Group #48005172 — subgroups

Subgroups — C₁₃₉×#10576 #48005172

Order 35584.

406 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 146 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	#2571×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1948×C₁₃₉	C₂	1	2	yes	maximal
3	#1845×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1296×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1279×C₁₃₉	C₂	1	2	yes	maximal
6	C₂×#107×C₁₃₉	—	2	2	no	—
7	C₂×#106×C₁₃₉	—	2	2	no	—
8	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
10	#400×C₁₃₉	—	2	2	no	—
11	#389×C₁₃₉	—	2	2	no	—
12	#384×C₁₃₉	C₂²	1	1	yes	characteristic
13	#384×C₁₃₉	C₂²	1	1	yes	characteristic
14	#382×C₁₃₉	—	2	2	no	—
15	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
16	#340×C₁₃₉	—	2	2	no	—
17	C₂²×C₈×C₁₃₉	—	2	1	no	—
18	C₂²×C₈×C₁₃₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
22	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₃₉	—	2	2	no	—
27	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
28	#107×C₁₃₉	—	4	4	no	—
29	#106×C₁₃₉	—	4	4	no	—
30	C₄⋊C₈×C₁₃₉	—	2	2	no	—
31	C₄⋊C₈×C₁₃₉	Q₈	1	4	yes	—
32	C₄×C₈×C₁₃₉	—	2	1	no	—
33	C₄×C₈×C₁₃₉	Q₈	1	2	yes	—
34	#95×C₁₃₉	—	2	2	no	—
35	#95×C₁₃₉	—	2	4	no	—
36	#95×C₁₃₉	—	2	2	no	—
37	C₂²×C₄×C₁₃₉	—	2	2	no	—
38	C₂²×C₄×C₁₃₉	—	2	2	no	—
39	C₂²×C₄×C₁₃₉	—	2	2	no	—
40	C₂²×C₄×C₁₃₉	—	4	1	no	—
41	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
43	C₂×C₈×C₁₃₉	—	2	2	no	—
44	C₂×C₈×C₁₃₉	—	2	2	no	—
45	C₂×C₈×C₁₃₉	—	2	2	no	—
46	C₂×C₈×C₁₃₉	—	2	4	no	—
47	C₂×C₈×C₁₃₉	—	4	2	no	—
48	C₂×C₈×C₁₃₉	—	4	2	no	—
49	C₄⋊C₄×C₁₃₉	—	2	2	no	—
50	C₄⋊C₄×C₁₃₉	—	2	2	no	—
51	C₄⋊C₄×C₁₃₉	—	2	2	no	—
52	C₄⋊C₄×C₁₃₉	—	2	2	no	—
53	C₄⋊C₄×C₁₃₉	—	4	2	no	—
54	C₄⋊C₄×C₁₃₉	—	4	2	no	—
55	C₄⋊C₄×C₁₃₉	—	4	2	no	—
56	C₄⋊C₄×C₁₃₉	—	4	2	no	—
57	C₄⋊C₄×C₁₃₉	—	4	2	no	—
58	C₄⋊C₄×C₁₃₉	—	4	2	no	—
59	C₄⋊C₄×C₁₃₉	—	8	2	no	—
60	C₄²×C₁₃₉	—	4	2	no	—
61	C₄²×C₁₃₉	—	4	2	no	—
62	C₄²×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₁₃₉	C₂×Q₈	1	2	yes	—
64	C₄²×C₁₃₉	#41	1	1	yes	characteristic
65	C₂³×C₁₃₉	#120	1	1	yes	characteristic
66	C₂×C₄×C₁₃₉	—	2	1	no	—
67	C₂×C₄×C₁₃₉	—	2	1	no	—
68	C₂×C₄×C₁₃₉	—	4	2	no	—
69	C₂×C₄×C₁₃₉	—	4	4	no	—
70	C₂×C₄×C₁₃₉	—	4	2	no	—
71	C₂×C₄×C₁₃₉	—	4	2	no	—
72	C₂×C₄×C₁₃₉	—	4	2	no	—
73	C₂×C₄×C₁₃₉	—	4	2	no	—
74	C₂×C₄×C₁₃₉	—	4	2	no	—
75	C₂×C₄×C₁₃₉	—	4	2	no	—
76	C₂×C₄×C₁₃₉	—	8	2	no	—
77	C₂×C₄×C₁₃₉	—	8	1	no	—
78	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
80	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	2	yes	—
82	C₂×C₄×C₁₃₉	#135	1	2	yes	—
83	C₂×C₄×C₁₃₉	#135	1	2	yes	—
84	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
85	C₂×C₄×C₁₃₉	#137	1	2	yes	—
86	C₈×C₁₃₉	—	2	4	no	—
87	C₈×C₁₃₉	—	4	4	no	—
88	C₂²×C₁₃₉	#395	1	1	yes	characteristic
89	C₂²×C₁₃₉	#449	1	2	yes	—
90	C₂²×C₁₃₉	#452	1	2	yes	—
91	C₂²×C₁₃₉	#453	1	1	yes	characteristic
92	C₂²×C₁₃₉	#456	1	1	yes	characteristic
93	C₄×C₁₃₉	—	2	1	no	—
94	C₄×C₁₃₉	—	2	1	no	—
95	C₄×C₁₃₉	—	8	2	no	—
96	C₄×C₁₃₉	—	8	2	no	—
97	C₄×C₁₃₉	—	8	2	no	—
98	C₄×C₁₃₉	—	16	1	no	—
99	C₄×C₁₃₉	#478	1	2	yes	—
100	C₄×C₁₃₉	#479	1	2	yes	—
101	C₄×C₁₃₉	#499	1	2	yes	—
102	C₄×C₁₃₉	#501	1	2	yes	—
103	C₂×C₁₃₉	#1620	1	1	yes	characteristic
