Subgroups — C₁₃₉×#10957 #48005553

Order 35584.

1014 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#419×C₁₃₉	C₂	1	2	yes	maximal
2	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#343×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	#419×C₁₃₉	—	2	4	no	—
12	#419×C₁₃₉	C₄	1	8	yes	complemented
13	C₂×#103×C₁₃₉	—	2	4	no	—
14	#391×C₁₃₉	—	2	2	no	—
15	#391×C₁₃₉	C₄	1	4	yes	complemented
16	C₄×C₄⋊C₄×C₁₃₉	—	2	4	no	—
17	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
18	C₂×#95×C₁₃₉	—	2	2	no	—
19	#343×C₁₃₉	—	2	2	no	—
20	#339×C₁₃₉	—	2	4	no	—
21	C₂²×Q₈×C₁₃₉	—	2	1	no	—
22	C₂²×Q₈×C₁₃₉	—	2	2	no	—
23	C₂²×Q₈×C₁₃₉	—	2	2	no	—
24	C₂²×Q₈×C₁₃₉	—	2	2	no	—
25	C₂²×Q₈×C₁₃₉	—	2	2	no	—
26	C₂²×Q₈×C₁₃₉	—	2	2	no	—
27	C₂²×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₃₉	—	2	1	no	—
30	C₂³×C₄×C₁₃₉	—	2	1	no	—
31	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
32	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₃₉	—	2	2	no	—
34	C₂×M₁₆×C₁₃₉	—	2	2	no	—
35	C₂×M₁₆×C₁₃₉	—	2	2	no	—
36	C₂×M₁₆×C₁₃₉	—	2	2	no	—
37	C₂×M₁₆×C₁₃₉	—	2	2	no	—
38	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₁₃₉	—	2	2	no	—
40	#117×C₁₃₉	—	2	2	no	—
41	#117×C₁₃₉	—	2	2	no	—
42	#117×C₁₃₉	C₂×C₄	1	4	yes	—
43	#117×C₁₃₉	D₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₄²×C₁₃₉	—	2	2	no	—
51	C₂×C₄²×C₁₃₉	—	2	2	no	—
52	C₂×C₄²×C₁₃₉	—	2	2	no	—
53	C₂×C₄²×C₁₃₉	—	2	1	no	—
54	C₂×C₄²×C₁₃₉	—	2	4	no	—
55	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
56	#103×C₁₃₉	—	2	16	no	—
57	#95×C₁₃₉	—	2	4	no	—
58	#95×C₁₃₉	—	2	8	no	—
59	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
60	C₂×Q₈×C₁₃₉	—	2	2	no	—
61	C₂×Q₈×C₁₃₉	—	2	4	no	—
62	C₂×Q₈×C₁₃₉	—	2	4	no	—
63	C₂×Q₈×C₁₃₉	—	2	4	no	—
64	C₂×Q₈×C₁₃₉	—	2	4	no	—
65	C₂×Q₈×C₁₃₉	—	2	4	no	—
66	C₂×Q₈×C₁₃₉	—	2	4	no	—
67	C₂×Q₈×C₁₃₉	—	2	4	no	—
68	C₂×Q₈×C₁₃₉	—	4	2	no	—
69	C₂×Q₈×C₁₃₉	—	4	2	no	—
70	C₂×Q₈×C₁₃₉	—	4	2	no	—
71	C₂×Q₈×C₁₃₉	—	4	2	no	—
72	C₂×Q₈×C₁₃₉	—	4	1	no	—
73	C₂×Q₈×C₁₃₉	—	4	2	no	—
74	C₂×Q₈×C₁₃₉	—	4	1	no	—
75	C₂×Q₈×C₁₃₉	C₄²	1	4	yes	complemented
76	C₂²×C₄×C₁₃₉	—	2	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	2	no	—
79	C₂²×C₄×C₁₃₉	—	2	4	no	—
80	C₂²×C₄×C₁₃₉	—	2	4	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	2	no	—
83	C₂²×C₄×C₁₃₉	—	4	2	no	—
84	C₂²×C₄×C₁₃₉	—	4	1	no	—
85	C₂²×C₄×C₁₃₉	—	4	2	no	—
86	C₂²×C₄×C₁₃₉	—	4	2	no	—
87	C₂²×C₄×C₁₃₉	—	4	1	no	—
88	C₂²×C₄×C₁₃₉	—	4	4	no	—
89	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
96	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
97	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
98	M₁₆×C₁₃₉	—	2	4	no	—
99	M₁₆×C₁₃₉	—	2	4	no	—
100	M₁₆×C₁₃₉	—	4	2	no	—
101	M₁₆×C₁₃₉	—	4	2	no	—
102	C₂×C₈×C₁₃₉	—	2	4	no	—
103	C₂×C₈×C₁₃₉	—	4	2	no	—
104	C₂×C₈×C₁₃₉	—	4	2	no	—
105	C₄⋊C₄×C₁₃₉	—	2	4	no	—
106	C₄⋊C₄×C₁₃₉	—	2	4	no	—
107	C₄⋊C₄×C₁₃₉	—	2	4	no	—
108	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
109	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
110	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
111	C₄²×C₁₃₉	—	2	4	no	—
112	C₄²×C₁₃₉	—	2	4	no	—
113	C₄²×C₁₃₉	—	2	4	no	—
114	C₄²×C₁₃₉	—	4	1	no	—
115	C₄²×C₁₃₉	—	4	1	no	—
116	C₄²×C₁₃₉	—	8	4	no	—
117	C₂³×C₁₃₉	—	2	2	no	—
118	C₂³×C₁₃₉	—	2	2	no	—
