Group #15765272 — subgroups

Subgroups — #15765272

Order 3328.

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

normal subgroups only

This group has 560 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	C₂×#11718752	C₂	1	2	yes	maximal
2	#13120209	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718048	C₂	1	2	yes	maximal
4	#13112719	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₂₆	C₂²	1	2	yes	—
8	C₂×C₁₃×#103	—	2	2	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#384	C₂²	1	1	yes	characteristic
11	#11718752	—	2	4	no	—
12	#11718752	—	2	4	no	—
13	#11718646	—	2	2	no	—
14	#11718644	—	2	2	no	—
15	#11718635	—	2	2	no	—
16	C₂×#88050	—	2	2	no	—
17	C₂×#88047	—	2	2	no	—
18	C₂×C₄⋊#1055	C₂²	1	2	yes	—
19	#11718048	—	2	4	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂²×Dic₂₆	D₄	1	2	yes	—
22	C₂²×C₈×C₁₃	—	2	1	no	—
23	C₁₃×C₄⋊Q₈	—	2	2	no	—
24	C₁₃×C₄⋊Q₈	—	2	1	no	—
25	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
29	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₃	—	2	2	no	—
31	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
32	C₂×#6101	—	2	2	no	—
33	C₂×C₄×Dic₁₃	—	2	2	no	—
34	C₂²×#1055	—	2	2	no	—
35	C₄×Dic₂₆	—	2	2	no	—
36	C₄×Dic₂₆	—	2	2	no	—
37	C₄×Dic₂₆	—	2	2	no	—
38	C₄×Dic₂₆	—	2	2	no	—
39	C₁₃×#103	—	4	4	no	—
40	C₄×C₈×C₁₃	—	2	2	no	—
41	#88071	—	2	2	no	—
42	#88071	—	2	4	no	—
43	#88050	—	2	8	no	—
44	#88047	—	2	8	no	—
45	C₄⋊#1055	—	2	2	no	—
46	C₄⋊#1055	D₄	1	4	yes	—
47	#10237	—	13	1	no	maximal, Sylow
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	2	no	—
51	C₂×Q₈×C₁₃	—	4	1	no	—
52	C₂²×C₄×C₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₃	—	4	1	no	—
54	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₃	—	2	2	no	—
57	C₂²×Dic₁₃	—	2	2	no	—
58	C₂×Dic₂₆	—	2	2	no	—
59	C₂×Dic₂₆	—	2	2	no	—
60	C₂×Dic₂₆	—	2	2	no	—
61	C₂×Dic₂₆	—	2	2	no	—
62	C₂×Dic₂₆	—	2	2	no	—
63	C₂×Dic₂₆	Q₁₆	1	4	yes	—
64	C₂×C₈×C₁₃	—	2	2	no	—
65	C₂×C₈×C₁₃	—	4	1	no	—
66	C₂×C₈×C₁₃	—	4	1	no	—
67	C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₃	C₂×D₄	1	2	yes	—
74	C₄²×C₁₃	#41	1	1	yes	characteristic
75	C₄⋊Dic₁₃	—	2	2	no	—
76	C₄⋊Dic₁₃	—	2	2	no	—
77	C₄⋊Dic₁₃	—	8	2	no	—
78	#6101	—	4	2	no	—
79	#6101	—	4	2	no	—
80	C₄×Dic₁₃	—	4	2	no	—
81	C₄×Dic₁₃	—	4	2	no	—
82	C₂×#1055	—	2	4	no	—
83	C₂×#1055	—	4	2	no	—
84	C₂×#1055	—	4	2	no	—
85	C₂×#477	—	13	2	no	—
86	#2582	—	13	1	no	—
