Subgroups — C₁₃₉×#23627 #48018223

Order 35584.

1038 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#416×C₁₃₉	C₂	1	2	yes	maximal
2	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2074×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2073×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2072×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2071×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1735×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×#336×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
12	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
15	#416×C₁₃₉	—	2	8	no	—
16	C₂×#103×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#102×C₁₃₉	C₂²	1	4	yes	—
18	#391×C₁₃₉	C₂²	1	1	yes	characteristic
19	#391×C₁₃₉	C₂²	1	1	yes	characteristic
20	#390×C₁₃₉	C₂²	1	1	yes	characteristic
21	#390×C₁₃₉	C₂²	1	1	yes	characteristic
22	#386×C₁₃₉	—	2	2	no	—
23	#384×C₁₃₉	C₂²	1	2	yes	—
24	#382×C₁₃₉	C₂²	1	2	yes	—
25	#380×C₁₃₉	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₃₉	—	2	2	no	—
27	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
28	#340×C₁₃₉	C₂²	1	4	yes	—
29	#340×C₁₃₉	C₂²	1	4	yes	—
30	#336×C₁₃₉	C₂²	1	2	yes	—
31	#336×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#41×C₁₃₉	—	2	2	no	—
33	C₂×#41×C₁₃₉	—	2	4	no	—
34	C₂×#41×C₁₃₉	—	2	4	no	—
35	C₂×#41×C₁₃₉	D₄	1	4	yes	—
36	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₃₉	—	2	1	no	—
38	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	—	2	1	no	—
40	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
41	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₉	—	2	4	no	—
43	C₂²×C₈×C₁₃₉	—	2	4	no	—
44	C₂²×C₈×C₁₃₉	—	2	4	no	—
45	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
46	#117×C₁₃₉	—	2	4	no	—
47	#117×C₁₃₉	—	2	4	no	—
48	#117×C₁₃₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄²×C₁₃₉	—	2	4	no	—
59	C₂×C₄²×C₁₃₉	—	2	1	no	—
60	C₂×C₄²×C₁₃₉	—	2	2	no	—
61	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
64	#103×C₁₃₉	—	2	8	no	—
65	#102×C₁₃₉	—	2	8	no	—
66	#95×C₁₃₉	—	2	2	no	—
67	#95×C₁₃₉	—	2	2	no	—
68	#95×C₁₃₉	—	2	4	no	—
69	C₂⁴×C₁₃₉	—	2	1	no	—
70	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
71	#41×C₁₃₉	—	2	16	no	—
72	#41×C₁₃₉	—	4	8	no	—
73	C₂×Q₈×C₁₃₉	—	2	1	no	—
74	C₂×Q₈×C₁₃₉	—	2	2	no	—
75	C₂×Q₈×C₁₃₉	—	2	2	no	—
76	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
77	C₂×D₄×C₁₃₉	—	2	4	no	—
78	C₂×D₄×C₁₃₉	—	2	2	no	—
79	C₂×D₄×C₁₃₉	—	2	2	no	—
80	C₂×D₄×C₁₃₉	—	2	1	no	—
81	C₂×D₄×C₁₃₉	—	4	2	no	—
82	C₂×D₄×C₁₃₉	—	4	2	no	—
83	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃₉	—	2	4	no	—
85	C₂²×C₄×C₁₃₉	—	2	1	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	2	4	no	—
88	C₂²×C₄×C₁₃₉	—	2	1	no	—
89	C₂²×C₄×C₁₃₉	—	2	1	no	—
90	C₂²×C₄×C₁₃₉	—	2	4	no	—
91	C₂²×C₄×C₁₃₉	—	4	2	no	—
92	C₂²×C₄×C₁₃₉	—	4	2	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
100	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₁₃₉	—	2	4	no	—
103	C₂×C₈×C₁₃₉	—	2	4	no	—
104	C₂×C₈×C₁₃₉	—	2	4	no	—
105	C₂×C₈×C₁₃₉	—	4	8	no	—
106	C₄⋊C₄×C₁₃₉	—	2	4	no	—
107	C₄⋊C₄×C₁₃₉	—	2	4	no	—
108	C₄⋊C₄×C₁₃₉	—	2	2	no	—
109	C₄⋊C₄×C₁₃₉	—	2	2	no	—
110	C₄⋊C₄×C₁₃₉	—	4	4	no	—
111	C₄⋊C₄×C₁₃₉	—	4	4	no	—
112	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
113	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
114	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
115	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
