Subgroups — C₁₃₉×#19137 #48013733

Order 35584.

662 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3160×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3101×C₁₃₉	C₂	1	2	yes	maximal
3	C₂×#436×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1695×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1693×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1691×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1564×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1542×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₁₃₉	—	2	1	no	—
10	#533×C₁₃₉	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	#500×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
13	#500×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
14	#499×C₁₃₉	—	2	1	no	—
15	#499×C₁₃₉	—	2	1	no	—
16	#498×C₁₃₉	C₂²	1	2	yes	complemented
17	#483×C₁₃₉	—	2	2	no	—
18	#476×C₁₃₉	C₂²	1	4	yes	—
19	#461×C₁₃₉	C₂²	1	4	yes	—
20	#450×C₁₃₉	—	2	2	no	—
21	C₄×SD₁₆×C₁₃₉	—	2	4	no	—
22	#436×C₁₃₉	—	2	1	no	—
23	#436×C₁₃₉	—	2	1	no	—
24	#436×C₁₃₉	C₂²	1	2	yes	—
25	#436×C₁₃₉	C₂²	1	2	yes	—
26	#431×C₁₃₉	C₂²	1	2	yes	—
27	#427×C₁₃₉	—	2	1	no	—
28	#427×C₁₃₉	—	2	1	no	—
29	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	#335×C₁₃₉	C₂²	1	2	yes	complemented
33	#334×C₁₃₉	C₂²	1	2	yes	complemented
34	#333×C₁₃₉	C₂²	1	4	yes	complemented
35	#332×C₁₃₉	C₂²	1	4	yes	complemented
36	C₂²×D₄×C₁₃₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₉	—	2	1	no	—
38	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
39	C₂×M₁₆×C₁₃₉	—	2	2	no	—
40	C₂×M₁₆×C₁₃₉	—	2	2	no	—
41	C₂×M₁₆×C₁₃₉	—	4	4	no	—
42	C₂²×C₈×C₁₃₉	—	2	1	no	—
43	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
45	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
46	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
47	#125×C₁₃₉	—	2	2	no	—
48	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
49	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
50	C₄×Q₈×C₁₃₉	—	2	2	no	—
51	C₄×Q₈×C₁₃₉	—	2	2	no	—
52	C₄×D₄×C₁₃₉	—	2	1	no	—
53	C₄×D₄×C₁₃₉	—	2	1	no	—
54	C₄×D₄×C₁₃₉	D₄	1	2	yes	—
55	C₄×D₄×C₁₃₉	C₂³	1	2	yes	—
56	#117×C₁₃₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
59	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
60	#107×C₁₃₉	—	2	1	no	—
61	#107×C₁₃₉	—	2	1	no	—
62	#107×C₁₃₉	—	2	1	no	—
63	#107×C₁₃₉	—	2	1	no	—
64	#106×C₁₃₉	—	2	2	no	—
65	#106×C₁₃₉	—	2	2	no	—
66	#106×C₁₃₉	—	2	4	no	—
67	C₄⋊C₈×C₁₃₉	—	2	1	no	—
68	C₄⋊C₈×C₁₃₉	C₂³	1	2	yes	—
69	C₄⋊C₈×C₁₃₉	C₂³	1	4	yes	—
70	#103×C₁₃₉	—	2	4	no	—
71	#102×C₁₃₉	—	2	4	no	—
72	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
73	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
74	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
75	C₄×C₈×C₁₃₉	—	2	2	no	—
76	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂⁴×C₁₃₉	—	2	1	no	—
81	C₂×Q₈×C₁₃₉	—	2	2	no	—
82	C₂×Q₈×C₁₃₉	—	2	2	no	—
