Group #15750891 — subgroups

Subgroups — #15750891

Order 3328.

444 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 159 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	#13114582	C₂	1	2	yes	maximal
2	#13112659	C₂	1	4	yes	maximal
3	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#125	C₄	1	1	yes	characteristic
5	C₁₃×#389	C₂²	1	2	yes	—
6	C₁₃×#387	—	2	2	no	—
7	C₁₃×#382	C₄	1	1	yes	characteristic
8	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
9	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
10	C₄³×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×#1055	—	2	2	no	—
12	#11718116	—	2	2	no	—
13	#11718116	C₂²	1	4	yes	—
14	C₁₃×#125	—	2	2	no	—
15	C₁₃×#125	C₈	1	4	yes	complemented
16	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
17	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₃	—	2	2	no	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₃	D₄	1	2	yes	—
24	C₂×C₄²×C₁₃	D₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₂²×#1055	—	2	4	no	—
27	C₁₃×#95	—	2	2	no	—
28	C₁₃×#95	—	2	2	no	—
29	C₁₃×#95	—	2	2	no	—
30	C₄×#1055	—	2	8	no	—
31	#7568	—	13	1	no	maximal, Sylow
32	C₂²×C₄×C₁₃	—	2	2	no	—
33	C₂²×C₄×C₁₃	—	2	2	no	—
34	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
39	C₁₃×C₄⋊C₄	—	2	8	no	—
40	C₁₃×C₄⋊C₄	—	2	2	no	—
41	C₁₃×C₄⋊C₄	—	4	2	no	—
42	C₁₃×C₄⋊C₄	—	4	4	no	—
43	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
44	C₄²×C₁₃	—	2	2	no	—
45	C₄²×C₁₃	—	2	4	no	—
46	C₄²×C₁₃	—	2	4	no	—
47	C₄²×C₁₃	—	4	1	no	—
48	C₄²×C₁₃	—	4	4	no	—
49	C₄²×C₁₃	C₂×C₈	1	2	yes	—
50	C₄²×C₁₃	M₁₆	1	2	yes	—
51	C₂×#1055	—	2	8	no	—
52	C₂×#1055	—	4	4	no	—
53	C₂×#1055	—	4	4	no	—
54	C₄×#125	D₁₃	1	1	yes	characteristic
55	#1744	—	13	2	no	—
56	#1271	—	13	4	no	—
57	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃	—	2	2	no	—
59	C₂×C₄×C₁₃	—	2	1	no	—
60	C₂×C₄×C₁₃	—	2	1	no	—
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	1	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	4	2	no	—
68	C₂×C₄×C₁₃	—	4	2	no	—
69	C₂×C₄×C₁₃	—	4	2	no	—
70	C₂×C₄×C₁₃	—	4	2	no	—
71	C₂×C₄×C₁₃	—	4	2	no	—
72	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
73	C₂×C₄×C₁₃	#101	1	2	yes	—
74	C₂×C₄×C₁₃	#104	1	4	yes	—
75	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#135	1	4	yes	—
78	#1055	—	4	8	no	—
79	C₂×#125	Dic₁₃	1	1	yes	characteristic
80	C₂×C₄×C₈	—	26	2	no	—
81	#389	C₂×D₁₃	1	2	yes	—
82	#387	—	2	2	no	—
83	#382	Dic₁₃	1	1	yes	characteristic
84	C₄×C₄⋊C₄	—	2	2	no	—
85	C₄×C₄⋊C₄	Dic₁₃	1	2	yes	—
86	C₄³	C₂×D₁₃	1	1	yes	characteristic
87	#336	—	13	4	no	—
88	#336	—	26	2	no	—
89	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
90	C₂²×C₁₃	#410	1	1	yes	characteristic
91	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
92	C₂²×C₁₃	#416	1	2	yes	—