87	#1956	D₁₃	1	1	yes	characteristic
88	C₂×Q₈⋊C₈	—	13	2	no	—
89	#1296	—	13	1	no	—
90	C₂³×C₁₃	#120	1	1	yes	characteristic
91	Q₈×C₁₃	—	4	4	no	—
92	Q₈×C₁₃	—	8	2	no	—
93	C₂×C₄×C₁₃	—	2	1	no	—
94	C₂×C₄×C₁₃	—	2	1	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	8	1	no	—
99	C₂×C₄×C₁₃	—	8	1	no	—
100	C₂×C₄×C₁₃	#120	1	2	yes	—
101	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#121	1	2	yes	—
103	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
105	C₂×C₄×C₁₃	#135	1	2	yes	—
106	C₂×C₄×C₁₃	#137	1	2	yes	—
107	C₂×C₄×C₁₃	#137	1	2	yes	—
108	C₂×Dic₁₃	—	2	4	no	—
109	C₂×Dic₁₃	—	4	2	no	—
110	C₂×Dic₁₃	—	4	2	no	—
111	C₂×Dic₁₃	—	4	2	no	—
112	C₂×Dic₁₃	—	4	2	no	—
113	C₂×Dic₁₃	—	4	2	no	—
114	Dic₂₆	—	2	4	no	—
115	Dic₂₆	—	2	4	no	—
116	Dic₂₆	—	4	2	no	—
117	Dic₂₆	—	4	2	no	—
118	C₈×C₁₃	—	4	2	no	—
119	#1055	—	4	4	no	—
120	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
121	C₂×C₄×Q₈	—	13	2	no	—
122	#477	—	26	4	no	—
123	#477	—	26	4	no	—
124	C₂×#107	—	26	2	no	—
125	C₂×C₄⋊C₈	—	13	2	no	—
126	C₂×#103	—	2	2	no	—
127	C₂×#103	—	26	2	no	—
128	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
129	#398	—	26	2	no	—
130	#391	—	26	2	no	—
131	#389	—	26	2	no	—
132	#384	C₂×D₁₃	1	1	yes	characteristic
133	Q₈⋊C₈	—	26	4	no	—
134	C₂²×C₁₃	#392	1	1	yes	characteristic
135	C₂²×C₁₃	#451	1	2	yes	—
136	C₂²×C₁₃	#452	1	2	yes	—
137	C₂²×C₁₃	#453	1	1	yes	characteristic
138	C₂²×C₁₃	#454	1	1	yes	characteristic
139	C₄×C₁₃	—	2	1	no	—
140	C₄×C₁₃	—	2	1	no	—
141	C₄×C₁₃	—	8	2	no	—
142	C₄×C₁₃	—	8	2	no	—
143	C₄×C₁₃	#451	1	2	yes	—
144	C₄×C₁₃	#452	1	2	yes	—
145	C₄×C₁₃	#467	1	2	yes	—
146	C₄×C₁₃	#470	1	2	yes	—
147	Dic₁₃	—	4	4	no	—
148	Dic₁₃	—	8	2	no	—
149	C₂²×Q₈	—	2	1	no	—
150	C₂²×Q₈	—	13	2	no	—
151	C₂²×C₈	—	2	1	no	—
152	C₂²×C₈	—	26	2	no	—
153	C₄⋊Q₈	—	2	1	no	—
154	C₄⋊Q₈	—	2	2	no	—
155	C₄⋊Q₈	D₅₂	1	2	yes	—
156	C₄×Q₈	—	26	2	no	—
157	C₄×Q₈	—	26	2	no	—
158	C₄×Q₈	—	26	2	no	—
159	C₄×Q₈	—	26	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	—	13	2	no	—
163	C₂×C₄⋊C₄	—	26	2	no	—
164	C₂×C₄⋊C₄	—	26	2	no	—
165	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	2	yes	—
166	C₂×C₄²	—	26	2	no	—
167	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
168	#107	—	26	8	no	—
169	C₄⋊C₈	—	13	4	no	—
170	C₄⋊C₈	—	26	2	no	—
171	#103	—	4	4	no	—
172	#103	—	26	8	no	—
173	C₄×C₈	—	2	2	no	—
174	#95	—	26	4	no	—
175	#95	—	26	2	no	—
