Group #18018393 — subgroups

Subgroups — C₁₉×#12434 #18018393

Order 4864.

230 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2247	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2169	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1669	C₂	1	2	yes	maximal
4	C₁₉×#1372	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1362	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×Q₃₂	—	2	1	no	—
7	C₂×C₁₉×Q₃₂	—	2	1	no	—
8	C₂×C₁₉×M₃₂	—	2	1	no	—
9	C₁₉×#494	C₂²	1	2	yes	—
10	C₁₉×#474	—	2	2	no	—
11	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
14	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#335	C₂²	1	2	yes	—
16	C₁₉×#332	—	2	2	no	—
17	C₂×Q₁₆×C₁₉	—	2	2	no	—
18	C₂×Q₁₆×C₁₉	—	2	2	no	—
19	C₂²×C₈×C₁₉	—	2	1	no	—
20	C₁₉×C₄⋊Q₈	—	2	2	no	—
21	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₁₉×Q₃₂	—	4	2	no	—
23	C₁₉×Q₃₂	—	4	2	no	—
24	C₁₉×M₃₂	—	4	2	no	—
25	C₂×C₁₆×C₁₉	—	2	1	no	—
26	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
28	C₁₉×#107	—	4	2	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
31	C₁₉×#102	—	4	2	no	—
32	C₁₉×C₂²⋊C₈	—	2	1	no	—
33	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×Q₈×C₁₉	—	4	2	no	—
35	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	Q₁₆×C₁₉	—	4	2	no	—
38	Q₁₆×C₁₉	—	4	2	no	—
39	Q₁₆×C₁₉	—	8	2	no	—
40	C₂×C₈×C₁₉	—	2	1	no	—
41	C₂×C₈×C₁₉	—	4	1	no	—
42	C₂×C₈×C₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	—	4	2	no	—
44	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
46	C₄⋊C₄×C₁₉	—	4	2	no	—
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
49	C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₁₆×C₁₉	—	2	1	no	—
52	C₁₆×C₁₉	—	4	1	no	—
53	C₁₆×C₁₉	D₈	1	2	yes	—
54	#12434	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂³×C₁₉	—	2	1	no	—
56	Q₈×C₁₉	—	8	2	no	—
57	Q₈×C₁₉	—	8	2	no	—
58	D₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	—	8	2	no	—
63	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
66	C₈×C₁₉	—	2	1	no	—
67	C₈×C₁₉	—	4	1	no	—
68	C₈×C₁₉	—	8	2	no	—
69	C₈×C₁₉	C₂×D₈	1	1	yes	characteristic
70	C₈×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
71	#2247	C₂×C₁₉	1	1	yes	characteristic, complemented
72	#2169	C₂×C₁₉	1	1	yes	characteristic
73	#1669	C₂×C₁₉	1	2	yes	—
74	#1372	C₂×C₁₉	1	1	yes	characteristic, complemented
75	#1362	C₂×C₁₉	1	2	yes	complemented
76	C₂²×C₁₉	—	4	1	no	—
77	C₂²×C₁₉	—	4	1	no	—
78	C₂²×C₁₉	—	4	1	no	—
79	C₂²×C₁₉	#466	1	1	yes	characteristic
80	C₄×C₁₉	—	2	1	no	—
81	C₄×C₁₉	—	4	1	no	—
82	C₄×C₁₉	—	16	2	no	—
83	C₄×C₁₉	#459	1	1	yes	characteristic
84	C₄×C₁₉	#472	1	1	yes	characteristic
85	C₄×C₁₉	#510	1	2	yes	—
86	C₂×Q₃₂	—	2	1	no	—
87	C₂×Q₃₂	—	2	1	no	—
