Group #15761992 — subgroups

Subgroups — #15761992

Order 3328.

478 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 159 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	#13114953	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718139	C₂	1	2	yes	maximal
4	C₂×#11718139	C₂	1	2	yes	maximal
5	C₁₃×#2862	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₃×#391	—	2	1	no	—
9	C₁₃×#391	—	2	1	no	—
10	C₁₃×#391	—	2	2	no	—
11	C₁₃×#382	C₄	1	4	yes	—
12	C₄³×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#1055	C₂²	1	2	yes	—
14	C₂×C₄⋊#1055	C₂²	1	2	yes	—
15	C₂×C₄×#1055	—	2	1	no	—
16	#11718139	—	2	4	no	—
17	#11718139	—	2	4	no	—
18	#11718116	—	2	1	no	—
19	#11718116	—	2	2	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂²×Q₈×C₁₃	—	2	1	no	—
22	C₁₃×C₄⋊Q₈	—	2	2	no	—
23	C₁₃×C₄⋊Q₈	—	2	2	no	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	D₄	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×#1055	—	2	2	no	—
36	C₂²×#1055	—	2	2	no	—
37	C₁₃×#95	—	2	4	no	—
38	C₁₃×#95	—	2	4	no	—
39	C₄⋊#1055	—	2	2	no	—
40	C₄⋊#1055	—	2	2	no	—
41	C₄⋊#1055	—	2	2	no	—
42	C₄⋊#1055	D₄	1	4	yes	—
43	C₄×#1055	—	4	2	no	—
44	#9700	—	13	1	no	maximal, Sylow
45	C₂×Q₈×C₁₃	—	4	2	no	—
46	C₂×Q₈×C₁₃	—	4	1	no	—
47	C₂×Q₈×C₁₃	—	4	1	no	—
48	C₂×Q₈×C₁₃	—	4	2	no	—
49	C₂×Q₈×C₁₃	—	4	4	no	—
50	C₂×Q₈×C₁₃	—	4	1	no	—
51	C₂×Q₈×C₁₃	—	4	1	no	—
52	C₂²×C₄×C₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₁₃×C₄⋊C₄	—	2	4	no	—
60	C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₁₃×C₄⋊C₄	—	4	1	no	—
63	C₁₃×C₄⋊C₄	—	4	1	no	—
64	C₄²×C₁₃	—	2	4	no	—
65	C₄²×C₁₃	—	2	4	no	—
66	C₄²×C₁₃	—	2	2	no	—
67	C₄²×C₁₃	—	2	1	no	—
68	C₄²×C₁₃	—	2	1	no	—
69	C₄²×C₁₃	C₂×D₄	1	2	yes	—
70	C₄²×C₁₃	#41	1	2	yes	—
71	C₂×#1055	—	2	4	no	—
72	C₂×#1055	—	4	2	no	—
73	C₂×#1055	—	4	2	no	—
74	C₂×#1055	—	4	2	no	—
75	C₂×#1055	—	4	4	no	—
76	#2862	D₁₃	1	1	yes	characteristic
77	#1831	—	13	1	no	—
78	C₄×C₄⋊C₈	—	13	1	no	—
79	C₂×#332	—	13	2	no	—
80	C₂×#332	—	13	2	no	—
81	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	Q₈×C₁₃	—	8	2	no	—
83	Q₈×C₁₃	—	8	2	no	—
84	Q₈×C₁₃	—	8	2	no	—
85	Q₈×C₁₃	—	8	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	—	2	2	no	—
92	C₂×C₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	#101	1	4	yes	—
98	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
99	C₂×C₄×C₁₃	#121	1	2	yes	—
100	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
101	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#135	1	2	yes	—
103	C₂×C₄×C₁₃	#135	1	4	yes	—
104	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
105	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
106	#1055	—	4	4	no	—
107	#1055	—	8	2	no	—
108	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
109	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
110	C₂×C₄⋊C₈	—	13	2	no	—
111	C₂×C₄⋊C₈	—	13	2	no	—
112	C₂×C₄×C₈	—	26	1	no	—
113	#391	—	2	1	no	—
114	#391	—	2	2	no	—
115	#391	—	2	1	no	—
116	#382	Dic₁₃	1	4	yes	—
117	C₄³	C₂×D₁₃	1	1	yes	characteristic
118	#336	—	26	2	no	—
119	#336	—	26	1	no	—
120	#332	—	26	4	no	—
121	#332	—	26	4	no	—
122	C₂²×C₁₃	#390	1	1	yes	characteristic
123	C₂²×C₁₃	C₂×#101	1	2	yes	—
