Group #48004017 — subgroups

Subgroups — C₁₃₉×#9421 #48004017

Order 35584.

488 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 118 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	#3152×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2980×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#1556×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#1536×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1291×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂×#137×C₁₃₉	—	2	2	no	—
7	#532×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
9	#497×C₁₃₉	—	2	2	no	—
10	#494×C₁₃₉	C₄	1	2	yes	—
11	#492×C₁₃₉	C₄	1	2	yes	—
12	#435×C₁₃₉	—	2	4	no	—
13	#432×C₁₃₉	C₂²	1	2	yes	—
14	#432×C₁₃₉	C₂²	1	2	yes	—
15	#408×C₁₃₉	—	2	2	no	—
16	C₄×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
17	#332×C₁₃₉	—	2	4	no	—
18	#329×C₁₃₉	—	2	2	no	—
19	C₂×#41×C₁₃₉	D₄	1	2	yes	—
20	C₂²×Q₈×C₁₃₉	—	2	1	no	—
21	#137×C₁₃₉	—	4	4	no	—
22	#137×C₁₃₉	—	4	4	no	—
23	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
24	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
25	C₂×M₁₆×C₁₃₉	—	2	1	no	—
26	C₂×M₁₆×C₁₃₉	—	2	2	no	—
27	C₂²×C₈×C₁₃₉	—	2	2	no	—
28	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
29	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
30	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
31	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
32	#127×C₁₃₉	C₂×C₄	1	1	yes	characteristic
33	#124×C₁₃₉	D₄	1	2	yes	—
34	#121×C₁₃₉	—	2	2	no	—
35	C₄×D₄×C₁₃₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
37	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₄⋊C₈×C₁₃₉	—	2	2	no	—
39	C₄⋊C₈×C₁₃₉	D₄	1	4	yes	—
40	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
41	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
42	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
43	#97×C₁₃₉	—	2	1	no	—
44	#97×C₁₃₉	—	2	2	no	—
45	#97×C₁₃₉	—	2	2	no	—
46	C₄×C₈×C₁₃₉	C₂×C₄	1	2	yes	—
47	#41×C₁₃₉	—	4	2	no	—
48	#41×C₁₃₉	—	4	2	no	—
49	C₂×Q₈×C₁₃₉	—	2	2	no	—
50	C₂×Q₈×C₁₃₉	—	4	2	no	—
51	C₂×Q₈×C₁₃₉	—	4	2	no	—
52	C₂×Q₈×C₁₃₉	—	4	1	no	—
53	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	2	yes	—
54	C₂×D₄×C₁₃₉	—	2	2	no	—
55	C₂×D₄×C₁₃₉	—	2	2	no	—
56	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₃₉	—	2	2	no	—
58	C₂²×C₄×C₁₃₉	—	4	1	no	—
59	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
61	Q₁₆×C₁₃₉	—	4	8	no	—
62	SD₁₆×C₁₃₉	—	4	8	no	—
63	M₁₆×C₁₃₉	—	2	4	no	—
64	M₁₆×C₁₃₉	—	8	2	no	—
65	C₂×C₈×C₁₃₉	—	2	2	no	—
66	C₂×C₈×C₁₃₉	—	2	4	no	—
67	C₂×C₈×C₁₃₉	—	4	2	no	—
68	C₂×C₈×C₁₃₉	—	8	2	no	—
69	C₄⋊C₄×C₁₃₉	—	2	2	no	—
70	C₄⋊C₄×C₁₃₉	—	2	4	no	—
71	C₄⋊C₄×C₁₃₉	—	4	2	no	—
72	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
73	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
76	C₂³×C₁₃₉	—	2	2	no	—
77	C₂³×C₁₃₉	#123	1	1	yes	characteristic
78	Q₈×C₁₃₉	—	4	2	no	—
79	Q₈×C₁₃₉	—	4	4	no	—
80	Q₈×C₁₃₉	—	8	2	no	—
81	D₄×C₁₃₉	—	4	2	no	—
82	D₄×C₁₃₉	—	8	2	no	—
83	D₄×C₁₃₉	—	8	2	no	—
84	C₂×C₄×C₁₃₉	—	2	2	no	—
85	C₂×C₄×C₁₃₉	—	2	2	no	—
86	C₂×C₄×C₁₃₉	—	4	2	no	—
87	C₂×C₄×C₁₃₉	—	4	2	no	—
88	C₂×C₄×C₁₃₉	—	4	2	no	—
89	C₂×C₄×C₁₃₉	—	4	2	no	—
90	C₂×C₄×C₁₃₉	—	8	1	no	—
91	C₂×C₄×C₁₃₉	—	8	1	no	—
92	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
95	C₂×C₄×C₁₃₉	#121	1	2	yes	—
96	C₈×C₁₃₉	—	2	4	no	—
97	C₈×C₁₃₉	—	4	4	no	—
98	C₈×C₁₃₉	—	8	2	no	—
99	C₂²×C₁₃₉	—	2	1	no	—
100	C₂²×C₁₃₉	—	2	2	no	—
101	C₂²×C₁₃₉	—	4	2	no	—
102	C₂²×C₁₃₉	—	4	4	no	—
