Subgroups — C₁₃₉×#11011 #48005607

Order 35584.

1506 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×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	#1728×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
6	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
7	#532×C₁₃₉	—	2	8	no	—
8	C₂×C₄⋊Q₈×C₁₃₉	C₄	1	1	yes	characteristic, complemented
9	C₂×#127×C₁₃₉	C₄	1	1	yes	characteristic, complemented
10	C₂×#124×C₁₃₉	C₄	1	2	yes	complemented
11	C₂×#121×C₁₃₉	—	2	2	no	—
12	C₂×C₄×D₄×C₁₃₉	—	2	2	no	—
13	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#104×C₁₃₉	—	2	8	no	—
16	C₂×#104×C₁₃₉	—	2	8	no	—
17	C₂×#104×C₁₃₉	—	2	8	no	—
18	C₂×#95×C₁₃₉	—	2	2	no	—
19	#336×C₁₃₉	—	2	2	no	—
20	C₂×#41×C₁₃₉	—	2	4	no	—
21	C₂×#41×C₁₃₉	—	2	4	no	—
22	C₂×#41×C₁₃₉	—	2	4	no	—
23	C₂×#41×C₁₃₉	—	2	4	no	—
24	C₂×#41×C₁₃₉	—	2	4	no	—
25	C₂×#41×C₁₃₉	D₄	1	8	yes	—
26	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
27	C₂²×D₄×C₁₃₉	—	2	2	no	—
28	C₂²×D₄×C₁₃₉	—	2	2	no	—
29	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₃₉	—	2	2	no	—
31	C₂³×C₄×C₁₃₉	—	2	2	no	—
32	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₃₉	—	2	2	no	—
35	C₂×M₁₆×C₁₃₉	—	2	4	no	—
36	C₂×M₁₆×C₁₃₉	—	2	4	no	—
37	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	complemented
38	C₂²×C₈×C₁₃₉	—	2	2	no	—
39	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
40	#127×C₁₃₉	—	2	4	no	—
41	#124×C₁₃₉	—	2	4	no	—
42	#124×C₁₃₉	—	2	4	no	—
43	#121×C₁₃₉	—	2	16	no	—
44	C₄×D₄×C₁₃₉	—	2	16	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
47	C₂×C₄²×C₁₃₉	—	2	4	no	—
48	C₂×C₄²×C₁₃₉	—	2	4	no	—
49	C₂×C₄²×C₁₃₉	—	2	4	no	—
50	C₂×C₄²×C₁₃₉	—	2	2	no	—
51	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
54	C₂×C₄²×C₁₃₉	D₄	1	4	yes	complemented
55	#104×C₁₃₉	—	2	32	no	—
56	#95×C₁₃₉	—	2	8	no	—
57	C₂⁴×C₁₃₉	—	2	2	no	—
58	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
59	#41×C₁₃₉	—	2	8	no	—
60	#41×C₁₃₉	—	2	8	no	—
61	#41×C₁₃₉	—	2	8	no	—
62	#41×C₁₃₉	—	2	8	no	—
63	#41×C₁₃₉	—	4	4	no	—
64	#41×C₁₃₉	—	4	4	no	—
65	#41×C₁₃₉	—	4	4	no	—
66	#41×C₁₃₉	—	4	4	no	—
67	C₂×Q₈×C₁₃₉	—	2	2	no	—
68	C₂×Q₈×C₁₃₉	—	2	4	no	—
69	C₂×Q₈×C₁₃₉	—	2	4	no	—
70	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	4	yes	—
71	C₂×D₄×C₁₃₉	—	2	8	no	—
72	C₂×D₄×C₁₃₉	—	2	8	no	—
73	C₂×D₄×C₁₃₉	—	2	2	no	—
74	C₂×D₄×C₁₃₉	—	2	4	no	—
75	C₂×D₄×C₁₃₉	—	2	4	no	—
76	C₂×D₄×C₁₃₉	—	4	4	no	—
77	C₂×D₄×C₁₃₉	—	4	4	no	—
78	C₂×D₄×C₁₃₉	—	4	2	no	—
79	C₂×D₄×C₁₃₉	—	4	2	no	—
80	C₂×D₄×C₁₃₉	—	4	4	no	—
81	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
82	C₂²×C₄×C₁₃₉	—	2	8	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	4	no	—
85	C₂²×C₄×C₁₃₉	—	2	4	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	2	8	no	—