116	C₄²×C₁₃₉	—	2	4	no	—
117	C₄²×C₁₃₉	—	2	2	no	—
118	C₄²×C₁₃₉	—	2	2	no	—
119	C₄²×C₁₃₉	—	4	4	no	—
120	C₄²×C₁₃₉	—	4	2	no	—
121	C₂³×C₁₃₉	—	2	2	no	—
122	C₂³×C₁₃₉	—	2	2	no	—
123	C₂³×C₁₃₉	—	2	2	no	—
124	C₂³×C₁₃₉	—	4	1	no	—
125	C₂³×C₁₃₉	—	4	1	no	—
126	C₂³×C₁₃₉	—	4	2	no	—
127	C₂³×C₁₃₉	—	4	2	no	—
128	C₂³×C₁₃₉	#121	1	2	yes	—
129	C₂³×C₁₃₉	#123	1	2	yes	—
130	C₂³×C₁₃₉	#124	1	2	yes	—
131	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₁₃₉	—	2	4	no	—
133	Q₈×C₁₃₉	—	4	2	no	—
134	D₄×C₁₃₉	—	2	4	no	—
135	D₄×C₁₃₉	—	4	8	no	—
136	D₄×C₁₃₉	—	4	2	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	2	2	no	—
142	C₂×C₄×C₁₃₉	—	2	2	no	—
143	C₂×C₄×C₁₃₉	—	4	8	no	—
144	C₂×C₄×C₁₃₉	—	4	1	no	—
145	C₂×C₄×C₁₃₉	—	4	1	no	—
146	C₂×C₄×C₁₃₉	—	4	8	no	—
147	C₂×C₄×C₁₃₉	—	4	4	no	—
148	C₂×C₄×C₁₃₉	—	4	1	no	—
149	C₂×C₄×C₁₃₉	—	4	1	no	—
150	C₂×C₄×C₁₃₉	—	4	2	no	—
151	C₂×C₄×C₁₃₉	—	4	4	no	—
152	C₂×C₄×C₁₃₉	—	4	2	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	#121	1	2	yes	—
155	C₂×C₄×C₁₃₉	#123	1	8	yes	—
156	C₂×C₄×C₁₃₉	#123	1	2	yes	—
157	C₂×C₄×C₁₃₉	#124	1	2	yes	—
158	C₂×C₄×C₁₃₉	#126	1	8	yes	—
159	C₂×C₄×C₁₃₉	#135	1	4	yes	—
160	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
162	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
163	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
164	C₈×C₁₃₉	—	4	4	no	—
165	C₂²×C₁₃₉	—	2	4	no	—
166	C₂²×C₁₃₉	—	2	2	no	—
167	C₂²×C₁₃₉	—	2	2	no	—
168	C₂²×C₁₃₉	—	2	4	no	—
169	C₂²×C₁₃₉	—	4	2	no	—
170	C₂²×C₁₃₉	—	4	4	no	—
171	C₂²×C₁₃₉	—	8	2	no	—
172	C₂²×C₁₃₉	—	8	1	no	—
173	C₂²×C₁₃₉	—	8	1	no	—
174	C₂²×C₁₃₉	#397	1	4	yes	—
175	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
176	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
177	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
178	C₂²×C₁₃₉	C₂×#135	1	2	yes	—
179	C₂²×C₁₃₉	#575	1	2	yes	—
180	C₄×C₁₃₉	—	2	4	no	—
181	C₄×C₁₃₉	—	4	2	no	—
182	C₄×C₁₃₉	—	4	2	no	—
183	C₄×C₁₃₉	—	8	1	no	—
184	C₄×C₁₃₉	—	8	1	no	—
185	C₄×C₁₃₉	—	8	4	no	—
186	C₄×C₁₃₉	#397	1	4	yes	—
187	C₄×C₁₃₉	C₂×#123	1	2	yes	—
188	C₄×C₁₃₉	C₂×#126	1	2	yes	—
189	C₂×C₁₃₉	—	2	4	no	—
190	C₂×C₁₃₉	—	8	2	no	—
191	C₂×C₁₃₉	C₂×#397	1	1	yes	characteristic
192	C₂×C₁₃₉	#3035	1	2	yes	—
193	C₂×C₁₃₉	#3091	1	2	yes	—
194	C₂×C₁₃₉	#3131	1	1	yes	characteristic
195	C₂×C₁₃₉	#3135	1	1	yes	characteristic
196	#23627	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₁₃₉	#23627	1	1	yes	characteristic, direct product factor, Sylow
198	C₂×#416	C₂×C₁₃₉	1	2	yes	—
199	#2297	C₂×C₁₃₉	1	1	yes	characteristic
200	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
201	#2074	C₂×C₁₃₉	1	2	yes	complemented
202	#2073	C₂×C₁₃₉	1	2	yes	complemented
203	#2072	C₂×C₁₃₉	1	2	yes	complemented
204	#2071	C₂×C₁₃₉	1	2	yes	complemented
205	#1735	C₂×C₁₃₉	1	2	yes	complemented
206	C₂×#336	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
209	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
210	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
212	#416	—	2	8	no	—
213	C₂×#103	C₂²×C₁₃₉	1	4	yes	—
214	C₂×#102	C₂²×C₁₃₉	1	4	yes	—
215	#391	C₂²×C₁₃₉	1	1	yes	characteristic
216	#391	C₂²×C₁₃₉	1	1	yes	characteristic
217	#390	C₂²×C₁₃₉	1	1	yes	characteristic
218	#390	C₂²×C₁₃₉	1	1	yes	characteristic
219	#386	—	2	2	no	—
220	#384	C₂²×C₁₃₉	1	2	yes	—
221	#382	C₂²×C₁₃₉	1	2	yes	—
222	#380	—	2	2	no	—
223	C₄×C₄⋊C₄	—	2	2	no	—
224	C₄×C₂²⋊C₄	—	2	2	no	—
225	#340	C₂²×C₁₃₉	1	4	yes	—
226	#340	C₂²×C₁₃₉	1	4	yes	—
