Group #14570565 — subgroups

Subgroups — #14570565

Order 2432.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10597381	C₂	1	2	yes	maximal
2	#11926474	C₂	1	2	yes	maximal, complemented
3	#11926469	C₂	1	4	yes	maximal, complemented
4	#11926442	C₂	1	2	yes	maximal, complemented
5	#11926419	C₂	1	4	yes	maximal, complemented
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	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
13	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
14	#10597381	—	2	8	no	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
19	C₁₉⋊#95	C₂²	1	4	yes	—
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	D₄	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
29	C₂²×Dic₁₉	—	2	4	no	—
30	C₂²×Dic₁₉	—	4	2	no	—
31	C₂²×Dic₁₉	—	4	2	no	—
32	C₂²×Dic₁₉	C₂³	1	4	yes	—
33	C₂²×Dic₁₉	C₂³	1	4	yes	—
34	C₄⋊C₄×C₁₉	—	4	1	no	—
35	C₂²⋊C₄×C₁₉	—	2	8	no	—
36	C₄²×C₁₉	—	4	1	no	—
37	C₂²⋊Dic₁₉	—	2	4	no	—
38	C₂²⋊Dic₁₉	—	2	8	no	—
39	C₄⋊Dic₁₉	—	2	4	no	—
40	C₄⋊Dic₁₉	—	4	2	no	—
41	C₄⋊Dic₁₉	—	4	2	no	—
42	Dic₁₉⋊C₄	—	2	8	no	—
43	C₂³×C₁₉	—	2	4	no	—
44	C₂³×C₁₉	—	2	2	no	—
45	C₂³×C₁₉	—	2	2	no	—
46	C₂³×C₁₉	—	2	4	no	—
47	C₂³×C₁₉	C₂×D₄	1	4	yes	—
48	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
49	D₄×C₁₉	—	4	4	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	#41	1	4	yes	—
58	C₂×Dic₁₉	—	2	4	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	—	4	8	no	—
65	#2724	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	2	4	no	—
67	C₂²×C₁₉	—	2	8	no	—
68	C₂²×C₁₉	—	4	4	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	4	2	no	—
71	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
72	C₂²×C₁₉	C₂×#41	1	2	yes	—
73	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
74	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
75	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	2	4	no	—
78	C₄×C₁₉	—	4	2	no	—
79	Dic₁₉	—	4	4	no	—
80	Dic₁₉	—	4	4	no	—
81	C₂×#123	—	19	2	no	—
82	#398	—	19	2	no	—
83	#397	—	19	4	no	—
84	#390	D₁₉	1	1	yes	characteristic
85	#389	—	19	2	no	—
86	#385	—	19	4	no	—
87	C₂×C₁₉	—	4	4	no	—
88	C₂×C₁₉	#534	1	1	yes	characteristic
89	C₂×C₁₉	#539	1	2	yes	—
90	C₂×C₁₉	#547	1	2	yes	—
91	C₂×C₁₉	#559	1	1	yes	characteristic
92	C₂×C₁₉	#563	1	1	yes	characteristic
93	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
94	C₂³×C₄	—	19	2	no	—
95	#123	—	38	8	no	—
96	C₂×C₄⋊C₄	—	19	4	no	—
97	C₂×C₄⋊C₄	—	19	2	no	—
98	C₂×C₄⋊C₄	—	19	2	no	—
99	C₂×C₄⋊C₄	—	19	2	no	—
100	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
101	C₂×C₂²⋊C₄	—	19	4	no	—
102	C₂×C₂²⋊C₄	—	19	2	no	—
103	C₂×C₂²⋊C₄	C₂×D₁₉	1	4	yes	—
104	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
105	#95	—	19	4	no	—
106	#95	—	19	4	no	—
107	#95	—	19	2	no	—
108	C₁₉	#2724	1	1	yes	characteristic, complemented, Sylow
109	C₂⁴	C₂²×D₁₉	1	2	yes	—
110	C₂×D₄	—	4	1	no	—
111	C₂×D₄	—	4	1	no	—
112	C₂×D₄	D₇₆	1	4	yes	—
113	C₂²×C₄	—	19	4	no	—
114	C₂²×C₄	—	19	4	no	—
115	C₂²×C₄	—	38	4	no	—
116	C₂²×C₄	—	76	2	no	—
117	C₂²×C₄	—	76	2	no	—
118	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
119	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
120	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
121	C₄⋊C₄	—	4	1	no	—
122	C₄⋊C₄	—	38	8	no	—
123	C₄⋊C₄	—	38	4	no	—
124	C₄⋊C₄	—	76	2	no	—
125	C₄⋊C₄	—	76	2	no	—
126	C₂²⋊C₄	—	2	8	no	—
127	C₂²⋊C₄	—	38	4	no	—
128	C₂²⋊C₄	—	38	8	no	—
129	C₄²	—	4	1	no	—
130	C₂³	—	2	4	no	—
131	C₂³	—	2	2	no	—
132	C₂³	—	2	2	no	—
133	C₂³	—	2	4	no	—
134	C₂³	C₂×D₇₆	1	4	yes	—
135	C₂³	C₂³×D₁₉	1	1	yes	characteristic
136	D₄	—	4	4	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	38	4	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	—	76	8	no	—
150	C₂×C₄	C₂×D₇₆	1	2	yes	—
151	C₂×C₄	#64543	1	4	yes	—
152	C₂²	—	2	4	no	—
153	C₂²	—	2	8	no	—
154	C₂²	—	4	4	no	—
155	C₂²	—	4	2	no	—
156	C₂²	—	4	2	no	—
157	C₂²	C₂²×D₇₆	1	1	yes	characteristic
158	C₂²	C₂×#64543	1	2	yes	—
159	C₂²	#10597430	1	1	yes	characteristic
160	C₂²	#10597430	1	1	yes	characteristic
161	C₂²	#10597436	1	2	yes	—
162	C₄	—	2	2	no	—
163	C₄	—	2	4	no	—
164	C₄	—	4	2	no	—
165	C₄	—	76	4	no	—
166	C₄	—	76	4	no	—
167	C₂	—	4	4	no	—
168	C₂	#11927106	1	1	yes	characteristic
169	C₂	#11927139	1	2	yes	—
170	C₂	#11927198	1	2	yes	—
171	C₂	#11927280	1	1	yes	characteristic
172	C₂	#11927294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597381

