Group #15753350 — subgroups

Subgroups — #15753350

Order 3328.

414 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 179 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	#13114581	C₂	1	2	yes	maximal
2	C₄×#88055	C₂	1	1	yes	maximal, characteristic
3	#13112663	C₂	1	1	yes	maximal, characteristic
4	#13112663	C₂	1	2	yes	maximal
5	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×#88055	C₄	1	2	yes	—
9	C₂×#88055	C₄	1	2	yes	—
10	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	2	yes	—
13	#11718142	C₄	1	4	yes	—
14	#11718142	C₄	1	4	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
22	C₂²×#1055	C₂×C₄	1	4	yes	—
23	C₂²×#1055	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₃	—	2	2	no	—
25	C₄×C₈×C₁₃	—	2	2	no	—
26	C₄×C₈×C₁₃	—	2	2	no	—
27	#88055	—	2	4	no	—
28	#88055	—	2	4	no	—
29	C₄×#1055	—	2	1	no	—
30	C₄×#1055	—	2	2	no	—
31	C₄×#1055	—	2	1	no	—
32	C₄×#1055	—	2	2	no	—
33	#8134	—	13	1	no	maximal, Sylow
34	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
36	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
37	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
38	C₂²×Dic₁₃	C₄²	1	2	yes	—
39	C₂×C₈×C₁₃	—	2	2	no	—
40	C₂×C₈×C₁₃	—	2	2	no	—
41	C₂×C₈×C₁₃	—	2	4	no	—
42	C₂×C₈×C₁₃	—	2	4	no	—
43	C₂×C₈×C₁₃	—	2	4	no	—
44	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
45	C₄²×C₁₃	#41	1	2	yes	—
46	C₄²×C₁₃	#41	1	1	yes	characteristic
47	C₄²×C₁₃	#41	1	1	yes	characteristic
48	C₄×Dic₁₃	—	2	2	no	—
49	C₄×Dic₁₃	—	2	2	no	—
50	C₄×Dic₁₃	—	2	4	no	—
51	C₄×Dic₁₃	—	2	4	no	—
52	C₂×#1055	—	2	2	no	—
53	C₂×#1055	—	2	2	no	—
54	C₂×#1055	—	2	4	no	—
55	C₂×#1055	—	2	4	no	—
56	C₂×#1055	—	2	4	no	—
57	C₂×#1055	M₁₆	1	4	yes	—
58	#1744	—	13	2	no	—
59	C₄×#97	—	13	1	no	—
60	#1273	—	13	2	no	—
61	#1273	—	13	1	no	—
62	#1273	D₁₃	1	1	yes	characteristic
63	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
65	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
66	C₂×C₄×C₁₃	#117	1	2	yes	—
67	C₂×C₄×C₁₃	#117	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
69	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
70	C₂×C₄×C₁₃	#131	1	4	yes	—
71	C₂×C₄×C₁₃	#131	1	4	yes	—
72	C₂×Dic₁₃	—	2	1	no	—
73	C₂×Dic₁₃	—	2	1	no	—
74	C₂×Dic₁₃	—	2	2	no	—
75	C₂×Dic₁₃	—	2	2	no	—
76	C₂×Dic₁₃	—	2	2	no	—
77	C₂×Dic₁₃	—	2	2	no	—
78	C₂×Dic₁₃	—	2	2	no	—
79	C₈×C₁₃	—	2	4	no	—
80	C₈×C₁₃	—	4	4	no	—
81	#1055	—	2	4	no	—
82	#1055	—	4	4	no	—
83	C₂×#97	—	13	2	no	—
84	C₂×#97	—	13	2	no	—
85	C₂×C₄×C₈	—	13	1	no	—
86	C₂×C₄×C₈	—	13	2	no	—
87	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
88	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
89	C₄³	—	13	1	no	—
90	#336	—	13	4	no	—
91	#336	—	13	4	no	—
92	C₂²×C₁₃	#376	1	1	yes	characteristic
