Group #15761713 — subgroups

Subgroups — #15761713

Order 3328.

698 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 171 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	C₄×#88128	C₂	1	1	yes	maximal, characteristic
2	#13114953	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718051	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88128	C₄	1	1	yes	characteristic
6	C₂×C₄×D₅₂	—	2	2	no	—
7	C₂×C₄×D₅₂	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	C₄³×C₁₃	C₂²	1	1	yes	characteristic
10	#11718600	—	2	2	no	—
11	#11718600	C₄	1	2	yes	—
12	#11718596	C₄	1	1	yes	characteristic
13	C₂×C₄⋊#1055	C₂²	1	2	yes	—
14	C₁₃×#336	—	2	2	no	—
15	#11718116	—	2	2	no	—
16	#11718051	—	2	8	no	—
17	C₂²×D₅₂	—	2	2	no	—
18	C₂²×D₅₂	C₂×C₄	1	2	yes	—
19	C₂²×C₄×D₁₃	—	2	2	no	—
20	C₂²×C₈×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	C₂×#6103	—	2	4	no	—
27	C₂×#6103	—	2	2	no	—
28	C₂×C₄⋊Dic₁₃	—	2	2	no	—
29	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
30	C₂²×#1055	—	2	2	no	—
31	#88128	—	2	2	no	—
32	#88128	C₈	1	4	yes	complemented
33	C₄×D₅₂	—	2	4	no	—
34	C₄×D₅₂	—	2	4	no	—
35	C₄×D₅₂	—	4	8	no	—
36	C₄×C₈×C₁₃	—	2	2	no	—
37	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
38	C₄⋊#1055	—	2	4	no	—
39	#9642	—	13	1	no	maximal, Sylow
40	C₂³×D₁₃	—	2	2	no	—
41	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×Dic₁₃	—	2	2	no	—
47	C₂×D₅₂	—	2	4	no	—
48	C₂×D₅₂	—	2	4	no	—
49	C₂×D₅₂	—	2	8	no	—
50	C₂×D₅₂	—	2	2	no	—
51	C₂×D₅₂	—	4	4	no	—
52	C₂×D₅₂	—	4	4	no	—
53	C₂×D₅₂	C₂×C₈	1	4	yes	—
54	C₂×C₄×D₁₃	—	4	2	no	—
55	C₂×C₄×D₁₃	—	4	2	no	—
56	C₂×C₄×D₁₃	—	4	8	no	—
57	C₂×C₈×C₁₃	—	2	4	no	—
58	C₂×C₈×C₁₃	—	4	4	no	—
59	C₄²×C₁₃	—	2	2	no	—
60	C₄²×C₁₃	—	2	4	no	—
61	C₄²×C₁₃	—	4	2	no	—
62	C₄²×C₁₃	C₂×C₈	1	2	yes	—
63	C₄²×C₁₃	M₁₆	1	2	yes	—
64	C₄²×C₁₃	C₂×D₄	1	2	yes	—
65	C₄²×C₁₃	#41	1	2	yes	—
66	#6103	—	4	8	no	—
67	#6103	—	4	4	no	—
68	C₄⋊Dic₁₃	—	2	4	no	—
69	C₄⋊Dic₁₃	—	4	4	no	—
70	C₂×#1055	—	4	2	no	—
71	C₂×#1055	—	4	4	no	—
72	C₄×#127	—	13	1	no	—
73	#1831	—	13	1	no	—
74	#1744	D₁₃	1	1	yes	characteristic, complemented
75	C₂×D₄⋊C₈	—	13	4	no	—
76	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×D₁₃	—	2	4	no	—
78	C₂²×D₁₃	—	4	2	no	—
79	C₂²×D₁₃	—	4	2	no	—
80	C₂²×D₁₃	—	4	4	no	—
81	C₂²×D₁₃	—	4	4	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
89	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
90	C₂×C₄×C₁₃	#121	1	2	yes	—
91	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
92	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#131	1	2	yes	—
96	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
97	C₂×Dic₁₃	—	4	2	no	—
98	C₂×Dic₁₃	—	4	4	no	—
99	D₅₂	—	2	8	no	—
100	D₅₂	—	4	16	no	—
101	D₅₂	—	4	4	no	—
102	C₄×D₁₃	—	8	4	no	—
103	C₄×D₁₃	—	8	4	no	—
104	C₈×C₁₃	—	4	4	no	—
105	#1055	—	8	2	no	—
106	C₂×#127	—	13	1	no	—
107	C₂×C₄×D₄	—	13	2	no	—
108	C₂×C₄×D₄	—	26	2	no	—
109	C₂×C₄⋊C₈	—	13	2	no	—
110	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
111	#390	—	13	2	no	—
112	#390	—	26	2	no	—
113	#384	—	13	1	no	—
114	C₄³	C₂×D₁₃	1	1	yes	characteristic
115	#336	—	2	2	no	—
116	#336	—	26	2	no	—
117	D₄⋊C₈	—	26	8	no	—
118	C₂²×C₁₃	#390	1	1	yes	characteristic
119	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
120	C₂²×C₁₃	#408	1	1	yes	characteristic
121	C₂²×C₁₃	#418	1	2	yes	—
122	C₂²×C₁₃	#421	1	2	yes	—
123	C₂×D₁₃	—	4	4	no	—
124	C₂×D₁₃	—	4	8	no	—