104	C₂×C₁₃₉	#1634	1	1	yes	characteristic
105	C₂×C₁₃₉	#1650	1	2	yes	—
106	C₂×C₁₃₉	#2059	1	2	yes	—
107	C₂×C₁₃₉	#2060	1	1	yes	characteristic
108	#10576	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₁₃₉	#10576	1	1	yes	characteristic, direct product factor, Sylow
110	#2571	C₂×C₁₃₉	1	1	yes	characteristic
111	#1948	C₂×C₁₃₉	1	2	yes	—
112	#1845	C₂×C₁₃₉	1	1	yes	characteristic
113	#1296	C₂×C₁₃₉	1	1	yes	characteristic
114	#1279	C₂×C₁₃₉	1	2	yes	—
115	C₂×#107	—	2	2	no	—
116	C₂×#106	—	2	2	no	—
117	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
118	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
119	#400	—	2	2	no	—
120	#389	—	2	2	no	—
121	#384	C₂²×C₁₃₉	1	1	yes	characteristic
122	#384	C₂²×C₁₃₉	1	1	yes	characteristic
123	#382	—	2	2	no	—
124	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
125	#340	—	2	2	no	—
126	C₂²×C₈	—	2	1	no	—
127	C₂²×C₈	—	2	2	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	1	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
133	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
134	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
135	C₂×C₄²	—	2	2	no	—
136	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
137	#107	—	4	4	no	—
138	#106	—	4	4	no	—
139	C₄⋊C₈	—	2	2	no	—
140	C₄⋊C₈	Q₈×C₁₃₉	1	4	yes	—
141	C₄×C₈	—	2	1	no	—
142	C₄×C₈	Q₈×C₁₃₉	1	2	yes	—
143	#95	—	2	2	no	—
144	#95	—	2	4	no	—
145	#95	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	4	1	no	—
150	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
151	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	—	4	2	no	—
157	C₂×C₈	—	4	2	no	—
158	C₄⋊C₄	—	2	2	no	—
159	C₄⋊C₄	—	2	2	no	—
160	C₄⋊C₄	—	2	2	no	—
161	C₄⋊C₄	—	2	2	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	8	2	no	—
169	C₄²	—	4	2	no	—
170	C₄²	—	4	2	no	—
171	C₄²	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
172	C₄²	C₂×Q₈×C₁₃₉	1	2	yes	—
173	C₄²	#41×C₁₃₉	1	1	yes	characteristic
174	C₂³	#120×C₁₃₉	1	1	yes	characteristic
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	—	4	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	8	2	no	—
186	C₂×C₄	—	8	1	no	—
187	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
188	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
189	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
190	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	2	yes	—
191	C₂×C₄	#135×C₁₃₉	1	2	yes	—
192	C₂×C₄	#135×C₁₃₉	1	2	yes	—
193	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
194	C₂×C₄	#137×C₁₃₉	1	2	yes	—
195	C₈	—	2	4	no	—
196	C₈	—	4	4	no	—
197	C₂²	#395×C₁₃₉	1	1	yes	characteristic
198	C₂²	#449×C₁₃₉	1	2	yes	—
199	C₂²	#452×C₁₃₉	1	2	yes	—
200	C₂²	#453×C₁₃₉	1	1	yes	characteristic
201	C₂²	#456×C₁₃₉	1	1	yes	characteristic
202	C₄	—	2	1	no	—
203	C₄	—	2	1	no	—
204	C₄	—	8	2	no	—
205	C₄	—	8	2	no	—
206	C₄	—	8	2	no	—
207	C₄	—	16	1	no	—
208	C₄	#478×C₁₃₉	1	2	yes	—
209	C₄	#479×C₁₃₉	1	2	yes	—
210	C₄	#499×C₁₃₉	1	2	yes	—
211	C₄	#501×C₁₃₉	1	2	yes	—
212	C₂	#1620×C₁₃₉	1	1	yes	characteristic
213	C₂	#1634×C₁₃₉	1	1	yes	characteristic
214	C₂	#1650×C₁₃₉	1	2	yes	—
215	C₂	#2059×C₁₃₉	1	2	yes	—
216	C₂	#2060×C₁₃₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#2571×C₁₃₉

