Group #14571954 — subgroups

Subgroups — #14571954

Order 2432.

582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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	C₂²×C₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926432	C₂	1	4	yes	maximal, complemented
3	#11926425	C₂	1	4	yes	maximal, complemented
4	#11926424	C₂	1	2	yes	maximal
5	#11926416	C₂	1	2	yes	maximal, complemented
6	#11926407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#123	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×Dic₁₉	C₂²	1	2	yes	—
11	C₁₉×#123	—	2	4	no	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
17	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
18	C₂×C₄×Dic₁₉	—	2	4	no	—
19	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₁₉⋊#95	C₂²	1	4	yes	—
22	C₁₉⋊#95	C₂²	1	4	yes	—
23	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
24	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×D₄×C₁₉	—	2	2	no	—
26	C₂×D₄×C₁₉	—	2	4	no	—
27	C₂²×C₄×C₁₉	—	2	4	no	—
28	C₂²×C₄×C₁₉	D₄	1	4	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
32	C₂²×Dic₁₉	—	2	4	no	—
33	C₂²×Dic₁₉	—	2	8	no	—
34	C₂²×Dic₁₉	C₂³	1	4	yes	—
35	C₂²×Dic₁₉	C₂³	1	4	yes	—
36	C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₂²⋊C₄×C₁₉	—	2	2	no	—
38	C₂²⋊C₄×C₁₉	—	2	4	no	—
39	C₂²⋊Dic₁₉	—	2	4	no	—
40	C₂²⋊Dic₁₉	—	2	8	no	—
41	Dic₁₉⋊C₄	—	2	8	no	—
42	C₄×Dic₁₉	—	2	8	no	—
43	C₂³×C₁₉	—	2	4	no	—
44	C₂³×C₁₉	—	2	1	no	—
45	C₂³×C₁₉	—	2	4	no	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	C₂×D₄	1	2	yes	—
48	C₂³×C₁₉	#41	1	4	yes	—
49	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
50	D₄×C₁₉	—	4	4	no	—
51	C₂×C₄×C₁₉	—	2	8	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	4	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
58	C₂×Dic₁₉	—	2	16	no	—
59	C₂×Dic₁₉	—	2	4	no	—
60	C₂×Dic₁₉	—	2	4	no	—
61	C₂×Dic₁₉	—	2	4	no	—
62	C₂×Dic₁₉	—	2	4	no	—
63	C₂×Dic₁₉	—	2	4	no	—
64	C₂×Dic₁₉	#41	1	8	yes	—
65	#2853	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	2	4	no	—
67	C₂²×C₁₉	—	2	8	no	—
68	C₂²×C₁₉	—	4	1	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	4	4	no	—
71	C₂²×C₁₉	#123	1	4	yes	—
72	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
73	C₂²×C₁₉	C₂×#41	1	2	yes	—
74	C₂²×C₁₉	C₂×#41	1	4	yes	—
75	C₄×C₁₉	—	2	4	no	—
76	C₄×C₁₉	—	4	1	no	—
77	C₄×C₁₉	—	4	2	no	—
78	Dic₁₉	—	2	8	no	—
79	Dic₁₉	—	4	4	no	—
80	C₂×#123	D₁₉	1	1	yes	characteristic
81	C₂²×C₄²	—	19	1	no	—
82	#388	—	19	4	no	—
83	#387	—	19	4	no	—
84	#386	—	19	2	no	—
85	#385	—	19	2	no	—
86	#381	—	19	1	no	—
87	C₂×C₁₉	—	2	4	no	—
88	C₂×C₁₉	—	8	1	no	—
89	C₂×C₁₉	C₂×#123	1	1	yes	characteristic
90	C₂×C₁₉	#525	1	2	yes	—
91	C₂×C₁₉	#529	1	4	yes	—
92	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
93	C₂³×C₄	—	19	2	no	—
94	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
95	#123	—	2	4	no	—
96	C₂×C₄⋊C₄	—	19	4	no	—
97	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
98	C₂×C₂²⋊C₄	—	19	2	no	—
99	C₂×C₂²⋊C₄	—	19	4	no	—
100	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
101	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
102	C₂×C₄²	—	19	4	no	—
103	C₂×C₄²	—	38	4	no	—
104	#95	—	19	4	no	—
105	#95	—	19	4	no	—
106	#95	—	19	4	no	—
107	C₁₉	#2853	1	1	yes	characteristic, complemented, Sylow
108	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
109	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
110	C₂×D₄	—	2	4	no	—
111	C₂×D₄	—	2	2	no	—
112	C₂²×C₄	—	2	4	no	—
113	C₂²×C₄	—	19	4	no	—
114	C₂²×C₄	—	19	4	no	—
115	C₂²×C₄	—	38	8	no	—
116	C₂²×C₄	—	38	4	no	—
117	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
118	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
119	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
120	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
121	C₄⋊C₄	—	2	4	no	—
122	C₄⋊C₄	—	38	8	no	—
123	C₂²⋊C₄	—	2	2	no	—
124	C₂²⋊C₄	—	2	4	no	—
125	C₂²⋊C₄	—	38	8	no	—
126	C₂²⋊C₄	—	38	4	no	—
127	C₄²	—	38	8	no	—
128	C₂³	—	2	4	no	—
129	C₂³	—	2	2	no	—
130	C₂³	—	2	4	no	—
131	C₂³	—	2	1	no	—
132	C₂³	#64543	1	4	yes	—
133	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
134	C₂³	C₂³×D₁₉	1	1	yes	characteristic
135	D₄	—	4	4	no	—
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	19	8	no	—
143	C₂×C₄	—	38	16	no	—
144	C₂×C₄	—	38	4	no	—
145	C₂×C₄	—	38	4	no	—
146	C₂×C₄	—	38	4	no	—
147	C₂×C₄	—	38	4	no	—
148	C₂×C₄	—	38	4	no	—
149	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
150	C₂²	—	2	4	no	—
151	C₂²	—	2	8	no	—
152	C₂²	—	4	1	no	—
153	C₂²	—	4	2	no	—
154	C₂²	—	4	4	no	—
155	C₂²	#10597381	1	4	yes	—
156	C₂²	C₂×#64543	1	2	yes	—
157	C₂²	#41×D₁₉	1	4	yes	—
158	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
159	C₄	—	2	4	no	—
160	C₄	—	4	1	no	—
161	C₄	—	4	2	no	—
162	C₄	—	38	8	no	—
163	C₄	—	76	4	no	—
164	C₂	—	2	4	no	—
165	C₂	—	8	1	no	—
166	C₂	C₂×#10597381	1	1	yes	characteristic
167	C₂	#11927051	1	2	yes	—
168	C₂	#11927071	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×Dic₁₉

