Subgroups — C₁₃₉×#19146 #48013742

Order 35584.

694 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3147×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#3103×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#446×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1690×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1688×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1686×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1564×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1540×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₁₃₉	—	2	1	no	—
10	C₂×#135×C₁₃₉	—	2	1	no	—
11	#532×C₁₃₉	C₂²	1	2	yes	—
12	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	#495×C₁₃₉	—	2	1	no	—
14	#495×C₁₃₉	—	2	1	no	—
15	#494×C₁₃₉	C₂²	1	1	yes	characteristic
16	#493×C₁₃₉	C₂²	1	1	yes	characteristic
17	#492×C₁₃₉	C₂²	1	2	yes	—
18	#481×C₁₃₉	—	2	2	no	—
19	#475×C₁₃₉	C₂²	1	4	yes	—
20	#460×C₁₃₉	C₂²	1	4	yes	—
21	#448×C₁₃₉	—	2	2	no	—
22	#446×C₁₃₉	—	2	1	no	—
23	#446×C₁₃₉	—	2	1	no	—
24	#446×C₁₃₉	C₂²	1	2	yes	—
25	#446×C₁₃₉	C₂²	1	2	yes	—
26	C₄×SD₁₆×C₁₃₉	—	2	4	no	—
27	#431×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₁₃₉	—	2	1	no	—
29	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#97×C₁₃₉	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	#335×C₁₃₉	C₂²	1	2	yes	—
33	#334×C₁₃₉	C₂²	1	2	yes	—
34	#332×C₁₃₉	C₂²	1	4	yes	—
35	#331×C₁₃₉	C₂²	1	4	yes	—
36	C₂×#41×C₁₃₉	—	2	2	no	—
37	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
38	#135×C₁₃₉	—	4	4	no	—
39	#135×C₁₃₉	—	4	4	no	—
40	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
41	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
42	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
43	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
44	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
45	C₂×D₈×C₁₃₉	—	2	1	no	—
46	C₂×D₈×C₁₃₉	—	2	1	no	—
47	C₂²×C₈×C₁₃₉	—	2	1	no	—
48	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
51	#127×C₁₃₉	C₂³	1	2	yes	—
52	#124×C₁₃₉	—	2	2	no	—
53	#121×C₁₃₉	—	2	2	no	—
54	#121×C₁₃₉	—	2	2	no	—
55	C₄×Q₈×C₁₃₉	—	2	1	no	—
56	C₄×Q₈×C₁₃₉	—	2	1	no	—
57	C₄×Q₈×C₁₃₉	D₄	1	2	yes	—
58	C₄×Q₈×C₁₃₉	C₂³	1	2	yes	—
59	C₄×D₄×C₁₃₉	—	2	2	no	—
60	C₄×D₄×C₁₃₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	—	2	1	no	—
64	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
65	#106×C₁₃₉	—	2	4	no	—
66	C₄⋊C₈×C₁₃₉	—	2	2	no	—
67	C₄⋊C₈×C₁₃₉	—	2	2	no	—
68	C₄⋊C₈×C₁₃₉	—	2	1	no	—
69	C₄⋊C₈×C₁₃₉	C₂³	1	2	yes	—
70	C₄⋊C₈×C₁₃₉	C₂³	1	4	yes	—
71	#103×C₁₃₉	—	2	4	no	—
72	#102×C₁₃₉	—	2	4	no	—
73	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
74	#97×C₁₃₉	—	2	2	no	—
75	#97×C₁₃₉	—	2	2	no	—
76	C₄×C₈×C₁₃₉	—	2	2	no	—
