Group #15780304 — subgroups

Subgroups — #15780304

Order 3328.

488 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₂²×#88052	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124417	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718089	C₂	1	2	yes	maximal, complemented
4	#13112933	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	#11719496	—	2	1	no	—
8	C₂×#88158	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#108	C₂²	1	2	yes	—
10	C₁₃×#407	—	2	1	no	—
11	#11718777	C₄	1	2	yes	—
12	#11718776	C₄	1	2	yes	—
13	#11718775	—	2	2	no	—
14	#11718774	—	2	1	no	—
15	#11718767	C₂²	1	1	yes	characteristic
16	C₂×#88052	—	2	4	no	—
17	C₂×#88052	—	2	2	no	—
18	C₂²×#6090	C₂²	1	2	yes	—
19	C₁₃×#341	—	2	1	no	—
20	#11718089	—	2	4	no	—
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂×#6127	—	2	1	no	—
23	C₂×C₁₃×M₁₆	—	2	2	no	—
24	C₂²×C₈×C₁₃	—	2	2	no	—
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₃	D₄	1	2	yes	—
28	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
30	#88207	—	4	1	no	—
31	#88184	—	2	2	no	—
32	#88183	—	4	1	no	—
33	C₄×C₂²⋊D₁₃	—	4	2	no	—
34	#88180	—	2	1	no	—
35	#88178	—	2	2	no	—
36	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic
37	#88158	—	2	2	no	—
38	#88158	—	2	2	no	—
39	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
40	C₂×#6095	—	2	1	no	—
41	C₁₃×#108	—	2	2	no	—
42	C₁₃×#108	—	2	2	no	—
43	C₁₃×C₂²⋊C₈	—	4	2	no	—
44	#88061	—	2	2	no	—
45	#88058	C₂×C₄	1	2	yes	—
46	#88057	—	2	1	no	—
47	#88056	—	2	2	no	—
48	#88052	—	2	8	no	—
49	C₂×#6090	—	2	2	no	—
50	C₂×#6090	—	2	2	no	—
51	C₂×#6090	D₄	1	4	yes	complemented
52	#13064	—	13	1	no	maximal, Sylow
53	C₂⁴×C₁₃	SD₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₃	D₈	1	2	yes	—
58	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₁₃	—	4	2	no	—
61	C₂×C₂²⋊D₁₃	—	4	1	no	—
62	#6127	—	4	2	no	—
63	#6127	—	4	2	no	—
64	C₂×D₅₂	—	2	1	no	—
65	C₂×C₄×D₁₃	—	4	1	no	—
66	C₂×Dic₂₆	—	2	1	no	—
67	C₁₃×M₁₆	—	4	2	no	—
68	C₁₃×M₁₆	—	4	2	no	—
69	C₂×C₈×C₁₃	—	2	2	no	—
70	C₂×C₈×C₁₃	—	2	4	no	—
71	C₂×C₈×C₁₃	—	2	2	no	—
72	C₂×C₈×C₁₃	—	2	2	no	—
73	C₂×C₈×C₁₃	—	4	2	no	—
74	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
75	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₃	#41	1	2	yes	—
79	C₂²⋊Dic₁₃	—	4	2	no	—
80	C₂²⋊Dic₁₃	—	4	1	no	—
81	#6103	—	4	2	no	—
82	C₄⋊Dic₁₃	—	2	2	no	—
83	#6101	—	4	2	no	—
84	C₄×Dic₁₃	—	4	1	no	—
85	Dic₅₂	—	2	2	no	—
86	D₁₀₄	—	2	2	no	—
87	#6095	—	4	1	no	—
88	#6095	—	4	1	no	—
89	#6090	—	2	4	no	—
90	C₂²×M₃₂	—	13	1	no	—