125	C₂×D₁₃	—	8	2	no	—
126	C₂×D₁₃	—	8	2	no	—
127	C₂×D₁₃	—	8	4	no	—
128	C₄×C₁₃	—	2	2	no	—
129	C₄×C₁₃	—	2	4	no	—
130	C₄×C₁₃	—	4	2	no	—
131	C₄×C₁₃	C₈×D₄	1	2	yes	—
132	C₄×C₁₃	#436	1	2	yes	—
133	C₄×C₁₃	#490	1	2	yes	—
134	C₄×C₁₃	#496	1	2	yes	—
135	Dic₁₃	—	8	2	no	—
136	C₂²×D₄	—	13	2	no	—
137	C₂²×D₄	—	26	2	no	—
138	C₂³×C₄	—	26	2	no	—
139	C₂²×C₈	—	2	2	no	—
140	C₂²×C₈	—	26	2	no	—
141	#127	—	13	4	no	—
142	#127	—	26	2	no	—
143	C₄×D₄	—	26	4	no	—
144	C₄×D₄	—	26	4	no	—
145	C₄×D₄	—	52	8	no	—
146	C₂×C₄⋊C₄	—	13	2	no	—
147	C₂×C₄⋊C₄	—	26	2	no	—
148	C₂×C₂²⋊C₄	—	26	4	no	—
149	C₂×C₂²⋊C₄	—	26	2	no	—
150	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
151	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
152	C₂×C₄²	D₅₂	1	2	yes	—
153	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
154	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
155	C₄⋊C₈	—	26	4	no	—
156	C₄×C₈	—	2	2	no	—
157	C₄×C₈	D₅₂	1	4	yes	complemented
158	C₂×C₁₃	#1478	1	2	yes	—
159	C₂×C₁₃	#1496	1	2	yes	—
160	C₂×C₁₃	#1954	1	1	yes	characteristic
161	C₂×C₁₃	#1961	1	1	yes	characteristic
162	C₂×C₁₃	#1963	1	1	yes	characteristic
163	D₁₃	—	8	4	no	—
164	C₂⁴	—	26	2	no	—
165	C₂×D₄	—	13	4	no	—
166	C₂×D₄	—	26	4	no	—
167	C₂×D₄	—	26	2	no	—
168	C₂×D₄	—	26	4	no	—
169	C₂×D₄	—	26	8	no	—
170	C₂×D₄	—	52	4	no	—
171	C₂×D₄	—	52	4	no	—
172	C₂²×C₄	—	26	2	no	—
173	C₂²×C₄	—	52	2	no	—
174	C₂²×C₄	—	52	2	no	—
175	C₂²×C₄	—	52	8	no	—
176	C₂²×C₄	#6103	1	2	yes	—
177	C₂²×C₄	#6103	1	2	yes	—
178	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	4	4	no	—
183	C₂×C₈	—	52	2	no	—
184	C₂×C₈	—	52	4	no	—
185	C₄⋊C₄	—	26	4	no	—
186	C₄⋊C₄	—	52	4	no	—
187	C₂²⋊C₄	—	52	8	no	—
188	C₂²⋊C₄	—	52	4	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	4	no	—
191	C₄²	—	4	2	no	—
192	C₄²	C₈×D₁₃	1	2	yes	—
193	C₄²	#6094	1	2	yes	—
194	C₄²	C₂×D₅₂	1	2	yes	—
195	C₄²	#6127	1	2	yes	—
196	C₁₃	#9642	1	1	yes	characteristic, complemented, Sylow
197	C₂³	—	26	4	no	—
198	C₂³	—	52	4	no	—
199	C₂³	—	52	2	no	—
200	C₂³	—	52	4	no	—
201	C₂³	—	52	2	no	—
202	C₂³	C₂×#6103	1	1	yes	characteristic
203	D₄	—	26	8	no	—
204	D₄	—	52	16	no	—
205	D₄	—	52	4	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	52	4	no	—
213	C₂×C₄	—	52	2	no	—
214	C₂×C₄	—	104	4	no	—
215	C₂×C₄	—	104	4	no	—
216	C₂×C₄	#88060	1	4	yes	—
217	C₂×C₄	C₄×D₅₂	1	2	yes	—
218	C₂×C₄	#88128	1	1	yes	characteristic
219	C₂×C₄	#88129	1	1	yes	characteristic
220	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
221	C₂×C₄	C₂×#6094	1	1	yes	characteristic
222	C₂×C₄	#88155	1	2	yes	—
223	C₂×C₄	#88162	1	4	yes	—
224	C₂×C₄	#88184	1	2	yes	—
225	C₈	—	4	4	no	—
226	C₈	—	104	2	no	—
227	C₂²	—	52	8	no	—
228	C₂²	—	52	4	no	—
229	C₂²	—	104	2	no	—
230	C₂²	—	104	2	no	—
231	C₂²	—	104	4	no	—
232	C₂²	#11718600	1	1	yes	characteristic
233	C₂²	#11718666	1	2	yes	—
234	C₂²	C₂×#88060	1	1	yes	characteristic
235	C₂²	#11718771	1	1	yes	characteristic
236	C₂²	#11718792	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	4	no	—
239	C₄	—	4	2	no	—
240	C₄	—	104	2	no	—
241	C₄	C₈×D₅₂	1	2	yes	—
242	C₄	#11718349	1	2	yes	—
243	C₄	#11718373	1	2	yes	—
244	C₄	#11718374	1	2	yes	—
245	C₂	—	104	4	no	—
246	C₂	#13113228	1	2	yes	—
247	C₂	#13113306	1	2	yes	—
248	C₂	#13115630	1	1	yes	characteristic
249	C₂	#13115660	1	1	yes	characteristic
250	C₂	#13115668	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#88128

