Group #15762025 — subgroups

Subgroups — #15762025

Order 3328.

486 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 151 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	#13123214	C₂	1	1	yes	maximal, characteristic
2	#13114689	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718074	C₂	1	2	yes	maximal
4	C₂×#11718078	C₂	1	2	yes	maximal
5	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic
6	C₂×#88123	C₂²	1	1	yes	characteristic
7	C₂×#88123	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₄³×C₁₃	C₂²	1	1	yes	characteristic
11	#11718597	C₄	1	4	yes	—
12	#11718590	—	2	1	no	—
13	#11718590	—	2	1	no	—
14	#11718590	—	2	2	no	—
15	C₂×C₄⋊#1055	C₂²	1	2	yes	—
16	C₂×#88043	—	2	1	no	—
17	#11718116	—	2	1	no	—
18	#11718078	—	2	4	no	—
19	#11718074	—	2	4	no	—
20	C₂²×Dic₂₆	—	2	1	no	—
21	C₂²×Dic₂₆	—	2	1	no	—
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	D₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₃	—	2	1	no	—
29	C₂×C₄⋊Dic₁₃	—	2	1	no	—
30	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
31	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
32	C₂²×#1055	—	2	2	no	—
33	#88123	—	2	2	no	—
34	#88123	—	2	2	no	—
35	#88123	—	2	2	no	—
36	#88123	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	4	4	no	—
40	#88071	—	2	4	no	—
41	#88071	—	2	4	no	—
42	C₄⋊#1055	—	2	2	no	—
43	C₄⋊#1055	D₄	1	4	yes	—
44	#88043	—	4	2	no	—
45	#9708	—	13	1	no	maximal, Sylow
46	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₃	—	2	2	no	—
52	C₂²×Dic₁₃	—	2	2	no	—
53	C₂×Dic₂₆	—	4	2	no	—
54	C₂×Dic₂₆	—	4	1	no	—
55	C₂×Dic₂₆	—	4	1	no	—
56	C₂×Dic₂₆	—	4	2	no	—
57	C₂×Dic₂₆	—	4	1	no	—
58	C₂×Dic₂₆	—	4	2	no	—
59	C₂×Dic₂₆	—	4	1	no	—
60	C₂×Dic₂₆	—	4	2	no	—
61	C₂×C₈×C₁₃	—	4	2	no	—
62	C₂×C₈×C₁₃	—	4	4	no	—
63	C₄²×C₁₃	—	2	4	no	—
64	C₄²×C₁₃	—	2	2	no	—
65	C₄²×C₁₃	—	2	2	no	—
66	C₄²×C₁₃	—	2	1	no	—
67	C₄²×C₁₃	—	2	1	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	2	no	—
74	C₄⋊Dic₁₃	—	4	1	no	—
75	C₄⋊Dic₁₃	—	4	1	no	—
76	C₂×#1055	—	2	4	no	—
77	C₂×#1055	—	4	2	no	—
78	C₂×#1055	—	4	2	no	—
79	#2862	—	13	1	no	—
80	#1842	D₁₃	1	1	yes	characteristic
81	#1767	—	13	1	no	—
82	C₂×#332	—	13	2	no	—
83	C₂×#332	—	13	2	no	—