91	#3050	—	13	1	no	—
92	C₂×#359	—	13	2	no	—
93	#1810	D₁₃	1	1	yes	characteristic, complemented
94	#1382	—	13	2	no	—
95	C₂³×C₁₃	—	2	2	no	—
96	C₂³×C₁₃	—	4	2	no	—
97	C₂³×C₁₃	#102	1	2	yes	—
98	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
99	C₂²×D₁₃	—	4	1	no	—
100	C₂×C₄×C₁₃	—	2	2	no	—
101	C₂×C₄×C₁₃	—	2	2	no	—
102	C₂×C₄×C₁₃	—	2	2	no	—
103	C₂×C₄×C₁₃	—	2	4	no	—
104	C₂×C₄×C₁₃	#102	1	2	yes	—
105	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	#121	1	2	yes	—
107	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
108	C₂×C₄×C₁₃	#135	1	2	yes	—
109	C₂²⋊D₁₃	—	8	4	no	—
110	C₂²⋊D₁₃	—	8	2	no	—
111	C₂×Dic₁₃	—	4	2	no	—
112	C₂×Dic₁₃	—	4	1	no	—
113	D₅₂	—	4	1	no	—
114	D₅₂	—	4	1	no	—
115	C₄×D₁₃	—	8	2	no	—
116	Dic₂₆	—	4	1	no	—
117	Dic₂₆	—	4	1	no	—
118	C₈×C₁₃	—	2	2	no	—
119	C₈×C₁₃	—	8	2	no	—
120	C₈×C₁₃	C₄×D₄	1	2	yes	—
121	C₈×C₁₃	#120	1	1	yes	characteristic
122	C₈×C₁₃	#123	1	1	yes	characteristic
123	C₂×#135	—	13	1	no	—
124	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
125	#525	—	26	1	no	—
126	C₂×M₃₂	—	26	4	no	—
127	C₂×M₃₂	—	26	2	no	—
128	C₂²×C₁₆	—	13	2	no	—
129	#467	—	13	2	no	—
130	#466	—	13	2	no	—
131	#465	—	26	2	no	—
132	C₂×#108	C₂×D₁₃	1	2	yes	—
133	#427	—	13	1	no	—
134	#416	—	26	1	no	—
135	#407	—	2	1	no	—
136	#359	—	26	4	no	—
137	#341	—	2	1	no	—
138	C₂²×C₁₃	—	2	2	no	—
139	C₂²×C₁₃	—	2	2	no	—
140	C₂²×C₁₃	—	2	2	no	—
141	C₂²×C₁₃	—	2	2	no	—
142	C₂²×C₁₃	—	4	4	no	—
143	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
144	C₂²×C₁₃	#465	1	2	yes	—
145	C₂×D₁₃	—	8	2	no	—
146	C₂×D₁₃	—	8	1	no	—
147	C₄×C₁₃	—	2	2	no	—
148	C₄×C₁₃	#386	1	1	yes	characteristic
149	C₄×C₁₃	#416	1	1	yes	characteristic
150	C₄×C₁₃	#466	1	2	yes	—
151	Dic₁₃	—	8	2	no	—
152	Dic₁₃	—	8	1	no	—
153	C₂×#41	—	26	1	no	—
154	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
155	#135	—	26	2	no	—
156	#135	—	26	2	no	—
157	C₂×Q₁₆	—	13	1	no	—
158	C₂×SD₁₆	—	26	1	no	—
159	C₂×D₈	—	13	1	no	—
160	C₂×M₁₆	—	2	2	no	—
161	C₂²×C₈	—	2	2	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	C₄×D₁₃	1	2	yes	—
164	C₂²×C₈	D₅₂	1	2	yes	—
165	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
166	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
167	#123	—	52	1	no	—
168	C₂²⋊Q₈	—	26	2	no	—
169	#121	—	26	2	no	—
170	#120	—	52	1	no	—
171	C₄×D₄	—	52	2	no	—
172	#117	—	26	1	no	—
173	M₃₂	—	26	8	no	—
174	C₂×C₁₆	—	13	4	no	—
175	C₂×C₁₆	—	26	2	no	—
176	C₂×C₁₆	—	26	2	no	—
177	#108	—	2	2	no	—
178	#108	—	2	2	no	—
179	#107	—	13	2	no	—
180	#106	—	26	1	no	—
181	#103	—	26	2	no	—
