Group #15699185 — subgroups

Subgroups — C₁₃×#12846 #15699185

Order 3328.

478 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 174 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×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2112	C₂	1	2	yes	maximal
3	C₁₃×#1377	C₂	1	4	yes	maximal, complemented
4	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄²×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
8	C₂×C₁₃×#97	—	2	4	no	—
9	C₂×C₁₃×#97	C₄	1	2	yes	—
10	C₂×C₁₃×#97	C₂²	1	2	yes	—
11	C₁₃×C₂²⋊C₁₆	—	2	4	no	—
12	C₂³×C₄×C₁₃	C₈	1	2	yes	—
13	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	—	2	2	no	—
15	C₂²×C₈×C₁₃	—	2	4	no	—
16	C₂²×C₈×C₁₃	—	2	4	no	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₃	D₄	1	4	yes	—
20	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	—	2	2	no	—
22	C₂×C₄²×C₁₃	—	2	2	no	—
23	C₂×C₄²×C₁₃	C₈	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
25	C₁₃×M₃₂	—	2	8	no	—
26	C₂×C₁₃×C₁₆	—	2	4	no	—
27	C₁₃×#97	—	2	4	no	—
28	C₁₃×#97	—	2	4	no	—
29	#12846	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	—	2	2	no	—
32	C₂²×C₄×C₁₃	—	2	2	no	—
33	C₂²×C₄×C₁₃	—	2	2	no	—
34	C₂²×C₄×C₁₃	—	2	2	no	—
35	C₂²×C₄×C₁₃	—	4	4	no	—
36	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
39	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	—	2	8	no	—
42	C₂×C₈×C₁₃	—	2	2	no	—
43	C₂×C₈×C₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	—	2	8	no	—
46	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
47	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
48	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
49	C₂×C₈×C₁₃	#41	1	4	yes	—
50	C₄²×C₁₃	—	2	4	no	—
51	C₄²×C₁₃	—	2	2	no	—
52	C₄²×C₁₃	—	2	2	no	—
53	C₁₃×C₁₆	—	4	4	no	—
54	C₂²×#97	C₂×C₁₃	1	1	yes	characteristic
55	#2112	C₂×C₁₃	1	2	yes	—
56	#1377	C₂×C₁₃	1	4	yes	complemented
57	C₂³×C₁₃	—	2	4	no	—
58	C₂³×C₁₃	—	2	2	no	—
59	C₂³×C₁₃	C₂²⋊C₈	1	2	yes	—
60	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	4	no	—
65	C₂×C₄×C₁₃	—	2	4	no	—
66	C₂×C₄×C₁₃	—	4	4	no	—
67	C₂×C₄×C₁₃	—	4	4	no	—
68	C₂×C₄×C₁₃	—	4	4	no	—
69	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
70	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₃	#117	1	2	yes	—
72	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
74	C₈×C₁₃	—	2	2	no	—
75	C₈×C₁₃	—	2	4	no	—
76	C₈×C₁₃	#123	1	4	yes	—
77	C₂³×C₈	C₄×C₁₃	1	1	yes	characteristic
78	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
79	C₂²×C₄²	C₄×C₁₃	1	1	yes	characteristic
80	C₂×M₃₂	C₂²×C₁₃	1	4	yes	—
81	C₂×#97	—	2	4	no	—
82	C₂×#97	C₄×C₁₃	1	2	yes	—
83	C₂×#97	C₂²×C₁₃	1	2	yes	—
84	C₂²⋊C₁₆	—	2	4	no	—
85	C₂²×C₁₃	—	2	8	no	—
86	C₂²×C₁₃	—	2	2	no	—
87	C₂²×C₁₃	—	2	2	no	—
88	C₂²×C₁₃	—	2	2	no	—
89	C₂²×C₁₃	#349	1	4	yes	—
90	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
