Group #48002784 — subgroups

Subgroups — C₁₃₉×#8188 #48002784

Order 35584.

412 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 182 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	#2922×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1476×C₁₃₉	C₂	1	2	yes	maximal
3	#1452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#322×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1278×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₄×#41×C₁₃₉	C₂²	1	1	yes	characteristic
7	#433×C₁₃₉	—	2	2	no	—
8	#431×C₁₃₉	—	2	2	no	—
9	#431×C₁₃₉	C₂²	1	2	yes	—
10	#424×C₁₃₉	C₄	1	2	yes	—
11	#408×C₁₃₉	C₄	1	2	yes	—
12	C₄×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	Q₈⋊C₈×C₁₃₉	C₄	1	4	yes	—
16	D₄⋊C₈×C₁₃₉	C₄	1	4	yes	—
17	#322×C₁₃₉	—	2	2	no	—
18	#322×C₁₃₉	—	2	2	no	—
19	C₂×#41×C₁₃₉	C₂×C₄	1	1	yes	characteristic
20	C₂×M₁₆×C₁₃₉	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₃₉	—	2	2	no	—
22	C₂²×C₈×C₁₃₉	C₂×C₄	1	2	yes	—
23	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
24	C₄×D₄×C₁₃₉	—	2	2	no	—
25	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
26	#117×C₁₃₉	—	2	1	no	—
27	#117×C₁₃₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃₉	—	2	1	no	—
29	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
30	C₄⋊C₈×C₁₃₉	—	2	4	no	—
31	C₄⋊C₈×C₁₃₉	C₂×C₄	1	4	yes	—
32	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
33	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
34	#97×C₁₃₉	—	2	1	no	—
35	C₄×C₈×C₁₃₉	—	2	2	no	—
36	C₄×C₈×C₁₃₉	—	2	1	no	—
37	C₄×C₈×C₁₃₉	—	2	2	no	—
38	C₄×C₈×C₁₃₉	C₂×C₄	1	4	yes	—
39	C₄×C₈×C₁₃₉	D₄	1	2	yes	—
40	C₄×C₈×C₁₃₉	D₄	1	2	yes	—
41	#41×C₁₃₉	—	2	4	no	—
42	C₂×Q₈×C₁₃₉	C₄²	1	1	yes	characteristic
43	C₂×D₄×C₁₃₉	—	2	1	no	—
44	C₂×D₄×C₁₃₉	C₄²	1	1	yes	characteristic
45	C₂²×C₄×C₁₃₉	—	2	1	no	—
46	C₂²×C₄×C₁₃₉	—	2	2	no	—
47	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
49	M₁₆×C₁₃₉	—	2	4	no	—
50	C₂×C₈×C₁₃₉	—	2	4	no	—
51	C₂×C₈×C₁₃₉	—	2	2	no	—
52	C₂×C₈×C₁₃₉	—	2	4	no	—
53	C₂×C₈×C₁₃₉	—	2	4	no	—
54	C₂×C₈×C₁₃₉	—	4	4	no	—
55	C₂×C₈×C₁₃₉	C₂²⋊C₄	1	4	yes	—
56	C₄⋊C₄×C₁₃₉	—	2	2	no	—
57	C₄⋊C₄×C₁₃₉	C₄²	1	2	yes	—
58	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
59	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
60	C₄²×C₁₃₉	—	2	1	no	—
61	C₄²×C₁₃₉	—	2	2	no	—
62	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
63	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
65	C₂³×C₁₃₉	—	2	1	no	—
66	C₂³×C₁₃₉	#117	1	1	yes	characteristic
67	Q₈×C₁₃₉	—	2	2	no	—
68	D₄×C₁₃₉	—	2	2	no	—
69	D₄×C₁₃₉	—	4	2	no	—
70	C₂×C₄×C₁₃₉	—	2	4	no	—
71	C₂×C₄×C₁₃₉	—	2	2	no	—
72	C₂×C₄×C₁₃₉	—	2	1	no	—
73	C₂×C₄×C₁₃₉	—	4	2	no	—
74	C₂×C₄×C₁₃₉	—	4	4	no	—
75	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
78	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
79	C₂×C₄×C₁₃₉	#131	1	4	yes	—
80	C₈×C₁₃₉	—	2	4	no	—
81	C₈×C₁₃₉	—	4	4	no	—
82	C₈×C₁₃₉	—	4	2	no	—
83	C₈×C₁₃₉	—	4	4	no	—
84	C₂²×C₁₃₉	—	2	2	no	—
85	C₂²×C₁₃₉	—	4	1	no	—
86	C₂²×C₁₃₉	—	4	2	no	—
87	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₁₃₉	#433	1	2	yes	—
89	C₄×C₁₃₉	—	2	2	no	—
90	C₄×C₁₃₉	—	4	1	no	—
91	C₄×C₁₃₉	—	4	2	no	—
92	C₄×C₁₃₉	#405	1	2	yes	—
93	C₄×C₁₃₉	#408	1	2	yes	—
94	C₄×C₁₃₉	#444	1	4	yes	—