124	C₂²×C₁₃	#416	1	1	yes	characteristic
125	C₂²×C₁₃	#416	1	2	yes	—
126	C₂²×C₁₃	#417	1	1	yes	characteristic
127	C₄×C₁₃	—	2	4	no	—
128	C₄×C₁₃	—	2	2	no	—
129	C₄×C₁₃	—	4	2	no	—
130	C₄×C₁₃	—	8	2	no	—
131	C₄×C₁₃	—	8	2	no	—
132	C₄×C₁₃	#463	1	2	yes	—
133	C₄×C₁₃	#464	1	2	yes	—
134	C₄×C₁₃	#488	1	2	yes	—
135	C₄×C₁₃	#495	1	2	yes	—
136	C₂²×Q₈	—	2	1	no	—
137	C₂²×Q₈	—	2	1	no	—
138	C₂²×C₈	—	26	2	no	—
139	C₂²×C₈	—	26	2	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	1	no	—
145	C₂×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
147	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
148	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
149	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
150	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
151	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
152	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
153	C₄⋊C₈	—	13	4	no	—
154	C₄⋊C₈	—	26	2	no	—
155	C₄⋊C₈	—	26	2	no	—
156	C₄⋊C₈	—	26	2	no	—
157	C₄×C₈	—	52	2	no	—
158	#95	—	2	4	no	—
159	#95	—	2	4	no	—
160	C₂×C₁₃	#1544	1	2	yes	—
161	C₂×C₁₃	#1552	1	2	yes	—
162	C₂×C₁₃	#1958	1	1	yes	characteristic
163	C₂×C₁₃	#1966	1	1	yes	characteristic
164	C₂×C₁₃	#1983	1	1	yes	characteristic
165	C₂×Q₈	—	4	1	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	—	4	1	no	—
168	C₂×Q₈	—	4	1	no	—
169	C₂×Q₈	—	4	2	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂×Q₈	—	4	1	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
175	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
176	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
179	C₂×C₈	—	26	4	no	—
180	C₂×C₈	—	52	2	no	—
181	C₂×C₈	—	52	2	no	—
182	C₂×C₈	—	52	2	no	—
183	C₂×C₈	—	52	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	1	no	—
189	C₄²	—	2	4	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	4	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	2	1	no	—
194	C₄²	D₄×D₁₃	1	2	yes	—
195	C₄²	#6129	1	2	yes	—
196	C₁₃	#9700	1	1	yes	characteristic, complemented, Sylow
197	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
198	Q₈	—	8	2	no	—
199	Q₈	—	8	2	no	—
200	Q₈	—	8	2	no	—
201	Q₈	—	8	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	#88076	1	4	yes	—
214	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
215	C₂×C₄	#88190	1	1	yes	characteristic
216	C₂×C₄	#88192	1	2	yes	—
217	C₂×C₄	#88194	1	1	yes	characteristic
218	C₂×C₄	#88203	1	1	yes	characteristic
219	C₂×C₄	#88204	1	2	yes	—
220	C₂×C₄	#88204	1	4	yes	—
221	C₂×C₄	#88205	1	1	yes	characteristic
222	C₈	—	52	4	no	—
223	C₈	—	104	2	no	—
224	C₂²	#11718882	1	1	yes	characteristic
225	C₂²	C₂×#88076	1	2	yes	—
226	C₂²	#11718893	1	1	yes	characteristic
227	C₂²	#11718894	1	2	yes	—
228	C₂²	#11718894	1	1	yes	characteristic
229	C₄	—	2	2	no	—
230	C₄	—	2	4	no	—
231	C₄	—	4	2	no	—
232	C₄	—	8	2	no	—
233	C₄	—	8	2	no	—
234	C₄	#11718715	1	2	yes	—
235	C₄	#11718717	1	2	yes	—
236	C₄	#11718718	1	2	yes	—
237	C₄	#11718720	1	2	yes	—
238	C₂	#13113501	1	2	yes	—
239	C₂	#13113536	1	2	yes	—
240	C₂	#13115648	1	1	yes	characteristic
241	C₂	#13115681	1	1	yes	characteristic
242	C₂	#13115769	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13114953

