Group #15765539 — subgroups

Subgroups — #15765539

Order 3328.

562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11718343	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718669	C₂	1	2	yes	maximal
3	C₂×#11718073	C₂	1	2	yes	maximal, complemented
4	#13112671	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88123	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88072	—	2	2	no	—
12	C₂×#88058	—	2	2	no	—
13	#11718669	—	2	4	no	—
14	#11718669	—	2	4	no	—
15	C₂×#88048	—	2	2	no	—
16	C₂×C₄⋊#1055	C₂²	1	2	yes	—
17	#11718343	—	2	4	no	—
18	#11718073	—	2	4	no	—
19	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₃	—	2	1	no	—
21	C₂²×Dic₂₆	—	2	2	no	—
22	C₂²×C₈×C₁₃	—	2	1	no	—
23	C₂²×C₈×C₁₃	D₄	1	2	yes	—
24	C₄×D₄×C₁₃	—	2	2	no	—
25	C₄×D₄×C₁₃	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
28	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₃	—	2	2	no	—
30	C₂×C₄⋊Dic₁₃	—	2	2	no	—
31	C₂²×#1055	—	2	2	no	—
32	#88123	—	2	2	no	—
33	#88123	—	2	2	no	—
34	#88123	—	2	2	no	—
35	#88123	D₄	1	4	yes	—
36	C₁₃×C₄⋊C₈	—	2	2	no	—
37	C₁₃×C₂²⋊C₈	—	4	4	no	—
38	C₄×C₈×C₁₃	—	2	2	no	—
39	#88072	—	2	8	no	—
40	#88058	—	2	8	no	—
41	#88048	—	2	8	no	—
42	C₄⋊#1055	—	2	2	no	—
43	C₄⋊#1055	D₄	1	4	yes	—
44	#10278	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	—	2	1	no	—
46	C₂×D₄×C₁₃	—	2	2	no	—
47	C₂×D₄×C₁₃	—	2	1	no	—
48	C₂×D₄×C₁₃	—	2	2	no	—
49	C₂×D₄×C₁₃	Q₁₆	1	2	yes	—
50	C₂²×C₄×C₁₃	—	2	1	no	—
51	C₂²×C₄×C₁₃	—	4	1	no	—
52	C₂²×C₄×C₁₃	—	4	1	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	—	4	2	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
58	C₂²×Dic₁₃	—	4	2	no	—
59	C₂×Dic₂₆	—	2	4	no	—
60	C₂×Dic₂₆	—	4	2	no	—
61	C₂×Dic₂₆	—	8	4	no	—
62	C₂×C₈×C₁₃	—	2	2	no	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	—	4	1	no	—
65	C₂×C₈×C₁₃	—	4	2	no	—
66	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
67	C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₁₃×C₂²⋊C₄	—	4	2	no	—
69	C₄²×C₁₃	C₂×D₄	1	2	yes	—
70	C₄²×C₁₃	C₂×D₄	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	2	no	—
75	C₂×#1055	—	2	4	no	—
76	C₂×#1055	—	4	2	no	—
77	C₂×#1055	—	4	2	no	—
78	C₂×#500	—	13	1	no	—
79	C₂×#476	—	13	2	no	—
80	#1954	D₁₃	1	1	yes	characteristic
81	C₂×#333	—	13	2	no	—
82	#1277	—	13	1	no	—
83	C₂³×C₁₃	—	2	2	no	—
84	C₂³×C₁₃	—	4	1	no	—
85	C₂³×C₁₃	—	4	2	no	—
86	C₂³×C₁₃	—	4	1	no	—
87	C₂³×C₁₃	—	4	2	no	—
88	C₂³×C₁₃	#121	1	1	yes	characteristic