91	C₂²×C₁₃	#431	1	2	yes	—
92	C₄×C₁₃	—	2	2	no	—
93	C₄×C₁₃	—	4	4	no	—
94	C₄×C₁₃	#381	1	1	yes	characteristic
95	C₄×C₁₃	#407	1	1	yes	characteristic
96	C₄×C₁₃	#432	1	2	yes	—
97	C₂³×C₄	C₈×C₁₃	1	2	yes	—
98	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
99	C₂²×C₈	—	2	2	no	—
100	C₂²×C₈	—	2	4	no	—
101	C₂²×C₈	—	2	4	no	—
102	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
103	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
104	C₂²×C₈	D₄×C₁₃	1	4	yes	—
105	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
106	C₂×C₄²	—	2	2	no	—
107	C₂×C₄²	—	2	2	no	—
108	C₂×C₄²	C₈×C₁₃	1	2	yes	—
109	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
110	M₃₂	—	2	8	no	—
111	C₂×C₁₆	—	2	4	no	—
112	#97	—	2	4	no	—
113	#97	—	2	4	no	—
114	C₂×C₁₃	—	2	4	no	—
115	C₂×C₁₃	—	2	2	no	—
116	C₂×C₁₃	#1817	1	1	yes	characteristic
117	C₂×C₁₃	C₂×#349	1	2	yes	—
118	C₂⁴	C₂×C₈×C₁₃	1	1	yes	characteristic
119	C₂²×C₄	—	2	2	no	—
120	C₂²×C₄	—	2	2	no	—
121	C₂²×C₄	—	2	2	no	—
122	C₂²×C₄	—	2	2	no	—
123	C₂²×C₄	—	4	4	no	—
124	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
125	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
126	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	—
127	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
128	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
129	C₂×C₈	—	2	8	no	—
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	2	8	no	—
134	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
135	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
136	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
137	C₂×C₈	C₁₃×#41	1	4	yes	—
138	C₄²	—	2	4	no	—
139	C₄²	—	2	2	no	—
140	C₄²	—	2	2	no	—
141	C₁₆	—	4	4	no	—
142	C₁₃	#12846	1	1	yes	characteristic, direct product factor, Sylow
143	C₂³	—	2	4	no	—
144	C₂³	—	2	2	no	—
145	C₂³	C₁₃×C₂²⋊C₈	1	2	yes	—
146	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	4	4	no	—
153	C₂×C₄	—	4	4	no	—
154	C₂×C₄	—	4	4	no	—
155	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
156	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄	C₁₃×#117	1	2	yes	—
158	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
159	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
160	C₈	—	2	2	no	—
161	C₈	—	2	4	no	—
162	C₈	C₁₃×#123	1	4	yes	—
163	C₂²	—	2	8	no	—
164	C₂²	—	2	2	no	—
165	C₂²	—	2	2	no	—
166	C₂²	—	2	2	no	—
167	C₂²	C₁₃×#349	1	4	yes	—
168	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²	C₁₃×#431	1	2	yes	—
170	C₄	—	2	2	no	—
171	C₄	—	4	4	no	—
172	C₄	C₁₃×#381	1	1	yes	characteristic
173	C₄	C₁₃×#407	1	1	yes	characteristic
174	C₄	C₁₃×#432	1	2	yes	—
175	C₂	—	2	4	no	—
176	C₂	—	2	2	no	—
177	C₂	C₁₃×#1817	1	1	yes	characteristic
178	C₂	C₂×C₁₃×#349	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₃×#97

