Group #18038836 — subgroups

Subgroups — C₁₉×#32877 #18038836

Order 4864.

594 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2091	C₂	1	4	yes	maximal, complemented
2	C₁₉×#2070	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2069	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1785	C₂	1	3	yes	maximal
5	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×#430	C₂²	1	12	yes	—
7	C₂×C₁₉×#101	C₂²	1	6	yes	—
8	C₂×C₁₉×#100	C₂²	1	6	yes	—
9	C₁₉×#407	C₂²	1	6	yes	—
10	C₁₉×#338	C₂²	1	4	yes	—
11	C₂×#41×C₁₉	—	4	6	no	—
12	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
13	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
14	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
16	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×M₁₆×C₁₉	C₂³	1	12	yes	—
18	C₁₉×#108	—	4	12	no	—
19	C₁₉×#101	—	4	6	no	—
20	C₁₉×#100	—	4	6	no	—
21	C₁₉×C₂²⋊C₈	—	4	6	no	—
22	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
23	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
24	#41×C₁₉	—	4	16	no	—
25	C₂×Q₈×C₁₉	—	2	6	no	—
26	C₂×D₄×C₁₉	—	2	6	no	—
27	C₂×D₄×C₁₉	—	4	6	no	—
28	C₂²×C₄×C₁₉	—	2	6	no	—
29	C₂²×C₄×C₁₉	—	4	6	no	—
30	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
32	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
33	M₁₆×C₁₉	—	2	12	no	—
34	M₁₆×C₁₉	—	2	12	no	—
35	C₂×C₈×C₁₉	—	2	12	no	—
36	#32877	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂³×C₁₉	—	2	3	no	—
38	C₂³×C₁₉	—	2	6	no	—
39	C₂³×C₁₉	—	8	1	no	—
40	C₂³×C₁₉	—	8	2	no	—
41	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
42	Q₈×C₁₉	—	4	4	no	—
43	D₄×C₁₉	—	4	8	no	—
44	D₄×C₁₉	—	4	4	no	—
45	C₂×C₄×C₁₉	—	2	3	no	—
46	C₂×C₄×C₁₉	—	2	6	no	—
47	C₂×C₄×C₁₉	—	4	8	no	—
48	C₂×C₄×C₁₉	—	4	4	no	—
49	C₂×C₄×C₁₉	H(5,𝔽₂)	1	6	yes	—
50	C₈×C₁₉	—	4	12	no	—
51	#2091	C₂×C₁₉	1	4	yes	complemented
52	#2070	C₂×C₁₉	1	4	yes	complemented
53	#2069	C₂×C₁₉	1	4	yes	complemented
54	#1785	C₂×C₁₉	1	3	yes	—
55	C₂²×C₁₉	—	4	1	no	—
56	C₂²×C₁₉	—	4	6	no	—
57	C₂²×C₁₉	—	4	1	no	—
58	C₂²×C₁₉	—	4	2	no	—
59	C₂²×C₁₉	—	8	6	no	—
60	C₂²×C₁₉	#543	1	3	yes	—
61	C₄×C₁₉	—	4	1	no	—
62	C₄×C₁₉	—	4	2	no	—
63	C₄×C₁₉	#560	1	4	yes	—
64	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
65	#430	C₂²×C₁₉	1	12	yes	—
66	C₂×#101	C₂²×C₁₉	1	6	yes	—
67	C₂×#100	C₂²×C₁₉	1	6	yes	—
68	#407	C₂²×C₁₉	1	6	yes	—
69	#338	C₂²×C₁₉	1	4	yes	—
70	C₂×C₁₉	—	2	3	no	—
71	C₂×C₁₉	—	8	1	no	—
72	C₂×C₁₉	—	8	2	no	—
73	C₂×C₁₉	#2842	1	1	yes	characteristic
74	C₂×#41	—	4	6	no	—
75	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
76	C₂²×D₄	Q₈×C₁₉	1	2	yes	—
77	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
78	C₂³×C₄	Q₈×C₁₉	1	2	yes	—
79	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
80	C₂×M₁₆	C₂³×C₁₉	1	12	yes	—
81	#108	—	4	12	no	—
82	#101	—	4	6	no	—
83	#100	—	4	6	no	—
84	C₂²⋊C₈	—	4	6	no	—
85	C₁₉	#32877	1	1	yes	characteristic, direct product factor, Sylow
86	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
87	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
88	#41	—	4	16	no	—
89	C₂×Q₈	—	2	6	no	—
90	C₂×D₄	—	2	6	no	—
91	C₂×D₄	—	4	6	no	—
92	C₂²×C₄	—	2	6	no	—
93	C₂²×C₄	—	4	6	no	—
94	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
95	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
96	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
97	M₁₆	—	2	12	no	—
98	M₁₆	—	2	12	no	—
99	C₂×C₈	—	2	12	no	—
100	C₂³	—	2	3	no	—
101	C₂³	—	2	6	no	—
102	C₂³	—	8	1	no	—
103	C₂³	—	8	2	no	—
104	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
105	Q₈	—	4	4	no	—
106	D₄	—	4	8	no	—
107	D₄	—	4	4	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	2	6	no	—
110	C₂×C₄	—	4	8	no	—
111	C₂×C₄	—	4	4	no	—
112	C₂×C₄	C₁₉×H(5,𝔽₂)	1	6	yes	—
113	C₈	—	4	12	no	—
114	C₂²	—	4	1	no	—
115	C₂²	—	4	6	no	—
116	C₂²	—	4	1	no	—
117	C₂²	—	4	2	no	—
118	C₂²	—	8	6	no	—
119	C₂²	C₁₉×#543	1	3	yes	—
120	C₄	—	4	1	no	—
121	C₄	—	4	2	no	—
122	C₄	C₁₉×#560	1	4	yes	—
123	C₂	—	2	3	no	—
124	C₂	—	8	1	no	—
125	C₂	—	8	2	no	—
126	C₂	C₁₉×#2842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2091

