Group #15699595 — subgroups

Subgroups — C₁₃×#13256 #15699595

Order 3328.

462 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 158 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×C₁₃×#494	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#362	C₂	1	4	yes	maximal
4	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×Q₁₆	—	2	1	no	—
6	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
8	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
9	C₁₃×#494	—	2	2	no	—
10	C₁₃×#494	C₄	1	4	yes	—
11	C₂×C₁₃×#108	C₂²	1	2	yes	—
12	C₄×C₁₃×M₁₆	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×C₄⋊C₁₆	—	2	2	no	—
15	C₁₃×#362	—	2	8	no	—
16	C₁₃×#341	—	2	1	no	—
17	C₂²×Q₈×C₁₃	—	2	2	no	—
18	C₂×C₁₃×Q₁₆	—	2	4	no	—
19	C₂×C₁₃×Q₁₆	—	2	4	no	—
20	C₂×C₁₃×Q₁₆	—	2	2	no	—
21	C₂×C₁₃×Q₁₆	—	2	4	no	—
22	C₂×C₁₃×Q₁₆	—	4	4	no	—
23	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
24	C₂×C₁₃×M₁₆	—	2	2	no	—
25	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₁₃×C₄⋊Q₈	—	2	4	no	—
28	C₁₃×C₄⋊Q₈	—	4	1	no	—
29	C₁₃×C₄⋊Q₈	—	4	1	no	—
30	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
31	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
32	C₁₃×M₃₂	—	2	4	no	—
33	C₂×C₁₃×C₁₆	—	2	2	no	—
34	C₁₃×#108	—	2	2	no	—
35	C₁₃×#108	D₄	1	4	yes	—
36	C₁₃×#97	—	4	1	no	—
37	C₄×C₈×C₁₃	—	4	1	no	—
38	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	#13256	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×Q₈×C₁₃	—	2	4	no	—
42	C₂×Q₈×C₁₃	—	4	2	no	—
43	C₂×Q₈×C₁₃	—	4	4	no	—
44	C₂×Q₈×C₁₃	—	4	4	no	—
45	C₂²×C₄×C₁₃	—	4	2	no	—
46	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₁₃×Q₁₆	—	2	8	no	—
49	C₁₃×Q₁₆	—	4	8	no	—
50	C₁₃×Q₁₆	—	4	2	no	—
51	C₁₃×Q₁₆	—	4	2	no	—
52	C₁₃×M₁₆	—	2	4	no	—
53	C₁₃×M₁₆	—	4	2	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	4	2	no	—
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	#41	1	2	yes	—
61	C₁₃×C₄⋊C₄	—	4	4	no	—
62	C₁₃×C₄⋊C₄	—	4	4	no	—
63	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₁₃	D₈	1	1	yes	characteristic
65	C₄²×C₁₃	D₈	1	1	yes	characteristic
66	C₁₃×C₁₆	—	4	2	no	—
67	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
68	#2150	C₂×C₁₃	1	1	yes	characteristic
69	C₂×#362	C₂×C₁₃	1	4	yes	—
70	C₄×#108	C₂×C₁₃	1	1	yes	characteristic
71	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
72	Q₈×C₁₃	—	4	4	no	—
73	Q₈×C₁₃	—	4	4	no	—
74	Q₈×C₁₃	—	8	4	no	—
75	C₂×C₄×C₁₃	—	2	4	no	—
76	C₂×C₄×C₁₃	—	4	4	no	—
77	C₂×C₄×C₁₃	—	8	4	no	—
78	C₂×C₄×C₁₃	#102	1	2	yes	—
79	C₂×C₄×C₁₃	#102	1	2	yes	—
80	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#121	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
84	C₈×C₁₃	—	2	2	no	—
85	C₈×C₁₃	—	4	4	no	—
86	C₈×C₁₃	C₄×D₄	1	2	yes	—
87	C₈×C₁₃	#124	1	1	yes	characteristic
88	C₈×C₁₃	#127	1	1	yes	characteristic
89	C₂²×Q₁₆	—	2	1	no	—
90	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
91	C₂×C₄⋊Q₈	—	2	1	no	—
92	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
93	#494	—	2	2	no	—
94	#494	C₄×C₁₃	1	4	yes	—
95	C₂×#108	C₂²×C₁₃	1	2	yes	—
96	C₄×M₁₆	—	2	1	no	—