93	C₂²×C₁₃	C₂×#104	1	2	yes	—
94	C₄×C₁₃	—	2	1	no	—
95	C₄×C₁₃	—	2	1	no	—
96	C₄×C₁₃	—	2	4	no	—
97	C₄×C₁₃	—	2	4	no	—
98	C₄×C₁₃	—	4	1	no	—
99	C₄×C₁₃	—	4	4	no	—
100	C₄×C₁₃	—	8	2	no	—
101	C₄×C₁₃	#330	1	4	yes	—
102	C₂²×C₈	—	26	4	no	—
103	#125	—	2	2	no	—
104	#125	#1055	1	4	yes	complemented
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	—	2	2	no	—
107	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
108	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
109	C₂×C₄²	—	2	2	no	—
110	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
111	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
112	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
113	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
114	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
115	C₄×C₈	—	26	8	no	—
116	#95	—	2	2	no	—
117	#95	—	2	2	no	—
118	#95	—	2	2	no	—
119	C₂×C₁₃	#1461	1	1	yes	characteristic
120	C₂×C₁₃	#1476	1	2	yes	—
121	C₂×C₁₃	#1500	1	2	yes	—
122	C₂×C₁₃	C₂×#330	1	1	yes	characteristic
123	C₂×C₁₃	#1544	1	1	yes	characteristic
124	C₂²×C₄	—	2	2	no	—
125	C₂²×C₄	—	2	2	no	—
126	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
127	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
128	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
129	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
130	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
131	C₂×C₈	—	26	8	no	—
132	C₂×C₈	—	52	4	no	—
133	C₂×C₈	—	52	4	no	—
134	C₄⋊C₄	—	2	8	no	—
135	C₄⋊C₄	—	2	2	no	—
136	C₄⋊C₄	—	4	2	no	—
137	C₄⋊C₄	—	4	4	no	—
138	C₄⋊C₄	C₂×#1055	1	4	yes	—
139	C₄²	—	2	2	no	—
140	C₄²	—	2	4	no	—
141	C₄²	—	2	4	no	—
142	C₄²	—	4	1	no	—
143	C₄²	—	4	4	no	—
144	C₄²	C₂×#1055	1	2	yes	—
145	C₄²	#6099	1	2	yes	—
146	C₁₃	#7568	1	1	yes	characteristic, complemented, Sylow
147	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	4	2	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	C₂²⋊#1055	1	4	yes	—
163	C₂×C₄	#88076	1	2	yes	—
164	C₂×C₄	#88077	1	4	yes	—
165	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
166	C₂×C₄	C₂×#6099	1	1	yes	characteristic
167	C₂×C₄	#88204	1	4	yes	—
168	C₈	—	52	8	no	—
169	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
170	C₂²	C₂×#88076	1	1	yes	characteristic
171	C₂²	#11718894	1	2	yes	—
172	C₂²	C₂×#88077	1	2	yes	—
173	C₂²	#11718901	1	1	yes	characteristic
174	C₄	—	2	1	no	—
175	C₄	—	2	1	no	—
176	C₄	—	2	4	no	—
177	C₄	—	2	4	no	—
178	C₄	—	4	4	no	—
179	C₄	—	4	1	no	—
180	C₄	—	8	2	no	—
181	C₄	#11718135	1	4	yes	—
182	C₂	#13113160	1	1	yes	characteristic
183	C₂	#13113218	1	2	yes	—
184	C₂	#13113322	1	2	yes	—
185	C₂	C₂×#11718135	1	1	yes	characteristic
186	C₂	#13113501	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13114582