119	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
121	C₂³×C₁₃₉	#120	1	1	yes	characteristic
122	C₂³×C₁₃₉	#121	1	2	yes	—
123	C₂³×C₁₃₉	#123	1	1	yes	characteristic
124	Q₈×C₁₃₉	—	2	8	no	—
125	Q₈×C₁₃₉	—	4	4	no	—
126	Q₈×C₁₃₉	—	4	4	no	—
127	Q₈×C₁₃₉	—	4	4	no	—
128	C₂×C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄×C₁₃₉	—	2	8	no	—
131	C₂×C₄×C₁₃₉	—	2	4	no	—
132	C₂×C₄×C₁₃₉	—	4	8	no	—
133	C₂×C₄×C₁₃₉	—	4	2	no	—
134	C₂×C₄×C₁₃₉	—	4	4	no	—
135	C₂×C₄×C₁₃₉	—	4	2	no	—
136	C₂×C₄×C₁₃₉	—	4	4	no	—
137	C₂×C₄×C₁₃₉	—	4	2	no	—
138	C₂×C₄×C₁₃₉	—	4	2	no	—
139	C₂×C₄×C₁₃₉	—	4	4	no	—
140	C₂×C₄×C₁₃₉	—	4	4	no	—
141	C₂×C₄×C₁₃₉	—	4	4	no	—
142	C₂×C₄×C₁₃₉	—	4	4	no	—
143	C₂×C₄×C₁₃₉	—	8	2	no	—
144	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₁₃₉	#117	1	2	yes	—
147	C₂×C₄×C₁₃₉	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₃₉	#121	1	2	yes	—
154	C₂×C₄×C₁₃₉	#121	1	2	yes	—
155	C₂×C₄×C₁₃₉	#123	1	2	yes	—
156	C₂×C₄×C₁₃₉	#124	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	#124	1	2	yes	—
158	C₂×C₄×C₁₃₉	#126	1	2	yes	—
159	C₂×C₄×C₁₃₉	#127	1	1	yes	characteristic
160	C₈×C₁₃₉	—	4	4	no	—
161	C₂²×C₁₃₉	—	2	4	no	—
162	C₂²×C₁₃₉	—	2	4	no	—
163	C₂²×C₁₃₉	—	2	1	no	—
164	C₂²×C₁₃₉	—	2	1	no	—
165	C₂²×C₁₃₉	—	2	1	no	—
166	C₂²×C₁₃₉	—	2	1	no	—
167	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₁₃₉	#386	1	2	yes	—
169	C₂²×C₁₃₉	#386	1	1	yes	characteristic
170	C₂²×C₁₃₉	#388	1	2	yes	—
171	C₂²×C₁₃₉	#390	1	1	yes	characteristic
172	C₂²×C₁₃₉	#455	1	2	yes	—
173	C₂²×C₁₃₉	#456	1	2	yes	—
174	C₄×C₁₃₉	—	4	4	no	—
175	C₄×C₁₃₉	—	4	8	no	—
176	C₄×C₁₃₉	—	4	4	no	—
177	C₄×C₁₃₉	—	4	4	no	—
178	C₄×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
179	C₄×C₁₃₉	#388	1	2	yes	—
180	C₄×C₁₃₉	#388	1	2	yes	—
181	C₄×C₁₃₉	#390	1	2	yes	—
182	C₂×C₁₃₉	—	2	1	no	—
183	C₂×C₁₃₉	—	2	1	no	—
184	C₂×C₁₃₉	—	2	2	no	—
185	C₂×C₁₃₉	#1437	1	1	yes	characteristic
186	C₂×C₁₃₉	#1882	1	4	yes	—
187	C₂×C₁₃₉	#1885	1	1	yes	characteristic
188	C₂×C₁₃₉	#1886	1	1	yes	characteristic
189	#10957	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₁₃₉	#10957	1	1	yes	characteristic, direct product factor, Sylow
191	C₂×#419	C₂×C₁₃₉	1	2	yes	—
192	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic
193	#2274	C₂×C₁₃₉	1	1	yes	characteristic
194	C₂×#343	C₂×C₁₃₉	1	1	yes	characteristic
195	C₂×#339	C₂×C₁₃₉	1	2	yes	—
196	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
197	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
198	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
200	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
201	#419	—	2	4	no	—
202	#419	C₄×C₁₃₉	1	8	yes	complemented
203	C₂×#103	—	2	4	no	—
204	#391	—	2	2	no	—
205	#391	C₄×C₁₃₉	1	4	yes	complemented
206	C₄×C₄⋊C₄	—	2	4	no	—
207	C₄×C₂²⋊C₄	—	2	2	no	—
208	C₂×#95	—	2	2	no	—
209	#343	—	2	2	no	—
210	#339	—	2	4	no	—
211	C₂²×Q₈	—	2	1	no	—
212	C₂²×Q₈	—	2	2	no	—
213	C₂²×Q₈	—	2	2	no	—
214	C₂²×Q₈	—	2	2	no	—
215	C₂²×Q₈	—	2	2	no	—
216	C₂²×Q₈	—	2	2	no	—
217	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
218	C₂²×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
222	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	2	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
229	C₂²×C₈	—	2	2	no	—
230	#117	—	2	2	no	—
