Group #15780374 — subgroups

Subgroups — #15780374

Order 3328.

458 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 131 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	#13127939	C₂	1	1	yes	maximal, characteristic
2	#13116556	C₂	1	2	yes	maximal, complemented
3	#13114882	C₂	1	1	yes	maximal, characteristic
4	#13112937	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
8	C₁₃×#536	—	2	1	no	—
9	C₁₃×#470	C₄	1	4	yes	complemented
10	C₁₃×#467	—	2	2	no	—
11	C₁₃×#427	C₂²	1	1	yes	characteristic
12	C₁₃×#419	—	2	1	no	—
13	#11718901	—	2	1	no	—
14	#11718801	—	2	4	no	—
15	#11718767	C₂²	1	2	yes	—
16	C₂×#88052	—	2	2	no	—
17	C₂×#88052	C₂²	1	2	yes	—
18	#11718156	—	2	4	no	—
19	#11718149	—	2	1	no	—
20	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
21	C₂²×Q₈×C₁₃	—	2	1	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	—	2	1	no	—
24	C₂×C₁₃×Q₁₆	—	2	2	no	—
25	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
26	C₁₃×#131	—	2	2	no	—
27	C₁₃×#131	—	2	2	no	—
28	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
29	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	D₄	1	2	yes	—
31	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
32	C₁₃×C₄⋊Q₈	—	4	1	no	—
33	C₁₃×#124	—	4	1	no	—
34	C₁₃×#123	—	4	2	no	—
35	C₁₃×C₂²⋊Q₈	—	2	4	no	—
36	C₁₃×#117	—	2	1	no	—
37	#88180	—	2	2	no	—
38	C₁₃×#107	—	2	1	no	—
39	C₁₃×#106	C₂×C₄	1	2	yes	—
40	C₁₃×#103	—	2	4	no	—
41	#88074	—	4	2	no	—
42	#88058	—	2	2	no	—
43	#88057	—	2	2	no	—
44	#88052	—	2	4	no	—
45	#88052	—	2	2	no	—
46	#88052	—	2	2	no	—
47	C₂×#6090	—	2	4	no	—
48	C₂×#6090	D₄	1	4	yes	—
49	#13075	—	13	1	no	maximal, Sylow
50	C₁₃×#41	—	2	2	no	—
51	C₁₃×#41	—	2	2	no	—
52	C₂×Q₈×C₁₃	—	2	2	no	—
53	C₂×Q₈×C₁₃	—	4	1	no	—
54	C₂×Q₈×C₁₃	—	4	2	no	—
55	C₂×Q₈×C₁₃	—	4	2	no	—
56	C₂×Q₈×C₁₃	SD₁₆	1	1	yes	characteristic
57	C₂×D₄×C₁₃	D₈	1	2	yes	—
58	C₂×D₄×C₁₃	SD₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	—	4	1	no	—
60	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₁₃×Q₁₆	—	2	4	no	—
63	C₁₃×Q₁₆	—	4	1	no	—
64	C₁₃×Q₁₆	—	4	1	no	—
65	C₁₃×M₁₆	—	2	2	no	—
66	C₁₃×M₁₆	—	2	4	no	—
67	C₂×C₈×C₁₃	—	2	2	no	—
68	C₂×C₈×C₁₃	—	2	2	no	—
69	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃	#41	1	2	yes	—
74	C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₁₃×C₄⋊C₄	—	4	4	no	—
76	C₁₃×C₂²⋊C₄	—	4	4	no	—
77	C₁₃×C₂²⋊C₄	—	4	1	no	—
78	C₄²×C₁₃	—	4	1	no	—
79	C₂²⋊Dic₁₃	—	4	2	no	—
80	C₄⋊Dic₁₃	—	4	2	no	—
81	C₄×Dic₁₃	—	4	2	no	—
82	#6090	—	2	4	no	—
83	#3407	—	13	1	no	—
84	#3059	D₁₃	1	1	yes	characteristic
85	#2141	—	13	2	no	—
86	#1812	—	13	1	no	—
87	#1384	—	13	2	no	—
88	C₂³×C₁₃	#102	1	2	yes	—
89	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
90	Q₈×C₁₃	—	2	2	no	—
91	Q₈×C₁₃	—	4	2	no	—
92	Q₈×C₁₃	—	4	2	no	—
93	Q₈×C₁₃	—	8	2	no	—
94	D₄×C₁₃	—	2	4	no	—
95	D₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	4	2	no	—
99	C₂×C₄×C₁₃	—	4	2	no	—
100	C₂×C₄×C₁₃	—	8	2	no	—
101	C₂×C₄×C₁₃	#102	1	2	yes	—
102	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#121	1	2	yes	—
104	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₃	#135	1	2	yes	—
106	C₂×Dic₁₃	—	8	2	no	—
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	C₄×D₄	1	2	yes	—
109	C₈×C₁₃	#120	1	1	yes	characteristic
110	C₈×C₁₃	#123	1	1	yes	characteristic
111	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
112	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
113	#536	—	2	1	no	—
114	#504	—	26	4	no	—