84	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	#101	1	4	yes	—
92	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₁₃	#121	1	2	yes	—
94	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#135	1	2	yes	—
97	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
99	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#137	1	2	yes	—
101	C₂×Dic₁₃	—	4	2	no	—
102	C₂×Dic₁₃	—	4	2	no	—
103	C₂×Dic₁₃	—	4	2	no	—
104	C₂×Dic₁₃	—	4	4	no	—
105	C₂×Dic₁₃	—	4	2	no	—
106	Dic₂₆	—	8	2	no	—
107	Dic₂₆	—	8	2	no	—
108	Dic₂₆	—	8	2	no	—
109	Dic₂₆	—	8	1	no	—
110	Dic₂₆	—	8	1	no	—
111	C₈×C₁₃	—	8	2	no	—
112	#1055	—	4	4	no	—
113	C₂×C₄⋊Q₈	—	13	1	no	—
114	C₂×C₄⋊Q₈	—	13	1	no	—
115	C₂×C₄⋊C₈	—	2	2	no	—
116	C₂×C₄⋊C₈	—	13	2	no	—
117	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
118	C₂×#97	—	26	1	no	—
119	#391	—	26	1	no	—
120	#391	—	26	1	no	—
121	#391	—	26	2	no	—
122	#382	—	13	4	no	—
123	C₄³	C₂×D₁₃	1	1	yes	characteristic
124	#336	—	26	1	no	—
125	#332	—	26	4	no	—
126	#332	—	26	4	no	—
127	C₂²×C₁₃	#390	1	1	yes	characteristic
128	C₂²×C₁₃	C₂×#101	1	2	yes	—
129	C₂²×C₁₃	#416	1	1	yes	characteristic
130	C₂²×C₁₃	#417	1	1	yes	characteristic
131	C₂²×C₁₃	#417	1	2	yes	—
132	C₄×C₁₃	—	2	4	no	—
133	C₄×C₁₃	—	2	2	no	—
134	C₄×C₁₃	—	4	2	no	—
135	C₄×C₁₃	#463	1	2	yes	—
136	C₄×C₁₃	#464	1	2	yes	—
137	C₄×C₁₃	#489	1	2	yes	—
138	C₄×C₁₃	#496	1	1	yes	characteristic
139	C₄×C₁₃	#497	1	1	yes	characteristic
140	Dic₁₃	—	8	2	no	—
141	Dic₁₃	—	8	2	no	—
142	C₂²×Q₈	—	26	1	no	—
143	C₂²×Q₈	—	26	1	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	26	2	no	—
146	C₄⋊Q₈	—	26	2	no	—
147	C₄⋊Q₈	—	26	2	no	—
148	C₄⋊Q₈	—	26	2	no	—
149	C₄⋊Q₈	—	26	2	no	—
150	C₂×C₄⋊C₄	—	13	2	no	—
151	C₂×C₄⋊C₄	—	13	2	no	—
152	C₂×C₄⋊C₄	—	26	1	no	—
153	C₂×C₄⋊C₄	—	26	1	no	—
154	C₂×C₄²	C₄×D₁₃	1	2	yes	—
155	C₂×C₄²	D₅₂	1	1	yes	characteristic
156	C₂×C₄²	D₅₂	1	1	yes	characteristic
157	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
158	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	4	4	no	—
162	C₄⋊C₈	—	13	4	no	—
163	C₄⋊C₈	—	26	2	no	—
164	#97	—	52	2	no	—
165	#95	—	26	4	no	—
166	#95	—	26	4	no	—
167	C₂×C₁₃	#1552	1	2	yes	—
168	C₂×C₁₃	#1561	1	2	yes	—
169	C₂×C₁₃	#1959	1	1	yes	characteristic
170	C₂×C₁₃	#1966	1	1	yes	characteristic
