Subgroups — C₁₃₉×#10886 #48005482

Order 35584.

890 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×M₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal
4	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal
5	C₄×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
7	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₄×M₁₆×C₁₃₉	—	2	4	no	—
12	C₂×#97×C₁₃₉	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃₉	—	2	1	no	—
14	#389×C₁₃₉	C₄	1	2	yes	complemented
15	#389×C₁₃₉	C₄	1	2	yes	complemented
16	#385×C₁₃₉	—	2	2	no	—
17	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
18	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
19	C₂×#95×C₁₃₉	—	2	2	no	—
20	#339×C₁₃₉	—	2	4	no	—
21	#339×C₁₃₉	C₄	1	8	yes	complemented
22	C₂³×C₄×C₁₃₉	—	2	2	no	—
23	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
24	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
25	C₂×M₁₆×C₁₃₉	—	2	2	no	—
26	C₂×M₁₆×C₁₃₉	—	2	2	no	—
27	C₂×M₁₆×C₁₃₉	—	2	2	no	—
28	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
29	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
30	C₂×M₁₆×C₁₃₉	Q₈	1	4	yes	—
31	C₂²×C₈×C₁₃₉	—	2	2	no	—
32	#117×C₁₃₉	—	2	2	no	—
33	#117×C₁₃₉	—	2	2	no	—
34	#117×C₁₃₉	—	2	2	no	—
35	#117×C₁₃₉	C₂×C₄	1	4	yes	—
36	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
43	C₂×C₄²×C₁₃₉	—	2	2	no	—
44	C₂×C₄²×C₁₃₉	—	2	1	no	—
45	C₂×C₄²×C₁₃₉	—	2	2	no	—
46	C₂×C₄²×C₁₃₉	—	2	2	no	—
47	C₂×C₄²×C₁₃₉	—	2	2	no	—
48	C₂×C₄²×C₁₃₉	—	2	2	no	—
49	C₂×C₄²×C₁₃₉	—	2	2	no	—
50	C₂×C₄²×C₁₃₉	—	2	1	no	—
51	C₂×C₄²×C₁₃₉	—	2	2	no	—
52	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
56	#97×C₁₃₉	—	2	4	no	—
57	C₄×C₈×C₁₃₉	—	2	4	no	—
58	#95×C₁₃₉	—	2	8	no	—
59	#95×C₁₃₉	—	2	2	no	—
60	#95×C₁₃₉	—	2	2	no	—
61	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃₉	—	2	8	no	—
63	C₂²×C₄×C₁₃₉	—	2	1	no	—
64	C₂²×C₄×C₁₃₉	—	2	1	no	—
65	C₂²×C₄×C₁₃₉	—	2	4	no	—
66	C₂²×C₄×C₁₃₉	—	2	4	no	—
67	C₂²×C₄×C₁₃₉	—	2	4	no	—
68	C₂²×C₄×C₁₃₉	—	2	2	no	—
69	C₂²×C₄×C₁₃₉	—	4	2	no	—
70	C₂²×C₄×C₁₃₉	—	4	4	no	—
71	C₂²×C₄×C₁₃₉	—	4	2	no	—
72	C₂²×C₄×C₁₃₉	—	4	2	no	—
73	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
81	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
82	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
83	M₁₆×C₁₃₉	—	2	4	no	—
84	M₁₆×C₁₃₉	—	2	4	no	—
85	M₁₆×C₁₃₉	—	2	4	no	—
86	M₁₆×C₁₃₉	C₄⋊C₄	1	8	yes	complemented
87	C₂×C₈×C₁₃₉	—	2	4	no	—
88	C₂×C₈×C₁₃₉	—	2	4	no	—
89	C₂×C₈×C₁₃₉	—	2	4	no	—
90	C₄⋊C₄×C₁₃₉	—	2	1	no	—
91	C₄⋊C₄×C₁₃₉	—	2	1	no	—
92	C₄⋊C₄×C₁₃₉	—	2	4	no	—
93	C₄⋊C₄×C₁₃₉	—	4	4	no	—
94	C₄⋊C₄×C₁₃₉	—	4	4	no	—
95	C₄⋊C₄×C₁₃₉	C₄²	1	2	yes	—
96	C₄⋊C₄×C₁₃₉	C₄²	1	2	yes	—
97	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
98	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
99	C₄²×C₁₃₉	—	2	4	no	—
100	C₄²×C₁₃₉	—	2	4	no	—
101	C₄²×C₁₃₉	—	2	1	no	—
102	C₄²×C₁₃₉	—	2	1	no	—
103	C₄²×C₁₃₉	—	2	1	no	—
104	C₄²×C₁₃₉	—	2	1	no	—
105	C₄²×C₁₃₉	—	2	4	no	—
106	C₄²×C₁₃₉	—	2	4	no	—
107	C₄²×C₁₃₉	—	4	1	no	—
108	C₄²×C₁₃₉	—	4	2	no	—
109	C₄²×C₁₃₉	—	4	1	no	—
110	C₄²×C₁₃₉	—	4	2	no	—
111	C₂³×C₁₃₉	—	2	2	no	—
112	C₂³×C₁₃₉	—	2	2	no	—
113	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
115	C₂³×C₁₃₉	#121	1	2	yes	—
116	C₂³×C₁₃₉	#124	1	1	yes	characteristic
117	C₂³×C₁₃₉	C₄⋊Q₈	1	1	yes	characteristic
118	C₂×C₄×C₁₃₉	—	2	2	no	—
119	C₂×C₄×C₁₃₉	—	2	2	no	—