83	C₂×D₄×C₁₃₉	—	2	1	no	—
84	C₂×D₄×C₁₃₉	—	4	2	no	—
85	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₃₉	—	2	1	no	—
87	C₂²×C₄×C₁₃₉	—	2	2	no	—
88	C₂²×C₄×C₁₃₉	—	2	2	no	—
89	C₂²×C₄×C₁₃₉	—	4	2	no	—
90	C₂²×C₄×C₁₃₉	—	4	2	no	—
91	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₉	#41	1	1	yes	characteristic
94	SD₁₆×C₁₃₉	—	4	8	no	—
95	M₁₆×C₁₃₉	—	4	4	no	—
96	M₁₆×C₁₃₉	—	4	4	no	—
97	C₂×C₈×C₁₃₉	—	2	2	no	—
98	C₂×C₈×C₁₃₉	—	2	4	no	—
99	C₂×C₈×C₁₃₉	—	2	2	no	—
100	C₂×C₈×C₁₃₉	—	4	2	no	—
101	C₂×C₈×C₁₃₉	SD₁₆	1	4	yes	complemented
102	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
106	C₄⋊C₄×C₁₃₉	—	2	1	no	—
107	C₄⋊C₄×C₁₃₉	—	2	2	no	—
108	C₄⋊C₄×C₁₃₉	—	2	2	no	—
109	C₄⋊C₄×C₁₃₉	—	2	2	no	—
110	C₄⋊C₄×C₁₃₉	—	2	2	no	—
111	C₄⋊C₄×C₁₃₉	—	4	2	no	—
112	C₄⋊C₄×C₁₃₉	—	4	2	no	—
113	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
114	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
115	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
116	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
117	C₄²×C₁₃₉	—	4	2	no	—
118	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₃₉	#41	1	1	yes	characteristic
121	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
122	C₂³×C₁₃₉	—	2	2	no	—
123	C₂³×C₁₃₉	—	4	2	no	—
124	C₂³×C₁₃₉	—	4	2	no	—
125	C₂³×C₁₃₉	—	4	2	no	—
126	C₂³×C₁₃₉	#121	1	1	yes	characteristic
127	Q₈×C₁₃₉	—	4	4	no	—
128	Q₈×C₁₃₉	—	8	2	no	—
129	D₄×C₁₃₉	—	2	4	no	—
130	D₄×C₁₃₉	—	4	2	no	—
131	C₂×C₄×C₁₃₉	—	2	2	no	—
132	C₂×C₄×C₁₃₉	—	2	2	no	—
133	C₂×C₄×C₁₃₉	—	4	1	no	—
134	C₂×C₄×C₁₃₉	—	4	2	no	—
135	C₂×C₄×C₁₃₉	—	4	2	no	—
136	C₂×C₄×C₁₃₉	—	4	2	no	—
137	C₂×C₄×C₁₃₉	—	4	4	no	—
138	C₂×C₄×C₁₃₉	—	4	2	no	—
139	C₂×C₄×C₁₃₉	—	4	2	no	—
140	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
144	C₂×C₄×C₁₃₉	#137	1	2	yes	—
145	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
148	C₈×C₁₃₉	—	2	1	no	—
149	C₈×C₁₃₉	—	2	1	no	—
150	C₈×C₁₃₉	—	4	2	no	—
151	C₈×C₁₃₉	—	4	4	no	—
152	C₈×C₁₃₉	C₂×SD₁₆	1	2	yes	—
153	C₈×C₁₃₉	C₂×SD₁₆	1	2	yes	—
154	C₂²×C₁₃₉	—	2	1	no	—
155	C₂²×C₁₃₉	—	2	1	no	—
156	C₂²×C₁₃₉	—	4	2	no	—
157	C₂²×C₁₃₉	—	4	2	no	—
158	C₂²×C₁₃₉	—	4	2	no	—
159	C₂²×C₁₃₉	—	8	4	no	—
160	C₂²×C₁₃₉	#461	1	2	yes	—
161	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
162	C₄×C₁₃₉	—	2	1	no	—
163	C₄×C₁₃₉	—	2	1	no	—
164	C₄×C₁₃₉	—	2	1	no	—
165	C₄×C₁₃₉	—	4	2	no	—
166	C₄×C₁₃₉	—	8	2	no	—
167	C₄×C₁₃₉	—	8	2	no	—
168	C₄×C₁₃₉	#461	1	2	yes	—
169	C₄×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
170	C₄×C₁₃₉	C₂×#137	1	1	yes	characteristic
171	C₄×C₁₃₉	#575	1	2	yes	—
172	C₂×C₁₃₉	—	2	2	no	—
173	C₂×C₁₃₉	—	8	2	no	—
174	C₂×C₁₃₉	C₂×#461	1	1	yes	characteristic
175	C₂×C₁₃₉	#3054	1	1	yes	characteristic
176	C₂×C₁₃₉	#3067	1	1	yes	characteristic
177	#19137	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₃₉	#19137	1	1	yes	characteristic, direct product factor, Sylow
179	#3160	C₂×C₁₃₉	1	1	yes	characteristic, complemented