176	C₂×C₁₃	#1630	1	1	yes	characteristic
177	C₂×C₁₃	#1633	1	1	yes	characteristic
178	C₂×C₁₃	#1636	1	2	yes	—
179	C₂×C₁₃	#2001	1	2	yes	—
180	C₂×C₁₃	#2006	1	1	yes	characteristic
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	13	4	no	—
186	C₂×Q₈	—	26	2	no	—
187	C₂×Q₈	—	26	2	no	—
188	C₂×Q₈	—	26	2	no	—
189	C₂×Q₈	—	26	2	no	—
190	C₂×Q₈	—	26	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	4	1	no	—
193	C₂²×C₄	—	26	2	no	—
194	C₂²×C₄	—	26	2	no	—
195	C₂²×C₄	D₄×D₁₃	1	2	yes	—
196	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	26	4	no	—
201	C₂×C₈	—	52	2	no	—
202	C₂×C₈	—	52	2	no	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	26	2	no	—
209	C₄⋊C₄	—	26	2	no	—
210	C₄⋊C₄	—	52	2	no	—
211	C₄⋊C₄	—	52	2	no	—
212	C₄⋊C₄	—	104	2	no	—
213	C₄²	—	52	2	no	—
214	C₄²	—	52	2	no	—
215	C₄²	C₂×D₅₂	1	1	yes	characteristic
216	C₄²	#6127	1	1	yes	characteristic
217	C₄²	D₄×D₁₃	1	2	yes	—
218	C₁₃	#10237	1	1	yes	characteristic, complemented, Sylow
219	C₂³	#88191	1	1	yes	characteristic
220	Q₈	—	4	4	no	—
221	Q₈	—	8	2	no	—
222	Q₈	—	26	4	no	—
223	Q₈	—	26	4	no	—
224	Q₈	—	52	2	no	—
225	Q₈	—	52	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	4	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	8	1	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	—	26	4	no	—
234	C₂×C₄	—	52	2	no	—
235	C₂×C₄	—	52	2	no	—
236	C₂×C₄	—	52	2	no	—
237	C₂×C₄	—	52	2	no	—
238	C₂×C₄	—	52	2	no	—
239	C₂×C₄	#88136	1	2	yes	—
240	C₂×C₄	#88138	1	2	yes	—
241	C₂×C₄	#88169	1	2	yes	—
242	C₂×C₄	#88170	1	2	yes	—
243	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
244	C₂×C₄	#88172	1	2	yes	—
245	C₂×C₄	#88184	1	1	yes	characteristic
246	C₂×C₄	#88194	1	1	yes	characteristic
247	C₈	—	4	2	no	—
248	C₈	—	52	4	no	—
249	C₂²	#11718621	1	1	yes	characteristic
250	C₂²	#11718723	1	1	yes	characteristic
251	C₂²	#11718738	1	1	yes	characteristic
252	C₂²	#11718834	1	2	yes	—
253	C₂²	#11718847	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	8	2	no	—
257	C₄	—	8	2	no	—
258	C₄	—	52	4	no	—
259	C₄	—	104	2	no	—
260	C₄	#11718469	1	2	yes	—
261	C₄	#11718471	1	2	yes	—
262	C₄	#11718474	1	2	yes	—
263	C₄	#11718477	1	2	yes	—
264	C₂	#13113955	1	1	yes	characteristic
265	C₂	#13113974	1	1	yes	characteristic
266	C₂	#13113991	1	2	yes	—
267	C₂	#13115845	1	2	yes	—
268	C₂	#13115877	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718752

