Group #15699754 — subgroups

Subgroups — C₁₃×#13415 #15699754

Order 3328.

436 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 114 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×C₁₃×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#362	C₂	1	2	yes	maximal
3	C₁₃×#2141	C₂	1	2	yes	maximal
4	C₁₃×#1945	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1376	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	—	2	1	no	—
7	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
10	C₁₃×#494	—	2	4	no	—
11	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
12	C₁₃×#427	C₂²	1	1	yes	characteristic
13	C₁₃×#424	—	2	1	no	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#362	—	2	4	no	—
16	C₁₃×#358	—	2	4	no	—
17	C₁₃×#339	—	2	1	no	—
18	C₂²×Q₈×C₁₃	—	2	2	no	—
19	C₂×C₁₃×Q₁₆	—	2	4	no	—
20	C₂×C₁₃×Q₁₆	—	2	2	no	—
21	C₂×C₁₃×Q₁₆	—	2	2	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	—	2	2	no	—
24	C₂×C₁₃×Q₁₆	—	2	2	no	—
25	C₂×C₁₃×Q₁₆	—	4	2	no	—
26	C₂×C₁₃×Q₁₆	—	4	2	no	—
27	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
28	C₂×C₁₃×M₁₆	—	2	1	no	—
29	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×C₄⋊Q₈	—	2	4	no	—
32	C₁₃×C₄⋊Q₈	—	4	2	no	—
33	C₁₃×#117	—	2	1	no	—
34	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
35	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
36	C₁₃×M₃₂	—	2	2	no	—
37	C₁₃×M₃₂	—	2	2	no	—
38	C₂×C₁₃×C₁₆	—	2	2	no	—
39	C₁₃×#108	—	2	2	no	—
40	C₁₃×#107	D₄	1	2	yes	—
41	C₁₃×#106	—	2	1	no	—
42	C₁₃×C₄⋊C₈	—	4	2	no	—
43	C₄×C₈×C₁₃	—	2	2	no	—
44	#13415	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×Q₈×C₁₃	—	2	4	no	—
46	C₂×Q₈×C₁₃	—	4	2	no	—
47	C₂×Q₈×C₁₃	—	4	2	no	—
48	C₂×Q₈×C₁₃	—	4	2	no	—
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	2	no	—
51	C₂²×C₄×C₁₃	—	2	1	no	—
52	C₂²×C₄×C₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₁₃×Q₁₆	—	2	4	no	—
55	C₁₃×Q₁₆	—	2	4	no	—
56	C₁₃×Q₁₆	—	4	8	no	—
57	C₁₃×Q₁₆	—	4	2	no	—
58	C₁₃×Q₁₆	—	4	2	no	—
59	C₁₃×M₁₆	—	4	1	no	—
60	C₁₃×M₁₆	—	4	1	no	—
61	C₂×C₈×C₁₃	—	2	1	no	—
62	C₂×C₈×C₁₃	—	2	1	no	—
63	C₂×C₈×C₁₃	—	4	1	no	—
64	C₂×C₈×C₁₃	D₈	1	2	yes	—
65	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₁₃	#41	1	2	yes	—
68	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
69	C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₁₃×C₄⋊C₄	—	4	8	no	—
71	C₁₃×C₂²⋊C₄	—	4	1	no	—
72	C₄²×C₁₃	—	2	1	no	—
73	C₄²×C₁₃	—	4	1	no	—
74	C₄²×C₁₃	SD₁₆	1	2	yes	—
75	C₁₃×C₁₆	—	4	2	no	—
76	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
77	C₂×#362	C₂×C₁₃	1	2	yes	—
78	#2141	C₂×C₁₃	1	2	yes	—
79	#1945	C₂×C₁₃	1	1	yes	characteristic
80	#1376	C₂×C₁₃	1	1	yes	characteristic
81	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
82	Q₈×C₁₃	—	4	4	no	—
83	Q₈×C₁₃	—	4	4	no	—
84	Q₈×C₁₃	—	8	2	no	—
85	Q₈×C₁₃	—	8	2	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	4	4	no	—
89	C₂×C₄×C₁₃	—	4	2	no	—
90	C₂×C₄×C₁₃	—	8	2	no	—
91	C₂×C₄×C₁₃	—	8	2	no	—
92	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
93	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
97	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₈×C₁₃	—	2	2	no	—
99	C₈×C₁₃	—	8	1	no	—
100	C₈×C₁₃	#121	1	2	yes	—
101	C₈×C₁₃	#123	1	2	yes	—
102	C₂²×Q₁₆	—	2	1	no	—
103	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
104	C₂×C₄⋊Q₈	—	2	1	no	—
105	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
106	#494	—	2	4	no	—
107	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
108	#427	C₂²×C₁₃	1	1	yes	characteristic
109	#424	—	2	1	no	—
110	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
111	#362	—	2	4	no	—
112	#358	—	2	4	no	—
113	#339	—	2	1	no	—
114	C₂²×C₁₃	—	2	2	no	—
115	C₂²×C₁₃	#450	1	1	yes	characteristic
116	C₂²×C₁₃	#459	1	1	yes	characteristic
117	C₂²×C₁₃	#490	1	1	yes	characteristic
118	C₄×C₁₃	—	2	4	no	—
119	C₄×C₁₃	—	8	2	no	—
120	C₄×C₁₃	—	8	4	no	—
121	C₄×C₁₃	#394	1	1	yes	characteristic
122	C₄×C₁₃	#447	1	1	yes	characteristic
123	C₄×C₁₃	#460	1	1	yes	characteristic
124	C₄×C₁₃	#486	1	1	yes	characteristic
125	C₂²×Q₈	—	2	2	no	—
126	C₂×Q₁₆	—	2	4	no	—
127	C₂×Q₁₆	—	2	2	no	—
128	C₂×Q₁₆	—	2	2	no	—
129	C₂×Q₁₆	—	2	2	no	—
130	C₂×Q₁₆	—	2	2	no	—
131	C₂×Q₁₆	—	2	2	no	—
132	C₂×Q₁₆	—	4	2	no	—
133	C₂×Q₁₆	—	4	2	no	—
134	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
135	C₂×M₁₆	—	2	1	no	—
136	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
137	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
138	C₄⋊Q₈	—	2	4	no	—
139	C₄⋊Q₈	—	4	2	no	—
140	#117	—	2	1	no	—
141	C₂×C₄⋊C₄	—	4	2	no	—
142	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
143	M₃₂	—	2	2	no	—
144	M₃₂	—	2	2	no	—
145	C₂×C₁₆	—	2	2	no	—
146	#108	—	2	2	no	—
147	#107	D₄×C₁₃	1	2	yes	—
148	#106	—	2	1	no	—
149	C₄⋊C₈	—	4	2	no	—
150	C₄×C₈	—	2	2	no	—
151	C₂×C₁₃	—	2	1	no	—
152	C₂×C₁₃	—	2	1	no	—
153	C₂×C₁₃	#2041	1	1	yes	characteristic
154	C₂×C₁₃	#2214	1	2	yes	—
155	C₂×Q₈	—	2	4	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
164	Q₁₆	—	2	4	no	—
165	Q₁₆	—	2	4	no	—
166	Q₁₆	—	4	8	no	—
167	Q₁₆	—	4	2	no	—
168	Q₁₆	—	4	2	no	—
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	C₁₃×D₈	1	2	yes	—
175	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
176	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
177	C₂×C₈	C₁₃×#41	1	2	yes	—
178	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	4	8	no	—
181	C₂²⋊C₄	—	4	1	no	—
182	C₄²	—	2	1	no	—
183	C₄²	—	4	1	no	—
184	C₄²	C₁₃×SD₁₆	1	2	yes	—
185	C₁₆	—	4	2	no	—
186	C₁₃	#13415	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
188	Q₈	—	4	4	no	—
189	Q₈	—	4	4	no	—
190	Q₈	—	8	2	no	—
191	Q₈	—	8	2	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	4	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	8	2	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
199	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
200	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
201	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
202	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
203	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₈	—	2	2	no	—
205	C₈	—	8	1	no	—
206	C₈	C₁₃×#121	1	2	yes	—
207	C₈	C₁₃×#123	1	2	yes	—
208	C₂²	—	2	2	no	—
209	C₂²	C₁₃×#450	1	1	yes	characteristic
210	C₂²	C₁₃×#459	1	1	yes	characteristic
211	C₂²	C₁₃×#490	1	1	yes	characteristic
212	C₄	—	2	4	no	—
213	C₄	—	8	4	no	—
214	C₄	—	8	2	no	—
215	C₄	C₁₃×#394	1	1	yes	characteristic
216	C₄	C₁₃×#447	1	1	yes	characteristic
217	C₄	C₁₃×#460	1	1	yes	characteristic
218	C₄	C₁₃×#486	1	1	yes	characteristic
219	C₂	—	2	1	no	—
220	C₂	—	2	1	no	—
221	C₂	C₁₃×#2041	1	1	yes	characteristic
222	C₂	C₁₃×#2214	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#494