C₂

yes

maximal

#13112659

C₂

yes

maximal

C₄×C₁₃×#125

C₂

yes

maximal, characteristic

C₂×C₁₃×#125

C₄

yes

characteristic

C₁₃×#389

C₂²

yes

—

C₁₃×#387

—

C₁₃×#382

C₄

yes

characteristic

C₄×C₁₃×C₄⋊C₄

—

C₄×C₁₃×C₄⋊C₄

C₄

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

C₂×C₄×#1055

—

#11718116

—

#11718116

C₂²

yes

—

C₁₃×#125

—

C₁₃×#125

C₈

yes

complemented

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂²×#1055

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

C₄×#1055

—

#7568

—

maximal, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

C₂×C₈

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

M₁₆

yes

—

—

—

—

D₁₃

yes

characteristic

#1744

—

#1271

—

C₂³×C₁₃

C₂×C₂²⋊C₄

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

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₈

yes

—

C₂×C₄×C₁₃

#101

yes

—

C₂×C₄×C₁₃

#104

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

#135

yes

—

#1055

—

C₂×#125

Dic₁₃

yes

characteristic

C₂×C₄×C₈

—

#389

C₂×D₁₃

yes

—

#387

—

#382

Dic₁₃

yes

characteristic

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

Dic₁₃

yes

—

C₄³

C₂×D₁₃

yes

characteristic

#336

—

#336

—

C₂²×C₁₃

C₂×C₂²⋊C₈

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₂²×C₁₃

C₂×#104

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

100

C₄×C₁₃

—

101

C₄×C₁₃

#330

yes

—

102

C₂²×C₈

—

103

#125

—

104

#125

#1055

yes

complemented

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

—

108

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

—

109

C₂×C₄²

—

110

C₂×C₄²

C₂×Dic₁₃

yes

characteristic

111

C₂×C₄²

C₂×Dic₁₃

yes

characteristic

112

C₂×C₄²

C₂²⋊D₁₃

yes

—

113

C₂×C₄²

C₂²⋊D₁₃

yes

—

114

C₂×C₄²

C₂²×D₁₃

yes

characteristic

115

C₄×C₈

—

116

#95

—

117

#95

—

118

#95

—

119

C₂×C₁₃

#1461

yes

characteristic

120

C₂×C₁₃

#1476

yes

—

121

C₂×C₁₃

#1500

yes

—

122

C₂×C₁₃

C₂×#330

yes

characteristic

123

C₂×C₁₃

#1544

yes

characteristic

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

C₂²⋊Dic₁₃

yes

characteristic

127

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

128

C₂²×C₄

C₂²⋊Dic₁₃

yes

characteristic

129

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

130

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

C₂×#1055

yes

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₄²

—

144

C₄²

C₂×#1055

yes

—

145

C₄²

#6099

yes

—

146

C₁₃

#7568

yes

characteristic, complemented, Sylow

147

C₂³

C₂×C₂²⋊Dic₁₃

yes

characteristic

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

C₂²⋊#1055

yes

—

163

C₂×C₄

#88076

yes

—

164

C₂×C₄

#88077

yes

—

165

C₂×C₄

C₂²×#1055

yes

characteristic

166

C₂×C₄

C₂×#6099

yes

characteristic

167

C₂×C₄

#88204

yes

—

168

C₈

—

169

C₂²

C₂×C₂²⋊#1055

yes

characteristic

170

C₂²

C₂×#88076

yes

characteristic

171

C₂²

#11718894

yes

—

172

C₂²

C₂×#88077

yes

—

173

C₂²

#11718901

yes

characteristic

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

#11718135

yes

—

182

C₂

#13113160

yes

characteristic

183

C₂

#13113218

yes

—

184

C₂

#13113322

yes

—

185

C₂

C₂×#11718135

yes

characteristic

186

C₂

#13113501

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄×C₁₃×#125	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#125	D₁₃
hypocenter	C₁₃	#7568
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#125

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₄×C₁₃×#125

C₂

socle, prime radical

C₂³×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#125

N	H ≅ G/N	type
15. C₁₃×#125	C₈	semidirect
104. #125	#1055	semidirect
146. C₁₃	#7568	semidirect

H ≅ G/N

type

15. C₁₃×#125

C₈

semidirect

104. #125

#1055

semidirect

146. C₁₃

#7568

semidirect

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

subgroup	index
#13114582	2
#13112659	2
C₄×C₁₃×#125	2
#7568	13

subgroup

index

#13114582

#13112659

C₄×C₁₃×#125

#7568

Subgroups — #15750891

Conjugacy classes of subgroups

Complements

Maximal subgroups