Group #15719273 — subgroups

Subgroups — C₁₃×#32934 #15719273

Order 3328.

1378 conjugacy classes of subgroups; only the 310 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 310 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×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#467	C₂	1	3	yes	maximal, complemented
3	C₁₃×#2616	C₂	1	2	yes	maximal
4	C₁₃×#1894	C₂	1	6	yes	maximal, complemented
5	C₁₃×#1808	C₂	1	3	yes	maximal, complemented
6	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#131	—	2	12	no	—
9	C₂²×C₁₃×M₁₆	C₂²	1	3	yes	—
10	C₂³×C₈×C₁₃	C₂²	1	3	yes	—
11	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	—
12	C₁₃×#467	—	2	12	no	—
13	C₂×C₁₃×#107	C₂²	1	3	yes	—
14	C₂×C₁₃×#103	C₂²	1	6	yes	—
15	C₁₃×#395	—	2	2	no	—
16	C₁₃×#394	—	2	6	no	—
17	C₁₃×#380	C₂²	1	6	yes	—
18	C₁₃×#340	C₂²	1	6	yes	—
19	C₂×C₁₃×#41	—	2	6	no	—
20	C₂×C₁₃×#41	—	2	6	no	—
21	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
23	C₂²×D₄×C₁₃	D₄	1	3	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
25	C₂×C₁₃×Q₁₆	—	2	6	no	—
26	C₁₃×#131	—	2	32	no	—
27	C₂×C₁₃×M₁₆	—	2	6	no	—
28	C₂×C₁₃×M₁₆	—	2	12	no	—
29	C₂²×C₈×C₁₃	—	2	12	no	—
30	C₂²×C₈×C₁₃	D₄	1	12	yes	—
31	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
32	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
33	C₁₃×C₂²⋊Q₈	—	2	12	no	—
34	C₁₃×C₂²⋊Q₈	—	2	12	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
36	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
37	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
38	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
39	C₁₃×#107	—	2	6	no	—
40	C₁₃×#103	—	2	12	no	—
41	C₁₃×#95	—	2	6	no	—
42	#32934	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
44	C₁₃×#41	—	2	8	no	—
45	C₁₃×#41	—	2	24	no	—
46	C₂×Q₈×C₁₃	—	2	6	no	—
47	C₂×Q₈×C₁₃	—	2	6	no	—
48	C₂×Q₈×C₁₃	—	2	6	no	—
49	C₂×D₄×C₁₃	—	2	12	no	—
50	C₂×D₄×C₁₃	—	2	6	no	—
51	C₂²×C₄×C₁₃	—	2	6	no	—
52	C₂²×C₄×C₁₃	—	2	6	no	—
53	C₂²×C₄×C₁₃	—	2	6	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
56	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
57	C₂²×C₄×C₁₃	#41	1	6	yes	—
58	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
59	C₁₃×Q₁₆	—	4	4	no	—
60	C₁₃×M₁₆	—	2	24	no	—
61	C₂×C₈×C₁₃	—	2	6	no	—
62	C₂×C₈×C₁₃	—	2	24	no	—
63	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
64	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
65	C₁₃×C₄⋊C₄	—	2	6	no	—
66	C₁₃×C₄⋊C₄	—	2	6	no	—
67	C₁₃×C₄⋊C₄	—	4	12	no	—
68	C₁₃×C₂²⋊C₄	—	4	12	no	—
69	C₁₃×C₂²⋊C₄	—	8	6	no	—
70	C₂²×#131	C₂×C₁₃	1	1	yes	characteristic
71	C₂×#467	C₂×C₁₃	1	3	yes	complemented
72	#2616	C₂×C₁₃	1	2	yes	—
73	#1894	C₂×C₁₃	1	6	yes	complemented
74	#1808	C₂×C₁₃	1	3	yes	complemented
75	C₂³×C₁₃	—	2	6	no	—
76	C₂³×C₁₃	—	2	3	no	—
77	C₂³×C₁₃	—	2	6	no	—
78	C₂³×C₁₃	—	2	3	no	—
79	C₂³×C₁₃	#121	1	6	yes	—
80	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
81	Q₈×C₁₃	—	2	8	no	—
82	Q₈×C₁₃	—	4	2	no	—
83	Q₈×C₁₃	—	4	6	no	—
84	D₄×C₁₃	—	2	24	no	—
85	C₂×C₄×C₁₃	—	2	6	no	—
86	C₂×C₄×C₁₃	—	2	6	no	—
87	C₂×C₄×C₁₃	—	2	6	no	—
88	C₂×C₄×C₁₃	—	2	12	no	—
89	C₂×C₄×C₁₃	—	4	6	no	—
90	C₂×C₄×C₁₃	—	4	6	no	—
91	C₂×C₄×C₁₃	—	4	6	no	—
92	C₂×C₄×C₁₃	—	4	6	no	—
93	C₂×C₄×C₁₃	#121	1	6	yes	—
94	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
95	C₂×C₄×C₁₃	C₂×#41	1	3	yes	—
96	C₈×C₁₃	—	2	6	no	—
97	C₈×C₁₃	#120	1	4	yes	—
98	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
99	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
100	C₂×#131	—	2	12	no	—
