Group #18018395 — subgroups

Subgroups — C₁₉×#12436 #18018395

Order 4864.

234 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2246	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2213	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1373	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1357	C₂	1	2	yes	maximal, complemented
6	C₁₉×#509	—	2	2	no	—
7	C₂×C₁₉×D₁₆	—	2	1	no	—
8	C₂×C₁₉×D₁₆	—	2	1	no	—
9	C₁₉×#504	—	2	1	no	—
10	C₁₉×#493	C₂²	1	2	yes	—
11	C₁₉×#443	C₂²	1	1	yes	characteristic
12	C₁₉×#364	C₂²	1	1	yes	characteristic
13	C₁₉×#364	C₂²	1	2	yes	—
14	C₁₉×#361	—	2	2	no	—
15	C₁₉×#350	—	2	1	no	—
16	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#135	D₄	1	1	yes	characteristic
18	C₂×D₈×C₁₉	—	2	2	no	—
19	C₂×D₈×C₁₉	—	2	2	no	—
20	C₁₉×#131	—	2	1	no	—
21	C₁₉×#127	—	2	2	no	—
22	C₁₉×SD₃₂	—	4	2	no	—
23	C₁₉×D₁₆	—	4	2	no	—
24	C₁₉×D₁₆	—	4	2	no	—
25	C₁₉×D₁₆	—	4	1	no	—
26	C₁₉×D₁₆	—	4	1	no	—
27	C₁₉×M₃₂	—	2	1	no	—
28	C₁₉×M₃₂	—	2	2	no	—
29	C₁₉×M₃₂	—	4	1	no	—
30	C₂×C₁₆×C₁₉	—	4	1	no	—
31	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
33	C₁₉×#108	D₄	1	1	yes	characteristic
34	C₁₉×#104	—	2	1	no	—
35	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
36	#41×C₁₉	—	2	1	no	—
37	C₂×D₄×C₁₉	—	4	2	no	—
38	C₂×D₄×C₁₉	—	8	2	no	—
39	Q₁₆×C₁₉	D₈	1	1	yes	characteristic
40	SD₁₆×C₁₉	—	2	1	no	—
41	D₈×C₁₉	—	4	2	no	—
42	D₈×C₁₉	—	4	2	no	—
43	D₈×C₁₉	—	4	2	no	—
44	D₈×C₁₉	—	4	2	no	—
45	D₈×C₁₉	D₈	1	1	yes	characteristic
46	M₁₆×C₁₉	—	2	1	no	—
47	M₁₆×C₁₉	—	4	1	no	—
48	C₂×C₈×C₁₉	—	4	1	no	—
49	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₄²×C₁₉	#41	1	1	yes	characteristic
52	C₁₆×C₁₉	—	2	1	no	—
53	C₁₆×C₁₉	—	4	1	no	—
54	C₁₆×C₁₉	—	4	2	no	—
55	C₁₆×C₁₉	D₈	1	1	yes	characteristic
56	C₁₆×C₁₉	D₈	1	1	yes	characteristic
57	#12436	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂³×C₁₉	—	8	2	no	—
59	Q₈×C₁₉	—	2	1	no	—
60	D₄×C₁₉	—	2	1	no	—
61	D₄×C₁₉	—	4	1	no	—
62	D₄×C₁₉	—	8	2	no	—
63	D₄×C₁₉	—	8	2	no	—
64	D₄×C₁₉	—	16	4	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	4	1	no	—
67	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
68	C₈×C₁₉	—	4	1	no	—
69	C₈×C₁₉	C₂×D₈	1	1	yes	characteristic
70	C₈×C₁₉	C₂×D₈	1	1	yes	characteristic
71	C₈×C₁₉	#135	1	1	yes	characteristic
72	C₈×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
73	#2246	C₂×C₁₉	1	1	yes	characteristic, complemented
74	#2213	C₂×C₁₉	1	2	yes	complemented
75	#2170	C₂×C₁₉	1	1	yes	characteristic, complemented
76	#1373	C₂×C₁₉	1	1	yes	characteristic, complemented
77	#1357	C₂×C₁₉	1	2	yes	complemented
78	C₂²×C₁₉	—	4	1	no	—
79	C₂²×C₁₉	—	16	4	no	—