C₂

yes

maximal, characteristic

C₄×C₄⋊#1055

C₂

yes

maximal, characteristic

C₂×#11718139

C₂

yes

maximal

C₂×#11718139

C₂

yes

maximal

C₁₃×#2862

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₁₃×#391

—

C₁₃×#391

—

C₁₃×#391

—

C₁₃×#382

C₄

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊#1055

C₂²

yes

—

C₂×C₄⋊#1055

C₂²

yes

—

C₂×C₄×#1055

—

—

—

—

—

C₂²×Q₈×C₁₃

—

C₂²×Q₈×C₁₃

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

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

C₂²×#1055

—

C₂²×#1055

—

C₁₃×#95

—

C₁₃×#95

—

—

—

—

D₄

yes

—

C₄×#1055

—

#9700

—

maximal, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

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

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

—

—

—

—

—

D₁₃

yes

characteristic

#1831

—

C₄×C₄⋊C₈

—

C₂×#332

—

C₂×#332

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

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

—

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

—

100

C₂×C₄×C₁₃

#124

yes

characteristic

101

C₂×C₄×C₁₃

#127

yes

characteristic

102

C₂×C₄×C₁₃

#135

yes

—

103

C₂×C₄×C₁₃

#135

yes

—

104

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

105

C₂×C₄×C₁₃

#137

yes

characteristic

106

#1055

—

107

#1055

—

108

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

109

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

110

C₂×C₄⋊C₈

—

111

C₂×C₄⋊C₈

—

112

C₂×C₄×C₈

—

113

#391

—

114

#391

—

115

#391

—

116

#382

Dic₁₃

yes

—

117

C₄³

C₂×D₁₃

yes

characteristic

118

#336

—

119

#336

—

120

#332

—

121

#332

—

122

C₂²×C₁₃

#390

yes

characteristic

123

C₂²×C₁₃

C₂×#101

yes

—

124

C₂²×C₁₃

#416

yes

characteristic

125

C₂²×C₁₃

#416

yes

—

126

C₂²×C₁₃

#417

yes

characteristic

127

C₄×C₁₃

—

128

C₄×C₁₃

—

129

C₄×C₁₃

—

130

C₄×C₁₃

—

131

C₄×C₁₃

—

132

C₄×C₁₃

#463

yes

—

133

C₄×C₁₃

#464

yes

—

134

C₄×C₁₃

#488

yes

—

135

C₄×C₁₃

#495

yes

—

136

C₂²×Q₈

—

137

C₂²×Q₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

—

147

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

—

148

C₂×C₄²

C₂×Dic₁₃

yes

—

149

C₂×C₄²

C₂²⋊D₁₃

yes

characteristic

150

C₂×C₄²

C₂²⋊D₁₃

yes

—

151

C₂×C₄²

C₂²⋊D₁₃

yes

characteristic

152

C₂×C₄²

C₂²×D₁₃

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄×C₈

—

158

#95

—

159

#95

—

160

C₂×C₁₃

#1544

yes

—

161

C₂×C₁₃

#1552

yes

—

162

C₂×C₁₃

#1958

yes

characteristic

163

C₂×C₁₃

#1966

yes

characteristic

164

C₂×C₁₃

#1983

yes

characteristic

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

175

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

176

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

D₄×D₁₃

yes

—

195

C₄²

#6129

yes

—

196

C₁₃

#9700

yes

characteristic, complemented, Sylow

197

C₂³

C₂×C₂²⋊Dic₁₃

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

#88076

yes

—

214

C₂×C₄

D₄×Dic₁₃

yes

—

215

C₂×C₄

#88190

yes

characteristic

216

C₂×C₄

#88192

yes

—

217

C₂×C₄

#88194

yes

characteristic

218

C₂×C₄

#88203

yes

characteristic

219

C₂×C₄

#88204

yes

—

220

C₂×C₄

#88204

yes

—

221

C₂×C₄

#88205

yes

characteristic

222

C₈

—

223

C₈

—

104

—

224

C₂²

#11718882

yes

characteristic

225

C₂²

C₂×#88076

yes

—

226

C₂²

#11718893

yes

characteristic

227

C₂²

#11718894

yes

—

228

C₂²

#11718894

yes

characteristic

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

#11718715

yes

—

235

C₄

#11718717

yes

—

236

C₄

#11718718

yes

—

237

C₄

#11718720

yes

—

238

C₂

#13113501

yes

—

239

C₂

#13113536

yes

—

240

C₂

#13115648

yes

characteristic

241

C₂

#13115681

yes

characteristic

242

C₂

#13115769

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#2862	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#2862	D₁₃
hypocenter	C₁₃	#9700
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₃

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#2862

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 ◁ #2862

N	H ≅ G/N	type
196. C₁₃	#9700	semidirect

H ≅ G/N

type

196. C₁₃

#9700

semidirect

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

subgroup	index
#13114953	2
C₄×C₄⋊#1055	2
C₂×#11718139	2
C₁₃×#2862	2
#9700	13

subgroup

index

#13114953

C₄×C₄⋊#1055

C₂×#11718139

C₁₃×#2862

#9700

Subgroups — #15761992

Conjugacy classes of subgroups

Complements

Maximal subgroups