Subgroups — C₁₃₉×#36166 #48030762

Order 35584.

1866 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2863×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2852×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2514×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#2510×C₁₃₉	C₂	1	6	yes	maximal, complemented
5	#2495×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2493×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2349×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	#2339×C₁₃₉	C₂	1	3	yes	maximal
9	C₄×#126×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#383×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
16	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
17	#401×C₁₃₉	C₂²	1	6	yes	—
18	#400×C₁₃₉	C₂²	1	6	yes	—
19	#400×C₁₃₉	C₂²	1	6	yes	—
20	#397×C₁₃₉	C₂²	1	6	yes	—
21	#391×C₁₃₉	C₂²	1	3	yes	—
22	#391×C₁₃₉	C₂²	1	3	yes	—
23	#389×C₁₃₉	C₂²	1	3	yes	—
24	#389×C₁₃₉	C₂²	1	3	yes	—
25	#388×C₁₃₉	C₂²	1	3	yes	—
26	#388×C₁₃₉	C₂²	1	6	yes	—
27	#387×C₁₃₉	C₂²	1	6	yes	—
28	#387×C₁₃₉	C₂²	1	6	yes	—
29	#387×C₁₃₉	C₂²	1	3	yes	—
30	#386×C₁₃₉	C₂²	1	6	yes	—
31	#386×C₁₃₉	C₂²	1	6	yes	—
32	#385×C₁₃₉	C₂²	1	6	yes	—
33	#385×C₁₃₉	C₂²	1	6	yes	—
34	#383×C₁₃₉	C₂²	1	6	yes	—
35	#383×C₁₃₉	C₂²	1	1	yes	characteristic
36	#383×C₁₃₉	C₂²	1	2	yes	—
37	#383×C₁₃₉	C₂²	1	6	yes	—
38	#382×C₁₃₉	C₂²	1	3	yes	—
39	#381×C₁₃₉	C₂²	1	6	yes	—
40	#380×C₁₃₉	C₂²	1	6	yes	—
41	#380×C₁₃₉	C₂²	1	3	yes	—
42	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
44	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
46	C₂×#95×C₁₃₉	C₂²	1	6	yes	—
47	C₂×#95×C₁₃₉	C₂²	1	6	yes	—
48	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×#41×C₁₃₉	—	2	12	no	—
50	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
56	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
57	#126×C₁₃₉	—	2	4	no	—
58	C₄×D₄×C₁₃₉	—	2	12	no	—
59	C₄×D₄×C₁₃₉	—	2	12	no	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
66	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
67	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
68	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
69	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
70	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
71	C₂×C₄²×C₁₃₉	—	2	8	no	—
72	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
73	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
74	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
75	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
76	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
77	#95×C₁₃₉	C₂³	1	6	yes	—
78	#95×C₁₃₉	C₂³	1	6	yes	—
79	#95×C₁₃₉	C₂³	1	6	yes	—
80	#95×C₁₃₉	C₂³	1	6	yes	—
81	#95×C₁₃₉	C₂³	1	3	yes	—
82	#95×C₁₃₉	C₂³	1	6	yes	—
83	#95×C₁₃₉	C₂³	1	6	yes	—
84	#95×C₁₃₉	C₂³	1	6	yes	—
85	#95×C₁₃₉	C₂³	1	6	yes	—
86	#95×C₁₃₉	C₂³	1	3	yes	—
87	#95×C₁₃₉	C₂³	1	3	yes	—
88	#95×C₁₃₉	C₂³	1	3	yes	—
89	#95×C₁₃₉	C₂³	1	6	yes	—
90	#95×C₁₃₉	C₂³	1	6	yes	—
91	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
92	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
93	#41×C₁₃₉	—	4	16	no	—
94	C₂×Q₈×C₁₃₉	—	2	6	no	—
95	C₂×D₄×C₁₃₉	—	2	12	no	—
96	C₂×D₄×C₁₃₉	#41	1	12	yes	—
97	C₂²×C₄×C₁₃₉	—	2	12	no	—
98	C₂²×C₄×C₁₃₉	—	2	12	no	—
