Group #18019646 — subgroups

Subgroups — C₁₉×#13687 #18019646

Order 4864.

212 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 78 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	C₂×C₁₉×SD₆₄	C₂	1	2	yes	maximal
2	C₁₉×#2247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1416	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×Q₃₂	—	2	1	no	—
7	C₂×C₁₉×Q₃₂	C₂²	1	2	yes	—
8	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
9	C₁₉×#494	—	2	1	no	—
10	C₄×D₈×C₁₉	—	2	1	no	—
11	C₁₉×SD₆₄	—	2	4	no	—
12	C₂×C₁₉×C₃₂	C₂²	1	2	yes	—
13	C₁₉×#366	C₂²	1	1	yes	characteristic
14	C₁₉×#357	—	2	1	no	—
15	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₁₉	—	2	2	no	—
17	C₂×Q₁₆×C₁₉	—	4	1	no	—
18	C₂×D₈×C₁₉	—	2	1	no	—
19	C₁₉×C₄⋊Q₈	—	4	1	no	—
20	C₄×D₄×C₁₉	—	4	1	no	—
21	C₁₉×Q₃₂	—	2	2	no	—
22	C₁₉×Q₃₂	—	2	2	no	—
23	C₁₉×Q₃₂	—	4	2	no	—
24	C₁₉×D₁₆	—	2	1	no	—
25	C₁₉×D₁₆	D₄	1	2	yes	—
26	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
28	C₁₉×#107	—	2	1	no	—
29	C₁₉×#102	—	4	1	no	—
30	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₁₉×C₃₂	—	2	2	no	—
32	C₂×Q₈×C₁₉	—	4	2	no	—
33	C₂×D₄×C₁₉	—	4	1	no	—
34	C₂²×C₄×C₁₉	—	8	1	no	—
35	Q₁₆×C₁₉	—	4	2	no	—
36	Q₁₆×C₁₉	—	4	2	no	—
37	Q₁₆×C₁₉	—	8	2	no	—
38	D₈×C₁₉	—	2	2	no	—
39	D₈×C₁₉	—	4	1	no	—
40	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₄⋊C₄×C₁₉	—	4	1	no	—
43	C₄⋊C₄×C₁₉	—	8	1	no	—
44	C₄⋊C₄×C₁₉	—	8	1	no	—
45	C₂²⋊C₄×C₁₉	—	8	1	no	—
46	C₄²×C₁₉	D₈	1	1	yes	characteristic
47	C₁₆×C₁₉	—	2	1	no	—
48	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₁₆×C₁₉	#41	1	1	yes	characteristic
50	#13687	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂³×C₁₉	—	8	1	no	—
52	Q₈×C₁₉	—	8	2	no	—
53	Q₈×C₁₉	—	8	2	no	—
54	D₄×C₁₉	—	4	2	no	—
55	D₄×C₁₉	—	8	1	no	—
56	C₂×C₄×C₁₉	—	8	1	no	—
57	C₂×C₄×C₁₉	—	8	2	no	—
58	C₂×C₄×C₁₉	—	16	2	no	—
59	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
60	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	#121	1	1	yes	characteristic
64	C₈×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂×SD₆₄	C₂×C₁₉	1	2	yes	—
66	#2247	C₂×C₁₉	1	1	yes	characteristic, complemented
67	C₄×D₁₆	C₂×C₁₉	1	1	yes	characteristic
68	C₄⋊C₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
69	#1416	C₂×C₁₉	1	2	yes	complemented
70	C₂²×C₁₉	—	8	2	no	—
71	C₂²×C₁₉	—	16	1	no	—
72	C₂²×C₁₉	—	16	1	no	—
73	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	16	2	no	—
76	C₄×C₁₉	—	16	1	no	—
77	C₄×C₁₉	SD₆₄	1	2	yes	complemented
78	C₄×C₁₉	#459	1	1	yes	characteristic
