×C₅×C₁₉	—	2	2	no	—
14	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	2	yes	complemented
15	C₃⋊Dic₅₇	—	25	1	no	Hall
16	C₃×D₅×C₁₉	—	5	8	no	—
17	C₃×D₅×C₁₉	—	10	8	no	—
18	C₅²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₅⋊D₅	D₁₉	1	1	yes	characteristic
20	C₁₉⋊AGL(1,𝔽₅)	—	45	2	no	—
21	C₂×C₃²×C₁₉	—	25	1	no	—
22	C₃⋊#1044	—	57	4	no	—
23	C₃×C₅×C₁₉	—	2	8	no	—
24	C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	1	8	yes	complemented
25	Dic₅₇	—	75	4	no	—
26	C₃²×C₅²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
27	D₅×C₁₉	—	5	2	no	—
28	D₅×C₁₉	—	10	2	no	—
29	C₃⋊ΓL(1,𝔽₁₆)	—	95	2	no	—
30	C₃²×C₁₉	#1044	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅⋊D₅	D₅₇	1	4	yes	—
32	C₂×C₃×C₁₉	—	25	4	no	—
33	#1044	—	171	1	no	Hall
34	C₅×C₁₉	—	2	2	no	—
35	C₅×C₁₉	C₃⋊ΓL(1,𝔽₁₆)	1	2	yes	complemented
36	C₃²×D₅	—	5	2	no	—
37	C₃²×D₅	—	10	2	no	—
38	Dic₁₉	—	225	1	no	Hall
39	C₃×C₅²	Dic₅₇	1	4	yes	complemented
40	ΓL(1,𝔽₁₆)	—	285	8	no	—
41	C₃×C₁₉	C₃⋊#1044	1	4	yes	complemented
42	C₅⋊D₅	C₃⋊D₅₇	1	1	yes	characteristic
43	C₃²×C₅	—	2	2	no	—
44	C₃²×C₅	C₁₉⋊AGL(1,𝔽₅)	1	2	yes	complemented
45	C₂×C₁₉	—	25	1	no	—
46	C₃⋊Dic₃	—	475	1	no	Hall
47	C₃×D₅	—	5	8	no	—
48	C₃×D₅	—	10	8	no	—
49	C₅²	C₃⋊Dic₅₇	1	1	yes	characteristic, complemented, Sylow
50	AGL(1,𝔽₅)	—	855	2	no	—
51	C₁₉	C₃⋊(C₃⋊#1044)	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃²	—	25	1	no	—
53	C₃×C₅	—	2	8	no	—
54	C₃×C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	1	8	yes	complemented
55	Dic₃	—	1425	4	no	—
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₃²	C₁₉⋊#1044	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	25	4	no	—
60	C₅	—	2	2	no	—
61	C₅	C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	1	2	yes	complemented
62	C₄	—	4275	1	no	Sylow
63	C₃	C₃⋊(C₁₉⋊#1044)	1	4	yes	complemented
64	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₉	C₄
prime radical, cosocle	C₃²×C₁₉×C₅⋊D₅	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
9. C₃×C₅²×C₁₉	Dic₃	semidirect
14. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
18. C₅²×C₁₉	C₃⋊Dic₃	semidirect
24. C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	semidirect
26. C₃²×C₅²	Dic₁₉	semidirect
30. C₃²×C₁₉	#1044	semidirect
35. C₅×C₁₉	C₃⋊ΓL(1,𝔽₁₆)	semidirect
39. C₃×C₅²	Dic₅₇	semidirect
41. C₃×C₁₉	C₃⋊#1044	semidirect
44. C₃²×C₅	C₁₉⋊AGL(1,𝔽₅)	semidirect
49. C₅²	C₃⋊Dic₅₇	semidirect
51. C₁₉	C₃⋊(C₃⋊#1044)	semidirect
54. C₃×C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	semidirect
58. C₃²	C₁₉⋊#1044	semidirect
61. C₅	C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	semidirect
63. C₃	C₃⋊(C₁₉⋊#1044)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₉×C₅⋊D₅	2
C₃⋊(C₁₉⋊#1044)	3
C₃⋊(C₃⋊(C₁₉⋊AGL(1,𝔽₅)))	5
C₃⋊(C₃⋊#1044)	19

Subgroups — C3⋊(C3⋊(C19⋊#1044)) #30685905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊(C₁₉⋊#1044)) #30685905