Group #15760289 — subgroups

Subgroups — #15760289

Order 3328.

506 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 135 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	#13119821	C₂	1	1	yes	maximal, characteristic
2	#13114832	C₂	1	1	yes	maximal, characteristic
3	#13113507	C₂	1	2	yes	maximal
4	#13112738	C₂	1	2	yes	maximal
5	C₁₃×#2982	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88198	—	2	1	no	—
8	C₂×#88123	C₂²	1	1	yes	characteristic
9	C₈×Q₈×C₁₃	—	2	4	no	—
10	C₁₃×#431	—	2	2	no	—
11	C₁₃×#431	C₂²	1	2	yes	—
12	C₂×#88076	—	2	1	no	—
13	#11718644	C₄	1	4	yes	—
14	#11718635	—	2	1	no	—
15	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
16	#11718589	—	2	2	no	—
17	#11718585	C₂²	1	2	yes	—
18	#11718122	—	2	1	no	—
19	#11718078	—	2	4	no	—
20	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×Dic₂₆	—	2	1	no	—
22	C₄×Q₈×C₁₃	—	2	2	no	—
23	C₄×Q₈×C₁₃	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	D₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	#88198	—	4	2	no	—
29	#88198	—	4	2	no	—
30	C₂×C₄⋊Dic₁₃	—	2	1	no	—
31	C₂×C₄⋊Dic₁₃	—	2	1	no	—
32	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
33	C₂×#6101	—	2	4	no	—
34	C₂×C₄×Dic₁₃	—	2	1	no	—
35	C₂×#6099	—	2	2	no	—
36	#88123	—	2	2	no	—
37	#88123	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	4	no	—
39	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
40	C₁₃×C₂²⋊C₈	—	2	2	no	—
41	C₄×C₈×C₁₃	—	2	4	no	—
42	C₄×C₈×C₁₃	—	2	2	no	—
43	#88076	—	4	2	no	—
44	#88071	—	2	4	no	—
45	#88071	C₂×C₄	1	2	yes	—
46	C₄⋊#1055	—	2	2	no	—
47	C₄⋊#1055	—	2	2	no	—
48	#9394	—	13	1	no	maximal, Sylow
49	C₂×Q₈×C₁₃	—	2	2	no	—
50	C₂×Q₈×C₁₃	—	2	2	no	—
51	C₂×Q₈×C₁₃	D₈	1	2	yes	—
52	C₂×Q₈×C₁₃	SD₁₆	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×Dic₁₃	—	2	2	no	—
59	C₂²×Dic₁₃	—	2	2	no	—
60	C₂×Dic₂₆	—	4	2	no	—
61	C₂×Dic₂₆	—	4	1	no	—
62	C₂×Dic₂₆	—	4	1	no	—
63	C₂×Dic₂₆	—	4	2	no	—
64	C₂×C₈×C₁₃	—	2	4	no	—
65	C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₄²×C₁₃	—	2	2	no	—
68	C₄²×C₁₃	—	2	2	no	—
69	C₄²×C₁₃	C₂×D₄	1	2	yes	—
70	C₄²×C₁₃	#41	1	2	yes	—
71	C₄⋊Dic₁₃	—	2	4	no	—
72	C₄⋊Dic₁₃	—	2	4	no	—
73	C₄⋊Dic₁₃	—	4	1	no	—
74	C₄⋊Dic₁₃	—	4	1	no	—
75	#6101	—	4	8	no	—
76	C₄×Dic₁₃	—	4	1	no	—
77	C₄×Dic₁₃	—	4	1	no	—
78	#6099	—	4	2	no	—
79	#6099	—	4	2	no	—