99	C₂²×C₄×C₁₃₉	—	2	12	no	—
100	C₂²×C₄×C₁₃₉	—	2	12	no	—
101	C₂²×C₄×C₁₃₉	—	2	6	no	—
102	C₂²×C₄×C₁₃₉	—	4	6	no	—
103	C₂²×C₄×C₁₃₉	—	4	6	no	—
104	C₂²×C₄×C₁₃₉	—	4	6	no	—
105	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
108	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
113	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₁₃₉	—	2	6	no	—
115	C₄⋊C₄×C₁₃₉	—	2	6	no	—
116	C₄⋊C₄×C₁₃₉	—	2	6	no	—
117	C₄⋊C₄×C₁₃₉	—	4	3	no	—
118	C₄⋊C₄×C₁₃₉	—	4	6	no	—
119	C₄⋊C₄×C₁₃₉	—	4	6	no	—
120	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
121	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
122	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
123	C₂²⋊C₄×C₁₃₉	—	4	3	no	—
124	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
125	C₄²×C₁₃₉	—	2	12	no	—
126	C₄²×C₁₃₉	—	2	6	no	—
127	C₄²×C₁₃₉	—	2	6	no	—
128	C₄²×C₁₃₉	—	4	3	no	—
129	C₄²×C₁₃₉	#41	1	4	yes	complemented
130	C₂³×C₁₃₉	—	2	2	no	—
131	C₂³×C₁₃₉	—	2	6	no	—
132	C₂³×C₁₃₉	—	2	1	no	—
133	C₂³×C₁₃₉	—	2	3	no	—
134	C₂³×C₁₃₉	—	2	3	no	—
135	C₂³×C₁₃₉	C₂×#41	1	12	yes	—
136	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
137	Q₈×C₁₃₉	—	4	4	no	—
138	D₄×C₁₃₉	—	4	8	no	—
139	D₄×C₁₃₉	#126	1	16	yes	complemented
140	C₂×C₄×C₁₃₉	—	2	3	no	—
141	C₂×C₄×C₁₃₉	—	2	3	no	—
142	C₂×C₄×C₁₃₉	—	2	6	no	—
143	C₂×C₄×C₁₃₉	—	2	3	no	—
144	C₂×C₄×C₁₃₉	—	2	3	no	—
145	C₂×C₄×C₁₃₉	—	2	3	no	—
146	C₂×C₄×C₁₃₉	—	2	3	no	—
147	C₂×C₄×C₁₃₉	—	2	6	no	—
148	C₂×C₄×C₁₃₉	—	2	6	no	—
149	C₂×C₄×C₁₃₉	—	2	3	no	—
150	C₂×C₄×C₁₃₉	—	2	6	no	—
151	C₂×C₄×C₁₃₉	—	2	3	no	—
152	C₂×C₄×C₁₃₉	—	2	3	no	—
153	C₂×C₄×C₁₃₉	—	2	6	no	—
154	C₂×C₄×C₁₃₉	—	2	6	no	—
155	C₂×C₄×C₁₃₉	—	2	3	no	—
156	C₂×C₄×C₁₃₉	—	2	3	no	—
157	C₂×C₄×C₁₃₉	—	2	6	no	—
158	C₂×C₄×C₁₃₉	—	2	3	no	—
159	C₂×C₄×C₁₃₉	—	4	24	no	—
160	C₂×C₄×C₁₃₉	—	4	8	no	—
161	C₂×C₄×C₁₃₉	—	4	4	no	—
162	C₂×C₄×C₁₃₉	—	8	12	no	—
163	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
164	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
165	C₂²×C₁₃₉	—	2	12	no	—
166	C₂²×C₁₃₉	—	2	12	no	—
167	C₂²×C₁₃₉	—	4	1	no	—
168	C₂²×C₁₃₉	—	4	3	no	—
169	C₂²×C₁₃₉	—	4	3	no	—
170	C₂²×C₁₃₉	C₂×#126	1	8	yes	—
171	C₂²×C₁₃₉	C₂²×#41	1	3	yes	—
172	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
173	C₂²×C₁₃₉	#585	1	3	yes	—
174	C₄×C₁₃₉	—	2	6	no	—
175	C₄×C₁₃₉	—	4	1	no	—
176	C₄×C₁₃₉	—	4	2	no	—
177	C₄×C₁₃₉	—	4	3	no	—
178	C₄×C₁₃₉	—	4	6	no	—
179	C₄×C₁₃₉	—	4	3	no	—
180	C₄×C₁₃₉	—	4	6	no	—
181	C₄×C₁₃₉	—	4	3	no	—
182	C₄×C₁₃₉	C₂×#126	1	4	yes	—
183	C₂×C₁₃₉	—	2	8	no	—
184	C₂×C₁₃₉	—	8	1	no	—
185	C₂×C₁₃₉	C₂²×#126	1	1	yes	characteristic
186	C₂×C₁₃₉	#3475	1	3	yes	—
187	C₂×C₁₃₉	#3521	1	3	yes	—
188	#36166	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃₉	#36166	1	1	yes	characteristic, direct product factor, Sylow
190	#2863	C₂×C₁₃₉	1	1	yes	characteristic, complemented
191	#2852	C₂×C₁₃₉	1	2	yes	complemented
192	#2514	C₂×C₁₃₉	1	3	yes	complemented
193	#2510	C₂×C₁₃₉	1	6	yes	complemented
194	#2495	C₂×C₁₃₉	1	3	yes	complemented
195	#2493	C₂×C₁₃₉	1	6	yes	complemented
196	#2349	C₂×C₁₃₉	1	3	yes	complemented
197	#2339	C₂×C₁₃₉	1	3	yes	—
198	C₄×#126	C₂×C₁₃₉	1	1	yes	characteristic, complemented
199	C₂×#383	C₂×C₁₃₉	1	2	yes	complemented
200	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
