Subgroups — C₁₉×C₃⋊#10596875 #45691908

Order 33516.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×#3862	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊(C₇⋊Dic₇)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#10596875	—	3	1	no	maximal
4	C₃×C₁₉×#3862	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×#3862	—	2	1	no	—
6	C₂×C₁₉×#3862	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₁₉×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	2	no	maximal
9	C₁₉×C₇⋊Dic₇	—	3	1	no	Hall
10	C₁₉×#3862	—	2	1	no	—
11	C₁₉×#3862	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
14	C₂×C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic
15	C₃⋊#10596875	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₉×Dic₂₁	—	7	2	no	—
17	C₁₉×Dic₂₁	—	21	2	no	—
18	C₁₉×ΓL(1,𝔽₈)⋊C₄	—	21	2	no	—
19	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
20	C₇²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×#3862	C₂×C₁₉	1	1	yes	characteristic
22	C₂×C₃×C₇×C₁₉	—	3	2	no	—
23	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	2	yes	—
24	C₂×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
25	C₂×C₁₉×ΓL(1,𝔽₈)	—	14	2	no	—
26	C₃×Dic₃×C₁₉	—	49	1	no	Hall
27	C₃⋊(C₇⋊Dic₇)	C₃×C₁₉	1	1	yes	characteristic, complemented
28	#10596875	—	3	1	no	—
29	C₁₉×Dic₇	—	21	2	no	—
30	C₁₉×Dic₇	—	63	2	no	—
31	C₃×#3862	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₉	—	3	2	no	—
33	C₃×C₇×C₁₉	ΓL(1,𝔽₈)⋊C₄	1	2	yes	complemented
34	C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
35	C₁₉×ΓL(1,𝔽₈)	—	14	2	no	—
36	C₂×C₃²×C₁₉	—	49	1	no	—
37	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
38	C₂×#3862	—	2	1	no	—
39	C₂×#3862	D₃×C₁₉	1	1	yes	characteristic
40	C₂×C₇×C₁₉	—	3	2	no	—
41	C₂×C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	1	2	yes	—
42	C₃⋊(ΓL(1,𝔽₈)⋊C₄)	—	7	2	no	—
43	C₃×C₄×C₁₉	—	147	1	no	—
44	Dic₃×C₁₉	—	49	1	no	—
45	C₇⋊Dic₇	—	3	1	no	Hall
46	C₃²×C₁₉	—	49	1	no	Hall
47	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
48	#3862	—	2	1	no	—
49	#3862	Dic₃×C₁₉	1	1	yes	characteristic, complemented
50	C₇×C₁₉	—	3	2	no	—
51	C₇×C₁₉	C₃⋊(ΓL(1,𝔽₈)⋊C₄)	1	2	yes	complemented
52	C₂×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
53	C₂×C₃×C₁₉	—	49	1	no	—
54	C₂×C₃×C₁₉	—	98	1	no	—
55	C₂×C₃×C₁₉	#64425	1	1	yes	characteristic
56	C₂×C₇²	C₃×D₃×C₁₉	1	1	yes	characteristic
57	Dic₂₁	—	7	2	no	—
58	Dic₂₁	—	21	2	no	—
59	ΓL(1,𝔽₈)⋊C₄	—	21	2	no	—
60	C₄×C₁₉	—	147	1	no	Hall
61	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
62	C₃×C₁₉	—	49	1	no	—
63	C₃×C₁₉	—	98	1	no	—
64	C₃×C₁₉	#10596875	1	1	yes	characteristic, complemented
65	C₇²	C₃×Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃×C₇	—	3	2	no	—
67	C₂×C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	2	yes	—
68	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
69	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
70	C₂×C₁₉	C₃⋊#64425	1	1	yes	characteristic
71	C₃×Dic₃	—	49	1	no	Hall
72	Dic₇	—	21	2	no	—
73	Dic₇	—	63	2	no	—
74	C₃×C₇	—	3	2	no	—
75	C₃×C₇	C₁₉×ΓL(1,𝔽₈)⋊C₄	1	2	yes	complemented
76	ΓL(1,𝔽₈)	—	7	2	no	—
77	ΓL(1,𝔽₈)	—	14	2	no	—
78	C₁₉	C₃⋊#10596875	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₃²	—	49	1	no	—
80	C₂×C₇	—	3	2	no	—
81	C₂×C₇	C₁₉×C₃⋊AGL(1,𝔽₇)	1	2	yes	—
82	C₃×C₄	—	147	1	no	—
83	Dic₃	—	49	1	no	—
84	C₃²	—	49	1	no	Sylow
85	C₇	—	3	2	no	—
86	C₇	C₁₉×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	1	2	yes	complemented
87	C₂×C₃	—	49	1	no	—
88	C₂×C₃	—	98	1	no	—
89	C₂×C₃	C₁₉×#64425	1	1	yes	characteristic
90	C₄	—	147	1	no	Sylow
91	C₃	—	49	1	no	—
92	C₃	—	98	1	no	—
93	C₃	C₁₉×#10596875	1	1	yes	characteristic, complemented
94	C₂	C₁₉×C₃⋊#64425	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×C₃⋊(C₇⋊Dic₇)	C₃	semidirect
4. C₃×C₁₉×#3862	C₄	semidirect
11. C₁₉×#3862	Dic₃	semidirect
12. C₃×C₇²×C₁₉	C₃×C₄	semidirect
15. C₃⋊#10596875	C₁₉	direct (N × H)
20. C₇²×C₁₉	C₃×Dic₃	semidirect
27. C₃⋊(C₇⋊Dic₇)	C₃×C₁₉	semidirect
31. C₃×#3862	C₄×C₁₉	semidirect
33. C₃×C₇×C₁₉	ΓL(1,𝔽₈)⋊C₄	semidirect
47. C₃×C₇²	C₃×C₄×C₁₉	semidirect
49. #3862	Dic₃×C₁₉	semidirect
51. C₇×C₁₉	C₃⋊(ΓL(1,𝔽₈)⋊C₄)	semidirect
64. C₃×C₁₉	#10596875	semidirect
65. C₇²	C₃×Dic₃×C₁₉	semidirect
75. C₃×C₇	C₁₉×ΓL(1,𝔽₈)⋊C₄	semidirect
78. C₁₉	C₃⋊#10596875	direct (N × H)
86. C₇	C₁₉×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	semidirect
93. C₃	C₁₉×#10596875	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉×#3862	2
C₁₉×C₃⋊(C₇⋊Dic₇)	3
C₁₉×#10596875	3
C₁₉×C₃⋊(ΓL(1,𝔽₈)⋊C₄)	7
C₃⋊#10596875	19

Subgroups — C19×C3⋊#10596875 #45691908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊#10596875 #45691908