Group #15699780 — subgroups

Subgroups — C₁₃×#13441 #15699780

Order 3328.

378 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 110 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×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2151	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#362	C₂	1	2	yes	maximal
4	C₁₃×#1979	C₂	1	2	yes	maximal
5	C₁₃×#1381	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×Q₃₂	—	2	4	no	—
8	C₂×C₁₃×Q₃₂	—	2	2	no	—
9	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#108	C₂²	1	2	yes	—
12	C₁₃×#419	—	2	2	no	—
13	C₂×C₁₃×#101	—	2	2	no	—
14	C₁₃×#405	C₂²	1	1	yes	characteristic
15	C₁₃×C₄⋊C₁₆	—	2	2	no	—
16	C₁₃×#362	—	2	4	no	—
17	C₂²×Q₈×C₁₃	—	2	2	no	—
18	C₂×C₁₃×Q₁₆	—	2	2	no	—
19	C₂×C₁₃×Q₁₆	—	2	2	no	—
20	C₂×C₁₃×Q₁₆	—	2	2	no	—
21	C₂×C₁₃×Q₁₆	—	2	2	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
24	C₂×C₁₃×M₁₆	—	2	2	no	—
25	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₁₃×#117	D₄	1	1	yes	characteristic
28	C₁₃×Q₃₂	—	2	8	no	—
29	C₁₃×M₃₂	—	2	2	no	—
30	C₂×C₁₃×C₁₆	—	2	2	no	—
31	C₂×C₁₃×C₁₆	—	2	1	no	—
32	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
33	C₁₃×#108	—	2	2	no	—
34	C₁₃×#108	—	2	2	no	—
35	C₁₃×#103	—	4	4	no	—
36	C₁₃×#101	—	4	4	no	—
37	C₁₃×#97	—	2	1	no	—
38	C₄×C₈×C₁₃	—	2	1	no	—
39	#13441	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×Q₈×C₁₃	—	2	4	no	—
41	C₂×Q₈×C₁₃	—	4	2	no	—
42	C₂×Q₈×C₁₃	—	4	2	no	—
43	C₂×Q₈×C₁₃	—	4	2	no	—
44	C₂×Q₈×C₁₃	—	4	2	no	—
45	C₂×Q₈×C₁₃	—	4	2	no	—
46	C₂²×C₄×C₁₃	—	4	2	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₁₃×Q₁₆	—	2	4	no	—
49	C₁₃×Q₁₆	—	2	4	no	—
50	C₁₃×Q₁₆	—	4	2	no	—
51	C₁₃×Q₁₆	—	4	2	no	—
52	C₁₃×M₁₆	—	2	2	no	—
53	C₁₃×M₁₆	—	4	2	no	—
54	C₁₃×M₁₆	—	4	2	no	—
55	C₂×C₈×C₁₃	—	2	1	no	—
56	C₂×C₈×C₁₃	—	4	2	no	—
57	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
60	C₂×C₈×C₁₃	#41	1	2	yes	—
61	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
62	C₁₃×C₂²⋊C₄	—	2	1	no	—
63	C₄²×C₁₃	—	2	1	no	—
64	C₁₃×C₁₆	—	2	2	no	—
65	C₁₃×C₁₆	—	4	1	no	—
66	C₂²×Q₃₂	C₂×C₁₃	1	1	yes	characteristic
67	#2151	C₂×C₁₃	1	1	yes	characteristic
68	C₂×#362	C₂×C₁₃	1	2	yes	—
69	#1979	C₂×C₁₃	1	2	yes	—
70	#1381	C₂×C₁₃	1	1	yes	characteristic
71	C₂³×C₁₃	#135	1	1	yes	characteristic
72	Q₈×C₁₃	—	4	4	no	—
73	Q₈×C₁₃	—	4	4	no	—
74	Q₈×C₁₃	—	8	2	no	—
75	Q₈×C₁₃	—	8	2	no	—
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	4	4	no	—
78	C₂×C₄×C₁₃	—	8	2	no	—
79	C₂×C₄×C₁₃	—	8	2	no	—
80	C₂×C₄×C₁₃	#121	1	2	yes	—
81	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
84	C₈×C₁₃	—	4	1	no	—
85	C₈×C₁₃	—	8	2	no	—
86	C₈×C₁₃	#120	1	1	yes	characteristic
87	C₈×C₁₃	#123	1	2	yes	—
88	C₈×C₁₃	#124	1	1	yes	characteristic
89	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
90	C₂×Q₃₂	—	2	4	no	—
91	C₂×Q₃₂	—	2	2	no	—
92	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
93	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
