Group #31815188 — subgroups

Subgroups — C₂×#22581057 #31815188

Order 17792.

480 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14555775	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×Dic₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#17984807	C₂	1	1	yes	maximal, characteristic
4	#22581057	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17984773	C₂	1	1	yes	maximal, characteristic
6	C₂×#17984767	C₂	1	1	yes	maximal, characteristic
7	C₂×#17984752	C₂	1	1	yes	maximal, characteristic
8	C₂×#103×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic
10	C₂×#14555775	C₄	1	8	yes	complemented
11	C₂×#14555775	C₂²	1	4	yes	—
12	C₂²×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
13	Q₈×Dic₁₃₉	—	2	2	no	—
14	Q₈×Dic₁₃₉	C₂²	1	4	yes	—
15	#17984807	—	2	2	no	—
16	#17984807	C₂²	1	4	yes	—
17	C₂×C₄⋊Dic₁₃₉	—	2	1	no	—
18	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₃₉⋊C₄	—	2	1	no	—
20	C₂×C₄×Dic₁₃₉	—	2	1	no	—
21	C₂×C₄×Dic₁₃₉	—	2	1	no	—
22	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
23	#17984773	C₂²	1	4	yes	—
24	#17984767	C₂²	1	4	yes	—
25	#17984752	C₂²	1	4	yes	—
26	C₂²×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	#103×C₁₃₉	C₂²	1	4	yes	—
30	C₂×Dic₂₇₈	—	2	1	no	—
31	C₂×Dic₂₇₈	—	2	2	no	—
32	C₂×Dic₂₇₈	C₂×C₄	1	4	yes	—
33	C₂×Dic₂₇₈	C₂³	1	2	yes	—
34	C₂²×Dic₁₃₉	—	2	1	no	—
35	C₂²×Dic₁₃₉	—	2	1	no	—
36	C₂²×Dic₁₃₉	D₄	1	1	yes	characteristic
37	C₂²×Dic₁₃₉	D₄	1	1	yes	characteristic
38	#14555775	C₂×C₄	1	16	yes	complemented
39	C₂×C₁₃₉⋊C₈	C₂×C₄	1	4	yes	—
40	C₂×C₁₃₉⋊C₈	C₂³	1	2	yes	—
41	C₄⋊Dic₁₃₉	—	2	4	no	—
42	C₄⋊Dic₁₃₉	—	2	1	no	—
43	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
44	Dic₁₃₉⋊C₄	—	2	4	no	—
45	C₄×Dic₁₃₉	—	2	4	no	—
46	C₄×Dic₁₃₉	—	2	4	no	—
47	C₄×Dic₁₃₉	D₄	1	2	yes	—
48	C₄×Dic₁₃₉	C₂³	1	2	yes	—
49	C₂×Q₈×C₁₃₉	—	2	1	no	—
50	C₂×Q₈×C₁₃₉	—	2	2	no	—
51	C₂×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
52	C₂×Q₈×C₁₃₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₁₃₉	—	2	1	no	—
54	C₂²×C₄×C₁₃₉	—	2	1	no	—
55	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₁₃₉	—	2	2	no	—
57	C₂×C₈×C₁₃₉	C₂³	1	2	yes	—
58	C₄⋊C₄×C₁₃₉	—	2	1	no	—
59	C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