115	C₂×M₃₂	—	13	2	no	—
116	C₂×M₃₂	—	26	2	no	—
117	#470	Dic₁₃	1	4	yes	complemented
118	#467	—	2	2	no	—
119	#427	—	13	2	no	—
120	#427	C₂×D₁₃	1	1	yes	characteristic
121	#419	—	2	1	no	—
122	#410	—	26	1	no	—
123	#358	—	26	4	no	—
124	H(3,ℤ/4)	—	26	1	no	—
125	C₂²×C₁₃	—	2	2	no	—
126	C₂²×C₁₃	—	4	1	no	—
127	C₂²×C₁₃	—	4	2	no	—
128	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
129	C₂²×C₁₃	#466	1	2	yes	—
130	C₄×C₁₃	—	2	2	no	—
131	C₄×C₁₃	—	8	2	no	—
132	C₄×C₁₃	—	8	2	no	—
133	C₄×C₁₃	#386	1	1	yes	characteristic
134	C₄×C₁₃	#416	1	1	yes	characteristic
135	C₄×C₁₃	#465	1	2	yes	—
136	Dic₁₃	—	16	2	no	—
137	C₂×#41	C₂²⋊D₁₃	1	1	yes	characteristic
138	C₂²×Q₈	—	2	1	no	—
139	C₂×Q₁₆	—	2	2	no	—
140	C₂×Q₁₆	—	2	2	no	—
141	C₂×Q₁₆	—	2	1	no	—
142	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
143	#131	—	2	2	no	—
144	#131	—	2	2	no	—
145	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
146	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
147	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
148	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
149	C₄⋊Q₈	—	4	1	no	—
150	#124	—	4	1	no	—
151	#123	—	4	2	no	—
152	C₂²⋊Q₈	—	2	4	no	—
153	#117	—	2	1	no	—
154	#117	—	26	2	no	—
155	M₃₂	—	26	4	no	—
156	M₃₂	—	26	2	no	—
157	M₃₂	—	26	2	no	—
158	C₂×C₁₆	—	13	4	no	—
159	C₂×C₁₆	—	26	4	no	—
160	#107	—	2	1	no	—
161	#107	—	26	2	no	—
162	#106	—	26	2	no	—
163	#106	C₂×Dic₁₃	1	2	yes	—
164	#103	—	2	4	no	—
165	#99	—	52	2	no	—
166	C₂×C₁₃	—	2	2	no	—
167	C₂×C₁₃	—	2	1	no	—
168	C₂×C₁₃	—	4	2	no	—
169	C₂×C₁₃	#1893	1	1	yes	characteristic
170	#41	—	2	2	no	—
171	#41	—	2	2	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	4	1	no	—
174	C₂×Q₈	—	4	2	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	#6105	1	1	yes	characteristic
177	C₂×D₄	#6104	1	2	yes	—
178	C₂×D₄	#6105	1	1	yes	characteristic
179	C₂²×C₄	—	4	1	no	—
180	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
181	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
182	Q₁₆	—	2	4	no	—
183	Q₁₆	—	4	1	no	—
184	Q₁₆	—	4	1	no	—
185	M₁₆	—	2	2	no	—
186	M₁₆	—	2	4	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
190	C₂×C₈	D₄×D₁₃	1	2	yes	—
191	C₂×C₈	#6129	1	2	yes	—
192	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
193	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	4	4	no	—
196	C₄⋊C₄	—	52	2	no	—
197	C₂²⋊C₄	—	4	4	no	—
198	C₂²⋊C₄	—	4	1	no	—
199	C₂²⋊C₄	—	52	2	no	—
200	C₄²	—	4	1	no	—
201	C₄²	—	52	2	no	—
202	C₁₆	—	26	4	no	—
203	C₁₃	#13075	1	1	yes	characteristic, complemented, Sylow
204	C₂³	#88072	1	2	yes	—
205	C₂³	C₂×#6104	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	4	2	no	—
209	Q₈	—	8	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	104	2	no	—
218	C₂×C₄	#88072	1	2	yes	—
219	C₂×C₄	C₂×#6105	1	1	yes	characteristic
220	C₂×C₄	#88193	1	2	yes	—
221	C₂×C₄	#88204	1	2	yes	—
222	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	D₄×Dic₁₃	1	2	yes	—
225	C₈	#88189	1	1	yes	characteristic
226	C₈	#88191	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	#11718699	1	2	yes	—
231	C₂²	C₂×#88072	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	8	2	no	—
234	C₄	—	8	2	no	—
235	C₄	—	208	2	no	—
236	C₄	#11718702	1	2	yes	—
237	C₄	#11718881	1	1	yes	characteristic
238	C₄	#11718894	1	1	yes	characteristic
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#13115265	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13127939

