Subgroups — C₃×C₁₉⋊#66776 #34084348

Order 19380.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#66776	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₇×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉⋊#595	—	5	1	no	maximal, Hall
5	C₁₉×D₈₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₉×D₁₇	—	5	1	no	—
7	C₅×C₁₇×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₁₉⋊#595	—	5	1	no	Hall
9	C₃×C₁₉⋊AGL(1,𝔽₅)	—	17	1	no	maximal, Hall
10	C₃×#66776	—	19	1	no	maximal, Hall
11	C₃×C₁₇×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₁₉×D₁₇	—	5	1	no	—
13	C₃×D₅×C₁₉	—	17	1	no	—
14	C₃×D₈₅	D₁₉	1	1	yes	characteristic
15	C₁₉⋊AGL(1,𝔽₅)	—	17	1	no	Hall
16	#66776	—	19	1	no	Hall
17	C₁₇×C₁₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×C₁₉	#595	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×C₁₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
20	C₃×Dic₁₉	—	85	1	no	Hall
21	C₃×#595	—	95	1	no	Hall
22	D₅×C₁₉	—	17	1	no	—
23	D₈₅	C₃×D₁₉	1	1	yes	characteristic
24	C₂×C₃×C₁₉	—	85	1	no	—
25	C₃×D₁₇	—	5	1	no	—
26	C₅×C₁₉	C₃×#595	1	1	yes	characteristic, complemented, Hall
27	C₅×C₁₇	C₃×Dic₁₉	1	1	yes	characteristic, complemented, Hall
28	Dic₁₉	—	85	1	no	Hall
29	#595	—	95	1	no	Hall
30	C₃×AGL(1,𝔽₅)	—	323	1	no	Hall
31	C₃×C₁₉	#66776	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₇	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₉	—	85	1	no	—
34	D₁₇	—	5	1	no	—
35	C₃×D₅	—	17	1	no	—
36	AGL(1,𝔽₅)	—	323	1	no	Hall
37	C₁₉	C₃×#66776	1	1	yes	characteristic, complemented, Sylow
38	C₁₇	C₃×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₁₉⋊#595	1	1	yes	characteristic, complemented, Hall
40	C₃×C₄	—	1615	1	no	Hall
41	D₅	—	17	1	no	—
42	C₂×C₃	—	85	1	no	—
43	C₅	C₃×C₁₉⋊#595	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	1615	1	no	Sylow
45	C₃	C₁₉⋊#66776	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₁₉⋊#66776
commutator, hypocenter	C₅×C₁₇×C₁₉	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₁₉	C₄
prime radical	C₃×C₁₉×D₈₅	C₂
cosocle	C₁₉×D₈₅	C₂×C₃
LCS	G ▷ C₅×C₁₇×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₁₉⋊#66776	C₃	direct (N × H)
3. C₃×C₅×C₁₇×C₁₉	C₄	semidirect
7. C₅×C₁₇×C₁₉	C₃×C₄	semidirect
11. C₃×C₁₇×C₁₉	AGL(1,𝔽₅)	semidirect
17. C₁₇×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
18. C₃×C₅×C₁₉	#595	semidirect
19. C₃×C₅×C₁₇	Dic₁₉	semidirect
26. C₅×C₁₉	C₃×#595	semidirect
27. C₅×C₁₇	C₃×Dic₁₉	semidirect
31. C₃×C₁₉	#66776	semidirect
32. C₃×C₁₇	C₁₉⋊AGL(1,𝔽₅)	semidirect
37. C₁₉	C₃×#66776	semidirect
38. C₁₇	C₃×C₁₉⋊AGL(1,𝔽₅)	semidirect
39. C₃×C₅	C₁₉⋊#595	semidirect
43. C₅	C₃×C₁₉⋊#595	semidirect
45. C₃	C₁₉⋊#66776	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₉×D₈₅	2
C₁₉⋊#66776	3
C₃×C₁₉⋊#595	5
C₃×C₁₉⋊AGL(1,𝔽₅)	17
C₃×#66776	19

Subgroups — C3×C19⋊#66776 #34084348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉⋊#66776 #34084348