180	#3101	C₂×C₁₃₉	1	2	yes	—
181	C₂×#436	C₂×C₁₃₉	1	1	yes	characteristic
182	#1695	C₂×C₁₃₉	1	2	yes	complemented
183	#1693	C₂×C₁₃₉	1	2	yes	complemented
184	#1691	C₂×C₁₃₉	1	4	yes	complemented
185	#1564	C₂×C₁₃₉	1	1	yes	characteristic, complemented
186	#1542	C₂×C₁₃₉	1	2	yes	complemented
187	C₂²×M₁₆	—	2	1	no	—
188	#533	C₂²×C₁₃₉	1	2	yes	—
189	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
190	#500	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
191	#500	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
192	#499	—	2	1	no	—
193	#499	—	2	1	no	—
194	#498	C₂²×C₁₃₉	1	2	yes	complemented
195	#483	—	2	2	no	—
196	#476	C₂²×C₁₃₉	1	4	yes	—
197	#461	C₂²×C₁₃₉	1	4	yes	—
198	#450	—	2	2	no	—
199	C₄×SD₁₆	—	2	4	no	—
200	#436	—	2	1	no	—
201	#436	—	2	1	no	—
202	#436	C₂²×C₁₃₉	1	2	yes	—
203	#436	C₂²×C₁₃₉	1	2	yes	—
204	#431	C₂²×C₁₃₉	1	2	yes	—
205	#427	—	2	1	no	—
206	#427	—	2	1	no	—
207	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
208	C₂×C₂²⋊C₈	—	2	1	no	—
209	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
210	#335	C₂²×C₁₃₉	1	2	yes	complemented
211	#334	C₂²×C₁₃₉	1	2	yes	complemented
212	#333	C₂²×C₁₃₉	1	4	yes	complemented
213	#332	C₂²×C₁₃₉	1	4	yes	complemented
214	C₂²×D₄	D₄×C₁₃₉	1	1	yes	characteristic
215	C₂³×C₄	—	2	1	no	—
216	C₂×SD₁₆	—	2	4	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	4	4	no	—
220	C₂²×C₈	—	2	1	no	—
221	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
222	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
223	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
224	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
225	#125	—	2	2	no	—
226	C₂²⋊Q₈	—	2	2	no	—
227	C₂²⋊Q₈	—	2	2	no	—
228	C₄×Q₈	—	2	2	no	—
229	C₄×Q₈	—	2	2	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	D₄×C₁₃₉	1	2	yes	—
233	C₄×D₄	C₂³×C₁₃₉	1	2	yes	—
234	#117	—	2	2	no	—
235	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
238	#107	—	2	1	no	—
239	#107	—	2	1	no	—
240	#107	—	2	1	no	—
241	#107	—	2	1	no	—
242	#106	—	2	2	no	—
243	#106	—	2	2	no	—
244	#106	—	2	4	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	C₂³×C₁₃₉	1	2	yes	—
247	C₄⋊C₈	C₂³×C₁₃₉	1	4	yes	—
248	#103	—	2	4	no	—
249	#102	—	2	4	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₄×C₈	—	2	2	no	—
254	C₄×C₈	D₄×C₁₃₉	1	1	yes	characteristic
255	C₄×C₈	D₄×C₁₃₉	1	1	yes	characteristic
256	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
258	C₂⁴	—	2	1	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
271	C₂²×C₄	#41×C₁₃₉	1	1	yes	characteristic
272	SD₁₆	—	4	8	no	—
273	M₁₆	—	4	4	no	—
274	M₁₆	—	4	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	4	2	no	—
279	C₂×C₈	SD₁₆×C₁₃₉	1	4	yes	complemented
280	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
281	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
282	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