80	C₂×#1055	—	4	2	no	—
81	#2982	D₁₃	1	1	yes	characteristic
82	#2546	—	13	1	no	—
83	#1801	—	13	1	no	—
84	#1546	—	13	2	no	—
85	#1303	—	13	2	no	—
86	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	Q₈×C₁₃	—	2	4	no	—
88	Q₈×C₁₃	—	2	4	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	4	1	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	#102	1	4	yes	—
96	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#121	1	2	yes	—
99	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#135	1	2	yes	—
103	C₂×Dic₁₃	—	2	4	no	—
104	C₂×Dic₁₃	—	4	2	no	—
105	C₂×Dic₁₃	—	4	2	no	—
106	C₂×Dic₁₃	—	4	2	no	—
107	C₂×Dic₁₃	—	4	2	no	—
108	C₂×Dic₁₃	—	4	2	no	—
109	Dic₂₆	—	8	2	no	—
110	Dic₂₆	—	8	2	no	—
111	C₈×C₁₃	—	4	4	no	—
112	#1055	—	8	2	no	—
113	C₂×C₄⋊Q₈	—	13	1	no	—
114	C₂×C₄⋊Q₈	—	26	1	no	—
115	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
116	C₈×Q₈	—	2	4	no	—
117	#431	—	2	2	no	—
118	#431	C₂×D₁₃	1	2	yes	—
119	#423	—	13	2	no	—
120	C₂×#101	—	26	1	no	—
121	#398	—	13	4	no	—
122	#391	—	26	1	no	—
123	#389	—	26	2	no	—
124	C₄×C₄⋊C₄	—	13	1	no	—
125	#343	—	26	1	no	—
126	#332	—	26	4	no	—
127	C₂²×C₁₃	—	2	1	no	—
128	C₂²×C₁₃	—	2	1	no	—
129	C₂²×C₁₃	#386	1	1	yes	characteristic
130	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
131	C₂²×C₁₃	#416	1	1	yes	characteristic
132	C₄×C₁₃	—	2	1	no	—
133	C₄×C₁₃	—	2	4	no	—
134	C₄×C₁₃	—	2	2	no	—
135	C₄×C₁₃	—	4	2	no	—
136	C₄×C₁₃	#456	1	2	yes	—
137	C₄×C₁₃	#465	1	2	yes	—
138	C₄×C₁₃	#466	1	2	yes	—
139	Dic₁₃	—	4	4	no	—
140	Dic₁₃	—	8	2	no	—
141	C₂²×Q₈	—	26	1	no	—
142	C₂²×Q₈	D₅₂	1	1	yes	characteristic
143	C₂×M₁₆	—	26	2	no	—
144	C₄⋊Q₈	—	26	2	no	—
145	C₄⋊Q₈	—	26	2	no	—
146	C₄⋊Q₈	—	52	2	no	—
147	C₄⋊Q₈	—	52	2	no	—
148	C₄×Q₈	—	2	2	no	—
149	C₄×Q₈	—	2	2	no	—
150	C₂×C₄⋊C₄	—	13	2	no	—
151	C₂×C₄⋊C₄	—	26	1	no	—
152	C₂×C₄⋊C₄	—	26	4	no	—
153	C₂×C₄⋊C₄	—	26	1	no	—
154	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
155	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
156	C₂×C₄²	—	26	1	no	—
157	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
158	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
159	C₄⋊C₈	—	2	4	no	—
160	C₄⋊C₈	—	26	2	no	—
161	C₄⋊C₈	—	26	2	no	—
162	C₄⋊C₈	C₂²⋊D₁₃	1	4	yes	—
163	#101	—	52	2	no	—
164	C₂²⋊C₈	—	2	2	no	—
165	C₄×C₈	—	2	4	no	—
166	C₄×C₈	—	2	2	no	—
