Group #15757386 — subgroups

Subgroups — #15757386

Order 3328.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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	#13117926	C₂	1	1	yes	maximal, characteristic
2	#13115639	C₂	1	1	yes	maximal, characteristic
3	#13115600	C₂	1	2	yes	maximal
4	#13112675	C₂	1	2	yes	maximal
5	C₂×C₁₃×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
8	#11718891	—	2	2	no	—
9	C₂×#88075	—	2	2	no	—
10	C₂×#88057	—	2	2	no	—
11	#11718646	—	2	2	no	—
12	C₄⋊C₄×Dic₁₃	—	2	2	no	—
13	#11718596	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₁₃×#333	C₄	1	4	yes	complemented
17	#11718143	—	2	2	no	—
18	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
19	C₂²×C₈×C₁₃	—	2	2	no	—
20	C₁₃×C₄⋊Q₈	—	2	2	no	—
21	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
22	C₁₃×C₄⋊Q₈	Q₈	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₃	—	2	2	no	—
26	C₂×C₄⋊Dic₁₃	—	2	1	no	—
27	C₂×C₄⋊Dic₁₃	—	2	2	no	—
28	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
30	C₂×C₄×Dic₁₃	—	2	2	no	—
31	C₂×C₄×Dic₁₃	—	2	2	no	—
32	C₂²×#1055	—	2	1	no	—
33	C₁₃×C₄⋊C₈	—	2	2	no	—
34	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
35	#88075	—	4	4	no	—
36	#88071	—	2	4	no	—
37	#88071	—	2	2	no	—
38	#88057	—	4	4	no	—
39	C₄×#1055	—	2	2	no	—
40	#8928	—	13	1	no	maximal, Sylow
41	C₂×Q₈×C₁₃	—	2	2	no	—
42	C₂×Q₈×C₁₃	—	4	2	no	—
43	C₂×Q₈×C₁₃	—	4	2	no	—
44	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₃	—	2	2	no	—
46	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
48	C₂²×Dic₁₃	—	2	2	no	—
49	C₂²×Dic₁₃	—	2	2	no	—
50	C₂²×Dic₁₃	—	4	1	no	—
51	C₂×C₈×C₁₃	—	2	4	no	—
52	C₂×C₈×C₁₃	—	4	2	no	—
53	C₂×C₈×C₁₃	—	4	2	no	—
54	C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
58	C₄²×C₁₃	#41	1	2	yes	—
59	C₄⋊Dic₁₃	—	2	2	no	—
60	C₄⋊Dic₁₃	—	2	2	no	—
61	C₄⋊Dic₁₃	—	2	2	no	—
62	C₄⋊Dic₁₃	—	4	2	no	—
63	C₄⋊Dic₁₃	—	4	2	no	—
64	C₄⋊Dic₁₃	—	4	2	no	—
65	C₄⋊Dic₁₃	—	8	2	no	—
66	C₄⋊Dic₁₃	SD₁₆	1	4	yes	—
67	C₄×Dic₁₃	—	4	2	no	—
68	C₄×Dic₁₃	—	4	2	no	—
69	C₄×Dic₁₃	—	8	2	no	—
70	C₂×#1055	—	2	2	no	—
71	C₂×#1055	—	4	1	no	—
72	C₂×#1055	—	4	1	no	—
73	#2369	—	13	1	no	—
74	#1956	—	13	1	no	—
75	#1948	—	13	2	no	—