60	Dic₂₇₈	—	2	4	no	—
61	Dic₂₇₈	—	2	2	no	—
62	Dic₂₇₈	C₂²×C₄	1	4	yes	—
63	C₂×Dic₁₃₉	—	2	4	no	—
64	C₂×Dic₁₃₉	—	2	2	no	—
65	C₂×Dic₁₃₉	—	2	2	no	—
66	C₂×Dic₁₃₉	—	2	2	no	—
67	C₂×Dic₁₃₉	—	2	2	no	—
68	C₂×Dic₁₃₉	—	4	2	no	—
69	C₂×Dic₁₃₉	C₂×D₄	1	2	yes	—
70	C₂×Dic₁₃₉	C₂×D₄	1	2	yes	—
71	C₁₃₉⋊C₈	C₂²×C₄	1	4	yes	—
72	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
73	Q₈×C₁₃₉	—	2	4	no	—
74	Q₈×C₁₃₉	—	2	2	no	—
75	Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
76	C₂×C₄×C₁₃₉	—	2	4	no	—
77	C₂×C₄×C₁₃₉	—	2	2	no	—
78	C₂×C₄×C₁₃₉	—	2	2	no	—
79	C₂×C₄×C₁₃₉	—	4	2	no	—
80	C₂×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
81	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃₉	#41	1	2	yes	—
83	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
84	C₈×C₁₃₉	—	2	2	no	—
85	C₂²×C₁₃₉	C₄×D₄	1	2	yes	—
86	C₂²×C₁₃₉	#137	1	2	yes	—
87	C₂²×C₁₃₉	#137	1	2	yes	—
88	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
89	C₄×C₁₃₉	—	2	4	no	—
90	C₄×C₁₃₉	—	4	2	no	—
91	C₄×C₁₃₉	C₄×D₄	1	2	yes	—
92	C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
93	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
94	Dic₁₃₉	—	2	4	no	—
95	Dic₁₃₉	—	2	2	no	—
96	Dic₁₃₉	—	2	2	no	—
97	Dic₁₃₉	—	4	2	no	—
98	C₂×C₁₃₉	#441	1	4	yes	complemented
99	C₂×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
100	C₂×C₁₃₉	C₂×#137	1	1	yes	characteristic
101	C₂×C₁₃₉	C₂×#137	1	1	yes	characteristic
102	C₁₃₉	C₂×#441	1	1	yes	characteristic, complemented, Sylow
103	C₂×#441	—	139	1	no	maximal, Sylow
104	C₂²×Q₁₆	—	139	1	no	—
105	C₂×C₄×Q₈	—	139	1	no	—
106	C₂×C₄×Q₈	—	139	1	no	—
107	#441	—	139	8	no	—
108	C₂×#106	—	139	1	no	—
109	C₂×#103	—	139	1	no	—
110	C₂×#103	D₁₃₉	1	1	yes	characteristic
111	C₂×#97	—	139	1	no	—
112	C₂²×Q₈	—	139	1	no	—
113	C₂²×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
114	C₂×Q₁₆	—	139	8	no	—
115	C₂×Q₁₆	—	139	4	no	—
116	C₂²×C₈	—	139	1	no	—
117	C₂²×C₈	C₂×D₁₃₉	1	1	yes	characteristic
118	C₄×Q₈	—	278	2	no	—
119	C₄×Q₈	—	278	2	no	—
120	C₄×Q₈	—	139	4	no	—
121	C₄×Q₈	—	139	4	no	—
122	C₂×C₄⋊C₄	—	278	1	no	—
123	C₂×C₄⋊C₄	—	278	1	no	—
124	C₂×C₄⋊C₄	—	139	1	no	—
125	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
126	C₂×C₄²	—	278	1	no	—
