Group #15756793 — subgroups

Subgroups — #15756793

Order 3328.

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

normal subgroups only

This group has 454 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	#13123877	C₂	1	1	yes	maximal, characteristic
2	#13115631	C₂	1	1	yes	maximal, characteristic
3	#13113588	C₂	1	2	yes	maximal, complemented
4	#13112674	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₃×#100	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#100	C₄	1	2	yes	—
8	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
9	#11718868	—	2	2	no	—
10	C₂×C₂²⋊#1055	—	2	2	no	—
11	#11718673	—	2	2	no	—
12	#11718673	—	2	2	no	—
13	#11718586	C₂²	1	2	yes	—
14	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₁₃×#343	C₄	1	1	yes	characteristic
17	C₁₃×#343	C₄	1	1	yes	characteristic
18	#11718050	—	2	2	no	—
19	#11718049	—	2	2	no	—
20	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	D₄	1	2	yes	—
22	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
23	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
24	C₄×D₄×C₁₃	—	2	2	no	—
25	C₄×D₄×C₁₃	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₄	Q₈	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×#6099	—	2	2	no	—
30	C₂×#6099	—	2	2	no	—
31	C₂²×#1055	—	2	1	no	—
32	C₂²×#1055	—	2	1	no	—
33	C₁₃×#100	—	2	4	no	—
34	C₁₃×#97	—	2	2	no	—
35	C₄×C₈×C₁₃	—	2	2	no	—
36	C₂²⋊#1055	—	2	4	no	—
37	C₂²⋊#1055	—	2	2	no	—
38	C₂²⋊#1055	—	4	4	no	—
39	C₄⋊#1055	—	2	2	no	—
40	C₄⋊#1055	D₄	1	2	yes	—
41	C₄⋊#1055	D₄	1	2	yes	—
42	C₄×#1055	—	2	2	no	—
43	C₄×#1055	—	2	2	no	—
44	#8837	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	C₄⋊C₄	1	2	yes	—
46	C₂×D₄×C₁₃	—	2	2	no	—
47	C₂×D₄×C₁₃	—	2	2	no	—
48	C₂×D₄×C₁₃	—	2	1	no	—
49	C₂×D₄×C₁₃	—	2	1	no	—
50	C₂²×C₄×C₁₃	—	2	2	no	—
51	C₂²×C₄×C₁₃	—	2	2	no	—
52	C₂²×C₄×C₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
58	C₁₃×M₁₆	—	2	2	no	—
59	C₁₃×M₁₆	—	2	2	no	—
60	C₁₃×M₁₆	—	2	2	no	—
61	C₁₃×M₁₆	M₁₆	1	4	yes	complemented
62	C₂×C₈×C₁₃	—	2	2	no	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₁₃×C₂²⋊C₄	—	2	4	no	—
66	C₄²×C₁₃	C₂×D₄	1	2	yes	—
67	C₄²×C₁₃	#41	1	2	yes	—
68	#6099	—	8	2	no	—
69	#6099	—	8	2	no	—
70	C₂×#1055	—	2	2	no	—
71	C₂×#1055	—	2	2	no	—
72	C₂×#1055	—	2	2	no	—
73	C₂×#1055	—	4	1	no	—
74	C₂×#1055	—	4	1	no	—
75	C₂×#1055	—	4	2	no	—
76	C₂×#1055	—	4	1	no	—
77	#2975	—	13	1	no	—
78	#1954	—	13	1	no	—
79	C₄×#100	D₁₃	1	1	yes	characteristic
80	#1565	—	13	2	no	—
81	#1278	—	13	2	no	—
82	C₂³×C₁₃	—	2	2	no	—
83	C₂³×C₁₃	—	2	2	no	—
84	C₂³×C₁₃	—	2	2	no	—
85	C₂³×C₁₃	—	4	2	no	—
86	C₂³×C₁₃	—	4	2	no	—
87	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
88	D₄×C₁₃	—	4	2	no	—
89	D₄×C₁₃	—	4	2	no	—
90	C₂×C₄×C₁₃	—	2	1	no	—
91	C₂×C₄×C₁₃	—	2	1	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	4	1	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	8	2	no	—
98	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
99	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
101	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
103	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
105	C₈×C₁₃	—	2	4	no	—
106	C₈×C₁₃	—	4	2	no	—
107	#1055	—	4	2	no	—
108	#1055	—	4	2	no	—
109	#1055	—	4	2	no	—
110	#1055	—	8	1	no	—
111	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
112	#436	—	26	2	no	—
113	#436	—	26	2	no	—
114	#431	—	13	2	no	—
115	C₂×C₄⋊C₈	—	13	1	no	—
116	C₂×#100	Dic₁₃	1	2	yes	—
117	#407	—	26	2	no	—
118	C₂×C₂²⋊C₈	—	26	2	no	—
119	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
120	C₂×C₄×C₈	—	13	1	no	—
121	#343	Dic₁₃	1	1	yes	characteristic
122	#343	Dic₁₃	1	1	yes	characteristic