89	D₄×C₁₃	—	2	4	no	—
90	D₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	4	1	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	—	8	2	no	—
95	C₂×C₄×C₁₃	—	8	1	no	—
96	C₂×C₄×C₁₃	—	8	1	no	—
97	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#120	1	2	yes	—
99	C₂×C₄×C₁₃	#121	1	2	yes	—
100	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
102	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#137	1	2	yes	—
105	C₂×C₄×C₁₃	#137	1	2	yes	—
106	C₂×Dic₁₃	—	4	4	no	—
107	C₂×Dic₁₃	—	8	4	no	—
108	Dic₂₆	—	8	4	no	—
109	Dic₂₆	—	8	4	no	—
110	C₈×C₁₃	—	2	4	no	—
111	C₈×C₁₃	—	8	1	no	—
112	#1055	—	4	4	no	—
113	C₂×C₄⋊Q₈	—	13	2	no	—
114	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
115	#500	—	26	4	no	—
116	#476	—	26	4	no	—
117	#476	—	26	4	no	—
118	C₂×#107	—	26	2	no	—
119	C₂×#106	—	26	2	no	—
120	C₂×C₄⋊C₈	—	13	2	no	—
121	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
122	C₂×#102	—	26	2	no	—
123	C₂×C₂²⋊C₈	—	2	2	no	—
124	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
125	#333	—	26	4	no	—
126	C₂²×C₁₃	—	4	4	no	—
127	C₂²×C₁₃	—	4	2	no	—
128	C₂²×C₁₃	—	8	2	no	—
129	C₂²×C₁₃	—	8	1	no	—
130	C₂²×C₁₃	—	8	1	no	—
131	C₂²×C₁₃	#392	1	1	yes	characteristic
132	C₂²×C₁₃	#461	1	2	yes	—
133	C₂²×C₁₃	#467	1	1	yes	characteristic
134	C₂²×C₁₃	#470	1	1	yes	characteristic
135	C₂²×C₁₃	#472	1	2	yes	—
136	C₄×C₁₃	—	2	2	no	—
137	C₄×C₁₃	—	8	1	no	—
138	C₄×C₁₃	#448	1	2	yes	—
139	C₄×C₁₃	#451	1	2	yes	—
140	C₄×C₁₃	#452	1	2	yes	—
141	C₄×C₁₃	#492	1	1	yes	characteristic
142	C₄×C₁₃	#497	1	1	yes	characteristic
143	Dic₁₃	—	8	4	no	—
144	C₂²×Q₈	—	26	2	no	—
145	C₂²×D₄	D₅₂	1	1	yes	characteristic
146	C₂³×C₄	—	2	1	no	—
147	C₂²×C₈	—	2	1	no	—
148	C₂²×C₈	—	26	2	no	—
149	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
150	C₄⋊Q₈	—	13	4	no	—
151	C₄⋊Q₈	—	26	2	no	—
152	C₄⋊Q₈	—	26	2	no	—
153	C₄⋊Q₈	—	26	2	no	—
154	C₄×D₄	—	2	2	no	—
155	C₄×D₄	—	2	2	no	—
156	C₂×C₄⋊C₄	—	26	2	no	—
157	C₂×C₄⋊C₄	—	26	2	no	—
158	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
159	C₂×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
161	#107	—	26	8	no	—
162	#106	—	26	8	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	13	4	no	—
165	C₄⋊C₈	—	26	2	no	—
166	#102	—	26	8	no	—
167	C₂²⋊C₈	—	4	4	no	—
168	C₄×C₈	—	2	2	no	—
169	C₂×C₁₃	—	8	2	no	—
170	C₂×C₁₃	#1675	1	2	yes	—
171	C₂×C₁₃	#1695	1	2	yes	—
172	C₂×C₁₃	#2001	1	1	yes	characteristic