88	C₂²×C₄×C₁₃₉	—	4	2	no	—
89	C₂²×C₄×C₁₃₉	—	4	4	no	—
90	C₂²×C₄×C₁₃₉	—	4	2	no	—
91	C₂²×C₄×C₁₃₉	—	4	2	no	—
92	C₂²×C₄×C₁₃₉	—	4	4	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	—	4	2	no	—
95	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
103	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
104	M₁₆×C₁₃₉	—	2	8	no	—
105	M₁₆×C₁₃₉	—	4	4	no	—
106	C₂×C₈×C₁₃₉	—	2	4	no	—
107	C₂×C₈×C₁₃₉	—	4	2	no	—
108	C₂×C₈×C₁₃₉	—	4	2	no	—
109	C₄⋊C₄×C₁₃₉	—	2	8	no	—
110	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
111	C₄²×C₁₃₉	—	2	2	no	—
112	C₄²×C₁₃₉	—	2	2	no	—
113	C₄²×C₁₃₉	—	2	4	no	—
114	C₄²×C₁₃₉	—	2	8	no	—
115	C₄²×C₁₃₉	—	4	4	no	—
116	C₂³×C₁₃₉	—	2	2	no	—
117	C₂³×C₁₃₉	—	2	2	no	—
118	C₂³×C₁₃₉	—	2	4	no	—
119	C₂³×C₁₃₉	—	4	2	no	—
120	C₂³×C₁₃₉	—	4	2	no	—
121	C₂³×C₁₃₉	—	4	4	no	—
122	C₂³×C₁₃₉	—	4	4	no	—
123	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂³×C₁₃₉	#120	1	2	yes	—
125	C₂³×C₁₃₉	#121	1	2	yes	—
126	C₂³×C₁₃₉	#124	1	1	yes	characteristic
127	C₂³×C₁₃₉	#127	1	1	yes	characteristic
128	Q₈×C₁₃₉	—	2	8	no	—
129	Q₈×C₁₃₉	—	4	4	no	—
130	D₄×C₁₃₉	—	2	8	no	—
131	D₄×C₁₃₉	—	4	16	no	—
132	D₄×C₁₃₉	—	4	8	no	—
133	D₄×C₁₃₉	—	4	8	no	—
134	D₄×C₁₃₉	—	4	4	no	—
135	C₂×C₄×C₁₃₉	—	2	2	no	—
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	2	8	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	4	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	2	2	no	—
142	C₂×C₄×C₁₃₉	—	4	8	no	—
143	C₂×C₄×C₁₃₉	—	4	4	no	—
144	C₂×C₄×C₁₃₉	—	4	8	no	—
145	C₂×C₄×C₁₃₉	—	4	8	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	2	no	—
148	C₂×C₄×C₁₃₉	—	4	4	no	—
149	C₂×C₄×C₁₃₉	—	4	8	no	—
150	C₂×C₄×C₁₃₉	—	4	8	no	—
151	C₂×C₄×C₁₃₉	#104	1	4	yes	complemented
152	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₁₃₉	#120	1	4	yes	—
156	C₂×C₄×C₁₃₉	#120	1	2	yes	—
157	C₂×C₄×C₁₃₉	#121	1	4	yes	—
158	C₂×C₄×C₁₃₉	#121	1	4	yes	—
159	C₂×C₄×C₁₃₉	#121	1	2	yes	—
160	C₂×C₄×C₁₃₉	#123	1	4	yes	—
161	C₂×C₄×C₁₃₉	#124	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	#127	1	1	yes	characteristic
163	C₈×C₁₃₉	—	4	4	no	—
164	C₂²×C₁₃₉	—	2	2	no	—
165	C₂²×C₁₃₉	—	2	2	no	—
166	C₂²×C₁₃₉	—	2	2	no	—
167	C₂²×C₁₃₉	—	2	2	no	—
168	C₂²×C₁₃₉	—	2	4	no	—
169	C₂²×C₁₃₉	—	4	4	no	—
170	C₂²×C₁₃₉	—	4	8	no	—
171	C₂²×C₁₃₉	—	8	2	no	—
172	C₂²×C₁₃₉	—	8	2	no	—
173	C₂²×C₁₃₉	—	8	4	no	—
174	C₂²×C₁₃₉	#379	1	1	yes	characteristic
175	C₂²×C₁₃₉	#390	1	1	yes	characteristic
176	C₂²×C₁₃₉	#390	1	1	yes	characteristic
177	C₂²×C₁₃₉	#392	1	2	yes	—
178	C₂²×C₁₃₉	#394	1	2	yes	—
179	C₂²×C₁₃₉	C₂×#104	1	2	yes	—
180	C₂²×C₁₃₉	#421	1	2	yes	—
181	C₄×C₁₃₉	—	2	4	no	—
182	C₄×C₁₃₉	—	4	8	no	—
183	C₄×C₁₃₉	—	4	4	no	—
184	C₄×C₁₃₉	—	4	2	no	—
185	C₄×C₁₃₉	#386	1	4	yes	—
186	C₄×C₁₃₉	#392	1	2	yes	—