93	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
94	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
95	C₂²×C₁₃	#405	1	2	yes	—
96	C₂²×C₁₃	#405	1	2	yes	—
97	C₄×C₁₃	#432	1	2	yes	—
98	C₄×C₁₃	#432	1	2	yes	—
99	C₄×C₁₃	#433	1	4	yes	—
100	C₄×C₁₃	#433	1	4	yes	—
101	Dic₁₃	—	4	1	no	—
102	Dic₁₃	—	4	2	no	—
103	Dic₁₃	—	4	1	no	—
104	C₂²×C₈	—	13	2	no	—
105	C₂²×C₈	—	13	4	no	—
106	C₂²×C₈	C₄×D₁₃	1	4	yes	—
107	C₂²×C₈	C₄×D₁₃	1	2	yes	—
108	C₂×C₄²	—	13	2	no	—
109	C₂×C₄²	—	13	2	no	—
110	C₂×C₄²	—	13	1	no	—
111	C₂×C₄²	—	13	1	no	—
112	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
113	#97	—	26	4	no	—
114	#97	—	26	4	no	—
115	C₄×C₈	—	2	2	no	—
116	C₄×C₈	—	2	2	no	—
117	C₄×C₈	—	2	2	no	—
118	C₄×C₈	—	26	1	no	—
119	C₄×C₈	—	26	2	no	—
120	C₄×C₈	—	26	1	no	—
121	C₄×C₈	—	26	2	no	—
122	C₂×C₁₃	#1453	1	1	yes	characteristic
123	C₂×C₁₃	#1453	1	2	yes	—
124	C₂×C₁₃	#1453	1	1	yes	characteristic
125	C₂×C₁₃	#1745	1	1	yes	characteristic
126	C₂×C₁₃	#1746	1	2	yes	—
127	C₂²×C₄	—	13	1	no	—
128	C₂²×C₄	—	13	1	no	—
129	C₂²×C₄	—	13	2	no	—
130	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
131	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	2	4	no	—
136	C₂×C₈	—	2	4	no	—
137	C₂×C₈	—	13	4	no	—
138	C₂×C₈	—	26	2	no	—
139	C₂×C₈	—	26	2	no	—
140	C₂×C₈	—	26	4	no	—
141	C₂×C₈	—	26	4	no	—
142	C₂×C₈	—	26	4	no	—
143	C₂×C₈	#6094	1	4	yes	—
144	C₄²	—	26	2	no	—
145	C₄²	—	26	4	no	—
146	C₄²	—	26	2	no	—
147	C₄²	—	26	4	no	—
148	C₄²	#6129	1	2	yes	—
149	C₄²	#6129	1	1	yes	characteristic
150	C₄²	#6131	1	1	yes	characteristic
151	C₁₃	#8134	1	1	yes	characteristic, complemented, Sylow
152	C₂³	C₄²×D₁₃	1	1	yes	characteristic
153	C₂×C₄	—	26	1	no	—
154	C₂×C₄	—	26	1	no	—
155	C₂×C₄	—	26	2	no	—
156	C₂×C₄	—	26	2	no	—
157	C₂×C₄	—	26	2	no	—
158	C₂×C₄	—	26	2	no	—
159	C₂×C₄	—	26	2	no	—
160	C₂×C₄	#88131	1	1	yes	characteristic
161	C₂×C₄	#88131	1	2	yes	—
162	C₂×C₄	#88146	1	1	yes	characteristic
163	C₂×C₄	#88146	1	2	yes	—
164	C₂×C₄	C₂×#6094	1	2	yes	—
165	C₂×C₄	#88155	1	4	yes	—
166	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
167	C₂×C₄	#88161	1	4	yes	—
168	C₈	—	2	4	no	—
169	C₈	—	4	4	no	—
170	C₈	—	26	4	no	—
171	C₈	—	52	4	no	—
172	C₂²	#11718309	1	1	yes	characteristic
173	C₂²	C₄×#6094	1	1	yes	characteristic
174	C₂²	#11718350	1	2	yes	—
175	C₂²	#11718368	1	1	yes	characteristic
176	C₂²	#11718369	1	2	yes	—
177	C₄	—	52	1	no	—
178	C₄	—	52	2	no	—
179	C₄	—	52	1	no	—
180	C₄	#11718380	1	2	yes	—
181	C₄	#11718381	1	4	yes	—
182	C₄	#11718496	1	2	yes	—
183	C₄	#11718501	1	4	yes	—
184	C₂	#13113130	1	1	yes	characteristic
185	C₂	#13113132	1	2	yes	—
186	C₂	#13113134	1	1	yes	characteristic
187	C₂	#13114583	1	1	yes	characteristic
188	C₂	#13114586	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13114581