C₂

yes

maximal, characteristic

#13114953

C₂

yes

maximal, characteristic, complemented

C₂×#11718051

C₂

yes

maximal, complemented

C₁₃×#1744

C₂

yes

maximal, characteristic, complemented

C₂×#88128

C₄

yes

characteristic

C₂×C₄×D₅₂

—

C₂×C₄×D₅₂

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

#11718600

—

#11718600

C₄

yes

—

#11718596

C₄

yes

characteristic

C₂×C₄⋊#1055

C₂²

yes

—

C₁₃×#336

—

#11718116

—

#11718051

—

C₂²×D₅₂

—

C₂²×D₅₂

C₂×C₄

yes

—

C₂²×C₄×D₁₃

—

C₂²×C₈×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

C₂×#6103

—

C₂×#6103

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

—

#88128

—

#88128

C₈

yes

complemented

C₄×D₅₂

—

C₄×D₅₂

—

C₄×D₅₂

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

D₄

yes

—

—

C₂³×D₁₃

—

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

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

C₂×C₈

yes

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

M₁₆

yes

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

#6103

—

#6103

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

D₁₃

yes

characteristic, complemented

C₂×D₄⋊C₈

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

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

C₄×D₄

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

#131

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

—

100

D₅₂

—

101

D₅₂

—

102

C₄×D₁₃

—

103

C₄×D₁₃

—

104

C₈×C₁₃

—

105

#1055

—

106

C₂×#127

—

107

C₂×C₄×D₄

—

108

C₂×C₄×D₄

—

109

C₂×C₄⋊C₈

—

110

C₂×C₄×C₈

C₂×D₁₃

yes

—

111

#390

—

112

#390

—

113

#384

—

114

C₄³

C₂×D₁₃

yes

characteristic

115

#336

—

116

#336

—

117

D₄⋊C₈

—

118

C₂²×C₁₃

#390

yes

characteristic

119

C₂²×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

120

C₂²×C₁₃

#408

yes

characteristic

121

C₂²×C₁₃

#418

yes

—

122

C₂²×C₁₃

#421

yes

—

123

C₂×D₁₃

—

124

C₂×D₁₃

—

125

C₂×D₁₃

—

126

C₂×D₁₃

—

127

C₂×D₁₃

—

128

C₄×C₁₃

—

129

C₄×C₁₃

—

130

C₄×C₁₃

—

131

C₄×C₁₃

C₈×D₄

yes

—

132

C₄×C₁₃

#436

yes

—

133

C₄×C₁₃

#490

yes

—

134

C₄×C₁₃

#496

yes

—

135

Dic₁₃

—

136

C₂²×D₄

—

137

C₂²×D₄

—

138

C₂³×C₄

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

#127

—

142

#127

—

143

C₄×D₄

—

144

C₄×D₄

—

145

C₄×D₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₂²⋊C₄

—

150

C₂×C₄²

C₄×D₁₃

yes

characteristic

151

C₂×C₄²

C₄×D₁₃

yes

characteristic

152

C₂×C₄²

D₅₂

yes

—

153

C₂×C₄²

C₂²⋊D₁₃

yes

—

154

C₂×C₄²

C₂²×D₁₃

yes

characteristic

155

C₄⋊C₈

—

156

C₄×C₈

—

157

C₄×C₈

D₅₂

yes

complemented

158

C₂×C₁₃

#1478

yes

—

159

C₂×C₁₃

#1496

yes

—

160

C₂×C₁₃

#1954

yes

characteristic

161

C₂×C₁₃

#1961

yes

characteristic

162

C₂×C₁₃