187	C₄×C₁₃₉	#394	1	2	yes	—
188	C₂×C₁₃₉	—	2	2	no	—
189	C₂×C₁₃₉	—	2	2	no	—
190	C₂×C₁₃₉	—	8	4	no	—
191	C₂×C₁₃₉	#1438	1	1	yes	characteristic
192	C₂×C₁₃₉	#1789	1	2	yes	—
193	C₂×C₁₃₉	#1962	1	1	yes	characteristic
194	C₂×C₁₃₉	#1963	1	1	yes	characteristic
195	C₂×C₁₃₉	#1980	1	2	yes	—
196	#11011	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₁₃₉	#11011	1	1	yes	characteristic, direct product factor, Sylow
198	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic
199	C₂²×#104	C₂×C₁₃₉	1	4	yes	complemented
200	#1728	C₂×C₁₃₉	1	1	yes	characteristic, complemented
201	C₄×#95	C₂×C₁₃₉	1	1	yes	characteristic, complemented
202	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
203	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
204	#532	—	2	8	no	—
205	C₂×C₄⋊Q₈	C₄×C₁₃₉	1	1	yes	characteristic, complemented
206	C₂×#127	C₄×C₁₃₉	1	1	yes	characteristic, complemented
207	C₂×#124	C₄×C₁₃₉	1	2	yes	complemented
208	C₂×#121	—	2	2	no	—
209	C₂×C₄×D₄	—	2	2	no	—
210	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
211	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
212	C₂×#104	—	2	8	no	—
213	C₂×#104	—	2	8	no	—
214	C₂×#104	—	2	8	no	—
215	C₂×#95	—	2	2	no	—
216	#336	—	2	2	no	—
217	C₂×#41	—	2	4	no	—
218	C₂×#41	—	2	4	no	—
219	C₂×#41	—	2	4	no	—
220	C₂×#41	—	2	4	no	—
221	C₂×#41	—	2	4	no	—
222	C₂×#41	D₄×C₁₃₉	1	8	yes	—
223	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
224	C₂²×D₄	—	2	2	no	—
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
227	C₂³×C₄	—	2	2	no	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
230	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	complemented
235	C₂²×C₈	—	2	2	no	—
236	C₄⋊Q₈	—	2	4	no	—
237	#127	—	2	4	no	—
238	#124	—	2	4	no	—
239	#124	—	2	4	no	—
240	#121	—	2	16	no	—
241	C₄×D₄	—	2	16	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	4	no	—
246	C₂×C₄²	—	2	4	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
251	C₂×C₄²	D₄×C₁₃₉	1	4	yes	complemented
252	#104	—	2	32	no	—
253	#95	—	2	8	no	—
254	C₂⁴	—	2	2	no	—
255	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
256	#41	—	2	8	no	—
257	#41	—	2	8	no	—
258	#41	—	2	8	no	—
259	#41	—	2	8	no	—
260	#41	—	4	4	no	—
261	#41	—	4	4	no	—
262	#41	—	4	4	no	—
263	#41	—	4	4	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	4	yes	—
268	C₂×D₄	—	2	8	no	—
269	C₂×D₄	—	2	8	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	4	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	4	no	—
278	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
299	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
300	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