94	C₂×#108	C₂²×C₁₃	1	2	yes	—
95	#419	—	2	2	no	—
96	C₂×#101	—	2	2	no	—
97	#405	C₂²×C₁₃	1	1	yes	characteristic
98	C₄⋊C₁₆	—	2	2	no	—
99	#362	—	2	4	no	—
100	C₂²×C₁₃	—	2	2	no	—
101	C₂²×C₁₃	#463	1	2	yes	—
102	C₂²×C₁₃	#466	1	1	yes	characteristic
103	C₄×C₁₃	—	4	2	no	—
104	C₄×C₁₃	—	8	4	no	—
105	C₄×C₁₃	#394	1	1	yes	characteristic
106	C₄×C₁₃	#459	1	2	yes	—
107	C₄×C₁₃	#469	1	1	yes	characteristic
108	C₂²×Q₈	—	2	2	no	—
109	C₂×Q₁₆	—	2	2	no	—
110	C₂×Q₁₆	—	2	2	no	—
111	C₂×Q₁₆	—	2	2	no	—
112	C₂×Q₁₆	—	2	2	no	—
113	C₂×Q₁₆	—	2	2	no	—
114	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
115	C₂×M₁₆	—	2	2	no	—
116	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
117	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
118	#117	D₄×C₁₃	1	1	yes	characteristic
119	Q₃₂	—	2	8	no	—
120	M₃₂	—	2	2	no	—
121	C₂×C₁₆	—	2	2	no	—
122	C₂×C₁₆	—	2	1	no	—
123	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
124	#108	—	2	2	no	—
125	#108	—	2	2	no	—
126	#103	—	4	4	no	—
127	#101	—	4	4	no	—
128	#97	—	2	1	no	—
129	C₄×C₈	—	2	1	no	—
130	C₂×C₁₃	—	2	2	no	—
131	C₂×C₁₃	#2054	1	1	yes	characteristic
132	C₂×C₁₃	#2222	1	2	yes	—
133	C₂×Q₈	—	2	4	no	—
134	C₂×Q₈	—	4	2	no	—
135	C₂×Q₈	—	4	2	no	—
136	C₂×Q₈	—	4	2	no	—
137	C₂×Q₈	—	4	2	no	—
138	C₂×Q₈	—	4	2	no	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
141	Q₁₆	—	2	4	no	—
142	Q₁₆	—	2	4	no	—
143	Q₁₆	—	4	2	no	—
144	Q₁₆	—	4	2	no	—
145	M₁₆	—	2	2	no	—
146	M₁₆	—	4	2	no	—
147	M₁₆	—	4	2	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	4	2	no	—
150	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
151	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
152	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
153	C₂×C₈	C₁₃×#41	1	2	yes	—
154	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
155	C₂²⋊C₄	—	2	1	no	—
156	C₄²	—	2	1	no	—
157	C₁₆	—	2	2	no	—
158	C₁₆	—	4	1	no	—
159	C₁₃	#13441	1	1	yes	characteristic, direct product factor, Sylow
160	C₂³	C₁₃×#135	1	1	yes	characteristic
161	Q₈	—	4	4	no	—
162	Q₈	—	4	4	no	—
163	Q₈	—	8	2	no	—
164	Q₈	—	8	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	—	8	2	no	—
168	C₂×C₄	—	8	2	no	—
169	C₂×C₄	C₁₃×#121	1	2	yes	—
170	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
171	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
172	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
173	C₈	—	4	1	no	—
174	C₈	—	8	2	no	—
175	C₈	C₁₃×#120	1	1	yes	characteristic
176	C₈	C₁₃×#123	1	2	yes	—
177	C₈	C₁₃×#124	1	1	yes	characteristic
178	C₂²	—	2	2	no	—
179	C₂²	C₁₃×#463	1	2	yes	—
180	C₂²	C₁₃×#466	1	1	yes	characteristic
181	C₄	—	4	2	no	—
182	C₄	—	8	4	no	—
183	C₄	C₁₃×#394	1	1	yes	characteristic
184	C₄	C₁₃×#459	1	2	yes	—
185	C₄	C₁₃×#469	1	1	yes	characteristic
186	C₂	—	2	2	no	—
187	C₂	C₁₃×#2054	1	1	yes	characteristic
188	C₂	C₁₃×#2222	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₃×Q₃₂