79	C₄×C₁₉	#509	1	1	yes	characteristic
80	C₂×Q₃₂	—	2	1	no	—
81	C₂×Q₃₂	C₂²×C₁₉	1	2	yes	—
82	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
83	#494	—	2	1	no	—
84	C₄×D₈	—	2	1	no	—
85	SD₆₄	—	2	4	no	—
86	C₂×C₃₂	C₂²×C₁₉	1	2	yes	—
87	#366	C₂²×C₁₉	1	1	yes	characteristic
88	#357	—	2	1	no	—
89	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
90	C₂×C₁₉	—	16	2	no	—
91	C₂×C₁₉	#2206	1	1	yes	characteristic
92	C₂×C₁₉	C₂×SD₆₄	1	1	yes	characteristic
93	C₂×C₁₉	#2264	1	1	yes	characteristic
94	C₂×Q₁₆	—	2	2	no	—
95	C₂×Q₁₆	—	4	1	no	—
96	C₂×D₈	—	2	1	no	—
97	C₄⋊Q₈	—	4	1	no	—
98	C₄×D₄	—	4	1	no	—
99	Q₃₂	—	2	2	no	—
100	Q₃₂	—	2	2	no	—
101	Q₃₂	—	4	2	no	—
102	D₁₆	—	2	1	no	—
103	D₁₆	D₄×C₁₉	1	2	yes	—
104	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
105	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
106	#107	—	2	1	no	—
107	#102	—	4	1	no	—
108	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
109	C₃₂	—	2	2	no	—
110	C₁₉	#13687	1	1	yes	characteristic, direct product factor, Sylow
111	C₂×Q₈	—	4	2	no	—
112	C₂×D₄	—	4	1	no	—
113	C₂²×C₄	—	8	1	no	—
114	Q₁₆	—	4	2	no	—
115	Q₁₆	—	4	2	no	—
116	Q₁₆	—	8	2	no	—
117	D₈	—	2	2	no	—
118	D₈	—	4	1	no	—
119	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
120	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
121	C₄⋊C₄	—	4	1	no	—
122	C₄⋊C₄	—	8	1	no	—
123	C₄⋊C₄	—	8	1	no	—
124	C₂²⋊C₄	—	8	1	no	—
125	C₄²	D₈×C₁₉	1	1	yes	characteristic
126	C₁₆	—	2	1	no	—
127	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
128	C₁₆	#41×C₁₉	1	1	yes	characteristic
129	C₂³	—	8	1	no	—
130	Q₈	—	8	2	no	—
131	Q₈	—	8	2	no	—
132	D₄	—	4	2	no	—
133	D₄	—	8	1	no	—
134	C₂×C₄	—	8	1	no	—
135	C₂×C₄	—	8	2	no	—
136	C₂×C₄	—	16	2	no	—
137	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
138	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
139	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
140	C₈	—	2	1	no	—
141	C₈	C₁₉×#121	1	1	yes	characteristic
142	C₈	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
143	C₂²	—	8	2	no	—
144	C₂²	—	16	1	no	—
145	C₂²	—	16	1	no	—
146	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	16	2	no	—
149	C₄	—	16	1	no	—
150	C₄	C₁₉×SD₆₄	1	2	yes	complemented
151	C₄	C₁₉×#459	1	1	yes	characteristic
152	C₄	C₁₉×#509	1	1	yes	characteristic
153	C₂	—	16	2	no	—
154	C₂	C₁₉×#2206	1	1	yes	characteristic
155	C₂	C₂×C₁₉×SD₆₄	1	1	yes	characteristic
156	C₂	C₁₉×#2264	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×SD₆₄