283	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	4	2	no	—
296	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
297	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
298	C₄²	#41×C₁₃₉	1	1	yes	characteristic
299	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
300	C₂³	—	2	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	#121×C₁₃₉	1	1	yes	characteristic
305	Q₈	—	4	4	no	—
306	Q₈	—	8	2	no	—
307	D₄	—	2	4	no	—
308	D₄	—	4	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
319	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
320	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
321	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
322	C₂×C₄	#137×C₁₃₉	1	2	yes	—
323	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
324	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
325	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
326	C₈	—	2	1	no	—
327	C₈	—	2	1	no	—
328	C₈	—	4	2	no	—
329	C₈	—	4	4	no	—
330	C₈	C₂×SD₁₆×C₁₃₉	1	2	yes	—
331	C₈	C₂×SD₁₆×C₁₃₉	1	2	yes	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	8	4	no	—
338	C₂²	#461×C₁₃₉	1	2	yes	—
339	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	4	2	no	—
344	C₄	—	8	2	no	—
345	C₄	—	8	2	no	—
346	C₄	#461×C₁₃₉	1	2	yes	—
347	C₄	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
348	C₄	C₂×#137×C₁₃₉	1	1	yes	characteristic
349	C₄	#575×C₁₃₉	1	2	yes	—
350	C₂	—	2	2	no	—
351	C₂	—	8	2	no	—
352	C₂	C₂×#461×C₁₃₉	1	1	yes	characteristic
353	C₂	#3054×C₁₃₉	1	1	yes	characteristic
354	C₂	#3067×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₉	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂×#121
prime radical	C₂²×D₄×C₁₃₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3160×C₁₃₉	C₂	semidirect
4. #1695×C₁₃₉	C₂	semidirect
5. #1693×C₁₃₉	C₂	semidirect
6. #1691×C₁₃₉	C₂	semidirect
7. #1564×C₁₃₉	C₂	semidirect
8. #1542×C₁₃₉	C₂	semidirect
12. #500×C₁₃₉	C₂²	semidirect
13. #500×C₁₃₉	C₂²	semidirect
16. #498×C₁₃₉	C₂²	semidirect
32. #335×C₁₃₉	C₂²	semidirect
33. #334×C₁₃₉	C₂²	semidirect
34. #333×C₁₃₉	C₂²	semidirect
35. #332×C₁₃₉	C₂²	semidirect
101. C₂×C₈×C₁₃₉	SD₁₆	semidirect
177. #19137	C₁₃₉	direct (N × H)
178. C₁₃₉	#19137	direct (N × H)
179. #3160	C₂×C₁₃₉	semidirect
182. #1695	C₂×C₁₃₉	semidirect
183. #1693	C₂×C₁₃₉	semidirect
184. #1691	C₂×C₁₃₉	semidirect
185. #1564	C₂×C₁₃₉	semidirect
186. #1542	C₂×C₁₃₉	semidirect
190. #500	C₂²×C₁₃₉	semidirect
191. #500	C₂²×C₁₃₉	semidirect
194. #498	C₂²×C₁₃₉	semidirect
210. #335	C₂²×C₁₃₉	semidirect
211. #334	C₂²×C₁₃₉	semidirect
212. #333	C₂²×C₁₃₉	semidirect
213. #332	C₂²×C₁₃₉	semidirect
279. C₂×C₈	SD₁₆×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3160×C₁₃₉	2
#3101×C₁₃₉	2
C₂×#436×C₁₃₉	2
#1695×C₁₃₉	2
#1693×C₁₃₉	2
#1691×C₁₃₉	2
#1564×C₁₃₉	2
#1542×C₁₃₉	2
#19137	139

Subgroups — C139×#19137 #48013733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#19137 #48013733