127	C₂×C₄²	—	278	1	no	—
128	C₂×C₄²	—	139	1	no	—
129	#106	—	139	4	no	—
130	#103	—	139	4	no	—
131	#103	C₂×D₁₃₉	1	4	yes	—
132	#97	—	139	4	no	—
133	C₂×Q₈	—	2	1	no	—
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	278	1	no	—
136	C₂×Q₈	—	278	2	no	—
137	C₂×Q₈	—	139	4	no	—
138	C₂×Q₈	—	139	2	no	—
139	C₂×Q₈	C₄×D₁₃₉	1	4	yes	—
140	C₂×Q₈	C₂²×D₁₃₉	1	2	yes	—
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	—	278	1	no	—
144	C₂²×C₄	—	278	1	no	—
145	C₂²×C₄	—	139	1	no	—
146	C₂²×C₄	—	139	1	no	—
147	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
148	Q₁₆	—	139	16	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	139	4	no	—
151	C₂×C₈	—	139	2	no	—
152	C₂×C₈	C₂²×D₁₃₉	1	2	yes	—
153	C₄⋊C₄	—	2	1	no	—
154	C₄⋊C₄	—	278	4	no	—
155	C₄⋊C₄	—	278	4	no	—
156	C₄⋊C₄	—	278	1	no	—
157	C₄⋊C₄	—	139	2	no	—
158	C₄⋊C₄	C₂²×D₁₃₉	1	2	yes	—
159	C₄²	—	278	4	no	—
160	C₄²	—	278	4	no	—
161	C₄²	—	139	2	no	—
162	C₄²	—	139	2	no	—
163	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
164	Q₈	—	2	4	no	—
165	Q₈	—	2	2	no	—
166	Q₈	—	278	4	no	—
167	Q₈	—	278	2	no	—
168	Q₈	—	139	4	no	—
169	Q₈	C₂×C₄×D₁₃₉	1	4	yes	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	278	4	no	—
175	C₂×C₄	—	278	2	no	—
176	C₂×C₄	—	278	2	no	—
177	C₂×C₄	—	278	2	no	—
178	C₂×C₄	—	278	2	no	—
179	C₂×C₄	—	556	2	no	—
180	C₂×C₄	—	139	2	no	—
181	C₂×C₄	—	139	2	no	—
182	C₂×C₄	C₂×C₄×D₁₃₉	1	2	yes	—
183	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
184	C₂×C₄	#14555784	1	2	yes	—
185	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
186	C₈	—	2	2	no	—
187	C₈	—	139	4	no	—
188	C₂²	(C₂²⋊D₁₃₉)⋊C₄	1	2	yes	—
189	C₂²	#17984871	1	2	yes	—
190	C₂²	#17984874	1	2	yes	—
191	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
192	C₄	—	2	4	no	—
193	C₄	—	4	2	no	—
194	C₄	—	278	4	no	—
195	C₄	—	278	2	no	—
196	C₄	—	278	2	no	—
197	C₄	—	556	2	no	—
198	C₄	(C₂²⋊D₁₃₉)⋊C₄	1	2	yes	—
199	C₄	C₂²×C₄×D₁₃₉	1	1	yes	characteristic
200	C₄	C₂×#14555784	1	1	yes	characteristic
201	C₂	#22581057	1	4	yes	direct product factor
202	C₂	C₂×(C₂²⋊D₁₃₉)⋊C₄	1	1	yes	characteristic
203	C₂	C₂×#17984871	1	1	yes	characteristic
204	C₂	C₂×#17984874	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14555775

