Group #18013084 — subgroups

Subgroups — C₁₉×#7125 #18013084

Order 4864.

182 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 70 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×#1946	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1375	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1281	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×M₃₂	—	2	1	no	—
5	C₁₉×#431	—	2	1	no	—
6	C₂×C₁₉×#108	C₄	1	1	yes	characteristic
7	C₁₉×#427	C₄	1	1	yes	characteristic
8	C₁₉×#424	—	2	1	no	—
9	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
10	C₁₉×#339	—	2	1	no	—
11	C₂×M₁₆×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₁₉×#117	—	2	1	no	—
15	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
16	C₁₉×M₃₂	—	4	1	no	—
17	C₁₉×M₃₂	—	4	1	no	—
18	C₂×C₁₆×C₁₉	—	2	2	no	—
19	C₁₉×#108	—	4	1	no	—
20	C₁₉×#107	—	2	1	no	—
21	C₁₉×#106	C₈	1	2	yes	complemented
22	C₁₉×C₄⋊C₈	—	4	1	no	—
23	C₁₉×C₄⋊C₈	—	4	1	no	—
24	C₁₉×C₄⋊C₈	—	4	1	no	—
25	C₁₉×C₂²⋊C₈	—	2	2	no	—
26	C₁₉×#97	—	4	1	no	—
27	C₄×C₈×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	M₁₆×C₁₉	—	4	1	no	—
31	M₁₆×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	—	2	1	no	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₂×C₈×C₁₉	—	4	1	no	—
38	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
39	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
40	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
41	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
42	C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂²⋊C₄×C₁₉	—	4	1	no	—
44	C₄²×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	4	1	no	—
46	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
47	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
48	C₁₆×C₁₉	—	4	2	no	—
49	#7125	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂³×C₁₉	#104	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	8	1	no	—
55	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	2	1	no	—
64	C₈×C₁₉	—	2	1	no	—
65	C₈×C₁₉	—	8	2	no	—
66	C₈×C₁₉	—	8	1	no	—
67	#1946	C₂×C₁₉	1	1	yes	characteristic
68	#1375	C₂×C₁₉	1	1	yes	characteristic
69	#1281	C₂×C₁₉	1	1	yes	characteristic
70	C₂²×C₁₉	—	4	1	no	—
71	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
72	C₂²×C₁₉	#328	1	1	yes	characteristic
73	C₂²×C₁₉	#330	1	1	yes	characteristic
74	C₄×C₁₉	—	4	1	no	—
75	C₄×C₁₉	—	4	1	no	—
76	C₄×C₁₉	—	8	2	no	—
77	C₄×C₁₉	#324	1	1	yes	characteristic
78	C₄×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
79	C₄×C₁₉	#327	1	1	yes	characteristic
80	C₄×C₁₉	#332	1	1	yes	characteristic
81	C₂×M₃₂	—	2	1	no	—
82	#431	—	2	1	no	—
83	C₂×#108	C₄×C₁₉	1	1	yes	characteristic
84	#427	C₄×C₁₉	1	1	yes	characteristic
85	#424	—	2	1	no	—
86	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
87	#339	—	2	1	no	—
88	C₂×C₁₉	—	2	1	no	—
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	—	2	1	no	—
91	C₂×C₁₉	#1271	1	1	yes	characteristic
92	C₂×M₁₆	—	2	1	no	—
93	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
94	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
95	#117	—	2	1	no	—
96	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
97	M₃₂	—	4	1	no	—
98	M₃₂	—	4	1	no	—
99	C₂×C₁₆	—	2	2	no	—
100	#108	—	4	1	no	—
101	#107	—	2	1	no	—
102	#106	C₈×C₁₉	1	2	yes	complemented
103	C₄⋊C₈	—	4	1	no	—
104	C₄⋊C₈	—	4	1	no	—
105	C₄⋊C₈	—	4	1	no	—
106	C₂²⋊C₈	—	2	2	no	—
107	#97	—	4	1	no	—
108	C₄×C₈	—	4	1	no	—
109	C₁₉	#7125	1	1	yes	characteristic, direct product factor, Sylow
110	C₂²×C₄	—	2	1	no	—
111	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
112	M₁₆	—	4	1	no	—
113	M₁₆	—	4	1	no	—
114	C₂×C₈	—	2	1	no	—
115	C₂×C₈	—	2	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	2	1	no	—
118	C₂×C₈	—	4	2	no	—
119	C₂×C₈	—	4	1	no	—
120	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
121	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
122	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
123	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
124	C₄⋊C₄	—	2	2	no	—
125	C₂²⋊C₄	—	4	1	no	—
126	C₄²	—	2	1	no	—
127	C₄²	—	4	1	no	—
128	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
129	C₄²	Q₁₆×C₁₉	1	1	yes	characteristic
130	C₁₆	—	4	2	no	—
131	C₂³	C₁₉×#104	1	1	yes	characteristic
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	8	1	no	—
136	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
137	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
138	C₂×C₄	C₁₉×#101	1	1	yes	characteristic
139	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
140	C₂×C₄	C₁₉×#103	1	1	yes	characteristic
141	C₂×C₄	C₁₉×#104	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	—	2	1	no	—
144	C₈	—	2	1	no	—
145	C₈	—	2	1	no	—
146	C₈	—	8	2	no	—
147	C₈	—	8	1	no	—
148	C₂²	—	4	1	no	—
149	C₂²	C₁₉×D₄⋊C₈	1	1	yes	characteristic
150	C₂²	C₁₉×#328	1	1	yes	characteristic
151	C₂²	C₁₉×#330	1	1	yes	characteristic
152	C₄	—	4	1	no	—
153	C₄	—	4	1	no	—
154	C₄	—	8	2	no	—
155	C₄	C₁₉×#324	1	1	yes	characteristic
156	C₄	C₁₉×Q₈⋊C₈	1	1	yes	characteristic
157	C₄	C₁₉×#327	1	1	yes	characteristic
158	C₄	C₁₉×#332	1	1	yes	characteristic
159	C₂	—	2	1	no	—
160	C₂	—	2	1	no	—
161	C₂	—	2	1	no	—
162	C₂	C₁₉×#1271	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1946