C₂

yes

maximal, characteristic

C₂×C₁₃×#362

C₂

yes

maximal

C₁₃×#2141

C₂

yes

maximal

C₁₃×#1945

C₂

yes

maximal, characteristic

C₁₃×#1376

C₂

yes

maximal, characteristic

C₂²×C₁₃×Q₁₆

—

C₂²×C₁₃×Q₁₆

C₂²

yes

—

C₂×C₁₃×C₄⋊Q₈

—

C₂×C₁₃×M₃₂

C₂²

yes

—

C₁₃×#494

—

C₂×C₁₃×#108

C₂²

yes

characteristic

C₁₃×#427

C₂²

yes

characteristic

C₁₃×#424

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#362

—

C₁₃×#358

—

C₁₃×#339

—

C₂²×Q₈×C₁₃

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

D₄

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×#117

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₁₃×M₃₂

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₁₃×#108

—

C₁₃×#107

D₄

yes

—

C₁₃×#106

—

C₁₃×C₄⋊C₈

—

C₄×C₈×C₁₃

—

#13415

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

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

C₂×D₄

yes

characteristic

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₈

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

#41

yes

—

C₂×C₈×C₁₃

#41

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

SD₁₆

yes

—

C₁₃×C₁₆

—

C₂×#494

C₂×C₁₃

yes

characteristic

C₂×#362

C₂×C₁₃

yes

—

#2141

C₂×C₁₃

yes

—

#1945

C₂×C₁₃

yes

characteristic

#1376

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

AGL(1,ℤ/8)