123	#335	—	26	2	no	—
124	#334	—	26	2	no	—
125	C₂²×C₁₃	—	2	1	no	—
126	C₂²×C₁₃	—	2	1	no	—
127	C₂²×C₁₃	—	4	4	no	—
128	C₂²×C₁₃	—	4	2	no	—
129	C₂²×C₁₃	—	4	2	no	—
130	C₂²×C₁₃	—	4	2	no	—
131	C₂²×C₁₃	—	8	2	no	—
132	C₂²×C₁₃	#385	1	1	yes	characteristic
133	C₂²×C₁₃	#423	1	1	yes	characteristic
134	C₂²×C₁₃	#424	1	1	yes	characteristic
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	—	2	2	no	—
137	C₄×C₁₃	—	4	2	no	—
138	C₄×C₁₃	#435	1	2	yes	—
139	C₄×C₁₃	#436	1	2	yes	—
140	C₄×C₁₃	#453	1	1	yes	characteristic
141	C₄×C₁₃	#455	1	1	yes	characteristic
142	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
143	C₂³×C₄	D₅₂	1	2	yes	—
144	C₂×M₁₆	—	26	2	no	—
145	C₂×M₁₆	—	26	2	no	—
146	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
147	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
148	C₂²×C₈	—	26	1	no	—
149	C₂²×C₈	—	26	1	no	—
150	C₄×D₄	—	2	2	no	—
151	C₄×D₄	—	2	2	no	—
152	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
153	C₂×C₂²⋊C₄	Dic₂₆	1	2	yes	—
154	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
155	C₄⋊C₈	—	13	2	no	—
156	C₄⋊C₈	—	13	2	no	—
157	C₄⋊C₈	—	26	2	no	—
158	#100	—	2	4	no	—
159	C₂²⋊C₈	—	26	4	no	—
160	C₂²⋊C₈	—	26	2	no	—
161	C₂²⋊C₈	—	52	4	no	—
162	#97	—	2	2	no	—
163	C₄×C₈	—	2	2	no	—
164	C₄×C₈	—	26	2	no	—
165	C₄×C₈	—	26	2	no	—
166	C₂×C₁₃	—	2	1	no	—
167	C₂×C₁₃	—	2	1	no	—
168	C₂×C₁₃	—	8	2	no	—
169	C₂×C₁₃	#1851	1	1	yes	characteristic
170	C₂×C₁₃	#1856	1	1	yes	characteristic
171	C₂×C₁₃	#1858	1	1	yes	characteristic
172	C₂⁴	C₄⋊Dic₁₃	1	2	yes	—
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	1	no	—
176	C₂×D₄	—	2	1	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	4	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
182	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
184	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
185	M₁₆	—	2	2	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	2	no	—
188	M₁₆	—	104	2	no	—
189	M₁₆	—	104	2	no	—
190	M₁₆	#6099	1	4	yes	complemented
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	26	2	no	—
194	C₂×C₈	—	26	2	no	—
195	C₂×C₈	—	26	2	no	—
196	C₂×C₈	—	52	1	no	—
197	C₂×C₈	—	52	1	no	—
198	C₂×C₈	—	52	2	no	—
199	C₂×C₈	—	52	1	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₂²⋊C₄	—	2	4	no	—
202	C₄²	D₄×D₁₃	1	2	yes	—
203	C₄²	#6129	1	2	yes	—
204	C₁₃	#8837	1	1	yes	characteristic, complemented, Sylow
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
211	D₄	—	4	2	no	—
212	D₄	—	4	2	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	#88132	1	2	yes	—
222	C₂×C₄	#88136	1	1	yes	characteristic
223	C₂×C₄	#88140	1	1	yes	characteristic
224	C₂×C₄	C₂×#6099	1	2	yes	—
225	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
226	C₂×C₄	#88202	1	1	yes	characteristic
227	C₂×C₄	#88202	1	1	yes	characteristic
228	C₈	—	2	4	no	—
229	C₈	—	4	2	no	—
230	C₈	—	52	2	no	—
231	C₈	—	52	2	no	—
232	C₈	—	52	2	no	—
233	C₈	—	104	1	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	4	4	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	4	2	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	#11718585	1	1	yes	characteristic
242	C₂²	#11718611	1	1	yes	characteristic
243	C₂²	#11718660	1	1	yes	characteristic
244	C₄	—	2	1	no	—
245	C₄	—	2	2	no	—
246	C₄	—	4	2	no	—
247	C₄	#11718407	1	1	yes	characteristic
248	C₄	#11718408	1	1	yes	characteristic
249	C₄	#11718672	1	2	yes	—
250	C₄	#11718673	1	2	yes	—
251	C₂	—	2	1	no	—
252	C₂	—	2	1	no	—
253	C₂	—	8	2	no	—
254	C₂	#13115021	1	1	yes	characteristic
255	C₂	#13115048	1	1	yes	characteristic
256	C₂	#13115058	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13123877