101	C₂²×M₁₆	C₂²×C₁₃	1	3	yes	—
102	C₂³×C₈	C₂²×C₁₃	1	3	yes	—
103	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	—
104	#467	—	2	12	no	—
105	C₂×#107	C₂²×C₁₃	1	3	yes	—
106	C₂×#103	C₂²×C₁₃	1	6	yes	—
107	#395	—	2	2	no	—
108	#394	—	2	6	no	—
109	#380	C₂²×C₁₃	1	6	yes	—
110	#340	C₂²×C₁₃	1	6	yes	—
111	C₂²×C₁₃	—	2	6	no	—
112	C₂²×C₁₃	—	2	6	no	—
113	C₂²×C₁₃	—	2	6	no	—
114	C₂²×C₁₃	—	4	6	no	—
115	C₂²×C₁₃	—	4	6	no	—
116	C₂²×C₁₃	C₂×#121	1	3	yes	—
117	C₂²×C₁₃	#576	1	1	yes	characteristic
118	C₂²×C₁₃	#578	1	3	yes	—
119	C₄×C₁₃	—	2	6	no	—
120	C₄×C₁₃	—	8	2	no	—
121	C₄×C₁₃	—	8	6	no	—
122	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
123	C₄×C₁₃	#525	1	3	yes	—
124	C₂×#41	—	2	6	no	—
125	C₂×#41	—	2	6	no	—
126	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
127	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
128	C₂²×D₄	D₄×C₁₃	1	3	yes	—
129	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
130	C₂×Q₁₆	—	2	6	no	—
131	#131	—	2	32	no	—
132	C₂×M₁₆	—	2	6	no	—
133	C₂×M₁₆	—	2	12	no	—
134	C₂²×C₈	—	2	12	no	—
135	C₂²×C₈	D₄×C₁₃	1	12	yes	—
136	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
137	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
138	C₂²⋊Q₈	—	2	12	no	—
139	C₂²⋊Q₈	—	2	12	no	—
140	C₂×C₄⋊C₄	—	2	6	no	—
141	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
142	C₂×C₂²⋊C₄	—	2	6	no	—
143	C₂×C₂²⋊C₄	—	2	6	no	—
144	#107	—	2	6	no	—
145	#103	—	2	12	no	—
146	#95	—	2	6	no	—
147	C₂×C₁₃	—	4	6	no	—
148	C₂×C₁₃	#2847	1	1	yes	characteristic
149	C₂×C₁₃	#3059	1	3	yes	—
150	C₂×C₁₃	#3061	1	3	yes	—
151	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
152	#41	—	2	8	no	—
153	#41	—	2	24	no	—
154	C₂×Q₈	—	2	6	no	—
155	C₂×Q₈	—	2	6	no	—
156	C₂×Q₈	—	2	6	no	—
157	C₂×D₄	—	2	12	no	—
158	C₂×D₄	—	2	6	no	—
159	C₂²×C₄	—	2	6	no	—
160	C₂²×C₄	—	2	6	no	—
161	C₂²×C₄	—	2	6	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
164	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
165	C₂²×C₄	C₁₃×#41	1	6	yes	—
166	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
167	Q₁₆	—	4	4	no	—
168	M₁₆	—	2	24	no	—
169	C₂×C₈	—	2	6	no	—
170	C₂×C₈	—	2	24	no	—
171	C₂×C₈	C₂×D₄×C₁₃	1	6	yes	—
172	C₂×C₈	C₂×D₄×C₁₃	1	6	yes	—
173	C₄⋊C₄	—	2	6	no	—
174	C₄⋊C₄	—	2	6	no	—
175	C₄⋊C₄	—	4	12	no	—
176	C₂²⋊C₄	—	4	12	no	—
177	C₂²⋊C₄	—	8	6	no	—
178	C₁₃	#32934	1	1	yes	characteristic, direct product factor, Sylow
179	C₂³	—	2	6	no	—
180	C₂³	—	2	3	no	—
181	C₂³	—	2	6	no	—
182	C₂³	—	2	3	no	—
183	C₂³	C₁₃×#121	1	6	yes	—
184	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
185	Q₈	—	2	8	no	—
186	Q₈	—	4	2	no	—
187	Q₈	—	4	6	no	—
188	D₄	—	2	24	no	—
189	C₂×C₄	—	2	6	no	—
190	C₂×C₄	—	2	6	no	—
191	C₂×C₄	—	2	6	no	—
192	C₂×C₄	—	2	12	no	—
193	C₂×C₄	—	4	6	no	—
194	C₂×C₄	—	4	6	no	—
195	C₂×C₄	—	4	6	no	—
196	C₂×C₄	—	4	6	no	—
197	C₂×C₄	C₁₃×#121	1	6	yes	—
198	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
199	C₂×C₄	C₂×C₁₃×#41	1	3	yes	—
200	C₈	—	2	6	no	—
201	C₈	C₁₃×#120	1	4	yes	—
202	C₂²	—	2	6	no	—
203	C₂²	—	2	6	no	—
204	C₂²	—	2	6	no	—
205	C₂²	—	4	6	no	—
206	C₂²	—	4	6	no	—
207	C₂²	C₂×C₁₃×#121	1	3	yes	—
208	C₂²	C₁₃×#576	1	1	yes	characteristic
209	C₂²	C₁₃×#578	1	3	yes	—
210	C₄	—	2	6	no	—
211	C₄	—	8	6	no	—
212	C₄	—	8	2	no	—
213	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
214	C₄	C₁₃×#525	1	3	yes	—
215	C₂	—	4	6	no	—
216	C₂	C₁₃×#2847	1	1	yes	characteristic
217	C₂	C₁₃×#3059	1	3	yes	—
218	C₂	C₁₃×#3061	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₃×#131