227	#336	C₂²×C₁₃₉	1	2	yes	—
228	#336	C₂²×C₁₃₉	1	2	yes	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	2	4	no	—
232	C₂×#41	D₄×C₁₃₉	1	4	yes	—
233	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
238	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
239	C₂²×C₈	—	2	4	no	—
240	C₂²×C₈	—	2	4	no	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
243	#117	—	2	4	no	—
244	#117	—	2	4	no	—
245	#117	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
259	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
261	#103	—	2	8	no	—
262	#102	—	2	8	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	4	no	—
266	C₂⁴	—	2	1	no	—
267	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
268	#41	—	2	16	no	—
269	#41	—	4	8	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
295	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
296	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
297	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	4	8	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	4	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₂²⋊C₄	—	4	4	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	4	4	no	—
317	C₄²	—	4	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	#121×C₁₃₉	1	2	yes	—
326	C₂³	#123×C₁₃₉	1	2	yes	—
327	C₂³	#124×C₁₃₉	1	2	yes	—
328	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
329	Q₈	—	2	4	no	—
330	Q₈	—	4	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	#121×C₁₃₉	1	2	yes	—
352	C₂×C₄	#123×C₁₃₉	1	2	yes	—
353	C₂×C₄	#123×C₁₃₉	1	8	yes	—
354	C₂×C₄	#124×C₁₃₉	1	2	yes	—
355	C₂×C₄	#126×C₁₃₉	1	8	yes	—
356	C₂×C₄	#135×C₁₃₉	1	4	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
359	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
360	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
361	C₈	—	4	4	no	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	#397×C₁₃₉	1	4	yes	—
372	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
373	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
374	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
375	C₂²	C₂×#135×C₁₃₉	1	2	yes	—
376	C₂²	#575×C₁₃₉	1	2	yes	—
377	C₄	—	2	4	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	4	no	—
381	C₄	—	8	1	no	—
382	C₄	—	8	1	no	—
383	C₄	#397×C₁₃₉	1	4	yes	—
384	C₄	C₂×#123×C₁₃₉	1	2	yes	—
385	C₄	C₂×#126×C₁₃₉	1	2	yes	—
386	C₂	—	2	4	no	—
387	C₂	—	8	2	no	—
388	C₂	C₂×#397×C₁₃₉	1	1	yes	characteristic
389	C₂	#3035×C₁₃₉	1	2	yes	—
390	C₂	#3091×C₁₃₉	1	2	yes	—
391	C₂	#3131×C₁₃₉	1	1	yes	characteristic
392	C₂	#3135×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂³×C₁₃₉	C₂²×D₄
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2285×C₁₃₉	C₂	semidirect
4. #2074×C₁₃₉	C₂	semidirect
5. #2073×C₁₃₉	C₂	semidirect
6. #2072×C₁₃₉	C₂	semidirect
7. #2071×C₁₃₉	C₂	semidirect
8. #1735×C₁₃₉	C₂	semidirect
9. C₂×#336×C₁₃₉	C₂	semidirect
196. #23627	C₁₃₉	direct (N × H)
197. C₁₃₉	#23627	direct (N × H)
200. #2285	C₂×C₁₃₉	semidirect
201. #2074	C₂×C₁₃₉	semidirect
202. #2073	C₂×C₁₃₉	semidirect
203. #2072	C₂×C₁₃₉	semidirect
204. #2071	C₂×C₁₃₉	semidirect
205. #1735	C₂×C₁₃₉	semidirect
206. C₂×#336	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#416×C₁₃₉	2
#2297×C₁₃₉	2
#2285×C₁₃₉	2
#2074×C₁₃₉	2
#2073×C₁₃₉	2
#2072×C₁₃₉	2
#2071×C₁₃₉	2
#1735×C₁₃₉	2
C₂×#336×C₁₃₉	2
#23627	139

Subgroups — C139×#23627 #48018223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#23627 #48018223