Subgroups — C₁₉×C₃⋊#64425 #30660824

Order 16758.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₃⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#64425	—	3	1	no	maximal
4	C₁₉×#3862	—	2	1	no	—
5	C₁₉×#3862	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×C₃⋊AGL(1,𝔽₇)	—	7	2	no	maximal
8	C₁₉×C₇⋊D₇	—	3	1	no	Hall
9	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
10	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#64425	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₉×D₂₁	—	7	2	no	—
13	C₁₉×D₂₁	—	21	2	no	—
14	C₁₉×AGL(1,𝔽₇)	—	21	2	no	—
15	C₃×#3862	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₁₉	—	3	2	no	—
17	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	2	yes	complemented
18	C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
19	C₁₉×ΓL(1,𝔽₈)	—	14	2	no	—
20	C₃×D₃×C₁₉	—	49	1	no	Hall
21	C₃⋊(C₇⋊D₇)	C₃×C₁₉	1	1	yes	characteristic, complemented
22	#64425	—	3	1	no	—
23	D₇×C₁₉	—	21	2	no	—
24	D₇×C₁₉	—	63	2	no	—
25	C₃²×C₁₉	—	49	1	no	Hall
26	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
27	#3862	—	2	1	no	—
28	#3862	D₃×C₁₉	1	1	yes	characteristic, complemented
29	C₇×C₁₉	—	3	2	no	—
30	C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
31	C₃⋊AGL(1,𝔽₇)	—	7	2	no	—
32	C₂×C₃×C₁₉	—	147	1	no	—
33	D₃×C₁₉	—	49	1	no	—
34	C₇⋊D₇	—	3	1	no	Hall
35	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
36	C₃×C₁₉	—	49	1	no	—
37	C₃×C₁₉	—	98	1	no	—
38	C₃×C₁₉	#64425	1	1	yes	characteristic, complemented
39	C₇²	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
40	D₂₁	—	7	2	no	—
41	D₂₁	—	21	2	no	—
42	AGL(1,𝔽₇)	—	21	2	no	—
43	C₂×C₁₉	—	147	1	no	Hall
44	C₃×C₇	—	3	2	no	—
45	C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	2	yes	complemented
46	ΓL(1,𝔽₈)	—	7	2	no	—
47	ΓL(1,𝔽₈)	—	14	2	no	—
48	C₁₉	C₃⋊#64425	1	1	yes	characteristic, direct product factor, Sylow
49	C₃×D₃	—	49	1	no	Hall
50	D₇	—	21	2	no	—
51	D₇	—	63	2	no	—
52	C₃²	—	49	1	no	Sylow
53	C₇	—	3	2	no	—
54	C₇	C₁₉×C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
55	C₂×C₃	—	147	1	no	—
56	D₃	—	49	1	no	—
57	C₃	—	49	1	no	—
58	C₃	—	98	1	no	—
59	C₃	C₁₉×#64425	1	1	yes	characteristic, complemented
60	C₂	—	147	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊#64425
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#3862	C₂	semidirect
2. C₁₉×C₃⋊(C₇⋊D₇)	C₃	semidirect
5. C₁₉×#3862	D₃	semidirect
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
10. C₇²×C₁₉	C₃×D₃	semidirect
11. C₃⋊#64425	C₁₉	direct (N × H)
15. C₃×#3862	C₂×C₁₉	semidirect
17. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
21. C₃⋊(C₇⋊D₇)	C₃×C₁₉	semidirect
26. C₃×C₇²	C₂×C₃×C₁₉	semidirect
28. #3862	D₃×C₁₉	semidirect
30. C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
38. C₃×C₁₉	#64425	semidirect
39. C₇²	C₃×D₃×C₁₉	semidirect
45. C₃×C₇	C₁₉×AGL(1,𝔽₇)	semidirect
48. C₁₉	C₃⋊#64425	direct (N × H)
54. C₇	C₁₉×C₃⋊AGL(1,𝔽₇)	semidirect
59. C₃	C₁₉×#64425	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#3862	2
C₁₉×C₃⋊(C₇⋊D₇)	3
C₁₉×#64425	3
C₁₉×C₃⋊AGL(1,𝔽₇)	7
C₃⋊#64425	19

Subgroups — C19×C3⋊#64425 #30660824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊#64425 #30660824