103	C₂²×C₁₃₉	#386	1	1	yes	characteristic
104	C₄×C₁₃₉	—	2	1	no	—
105	C₄×C₁₃₉	—	2	2	no	—
106	C₄×C₁₃₉	—	2	2	no	—
107	C₄×C₁₃₉	—	4	2	no	—
108	C₄×C₁₃₉	—	8	2	no	—
109	C₄×C₁₃₉	#453	1	2	yes	—
110	C₂×C₁₃₉	—	4	1	no	—
111	C₂×C₁₃₉	—	8	2	no	—
112	C₂×C₁₃₉	#1887	1	1	yes	characteristic
113	C₂×C₁₃₉	#1902	1	2	yes	—
114	#9421	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₁₃₉	#9421	1	1	yes	characteristic, direct product factor, Sylow
116	#3152	C₂×C₁₃₉	1	1	yes	characteristic
117	#2980	C₂×C₁₃₉	1	1	yes	characteristic
118	#1556	C₂×C₁₃₉	1	2	yes	complemented
119	#1536	C₂×C₁₃₉	1	1	yes	characteristic
120	#1291	C₂×C₁₃₉	1	2	yes	complemented
121	C₂×#137	—	2	2	no	—
122	#532	C₂²×C₁₃₉	1	1	yes	characteristic
123	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
124	#497	—	2	2	no	—
125	#494	C₄×C₁₃₉	1	2	yes	—
126	#492	C₄×C₁₃₉	1	2	yes	—
127	#435	—	2	4	no	—
128	#432	C₂²×C₁₃₉	1	2	yes	—
129	#432	C₂²×C₁₃₉	1	2	yes	—
130	#408	—	2	2	no	—
131	C₄×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
132	#332	—	2	4	no	—
133	#329	—	2	2	no	—
134	C₂×#41	D₄×C₁₃₉	1	2	yes	—
135	C₂²×Q₈	—	2	1	no	—
136	#137	—	4	4	no	—
137	#137	—	4	4	no	—
138	C₂×Q₁₆	—	2	4	no	—
139	C₂×SD₁₆	—	2	4	no	—
140	C₂×M₁₆	—	2	1	no	—
141	C₂×M₁₆	—	2	2	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	1	no	—
145	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
146	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
147	#127	C₂×C₄×C₁₃₉	1	1	yes	characteristic
148	#124	D₄×C₁₃₉	1	2	yes	—
149	#121	—	2	2	no	—
150	C₄×D₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	D₄×C₁₃₉	1	4	yes	—
155	C₂²⋊C₈	—	2	4	no	—
156	C₂²⋊C₈	—	2	2	no	—
157	C₂²⋊C₈	—	2	2	no	—
158	#97	—	2	1	no	—
159	#97	—	2	2	no	—
160	#97	—	2	2	no	—
161	C₄×C₈	C₂×C₄×C₁₃₉	1	2	yes	—
162	#41	—	4	2	no	—
163	#41	—	4	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	—	4	1	no	—
168	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	2	yes	—
169	C₂×D₄	—	2	2	no	—
170	C₂×D₄	—	2	2	no	—
171	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	4	1	no	—
174	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
175	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
176	Q₁₆	—	4	8	no	—
177	SD₁₆	—	4	8	no	—
178	M₁₆	—	2	4	no	—
179	M₁₆	—	8	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	8	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₂²⋊C₄	—	2	4	no	—
188	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
189	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
190	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
191	C₂³	—	2	2	no	—
192	C₂³	#123×C₁₃₉	1	1	yes	characteristic
193	Q₈	—	4	2	no	—
194	Q₈	—	4	4	no	—
195	Q₈	—	8	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	2	no	—
198	D₄	—	8	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	8	1	no	—
206	C₂×C₄	—	8	1	no	—
207	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
208	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
209	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
210	C₂×C₄	#121×C₁₃₉	1	2	yes	—
211	C₈	—	2	4	no	—
212	C₈	—	4	4	no	—
213	C₈	—	8	2	no	—
214	C₂²	—	2	1	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	—	4	4	no	—
218	C₂²	#386×C₁₃₉	1	1	yes	characteristic
219	C₄	—	2	1	no	—
220	C₄	—	2	2	no	—
221	C₄	—	2	2	no	—
222	C₄	—	4	2	no	—
223	C₄	—	8	2	no	—
224	C₄	#453×C₁₃₉	1	2	yes	—
225	C₂	—	4	1	no	—
226	C₂	—	8	2	no	—
227	C₂	#1887×C₁₃₉	1	1	yes	characteristic
228	C₂	#1902×C₁₃₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#3152×C₁₃₉