C₂

yes

maximal, characteristic

#13115631

C₂

yes

maximal, characteristic

#13113588

C₂

yes

maximal, complemented

#13112674

C₂

yes

maximal, complemented

C₄×C₁₃×#100

C₂

yes

maximal, characteristic

C₂×C₄×D₄×C₁₃

C₂²

yes

characteristic

C₂×C₁₃×#100

C₄

yes

—

C₄×C₁₃×M₁₆

C₂²

yes

—

#11718868

—

C₂×C₂²⋊#1055

—

#11718673

—

#11718673

—

#11718586

C₂²

yes

—

C₂×C₄⋊#1055

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

C₁₃×#343

C₄

yes

characteristic

C₁₃×#343

C₄

yes

characteristic

#11718050

—

#11718049

—

C₂²×D₄×C₁₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₃

D₄

yes

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

—

C₄×D₄×C₁₃

—

C₄×D₄×C₁₃

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

characteristic

C₂×C₁₃×C₂²⋊C₄

Q₈

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×#6099

—

C₂×#6099

—

C₂²×#1055

—

C₂²×#1055

—

C₁₃×#100

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

C₂²⋊#1055

—

C₂²⋊#1055

—

C₂²⋊#1055

—

C₄⋊#1055

—

C₄⋊#1055

D₄

yes

—

C₄⋊#1055

D₄

yes

—

—

—

—

C₂⁴×C₁₃

C₄⋊C₄

yes

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₄⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