201	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
202	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
204	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
205	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
206	#401	C₂²×C₁₃₉	1	6	yes	—
207	#400	C₂²×C₁₃₉	1	6	yes	—
208	#400	C₂²×C₁₃₉	1	6	yes	—
209	#397	C₂²×C₁₃₉	1	6	yes	—
210	#391	C₂²×C₁₃₉	1	3	yes	—
211	#391	C₂²×C₁₃₉	1	3	yes	—
212	#389	C₂²×C₁₃₉	1	3	yes	—
213	#389	C₂²×C₁₃₉	1	3	yes	—
214	#388	C₂²×C₁₃₉	1	3	yes	—
215	#388	C₂²×C₁₃₉	1	6	yes	—
216	#387	C₂²×C₁₃₉	1	3	yes	—
217	#387	C₂²×C₁₃₉	1	6	yes	—
218	#387	C₂²×C₁₃₉	1	6	yes	—
219	#386	C₂²×C₁₃₉	1	6	yes	—
220	#386	C₂²×C₁₃₉	1	6	yes	—
221	#385	C₂²×C₁₃₉	1	6	yes	—
222	#385	C₂²×C₁₃₉	1	6	yes	—
223	#383	C₂²×C₁₃₉	1	1	yes	characteristic
224	#383	C₂²×C₁₃₉	1	2	yes	—
225	#383	C₂²×C₁₃₉	1	6	yes	—
226	#383	C₂²×C₁₃₉	1	6	yes	—
227	#382	C₂²×C₁₃₉	1	3	yes	—
228	#381	C₂²×C₁₃₉	1	6	yes	—
229	#380	C₂²×C₁₃₉	1	3	yes	—
230	#380	C₂²×C₁₃₉	1	6	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
233	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
234	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
235	C₂×#95	C₂²×C₁₃₉	1	6	yes	—
236	C₂×#95	C₂²×C₁₃₉	1	6	yes	—
237	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
238	C₂×#41	—	2	12	no	—
239	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
240	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
241	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
243	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
244	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
245	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
246	#126	—	2	4	no	—
247	C₄×D₄	—	2	12	no	—
248	C₄×D₄	—	2	12	no	—
249	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
252	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
260	C₂×C₄²	—	2	8	no	—
261	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
262	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
263	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
264	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
265	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
266	#95	C₂³×C₁₃₉	1	3	yes	—
267	#95	C₂³×C₁₃₉	1	3	yes	—
268	#95	C₂³×C₁₃₉	1	6	yes	—
269	#95	C₂³×C₁₃₉	1	6	yes	—
270	#95	C₂³×C₁₃₉	1	6	yes	—
271	#95	C₂³×C₁₃₉	1	6	yes	—
272	#95	C₂³×C₁₃₉	1	6	yes	—
273	#95	C₂³×C₁₃₉	1	6	yes	—
274	#95	C₂³×C₁₃₉	1	6	yes	—
275	#95	C₂³×C₁₃₉	1	3	yes	—
276	#95	C₂³×C₁₃₉	1	3	yes	—
277	#95	C₂³×C₁₃₉	1	6	yes	—
278	#95	C₂³×C₁₃₉	1	6	yes	—
279	#95	C₂³×C₁₃₉	1	6	yes	—
280	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
281	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
282	#41	—	4	16	no	—
283	C₂×Q₈	—	2	6	no	—
284	C₂×D₄	—	2	12	no	—
285	C₂×D₄	#41×C₁₃₉	1	12	yes	—
286	C₂²×C₄	—	2	12	no	—
287	C₂²×C₄	—	2	12	no	—
288	C₂²×C₄	—	2	12	no	—
289	C₂²×C₄	—	2	12	no	—
290	C₂²×C₄	—	2	6	no	—
291	C₂²×C₄	—	4	6	no	—
292	C₂²×C₄	—	4	6	no	—
293	C₂²×C₄	—	4	6	no	—
294	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
297	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
298	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
299	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