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₁₃₉

C₂

yes

maximal, characteristic

C₂×#17984807

C₂

yes

maximal, characteristic

#22581057

C₂

yes

maximal, direct product factor

C₂×#17984773

C₂

yes

maximal, characteristic

C₂×#17984767

C₂

yes

maximal, characteristic

C₂×#17984752

C₂

yes

maximal, characteristic

C₂×#103×C₁₃₉

C₂

yes

maximal, characteristic

C₂²×Dic₂₇₈

C₂²

yes

characteristic

C₂×#14555775

C₄

yes

complemented

C₂×#14555775

C₂²

yes

—

C₂²×C₁₃₉⋊C₈

C₂²

yes

characteristic

Q₈×Dic₁₃₉

—

Q₈×Dic₁₃₉

C₂²

yes

—

#17984807

—

#17984807

C₂²

yes

—

C₂×C₄⋊Dic₁₃₉

—

C₂×C₄⋊Dic₁₃₉

C₂²

yes

characteristic

C₂×Dic₁₃₉⋊C₄

—

C₂×C₄×Dic₁₃₉

—

C₂×C₄×Dic₁₃₉

—

C₂×C₄×Dic₁₃₉

C₂²

yes

characteristic

#17984773

C₂²

yes

—

#17984767

C₂²

yes

—

#17984752

C₂²

yes

—

C₂²×Q₈×C₁₃₉

C₂²

yes

characteristic

C₂²×C₈×C₁₃₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₃₉

C₂²

yes

characteristic

#103×C₁₃₉

C₂²

yes

—

C₂×Dic₂₇₈

—

C₂×Dic₂₇₈

—

C₂×Dic₂₇₈

C₂×C₄

yes

—

C₂×Dic₂₇₈

C₂³

yes

—

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

D₄

yes

characteristic

C₂²×Dic₁₃₉

D₄

yes

characteristic

#14555775

C₂×C₄

yes

complemented

C₂×C₁₃₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₃₉⋊C₈

C₂³

yes

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

C₂³

yes

—

Dic₁₃₉⋊C₄

—

C₄×Dic₁₃₉

—

C₄×Dic₁₃₉

—

C₄×Dic₁₃₉

D₄

yes

—

C₄×Dic₁₃₉

C₂³

yes

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

C₂×C₄

yes

—

C₂×Q₈×C₁₃₉

C₂³

yes

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

C₂³

yes

characteristic

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

C₂³

yes

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

C₂³

yes

—

Dic₂₇₈

—

Dic₂₇₈

—

Dic₂₇₈

C₂²×C₄

yes

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

C₂×D₄

yes

—

C₂×Dic₁₃₉

C₂×D₄

yes

—

C₁₃₉⋊C₈

C₂²×C₄

yes

—

C₂³×C₁₃₉

C₂×D₄

yes

characteristic

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

Q₈×C₁₃₉

C₂²×C₄

yes

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂²×C₄

yes

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃₉

#41

yes

—

C₂×C₄×C₁₃₉

C₂⁴

yes

characteristic

C₈×C₁₃₉

—

C₂²×C₁₃₉

C₄×D₄

yes

—

C₂²×C₁₃₉

#137

yes

—

C₂²×C₁₃₉

#137

yes

—

C₂²×C₁₃₉

C₂²×D₄

yes

characteristic

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₄×D₄

yes

—

C₄×C₁₃₉

C₂³×C₄

yes

characteristic

C₄×C₁₃₉

C₂×#41

yes

characteristic

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

C₂×C₁₃₉

#441

yes

complemented

C₂×C₁₃₉

C₂×C₄×D₄

yes

characteristic

100

C₂×C₁₃₉

C₂×#137

yes

characteristic

101

C₂×C₁₃₉

C₂×#137

yes

characteristic

102

C₁₃₉

C₂×#441

yes

characteristic, complemented, Sylow

103

C₂×#441

—

139

maximal, Sylow

104

C₂²×Q₁₆

—

139

—

105

C₂×C₄×Q₈

—

139

—

106

C₂×C₄×Q₈

—

139

—

107

#441

—

139

—

108

C₂×#106

—

139

—

109

C₂×#103

—

139

—

110

C₂×#103

D₁₃₉

yes

characteristic

111

C₂×#97

—

139

—

112

C₂²×Q₈

—

139

—

113

C₂²×Q₈

C₂×D₁₃₉

yes

characteristic

114

C₂×Q₁₆

—

139

—

115

C₂×Q₁₆

—

139

—

116

C₂²×C₈

—

139

—

117

C₂²×C₈

C₂×D₁₃₉

yes

characteristic

118

C₄×Q₈

—

278

—

119

C₄×Q₈

—

278

—

120

C₄×Q₈

—

139

—

121

C₄×Q₈

—

139

—

122

C₂×C₄⋊C₄

—

278

—

123

C₂×C₄⋊C₄

—

278

—

124

C₂×C₄⋊C₄

—

139

—

125