C₂

yes

maximal

C₁₉×#2247

C₂

yes

maximal, characteristic, complemented

C₄×C₁₉×D₁₆

C₂

yes

maximal, characteristic

C₁₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic, complemented

C₁₉×#1416

C₂

yes

maximal, complemented

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

C₂²

yes

—

C₂×C₁₉×D₁₆

C₂²

yes

characteristic

C₁₉×#494

—

C₄×D₈×C₁₉

—

C₁₉×SD₆₄

—

C₂×C₁₉×C₃₂

C₂²

yes

—

C₁₉×#366

C₂²

yes

characteristic

C₁₉×#357

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₄×D₄×C₁₉

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×D₁₆

—

C₁₉×D₁₆

D₄

yes

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#102

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×D₄

yes

C₁₆×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×SD₆₄

C₂×C₁₉

yes

—

#2247

C₂×C₁₉

yes

characteristic, complemented

C₄×D₁₆

C₂×C₁₉

yes

characteristic

C₄⋊C₃₂

C₂×C₁₉

yes

characteristic, complemented

#1416

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

SD₆₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

—

C₂×Q₃₂

C₂²×C₁₉

yes

—

C₂×D₁₆

C₂²×C₁₉

yes

characteristic

#494

—

C₄×D₈

—

SD₆₄

—

C₂×C₃₂

C₂²×C₁₉

yes

—

#366

C₂²×C₁₉

yes

characteristic

#357

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#2206

yes

characteristic

C₂×C₁₉

C₂×SD₆₄

yes

characteristic

C₂×C₁₉

#2264

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

C₄×D₄

—

Q₃₂

—

100

Q₃₂

—

101

Q₃₂

—

102

D₁₆

—

103

D₁₆

D₄×C₁₉

yes

—

104

C₂×C₁₆

D₄×C₁₉

yes

characteristic

105

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

106

#107

—

107

#102

—

108

C₄×C₈

D₄×C₁₉

yes

characteristic

109

C₃₂

—

110

C₁₉

#13687

yes

characteristic, direct product factor, Sylow

111

C₂×Q₈

—

112

C₂×D₄

—

113

C₂²×C₄

—

114

Q₁₆

—

115

Q₁₆

—

116

Q₁₆

—

117

D₈

—

118

D₈

—

119

C₂×C₈

D₈×C₁₉

yes

characteristic

120

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

D₈×C₁₉

yes

characteristic

126

C₁₆

—

127

C₁₆

C₂×D₄×C₁₉

yes

characteristic

128

C₁₆

#41×C₁₉

yes

characteristic

129

C₂³

—

130

Q₈

—

131

Q₈

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

C₁₉×D₁₆

yes

characteristic

138

C₂×C₄

C₁₉×D₁₆

yes

characteristic

139

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

140

C₈

—

141

C₈

C₁₉×#121

yes

characteristic

142

C₈

C₁₉×AGL(1,ℤ/8)

yes

characteristic

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

C₁₉×SD₆₄

yes

complemented

151

C₄

C₁₉×#459

yes

characteristic

152

C₄

C₁₉×#509

yes

characteristic

153

C₂

—

154

C₂

C₁₉×#2206

yes

characteristic

155

C₂

C₂×C₁₉×SD₆₄

yes

characteristic

156

C₂

C₁₉×#2264

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

prime radical

C₂×C₁₉×D₁₆

C₂²

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2247	C₂	semidirect
4. C₁₉×C₄⋊C₃₂	C₂	semidirect
5. C₁₉×#1416	C₂	semidirect
50. #13687	C₁₉	direct (N × H)
66. #2247	C₂×C₁₉	semidirect
68. C₄⋊C₃₂	C₂×C₁₉	semidirect
69. #1416	C₂×C₁₉	semidirect
77. C₄×C₁₉	SD₆₄	semidirect
110. C₁₉	#13687	direct (N × H)
150. C₄	C₁₉×SD₆₄	semidirect

H ≅ G/N

type

2. C₁₉×#2247

C₂

semidirect

4. C₁₉×C₄⋊C₃₂

C₂

semidirect

5. C₁₉×#1416

C₂

semidirect

50. #13687

C₁₉

direct (N × H)

66. #2247

C₂×C₁₉

semidirect

68. C₄⋊C₃₂

C₂×C₁₉

semidirect

69. #1416

C₂×C₁₉

semidirect

77. C₄×C₁₉

SD₆₄

semidirect

110. C₁₉

#13687

direct (N × H)

150. C₄

C₁₉×SD₆₄

semidirect

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

subgroup	index
C₂×C₁₉×SD₆₄	2
C₁₉×#2247	2
C₄×C₁₉×D₁₆	2
C₁₉×C₄⋊C₃₂	2
C₁₉×#1416	2
#13687	19

subgroup

index

C₂×C₁₉×SD₆₄

C₁₉×#2247

C₄×C₁₉×D₁₆

C₁₉×C₄⋊C₃₂

C₁₉×#1416

#13687

Subgroups — C₁₉×#13687 #18019646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13687 #18019646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13687 #18019646