300	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
301	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
302	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
303	C₄⋊C₄	—	2	6	no	—
304	C₄⋊C₄	—	2	6	no	—
305	C₄⋊C₄	—	2	6	no	—
306	C₄⋊C₄	—	4	3	no	—
307	C₄⋊C₄	—	4	6	no	—
308	C₄⋊C₄	—	4	6	no	—
309	C₂²⋊C₄	—	2	12	no	—
310	C₂²⋊C₄	—	2	12	no	—
311	C₂²⋊C₄	—	2	6	no	—
312	C₂²⋊C₄	—	4	3	no	—
313	C₂²⋊C₄	—	4	6	no	—
314	C₄²	—	2	12	no	—
315	C₄²	—	2	6	no	—
316	C₄²	—	2	6	no	—
317	C₄²	—	4	3	no	—
318	C₄²	#41×C₁₃₉	1	4	yes	complemented
319	C₂³	—	2	2	no	—
320	C₂³	—	2	6	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	3	no	—
323	C₂³	—	2	3	no	—
324	C₂³	C₂×#41×C₁₃₉	1	12	yes	—
325	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
326	Q₈	—	4	4	no	—
327	D₄	—	4	8	no	—
328	D₄	#126×C₁₃₉	1	16	yes	complemented
329	C₂×C₄	—	2	3	no	—
330	C₂×C₄	—	2	3	no	—
331	C₂×C₄	—	2	6	no	—
332	C₂×C₄	—	2	3	no	—
333	C₂×C₄	—	2	3	no	—
334	C₂×C₄	—	2	3	no	—
335	C₂×C₄	—	2	3	no	—
336	C₂×C₄	—	2	6	no	—
337	C₂×C₄	—	2	6	no	—
338	C₂×C₄	—	2	3	no	—
339	C₂×C₄	—	2	6	no	—
340	C₂×C₄	—	2	3	no	—
341	C₂×C₄	—	2	3	no	—
342	C₂×C₄	—	2	6	no	—
343	C₂×C₄	—	2	6	no	—
344	C₂×C₄	—	2	3	no	—
345	C₂×C₄	—	2	3	no	—
346	C₂×C₄	—	2	6	no	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	4	24	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	8	12	no	—
352	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
353	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
354	C₂²	—	2	12	no	—
355	C₂²	—	2	12	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	3	no	—
358	C₂²	—	4	3	no	—
359	C₂²	C₂×#126×C₁₃₉	1	8	yes	—
360	C₂²	C₂²×#41×C₁₃₉	1	3	yes	—
361	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
362	C₂²	#585×C₁₃₉	1	3	yes	—
363	C₄	—	2	6	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	6	no	—
367	C₄	—	4	3	no	—
368	C₄	—	4	3	no	—
369	C₄	—	4	6	no	—
370	C₄	—	4	3	no	—
371	C₄	C₂×#126×C₁₃₉	1	4	yes	—
372	C₂	—	2	8	no	—
373	C₂	—	8	1	no	—
374	C₂	C₂²×#126×C₁₃₉	1	1	yes	characteristic
375	C₂	#3475×C₁₃₉	1	3	yes	—
376	C₂	#3521×C₁₃₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #2863×C₁₃₉	C₂	semidirect
2. #2852×C₁₃₉	C₂	semidirect
3. #2514×C₁₃₉	C₂	semidirect
4. #2510×C₁₃₉	C₂	semidirect
5. #2495×C₁₃₉	C₂	semidirect
6. #2493×C₁₃₉	C₂	semidirect
7. #2349×C₁₃₉	C₂	semidirect
9. C₄×#126×C₁₃₉	C₂	semidirect
10. C₂×#383×C₁₃₉	C₂	semidirect
11. C₄²×D₄×C₁₃₉	C₂	semidirect
129. C₄²×C₁₃₉	#41	semidirect
139. D₄×C₁₃₉	#126	semidirect
188. #36166	C₁₃₉	direct (N × H)
189. C₁₃₉	#36166	direct (N × H)
190. #2863	C₂×C₁₃₉	semidirect
191. #2852	C₂×C₁₃₉	semidirect
192. #2514	C₂×C₁₃₉	semidirect
193. #2510	C₂×C₁₃₉	semidirect
194. #2495	C₂×C₁₃₉	semidirect
195. #2493	C₂×C₁₃₉	semidirect
196. #2349	C₂×C₁₃₉	semidirect
198. C₄×#126	C₂×C₁₃₉	semidirect
199. C₂×#383	C₂×C₁₃₉	semidirect
200. C₄²×D₄	C₂×C₁₃₉	semidirect
318. C₄²	#41×C₁₃₉	semidirect
328. D₄	#126×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2863×C₁₃₉	2
#2852×C₁₃₉	2
#2514×C₁₃₉	2
#2510×C₁₃₉	2
#2495×C₁₃₉	2
#2493×C₁₃₉	2
#2349×C₁₃₉	2
#2339×C₁₃₉	2
C₄×#126×C₁₃₉	2
C₂×#383×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36166	139

Subgroups — C139×#36166 #48030762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36166 #48030762