Subgroups — C₁₉×C₃⋊#10596885 #45692269

Order 33516.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#64425	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#5997	—	3	1	no	maximal
3	C₁₉×#10596885	—	3	3	no	maximal
4	C₃×C₁₉×#3862	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic
6	C₁₉×#64425	D₃	1	3	yes	—
7	C₁₉×#5997	—	9	1	no	Hall
8	C₁₉×#3862	Dic₃	1	3	yes	complemented
9	C₃×C₇²×C₁₉	Dic₃	1	1	yes	characteristic, complemented
10	C₃×C₁₉×AGL(1,𝔽₇)	—	14	1	no	—
11	C₁₉×C₇⋊D₇	C₃⋊D₃	1	1	yes	characteristic
12	C₃⋊#10596885	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
14	C₇²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	C₃×#64425	C₂×C₁₉	1	1	yes	characteristic
16	C₃×D₇×C₁₉	—	14	1	no	—
17	C₃×D₇×C₁₉	—	42	1	no	—
18	C₁₉×AGL(1,𝔽₇)	—	14	3	no	—
19	C₁₉×C₃⋊Dic₃	—	49	1	no	maximal, Hall
20	C₃⋊#5997	—	3	1	no	—
21	#10596885	—	3	3	no	—
22	C₃×#3862	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	—	2	1	no	—
24	C₃×C₇×C₁₉	—	6	1	no	—
25	C₁₉×ΓL(1,𝔽₈)	—	14	3	no	—
26	C₂×C₃²×C₁₉	—	49	1	no	—
27	C₃×C₇⋊D₇	D₃×C₁₉	1	1	yes	characteristic
28	#64425	D₃×C₁₉	1	3	yes	—
29	D₇×C₁₉	—	14	1	no	—
30	D₇×C₁₉	—	42	1	no	—
31	Dic₃×C₁₉	—	147	1	no	—
32	Dic₃×C₁₉	—	147	3	no	—
33	#5997	—	9	1	no	Hall
34	C₃²×C₁₉	—	49	1	no	Hall
35	C₃×C₇²	Dic₃×C₁₉	1	1	yes	characteristic, complemented
36	#3862	Dic₃×C₁₉	1	3	yes	complemented
37	C₇×C₁₉	—	2	1	no	—
38	C₇×C₁₉	—	6	1	no	—
39	C₃×AGL(1,𝔽₇)	—	14	1	no	—
40	C₂×C₃×C₁₉	—	49	3	no	—
41	C₂×C₃×C₁₉	—	49	1	no	—
42	C₇⋊D₇	C₃⋊D₃×C₁₉	1	1	yes	characteristic
43	C₄×C₁₉	—	441	1	no	Hall
44	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
45	C₃×C₁₉	—	49	3	no	—
46	C₃×C₁₉	#10596885	1	1	yes	characteristic, complemented
47	C₇²	C₁₉×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
48	C₃×D₇	—	14	1	no	—
49	C₃×D₇	—	42	1	no	—
50	AGL(1,𝔽₇)	—	14	3	no	—
51	C₂×C₁₉	—	49	1	no	—
52	C₃⋊Dic₃	—	49	1	no	Hall
53	C₃×C₇	—	2	1	no	—
54	C₃×C₇	—	6	1	no	—
55	ΓL(1,𝔽₈)	—	14	3	no	—
56	C₁₉	C₃⋊#10596885	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃²	—	49	1	no	—
58	D₇	—	14	1	no	—
59	D₇	—	42	1	no	—
60	Dic₃	—	147	3	no	—
61	Dic₃	—	147	1	no	—
62	C₃²	—	49	1	no	Sylow
63	C₇	—	2	1	no	—
64	C₇	—	6	1	no	—
65	C₂×C₃	—	49	3	no	—
66	C₂×C₃	—	49	1	no	—
67	C₄	—	441	1	no	Sylow
68	C₃	—	49	3	no	—
69	C₃	C₁₉×#10596885	1	1	yes	characteristic, complemented
70	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊#10596885
commutator, hypocenter	C₃×#3862	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	Dic₃
prime radical	C₃×C₁₉×#64425	C₂
cosocle	C₃×#64425	C₂×C₁₉
LCS	G ▷ C₃×#3862
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
4. C₃×C₁₉×#3862	C₄	semidirect
8. C₁₉×#3862	Dic₃	semidirect
9. C₃×C₇²×C₁₉	Dic₃	semidirect
12. C₃⋊#10596885	C₁₉	direct (N × H)
14. C₇²×C₁₉	C₃⋊Dic₃	semidirect
22. C₃×#3862	C₄×C₁₉	semidirect
35. C₃×C₇²	Dic₃×C₁₉	semidirect
36. #3862	Dic₃×C₁₉	semidirect
46. C₃×C₁₉	#10596885	semidirect
47. C₇²	C₁₉×C₃⋊Dic₃	semidirect
56. C₁₉	C₃⋊#10596885	direct (N × H)
69. C₃	C₁₉×#10596885	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#64425	2
C₁₉×C₃⋊#5997	3
C₁₉×#10596885	3
C₃⋊#10596885	19
C₁₉×C₃⋊Dic₃	49

Subgroups — C19×C3⋊#10596885 #45692269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊#10596885 #45692269