C₂

yes

maximal, characteristic

C₂×C₁₃×#467

C₂

yes

maximal, complemented

C₁₃×#2616

C₂

yes

maximal

C₁₃×#1894

C₂

yes

maximal, complemented

C₁₃×#1808

C₂

yes

maximal, complemented

C₂²×C₁₃×#41

C₂²

yes

characteristic

C₂²×C₁₃×Q₁₆

C₂²

yes

characteristic

C₂×C₁₃×#131

—

C₂²×C₁₃×M₁₆

C₂²

yes

—

C₂³×C₈×C₁₃

C₂²

yes

—

C₂×C₁₃×C₂²⋊Q₈

C₂²

yes

—

C₁₃×#467

—

C₂×C₁₃×#107

C₂²

yes

—

C₂×C₁₃×#103

C₂²

yes

—

C₁₃×#395

—

C₁₃×#394

—

C₁₃×#380

C₂²

yes

—

C₁₃×#340

C₂²

yes

—

C₂×C₁₃×#41

—

C₂×C₁₃×#41

—

C₂²×Q₈×C₁₃

D₄

yes

characteristic

C₂²×Q₈×C₁₃

C₂³

yes

—

C₂²×D₄×C₁₃

D₄

yes

—

C₂³×C₄×C₁₃

C₂³

yes

—

C₂×C₁₃×Q₁₆

—

C₁₃×#131

—

C₂×C₁₃×M₁₆

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×C₂²⋊Q₈

—

C₁₃×C₂²⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂³

yes

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₁₃×#107

—

C₁₃×#103

—

C₁₃×#95

—

#32934

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

C₂×D₄

yes

—

C₁₃×#41

—

C₁₃×#41

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

#41

yes

—

C₂²×C₄×C₁₃

C₂⁴

yes

characteristic

C₁₃×Q₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₂²×#131

C₂×C₁₃

yes

characteristic

C₂×#467

C₂×C₁₃

yes

complemented

#2616

C₂×C₁₃

yes

—

#1894

C₂×C₁₃

yes

complemented

#1808

C₂×C₁₃

yes

complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#121

yes

—

C₂³×C₁₃

C₂²×D₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×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