C₂

yes

maximal, characteristic

#13116556

C₂

yes

maximal, complemented

#13114882

C₂

yes

maximal, characteristic

#13112937

C₂

yes

maximal, complemented

C₁₃×#3059

C₂

yes

maximal, characteristic

C₂²×C₁₃×Q₁₆

C₂²

yes

characteristic

C₂×C₁₃×#131

C₂²

yes

characteristic

C₁₃×#536

—

C₁₃×#470

C₄

yes

complemented

C₁₃×#467

—

C₁₃×#427

C₂²

yes

characteristic

C₁₃×#419

—

#11718901

—

#11718801

—

#11718767

C₂²

yes

—

C₂×#88052

—

C₂×#88052

C₂²

yes

—

#11718156

—

#11718149

—

C₂×C₁₃×#41

D₄

yes

characteristic

C₂²×Q₈×C₁₃

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

C₂×C₄

yes

—

C₁₃×#131

—

C₁₃×#131

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₁₃×M₁₆

D₄

yes

characteristic

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊Q₈

—

C₁₃×#124

—

C₁₃×#123

—

C₁₃×C₂²⋊Q₈

—

C₁₃×#117

—

#88180

—

C₁₃×#107

—

C₁₃×#106

C₂×C₄

yes

—

C₁₃×#103

—

—

—

—

—

—

—

—

D₄

yes

—

#13075

—

maximal, Sylow

C₁₃×#41

—

C₁₃×#41

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

SD₁₆

yes

characteristic

C₂×D₄×C₁₃

D₈

yes

—

C₂×D₄×C₁₃

SD₁₆

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

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

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

#6090

—

#3407

—

#3059

D₁₃

yes

—

—

—

C₂³×C₁₃

#102

yes

—

C₂³×C₁₃

C₂×D₈

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

#102

yes

—

102

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

103

C₂×C₄×C₁₃

#121

yes

—

104

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

105

C₂×C₄×C₁₃

#135

yes

—

106

C₂×Dic₁₃

—

107

C₈×C₁₃

—

108

C₈×C₁₃

C₄×D₄

yes

—

109

C₈×C₁₃

#120

yes

characteristic

110

C₈×C₁₃

#123

yes

characteristic

111

C₂²×Q₁₆

C₂×D₁₃

yes

characteristic

112

C₂×#131

C₂×D₁₃

yes

characteristic

113

#536

—

114

#504

—

115

C₂×M₃₂

—

116

C₂×M₃₂

—

117

#470

Dic₁₃

yes

complemented

118

#467

—

119

#427

—

120

#427

C₂×D₁₃

yes

characteristic

121

#419

—

122

#410

—

123

#358

—

124

H(3,ℤ/4)