C₂

yes

maximal

#11926474

C₂

yes

maximal, complemented

#11926469

C₂

yes

maximal, complemented

#11926442

C₂

yes

maximal, complemented

#11926419

C₂

yes

maximal, complemented

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

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

—

#10597381

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×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

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

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

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2724

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

#389

—

#385

—

C₂×C₁₉

—

C₂×C₁₉

#534

yes

characteristic

C₂×C₁₉

#539

yes

—

C₂×C₁₉

#547

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂³×C₄

—

#123

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

101

C₂×C₂²⋊C₄

—

102

C₂×C₂²⋊C₄

—

103

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

104

C₂×C₄²

C₂×D₁₉

yes

characteristic

105

#95

—

106

#95

—

107

#95

—

108

C₁₉

#2724

yes

characteristic, complemented, Sylow

109

C₂⁴

C₂²×D₁₉

yes

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

D₇₆

yes

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂²×D₁₉

yes

—

119

C₂²×C₄

C₂²×D₁₉

yes

characteristic

120

C₂²×C₄

C₂²×D₁₉

yes

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₂²⋊C₄

—

129

C₄²

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

C₂×D₇₆

yes

—

135

C₂³

C₂³×D₁₉

yes

characteristic

136

D₄

—

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

—

150

C₂×C₄

C₂×D₇₆

yes

—

151

C₂×C₄

#64543

yes

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

C₂²×D₇₆

yes

characteristic

158

C₂²

C₂×#64543

yes

—

159

C₂²

#10597430

yes

characteristic

160

C₂²

#10597430

yes

characteristic

161

C₂²

#10597436

yes

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₂

—

168

C₂

#11927106

yes

characteristic

169

C₂

#11927139

yes

—

170

C₂

#11927198

yes

—

171

C₂

#11927280

yes

characteristic

172

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	#2724
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
2. #11926474	C₂	semidirect
3. #11926469	C₂	semidirect
4. #11926442	C₂	semidirect
5. #11926419	C₂	semidirect
108. C₁₉	#2724	semidirect

H ≅ G/N

type

2. #11926474

C₂

semidirect

3. #11926469

C₂

semidirect

4. #11926442

C₂

semidirect

5. #11926419

C₂

semidirect

108. C₁₉

#2724

semidirect

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

subgroup	index
C₂×#10597381	2
#11926474	2
#11926469	2
#11926442	2
#11926419	2
C₁₉×#390	2
#2724	19

subgroup

index

C₁₉×#390

Subgroups — #14570565

Conjugacy classes of subgroups

Complements

Maximal subgroups