171	C₂×C₁₃	#1983	1	1	yes	characteristic
172	C₂×Q₈	—	52	2	no	—
173	C₂×Q₈	—	52	2	no	—
174	C₂×Q₈	—	52	1	no	—
175	C₂×Q₈	—	52	1	no	—
176	C₂×Q₈	—	52	2	no	—
177	C₂×Q₈	—	52	1	no	—
178	C₂×Q₈	—	52	2	no	—
179	C₂×Q₈	—	52	1	no	—
180	C₂²×C₄	—	26	2	no	—
181	C₂²×C₄	—	26	2	no	—
182	C₂²×C₄	#6103	1	2	yes	—
183	C₂²×C₄	#6103	1	2	yes	—
184	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
187	C₂×C₈	—	4	4	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	26	4	no	—
190	C₂×C₈	—	52	2	no	—
191	C₂×C₈	—	52	2	no	—
192	C₄⋊C₄	—	26	4	no	—
193	C₄⋊C₄	—	26	4	no	—
194	C₄⋊C₄	—	52	2	no	—
195	C₄⋊C₄	—	52	1	no	—
196	C₄⋊C₄	—	52	1	no	—
197	C₄²	—	2	4	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	1	no	—
200	C₄²	—	2	1	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	D₄×D₁₃	1	2	yes	—
204	C₄²	#6131	1	2	yes	—
205	C₁₃	#9708	1	1	yes	characteristic, complemented, Sylow
206	C₂³	C₂×#6103	1	1	yes	characteristic
207	Q₈	—	104	1	no	—
208	Q₈	—	104	1	no	—
209	Q₈	—	104	2	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	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	52	2	no	—
219	C₂×C₄	—	52	2	no	—
220	C₂×C₄	—	52	4	no	—
221	C₂×C₄	—	52	2	no	—
222	C₂×C₄	—	52	2	no	—
223	C₂×C₄	#88064	1	4	yes	—
224	C₂×C₄	#88147	1	2	yes	—
225	C₂×C₄	#88149	1	2	yes	—
226	C₂×C₄	#88158	1	2	yes	—
227	C₂×C₄	#88162	1	1	yes	characteristic
228	C₂×C₄	#88163	1	1	yes	characteristic
229	C₂×C₄	#88186	1	2	yes	—
230	C₂×C₄	#88194	1	1	yes	characteristic
231	C₂×C₄	#88196	1	2	yes	—
232	C₂×C₄	#88201	1	1	yes	characteristic
233	C₈	—	8	2	no	—
234	C₈	—	52	4	no	—
235	C₂²	#11718627	1	2	yes	—
236	C₂²	#11718649	1	1	yes	characteristic
237	C₂²	#11718774	1	1	yes	characteristic
238	C₂²	#11718794	1	1	yes	characteristic
239	C₂²	C₂×#88064	1	2	yes	—
240	C₄	—	2	2	no	—
241	C₄	—	2	4	no	—
242	C₄	—	4	2	no	—
243	C₄	—	104	2	no	—
244	C₄	—	104	2	no	—
245	C₄	#11718505	1	2	yes	—
246	C₄	#11718506	1	2	yes	—
247	C₄	#11718735	1	1	yes	characteristic
248	C₄	#11718747	1	1	yes	characteristic
249	C₄	#11718750	1	2	yes	—
250	C₂	#13113534	1	2	yes	—
251	C₂	#13113573	1	2	yes	—
252	C₂	#13115650	1	1	yes	characteristic
253	C₂	#13115679	1	1	yes	characteristic
254	C₂	#13115766	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13123214