#121

yes

—

C₂×C₄×C₁₃

C₂²×D₄

yes

—

C₂×C₄×C₁₃

C₂×#41

yes

—

C₈×C₁₃

—

C₈×C₁₃

#120

yes

—

C₂²×#41

C₂²×C₁₃

yes

characteristic

C₂²×Q₁₆

C₂²×C₁₃

yes

characteristic

100

C₂×#131

—

101

C₂²×M₁₆

C₂²×C₁₃

yes

—

102

C₂³×C₈

C₂²×C₁₃

yes

—

103

C₂×C₂²⋊Q₈

C₂²×C₁₃

yes

—

104

#467

—

105

C₂×#107

C₂²×C₁₃

yes

—

106

C₂×#103

C₂²×C₁₃

yes

—

107

#395

—

108

#394

—

109

#380

C₂²×C₁₃

yes

—

110

#340

C₂²×C₁₃

yes

—

111

C₂²×C₁₃

—

112

C₂²×C₁₃

—

113

C₂²×C₁₃

—

114

C₂²×C₁₃

—

115

C₂²×C₁₃

—

116

C₂²×C₁₃

C₂×#121

yes

—

117

C₂²×C₁₃

#576

yes

characteristic

118

C₂²×C₁₃

#578

yes

—

119

C₄×C₁₃

—

120

C₄×C₁₃

—

121

C₄×C₁₃

—

122

C₄×C₁₃

C₂×#120

yes

characteristic

123

C₄×C₁₃

#525

yes

—

124

C₂×#41

—

125

C₂×#41

—

126

C₂²×Q₈

D₄×C₁₃

yes

characteristic

127

C₂²×Q₈

C₂³×C₁₃

yes

—

128

C₂²×D₄

D₄×C₁₃

yes

—

129

C₂³×C₄

C₂³×C₁₃

yes

—

130

C₂×Q₁₆

—

131

#131

—

132

C₂×M₁₆

—

133

C₂×M₁₆

—

134

C₂²×C₈

—

135

C₂²×C₈

D₄×C₁₃

yes

—

136

C₂²×C₈

C₂³×C₁₃

yes

—

137

C₂²×C₈

C₂³×C₁₃

yes

characteristic

138

C₂²⋊Q₈

—

139

C₂²⋊Q₈

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

C₂³×C₁₃

yes

—

142

C₂×C₂²⋊C₄

—

143

C₂×C₂²⋊C₄

—

144

#107

—

145

#103

—

146

#95

—

147

C₂×C₁₃

—

148

C₂×C₁₃

#2847

yes

characteristic

149

C₂×C₁₃

#3059

yes

—

150

C₂×C₁₃

#3061

yes

—

151

C₂⁴

C₂×D₄×C₁₃

yes

—

152

#41

—

153

#41

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

C₂×D₄×C₁₃

yes

—

164

C₂²×C₄

C₂×D₄×C₁₃

yes

—

165

C₂²×C₄

C₁₃×#41

yes

—

166

C₂²×C₄

C₂⁴×C₁₃

yes

characteristic

167

Q₁₆

—

168

M₁₆

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

C₂×D₄×C₁₃

yes

—

172

C₂×C₈

C₂×D₄×C₁₃

yes

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₂²⋊C₄

—

177

C₂²⋊C₄

—

178

C₁₃

#32934

yes

characteristic, direct product factor, Sylow

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

C₁₃×#121

yes

—

184

C₂³

C₂²×D₄×C₁₃

yes

characteristic

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

D₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

C₁₃×#121

yes

—

198

C₂×C₄

C₂²×D₄×C₁₃

yes

—

199

C₂×C₄

C₂×C₁₃×#41

yes

—

200

C₈

—

201

C₈

C₁₃×#120

yes

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

C₂×C₁₃×#121

yes

—

208

C₂²

C₁₃×#576

yes

characteristic

209

C₂²

C₁₃×#578

yes

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

C₂×C₁₃×#120

yes

characteristic

214

C₄

C₁₃×#525

yes

—

215

C₂

—

216

C₂

C₁₃×#2847

yes

characteristic

217

C₂

C₁₃×#3059

yes

—

218

C₂

C₁₃×#3061

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₃

prime radical

C₂²×C₁₃×#41

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

N	H ≅ G/N	type
2. C₂×C₁₃×#467	C₂	semidirect
4. C₁₃×#1894	C₂	semidirect
5. C₁₃×#1808	C₂	semidirect
42. #32934	C₁₃	direct (N × H)
71. C₂×#467	C₂×C₁₃	semidirect
73. #1894	C₂×C₁₃	semidirect
74. #1808	C₂×C₁₃	semidirect
178. C₁₃	#32934	direct (N × H)

H ≅ G/N

type

2. C₂×C₁₃×#467

C₂

semidirect

4. C₁₃×#1894

C₂

semidirect

5. C₁₃×#1808

C₂

semidirect

42. #32934

C₁₃

direct (N × H)

71. C₂×#467

C₂×C₁₃

semidirect

73. #1894

C₂×C₁₃

semidirect

74. #1808

C₂×C₁₃

semidirect

178. C₁₃

#32934

direct (N × H)

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

subgroup	index
C₂²×C₁₃×#131	2
C₂×C₁₃×#467	2
C₁₃×#2616	2
C₁₃×#1894	2
C₁₃×#1808	2
#32934	13

subgroup

index

C₂²×C₁₃×#131

C₂×C₁₃×#467

C₁₃×#2616

C₁₃×#1894

C₁₃×#1808

#32934

Subgroups — C₁₃×#32934 #15719273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#32934 #15719273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32934 #15719273