80	C₂²×C₁₉	—	16	2	no	—
81	C₂²×C₁₉	#472	1	1	yes	characteristic
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	4	1	no	—
84	C₄×C₁₉	#459	1	1	yes	characteristic
85	C₄×C₁₉	#466	1	1	yes	characteristic
86	#509	—	2	2	no	—
87	C₂×D₁₆	—	2	1	no	—
88	C₂×D₁₆	—	2	1	no	—
89	#504	—	2	1	no	—
90	#493	C₂²×C₁₉	1	2	yes	—
91	#443	C₂²×C₁₉	1	1	yes	characteristic
92	#364	C₂²×C₁₉	1	1	yes	characteristic
93	#364	C₂²×C₁₉	1	2	yes	—
94	#361	—	2	2	no	—
95	#350	—	2	1	no	—
96	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
97	C₂×C₁₉	—	2	1	no	—
98	C₂×C₁₉	—	8	1	no	—
99	C₂×C₁₉	—	32	2	no	—
100	C₂×C₁₉	#1667	1	1	yes	characteristic
101	#135	D₄×C₁₉	1	1	yes	characteristic
102	C₂×D₈	—	2	2	no	—
103	C₂×D₈	—	2	2	no	—
104	#131	—	2	1	no	—
105	#127	—	2	2	no	—
106	SD₃₂	—	4	2	no	—
107	D₁₆	—	4	2	no	—
108	D₁₆	—	4	2	no	—
109	D₁₆	—	4	1	no	—
110	D₁₆	—	4	1	no	—
111	M₃₂	—	2	1	no	—
112	M₃₂	—	2	2	no	—
113	M₃₂	—	4	1	no	—
114	C₂×C₁₆	—	4	1	no	—
115	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
116	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
117	#108	D₄×C₁₉	1	1	yes	characteristic
118	#104	—	2	1	no	—
119	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
120	C₁₉	#12436	1	1	yes	characteristic, direct product factor, Sylow
121	#41	—	2	1	no	—
122	C₂×D₄	—	4	2	no	—
123	C₂×D₄	—	8	2	no	—
124	Q₁₆	D₈×C₁₉	1	1	yes	characteristic
125	SD₁₆	—	2	1	no	—
126	D₈	—	4	2	no	—
127	D₈	—	4	2	no	—
128	D₈	—	4	2	no	—
129	D₈	—	4	2	no	—
130	D₈	D₈×C₁₉	1	1	yes	characteristic
131	M₁₆	—	2	1	no	—
132	M₁₆	—	4	1	no	—
133	C₂×C₈	—	4	1	no	—
134	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
135	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
136	C₄²	#41×C₁₉	1	1	yes	characteristic
137	C₁₆	—	2	1	no	—
138	C₁₆	—	4	1	no	—
139	C₁₆	—	4	2	no	—
140	C₁₆	D₈×C₁₉	1	1	yes	characteristic
141	C₁₆	D₈×C₁₉	1	1	yes	characteristic
142	C₂³	—	8	2	no	—
143	Q₈	—	2	1	no	—
144	D₄	—	2	1	no	—
145	D₄	—	4	1	no	—
146	D₄	—	8	2	no	—
147	D₄	—	8	2	no	—
148	D₄	—	16	4	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
152	C₈	—	4	1	no	—
153	C₈	C₂×D₈×C₁₉	1	1	yes	characteristic
154	C₈	C₂×D₈×C₁₉	1	1	yes	characteristic
155	C₈	C₁₉×#135	1	1	yes	characteristic
156	C₈	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂²	—	4	1	no	—
158	C₂²	—	16	4	no	—
159	C₂²	—	16	2	no	—
160	C₂²	C₁₉×#472	1	1	yes	characteristic
161	C₄	—	2	2	no	—
162	C₄	—	4	1	no	—
163	C₄	C₁₉×#459	1	1	yes	characteristic
164	C₄	C₁₉×#466	1	1	yes	characteristic
165	C₂	—	2	1	no	—
166	C₂	—	8	1	no	—
167	C₂	—	32	2	no	—
168	C₂	C₁₉×#1667	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2246