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

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

—

100

C₈×C₁₃

#121

yes

—

101

C₈×C₁₃

#123

yes

—

102

C₂²×Q₁₆

—

103

C₂²×Q₁₆

C₂²×C₁₃

yes

—

104

C₂×C₄⋊Q₈

—

105

C₂×M₃₂

C₂²×C₁₃

yes

—

106

#494

—

107

C₂×#108

C₂²×C₁₃

yes

characteristic

108

#427

C₂²×C₁₃

yes

characteristic

109

#424

—

110

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

111

#362

—

112

#358

—

113

#339

—

114

C₂²×C₁₃

—

115

C₂²×C₁₃

#450

yes

characteristic

116

C₂²×C₁₃

#459

yes

characteristic

117

C₂²×C₁₃

#490

yes

characteristic

118

C₄×C₁₃

—

119

C₄×C₁₃

—

120

C₄×C₁₃

—

121

C₄×C₁₃

#394

yes

characteristic

122

C₄×C₁₃

#447

yes

characteristic

123

C₄×C₁₃

#460

yes

characteristic

124

C₄×C₁₃

#486

yes

characteristic

125

C₂²×Q₈

—

126

C₂×Q₁₆

—

127

C₂×Q₁₆

—

128

C₂×Q₁₆

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

D₄×C₁₃

yes

—

135

C₂×M₁₆

—

136

C₂²×C₈

D₄×C₁₃

yes

characteristic

137

C₂²×C₈

C₂³×C₁₃

yes

characteristic

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

#117

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄²

D₄×C₁₃

yes

characteristic

143

M₃₂

—

144

M₃₂

—

145

C₂×C₁₆

—

146

#108

—

147

#107

D₄×C₁₃

yes

—

148

#106

—

149

C₄⋊C₈

—

150

C₄×C₈

—

151

C₂×C₁₃

—

152

C₂×C₁₃

—

153

C₂×C₁₃

#2041

yes

characteristic

154

C₂×C₁₃

#2214

yes

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

164

Q₁₆

—

165

Q₁₆

—

166

Q₁₆

—

167

Q₁₆

—

168

Q₁₆

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

C₁₃×D₈

yes

—

175

C₂×C₈

C₂×D₄×C₁₃

yes

characteristic

176

C₂×C₈

C₂×D₄×C₁₃

yes

—

177

C₂×C₈

C₁₃×#41

yes

—

178

C₂×C₈

C₁₃×#41

yes

characteristic

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₄²

C₁₃×SD₁₆

yes

—

185

C₁₆

—

186

C₁₃

#13415

yes

characteristic, direct product factor, Sylow

187

C₂³

C₁₃×AGL(1,ℤ/8)

yes

characteristic

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

C₁₃×#120

yes

characteristic

199

C₂×C₄

C₁₃×#121

yes

characteristic

200

C₂×C₄

C₁₃×#124

yes

characteristic

201

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

202

C₂×C₄

C₂×C₁₃×SD₁₆

yes

characteristic

203

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

characteristic

204

C₈

—

205

C₈

—

206

C₈

C₁₃×#121

yes

—

207

C₈

C₁₃×#123

yes

—

208

C₂²

—

209

C₂²

C₁₃×#450

yes

characteristic

210

C₂²

C₁₃×#459

yes

characteristic

211

C₂²

C₁₃×#490

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

C₁₃×#394

yes

characteristic

216

C₄

C₁₃×#447

yes

characteristic

217

C₄

C₁₃×#460

yes

characteristic

218

C₄

C₁₃×#486

yes

characteristic

219

C₂

—

220

C₂

—

221

C₂

C₁₃×#2041

yes

characteristic

222

C₂

C₁₃×#2214

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#459

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

prime radical

C₂³×C₁₃

AGL(1,ℤ/8)

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
44. #13415	C₁₃	direct (N × H)
186. C₁₃	#13415	direct (N × H)

H ≅ G/N

type

44. #13415

C₁₃

direct (N × H)

186. C₁₃

#13415

direct (N × H)

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

subgroup	index
C₂×C₁₃×#494	2
C₂×C₁₃×#362	2
C₁₃×#2141	2
C₁₃×#1945	2
C₁₃×#1376	2
#13415	13

subgroup

index

C₂×C₁₃×#494

C₂×C₁₃×#362

C₁₃×#2141

C₁₃×#1945

C₁₃×#1376

#13415

Subgroups — C₁₃×#13415 #15699754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13415 #15699754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13415 #15699754