95	C₂×C₁₃₉	—	2	2	no	—
96	C₂×C₁₃₉	—	8	1	no	—
97	C₂×C₁₃₉	#1750	1	1	yes	characteristic
98	C₂×C₁₃₉	#1765	1	2	yes	—
99	#8188	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₁₃₉	#8188	1	1	yes	characteristic, direct product factor, Sylow
101	#2922	C₂×C₁₃₉	1	1	yes	characteristic
102	#1476	C₂×C₁₃₉	1	2	yes	—
103	#1452	C₂×C₁₃₉	1	1	yes	characteristic, complemented
104	C₂×#322	C₂×C₁₃₉	1	1	yes	characteristic, complemented
105	#1278	C₂×C₁₃₉	1	2	yes	complemented
106	C₄×#41	C₂²×C₁₃₉	1	1	yes	characteristic
107	#433	—	2	2	no	—
108	#431	—	2	2	no	—
109	#431	C₂²×C₁₃₉	1	2	yes	—
110	#424	C₄×C₁₃₉	1	2	yes	—
111	#408	C₄×C₁₃₉	1	2	yes	—
112	C₄×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
114	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
115	Q₈⋊C₈	C₄×C₁₃₉	1	4	yes	—
116	D₄⋊C₈	C₄×C₁₃₉	1	4	yes	—
117	#322	—	2	2	no	—
118	#322	—	2	2	no	—
119	C₂×#41	C₂×C₄×C₁₃₉	1	1	yes	characteristic
120	C₂×M₁₆	C₂×C₄×C₁₃₉	1	2	yes	—
121	C₂²×C₈	—	2	2	no	—
122	C₂²×C₈	C₂×C₄×C₁₃₉	1	2	yes	—
123	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
124	C₄×D₄	—	2	2	no	—
125	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
126	#117	—	2	1	no	—
127	#117	C₂×C₄×C₁₃₉	1	1	yes	characteristic
128	C₂×C₄²	—	2	1	no	—
129	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
130	C₄⋊C₈	—	2	4	no	—
131	C₄⋊C₈	C₂×C₄×C₁₃₉	1	4	yes	—
132	C₂²⋊C₈	—	2	2	no	—
133	C₂²⋊C₈	—	2	4	no	—
134	#97	—	2	1	no	—
135	C₄×C₈	—	2	2	no	—
136	C₄×C₈	—	2	2	no	—
137	C₄×C₈	—	2	1	no	—
138	C₄×C₈	C₂×C₄×C₁₃₉	1	4	yes	—
139	C₄×C₈	D₄×C₁₃₉	1	2	yes	—
140	C₄×C₈	D₄×C₁₃₉	1	2	yes	—
141	#41	—	2	4	no	—
142	C₂×Q₈	C₄²×C₁₃₉	1	1	yes	characteristic
143	C₂×D₄	—	2	1	no	—
144	C₂×D₄	C₄²×C₁₃₉	1	1	yes	characteristic
145	C₂²×C₄	—	2	1	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
148	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
149	M₁₆	—	2	4	no	—
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	—	4	4	no	—
155	C₂×C₈	C₂²⋊C₄×C₁₃₉	1	4	yes	—
156	C₄⋊C₄	—	2	2	no	—
157	C₄⋊C₄	C₄²×C₁₃₉	1	2	yes	—
158	C₂²⋊C₄	—	2	1	no	—
159	C₂²⋊C₄	—	2	2	no	—
160	C₄²	—	2	1	no	—
161	C₄²	—	2	2	no	—
162	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
163	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
164	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
165	C₂³	—	2	1	no	—
166	C₂³	#117×C₁₃₉	1	1	yes	characteristic
167	Q₈	—	2	2	no	—
168	D₄	—	2	2	no	—
169	D₄	—	4	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
176	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
177	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
178	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
179	C₂×C₄	#131×C₁₃₉	1	4	yes	—
180	C₈	—	2	4	no	—
181	C₈	—	4	4	no	—
182	C₈	—	4	2	no	—
183	C₈	—	4	4	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	4	1	no	—
186	C₂²	—	4	2	no	—
187	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
188	C₂²	#433×C₁₃₉	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	4	1	no	—
191	C₄	—	4	2	no	—
192	C₄	#405×C₁₃₉	1	2	yes	—
193	C₄	#408×C₁₃₉	1	2	yes	—
194	C₄	#444×C₁₃₉	1	4	yes	—
195	C₂	—	2	2	no	—
196	C₂	—	8	1	no	—
197	C₂	#1750×C₁₃₉	1	1	yes	characteristic
198	C₂	#1765×C₁₃₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#2922×C₁₃₉