C₂

yes

maximal, characteristic, complemented

C₁₉×#2213

C₂

yes

maximal, complemented

C₁₉×#2170

C₂

yes

maximal, characteristic, complemented

C₁₉×#1373

C₂

yes

maximal, characteristic, complemented

C₁₉×#1357

C₂

yes

maximal, complemented

C₁₉×#509

—

C₂×C₁₉×D₁₆

—

C₂×C₁₉×D₁₆

—

C₁₉×#504

—

C₁₉×#493

C₂²

yes

—

C₁₉×#443

C₂²

yes

characteristic

C₁₉×#364

C₂²

yes

characteristic

C₁₉×#364

C₂²

yes

—

C₁₉×#361

—

C₁₉×#350

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#135

D₄

yes

characteristic

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×#131

—

C₁₉×#127

—

C₁₉×SD₃₂

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#108

D₄

yes

characteristic

C₁₉×#104

—

C₄×C₈×C₁₉

C₂³

yes

characteristic

#41×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

D₈

yes

characteristic

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

D₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

D₈

yes

characteristic

#12436

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

C₂×D₈

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic, complemented

#2213

C₂×C₁₉

yes

complemented

#2170

C₂×C₁₉

yes

characteristic, complemented

#1373

C₂×C₁₉

yes

characteristic, complemented

#1357

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#472

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×D₁₆

—

C₂×D₁₆

—

#504

—

#493

C₂²×C₁₉

yes

—

#443

C₂²×C₁₉

yes

characteristic

#364

C₂²×C₁₉

yes

characteristic

#364

C₂²×C₁₉

yes

—

#361

—

#350

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

100

C₂×C₁₉

#1667

yes

characteristic

101

#135

D₄×C₁₉

yes

characteristic

102

C₂×D₈

—

103

C₂×D₈

—

104

#131

—

105

#127

—

106

SD₃₂

—

107

D₁₆

—

108

D₁₆

—

109

D₁₆

—

110

D₁₆

—

111

M₃₂

—

112

M₃₂

—

113

M₃₂

—

114

C₂×C₁₆

—

115

C₂×C₁₆

D₄×C₁₉

yes

characteristic

116

C₂×C₁₆

D₄×C₁₉

yes

characteristic

117

#108

D₄×C₁₉

yes

characteristic

118

#104

—

119

C₄×C₈

C₂³×C₁₉

yes

characteristic

120

C₁₉

#12436

yes

characteristic, direct product factor, Sylow

121

#41

—

122

C₂×D₄

—

123

C₂×D₄

—

124

Q₁₆

D₈×C₁₉

yes

characteristic

125

SD₁₆

—

126

D₈

—

127

D₈

—

128

D₈

—

129

D₈

—

130

D₈

D₈×C₁₉

yes

characteristic

131

M₁₆

—

132

M₁₆

—

133

C₂×C₈

—

134

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

135

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

136

C₄²

#41×C₁₉

yes

characteristic

137

C₁₆

—

138

C₁₆

—

139

C₁₆

—

140

C₁₆

D₈×C₁₉

yes

characteristic

141

C₁₆

D₈×C₁₉

yes

characteristic

142

C₂³

—

143

Q₈

—

144

D₄

—

145

D₄

—

146

D₄

—

147

D₄

—

148

D₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

C₁₉×#121

yes

characteristic

152

C₈

—

153

C₈

C₂×D₈×C₁₉

yes

characteristic

154

C₈

C₂×D₈×C₁₉

yes

characteristic

155

C₈

C₁₉×#135

yes

characteristic

156

C₈

C₁₉×AGL(1,ℤ/8)

yes

characteristic

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

C₁₉×#472

yes

characteristic

161

C₄

—

162

C₄

—

163

C₄

C₁₉×#459

yes

characteristic

164

C₄

C₁₉×#466

yes

characteristic

165

C₂

—

166

C₂

—

167

C₂

—

168

C₂

C₁₉×#1667

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#1667

commutator, Frattini, cosocle

C₄×C₈

C₂³×C₁₉

LCS

G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#2246	C₂	semidirect
2. C₁₉×#2213	C₂	semidirect
3. C₁₉×#2170	C₂	semidirect
4. C₁₉×#1373	C₂	semidirect
5. C₁₉×#1357	C₂	semidirect
57. #12436	C₁₉	direct (N × H)
73. #2246	C₂×C₁₉	semidirect
74. #2213	C₂×C₁₉	semidirect
75. #2170	C₂×C₁₉	semidirect
76. #1373	C₂×C₁₉	semidirect
77. #1357	C₂×C₁₉	semidirect
120. C₁₉	#12436	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2246

C₂

semidirect

2. C₁₉×#2213

C₂

semidirect

3. C₁₉×#2170

C₂

semidirect

4. C₁₉×#1373

C₂

semidirect

5. C₁₉×#1357

C₂

semidirect

57. #12436

C₁₉

direct (N × H)

73. #2246

C₂×C₁₉

semidirect

74. #2213

C₂×C₁₉

semidirect

75. #2170

C₂×C₁₉

semidirect

76. #1373

C₂×C₁₉

semidirect

77. #1357

C₂×C₁₉

semidirect

120. C₁₉

#12436

direct (N × H)

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

subgroup	index
C₁₉×#2246	2
C₁₉×#2213	2
C₁₉×#2170	2
C₁₉×#1373	2
C₁₉×#1357	2
#12436	19

subgroup

index

C₁₉×#2246

C₁₉×#2213

C₁₉×#2170

C₁₉×#1373

C₁₉×#1357

#12436

Subgroups — C₁₉×#12436 #18018395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12436 #18018395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12436 #18018395