Group #14570007 — subgroups

Subgroups — #14570007

Order 2432.

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

normal subgroups only

This group has 592 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	C₂×#10597324	C₂	1	4	yes	maximal, complemented
2	#11926467	C₂	1	4	yes	maximal, complemented
3	#11926464	C₂	1	2	yes	maximal, complemented
4	#11926442	C₂	1	2	yes	maximal, complemented
5	#11926424	C₂	1	2	yes	maximal
6	C₁₉×#390	C₂	1	1	yes	maximal, characteristic
7	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×Dic₁₉	C₂²	1	2	yes	—
9	C₂²×Dic₃₈	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
14	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
18	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
19	#10597324	—	2	16	no	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₁₉⋊#95	C₂²	1	2	yes	—
22	C₂⁴×C₁₉	C₂³	1	2	yes	—
23	C₂×D₄×C₁₉	—	4	1	no	—
24	C₂×D₄×C₁₉	—	4	1	no	—
25	C₂×D₄×C₁₉	Q₈	1	4	yes	complemented
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	8	no	—
30	C₂²×Dic₁₉	—	4	2	no	—
31	C₂²×Dic₁₉	C₂³	1	4	yes	—
32	C₂²×Dic₁₉	C₂³	1	4	yes	—
33	C₂×Dic₃₈	—	2	8	no	—
34	C₂×Dic₃₈	—	4	2	no	—
35	C₄⋊C₄×C₁₉	—	4	1	no	—
36	C₂²⋊C₄×C₁₉	—	2	8	no	—
37	C₄²×C₁₉	—	4	1	no	—
38	C₂²⋊Dic₁₉	—	2	8	no	—
39	C₂²⋊Dic₁₉	—	4	2	no	—
40	C₄⋊Dic₁₉	—	4	2	no	—
41	C₄⋊Dic₁₉	D₄	1	8	yes	complemented
42	Dic₁₉⋊C₄	—	2	8	no	—
43	Dic₁₉⋊C₄	—	2	8	no	—
44	C₂³×C₁₉	—	2	4	no	—
45	C₂³×C₁₉	—	2	2	no	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	—	2	4	no	—
48	C₂³×C₁₉	C₂×Q₈	1	4	yes	—
49	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
50	D₄×C₁₉	—	4	4	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	2	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×C₄×C₁₉	C₂×Q₈	1	2	yes	—
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	—	4	8	no	—
65	C₂×Dic₁₉	C₂×D₄	1	8	yes	—
66	Dic₃₈	—	4	8	no	—
67	#2683	—	19	1	no	maximal, Sylow
68	C₂²×C₁₉	—	2	4	no	—
69	C₂²×C₁₉	—	2	8	no	—
70	C₂²×C₁₉	—	4	4	no	—
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	—	4	2	no	—
73	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
74	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
75	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
76	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
77	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
78	C₄×C₁₉	—	2	4	no	—
79	C₄×C₁₉	—	2	2	no	—
80	C₄×C₁₉	—	4	2	no	—
81	Dic₁₉	—	2	8	no	—
82	Dic₁₉	—	4	4	no	—
83	C₂×C₂²⋊Q₈	—	19	4	no	—
84	#396	—	19	4	no	—
85	#395	—	19	2	no	—
86	#390	D₁₉	1	1	yes	characteristic
87	#389	—	19	2	no	—
88	#386	—	19	2	no	—
89	C₂×C₁₉	—	4	4	no	—
90	C₂×C₁₉	#537	1	2	yes	—
91	C₂×C₁₉	#543	1	1	yes	characteristic
92	C₂×C₁₉	D₄²	1	1	yes	characteristic
93	C₂×C₁₉	D₄×Q₈	1	2	yes	—
94	C₂×C₁₉	#563	1	1	yes	characteristic
95	C₂²×Q₈	—	19	2	no	—
96	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
97	C₂³×C₄	—	19	2	no	—
98	C₂²⋊Q₈	—	38	16	no	—
99	C₂×C₄⋊C₄	—	19	2	no	—
100	C₂×C₄⋊C₄	—	19	4	no	—
101	C₂×C₄⋊C₄	—	19	4	no	—
102	C₂×C₄⋊C₄	—	19	2	no	—
103	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
104	C₂×C₂²⋊C₄	—	19	4	no	—
105	C₂×C₂²⋊C₄	—	19	2	no	—
106	C₂×C₂²⋊C₄	C₂×D₁₉	1	4	yes	—
107	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
108	#95	—	19	4	no	—
109	#95	—	19	2	no	—
110	C₁₉	#2683	1	1	yes	characteristic, complemented, Sylow
111	C₂⁴	C₂²×D₁₉	1	2	yes	—
112	C₂×Q₈	—	38	8	no	—
113	C₂×Q₈	—	76	2	no	—
114	C₂×D₄	—	4	1	no	—
115	C₂×D₄	—	4	1	no	—
116	C₂×D₄	Dic₃₈	1	4	yes	complemented
117	C₂²×C₄	—	19	4	no	—
118	C₂²×C₄	—	19	4	no	—
119	C₂²×C₄	—	38	8	no	—
120	C₂²×C₄	—	76	2	no	—
121	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
122	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
123	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
124	C₄⋊C₄	—	4	1	no	—
125	C₄⋊C₄	—	19	8	no	—
126	C₄⋊C₄	—	38	8	no	—
127	C₄⋊C₄	—	38	8	no	—
128	C₄⋊C₄	—	76	2	no	—
129	C₂²⋊C₄	—	2	8	no	—
130	C₂²⋊C₄	—	38	8	no	—
131	C₂²⋊C₄	—	76	2	no	—
132	C₄²	—	4	1	no	—
133	C₂³	—	2	4	no	—
134	C₂³	—	2	2	no	—
135	C₂³	—	2	2	no	—
136	C₂³	—	2	4	no	—
137	C₂³	C₂×Dic₃₈	1	4	yes	—
138	C₂³	C₂³×D₁₉	1	1	yes	characteristic
139	Q₈	—	76	8	no	—
140	D₄	—	4	4	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	19	8	no	—
148	C₂×C₄	—	38	4	no	—
149	C₂×C₄	—	38	4	no	—
150	C₂×C₄	—	38	4	no	—
151	C₂×C₄	—	38	4	no	—
152	C₂×C₄	—	38	4	no	—
153	C₂×C₄	—	76	8	no	—
154	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
155	C₂×C₄	D₄×D₁₉	1	4	yes	—
156	C₂²	—	2	4	no	—
157	C₂²	—	2	8	no	—
158	C₂²	—	4	4	no	—
159	C₂²	—	4	2	no	—
160	C₂²	—	4	2	no	—
161	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
162	C₂²	C₂×D₄×D₁₉	1	2	yes	—
163	C₂²	#10597430	1	1	yes	characteristic
164	C₂²	#10597430	1	1	yes	characteristic
165	C₂²	#10597436	1	2	yes	—
166	C₄	—	2	4	no	—
167	C₄	—	2	2	no	—
168	C₄	—	4	2	no	—
169	C₄	—	38	8	no	—
170	C₄	—	76	4	no	—
171	C₂	—	4	4	no	—
172	C₂	#11927121	1	2	yes	—
173	C₂	#11927170	1	1	yes	characteristic
174	C₂	#11927179	1	1	yes	characteristic
175	C₂	D₄×Dic₃₈	1	2	yes	—
176	C₂	#11927294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597324