C₂

yes

maximal, characteristic

#1476×C₁₃₉

C₂

yes

maximal

#1452×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×#322×C₁₃₉

C₂

yes

maximal, characteristic, complemented

#1278×C₁₃₉

C₂

yes

maximal, complemented

C₄×#41×C₁₃₉

C₂²

yes

characteristic

#433×C₁₃₉

—

#431×C₁₃₉

—

#431×C₁₃₉

C₂²

yes

—

#424×C₁₃₉

C₄

yes

—

#408×C₁₃₉

C₄

yes

—

C₄×M₁₆×C₁₃₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃₉

C₂²

yes

—

C₂×C₄×C₈×C₁₃₉

C₂²

yes

characteristic

Q₈⋊C₈×C₁₃₉

C₄

yes

—

D₄⋊C₈×C₁₃₉

C₄

yes

—

#322×C₁₃₉

—

#322×C₁₃₉

—

C₂×#41×C₁₃₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₃₉

C₂×C₄

yes

—

C₂²×C₈×C₁₃₉

—

C₂²×C₈×C₁₃₉

C₂×C₄

yes

—

C₄×Q₈×C₁₃₉

C₂×C₄

yes

—

C₄×D₄×C₁₃₉

—

C₄×D₄×C₁₃₉

C₂×C₄

yes

—

#117×C₁₃₉

—

#117×C₁₃₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃₉

—

C₂×C₄²×C₁₃₉

C₂³

yes

characteristic

C₄⋊C₈×C₁₃₉

—

C₄⋊C₈×C₁₃₉

C₂×C₄

yes

—

C₂²⋊C₈×C₁₃₉

—

C₂²⋊C₈×C₁₃₉

—

#97×C₁₃₉

—

C₄×C₈×C₁₃₉

—

C₄×C₈×C₁₃₉

—

C₄×C₈×C₁₃₉

—

C₄×C₈×C₁₃₉

C₂×C₄

yes

—

C₄×C₈×C₁₃₉

D₄

yes

—

C₄×C₈×C₁₃₉

D₄

yes

—

#41×C₁₃₉

—

C₂×Q₈×C₁₃₉

C₄²

yes

characteristic

C₂×D₄×C₁₃₉

—

C₂×D₄×C₁₃₉

C₄²

yes

characteristic

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃₉

#41

yes

—

M₁₆×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

C₄²

yes

—

C₂²⋊C₄×C₁₃₉

—

C₂²⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

—

C₄²×C₁₃₉

—

C₄²×C₁₃₉

C₂²×C₄

yes

—

C₄²×C₁₃₉

C₂×D₄

yes

characteristic

C₄²×C₁₃₉

C₂×D₄

yes

characteristic

C₂³×C₁₃₉

—

C₂³×C₁₃₉

#117

yes

characteristic

Q₈×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃₉

C₄×D₄

yes

—

C₂×C₄×C₁₃₉

C₄×D₄

yes

—

C₂×C₄×C₁₃₉

#131

yes

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

C₄×C₂²⋊C₄

yes

characteristic

C₂²×C₁₃₉

#433

yes

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

#405

yes

—

C₄×C₁₃₉

#408

yes

—

C₄×C₁₃₉

#444

yes

—

C₂×C₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

#1750

yes

characteristic

C₂×C₁₃₉

#1765

yes

—

#8188

C₁₃₉

yes

maximal, characteristic, direct product factor, Sylow

100

C₁₃₉

#8188

yes

characteristic, direct product factor, Sylow

101

#2922

C₂×C₁₃₉

yes

characteristic

102

#1476

C₂×C₁₃₉

yes

—

103

#1452

C₂×C₁₃₉

yes

characteristic, complemented

104

C₂×#322

C₂×C₁₃₉

yes

characteristic, complemented

105

#1278

C₂×C₁₃₉

yes

complemented

106

C₄×#41

C₂²×C₁₃₉

yes

characteristic

107

#433

—

108

#431

—

109

#431

C₂²×C₁₃₉

yes

—

110

#424

C₄×C₁₃₉

yes

—

111

#408

C₄×C₁₃₉

yes

—

112

C₄×M₁₆

C₂²×C₁₃₉

yes

characteristic

113

C₂×C₄×C₈

C₂²×C₁₃₉

yes

—

114

C₂×C₄×C₈

C₂²×C₁₃₉

yes

characteristic

115

Q₈⋊C₈

C₄×C₁₃₉

yes

—

116

D₄⋊C₈

C₄×C₁₃₉

yes

—

117

#322

—

118

#322

—

119

C₂×#41

C₂×C₄×C₁₃₉

yes

characteristic

120

C₂×M₁₆

C₂×C₄×C₁₃₉

yes

—

121

C₂²×C₈

—

122

C₂²×C₈

C₂×C₄×C₁₃₉

yes

—

123

C₄×Q₈

C₂×C₄×C₁₃₉

yes

—

124

C₄×D₄

—

125

C₄×D₄

C₂×C₄×C₁₃₉

yes

—

126

#117