C₂

yes

maximal, characteristic, complemented

#11926432

C₂

yes

maximal, complemented

#11926425

C₂

yes

maximal, complemented

#11926424

C₂

yes

maximal

#11926416

C₂

yes

maximal, complemented

#11926407

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#123

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₁₉×#123

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#41

yes

—

#2853

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#123

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#123

D₁₉

yes

characteristic

C₂²×C₄²

—

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#123

yes

characteristic

C₂×C₁₉

#525

yes

—

C₂×C₁₉

#529

yes

—

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂³×C₄

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

#123

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

100

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

101

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

102

C₂×C₄²

—

103

C₂×C₄²

—

104

#95

—

105

#95

—

106

#95

—

107

C₁₉

#2853

yes

characteristic, complemented, Sylow

108

C₂⁴

C₂²×D₁₉

yes

characteristic

109

C₂⁴

C₂²×D₁₉

yes

characteristic

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂²⋊D₁₉

yes

—

118

C₂²×C₄

C₂²×D₁₉

yes

characteristic

119

C₂²×C₄

C₂²×D₁₉

yes

—

120

C₂²×C₄

C₂²×D₁₉

yes

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₂²⋊C₄

—

125

C₂²⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

#64543

yes

—

133

C₂³

C₂×C₂²⋊D₁₉

yes

—

134

C₂³

C₂³×D₁₉

yes

characteristic

135

D₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

#10597381

yes

—

156

C₂²

C₂×#64543

yes

—

157

C₂²

#41×D₁₉

yes

—

158

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

164

C₂

—

165

C₂

—

166

C₂

C₂×#10597381

yes

characteristic

167

C₂

#11927051

yes

—

168

C₂

#11927071

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#123	C₂
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×#123	D₁₉
hypocenter	C₁₉	#2853
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#123

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#123

C₂

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#123

N	H ≅ G/N	type
1. C₂²×C₄×Dic₁₉	C₂	semidirect
2. #11926432	C₂	semidirect
3. #11926425	C₂	semidirect
5. #11926416	C₂	semidirect
6. #11926407	C₂	semidirect
107. C₁₉	#2853	semidirect

H ≅ G/N

type

1. C₂²×C₄×Dic₁₉

C₂

semidirect

2. #11926432

C₂

semidirect

3. #11926425

C₂

semidirect

5. #11926416

C₂

semidirect

6. #11926407

C₂

semidirect

107. C₁₉

#2853

semidirect

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

subgroup	index
C₂²×C₄×Dic₁₉	2
#11926432	2
#11926425	2
#11926424	2
#11926416	2
#11926407	2
C₂×C₁₉×#123	2
#2853	19

subgroup

index

C₂²×C₄×Dic₁₉

C₂×C₁₉×#123

Subgroups — #14571954

Conjugacy classes of subgroups

Complements

Maximal subgroups