C₂

yes

maximal, characteristic

C₁₉×#1375

C₂

yes

maximal, characteristic

C₁₉×#1281

C₂

yes

maximal, characteristic

C₂×C₁₉×M₃₂

—

C₁₉×#431

—

C₂×C₁₉×#108

C₄

yes

characteristic

C₁₉×#427

C₄

yes

characteristic

C₁₉×#424

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#339

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×#117

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#108

—

C₁₉×#107

—

C₁₉×#106

C₈

yes

complemented

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₁₆×C₁₉

—

#7125

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#104

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1946

C₂×C₁₉

yes

characteristic

#1375

C₂×C₁₉

yes

characteristic

#1281

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

D₄⋊C₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#324

yes

characteristic

C₄×C₁₉

Q₈⋊C₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×M₃₂

—

#431

—

C₂×#108

C₄×C₁₉

yes

characteristic

#427

C₄×C₁₉

yes

characteristic

#424

—

C₂×#97

C₂²×C₁₉

yes

characteristic

#339

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1271

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₈

D₄×C₁₉

yes

characteristic

#117

—

C₂×C₄²

D₄×C₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

#108

—

101

#107

—

102

#106

C₈×C₁₉

yes

complemented

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₄⋊C₈

—

106

C₂²⋊C₈

—

107

#97

—

108

C₄×C₈

—

109

C₁₉

#7125

yes

characteristic, direct product factor, Sylow

110

C₂²×C₄

—

111

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

112

M₁₆

—

113

M₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

C₂×C₈×C₁₉

yes

characteristic

121

C₂×C₈

M₁₆×C₁₉

yes

characteristic

122

C₂×C₈

D₈×C₁₉

yes

characteristic

123

C₂×C₈

SD₁₆×C₁₉

yes

characteristic

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₄²

—

127

C₄²

—

128

C₄²

SD₁₆×C₁₉

yes

characteristic

129

C₄²

Q₁₆×C₁₉

yes

characteristic

130

C₁₆

—

131

C₂³

C₁₉×#104

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

137

C₂×C₄

C₁₉×#99

yes

characteristic

138

C₂×C₄

C₁₉×#101

yes

characteristic

139

C₂×C₄

C₁₉×#102

yes

characteristic

140

C₂×C₄

C₁₉×#103

yes

characteristic

141

C₂×C₄

C₁₉×#104

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

—

148

C₂²

—

149

C₂²

C₁₉×D₄⋊C₈

yes

characteristic

150

C₂²

C₁₉×#328

yes

characteristic

151

C₂²

C₁₉×#330

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

C₁₉×#324

yes

characteristic

156

C₄

C₁₉×Q₈⋊C₈

yes

characteristic

157

C₄

C₁₉×#327

yes

characteristic

158

C₄

C₁₉×#332

yes

characteristic

159

C₂

—

160

C₂

—

161

C₂

—

162

C₂

C₁₉×#1271

yes

characteristic

	subgroup	G/H
center	C₄×C₁₉	#327
commutator	C₂×C₈	C₂×C₈×C₁₉
Frattini, cosocle	C₂×#97	C₂²×C₁₉
socle	C₂×C₁₉	#1271
prime radical	C₂³×C₁₉	#104
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

subgroup

G/H

center

C₄×C₁₉

#327

commutator

C₂×C₈

C₂×C₈×C₁₉

Frattini, cosocle

C₂×#97

C₂²×C₁₉

C₂×C₁₉

C₂³×C₁₉

G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

N	H ≅ G/N	type
21. C₁₉×#106	C₈	semidirect
49. #7125	C₁₉	direct (N × H)
102. #106	C₈×C₁₉	semidirect
109. C₁₉	#7125	direct (N × H)

H ≅ G/N

type

21. C₁₉×#106

C₈

semidirect

49. #7125

C₁₉

direct (N × H)

102. #106

C₈×C₁₉

semidirect

109. C₁₉

#7125

direct (N × H)

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

subgroup	index
C₁₉×#1946	2
C₁₉×#1375	2
C₁₉×#1281	2
#7125	19

subgroup

index

C₁₉×#1946

C₁₉×#1375

C₁₉×#1281

#7125

Subgroups — C₁₉×#7125 #18013084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7125 #18013084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7125 #18013084