—

127

#117

C₂×C₄×C₁₃₉

yes

characteristic

128

C₂×C₄²

—

129

C₂×C₄²

C₂³×C₁₃₉

yes

characteristic

130

C₄⋊C₈

—

131

C₄⋊C₈

C₂×C₄×C₁₃₉

yes

—

132

C₂²⋊C₈

—

133

C₂²⋊C₈

—

134

#97

—

135

C₄×C₈

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₄×C₈

C₂×C₄×C₁₃₉

yes

—

139

C₄×C₈

D₄×C₁₃₉

yes

—

140

C₄×C₈

D₄×C₁₃₉

yes

—

141

#41

—

142

C₂×Q₈

C₄²×C₁₃₉

yes

characteristic

143

C₂×D₄

—

144

C₂×D₄

C₄²×C₁₃₉

yes

characteristic

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²×C₄×C₁₃₉

yes

characteristic

148

C₂²×C₄

#41×C₁₃₉

yes

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

C₂²⋊C₄×C₁₃₉

yes

—

156

C₄⋊C₄

—

157

C₄⋊C₄

C₄²×C₁₃₉

yes

—

158

C₂²⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

C₂²×C₄×C₁₃₉

yes

—

163

C₄²

C₂×D₄×C₁₃₉

yes

characteristic

164

C₄²

C₂×D₄×C₁₃₉

yes

characteristic

165

C₂³

—

166

C₂³

#117×C₁₃₉

yes

characteristic

167

Q₈

—

168

D₄

—

169

D₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

C₂×C₄²×C₁₃₉

yes

characteristic

176

C₂×C₄

C₂×C₂²⋊C₄×C₁₃₉

yes

characteristic

177

C₂×C₄

C₄×D₄×C₁₃₉

yes

—

178

C₂×C₄

C₄×D₄×C₁₃₉

yes

—

179

C₂×C₄

#131×C₁₃₉

yes

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₈

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

C₄×C₂²⋊C₄×C₁₃₉

yes

characteristic

188

C₂²

#433×C₁₃₉

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

#405×C₁₃₉

yes

—

193

C₄

#408×C₁₃₉

yes

—

194

C₄

#444×C₁₃₉

yes

—

195

C₂

—

196

C₂

—

197

C₂

#1750×C₁₃₉

yes

characteristic

198

C₂

#1765×C₁₃₉

yes

—

	subgroup	G/H
center	C₄²×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	C₄×C₂²⋊C₄
prime radical	C₂×#41×C₁₃₉	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃₉ ◁ C₂×C₄×C₈×C₁₃₉ ◁ G

subgroup

G/H

center

C₄²×C₁₃₉

C₂×D₄

commutator

C₂×C₄

C₂×C₄²×C₁₃₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₃₉

socle

C₂²×C₁₃₉

C₄×C₂²⋊C₄

prime radical

C₂×#41×C₁₃₉

C₂×C₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄²×C₁₃₉ ◁ C₂×C₄×C₈×C₁₃₉ ◁ G

N	H ≅ G/N	type
3. #1452×C₁₃₉	C₂	semidirect
4. C₂×#322×C₁₃₉	C₂	semidirect
5. #1278×C₁₃₉	C₂	semidirect
99. #8188	C₁₃₉	direct (N × H)
100. C₁₃₉	#8188	direct (N × H)
103. #1452	C₂×C₁₃₉	semidirect
104. C₂×#322	C₂×C₁₃₉	semidirect
105. #1278	C₂×C₁₃₉	semidirect

H ≅ G/N

type

3. #1452×C₁₃₉

C₂

semidirect

4. C₂×#322×C₁₃₉

C₂

semidirect

5. #1278×C₁₃₉

C₂

semidirect

99. #8188

C₁₃₉

direct (N × H)

100. C₁₃₉

#8188

direct (N × H)

103. #1452

C₂×C₁₃₉

semidirect

104. C₂×#322

C₂×C₁₃₉

semidirect

105. #1278

C₂×C₁₃₉

semidirect

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

subgroup	index
#2922×C₁₃₉	2
#1476×C₁₃₉	2
#1452×C₁₃₉	2
C₂×#322×C₁₃₉	2
#1278×C₁₃₉	2
#8188	139

subgroup

index

#2922×C₁₃₉

#1476×C₁₃₉

#1452×C₁₃₉

C₂×#322×C₁₃₉

#1278×C₁₃₉

#8188

139

Subgroups — C₁₃₉×#8188 #48002784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C139×#8188 #48002784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#8188 #48002784