301	M₁₆	—	2	8	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	4	2	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	8	no	—
312	C₄²	—	4	4	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
321	C₂³	#120×C₁₃₉	1	2	yes	—
322	C₂³	#121×C₁₃₉	1	2	yes	—
323	C₂³	#124×C₁₃₉	1	1	yes	characteristic
324	C₂³	#127×C₁₃₉	1	1	yes	characteristic
325	Q₈	—	2	8	no	—
326	Q₈	—	4	4	no	—
327	D₄	—	2	8	no	—
328	D₄	—	4	16	no	—
329	D₄	—	4	8	no	—
330	D₄	—	4	8	no	—
331	D₄	—	4	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	#104×C₁₃₉	1	4	yes	complemented
349	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
350	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
352	C₂×C₄	#120×C₁₃₉	1	4	yes	—
353	C₂×C₄	#120×C₁₃₉	1	2	yes	—
354	C₂×C₄	#121×C₁₃₉	1	4	yes	—
355	C₂×C₄	#121×C₁₃₉	1	4	yes	—
356	C₂×C₄	#121×C₁₃₉	1	2	yes	—
357	C₂×C₄	#123×C₁₃₉	1	4	yes	—
358	C₂×C₄	#124×C₁₃₉	1	1	yes	characteristic
359	C₂×C₄	#127×C₁₃₉	1	1	yes	characteristic
360	C₈	—	4	4	no	—
361	C₂²	—	2	4	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	8	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	4	no	—
371	C₂²	#379×C₁₃₉	1	1	yes	characteristic
372	C₂²	#390×C₁₃₉	1	1	yes	characteristic
373	C₂²	#390×C₁₃₉	1	1	yes	characteristic
374	C₂²	#392×C₁₃₉	1	2	yes	—
375	C₂²	#394×C₁₃₉	1	2	yes	—
376	C₂²	C₂×#104×C₁₃₉	1	2	yes	—
377	C₂²	#421×C₁₃₉	1	2	yes	—
378	C₄	—	2	4	no	—
379	C₄	—	4	8	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	4	no	—
382	C₄	#386×C₁₃₉	1	4	yes	—
383	C₄	#392×C₁₃₉	1	2	yes	—
384	C₄	#394×C₁₃₉	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	8	4	no	—
388	C₂	#1438×C₁₃₉	1	1	yes	characteristic
389	C₂	#1789×C₁₃₉	1	2	yes	—
390	C₂	#1962×C₁₃₉	1	1	yes	characteristic
391	C₂	#1963×C₁₃₉	1	1	yes	characteristic
392	C₂	#1980×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
prime radical	C₂×#532×C₁₃₉	C₂
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
2. C₂²×#104×C₁₃₉	C₂	semidirect
3. #1728×C₁₃₉	C₂	semidirect
4. C₄×#95×C₁₃₉	C₂	semidirect
8. C₂×C₄⋊Q₈×C₁₃₉	C₄	semidirect
9. C₂×#127×C₁₃₉	C₄	semidirect
10. C₂×#124×C₁₃₉	C₄	semidirect
37. C₂×M₁₆×C₁₃₉	D₄	semidirect
54. C₂×C₄²×C₁₃₉	D₄	semidirect
151. C₂×C₄×C₁₃₉	#104	semidirect
196. #11011	C₁₃₉	direct (N × H)
197. C₁₃₉	#11011	direct (N × H)
199. C₂²×#104	C₂×C₁₃₉	semidirect
200. #1728	C₂×C₁₃₉	semidirect
201. C₄×#95	C₂×C₁₃₉	semidirect
205. C₂×C₄⋊Q₈	C₄×C₁₃₉	semidirect
206. C₂×#127	C₄×C₁₃₉	semidirect
207. C₂×#124	C₄×C₁₃₉	semidirect
234. C₂×M₁₆	D₄×C₁₃₉	semidirect
251. C₂×C₄²	D₄×C₁₃₉	semidirect
348. C₂×C₄	#104×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₃₉	2
C₂²×#104×C₁₃₉	2
#1728×C₁₃₉	2
C₄×#95×C₁₃₉	2
#11011	139

Subgroups — C139×#11011 #48005607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#11011 #48005607