97	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
98	C₄⋊C₁₆	—	2	2	no	—
99	#362	—	2	8	no	—
100	#341	—	2	1	no	—
101	C₂²×C₁₃	—	2	2	no	—
102	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
103	C₂²×C₁₃	#460	1	2	yes	—
104	C₄×C₁₃	—	2	2	no	—
105	C₄×C₁₃	—	8	4	no	—
106	C₄×C₁₃	#362	1	4	yes	complemented
107	C₄×C₁₃	#390	1	1	yes	characteristic
108	C₄×C₁₃	#418	1	1	yes	characteristic
109	C₄×C₁₃	#459	1	2	yes	—
110	C₂²×Q₈	—	2	2	no	—
111	C₂×Q₁₆	—	2	4	no	—
112	C₂×Q₁₆	—	2	4	no	—
113	C₂×Q₁₆	—	2	2	no	—
114	C₂×Q₁₆	—	2	4	no	—
115	C₂×Q₁₆	—	4	4	no	—
116	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
117	C₂×M₁₆	—	2	2	no	—
118	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
119	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
120	C₄⋊Q₈	—	2	4	no	—
121	C₄⋊Q₈	—	4	1	no	—
122	C₄⋊Q₈	—	4	1	no	—
123	C₂×C₄⋊C₄	—	4	2	no	—
124	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
125	M₃₂	—	2	4	no	—
126	C₂×C₁₆	—	2	2	no	—
127	#108	—	2	2	no	—
128	#108	D₄×C₁₃	1	4	yes	—
129	#97	—	4	1	no	—
130	C₄×C₈	—	4	1	no	—
131	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
132	C₄×C₈	D₄×C₁₃	1	2	yes	—
133	C₂×C₁₃	—	2	2	no	—
134	C₂×C₁₃	#1982	1	1	yes	characteristic
135	C₂×C₁₃	C₂×#362	1	2	yes	—
136	C₂×Q₈	—	2	4	no	—
137	C₂×Q₈	—	4	2	no	—
138	C₂×Q₈	—	4	4	no	—
139	C₂×Q₈	—	4	4	no	—
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
142	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
143	Q₁₆	—	2	8	no	—
144	Q₁₆	—	4	8	no	—
145	Q₁₆	—	4	2	no	—
146	Q₁₆	—	4	2	no	—
147	M₁₆	—	2	4	no	—
148	M₁₆	—	4	2	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
152	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
153	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
154	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
155	C₂×C₈	C₁₃×#41	1	2	yes	—
156	C₄⋊C₄	—	4	4	no	—
157	C₄⋊C₄	—	4	4	no	—
158	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
159	C₄²	C₁₃×D₈	1	1	yes	characteristic
160	C₄²	C₁₃×D₈	1	1	yes	characteristic
161	C₁₆	—	4	2	no	—
162	C₁₃	#13256	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
164	Q₈	—	4	4	no	—
165	Q₈	—	4	4	no	—
166	Q₈	—	8	4	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	8	4	no	—
170	C₂×C₄	C₁₃×#102	1	2	yes	—
171	C₂×C₄	C₁₃×#102	1	2	yes	—
172	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄	C₁₃×#121	1	2	yes	—
174	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
175	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
176	C₈	—	2	2	no	—
177	C₈	—	4	4	no	—
178	C₈	C₄×D₄×C₁₃	1	2	yes	—
179	C₈	C₁₃×#124	1	1	yes	characteristic
180	C₈	C₁₃×#127	1	1	yes	characteristic
181	C₂²	—	2	2	no	—
182	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
183	C₂²	C₁₃×#460	1	2	yes	—
184	C₄	—	2	2	no	—
185	C₄	—	8	4	no	—
186	C₄	C₁₃×#362	1	4	yes	complemented
187	C₄	C₁₃×#390	1	1	yes	characteristic
188	C₄	C₁₃×#418	1	1	yes	characteristic
189	C₄	C₁₃×#459	1	2	yes	—
190	C₂	—	2	2	no	—
191	C₂	C₁₃×#1982	1	1	yes	characteristic
192	C₂	C₂×C₁₃×#362	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#494