C₂×C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

126

C₂×C₄²

—

278

—

127

C₂×C₄²

—

278

—

128

C₂×C₄²

—

139

—

129

#106

—

139

—

130

#103

—

139

—

131

#103

C₂×D₁₃₉

yes

—

132

#97

—

139

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

278

—

136

C₂×Q₈

—

278

—

137

C₂×Q₈

—

139

—

138

C₂×Q₈

—

139

—

139

C₂×Q₈

C₄×D₁₃₉

yes

—

140

C₂×Q₈

C₂²×D₁₃₉

yes

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

278

—

144

C₂²×C₄

—

278

—

145

C₂²×C₄

—

139

—

146

C₂²×C₄

—

139

—

147

C₂²×C₄

C₂²×D₁₃₉

yes

characteristic

148

Q₁₆

—

139

—

149

C₂×C₈

—

150

C₂×C₈

—

139

—

151

C₂×C₈

—

139

—

152

C₂×C₈

C₂²×D₁₃₉

yes

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

278

—

155

C₄⋊C₄

—

278

—

156

C₄⋊C₄

—

278

—

157

C₄⋊C₄

—

139

—

158

C₄⋊C₄

C₂²×D₁₃₉

yes

—

159

C₄²

—

278

—

160

C₄²

—

278

—

161

C₄²

—

139

—

162

C₄²

—

139

—

163

C₂³

D₄×D₁₃₉

yes

characteristic

164

Q₈

—

165

Q₈

—

166

Q₈

—

278

—

167

Q₈

—

278

—

168

Q₈

—

139

—

169

Q₈

C₂×C₄×D₁₃₉

yes

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

278

—

175

C₂×C₄

—

278

—

176

C₂×C₄

—

278

—

177

C₂×C₄

—

278

—

178

C₂×C₄

—

278

—

179

C₂×C₄

—

556

—

180

C₂×C₄

—

139

—

181

C₂×C₄

—

139

—

182

C₂×C₄

C₂×C₄×D₁₃₉

yes

—

183

C₂×C₄

D₄×D₁₃₉

yes

characteristic

184

C₂×C₄

#14555784

yes

—

185

C₂×C₄

C₂³×D₁₃₉

yes

characteristic

186

C₈

—

187

C₈

—

139

—

188

C₂²

(C₂²⋊D₁₃₉)⋊C₄

yes

—

189

C₂²

#17984871

yes

—

190

C₂²

#17984874

yes

—

191

C₂²

C₂×D₄×D₁₃₉

yes

characteristic

192

C₄

—

193

C₄

—

194

C₄

—

278

—

195

C₄

—

278

—

196

C₄

—

278

—

197

C₄

—

556

—

198

C₄

(C₂²⋊D₁₃₉)⋊C₄

yes

—

199

C₄

C₂²×C₄×D₁₃₉

yes

characteristic

200

C₄

C₂×#14555784

yes

characteristic

201

C₂

#22581057

yes

direct product factor

202

C₂

C₂×(C₂²⋊D₁₃₉)⋊C₄

yes

characteristic

203

C₂

C₂×#17984871

yes

characteristic

204

C₂

C₂×#17984874

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₃₉
commutator	C₄×C₁₃₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	C₂×#103×C₁₃₉	C₂
socle, prime radical	C₂³×C₁₃₉	C₂×D₄
cosocle	C₂×C₄×C₁₃₉	C₂⁴
hypercenter	C₂×#103	D₁₃₉
hypocenter	C₁₃₉	C₂×#441
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₁₃₉

commutator

C₄×C₁₃₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₁₃₉

Fitting

C₂×#103×C₁₃₉

C₂

socle, prime radical

C₂³×C₁₃₉

C₂×D₄

cosocle

C₂×C₄×C₁₃₉

C₂⁴

D₁₃₉

C₁₃₉

G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
4. #22581057	C₂	direct (N × H)
10. C₂×#14555775	C₄	semidirect
38. #14555775	C₂×C₄	semidirect
98. C₂×C₁₃₉	#441	semidirect
102. C₁₃₉	C₂×#441	semidirect
201. C₂	#22581057	direct (N × H)

H ≅ G/N

type

4. #22581057

C₂

direct (N × H)

10. C₂×#14555775

C₄

semidirect

38. #14555775

C₂×C₄

semidirect

98. C₂×C₁₃₉

#441

semidirect

102. C₁₃₉

C₂×#441

semidirect

201. C₂

#22581057

direct (N × H)

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

subgroup	index
C₂²×#14555775	2
C₂×Q₈×Dic₁₃₉	2
C₂×#17984807	2
#22581057	2
C₂×#17984773	2
C₂×#17984767	2
C₂×#17984752	2
C₂×#103×C₁₃₉	2
C₂×#441	139

subgroup

index

C₂×Q₈×Dic₁₃₉

C₂×#103×C₁₃₉

139

Subgroups — C₂×#22581057 #31815188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#22581057 #31815188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22581057 #31815188