C₂

yes

maximal, complemented

C₁₉×#2070

C₂

yes

maximal, complemented

C₁₉×#2069

C₂

yes

maximal, complemented

C₁₉×#1785

C₂

yes

maximal

C₂²×#41×C₁₉

C₂²

yes

characteristic

C₁₉×#430

C₂²

yes

—

C₂×C₁₉×#101

C₂²

yes

—

C₂×C₁₉×#100

C₂²

yes

—

C₁₉×#407

C₂²

yes

—

C₁₉×#338

C₂²

yes

—

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

C₂³

yes

characteristic

C₂²×D₄×C₁₉

Q₈

yes

—

C₂²×D₄×C₁₉

C₂³

yes

characteristic

C₂³×C₄×C₁₉

Q₈

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

C₂³

yes

—

C₁₉×#108

—

C₁₉×#101

—

C₁₉×#100

—

C₁₉×C₂²⋊C₈

—

C₂⁴×C₁₉

C₂×Q₈

yes

—

C₂⁴×C₁₉

C₂×Q₈

yes

characteristic

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

—

C₂²×C₄×C₁₉

C₂⁴

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

#32877

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×Q₈

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

H(5,𝔽₂)

yes

—

C₈×C₁₉

—

#2091

C₂×C₁₉

yes

complemented

#2070

C₂×C₁₉

yes

complemented

#2069

C₂×C₁₉

yes

complemented

#1785

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#543

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#560

yes

—

C₂²×#41

C₂²×C₁₉

yes

characteristic

#430

C₂²×C₁₉

yes

—

C₂×#101

C₂²×C₁₉

yes

—

C₂×#100

C₂²×C₁₉

yes

—

#407

C₂²×C₁₉

yes

—

#338

C₂²×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2842

yes

characteristic

C₂×#41

—

C₂²×Q₈

C₂³×C₁₉

yes

characteristic

C₂²×D₄

Q₈×C₁₉

yes

—

C₂²×D₄

C₂³×C₁₉

yes

characteristic

C₂³×C₄

Q₈×C₁₉

yes

—

C₂³×C₄

C₂³×C₁₉

yes

characteristic

C₂×M₁₆

C₂³×C₁₉

yes

—

#108

—

#101

—

#100

—

C₂²⋊C₈

—

C₁₉

#32877

yes

characteristic, direct product factor, Sylow

C₂⁴

C₂×Q₈×C₁₉

yes

—

C₂⁴

C₂×Q₈×C₁₉

yes

characteristic

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Q₈×C₁₉

yes

characteristic

C₂²×C₄

C₂×Q₈×C₁₉

yes

—

C₂²×C₄

C₂⁴×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

C₂²×Q₈×C₁₉

yes

characteristic

105

Q₈

—

106

D₄

—

107

D₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₁₉×H(5,𝔽₂)

yes

—

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

C₁₉×#543

yes

—

120

C₄

—

121

C₄

—

122

C₄

C₁₉×#560

yes

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

C₁₉×#2842

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#2842

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₉

prime radical

C₂²×#41×C₁₉

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#2091	C₂	semidirect
2. C₁₉×#2070	C₂	semidirect
3. C₁₉×#2069	C₂	semidirect
36. #32877	C₁₉	direct (N × H)
51. #2091	C₂×C₁₉	semidirect
52. #2070	C₂×C₁₉	semidirect
53. #2069	C₂×C₁₉	semidirect
85. C₁₉	#32877	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2091

C₂

semidirect

2. C₁₉×#2070

C₂

semidirect

3. C₁₉×#2069

C₂

semidirect

36. #32877

C₁₉

direct (N × H)

51. #2091

C₂×C₁₉

semidirect

52. #2070

C₂×C₁₉

semidirect

53. #2069

C₂×C₁₉

semidirect

85. C₁₉

#32877

direct (N × H)

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

subgroup	index
C₁₉×#2091	2
C₁₉×#2070	2
C₁₉×#2069	2
C₁₉×#1785	2
#32877	19

subgroup

index

C₁₉×#2091

C₁₉×#2070

C₁₉×#2069

C₁₉×#1785

#32877

Subgroups — C₁₉×#32877 #18038836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#32877 #18038836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32877 #18038836