C₂

yes

maximal, characteristic

#13114689

C₂

yes

maximal, characteristic

C₂×#11718074

C₂

yes

maximal

C₂×#11718078

C₂

yes

maximal

C₁₃×#1842

C₂

yes

maximal, characteristic

C₂×#88123

C₂²

yes

characteristic

C₂×#88123

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₈

—

C₂×C₁₃×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

#11718597

C₄

yes

—

#11718590

—

#11718590

—

#11718590

—

C₂×C₄⋊#1055

C₂²

yes

—

—

—

—

—

C₂²×Dic₂₆

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

—

—

—

—

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

—

—

—

D₄

yes

—

#88043

—

#9708

—

maximal, Sylow

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×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

D₁₃

yes

—

—

—

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

#101

yes

—

C₂×C₄×C₁₃

C₄×D₄

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃

#137

yes

characteristic

100

C₂×C₄×C₁₃

#137

yes

—

101

C₂×Dic₁₃

—

102

C₂×Dic₁₃

—

103

C₂×Dic₁₃

—

104

C₂×Dic₁₃

—

105

C₂×Dic₁₃

—

106

Dic₂₆

—

107

Dic₂₆

—

108

Dic₂₆

—

109

Dic₂₆

—

110

Dic₂₆

—

111

C₈×C₁₃

—

112

#1055

—

113

C₂×C₄⋊Q₈

—

114

C₂×C₄⋊Q₈

—

115

C₂×C₄⋊C₈

—

116

C₂×C₄⋊C₈

—

117

C₂×C₄⋊C₈

C₂×D₁₃

yes

—

118

C₂×#97

—

119

#391

—

120

#391

—

121

#391

—

122

#382

—

123

C₄³

C₂×D₁₃

yes

characteristic

124

#336

—

125

#332

—

126

#332

—

127

C₂²×C₁₃

#390

yes

characteristic

128

C₂²×C₁₃

C₂×#101

yes

—

129

C₂²×C₁₃

#416

yes

characteristic

130

C₂²×C₁₃

#417

yes

characteristic

131

C₂²×C₁₃

#417

yes

—

132

C₄×C₁₃

—

133

C₄×C₁₃

—

134

C₄×C₁₃

—

135

C₄×C₁₃

#463

yes

—

136

C₄×C₁₃

#464

yes

—

137

C₄×C₁₃

#489

yes

—

138

C₄×C₁₃

#496

yes

characteristic

139

C₄×C₁₃

#497

yes

characteristic

140

Dic₁₃

—

141

Dic₁₃

—

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×C₈

—

145

C₂²×C₈

—

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×C₄²

C₄×D₁₃

yes

—

155

C₂×C₄²

D₅₂

yes

characteristic

156

C₂×C₄²

D₅₂

yes

characteristic

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

—

163

C₄⋊C₈

—

164

#97

—

165

#95

—

166

#95

—

167

C₂×C₁₃

#1552

yes

—

168

C₂×C₁₃

#1561

yes

—

169

C₂×C₁₃

#1959

yes

characteristic

170

C₂×C₁₃

#1966

yes

characteristic

171

C₂×C₁₃

#1983

yes

characteristic

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

#6103

yes

—

183

C₂²×C₄

#6103

yes

—

184

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

185

C₂²×C₄

C₂×D₅₂

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

D₄×D₁₃

yes

—

204

C₄²

#6131

yes

—

205

C₁₃

#9708

yes

characteristic, complemented, Sylow

206

C₂³

C₂×#6103

yes

characteristic

207

Q₈

—

104

—

208

Q₈

—

104

—

209

Q₈

—

104

—

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

#88064

yes

—

224

C₂×C₄

#88147

yes

—

225

C₂×C₄

#88149

yes

—

226

C₂×C₄

#88158

yes

—

227

C₂×C₄

#88162

yes

characteristic

228

C₂×C₄

#88163

yes

characteristic

229

C₂×C₄

#88186

yes

—

230

C₂×C₄

#88194

yes

characteristic

231

C₂×C₄

#88196

yes

—

232

C₂×C₄

#88201

yes

characteristic

233

C₈

—

234

C₈

—

235

C₂²

#11718627

yes

—

236

C₂²

#11718649

yes

characteristic

237

C₂²

#11718774

yes

characteristic

238

C₂²

#11718794

yes

characteristic

239

C₂²

C₂×#88064

yes

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

104

—

244

C₄

—

104

—

245

C₄

#11718505

yes

—

246

C₄

#11718506

yes

—

247

C₄

#11718735

yes

characteristic

248

C₄

#11718747

yes

characteristic

249

C₄

#11718750

yes

—

250

C₂

#13113534

yes

—

251

C₂

#13113573

yes

—

252

C₂

#13115650

yes

characteristic

253

C₂

#13115679

yes

characteristic

254

C₂

#13115766

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#6103
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1842	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1842	D₁₃
hypocenter	C₁₃	#9708
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂³

C₂×#6103

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1842

C₂

socle, prime radical

C₂³×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
205. C₁₃	#9708	semidirect

H ≅ G/N

type

205. C₁₃

#9708

semidirect

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

subgroup	index
#13123214	2
#13114689	2
C₂×#11718074	2
C₂×#11718078	2
C₁₃×#1842	2
#9708	13

subgroup

index

C₁₃×#1842

Subgroups — #15762025

Conjugacy classes of subgroups

Complements

Maximal subgroups