C₂

yes

maximal, complemented

#11926467

C₂

yes

maximal, complemented

#11926464

C₂

yes

maximal, complemented

#11926442

C₂

yes

maximal, complemented

#11926424

C₂

yes

maximal

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597324

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

complemented

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

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×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

#2683

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₂²⋊Q₈

—

#396

—

#395

—

#390

D₁₉

yes

characteristic

#389

—

#386

—

C₂×C₁₉

—

C₂×C₁₉

#537

yes

—

C₂×C₁₉

#543

yes

characteristic

C₂×C₁₉

D₄²

yes

characteristic

C₂×C₁₉

D₄×Q₈

yes

—

C₂×C₁₉

#563

yes

characteristic

C₂²×Q₈

—

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂³×C₄

—

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

104

C₂×C₂²⋊C₄

—

105

C₂×C₂²⋊C₄

—

106

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

107

C₂×C₄²

C₂×D₁₉

yes

characteristic

108

#95

—

109

#95

—

110

C₁₉

#2683

yes

characteristic, complemented, Sylow

111

C₂⁴

C₂²×D₁₉

yes

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

Dic₃₈

yes

complemented

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

C₂²×D₁₉

yes

—

122

C₂²×C₄

C₂²×D₁₉

yes

characteristic

123

C₂²×C₄

C₂²×D₁₉

yes

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₂²⋊C₄

—

130

C₂²⋊C₄

—

131

C₂²⋊C₄

—

132

C₄²

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

C₂×Dic₃₈

yes

—

138

C₂³

C₂³×D₁₉

yes

characteristic

139

Q₈

—

140

D₄

—

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

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

C₂×Dic₃₈

yes

—

155

C₂×C₄

D₄×D₁₉

yes

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

C₂²×Dic₃₈

yes

characteristic

162

C₂²

C₂×D₄×D₁₉

yes

—

163

C₂²

#10597430

yes

characteristic

164

C₂²

#10597430

yes

characteristic

165

C₂²

#10597436

yes

—

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

—

171

C₂

—

172

C₂

#11927121

yes

—

173

C₂

#11927170

yes

characteristic

174

C₂

#11927179

yes

characteristic

175

C₂

D₄×Dic₃₈

yes

—

176

C₂

#11927294

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#390	C₂
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2683
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #390

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#390

C₂

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #390

N	H ≅ G/N	type
1. C₂×#10597324	C₂	semidirect
2. #11926467	C₂	semidirect
3. #11926464	C₂	semidirect
4. #11926442	C₂	semidirect
25. C₂×D₄×C₁₉	Q₈	semidirect
41. C₄⋊Dic₁₉	D₄	semidirect
110. C₁₉	#2683	semidirect
116. C₂×D₄	Dic₃₈	semidirect

H ≅ G/N

type

1. C₂×#10597324

C₂

semidirect

2. #11926467

C₂

semidirect

3. #11926464

C₂

semidirect

4. #11926442

C₂

semidirect

25. C₂×D₄×C₁₉

Q₈

semidirect

41. C₄⋊Dic₁₉

D₄

semidirect

110. C₁₉

#2683

semidirect

116. C₂×D₄

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597324	2
#11926467	2
#11926464	2
#11926442	2
#11926424	2
C₁₉×#390	2
#2683	19

subgroup

index

C₁₉×#390

Subgroups — #14570007

Conjugacy classes of subgroups

Complements

Maximal subgroups