#1963

yes

characteristic

163

D₁₃

—

164

C₂⁴

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

#6103

yes

—

177

C₂²×C₄

#6103

yes

—

178

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

179

C₂²×C₄

C₂×D₅₂

yes

characteristic

180

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

C₈×D₁₃

yes

—

193

C₄²

#6094

yes

—

194

C₄²

C₂×D₅₂

yes

—

195

C₄²

#6127

yes

—

196

C₁₃

#9642

yes

characteristic, complemented, Sylow

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

C₂×#6103

yes

characteristic

203

D₄

—

204

D₄

—

205

D₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

104

—

215

C₂×C₄

—

104

—

216

C₂×C₄

#88060

yes

—

217

C₂×C₄

C₄×D₅₂

yes

—

218

C₂×C₄

#88128

yes

characteristic

219

C₂×C₄

#88129

yes

characteristic

220

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

221

C₂×C₄

C₂×#6094

yes

characteristic

222

C₂×C₄

#88155

yes

—

223

C₂×C₄

#88162

yes

—

224

C₂×C₄

#88184

yes

—

225

C₈

—

226

C₈

—

104

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

104

—

230

C₂²

—

104

—

231

C₂²

—

104

—

232

C₂²

#11718600

yes

characteristic

233

C₂²

#11718666

yes

—

234

C₂²

C₂×#88060

yes

characteristic

235

C₂²

#11718771

yes

characteristic

236

C₂²

#11718792

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

104

—

241

C₄

C₈×D₅₂

yes

—

242

C₄

#11718349

yes

—

243

C₄

#11718373

yes

—

244

C₄

#11718374

yes

—

245

C₂

—

104

—

246

C₂

#13113228

yes

—

247

C₂

#13113306

yes

—

248

C₂

#13115630

yes

characteristic

249

C₂

#13115660

yes

characteristic

250

C₂

#13115668

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1744	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂×#88128	C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1744	D₁₃
hypocenter	C₁₃	#9642
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₅₂

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1744

C₂

socle

C₂³×C₁₃

C₂×C₂²⋊C₄

prime radical

C₂×#88128

C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
2. #13114953	C₂	semidirect
3. C₂×#11718051	C₂	semidirect
4. C₁₃×#1744	C₂	semidirect
32. #88128	C₈	semidirect
37. C₄×C₈×C₁₃	D₄	semidirect
74. #1744	D₁₃	semidirect
157. C₄×C₈	D₅₂	semidirect
196. C₁₃	#9642	semidirect

H ≅ G/N

type

2. #13114953

C₂

semidirect

3. C₂×#11718051

C₂

semidirect

4. C₁₃×#1744

C₂

semidirect

32. #88128

C₈

semidirect

37. C₄×C₈×C₁₃

D₄

semidirect

74. #1744

D₁₃

semidirect

157. C₄×C₈

D₅₂

semidirect

196. C₁₃

#9642

semidirect

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

subgroup	index
C₄×#88128	2
#13114953	2
C₂×#11718051	2
C₁₃×#1744	2
#9642	13

subgroup

index

C₁₃×#1744

Subgroups — #15761713

Conjugacy classes of subgroups

Complements

Maximal subgroups