C₂

yes

maximal, characteristic

C₁₃×#2150

C₂

yes

maximal, characteristic

C₂×C₁₃×#362

C₂

yes

maximal

C₄×C₁₃×#108

C₂

yes

maximal, characteristic

C₂²×C₁₃×Q₁₆

—

C₂²×C₁₃×Q₁₆

C₂²

yes

—

C₂×C₁₃×C₄⋊Q₈

—

C₂×C₁₃×M₃₂

C₂²

yes

—

C₁₃×#494

—

C₁₃×#494

C₄

yes

—

C₂×C₁₃×#108

C₂²

yes

—

C₄×C₁₃×M₁₆

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×C₄⋊C₁₆

—

C₁₃×#362

—

C₁₃×#341

—

C₂²×Q₈×C₁₃

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

C₂×C₄

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₁₃×#108

—

C₁₃×#108

D₄

yes

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

D₄

yes

—

#13256

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

SD₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²⋊C₄

yes

—

C₄²×C₁₃

D₈

yes

characteristic

C₄²×C₁₃

D₈

yes

characteristic

C₁₃×C₁₆

—

C₂×#494

C₂×C₁₃

yes

characteristic

#2150

C₂×C₁₃

yes

characteristic

C₂×#362

C₂×C₁₃

yes

—

C₄×#108

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

C₂×SD₁₆

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#102

yes

—

C₂×C₄×C₁₃

#102

yes

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

C₄×D₄

yes

—

C₈×C₁₃

yes

C₈×C₁₃

yes

C₂²×Q₁₆

—

C₂²×Q₁₆

C₂²×C₁₃

yes

—

C₂×C₄⋊Q₈

—

C₂×M₃₂

C₂²×C₁₃

yes

—

#494

—

#494

C₄×C₁₃

yes

—

C₂×#108

C₂²×C₁₃

yes

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

C₄⋊C₁₆

—

#362

—

100

#341

—

101

C₂²×C₁₃

—

102

C₂²×C₁₃

C₂×#102

yes

characteristic

103

C₂²×C₁₃

#460

yes

—

104

C₄×C₁₃

—

105

C₄×C₁₃

—

106

C₄×C₁₃

#362

yes

complemented

107

C₄×C₁₃

#390

yes

characteristic

108

C₄×C₁₃

#418

yes

characteristic

109

C₄×C₁₃

#459

yes

—

110

C₂²×Q₈

—

111

C₂×Q₁₆

—

112

C₂×Q₁₆

—

113

C₂×Q₁₆

—

114

C₂×Q₁₆

—

115

C₂×Q₁₆

—

116

C₂×Q₁₆

C₂×C₄×C₁₃

yes

—

117

C₂×M₁₆

—

118

C₂²×C₈

D₄×C₁₃

yes

characteristic

119

C₂²×C₈

C₂³×C₁₃

yes

characteristic

120

C₄⋊Q₈

—

121

C₄⋊Q₈

—

122

C₄⋊Q₈

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄²

D₄×C₁₃

yes

characteristic

125

M₃₂

—

126

C₂×C₁₆

—

127

#108

—

128

#108

D₄×C₁₃

yes

—

129

#97

—

130

C₄×C₈

—

131

C₄×C₈

C₂×C₄×C₁₃

yes

—

132

C₄×C₈

D₄×C₁₃

yes

—

133

C₂×C₁₃

—

134

C₂×C₁₃

#1982

yes

characteristic

135

C₂×C₁₃

C₂×#362

yes

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂²×C₄

—

141

C₂²×C₄

C₁₃×SD₁₆

yes

—

142

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

143

Q₁₆

—

144

Q₁₆

—

145

Q₁₆

—

146

Q₁₆

—

147

M₁₆

—

148

M₁₆

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

C₁₃×C₂²⋊C₄

yes

—

152

C₂×C₈

C₂²×C₄×C₁₃

yes

characteristic

153

C₂×C₈

C₂×D₄×C₁₃

yes

—

154

C₂×C₈

C₂×D₄×C₁₃

yes

characteristic

155

C₂×C₈

C₁₃×#41

yes

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄²

C₁₃×C₂²⋊C₄

yes

—

159

C₄²

C₁₃×D₈

yes

characteristic

160

C₄²

C₁₃×D₈

yes

characteristic

161

C₁₆

—

162

C₁₃

#13256

yes

characteristic, direct product factor, Sylow

163

C₂³

C₂×C₁₃×SD₁₆

yes

characteristic

164

Q₈

—

165

Q₈

—

166

Q₈

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

C₁₃×#102

yes

—

171

C₂×C₄

C₁₃×#102

yes

—

172

C₂×C₄

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

173

C₂×C₄

C₁₃×#121

yes

—

174

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

175

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

176

C₈

—

177

C₈

—

178

C₈

C₄×D₄×C₁₃

yes

—

179

C₈

C₁₃×#124

yes

characteristic

180

C₈

C₁₃×#127

yes

characteristic

181

C₂²

—

182

C₂²

C₂×C₁₃×#102

yes

characteristic

183

C₂²

C₁₃×#460

yes

—

184

C₄

—

185

C₄

—

186

C₄

C₁₃×#362

yes

complemented

187

C₄

C₁₃×#390

yes

characteristic

188

C₄

C₁₃×#418

yes

characteristic

189

C₄

C₁₃×#459

yes

—

190

C₂

—

191

C₂

C₁₃×#1982

yes

characteristic

192

C₂

C₂×C₁₃×#362

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

C₂×#102

commutator

C₂×C₈

C₂²×C₄×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

prime radical

C₂³×C₁₃

C₂×SD₁₆

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
40. #13256	C₁₃	direct (N × H)
106. C₄×C₁₃	#362	semidirect
162. C₁₃	#13256	direct (N × H)
186. C₄	C₁₃×#362	semidirect

H ≅ G/N

type

40. #13256

C₁₃

direct (N × H)

106. C₄×C₁₃

#362

semidirect

162. C₁₃

#13256

direct (N × H)

186. C₄

C₁₃×#362

semidirect

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

subgroup	index
C₂×C₁₃×#494	2
C₁₃×#2150	2
C₂×C₁₃×#362	2
C₄×C₁₃×#108	2
#13256	13

subgroup

index

C₂×C₁₃×#494

C₁₃×#2150

C₂×C₁₃×#362

C₄×C₁₃×#108

#13256

Subgroups — C₁₃×#13256 #15699595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13256 #15699595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13256 #15699595