120	C₂×C₄×C₁₃₉	—	2	8	no	—
121	C₂×C₄×C₁₃₉	—	2	2	no	—
122	C₂×C₄×C₁₃₉	—	2	2	no	—
123	C₂×C₄×C₁₃₉	—	2	2	no	—
124	C₂×C₄×C₁₃₉	—	2	2	no	—
125	C₂×C₄×C₁₃₉	—	2	2	no	—
126	C₂×C₄×C₁₃₉	—	4	8	no	—
127	C₂×C₄×C₁₃₉	—	4	8	no	—
128	C₂×C₄×C₁₃₉	—	4	8	no	—
129	C₂×C₄×C₁₃₉	—	4	4	no	—
130	C₂×C₄×C₁₃₉	—	4	4	no	—
131	C₂×C₄×C₁₃₉	—	4	2	no	—
132	C₂×C₄×C₁₃₉	—	4	2	no	—
133	C₂×C₄×C₁₃₉	—	4	2	no	—
134	C₂×C₄×C₁₃₉	—	4	2	no	—
135	C₂×C₄×C₁₃₉	—	4	2	no	—
136	C₂×C₄×C₁₃₉	#104	1	4	yes	—
137	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₃₉	#117	1	2	yes	—
140	C₂×C₄×C₁₃₉	#117	1	1	yes	characteristic
141	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₃₉	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₁₃₉	C₄×Q₈	1	2	yes	—
146	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
148	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₁₃₉	#123	1	2	yes	—
150	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₁₃₉	#125	1	2	yes	—
152	C₂×C₄×C₁₃₉	#126	1	2	yes	—
153	C₈×C₁₃₉	—	2	8	no	—
154	C₂²×C₁₃₉	—	2	4	no	—
155	C₂²×C₁₃₉	—	2	2	no	—
156	C₂²×C₁₃₉	—	2	2	no	—
157	C₂²×C₁₃₉	—	2	2	no	—
158	C₂²×C₁₃₉	—	2	2	no	—
159	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₁₃₉	#386	1	1	yes	characteristic
161	C₂²×C₁₃₉	#388	1	2	yes	—
162	C₂²×C₁₃₉	#389	1	2	yes	—
163	C₂²×C₁₃₉	#391	1	1	yes	characteristic
164	C₂²×C₁₃₉	C₂×#104	1	2	yes	—
165	C₂²×C₁₃₉	#421	1	2	yes	—
166	C₄×C₁₃₉	—	2	4	no	—
167	C₄×C₁₃₉	—	4	8	no	—
168	C₄×C₁₃₉	—	4	2	no	—
169	C₄×C₁₃₉	—	4	2	no	—
170	C₄×C₁₃₉	—	4	2	no	—
171	C₄×C₁₃₉	—	8	2	no	—
172	C₄×C₁₃₉	C₄×C₄⋊C₄	1	2	yes	—
173	C₄×C₁₃₉	#385	1	2	yes	—
174	C₄×C₁₃₉	#387	1	2	yes	—
175	C₄×C₁₃₉	#387	1	2	yes	—
176	C₂×C₁₃₉	—	2	2	no	—
177	C₂×C₁₃₉	—	2	2	no	—
178	C₂×C₁₃₉	#1436	1	1	yes	characteristic
179	C₂×C₁₃₉	C₄×#104	1	1	yes	characteristic
180	C₂×C₁₃₉	#1759	1	1	yes	characteristic
181	C₂×C₁₃₉	#1871	1	2	yes	—
182	C₂×C₁₃₉	#1986	1	2	yes	—
183	#10886	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₉	#10886	1	1	yes	characteristic, direct product factor, Sylow
185	C₂×C₄×M₁₆	C₂×C₁₃₉	1	1	yes	characteristic
186	#2296	C₂×C₁₃₉	1	1	yes	characteristic
187	C₂×#339	C₂×C₁₃₉	1	2	yes	—
188	C₂×#339	C₂×C₁₃₉	1	2	yes	—
189	C₄×#95	C₂×C₁₃₉	1	1	yes	characteristic
190	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
191	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
192	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
193	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
194	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
195	C₄×M₁₆	—	2	4	no	—
196	C₂×#97	—	2	1	no	—
197	C₂×C₄×C₈	—	2	1	no	—
198	#389	C₄×C₁₃₉	1	2	yes	complemented
199	#389	C₄×C₁₃₉	1	2	yes	complemented
200	#385	—	2	2	no	—
201	C₄×C₄⋊C₄	—	2	1	no	—
202	C₄×C₄⋊C₄	—	2	1	no	—
203	C₂×#95	—	2	2	no	—
204	#339	—	2	4	no	—
205	#339	C₄×C₁₃₉	1	8	yes	complemented
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
208	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
213	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
214	C₂×M₁₆	Q₈×C₁₃₉	1	4	yes	—
215	C₂²×C₈	—	2	2	no	—
216	#117	—	2	2	no	—
217	#117	—	2	2	no	—
218	#117	—	2	2	no	—
219	#117	C₂×C₄×C₁₃₉	1	4	yes	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
225	C₂×C₂²⋊C₄	—	2	1	no	—
226	C₂×C₂²⋊C₄	—	2	1	no	—
227	C₂×C₄²	—	2	1	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
237	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