C₂

yes

maximal, characteristic

C₁₃×#2151

C₂

yes

maximal, characteristic

C₂×C₁₃×#362

C₂

yes

maximal

C₁₃×#1979

C₂

yes

maximal

C₁₃×#1381

C₂

yes

maximal, characteristic

C₂²×C₁₃×Q₁₆

C₂²

yes

—

C₂×C₁₃×Q₃₂

—

C₂×C₁₃×Q₃₂

—

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₂×C₁₃×#108

C₂²

yes

—

C₁₃×#419

—

C₂×C₁₃×#101

—

C₁₃×#405

C₂²

yes

characteristic

C₁₃×C₄⋊C₁₆

—

C₁₃×#362

—

C₂²×Q₈×C₁₃

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

D₄

yes

—

C₂×C₁₃×M₁₆

—

C₂×C₁₃×M₁₆

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×#117

D₄

yes

characteristic

C₁₃×Q₃₂

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

D₄

yes

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×#103

—

C₁₃×#101

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

#13441

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

C₂×C₈×C₁₃

yes

C₂×C₈×C₁₃

yes

—

C₁₃×C₄⋊C₄

D₈

yes

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₁₃×C₁₆

—

C₁₃×C₁₆

—

C₂²×Q₃₂

C₂×C₁₃

yes

characteristic

#2151

C₂×C₁₃

yes

characteristic

C₂×#362

C₂×C₁₃

yes

—

#1979

C₂×C₁₃

yes

—

#1381

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

#135

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

#121

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#120

yes

characteristic

C₈×C₁₃

#123

yes

—

C₈×C₁₃

#124

yes

characteristic

C₂²×Q₁₆

C₂²×C₁₃

yes

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×M₃₂

C₂²×C₁₃

yes

characteristic

C₂²×C₁₆

C₂²×C₁₃

yes

characteristic

C₂×#108

C₂²×C₁₃

yes

—

#419

—

C₂×#101

—

#405

C₂²×C₁₃

yes

characteristic

C₄⋊C₁₆

—

#362

—

100

C₂²×C₁₃

—

101

C₂²×C₁₃

#463

yes

—

102

C₂²×C₁₃

#466

yes

characteristic

103

C₄×C₁₃

—

104

C₄×C₁₃

—

105

C₄×C₁₃

#394

yes

characteristic

106

C₄×C₁₃

#459

yes

—

107

C₄×C₁₃

#469

yes

characteristic

108

C₂²×Q₈

—

109

C₂×Q₁₆

—

110

C₂×Q₁₆

—

111

C₂×Q₁₆

—

112

C₂×Q₁₆

—

113

C₂×Q₁₆

—

114

C₂×Q₁₆

D₄×C₁₃

yes

—

115

C₂×M₁₆

—

116

C₂×M₁₆

D₄×C₁₃

yes

characteristic

117

C₂²×C₈

C₂³×C₁₃

yes

characteristic

118

#117

D₄×C₁₃

yes

characteristic

119

Q₃₂

—

120

M₃₂

—

121

C₂×C₁₆

—

122

C₂×C₁₆

—

123

C₂×C₁₆

D₄×C₁₃

yes

—

124

#108

—

125

#108

—

126

#103

—

127

#101

—

128

#97

—

129

C₄×C₈

—

130

C₂×C₁₃

—

131

C₂×C₁₃

#2054

yes

characteristic

132

C₂×C₁₃

#2222

yes

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂²×C₄

—

140

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

141

Q₁₆

—

142

Q₁₆

—

143

Q₁₆

—

144

Q₁₆

—

145

M₁₆

—

146

M₁₆

—

147

M₁₆

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

C₂×D₄×C₁₃

yes

—

151

C₂×C₈

C₂×D₄×C₁₃

yes

characteristic

152

C₂×C₈

C₁₃×#41

yes

characteristic

153

C₂×C₈

C₁₃×#41

yes

—

154

C₄⋊C₄

C₁₃×D₈

yes

—

155

C₂²⋊C₄

—

156

C₄²

—

157

C₁₆

—

158

C₁₆

—

159

C₁₃

#13441

yes

characteristic, direct product factor, Sylow

160

C₂³

C₁₃×#135

yes

characteristic

161

Q₈

—

162

Q₈

—

163

Q₈

—

164

Q₈

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

C₁₃×#121

yes

—

170

C₂×C₄

C₁₃×#121

yes

characteristic

171

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

172

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

173

C₈

—

174

C₈

—

175

C₈

C₁₃×#120

yes

characteristic

176

C₈

C₁₃×#123

yes

—

177

C₈

C₁₃×#124

yes

characteristic

178

C₂²

—

179

C₂²

C₁₃×#463

yes

—

180

C₂²

C₁₃×#466

yes

characteristic

181

C₄

—

182

C₄

—

183

C₄

C₁₃×#394

yes

characteristic

184

C₄

C₁₃×#459

yes

—

185

C₄

C₁₃×#469

yes

characteristic

186

C₂

—

187

C₂

C₁₃×#2054

yes

characteristic

188

C₂

C₁₃×#2222

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#466

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

prime radical

C₂³×C₁₃

#135

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

N	H ≅ G/N	type
39. #13441	C₁₃	direct (N × H)
159. C₁₃	#13441	direct (N × H)

H ≅ G/N

type

39. #13441

C₁₃

direct (N × H)

159. C₁₃

#13441

direct (N × H)

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

subgroup	index
C₂²×C₁₃×Q₃₂	2
C₁₃×#2151	2
C₂×C₁₃×#362	2
C₁₃×#1979	2
C₁₃×#1381	2
#13441	13

subgroup

index

C₂²×C₁₃×Q₃₂

C₁₃×#2151

C₂×C₁₃×#362

C₁₃×#1979

C₁₃×#1381

#13441

Subgroups — C₁₃×#13441 #15699780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13441 #15699780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13441 #15699780