88	C₂×M₃₂	—	2	1	no	—
89	#494	C₂²×C₁₉	1	2	yes	—
90	#474	—	2	2	no	—
91	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
92	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
93	C₂²⋊C₁₆	—	2	1	no	—
94	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
95	#335	C₂²×C₁₉	1	2	yes	—
96	#332	—	2	2	no	—
97	C₂×C₁₉	—	8	1	no	—
98	C₂×C₁₉	#1667	1	1	yes	characteristic
99	C₂×C₁₉	#2219	1	1	yes	characteristic
100	C₂×C₁₉	#2222	1	1	yes	characteristic
101	C₂×Q₁₆	—	2	2	no	—
102	C₂×Q₁₆	—	2	2	no	—
103	C₂²×C₈	—	2	1	no	—
104	C₄⋊Q₈	—	2	2	no	—
105	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
106	Q₃₂	—	4	2	no	—
107	Q₃₂	—	4	2	no	—
108	M₃₂	—	4	2	no	—
109	C₂×C₁₆	—	2	1	no	—
110	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
111	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
112	#107	—	4	2	no	—
113	C₄⋊C₈	—	2	2	no	—
114	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
115	#102	—	4	2	no	—
116	C₂²⋊C₈	—	2	1	no	—
117	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
118	C₁₉	#12434	1	1	yes	characteristic, direct product factor, Sylow
119	C₂×Q₈	—	4	2	no	—
120	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
121	C₂²×C₄	—	2	1	no	—
122	Q₁₆	—	4	2	no	—
123	Q₁₆	—	4	2	no	—
124	Q₁₆	—	8	2	no	—
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	4	1	no	—
127	C₂×C₈	—	4	1	no	—
128	C₂×C₈	—	4	2	no	—
129	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
130	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
131	C₄⋊C₄	—	4	2	no	—
132	C₄⋊C₄	—	4	2	no	—
133	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
134	C₂²⋊C₄	—	2	1	no	—
135	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
136	C₁₆	—	2	1	no	—
137	C₁₆	—	4	1	no	—
138	C₁₆	D₈×C₁₉	1	2	yes	—
139	C₂³	—	2	1	no	—
140	Q₈	—	8	2	no	—
141	Q₈	—	8	2	no	—
142	D₄	—	2	2	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	4	1	no	—
145	C₂×C₄	—	4	1	no	—
146	C₂×C₄	—	8	2	no	—
147	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
148	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
149	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
150	C₈	—	2	1	no	—
151	C₈	—	4	1	no	—
152	C₈	—	8	2	no	—
153	C₈	C₂×D₈×C₁₉	1	1	yes	characteristic
154	C₈	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂²	—	4	1	no	—
156	C₂²	—	4	1	no	—
157	C₂²	—	4	1	no	—
158	C₂²	C₁₉×#466	1	1	yes	characteristic
159	C₄	—	2	1	no	—
160	C₄	—	4	1	no	—
161	C₄	—	16	2	no	—
162	C₄	C₁₉×#459	1	1	yes	characteristic
163	C₄	C₁₉×#472	1	1	yes	characteristic
164	C₄	C₁₉×#510	1	2	yes	—
165	C₂	—	8	1	no	—
166	C₂	C₁₉×#1667	1	1	yes	characteristic
167	C₂	C₁₉×#2219	1	1	yes	characteristic
168	C₂	C₁₉×#2222	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2247