231	#117	—	2	2	no	—
232	#117	C₂×C₄×C₁₃₉	1	4	yes	—
233	#117	D₄×C₁₃₉	1	4	yes	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
237	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
238	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
246	#103	—	2	16	no	—
247	#95	—	2	4	no	—
248	#95	—	2	8	no	—
249	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
250	C₂×Q₈	—	2	2	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	2	4	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	4	2	no	—
259	C₂×Q₈	—	4	2	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	C₄²×C₁₃₉	1	4	yes	complemented
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
280	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
285	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
286	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
287	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	4	no	—
290	M₁₆	—	4	2	no	—
291	M₁₆	—	4	2	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	4	1	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	8	4	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
310	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
311	C₂³	#120×C₁₃₉	1	1	yes	characteristic
312	C₂³	#121×C₁₃₉	1	2	yes	—
313	C₂³	#123×C₁₃₉	1	1	yes	characteristic
314	Q₈	—	2	8	no	—
315	Q₈	—	4	4	no	—
316	Q₈	—	4	4	no	—
317	Q₈	—	4	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
336	C₂×C₄	#117×C₁₃₉	1	2	yes	—
337	C₂×C₄	#117×C₁₃₉	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
339	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
340	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
341	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
342	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
343	C₂×C₄	#121×C₁₃₉	1	2	yes	—
344	C₂×C₄	#121×C₁₃₉	1	2	yes	—
345	C₂×C₄	#123×C₁₃₉	1	2	yes	—
346	C₂×C₄	#124×C₁₃₉	1	1	yes	characteristic
347	C₂×C₄	#124×C₁₃₉	1	2	yes	—
348	C₂×C₄	#126×C₁₃₉	1	2	yes	—
349	C₂×C₄	#127×C₁₃₉	1	1	yes	characteristic
350	C₈	—	4	4	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
358	C₂²	#386×C₁₃₉	1	2	yes	—
359	C₂²	#386×C₁₃₉	1	1	yes	characteristic
360	C₂²	#388×C₁₃₉	1	2	yes	—
361	C₂²	#390×C₁₃₉	1	1	yes	characteristic
362	C₂²	#455×C₁₃₉	1	2	yes	—
363	C₂²	#456×C₁₃₉	1	2	yes	—
364	C₄	—	4	4	no	—
365	C₄	—	4	8	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
369	C₄	#388×C₁₃₉	1	2	yes	—
370	C₄	#388×C₁₃₉	1	2	yes	—
371	C₄	#390×C₁₃₉	1	2	yes	—
372	C₂	—	2	1	no	—
373	C₂	—	2	1	no	—
374	C₂	—	2	2	no	—
375	C₂	#1437×C₁₃₉	1	1	yes	characteristic
376	C₂	#1882×C₁₃₉	1	4	yes	—
377	C₂	#1885×C₁₃₉	1	1	yes	characteristic
378	C₂	#1886×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	#120
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
12. #419×C₁₃₉	C₄	semidirect
15. #391×C₁₃₉	C₄	semidirect
75. C₂×Q₈×C₁₃₉	C₄²	semidirect
189. #10957	C₁₃₉	direct (N × H)
190. C₁₃₉	#10957	direct (N × H)
202. #419	C₄×C₁₃₉	semidirect
205. #391	C₄×C₁₃₉	semidirect
265. C₂×Q₈	C₄²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#419×C₁₃₉	2
C₂×#391×C₁₃₉	2
#2274×C₁₃₉	2
C₂×#343×C₁₃₉	2
C₂×#339×C₁₃₉	2
#10957	139

Subgroups — C139×#10957 #48005553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10957 #48005553