M₁₆

yes

complemented

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

—

—

—

—

—

—

—

—

—

—

—

D₁₃

yes

characteristic

#1565

—

#1278

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×C₄⋊C₄

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

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄×D₄

yes

—

C₂×C₄×C₁₃

#120

yes

characteristic

100

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

101

C₂×C₄×C₁₃

#123

yes

characteristic

102

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

103

C₂×C₄×C₁₃

#131

yes

characteristic

104

C₂×C₄×C₁₃

#131

yes

characteristic

105

C₈×C₁₃

—

106

C₈×C₁₃

—

107

#1055

—

108

#1055

—

109

#1055

—

110

#1055

—

111

C₂×C₄×D₄

C₂×D₁₃

yes

characteristic

112

#436

—

113

#436

—

114

#431

—

115

C₂×C₄⋊C₈

—

116

C₂×#100

Dic₁₃

yes

—

117

#407

—

118

C₂×C₂²⋊C₈

—

119

C₄×M₁₆

C₂×D₁₃

yes

—

120

C₂×C₄×C₈

—

121

#343

Dic₁₃

yes

characteristic

122

#343

Dic₁₃

yes

characteristic

123

#335

—

124

#334

—

125

C₂²×C₁₃

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

—

131

C₂²×C₁₃

—

132

C₂²×C₁₃

#385

yes

characteristic

133

C₂²×C₁₃

#423

yes

characteristic

134

C₂²×C₁₃

#424

yes

characteristic

135

C₄×C₁₃

—

136

C₄×C₁₃

—

137

C₄×C₁₃

—

138

C₄×C₁₃

#435

yes

—

139

C₄×C₁₃

#436

yes

—

140

C₄×C₁₃

#453

yes

characteristic

141

C₄×C₁₃

#455

yes

characteristic

142

C₂²×D₄

C₂×Dic₁₃

yes

characteristic

143

C₂³×C₄

D₅₂

yes

—

144

C₂×M₁₆

—

145

C₂×M₁₆

—

146

C₂×M₁₆

C₂×Dic₁₃

yes

—

147

C₂×M₁₆

C₂×Dic₁₃

yes

—

148

C₂²×C₈

—

149

C₂²×C₈

—

150

C₄×D₄

—

151

C₄×D₄

—

152

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

characteristic

153

C₂×C₂²⋊C₄

Dic₂₆

yes

—

154

C₂×C₄²

C₂²×D₁₃

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

#100

—

159

C₂²⋊C₈

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

162

#97

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₂×C₁₃

—

167

C₂×C₁₃

—

168

C₂×C₁₃

—

169

C₂×C₁₃

#1851

yes

characteristic

170

C₂×C₁₃

#1856

yes

characteristic

171

C₂×C₁₃

#1858

yes

characteristic

172

C₂⁴

C₄⋊Dic₁₃

yes

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

C₄⋊Dic₁₃

yes

—

182

C₂²×C₄

C₂×Dic₂₆

yes

characteristic

183

C₂²×C₄

C₂×D₅₂

yes

characteristic

184

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

104

—

189

M₁₆

—

104

—

190

M₁₆

#6099

yes

complemented

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₄⋊C₄

—

201

C₂²⋊C₄

—

202

C₄²

D₄×D₁₃

yes

—

203

C₄²

#6129

yes

—

204

C₁₃

#8837

yes

characteristic, complemented, Sylow

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×C₄⋊Dic₁₃

yes

characteristic

211

D₄

—

212

D₄

—

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

#88132

yes

—

222

C₂×C₄

#88136

yes

characteristic

223

C₂×C₄

#88140

yes

characteristic

224

C₂×C₄

C₂×#6099

yes

—

225

C₂×C₄

D₄×Dic₁₃

yes

—

226

C₂×C₄

#88202

yes

characteristic

227

C₂×C₄

#88202

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

233

C₈

—

104

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

#11718585

yes

characteristic

242

C₂²

#11718611

yes

characteristic

243

C₂²

#11718660

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#11718407

yes

characteristic

248

C₄

#11718408

yes

characteristic

249

C₄

#11718672

yes

—

250

C₄

#11718673

yes

—

251

C₂

—

252

C₂

—

253

C₂

—

254

C₂

#13115021

yes

characteristic

255

C₂

#13115048

yes

characteristic

256

C₂

#13115058

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#88136
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄×C₁₃×#100	C₂
socle	C₂²×C₁₃	#385
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#100	D₁₃
hypocenter	C₁₃	#8837
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

subgroup

G/H

center

C₂×C₄

#88136

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₄×C₁₃×#100

C₂

socle

C₂²×C₁₃

#385

prime radical

C₂²×D₄×C₁₃

C₂×C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

N	H ≅ G/N	type
3. #13113588	C₂	semidirect
4. #13112674	C₂	semidirect
61. C₁₃×M₁₆	M₁₆	semidirect
190. M₁₆	#6099	semidirect
204. C₁₃	#8837	semidirect

H ≅ G/N

type

3. #13113588

C₂

semidirect

4. #13112674

C₂

semidirect

61. C₁₃×M₁₆

M₁₆

semidirect

190. M₁₆

#6099

semidirect

204. C₁₃

#8837

semidirect

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

subgroup	index
#13123877	2
#13115631	2
#13113588	2
#13112674	2
C₄×C₁₃×#100	2
#8837	13

subgroup

index

C₄×C₁₃×#100

Subgroups — #15756793

Conjugacy classes of subgroups

Complements

Maximal subgroups