173	C₂×C₁₃	#2013	1	1	yes	characteristic
174	C₂×C₁₃	#2018	1	1	yes	characteristic
175	C₂⁴	—	2	1	no	—
176	C₂×Q₈	—	26	4	no	—
177	C₂×Q₈	—	52	2	no	—
178	C₂×Q₈	—	104	4	no	—
179	C₂×D₄	—	2	2	no	—
180	C₂×D₄	—	2	1	no	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	Dic₅₂	1	2	yes	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	4	1	no	—
186	C₂²×C₄	—	4	1	no	—
187	C₂²×C₄	—	4	2	no	—
188	C₂²×C₄	—	52	2	no	—
189	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
190	C₂²×C₄	#6127	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	26	4	no	—
197	C₂×C₈	—	52	2	no	—
198	C₂×C₈	—	52	2	no	—
199	C₂×C₈	#6105	1	4	yes	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	26	4	no	—
202	C₄⋊C₄	—	26	4	no	—
203	C₄⋊C₄	—	52	2	no	—
204	C₄⋊C₄	—	52	2	no	—
205	C₂²⋊C₄	—	4	2	no	—
206	C₄²	D₄×D₁₃	1	2	yes	—
207	C₄²	D₄×D₁₃	1	2	yes	—
208	C₁₃	#10278	1	1	yes	characteristic, complemented, Sylow
209	C₂³	—	2	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	1	no	—
212	C₂³	—	4	2	no	—
213	C₂³	—	4	1	no	—
214	C₂³	#88184	1	1	yes	characteristic
215	Q₈	—	104	4	no	—
216	Q₈	—	104	4	no	—
217	D₄	—	2	4	no	—
218	D₄	—	4	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	—	8	1	no	—
224	C₂×C₄	—	8	1	no	—
225	C₂×C₄	—	52	4	no	—
226	C₂×C₄	—	104	4	no	—
227	C₂×C₄	#88136	1	2	yes	—
228	C₂×C₄	#88138	1	2	yes	—
229	C₂×C₄	#88158	1	1	yes	characteristic
230	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
231	C₂×C₄	#88163	1	2	yes	—
232	C₂×C₄	C₂×#6105	1	2	yes	—
233	C₂×C₄	#88191	1	1	yes	characteristic
234	C₂×C₄	#88194	1	1	yes	characteristic
235	C₂×C₄	#88205	1	2	yes	—
236	C₈	—	2	4	no	—
237	C₈	—	8	1	no	—
238	C₈	—	52	4	no	—
239	C₂²	—	4	4	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	8	1	no	—
242	C₂²	—	8	1	no	—
243	C₂²	—	8	2	no	—
244	C₂²	#11718621	1	1	yes	characteristic
245	C₂²	#11718680	1	2	yes	—
246	C₂²	#11718777	1	1	yes	characteristic
247	C₂²	#11718798	1	1	yes	characteristic
248	C₂²	#11718803	1	2	yes	—
249	C₄	—	2	2	no	—
250	C₄	—	8	1	no	—
251	C₄	—	104	4	no	—
252	C₄	#11718394	1	2	yes	—
253	C₄	#11718400	1	2	yes	—
254	C₄	#11718701	1	2	yes	—
255	C₄	#11718721	1	1	yes	characteristic
256	C₄	#11718737	1	1	yes	characteristic
257	C₂	—	8	2	no	—
258	C₂	#13114235	1	2	yes	—
259	C₂	#13114359	1	2	yes	—
260	C₂	#13115846	1	1	yes	characteristic
261	C₂	#13115918	1	1	yes	characteristic
262	C₂	#13115945	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718343