C₂

yes

maximal, characteristic

#1948×C₁₃₉

C₂

yes

maximal

#1845×C₁₃₉

C₂

yes

maximal, characteristic

#1296×C₁₃₉

C₂

yes

maximal, characteristic

#1279×C₁₃₉

C₂

yes

maximal

C₂×#107×C₁₃₉

—

C₂×#106×C₁₃₉

—

C₂×C₄⋊C₈×C₁₃₉

C₂²

yes

—

C₂×C₄×C₈×C₁₃₉

C₂²

yes

characteristic

#400×C₁₃₉

—

#389×C₁₃₉

—

#384×C₁₃₉

C₂²

yes

characteristic

#384×C₁₃₉

C₂²

yes

characteristic

#382×C₁₃₉

—

C₄×C₄⋊C₄×C₁₃₉

C₂²

yes

—

#340×C₁₃₉

—

C₂²×C₈×C₁₃₉

—

C₂²×C₈×C₁₃₉

—

C₂×C₄⋊C₄×C₁₃₉

—

C₂×C₄⋊C₄×C₁₃₉

—

C₂×C₄⋊C₄×C₁₃₉

—

C₂×C₄⋊C₄×C₁₃₉

—

C₂×C₄⋊C₄×C₁₃₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₃₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₃₉

D₄

yes

—

C₂×C₄²×C₁₃₉

—

C₂×C₄²×C₁₃₉

C₂³

yes

characteristic

#107×C₁₃₉

—

#106×C₁₃₉

—

C₄⋊C₈×C₁₃₉

—

C₄⋊C₈×C₁₃₉

Q₈

yes

—

C₄×C₈×C₁₃₉

—

C₄×C₈×C₁₃₉

Q₈

yes

—

#95×C₁₃₉

—

#95×C₁₃₉

—

#95×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃₉

C₂×D₄

yes

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

—

C₄²×C₁₃₉

—

C₄²×C₁₃₉

C₂×Q₈

yes

characteristic

C₄²×C₁₃₉

C₂×Q₈

yes

—

C₄²×C₁₃₉

yes

C₂³×C₁₃₉

yes

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₃₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₃₉