182	#102	—	26	2	no	—
183	C₂²⋊C₈	—	4	2	no	—
184	C₂×C₁₃	—	2	2	no	—
185	C₂×C₁₃	—	4	2	no	—
186	C₂×C₁₃	#1893	1	1	yes	characteristic
187	C₂×C₁₃	#2143	1	2	yes	—
188	D₁₃	—	16	1	no	—
189	C₂⁴	#6106	1	1	yes	characteristic
190	#41	—	52	2	no	—
191	#41	—	52	2	no	—
192	C₂×Q₈	—	26	1	no	—
193	C₂×D₄	—	26	1	no	—
194	C₂×D₄	—	52	1	no	—
195	C₂×D₄	—	52	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	52	1	no	—
199	C₂²×C₄	#6103	1	2	yes	—
200	C₂²×C₄	#6104	1	2	yes	—
201	C₂²×C₄	#6106	1	1	yes	characteristic
202	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
203	Q₁₆	—	26	2	no	—
204	SD₁₆	—	52	1	no	—
205	SD₁₆	—	52	1	no	—
206	D₈	—	26	2	no	—
207	M₁₆	—	4	2	no	—
208	M₁₆	—	4	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	2	4	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	4	2	no	—
214	C₂×C₈	#6103	1	2	yes	—
215	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
216	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
217	C₂×C₈	D₄×D₁₃	1	2	yes	—
218	C₂×C₈	#6129	1	2	yes	—
219	C₄⋊C₄	—	26	2	no	—
220	C₄⋊C₄	—	52	2	no	—
221	C₂²⋊C₄	—	52	1	no	—
222	C₂²⋊C₄	—	52	2	no	—
223	C₂²⋊C₄	—	52	2	no	—
224	C₄²	—	52	1	no	—
225	C₁₆	—	26	4	no	—
226	C₁₃	#13064	1	1	yes	characteristic, complemented, Sylow
227	C₂³	—	2	2	no	—
228	C₂³	—	4	2	no	—
229	C₂³	—	52	1	no	—
230	C₂³	#88049	1	2	yes	—
231	C₂³	C₂×#6106	1	1	yes	characteristic
232	Q₈	—	52	1	no	—
233	Q₈	—	52	1	no	—
234	D₄	—	52	1	no	—
235	D₄	—	52	1	no	—
236	D₄	—	104	4	no	—
237	D₄	—	104	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	4	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	52	2	no	—
243	C₂×C₄	—	52	1	no	—
244	C₂×C₄	—	104	2	no	—
245	C₂×C₄	#88049	1	2	yes	—
246	C₂×C₄	C₂×#6103	1	1	yes	characteristic
247	C₂×C₄	C₂×#6104	1	1	yes	characteristic
248	C₂×C₄	#88193	1	2	yes	—
249	C₂×C₄	#88204	1	2	yes	—
250	C₈	—	2	2	no	—
251	C₈	—	8	2	no	—
252	C₈	#88135	1	2	yes	—
253	C₈	#88136	1	1	yes	characteristic
254	C₈	#88140	1	1	yes	characteristic
255	C₂²	—	2	2	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	2	no	—
259	C₂²	—	4	4	no	—
260	C₂²	—	104	1	no	—
261	C₂²	—	104	2	no	—
262	C₂²	C₂×#88049	1	1	yes	characteristic
263	C₂²	#11718709	1	2	yes	—
264	C₄	—	2	2	no	—
265	C₄	—	104	1	no	—
266	C₄	—	104	2	no	—
267	C₄	#11718619	1	1	yes	characteristic
268	C₄	#11718663	1	1	yes	characteristic
269	C₄	#11718699	1	2	yes	—
270	C₂	—	2	2	no	—
271	C₂	—	4	2	no	—
272	C₂	—	208	1	no	—
273	C₂	#13115262	1	1	yes	characteristic
274	C₂	#13116563	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#88052