C₂

yes

maximal, characteristic, complemented

C₂×#11718669

C₂

yes

maximal

C₂×#11718073

C₂

yes

maximal, complemented

#13112671

C₂

yes

maximal, characteristic, complemented

C₁₃×#1954

C₂

yes

maximal, characteristic

C₂×C₄×D₄×C₁₃

C₂²

yes

characteristic

C₂×#88123

C₂²

yes

—

C₂×C₁₃×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₃×C₂²⋊C₈

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

—

—

—

—

C₂×C₄⋊#1055

C₂²

yes

—

#11718343

—

#11718073

—

C₂²×D₄×C₁₃

D₄

yes

characteristic

C₂³×C₄×C₁₃

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

D₄

yes

—

C₄×D₄×C₁₃

—

C₄×D₄×C₁₃

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

characteristic

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂²×#1055

—

—

—

—

D₄

yes

—

C₁₃×C₄⋊C₈

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

—

—

—

—

—

D₄

yes

—

#10278

—

maximal, Sylow

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

characteristic

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

—

D₁₃

yes

characteristic

C₂×#333

—

#1277

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#121

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

100

C₂×C₄×C₁₃

#127

yes

characteristic

101

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

102

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

103

C₂×C₄×C₁₃

#135

yes

characteristic

104

C₂×C₄×C₁₃

#137

yes

—

105

C₂×C₄×C₁₃

#137

yes

—

106

C₂×Dic₁₃

—

107

C₂×Dic₁₃

—

108

Dic₂₆

—

109

Dic₂₆

—

110

C₈×C₁₃

—

111

C₈×C₁₃

—

112

#1055

—

113

C₂×C₄⋊Q₈

—

114

C₂×C₄×D₄

C₂×D₁₃

yes

characteristic

115

#500

—

116

#476

—

117

#476

—

118

C₂×#107

—

119

C₂×#106

—

120

C₂×C₄⋊C₈

—

121

C₂×C₄⋊C₈

C₂×D₁₃

yes

characteristic

122

C₂×#102

—

123

C₂×C₂²⋊C₈

—

124

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

125

#333

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

—

131

C₂²×C₁₃

#392

yes

characteristic

132

C₂²×C₁₃

#461

yes

—

133

C₂²×C₁₃

#467

yes

characteristic

134

C₂²×C₁₃

#470

yes

characteristic

135

C₂²×C₁₃

#472

yes

—

136

C₄×C₁₃

—

137

C₄×C₁₃

—

138

C₄×C₁₃

#448

yes

—

139

C₄×C₁₃

#451

yes

—

140

C₄×C₁₃

#452

yes

—

141

C₄×C₁₃

#492

yes

characteristic

142

C₄×C₁₃

#497

yes

characteristic

143

Dic₁₃

—

144

C₂²×Q₈

—

145

C₂²×D₄

D₅₂

yes

characteristic

146

C₂³×C₄

—

147

C₂²×C₈

—

148

C₂²×C₈

—

149

C₂²×C₈

C₂²⋊D₁₃

yes

—

150

C₄⋊Q₈

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄×D₄

—

155

C₄×D₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

D₅₂

yes

characteristic

159

C₂×C₂²⋊C₄

—

160

C₂×C₄²

C₂²×D₁₃

yes

characteristic

161

#107

—

162

#106

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#102

—

167

C₂²⋊C₈

—

168

C₄×C₈

—

169

C₂×C₁₃

—

170

C₂×C₁₃

#1675

yes

—

171

C₂×C₁₃

#1695

yes

—

172

C₂×C₁₃

#2001

yes

characteristic

173

C₂×C₁₃

#2013

yes

characteristic

174

C₂×C₁₃

#2018

yes

characteristic

175

C₂⁴

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

104

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

Dic₅₂

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂×D₅₂

yes

characteristic

190

C₂²×C₄

#6127

yes

characteristic

191

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

#6105

yes

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₄²

D₄×D₁₃

yes

—

207

C₄²

D₄×D₁₃

yes

—

208

C₁₃

#10278

yes

characteristic, complemented, Sylow

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

#88184

yes

characteristic

215

Q₈

—

104

—

216

Q₈

—

104

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

104

—

227

C₂×C₄

#88136

yes

—

228

C₂×C₄

#88138

yes

—

229

C₂×C₄

#88158

yes

characteristic

230

C₂×C₄

C₂×Dic₅₂

yes

characteristic

231

C₂×C₄

#88163

yes

—

232

C₂×C₄

C₂×#6105

yes

—

233

C₂×C₄

#88191

yes

characteristic

234

C₂×C₄

#88194

yes

characteristic

235

C₂×C₄

#88205

yes

—

236

C₈

—

237

C₈

—

238

C₈

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

#11718621

yes

characteristic

245

C₂²

#11718680

yes

—

246

C₂²

#11718777

yes

characteristic

247

C₂²

#11718798

yes

characteristic

248

C₂²

#11718803

yes

—

249

C₄

—

250

C₄

—

251

C₄

—

104

—

252

C₄

#11718394

yes

—

253

C₄

#11718400

yes

—

254

C₄

#11718701

yes

—

255

C₄

#11718721

yes

characteristic

256

C₄

#11718737

yes

characteristic

257

C₂

—

258

C₂

#13114235

yes

—

259

C₂

#13114359

yes

—

260

C₂

#13115846

yes

characteristic

261

C₂

#13115918

yes

characteristic

262

C₂

#13115945

yes

characteristic

	subgroup	G/H
center	C₂³	#88184
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1954	C₂
socle	C₂³×C₁₃	#121
prime radical	C₂²×D₄×C₁₃	D₄
hypercenter	#1954	D₁₃
hypocenter	C₁₃	#10278
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#88184

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1954

C₂

socle

C₂³×C₁₃

#121

prime radical

C₂²×D₄×C₁₃

D₄

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. C₂×#11718343	C₂	semidirect
3. C₂×#11718073	C₂	semidirect
4. #13112671	C₂	semidirect
208. C₁₃	#10278	semidirect

H ≅ G/N

type

1. C₂×#11718343

C₂

semidirect

3. C₂×#11718073

C₂

semidirect

4. #13112671

C₂

semidirect

208. C₁₃

#10278

semidirect

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

subgroup	index
C₂×#11718343	2
C₂×#11718669	2
C₂×#11718073	2
#13112671	2
C₁₃×#1954	2
#10278	13

subgroup

index

C₁₃×#1954

Subgroups — #15765539

Conjugacy classes of subgroups

Complements

Maximal subgroups