—

125

C₂²×C₁₃

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

C₂×#102

yes

characteristic

129

C₂²×C₁₃

#466

yes

—

130

C₄×C₁₃

—

131

C₄×C₁₃

—

132

C₄×C₁₃

—

133

C₄×C₁₃

#386

yes

characteristic

134

C₄×C₁₃

#416

yes

characteristic

135

C₄×C₁₃

#465

yes

—

136

Dic₁₃

—

137

C₂×#41

C₂²⋊D₁₃

yes

characteristic

138

C₂²×Q₈

—

139

C₂×Q₁₆

—

140

C₂×Q₁₆

—

141

C₂×Q₁₆

—

142

C₂×Q₁₆

C₂×Dic₁₃

yes

—

143

#131

—

144

#131

—

145

C₂×M₁₆

C₂×Dic₁₃

yes

—

146

C₂×M₁₆

C₂²⋊D₁₃

yes

characteristic

147

C₂²×C₈

C₂²⋊D₁₃

yes

—

148

C₂²×C₈

C₂²×D₁₃

yes

characteristic

149

C₄⋊Q₈

—

150

#124

—

151

#123

—

152

C₂²⋊Q₈

—

153

#117

—

154

#117

—

155

M₃₂

—

156

M₃₂

—

157

M₃₂

—

158

C₂×C₁₆

—

159

C₂×C₁₆

—

160

#107

—

161

#107

—

162

#106

—

163

#106

C₂×Dic₁₃

yes

—

164

#103

—

165

#99

—

166

C₂×C₁₃

—

167

C₂×C₁₃

—

168

C₂×C₁₃

—

169

C₂×C₁₃

#1893

yes

characteristic

170

#41

—

171

#41

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

#6105

yes

characteristic

177

C₂×D₄

#6104

yes

—

178

C₂×D₄

#6105

yes

characteristic

179

C₂²×C₄

—

180

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

181

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

182

Q₁₆

—

183

Q₁₆

—

184

Q₁₆

—

185

M₁₆

—

186

M₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

C₂²⋊Dic₁₃

yes

—

190

C₂×C₈

D₄×D₁₃

yes

—

191

C₂×C₈

#6129

yes

—

192

C₂×C₈

C₂²×Dic₁₃

yes

characteristic

193

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₂²⋊C₄

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₄²

—

201

C₄²

—

202

C₁₆

—

203

C₁₃

#13075

yes

characteristic, complemented, Sylow

204

C₂³

#88072

yes

—

205

C₂³

C₂×#6104

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

104

—

218

C₂×C₄

#88072

yes

—

219

C₂×C₄

C₂×#6105

yes

characteristic

220

C₂×C₄

#88193

yes

—

221

C₂×C₄

#88204

yes

—

222

C₂×C₄

C₂×C₂²⋊Dic₁₃

yes

characteristic

223

C₈

—

224

C₈

D₄×Dic₁₃

yes

—

225

C₈

#88189

yes

characteristic

226

C₈

#88191

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

#11718699

yes

—

231

C₂²

C₂×#88072

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

208

—

236

C₄

#11718702

yes

—

237

C₄

#11718881

yes

characteristic

238

C₄

#11718894

yes

characteristic

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#13115265

yes

characteristic

	subgroup	G/H
center	C₂	#13115265
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#3059	C₂
socle	C₂×C₁₃	#1893
prime radical	C₂×C₁₃×#41	D₄
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#3059	D₁₃
hypocenter	C₁₃	#13075
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

subgroup

G/H

center

C₂

#13115265

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#3059

C₂

socle

C₂×C₁₃

#1893

prime radical

C₂×C₁₃×#41

D₄

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

N	H ≅ G/N	type
2. #13116556	C₂	semidirect
4. #13112937	C₂	semidirect
9. C₁₃×#470	C₄	semidirect
117. #470	Dic₁₃	semidirect
203. C₁₃	#13075	semidirect

H ≅ G/N

type

2. #13116556

C₂

semidirect

4. #13112937

C₂

semidirect

9. C₁₃×#470

C₄

semidirect

117. #470

Dic₁₃

semidirect

203. C₁₃

#13075

semidirect

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

subgroup	index
#13127939	2
#13116556	2
#13114882	2
#13112937	2
C₁₃×#3059	2
#13075	13

subgroup

index

C₁₃×#3059

Subgroups — #15780374

Conjugacy classes of subgroups

Complements

Maximal subgroups