C₂

yes

maximal

C₄×#88055

C₂

yes

maximal, characteristic

#13112663

C₂

yes

maximal, characteristic

#13112663

C₂

yes

maximal

C₁₃×#1273

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×#88055

C₄

yes

—

C₂×#88055

C₄

yes

—

C₄²×Dic₁₃

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

—

#11718142

C₄

yes

—

#11718142

C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

—

—

—

—

—

—

—

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×Dic₁₃

C₄²

yes

characteristic

C₂²×Dic₁₃

C₄²

yes

characteristic

C₂²×Dic₁₃

C₄²

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₄²×C₁₃

#41

yes

—

C₄²×C₁₃

yes

C₄²×C₁₃

yes

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

—

M₁₆

yes

—

#1744

—

C₄×#97

—

#1273

—

#1273

—

#1273

D₁₃

yes

characteristic

C₂³×C₁₃

C₂×C₄²

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

—

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#1055

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄×C₈

C₂×D₁₃

yes

—

C₄³

—

#336

—

#336

—

C₂²×C₁₃

#376

yes

characteristic

C₂²×C₁₃

C₄×M₁₆

yes

characteristic

C₂²×C₁₃

C₄×M₁₆

yes

characteristic

C₂²×C₁₃

#405

yes

—

C₂²×C₁₃

#405

yes

—

C₄×C₁₃

#432

yes

—

C₄×C₁₃

#432

yes

—

C₄×C₁₃

#433

yes

—

100

C₄×C₁₃

#433

yes

—

101

Dic₁₃

—

102

Dic₁₃

—

103

Dic₁₃

—

104

C₂²×C₈

—

105

C₂²×C₈

—

106

C₂²×C₈

C₄×D₁₃

yes

—

107

C₂²×C₈

C₄×D₁₃

yes

—

108

C₂×C₄²

—

109

C₂×C₄²

—

110

C₂×C₄²

—

111

C₂×C₄²

—

112

C₂×C₄²

C₂²×D₁₃

yes

characteristic

113

#97

—

114

#97

—

115

C₄×C₈

—

116

C₄×C₈

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₄×C₈

—

120

C₄×C₈

—

121

C₄×C₈

—

122

C₂×C₁₃

#1453

yes

characteristic

123

C₂×C₁₃

#1453

yes

—

124

C₂×C₁₃

#1453

yes

characteristic

125

C₂×C₁₃

#1745

yes

characteristic

126

C₂×C₁₃

#1746

yes

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

131

C₂²×C₄

C₂×C₄×D₁₃

yes

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

#6094

yes

—

144

C₄²

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₄²

#6129

yes

—

149

C₄²

#6129

yes

characteristic

150

C₄²

#6131

yes

characteristic

151

C₁₃

#8134

yes

characteristic, complemented, Sylow

152

C₂³

C₄²×D₁₃

yes

characteristic

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

#88131

yes

characteristic

161

C₂×C₄

#88131

yes

—

162

C₂×C₄

#88146

yes

characteristic

163

C₂×C₄

#88146

yes

—

164

C₂×C₄

C₂×#6094

yes

—

165

C₂×C₄

#88155

yes

—

166

C₂×C₄

M₁₆×D₁₃

yes

—

167

C₂×C₄

#88161

yes

—

168

C₈

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₂²

#11718309

yes

characteristic

173

C₂²

C₄×#6094

yes

characteristic

174

C₂²

#11718350

yes

—

175

C₂²

#11718368

yes

characteristic

176

C₂²

#11718369

yes

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

#11718380

yes

—

181

C₄

#11718381

yes

—

182

C₄

#11718496

yes

—

183

C₄

#11718501

yes

—

184

C₂

#13113130

yes

characteristic

185

C₂

#13113132

yes

—

186

C₂

#13113134

yes

characteristic

187

C₂

#13114583

yes

characteristic

188

C₂

#13114586

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂×C₄²
Fitting	C₁₃×#1273	C₂
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1273	D₁₃
hypocenter	C₁₃	#8134
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₃

commutator, socle, prime radical

C₂³×C₁₃

C₂×C₄²

Fitting

C₁₃×#1273

C₂

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
151. C₁₃	#8134	semidirect

H ≅ G/N

type

151. C₁₃

#8134

semidirect

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

subgroup	index
#13114581	2
C₄×#88055	2
#13112663	2
C₁₃×#1273	2
#8134	13

subgroup

index

C₁₃×#1273

Subgroups — #15753350

Conjugacy classes of subgroups

Complements

Maximal subgroups