C₂

yes

maximal, characteristic, complemented

#13124417

C₂

yes

maximal, characteristic

C₂×#11718089

C₂

yes

maximal, complemented

#13112933

C₂

yes

maximal, complemented

C₁₃×#1810

C₂

yes

maximal, characteristic, complemented

C₂³×C₈×C₁₃

C₂²

yes

characteristic

#11719496

—

C₂×#88158

C₂²

yes

characteristic

C₂×C₁₃×#108

C₂²

yes

—

C₁₃×#407

—

#11718777

C₄

yes

—

#11718776

C₄

yes

—

#11718775

—

#11718774

—

#11718767

C₂²

yes

characteristic

C₂×#88052

—

C₂×#88052

—

C₂²×#6090

C₂²

yes

—

C₁₃×#341

—

#11718089

—

C₂³×C₄×C₁₃

D₄

yes

characteristic

C₂×#6127

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

—

—

—

C₄×C₂²⋊D₁₃

—

#88180

—

#88178

—

C₂×Dic₅₂

C₂×C₄

yes

characteristic

#88158

—

#88158

—

C₂×D₁₀₄

C₂×C₄

yes

characteristic

C₂×#6095

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×C₂²⋊C₈

—

#88061

—

#88058

C₂×C₄

yes

—

—

—

—

—

—

D₄

yes

complemented

#13064

—

maximal, Sylow

C₂⁴×C₁₃

SD₁₆

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

D₈

yes

—

C₂²×C₄×C₁₃

SD₁₆

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₃

—

C₂×C₂²⋊D₁₃

—

#6127

—

#6127

—

C₂×D₅₂

—

C₂×C₄×D₁₃

—

C₂×Dic₂₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₂²⋊Dic₁₃

—

C₂²⋊Dic₁₃

—

#6103

—

C₄⋊Dic₁₃

—

#6101

—

C₄×Dic₁₃

—

Dic₅₂

—

D₁₀₄

—

#6095

—

#6095

—

#6090

—

C₂²×M₃₂

—

#3050

—

C₂×#359

—

#1810

D₁₃

yes

characteristic, complemented

#1382

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#102

yes

—

C₂³×C₁₃

C₂×SD₁₆

yes

characteristic

C₂²×D₁₃

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

—

102

C₂×C₄×C₁₃

—

103

C₂×C₄×C₁₃

—

104

C₂×C₄×C₁₃

#102

yes

—

105

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

106

C₂×C₄×C₁₃

#121

yes

—

107

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

108

C₂×C₄×C₁₃

#135

yes

—

109

C₂²⋊D₁₃

—

110

C₂²⋊D₁₃

—

111

C₂×Dic₁₃

—

112

C₂×Dic₁₃

—

113

D₅₂

—

114

D₅₂

—

115

C₄×D₁₃

—

116

Dic₂₆

—

117

Dic₂₆

—

118

C₈×C₁₃

—

119

C₈×C₁₃

—

120

C₈×C₁₃

C₄×D₄

yes

—

121

C₈×C₁₃

#120

yes

characteristic

122

C₈×C₁₃

#123

yes

characteristic

123

C₂×#135

—

124

C₂³×C₈

C₂×D₁₃

yes

characteristic

125

#525

—

126

C₂×M₃₂

—

127

C₂×M₃₂

—

128

C₂²×C₁₆

—

129

#467

—

130

#466

—

131

#465

—

132

C₂×#108

C₂×D₁₃

yes

—

133

#427

—

134

#416

—

135

#407

—

136

#359

—

137

#341

—

138

C₂²×C₁₃

—

139

C₂²×C₁₃

—

140

C₂²×C₁₃

—

141

C₂²×C₁₃

—

142

C₂²×C₁₃

—

143

C₂²×C₁₃

C₂×#102

yes

characteristic

144

C₂²×C₁₃

#465

yes

—

145

C₂×D₁₃

—

146

C₂×D₁₃

—

147

C₄×C₁₃

—

148

C₄×C₁₃

#386

yes

characteristic

149

C₄×C₁₃

#416

yes

characteristic

150

C₄×C₁₃

#466

yes

—

151

Dic₁₃

—

152

Dic₁₃

—

153

C₂×#41

—

154

C₂³×C₄

C₂²⋊D₁₃

yes

characteristic

155

#135

—

156

#135

—

157

C₂×Q₁₆

—

158

C₂×SD₁₆

—

159

C₂×D₈

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

C₄×D₁₃

yes

—

164

C₂²×C₈

D₅₂

yes

—

165

C₂²×C₈

C₂²⋊D₁₃

yes

characteristic

166

C₂²×C₈

C₂²×D₁₃

yes

characteristic

167

#123

—

168

C₂²⋊Q₈

—

169

#121

—

170

#120

—

171

C₄×D₄

—

172

#117

—

173