C₂

yes

maximal, characteristic, complemented

C₁₉×#2169

C₂

yes

maximal, characteristic

C₁₉×#1669

C₂

yes

maximal

C₁₉×#1372

C₂

yes

maximal, characteristic, complemented

C₁₉×#1362

C₂

yes

maximal, complemented

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×M₃₂

—

C₁₉×#494

C₂²

yes

—

C₁₉×#474

—

C₈×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#335

C₂²

yes

—

C₁₉×#332

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₄×D₄×C₁₉

D₄

yes

characteristic

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

characteristic

C₁₉×#102

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₂×C₈×C₁₉

#41

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₈

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

—

#12434

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₈

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic, complemented

#2169

C₂×C₁₉

yes

characteristic

#1669

C₂×C₁₉

yes

—

#1372

C₂×C₁₉

yes

characteristic, complemented

#1362

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#466

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×M₃₂

—

#494

C₂²×C₁₉

yes

—

#474

—

C₈×D₄

C₂²×C₁₉

yes

characteristic

C₄⋊C₁₆

C₂²×C₁₉

yes

characteristic

C₂²⋊C₁₆

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

#335

C₂²×C₁₉

yes

—

#332

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

100

C₂×C₁₉

#2222

yes

characteristic

101

C₂×Q₁₆

—

102

C₂×Q₁₆

—

103

C₂²×C₈

—

104

C₄⋊Q₈

—

105

C₄×D₄

D₄×C₁₉

yes

characteristic

106

Q₃₂

—

107

Q₃₂

—

108

M₃₂

—

109

C₂×C₁₆

—

110

C₂×C₁₆

D₄×C₁₉

yes

characteristic

111

C₂×C₁₆

D₄×C₁₉

yes

characteristic

112

#107

—

113

C₄⋊C₈

—

114

C₄⋊C₈

D₄×C₁₉

yes

characteristic

115

#102

—

116

C₂²⋊C₈

—

117

C₄×C₈

C₂³×C₁₉

yes

characteristic

118

C₁₉

#12434

yes

characteristic, direct product factor, Sylow

119

C₂×Q₈

—

120

C₂×D₄

D₈×C₁₉

yes

characteristic

121

C₂²×C₄

—

122

Q₁₆

—

123

Q₁₆

—

124

Q₁₆

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

130

C₂×C₈

#41×C₁₉

yes

characteristic

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

D₈×C₁₉

yes

characteristic

134

C₂²⋊C₄

—

135

C₄²

C₂×D₄×C₁₉

yes

characteristic

136

C₁₆

—

137

C₁₆

—

138

C₁₆

D₈×C₁₉

yes

—

139

C₂³

—

140

Q₈

—

141

Q₈

—

142

D₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

C₁₉×#121

yes

characteristic

148

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

149

C₂×C₄

C₁₉×#135

yes

characteristic

150

C₈

—

151

C₈

—

152

C₈

—

153

C₈

C₂×D₈×C₁₉

yes

characteristic

154

C₈

C₁₉×AGL(1,ℤ/8)

yes

characteristic

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

C₁₉×#466

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

C₁₉×#459

yes

characteristic

163

C₄

C₁₉×#472

yes

characteristic

164

C₄

C₁₉×#510

yes

—

165

C₂

—

166

C₂

C₁₉×#1667

yes

characteristic

167

C₂

C₁₉×#2219

yes

characteristic

168

C₂

C₁₉×#2222

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#466

commutator, Frattini, cosocle

C₄×C₈

C₂³×C₁₉

prime radical

C₂×D₄×C₁₉

D₈

LCS

G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#2247	C₂	semidirect
4. C₁₉×#1372	C₂	semidirect
5. C₁₉×#1362	C₂	semidirect
54. #12434	C₁₉	direct (N × H)
71. #2247	C₂×C₁₉	semidirect
74. #1372	C₂×C₁₉	semidirect
75. #1362	C₂×C₁₉	semidirect
118. C₁₉	#12434	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2247

C₂

semidirect

4. C₁₉×#1372

C₂

semidirect

5. C₁₉×#1362

C₂

semidirect

54. #12434

C₁₉

direct (N × H)

71. #2247

C₂×C₁₉

semidirect

74. #1372

C₂×C₁₉

semidirect

75. #1362

C₂×C₁₉

semidirect

118. C₁₉

#12434

direct (N × H)

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

subgroup	index
C₁₉×#2247	2
C₁₉×#2169	2
C₁₉×#1669	2
C₁₉×#1372	2
C₁₉×#1362	2
#12434	19

subgroup

index

C₁₉×#2247

C₁₉×#2169

C₁₉×#1669

C₁₉×#1372

C₁₉×#1362

#12434

Subgroups — C₁₉×#12434 #18018393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12434 #18018393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12434 #18018393