76	C₂×#333	D₁₃	1	1	yes	characteristic
77	#1279	—	13	2	no	—
78	C₂³×C₁₃	#120	1	1	yes	characteristic
79	Q₈×C₁₃	—	4	4	no	—
80	Q₈×C₁₃	—	8	2	no	—
81	C₂×C₄×C₁₃	—	2	1	no	—
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	4	no	—
84	C₂×C₄×C₁₃	—	4	2	no	—
85	C₂×C₄×C₁₃	—	4	2	no	—
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
89	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₁₃	#135	1	2	yes	—
92	C₂×C₄×C₁₃	#137	1	2	yes	—
93	C₂×C₄×C₁₃	#137	1	2	yes	—
94	C₂×Dic₁₃	—	2	4	no	—
95	C₂×Dic₁₃	—	4	2	no	—
96	C₂×Dic₁₃	—	4	2	no	—
97	C₂×Dic₁₃	—	4	2	no	—
98	C₂×Dic₁₃	—	4	2	no	—
99	C₂×Dic₁₃	—	4	2	no	—
100	C₂×Dic₁₃	—	8	2	no	—
101	C₂×Dic₁₃	—	8	1	no	—
102	C₈×C₁₃	—	4	4	no	—
103	#1055	—	4	2	no	—
104	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
105	C₂×#106	—	26	2	no	—
106	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
107	C₂×#103	—	26	2	no	—
108	C₂×C₄×C₈	—	13	1	no	—
109	#391	—	26	2	no	—
110	#389	—	26	2	no	—
111	#384	—	13	1	no	—
112	C₄×C₄⋊C₄	—	13	2	no	—
113	C₄×C₄⋊C₄	—	26	2	no	—
114	#340	—	26	2	no	—
115	#333	Dic₁₃	1	4	yes	complemented
116	C₂²×C₁₃	#385	1	1	yes	characteristic
117	C₂²×C₁₃	#448	1	2	yes	—
118	C₂²×C₁₃	#452	1	2	yes	—
119	C₂²×C₁₃	#453	1	1	yes	characteristic
120	C₂²×C₁₃	#455	1	1	yes	characteristic
121	C₄×C₁₃	—	2	1	no	—
122	C₄×C₁₃	—	2	1	no	—
123	C₄×C₁₃	—	4	4	no	—
124	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
125	C₄×C₁₃	#441	1	2	yes	—
126	C₄×C₁₃	#475	1	2	yes	—
127	C₄×C₁₃	#479	1	2	yes	—
128	Dic₁₃	—	4	4	no	—
129	Dic₁₃	—	8	2	no	—
130	Dic₁₃	—	16	1	no	—
131	C₂²×Q₈	D₅₂	1	2	yes	—
132	C₂²×C₈	—	2	2	no	—
133	C₂²×C₈	—	26	1	no	—
134	C₄⋊Q₈	—	2	2	no	—
135	C₄⋊Q₈	Dic₂₆	1	2	yes	—
136	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	13	2	no	—
139	C₂×C₄⋊C₄	—	13	2	no	—
140	C₂×C₄⋊C₄	—	26	1	no	—
141	C₂×C₄⋊C₄	—	26	2	no	—
142	C₂×C₄⋊C₄	—	26	2	no	—
143	C₂×C₄²	—	26	2	no	—
144	C₂×C₄²	—	26	2	no	—
145	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
146	#106	—	52	4	no	—
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
149	#103	—	52	4	no	—
150	C₄×C₈	—	26	2	no	—
151	#95	—	26	4	no	—
152	#95	—	26	2	no	—
153	C₂×C₁₃	#1623	1	1	yes	characteristic
154	C₂×C₁₃	#1634	1	1	yes	characteristic
155	C₂×C₁₃	#1643	1	2	yes	—