238	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
240	#97	—	2	4	no	—
241	C₄×C₈	—	2	4	no	—
242	#95	—	2	8	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
258	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
264	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
265	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
266	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
267	M₁₆	—	2	4	no	—
268	M₁₆	—	2	4	no	—
269	M₁₆	—	2	4	no	—
270	M₁₆	C₄⋊C₄×C₁₃₉	1	8	yes	complemented
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	C₄²×C₁₃₉	1	2	yes	—
280	C₄⋊C₄	C₄²×C₁₃₉	1	2	yes	—
281	C₂²⋊C₄	—	2	4	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₄²	—	2	4	no	—
284	C₄²	—	2	4	no	—
285	C₄²	—	2	1	no	—
286	C₄²	—	2	1	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	4	no	—
290	C₄²	—	2	4	no	—
291	C₄²	—	4	1	no	—
292	C₄²	—	4	2	no	—
293	C₄²	—	4	1	no	—
294	C₄²	—	4	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
298	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
299	C₂³	#121×C₁₃₉	1	2	yes	—
300	C₂³	#124×C₁₃₉	1	1	yes	characteristic
301	C₂³	C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	8	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	#104×C₁₃₉	1	4	yes	—
321	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
322	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
323	C₂×C₄	#117×C₁₃₉	1	2	yes	—
324	C₂×C₄	#117×C₁₃₉	1	1	yes	characteristic
325	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
326	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
327	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
328	C₂×C₄	C₄×Q₈×C₁₃₉	1	2	yes	—
329	C₂×C₄	C₄×Q₈×C₁₃₉	1	2	yes	—
330	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
331	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
332	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
333	C₂×C₄	#123×C₁₃₉	1	2	yes	—
334	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
335	C₂×C₄	#125×C₁₃₉	1	2	yes	—
336	C₂×C₄	#126×C₁₃₉	1	2	yes	—
337	C₈	—	2	8	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
344	C₂²	#386×C₁₃₉	1	1	yes	characteristic
345	C₂²	#388×C₁₃₉	1	2	yes	—
346	C₂²	#389×C₁₃₉	1	2	yes	—
347	C₂²	#391×C₁₃₉	1	1	yes	characteristic
348	C₂²	C₂×#104×C₁₃₉	1	2	yes	—
349	C₂²	#421×C₁₃₉	1	2	yes	—
350	C₄	—	2	4	no	—
351	C₄	—	4	8	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	8	2	no	—
356	C₄	C₄×C₄⋊C₄×C₁₃₉	1	2	yes	—
357	C₄	#385×C₁₃₉	1	2	yes	—
358	C₄	#387×C₁₃₉	1	2	yes	—
359	C₄	#387×C₁₃₉	1	2	yes	—
360	C₂	—	2	2	no	—
361	C₂	—	2	2	no	—
362	C₂	#1436×C₁₃₉	1	1	yes	characteristic
363	C₂	C₄×#104×C₁₃₉	1	1	yes	characteristic
364	C₂	#1759×C₁₃₉	1	1	yes	characteristic
365	C₂	#1871×C₁₃₉	1	2	yes	—
366	C₂	#1986×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₃₉	C₂×D₄
LCS	G ▷ C₂×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
14. #389×C₁₃₉	C₄	semidirect
15. #389×C₁₃₉	C₄	semidirect
21. #339×C₁₃₉	C₄	semidirect
86. M₁₆×C₁₃₉	C₄⋊C₄	semidirect
183. #10886	C₁₃₉	direct (N × H)
184. C₁₃₉	#10886	direct (N × H)
198. #389	C₄×C₁₃₉	semidirect
199. #389	C₄×C₁₃₉	semidirect
205. #339	C₄×C₁₃₉	semidirect
270. M₁₆	C₄⋊C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×M₁₆×C₁₃₉	2
#2296×C₁₃₉	2
C₂×#339×C₁₃₉	2
C₄×#95×C₁₃₉	2
#10886	139

Subgroups — C139×#10886 #48005482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10886 #48005482