167	#95	—	13	2	no	—
168	#95	—	26	4	no	—
169	C₂×C₁₃	—	2	1	no	—
170	C₂×C₁₃	—	2	1	no	—
171	C₂×C₁₃	#1886	1	1	yes	characteristic
172	C₂×C₁₃	#1893	1	1	yes	characteristic
173	C₂×C₁₃	#1915	1	1	yes	characteristic
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	52	1	no	—
177	C₂×Q₈	—	52	1	no	—
178	C₂×Q₈	—	52	2	no	—
179	C₂×Q₈	—	52	2	no	—
180	C₂×Q₈	#6095	1	2	yes	—
181	C₂×Q₈	D₁₀₄	1	2	yes	—
182	C₂²×C₄	—	26	2	no	—
183	C₂²×C₄	—	26	2	no	—
184	C₂²×C₄	#6103	1	2	yes	—
185	C₂²×C₄	#6103	1	2	yes	—
186	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
189	M₁₆	—	52	2	no	—
190	M₁₆	—	52	2	no	—
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	—	52	2	no	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	26	4	no	—
196	C₄⋊C₄	—	26	4	no	—
197	C₄⋊C₄	—	52	1	no	—
198	C₄⋊C₄	—	52	1	no	—
199	C₄⋊C₄	—	52	8	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	52	1	no	—
203	C₄²	—	52	1	no	—
204	C₄²	#6127	1	2	yes	—
205	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
206	C₁₃	#9394	1	1	yes	characteristic, complemented, Sylow
207	C₂³	C₂×#6103	1	1	yes	characteristic
208	Q₈	—	2	4	no	—
209	Q₈	—	2	4	no	—
210	Q₈	—	104	2	no	—
211	Q₈	—	104	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	26	4	no	—
219	C₂×C₄	—	52	2	no	—
220	C₂×C₄	—	52	2	no	—
221	C₂×C₄	—	52	2	no	—
222	C₂×C₄	—	52	2	no	—
223	C₂×C₄	—	52	2	no	—
224	C₂×C₄	#88061	1	4	yes	—
225	C₂×C₄	C₂×#6095	1	1	yes	characteristic
226	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
227	C₂×C₄	#88158	1	2	yes	—
228	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
229	C₂×C₄	#88183	1	1	yes	characteristic
230	C₂×C₄	#88184	1	2	yes	—
231	C₂×C₄	#88207	1	1	yes	characteristic
232	C₈	—	4	4	no	—
233	C₈	—	104	2	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	C₂×#88061	1	1	yes	characteristic
237	C₂²	#11718774	1	1	yes	characteristic
238	C₂²	#11718874	1	1	yes	characteristic
239	C₄	—	2	1	no	—
240	C₄	—	2	4	no	—
241	C₄	—	2	2	no	—
242	C₄	—	4	2	no	—
243	C₄	—	52	4	no	—
244	C₄	—	104	2	no	—
245	C₄	#11718775	1	2	yes	—
246	C₄	#11718776	1	2	yes	—
247	C₄	#11718907	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	1	no	—
250	C₂	#13115229	1	1	yes	characteristic
251	C₂	#13115264	1	1	yes	characteristic
252	C₂	#13115388	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13119821