#135

yes

—

C₂×C₄×C₁₃₉

#135

yes

—

C₂×C₄×C₁₃₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃₉

#137

yes

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₂²×C₁₃₉

#395

yes

characteristic

C₂²×C₁₃₉

#449

yes

—

C₂²×C₁₃₉

#452

yes

—

C₂²×C₁₃₉

yes

C₂²×C₁₃₉

yes

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

#478

yes

—

100

C₄×C₁₃₉

#479

yes

—

101

C₄×C₁₃₉

#499

yes

—

102

C₄×C₁₃₉

#501

yes

—

103

C₂×C₁₃₉

#1620

yes

characteristic

104

C₂×C₁₃₉

#1634

yes

characteristic

105

C₂×C₁₃₉

#1650

yes

—

106

C₂×C₁₃₉

#2059

yes

—

107

C₂×C₁₃₉

#2060

yes

characteristic

108

#10576

C₁₃₉

yes

maximal, characteristic, direct product factor, Sylow

109

C₁₃₉

#10576

yes

characteristic, direct product factor, Sylow

110

#2571

C₂×C₁₃₉

yes

characteristic

111

#1948

C₂×C₁₃₉

yes

—

112

#1845

C₂×C₁₃₉

yes

characteristic

113

#1296

C₂×C₁₃₉

yes

characteristic

114

#1279

C₂×C₁₃₉

yes

—

115

C₂×#107

—

116

C₂×#106

—

117

C₂×C₄⋊C₈

C₂²×C₁₃₉

yes

—

118

C₂×C₄×C₈

C₂²×C₁₃₉

yes

characteristic

119

#400

—

120

#389

—

121

#384

C₂²×C₁₃₉

yes

characteristic

122

#384

C₂²×C₁₃₉

yes

characteristic

123

#382

—

124

C₄×C₄⋊C₄

C₂²×C₁₃₉

yes

—

125

#340

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

D₄×C₁₃₉

yes

—

133

C₂×C₄⋊C₄

D₄×C₁₃₉

yes

—

134

C₂×C₄⋊C₄

D₄×C₁₃₉

yes

—

135

C₂×C₄²

—

136

C₂×C₄²

C₂³×C₁₃₉

yes

characteristic

137

#107

—

138

#106

—

139

C₄⋊C₈

—

140

C₄⋊C₈

Q₈×C₁₃₉

yes

—

141

C₄×C₈

—

142

C₄×C₈

Q₈×C₁₃₉

yes

—

143

#95

—

144

#95

—

145

#95

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

C₂×D₄×C₁₃₉

yes

characteristic

151

C₂²×C₄

C₂×D₄×C₁₃₉

yes

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄²

—

170

C₄²

—

171

C₄²

C₂×Q₈×C₁₃₉

yes

characteristic

172

C₄²

C₂×Q₈×C₁₃₉

yes

—

173

C₄²

#41×C₁₃₉

yes

characteristic

174

C₂³

#120×C₁₃₉

yes

characteristic

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

C₂²⋊Q₈×C₁₃₉

yes

characteristic

188

C₂×C₄

C₂²⋊Q₈×C₁₃₉

yes

—

189

C₂×C₄

C₄⋊Q₈×C₁₃₉

yes

characteristic

190

C₂×C₄

C₄⋊Q₈×C₁₃₉

yes

—

191

C₂×C₄

#135×C₁₃₉

yes

—

192

C₂×C₄

#135×C₁₃₉

yes

—

193

C₂×C₄

AGL(1,ℤ/8)×C₁₃₉

yes

—

194

C₂×C₄

#137×C₁₃₉

yes

—

195

C₈

—

196

C₈

—

197

C₂²

#395×C₁₃₉

yes

characteristic

198

C₂²

#449×C₁₃₉

yes

—

199

C₂²

#452×C₁₃₉

yes

—

200

C₂²

#453×C₁₃₉

yes

characteristic

201

C₂²

#456×C₁₃₉

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

#478×C₁₃₉

yes

—

209

C₄

#479×C₁₃₉

yes

—

210

C₄

#499×C₁₃₉

yes

—

211

C₄

#501×C₁₃₉

yes

—

212

C₂

#1620×C₁₃₉

yes

characteristic

213

C₂

#1634×C₁₃₉

yes

characteristic

214

C₂

#1650×C₁₃₉

yes

—

215

C₂

#2059×C₁₃₉

yes

—

216

C₂

#2060×C₁₃₉

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃₉

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃₉

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

N	H ≅ G/N	type
108. #10576	C₁₃₉	direct (N × H)
109. C₁₃₉	#10576	direct (N × H)

H ≅ G/N

type

108. #10576

C₁₃₉

direct (N × H)

109. C₁₃₉

#10576

direct (N × H)

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

subgroup	index
#2571×C₁₃₉	2
#1948×C₁₃₉	2
#1845×C₁₃₉	2
#1296×C₁₃₉	2
#1279×C₁₃₉	2
#10576	139

subgroup

index

#2571×C₁₃₉

#1948×C₁₃₉

#1845×C₁₃₉

#1296×C₁₃₉

#1279×C₁₃₉

#10576

139

Subgroups — C₁₃₉×#10576 #48005172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C139×#10576 #48005172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10576 #48005172