Subgroups — C₃⋊(C₁₉⋊#64480) #30685802

Order 17100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#1044)	—	3	1	no	maximal
3	C₁₉⋊#64480	—	3	3	no	maximal
4	C₃×C₁₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₁₉×(C₅⋊D₅)⋊C₃	D₃	1	3	yes	—
7	C₁₉⋊#1044	—	9	1	no	Hall
8	C₃×C₅²×C₁₉	Dic₃	1	1	yes	characteristic, complemented
9	C₁₉×C₅²⋊C₃	Dic₃	1	3	yes	complemented
10	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	1	no	—
11	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	1	no	—
12	C₁₉×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
13	C₃⋊#64480	—	19	1	no	maximal, Hall
14	C₃⋊Dic₅₇	—	25	1	no	maximal, Hall
15	C₃×D₅×C₁₉	—	15	1	no	—
16	C₃×D₅×C₁₉	—	30	1	no	—
17	C₅²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₃×(C₅⋊D₅)⋊C₃	D₁₉	1	1	yes	characteristic
19	C₁₉⋊AGL(1,𝔽₅)	—	45	1	no	—
20	C₁₉⋊AGL(1,𝔽₅)	—	45	1	no	—
21	C₂×C₃²×C₁₉	—	25	1	no	—
22	C₃⋊#1044	—	57	1	no	—
23	#64480	—	57	3	no	—
24	C₃×C₅×C₁₉	—	3	1	no	—
25	C₃×C₅×C₁₉	—	6	1	no	—
26	Dic₅₇	—	75	1	no	—
27	Dic₅₇	—	75	3	no	—
28	C₃×C₅²⋊C₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
29	D₅×C₁₉	—	30	1	no	—
30	D₅×C₁₉	—	30	1	no	—
31	C₃²×C₁₉	—	100	1	no	Hall
32	C₃×C₅⋊D₅	D₅₇	1	1	yes	characteristic
33	(C₅⋊D₅)⋊C₃	D₅₇	1	3	yes	—
34	C₂×C₃×C₁₉	—	25	3	no	—
35	C₂×C₃×C₁₉	—	25	1	no	—
36	#1044	—	171	1	no	Hall
37	C₅×C₁₉	—	6	1	no	—
38	C₅×C₁₉	—	6	1	no	—
39	Dic₁₉	—	225	1	no	Hall
40	C₃×C₅²	Dic₅₇	1	1	yes	characteristic, complemented
41	C₅²⋊C₃	Dic₅₇	1	3	yes	complemented
42	ΓL(1,𝔽₁₆)	—	285	1	no	—
43	ΓL(1,𝔽₁₆)	—	285	1	no	—
44	C₃×C₁₉	—	100	3	no	—
45	C₃×C₁₉	#64480	1	1	yes	characteristic, complemented
46	C₅⋊D₅	C₃⋊D₅₇	1	1	yes	characteristic
47	C₂×C₁₉	—	25	1	no	—
48	C₃⋊Dic₃	—	475	1	no	Hall
49	C₃×D₅	—	30	1	no	—
50	C₃×D₅	—	30	1	no	—
51	C₅²	C₃⋊Dic₅₇	1	1	yes	characteristic, complemented, Sylow
52	AGL(1,𝔽₅)	—	855	1	no	—
53	AGL(1,𝔽₅)	—	855	1	no	—
54	C₁₉	C₃⋊#64480	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃²	—	25	1	no	—
56	C₃×C₅	—	6	1	no	—
57	C₃×C₅	—	6	1	no	—
58	Dic₃	—	1425	1	no	—
59	Dic₃	—	1425	3	no	—
60	D₅	—	15	1	no	—
61	D₅	—	30	1	no	—
62	C₃²	—	100	1	no	Sylow
63	C₂×C₃	—	25	3	no	—
64	C₂×C₃	—	25	1	no	—
65	C₅	—	3	1	no	—
66	C₅	—	6	1	no	—
67	C₄	—	4275	1	no	Sylow
68	C₃	—	100	3	no	—
69	C₃	C₁₉⋊#64480	1	1	yes	characteristic, complemented
70	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
4. C₃×C₁₉×C₅²⋊C₃	C₄	semidirect
8. C₃×C₅²×C₁₉	Dic₃	semidirect
9. C₁₉×C₅²⋊C₃	Dic₃	semidirect
17. C₅²×C₁₉	C₃⋊Dic₃	semidirect
28. C₃×C₅²⋊C₃	Dic₁₉	semidirect
40. C₃×C₅²	Dic₅₇	semidirect
41. C₅²⋊C₃	Dic₅₇	semidirect
45. C₃×C₁₉	#64480	semidirect
51. C₅²	C₃⋊Dic₅₇	semidirect
54. C₁₉	C₃⋊#64480	semidirect
69. C₃	C₁₉⋊#64480	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×(C₅⋊D₅)⋊C₃	2
C₃⋊(C₁₉⋊#1044)	3
C₁₉⋊#64480	3
C₃⋊#64480	19
C₃⋊Dic₅₇	25

Subgroups — C3⋊(C19⋊#64480) #30685802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₁₉⋊#64480) #30685802