C₂

yes

maximal, characteristic

#13114832

C₂

yes

maximal, characteristic

#13113507

C₂

yes

maximal

#13112738

C₂

yes

maximal

C₁₃×#2982

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₃

C₂²

yes

characteristic

C₂×#88198

—

C₂×#88123

C₂²

yes

characteristic

C₈×Q₈×C₁₃

—

C₁₃×#431

—

C₁₃×#431

C₂²

yes

—

C₂×#88076

—

#11718644

C₄

yes

—

#11718635

—

C₄×C₄⋊Dic₁₃

C₂²

yes

characteristic

#11718589

—

#11718585

C₂²

yes

—

#11718122

—

#11718078

—

C₂²×Q₈×C₁₃

D₄

yes

characteristic

C₂²×Dic₂₆

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

#88198

—

#88198

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂×#6101

—

C₂×C₄×Dic₁₃

—

C₂×#6099

—

#88123

—

#88123

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

D₄

yes

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

—

#88076

—

#88071

—

#88071

C₂×C₄

yes

—

—

—

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

D₈

yes

—

C₂×Q₈×C₁₃

SD₁₆

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

D₁₃

yes

—

—

—

—

C₂³×C₁₃

C₂×C₂²⋊C₄

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×C₁₃

#102

yes

—

C₂×C₄×C₁₃

C₄×D₄

yes

—

C₂×C₄×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

#123

yes

characteristic

100

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

101

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₁₃

#135

yes

—

103

C₂×Dic₁₃

—

104

C₂×Dic₁₃

—

105

C₂×Dic₁₃

—

106

C₂×Dic₁₃

—

107

C₂×Dic₁₃

—

108

C₂×Dic₁₃

—

109

Dic₂₆

—

110

Dic₂₆

—

111

C₈×C₁₃

—

112

#1055

—

113

C₂×C₄⋊Q₈

—

114

C₂×C₄⋊Q₈

—

115

C₂×C₄×Q₈

C₂×D₁₃

yes

characteristic

116

C₈×Q₈

—

117

#431

—

118

#431

C₂×D₁₃

yes

—

119

#423

—

120

C₂×#101

—

121

#398

—

122

#391

—

123

#389

—

124

C₄×C₄⋊C₄

—

125

#343

—

126

#332

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

#386

yes

characteristic

130

C₂²×C₁₃

C₂×#102

yes

characteristic

131

C₂²×C₁₃

#416

yes

characteristic

132

C₄×C₁₃

—

133

C₄×C₁₃

—

134

C₄×C₁₃

—

135

C₄×C₁₃

—

136

C₄×C₁₃

#456

yes

—

137

C₄×C₁₃

#465

yes

—

138

C₄×C₁₃

#466

yes

—

139

Dic₁₃

—

140

Dic₁₃

—

141

C₂²×Q₈

—

142

C₂²×Q₈

D₅₂

yes

characteristic

143

C₂×M₁₆

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

C₄×D₁₃

yes

—

155

C₂×C₄⋊C₄

D₅₂

yes

characteristic

156

C₂×C₄²

—

157

C₂×C₄²

C₂²⋊D₁₃

yes

—

158

C₂×C₄²

C₂²×D₁₃

yes

characteristic

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

C₂²⋊D₁₃

yes

—

163

#101

—

164

C₂²⋊C₈

—

165

C₄×C₈

—

166

C₄×C₈

—

167

#95

—

168

#95

—

169

C₂×C₁₃

—

170

C₂×C₁₃

—

171

C₂×C₁₃

#1886

yes

characteristic

172

C₂×C₁₃

#1893

yes

characteristic

173

C₂×C₁₃

#1915

yes

characteristic

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

#6095

yes

—

181

C₂×Q₈

D₁₀₄

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

#6103

yes

—

185

C₂²×C₄

#6103

yes

—

186

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

187

C₂²×C₄

C₂×D₅₂

yes

characteristic

188

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

189

M₁₆

—

190

M₁₆

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

#6127

yes

—

205

C₄²

C₂×C₂²⋊D₁₃

yes

—

206

C₁₃

#9394

yes

characteristic, complemented, Sylow

207

C₂³

C₂×#6103

yes

characteristic

208

Q₈

—

209

Q₈

—

210

Q₈

—

104

—

211

Q₈

—

104

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

#88061

yes

—

225

C₂×C₄

C₂×#6095

yes

characteristic

226

C₂×C₄

C₂×D₁₀₄

yes

characteristic

227

C₂×C₄

#88158

yes

—

228

C₂×C₄

C₄×C₂²⋊D₁₃

yes

—

229

C₂×C₄

#88183

yes

characteristic

230

C₂×C₄

#88184

yes

—

231

C₂×C₄

#88207

yes

characteristic

232

C₈

—

233

C₈

—

104

—

234

C₂²

—

235

C₂²

—

236

C₂²

C₂×#88061

yes

characteristic

237

C₂²

#11718774

yes

characteristic

238

C₂²

#11718874

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

104

—

245

C₄

#11718775

yes

—

246

C₄

#11718776

yes

—

247

C₄

#11718907

yes

—

248

C₂

—

249

C₂

—

250

C₂

#13115229

yes

characteristic

251

C₂

#13115264

yes

characteristic

252

C₂

#13115388

yes

characteristic

	subgroup	G/H
center	C₂²	#11718874
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#2982	C₂
socle	C₂²×C₁₃	#386
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#2982	D₁₃
hypocenter	C₁₃	#9394
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2982

subgroup

G/H

center

C₂²

#11718874

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#2982

C₂

socle

C₂²×C₁₃

#386

prime radical

C₂³×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2982

N	H ≅ G/N	type
206. C₁₃	#9394	semidirect

H ≅ G/N

type

206. C₁₃

#9394

semidirect

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

subgroup	index
#13119821	2
#13114832	2
#13113507	2
#13112738	2
C₁₃×#2982	2
#9394	13

subgroup

index

C₁₃×#2982

Subgroups — #15760289

Conjugacy classes of subgroups

Complements

Maximal subgroups