156	C₂×C₁₃	#1856	1	1	yes	characteristic
157	C₂×C₁₃	#1865	1	2	yes	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	C₄⋊Dic₁₃	1	4	yes	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	26	2	no	—
164	C₂²×C₄	—	26	2	no	—
165	C₂²×C₄	—	52	1	no	—
166	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
167	C₂²×C₄	D₄×D₁₃	1	2	yes	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	26	2	no	—
172	C₂×C₈	—	52	1	no	—
173	C₂×C₈	—	52	1	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	13	4	no	—
177	C₄⋊C₄	—	26	2	no	—
178	C₄⋊C₄	—	26	2	no	—
179	C₄⋊C₄	—	26	2	no	—
180	C₄⋊C₄	—	52	2	no	—
181	C₄⋊C₄	—	52	2	no	—
182	C₄⋊C₄	—	52	2	no	—
183	C₄⋊C₄	—	104	2	no	—
184	C₄²	—	52	2	no	—
185	C₄²	—	52	2	no	—
186	C₄²	—	104	2	no	—
187	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
188	C₄²	#6129	1	2	yes	—
189	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
190	C₁₃	#8928	1	1	yes	characteristic, complemented, Sylow
191	C₂³	#88136	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	26	4	no	—
200	C₂×C₄	—	52	2	no	—
201	C₂×C₄	—	52	2	no	—
202	C₂×C₄	—	52	2	no	—
203	C₂×C₄	—	52	2	no	—
204	C₂×C₄	—	52	2	no	—
205	C₂×C₄	—	104	1	no	—
206	C₂×C₄	—	104	2	no	—
207	C₂×C₄	#88132	1	2	yes	—
208	C₂×C₄	#88140	1	1	yes	characteristic
209	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
210	C₂×C₄	#88170	1	2	yes	—
211	C₂×C₄	#88172	1	2	yes	—
212	C₂×C₄	#88172	1	2	yes	—
213	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
214	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
215	C₈	—	4	4	no	—
216	C₈	—	52	2	no	—
217	C₂²	#11718407	1	1	yes	characteristic
218	C₂²	#11718408	1	1	yes	characteristic
219	C₂²	#11718467	1	2	yes	—
220	C₂²	#11718471	1	2	yes	—
221	C₂²	#11718611	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	52	4	no	—
226	C₄	—	104	2	no	—
227	C₄	—	208	1	no	—
228	C₄	#11718452	1	2	yes	—
229	C₄	#11718460	1	2	yes	—
230	C₄	SD₁₆×Dic₁₃	1	2	yes	—
231	C₄	#11718845	1	2	yes	—
232	C₂	#13113915	1	1	yes	characteristic
233	C₂	#13113982	1	1	yes	characteristic
234	C₂	#13114044	1	2	yes	—
235	C₂	#13115048	1	1	yes	characteristic
236	C₂	#13115106	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13117926