C₂

yes

maximal, characteristic

C₁₃×#2112

C₂

yes

maximal

C₁₃×#1377

C₂

yes

maximal, complemented

C₂³×C₈×C₁₃

C₄

yes

characteristic

C₂³×C₈×C₁₃

C₂²

yes

characteristic

C₂²×C₄²×C₁₃

C₄

yes

characteristic

C₂×C₁₃×M₃₂

C₂²

yes

—

C₂×C₁₃×#97

—

C₂×C₁₃×#97

C₄

yes

—

C₂×C₁₃×#97

C₂²

yes

—

C₁₃×C₂²⋊C₁₆

—

C₂³×C₄×C₁₃

C₈

yes

—

C₂³×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₈

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₁₃×#97

—

C₁₃×#97

—

#12846

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

M₁₆

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₁₃×C₁₆

—

C₂²×#97

C₂×C₁₃

yes

characteristic

#2112

C₂×C₁₃

yes

—

#1377

C₂×C₁₃

yes

complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂²⋊C₈

yes

—

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#123

yes

—

C₂³×C₈

C₄×C₁₃

yes

characteristic

C₂³×C₈

C₂²×C₁₃

yes

characteristic

C₂²×C₄²

C₄×C₁₃

yes

characteristic

C₂×M₃₂

C₂²×C₁₃

yes

—

C₂×#97

—

C₂×#97

C₄×C₁₃

yes

—

C₂×#97

C₂²×C₁₃

yes

—

C₂²⋊C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#349

yes

—

C₂²×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₁₃

#431

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂³×C₄

C₈×C₁₃

yes

—

C₂³×C₄

C₂×C₄×C₁₃

yes

characteristic

C₂²×C₈

—

100

C₂²×C₈

—

101

C₂²×C₈

—

102

C₂²×C₈

C₂×C₄×C₁₃

yes

characteristic

103

C₂²×C₈

C₂×C₄×C₁₃

yes

—

104

C₂²×C₈

D₄×C₁₃

yes

—

105

C₂²×C₈

C₂³×C₁₃

yes

characteristic

106

C₂×C₄²

—

107

C₂×C₄²

—

108

C₂×C₄²

C₈×C₁₃

yes

—

109

C₂×C₄²

C₂×C₄×C₁₃

yes

—

110

M₃₂

—

111

C₂×C₁₆

—

112

#97

—

113

#97

—

114

C₂×C₁₃

—

115

C₂×C₁₃

—

116

C₂×C₁₃

#1817

yes

characteristic

117

C₂×C₁₃

C₂×#349

yes

—

118

C₂⁴

C₂×C₈×C₁₃

yes

characteristic

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

125

C₂²×C₄

C₂×C₈×C₁₃

yes

characteristic

126

C₂²×C₄

C₂×C₈×C₁₃

yes

—

127

C₂²×C₄

C₁₃×M₁₆

yes

—

128

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

C₁₃×C₂²⋊C₄

yes

—

135

C₂×C₈

C₁₃×M₁₆

yes

—

136

C₂×C₈

C₂×D₄×C₁₃

yes

—

137

C₂×C₈

C₁₃×#41

yes

—

138

C₄²

—

139

C₄²

—

140

C₄²

—

141

C₁₆

—

142

C₁₃

#12846

yes

characteristic, direct product factor, Sylow

143

C₂³

—

144

C₂³

—

145

C₂³

C₁₃×C₂²⋊C₈

yes

—

146

C₂³

C₂²×C₈×C₁₃

yes

characteristic

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

C₁₃×C₂²⋊C₈

yes

—

156

C₂×C₄

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

157

C₂×C₄

C₁₃×#117

yes

—

158

C₂×C₄

C₂×C₁₃×M₁₆

yes

—

159

C₂×C₄

C₂×C₁₃×M₁₆

yes

characteristic

160

C₈

—

161

C₈

—

162

C₈

C₁₃×#123

yes

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

—

167

C₂²

C₁₃×#349

yes

—

168

C₂²

C₂×C₁₃×C₂²⋊C₈

yes

characteristic

169

C₂²

C₁₃×#431

yes

—

170

C₄

—

171

C₄

—

172

C₄

C₁₃×#381

yes

characteristic

173

C₄

C₁₃×#407

yes

characteristic

174

C₄

C₁₃×#432

yes

—

175

C₂

—

176

C₂

—

177

C₂

C₁₃×#1817

yes

characteristic

178

C₂

C₂×C₁₃×#349

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₈×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle

C₂²×C₁₃

C₂×C₂²⋊C₈

prime radical

C₂⁴×C₁₃

C₂×C₈

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
3. C₁₃×#1377	C₂	semidirect
29. #12846	C₁₃	direct (N × H)
56. #1377	C₂×C₁₃	semidirect
142. C₁₃	#12846	direct (N × H)

H ≅ G/N

type

3. C₁₃×#1377

C₂

semidirect

29. #12846

C₁₃

direct (N × H)

56. #1377

C₂×C₁₃

semidirect

142. C₁₃

#12846

direct (N × H)

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

subgroup	index
C₂²×C₁₃×#97	2
C₁₃×#2112	2
C₁₃×#1377	2
#12846	13

subgroup

index

C₂²×C₁₃×#97

C₁₃×#2112

C₁₃×#1377

#12846

Subgroups — C₁₃×#12846 #15699185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12846 #15699185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12846 #15699185