C₂

yes

maximal

#13120209

C₂

yes

maximal, characteristic

C₂×#11718048

C₂

yes

maximal

#13112719

C₂

yes

maximal, characteristic

C₁₃×#1956

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×Dic₂₆

C₂²

yes

—

C₂×C₁₃×#103

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

—

—

—

—

—

—

—

C₂×C₄⋊#1055

C₂²

yes

—

#11718048

—

C₂²×Q₈×C₁₃

—

C₂²×Dic₂₆

D₄

yes

—

C₂²×C₈×C₁₃

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

D₄

yes

—

C₂×#6101

—

C₂×C₄×Dic₁₃

—

C₂²×#1055

—

C₄×Dic₂₆

—

C₄×Dic₂₆

—

C₄×Dic₂₆

—

C₄×Dic₂₆

—

C₁₃×#103

—

C₄×C₈×C₁₃

—

—

—

—

—

—

D₄

yes

—

#10237

—

maximal, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

Q₁₆

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

—

D₁₃

yes

characteristic

C₂×Q₈⋊C₈

—

#1296

—

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×C₁₃

—

100

C₂×C₄×C₁₃

#120

yes

—

101

C₂×C₄×C₁₃

#121

yes

characteristic

102

C₂×C₄×C₁₃

#121

yes

—

103

C₂×C₄×C₁₃

#127

yes

characteristic

104

C₂×C₄×C₁₃

C₂×Q₁₆

yes

—

105

C₂×C₄×C₁₃

#135

yes

—

106

C₂×C₄×C₁₃

#137

yes

—

107

C₂×C₄×C₁₃

#137

yes

—

108

C₂×Dic₁₃

—

109

C₂×Dic₁₃

—

110

C₂×Dic₁₃

—

111

C₂×Dic₁₃

—

112

C₂×Dic₁₃

—

113

C₂×Dic₁₃

—

114

Dic₂₆

—

115

Dic₂₆

—

116

Dic₂₆

—

117

Dic₂₆

—

118

C₈×C₁₃

—

119

#1055

—

120

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

121

C₂×C₄×Q₈

—

122

#477

—

123

#477

—

124

C₂×#107

—

125

C₂×C₄⋊C₈

—

126

C₂×#103

—

127

C₂×#103

—

128

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

129

#398

—

130

#391

—

131

#389

—

132

#384

C₂×D₁₃

yes

characteristic

133

Q₈⋊C₈

—

134

C₂²×C₁₃

#392

yes

characteristic

135

C₂²×C₁₃

#451

yes

—

136

C₂²×C₁₃

#452

yes

—

137

C₂²×C₁₃

#453

yes

characteristic

138

C₂²×C₁₃

#454

yes

characteristic

139

C₄×C₁₃

—

140

C₄×C₁₃

—

141

C₄×C₁₃

—

142

C₄×C₁₃

—

143

C₄×C₁₃

#451

yes

—

144

C₄×C₁₃

#452

yes

—

145

C₄×C₁₃

#467

yes

—

146

C₄×C₁₃

#470

yes

—

147

Dic₁₃

—

148

Dic₁₃

—

149

C₂²×Q₈

—

150

C₂²×Q₈

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

C₄⋊Q₈

D₅₂

yes

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₄×Q₈

—

159

C₄×Q₈

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

C₂²⋊D₁₃

yes

—

166

C₂×C₄²

—

167

C₂×C₄²

C₂²×D₁₃

yes

characteristic

168

#107

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

#103

—

172

#103

—

173

C₄×C₈

—

174

#95

—

175

#95

—

176

C₂×C₁₃

#1630

yes

characteristic

177

C₂×C₁₃

#1633

yes

characteristic

178

C₂×C₁₃

#1636

yes

—

179

C₂×C₁₃

#2001

yes

—

180

C₂×C₁₃

#2006

yes

characteristic

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

D₄×D₁₃

yes

—

196

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

104

—

213

C₄²

—

214

C₄²

—

215

C₄²

C₂×D₅₂

yes

characteristic

216

C₄²

#6127

yes

characteristic

217

C₄²

D₄×D₁₃

yes

—

218

C₁₃

#10237

yes

characteristic, complemented, Sylow

219

C₂³

#88191

yes

characteristic

220

Q₈

—

221

Q₈

—

222

Q₈

—

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

#88136

yes

—

240

C₂×C₄

#88138

yes

—

241

C₂×C₄

#88169

yes

—

242

C₂×C₄

#88170

yes

—

243

C₂×C₄

Q₁₆×D₁₃

yes

—

244

C₂×C₄

#88172

yes

—

245

C₂×C₄

#88184

yes

characteristic

246

C₂×C₄

#88194

yes

characteristic

247

C₈

—

248

C₈

—

249

C₂²

#11718621

yes

characteristic

250

C₂²

#11718723

yes

characteristic

251

C₂²

#11718738

yes

characteristic

252

C₂²

#11718834

yes

—

253

C₂²

#11718847

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

104

—

260

C₄

#11718469

yes

—

261

C₄

#11718471

yes

—

262

C₄

#11718474

yes

—

263

C₄

#11718477

yes

—

264

C₂

#13113955

yes

characteristic

265

C₂

#13113974

yes

characteristic

266

C₂

#13113991

yes

—

267

C₂

#13115845

yes

—

268

C₂

#13115877

yes

characteristic

	subgroup	G/H
center	C₂³	#88191
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1956	C₂
socle, prime radical	C₂³×C₁₃	#120
hypercenter	#1956	D₁₃
hypocenter	C₁₃	#10237
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#88191

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1956

C₂

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
218. C₁₃	#10237	semidirect

H ≅ G/N

type

218. C₁₃

#10237

semidirect

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

subgroup	index
C₂×#11718752	2
#13120209	2
C₂×#11718048	2
#13112719	2
C₁₃×#1956	2
#10237	13

subgroup

index

C₁₃×#1956

Subgroups — #15765272

Conjugacy classes of subgroups

Complements

Maximal subgroups