C₂

yes

maximal, characteristic

#13115639

C₂

yes

maximal, characteristic

#13115600

C₂

yes

maximal

#13112675

C₂

yes

maximal

C₂×C₁₃×#333

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₈

C₂²

yes

—

—

—

—

—

C₄⋊C₄×Dic₁₃

—

#11718596

C₂²

yes

characteristic

C₄×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄×#1055

C₂²

yes

characteristic

C₁₃×#333

C₄

yes

complemented

#11718143

—

C₂²×Q₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

C₂×C₄

yes

—

C₁₃×C₄⋊Q₈

Q₈

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

D₄

yes

—

C₂×C₄⋊Dic₁₃

D₄

yes

—

C₂×C₄×Dic₁₃

—

C₂×C₄×Dic₁₃

—

C₂²×#1055

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

C₂×C₄

yes

—

—

—

—

—

—

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

C₄⋊C₄

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

SD₁₆

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

—

—

D₁₃

yes

characteristic

#1279

—

C₂³×C₁₃

#120

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#123

yes

characteristic

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

100

C₂×Dic₁₃

—

101

C₂×Dic₁₃

—

102

C₈×C₁₃

—

103

#1055

—

104

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

105

C₂×#106

—

106

C₂×C₄⋊C₈

C₂×D₁₃

yes

—

107

C₂×#103

—

108

C₂×C₄×C₈

—

109

#391

—

110

#389

—

111

#384

—

112

C₄×C₄⋊C₄

—

113

C₄×C₄⋊C₄

—

114

#340

—

115

#333

Dic₁₃

yes

complemented

116

C₂²×C₁₃

#385

yes

characteristic

117

C₂²×C₁₃

#448

yes

—

118

C₂²×C₁₃

#452

yes

—

119

C₂²×C₁₃

#453

yes

characteristic

120

C₂²×C₁₃

#455

yes

characteristic

121

C₄×C₁₃

—

122

C₄×C₁₃

—

123

C₄×C₁₃

—

124

C₄×C₁₃

C₄×SD₁₆

yes

—

125

C₄×C₁₃

#441

yes

—

126

C₄×C₁₃

#475

yes

—

127

C₄×C₁₃

#479

yes

—

128

Dic₁₃

—

129

Dic₁₃

—

130

Dic₁₃

—

131

C₂²×Q₈

D₅₂

yes

—

132

C₂²×C₈

—

133

C₂²×C₈

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

Dic₂₆

yes

—

136

C₄⋊Q₈

C₂×Dic₁₃

yes

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄²

—

144

C₂×C₄²

—

145

C₂×C₄²

C₂²×D₁₃

yes

characteristic

146

#106

—

147

C₄⋊C₈

—

148

C₄⋊C₈

C₂×Dic₁₃

yes

—

149

#103

—

150

C₄×C₈

—

151

#95

—

152

#95

—

153

C₂×C₁₃

#1623

yes

characteristic

154

C₂×C₁₃

#1634

yes

characteristic

155

C₂×C₁₃

#1643

yes

—

156

C₂×C₁₃

#1856

yes

characteristic

157

C₂×C₁₃

#1865

yes

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₄⋊Dic₁₃

yes

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂×D₅₂

yes

characteristic

167

C₂²×C₄

D₄×D₁₃

yes

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

104

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

104

—

187

C₄²

C₂×Dic₂₆

yes

characteristic

188

C₄²

#6129

yes

—

189

C₄²

C₂²×Dic₁₃

yes

characteristic

190

C₁₃

#8928

yes

characteristic, complemented, Sylow

191

C₂³

#88136

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

104

—

206

C₂×C₄

—

104

—

207

C₂×C₄

#88132

yes

—

208

C₂×C₄

#88140

yes

characteristic

209

C₂×C₄

SD₁₆×D₁₃

yes

—

210

C₂×C₄

#88170

yes

—

211

C₂×C₄

#88172

yes

—

212

C₂×C₄

#88172

yes

—

213

C₂×C₄

C₂×C₄⋊Dic₁₃

yes

characteristic

214

C₂×C₄

D₄×Dic₁₃

yes

—

215

C₈

—

216

C₈

—

217

C₂²

#11718407

yes

characteristic

218

C₂²

#11718408

yes

characteristic

219

C₂²

#11718467

yes

—

220

C₂²

#11718471

yes

—

221

C₂²

#11718611

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

104

—

227

C₄

—

208

—

228

C₄

#11718452

yes

—

229

C₄

#11718460

yes

—

230

C₄

SD₁₆×Dic₁₃

yes

—

231

C₄

#11718845

yes

—

232

C₂

#13113915

yes

characteristic

233

C₂

#13113982

yes

characteristic

234

C₂

#13114044

yes

—

235

C₂

#13115048

yes

characteristic

236

C₂

#13115106

yes

—

	subgroup	G/H
center	C₂³	#88136
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#333	C₂
socle, prime radical	C₂³×C₁₃	#120
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#333	D₁₃
hypocenter	C₁₃	#8928
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

#88136

commutator

C₄²×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₂×C₁₃×#333

C₂

socle, prime radical

C₂³×C₁₃

#120

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
16. C₁₃×#333	C₄	semidirect
115. #333	Dic₁₃	semidirect
190. C₁₃	#8928	semidirect

H ≅ G/N

type

16. C₁₃×#333

C₄

semidirect

115. #333

Dic₁₃

semidirect

190. C₁₃

#8928

semidirect

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

subgroup	index
#13117926	2
#13115639	2
#13115600	2
#13112675	2
C₂×C₁₃×#333	2
#8928	13

subgroup

index

C₂×C₁₃×#333

Subgroups — #15757386

Conjugacy classes of subgroups

Complements

Maximal subgroups