M₃₂

—

174

C₂×C₁₆

—

175

C₂×C₁₆

—

176

C₂×C₁₆

—

177

#108

—

178

#108

—

179

#107

—

180

#106

—

181

#103

—

182

#102

—

183

C₂²⋊C₈

—

184

C₂×C₁₃

—

185

C₂×C₁₃

—

186

C₂×C₁₃

#1893

yes

characteristic

187

C₂×C₁₃

#2143

yes

—

188

D₁₃

—

189

C₂⁴

#6106

yes

characteristic

190

#41

—

191

#41

—

192

C₂×Q₈

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

#6103

yes

—

200

C₂²×C₄

#6104

yes

—

201

C₂²×C₄

#6106

yes

characteristic

202

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

203

Q₁₆

—

204

SD₁₆

—

205

SD₁₆

—

206

D₈

—

207

M₁₆

—

208

M₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

#6103

yes

—

215

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

216

C₂×C₈

C₂×D₅₂

yes

characteristic

217

C₂×C₈

D₄×D₁₃

yes

—

218

C₂×C₈

#6129

yes

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₂²⋊C₄

—

222

C₂²⋊C₄

—

223

C₂²⋊C₄

—

224

C₄²

—

225

C₁₆

—

226

C₁₃

#13064

yes

characteristic, complemented, Sylow

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

#88049

yes

—

231

C₂³

C₂×#6106

yes

characteristic

232

Q₈

—

233

Q₈

—

234

D₄

—

235

D₄

—

236

D₄

—

104

—

237

D₄

—

104

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

104

—

245

C₂×C₄

#88049

yes

—

246

C₂×C₄

C₂×#6103

yes

characteristic

247

C₂×C₄

C₂×#6104

yes

characteristic

248

C₂×C₄

#88193

yes

—

249

C₂×C₄

#88204

yes

—

250

C₈

—

251

C₈

—

252

C₈

#88135

yes

—

253

C₈

#88136

yes

characteristic

254

C₈

#88140

yes

characteristic

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

104

—

261

C₂²

—

104

—

262

C₂²

C₂×#88049

yes

characteristic

263

C₂²

#11718709

yes

—

264

C₄

—

265

C₄

—

104

—

266

C₄

—

104

—

267

C₄

#11718619

yes

characteristic

268

C₄

#11718663

yes

characteristic

269

C₄

#11718699

yes

—

270

C₂

—

271

C₂

—

272

C₂

—

208

—

273

C₂

#13115262

yes

characteristic

274

C₂

#13116563

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#6104
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1810	C₂
socle	C₂²×C₁₃	C₂×#102
prime radical	#13124417	C₂
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1810	D₁₃
hypocenter	C₁₃	#13064
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

subgroup

G/H

center

C₂×C₄

C₂×#6104

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#1810

C₂

C₂²×C₁₃

C₂

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

N	H ≅ G/N	type
1. C₂²×#88052	C₂	semidirect
3. C₂×#11718089	C₂	semidirect
4. #13112933	C₂	semidirect
5. C₁₃×#1810	C₂	semidirect
51. C₂×#6090	D₄	semidirect
93. #1810	D₁₃	semidirect
226. C₁₃	#13064	semidirect

H ≅ G/N

type

1. C₂²×#88052

C₂

semidirect

3. C₂×#11718089

C₂

semidirect

4. #13112933

C₂

semidirect

5. C₁₃×#1810

C₂

semidirect

51. C₂×#6090

D₄

semidirect

93. #1810

D₁₃

semidirect

226. C₁₃

#13064

semidirect

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

subgroup	index
C₂²×#88052	2
#13124417	2
C₂×#11718089	2
#13112933	2
C₁₃×#1810	2
#13064	13

subgroup

index

C₂²×#88052

C₁₃×#1810

Subgroups — #15780304

Conjugacy classes of subgroups

Complements

Maximal subgroups