C₂

yes

maximal, characteristic

#2980×C₁₃₉

C₂

yes

maximal, characteristic

#1556×C₁₃₉

C₂

yes

maximal, complemented

#1536×C₁₃₉

C₂

yes

maximal, characteristic

#1291×C₁₃₉

C₂

yes

maximal, complemented

C₂×#137×C₁₃₉

—

#532×C₁₃₉

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₁₃₉

C₂²

yes

characteristic

#497×C₁₃₉

—

#494×C₁₃₉

C₄

yes

—

#492×C₁₃₉

C₄

yes

—

#435×C₁₃₉

—

#432×C₁₃₉

C₂²

yes

—

#432×C₁₃₉

C₂²

yes

—

#408×C₁₃₉

—

C₄×M₁₆×C₁₃₉

C₂²

yes

characteristic

#332×C₁₃₉

—

#329×C₁₃₉

—

C₂×#41×C₁₃₉

D₄

yes

—

C₂²×Q₈×C₁₃₉

—

#137×C₁₃₉

—

#137×C₁₃₉

—

C₂×Q₁₆×C₁₃₉

—

C₂×SD₁₆×C₁₃₉

—

C₂×M₁₆×C₁₃₉

—

C₂×M₁₆×C₁₃₉

—

C₂²×C₈×C₁₃₉

—

C₄⋊Q₈×C₁₃₉

—

C₄⋊Q₈×C₁₃₉

—

C₄⋊Q₈×C₁₃₉

C₂×C₄

yes

—

C₄⋊Q₈×C₁₃₉

C₂×C₄

yes

characteristic

#127×C₁₃₉

C₂×C₄

yes

characteristic

#124×C₁₃₉

D₄

yes

—

#121×C₁₃₉

—

C₄×D₄×C₁₃₉

—

C₂×C₄⋊C₄×C₁₃₉

—

C₂×C₄²×C₁₃₉

C₂³

yes

characteristic

C₄⋊C₈×C₁₃₉

—

C₄⋊C₈×C₁₃₉

D₄

yes

—

C₂²⋊C₈×C₁₃₉

—

C₂²⋊C₈×C₁₃₉

—

C₂²⋊C₈×C₁₃₉

—

#97×C₁₃₉

—

#97×C₁₃₉

—

#97×C₁₃₉

—

C₄×C₈×C₁₃₉

C₂×C₄

yes

—

#41×C₁₃₉

—

#41×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₃₉

—

C₂×D₄×C₁₃₉

—

C₂×D₄×C₁₃₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃₉

#41

yes

—

Q₁₆×C₁₃₉

—

SD₁₆×C₁₃₉

—

M₁₆×C₁₃₉

—

M₁₆×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₂²⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

C₂²×C₄

yes

characteristic

C₄²×C₁₃₉

C₂×D₄

yes

characteristic

C₄²×C₁₃₉

C₂×D₄

yes

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

#123

yes

characteristic

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

D₄×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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃₉

C₄×D₄

yes

—

C₂×C₄×C₁₃₉

#120

yes

characteristic

C₂×C₄×C₁₃₉

#121

yes

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₂²×C₁₃₉

—

100

C₂²×C₁₃₉

—

101

C₂²×C₁₃₉

—

102

C₂²×C₁₃₉

—

103

C₂²×C₁₃₉

#386

yes

characteristic

104

C₄×C₁₃₉

—

105

C₄×C₁₃₉

—

106

C₄×C₁₃₉

—

107

C₄×C₁₃₉

—

108

C₄×C₁₃₉

—

109

C₄×C₁₃₉

#453

yes

—

110

C₂×C₁₃₉

—

111

C₂×C₁₃₉

—

112

C₂×C₁₃₉

#1887

yes

characteristic

113

C₂×C₁₃₉

#1902

yes

—

114

#9421

C₁₃₉

yes

maximal, characteristic, direct product factor, Sylow

115

C₁₃₉

#9421

yes

characteristic, direct product factor, Sylow

116

#3152

C₂×C₁₃₉

yes

characteristic

117

#2980

C₂×C₁₃₉

yes

characteristic

118

#1556

C₂×C₁₃₉

yes

complemented

119

#1536

C₂×C₁₃₉

yes

characteristic

120

#1291

C₂×C₁₃₉

yes

complemented

121

C₂×#137

—

122

#532

C₂²×C₁₃₉

yes

characteristic

123

C₂×C₄⋊Q₈

C₂²×C₁₃₉

yes

characteristic

124

#497

—

125

#494

C₄×C₁₃₉

yes

—

126

#492

C₄×C₁₃₉

yes

—

127

#435

—

128

#432

C₂²×C₁₃₉

yes

—

129

#432

C₂²×C₁₃₉

yes

—

130

#408

—

131

C₄×M₁₆

C₂²×C₁₃₉

yes

characteristic

132

#332

—

133

#329

—

134

C₂×#41

D₄×C₁₃₉

yes

—

135

C₂²×Q₈

—

136

#137

—

137

#137

—

138

C₂×Q₁₆

—

139

C₂×SD₁₆

—

140

C₂×M₁₆

—

141

C₂×M₁₆

—

142

C₂²×C₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

C₂×C₄×C₁₃₉

yes

—

146

C₄⋊Q₈

C₂×C₄×C₁₃₉

yes

characteristic

147

#127

C₂×C₄×C₁₃₉

yes

characteristic

148

#124

D₄×C₁₃₉

yes

—

149

#121

—

150

C₄×D₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

C₂³×C₁₃₉

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

D₄×C₁₃₉

yes

—

155

C₂²⋊C₈

—

156

C₂²⋊C₈

—

157

C₂²⋊C₈

—

158

#97

—

159

#97

—

160

#97

—

161

C₄×C₈

C₂×C₄×C₁₃₉

yes

—

162

#41

—

163

#41

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

C₂²⋊C₄×C₁₃₉

yes

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

C₂²⋊C₄×C₁₃₉

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂×D₄×C₁₃₉

yes

characteristic

175

C₂²×C₄

#41×C₁₃₉

yes

—

176

Q₁₆

—

177

SD₁₆

—

178

M₁₆

—

179

M₁₆

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₄²

C₂²×C₄×C₁₃₉

yes

characteristic

189

C₄²

C₂×D₄×C₁₃₉

yes

characteristic

190

C₄²

C₂×D₄×C₁₃₉

yes

—

191

C₂³

—

192

C₂³

#123×C₁₃₉

yes

characteristic

193

Q₈

—

194

Q₈

—

195

Q₈

—

196

D₄

—

197

D₄

—

198

D₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

C₂×C₂²⋊C₄×C₁₃₉

yes

characteristic

208

C₂×C₄

C₄×D₄×C₁₃₉

yes

—

209

C₂×C₄

#120×C₁₃₉

yes

characteristic

210

C₂×C₄

#121×C₁₃₉

yes

—

211

C₈

—

212

C₈

—

213

C₈

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#386×C₁₃₉

yes

characteristic

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

#453×C₁₃₉

yes

—

225

C₂

—

226

C₂

—

227

C₂

#1887×C₁₃₉

yes

characteristic

228

C₂

#1902×C₁₃₉

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃₉	#386
commutator	C₄²	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
prime radical	#532×C₁₃₉	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃₉

#386

commutator

C₄²

C₂²×C₄×C₁₃₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₃₉

prime radical

#532×C₁₃₉

C₂²

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

N	H ≅ G/N	type
3. #1556×C₁₃₉	C₂	semidirect
5. #1291×C₁₃₉	C₂	semidirect
114. #9421	C₁₃₉	direct (N × H)
115. C₁₃₉	#9421	direct (N × H)
118. #1556	C₂×C₁₃₉	semidirect
120. #1291	C₂×C₁₃₉	semidirect

H ≅ G/N

type

3. #1556×C₁₃₉

C₂

semidirect

5. #1291×C₁₃₉

C₂

semidirect

114. #9421

C₁₃₉

direct (N × H)

115. C₁₃₉

#9421

direct (N × H)

118. #1556

C₂×C₁₃₉

semidirect

120. #1291

C₂×C₁₃₉

semidirect

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

subgroup	index
#3152×C₁₃₉	2
#2980×C₁₃₉	2
#1556×C₁₃₉	2
#1536×C₁₃₉	2
#1291×C₁₃₉	2
#9421	139

subgroup

index

#3152×C₁₃₉

#2980×C₁₃₉

#1556×C₁₃₉

#1536×C₁₃₉

#1291×C₁₃₉

#9421

139

Subgroups — C₁₃₉×#9421 #48004017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C139×#9421 #48004017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#9421 #48004017