77	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
81	#41×C₁₃₉	—	4	4	no	—
82	#41×C₁₃₉	—	4	4	no	—
83	C₂×Q₈×C₁₃₉	—	2	1	no	—
84	C₂×Q₈×C₁₃₉	—	2	2	no	—
85	C₂×Q₈×C₁₃₉	—	4	2	no	—
86	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₁₃₉	—	2	2	no	—
88	C₂×D₄×C₁₃₉	—	2	2	no	—
89	C₂×D₄×C₁₃₉	—	2	2	no	—
90	C₂×D₄×C₁₃₉	—	4	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	1	no	—
92	C₂²×C₄×C₁₃₉	—	2	1	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₉	#41	1	1	yes	characteristic
97	Q₁₆×C₁₃₉	—	4	2	no	—
98	Q₁₆×C₁₃₉	—	4	2	no	—
99	SD₁₆×C₁₃₉	—	4	4	no	—
100	SD₁₆×C₁₃₉	—	4	8	no	—
101	SD₁₆×C₁₃₉	—	4	4	no	—
102	D₈×C₁₃₉	—	4	2	no	—
103	D₈×C₁₃₉	—	4	2	no	—
104	C₂×C₈×C₁₃₉	—	2	2	no	—
105	C₂×C₈×C₁₃₉	—	2	4	no	—
106	C₂×C₈×C₁₃₉	—	2	2	no	—
107	C₂×C₈×C₁₃₉	—	4	2	no	—
108	C₂×C₈×C₁₃₉	SD₁₆	1	4	yes	complemented
109	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₄⋊C₄×C₁₃₉	—	2	2	no	—
114	C₄⋊C₄×C₁₃₉	—	2	1	no	—
115	C₄⋊C₄×C₁₃₉	—	2	2	no	—
116	C₄⋊C₄×C₁₃₉	—	2	2	no	—
117	C₄⋊C₄×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
119	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
121	C₄²×C₁₃₉	—	2	2	no	—
122	C₄²×C₁₃₉	—	2	2	no	—
123	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃₉	#41	1	1	yes	characteristic
126	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
127	C₂³×C₁₃₉	—	4	2	no	—
128	C₂³×C₁₃₉	#121	1	1	yes	characteristic
129	Q₈×C₁₃₉	—	2	4	no	—
130	Q₈×C₁₃₉	—	4	2	no	—
131	Q₈×C₁₃₉	—	4	2	no	—
132	Q₈×C₁₃₉	—	4	2	no	—
133	D₄×C₁₃₉	—	4	2	no	—
134	D₄×C₁₃₉	—	4	2	no	—
135	D₄×C₁₃₉	—	4	4	no	—
136	D₄×C₁₃₉	—	8	2	no	—
137	D₄×C₁₃₉	—	8	4	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	—	4	1	no	—
142	C₂×C₄×C₁₃₉	—	4	2	no	—
143	C₂×C₄×C₁₃₉	—	4	2	no	—
144	C₂×C₄×C₁₃₉	—	4	2	no	—
145	C₂×C₄×C₁₃₉	—	8	4	no	—
146	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
150	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
154	C₈×C₁₃₉	—	2	1	no	—
155	C₈×C₁₃₉	—	2	1	no	—
156	C₈×C₁₃₉	—	4	2	no	—
157	C₈×C₁₃₉	—	4	4	no	—
158	C₈×C₁₃₉	C₂×SD₁₆	1	2	yes	—
159	C₈×C₁₃₉	C₂×SD₁₆	1	2	yes	—
160	C₂²×C₁₃₉	—	2	1	no	—
161	C₂²×C₁₃₉	—	2	1	no	—
162	C₂²×C₁₃₉	—	8	2	no	—
163	C₂²×C₁₃₉	—	8	2	no	—
164	C₂²×C₁₃₉	—	8	2	no	—
165	C₂²×C₁₃₉	#460	1	2	yes	—
166	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
167	C₄×C₁₃₉	—	2	1	no	—
168	C₄×C₁₃₉	—	2	1	no	—
169	C₄×C₁₃₉	—	2	1	no	—
170	C₄×C₁₃₉	—	4	2	no	—
171	C₄×C₁₃₉	—	4	2	no	—
172	C₄×C₁₃₉	—	8	2	no	—
173	C₄×C₁₃₉	#460	1	2	yes	—
174	C₄×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
175	C₄×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₄×C₁₃₉	#575	1	2	yes	—
177	C₂×C₁₃₉	—	2	2	no	—
178	C₂×C₁₃₉	—	16	2	no	—
179	C₂×C₁₃₉	C₂×#460	1	1	yes	characteristic
180	C₂×C₁₃₉	#3054	1	1	yes	characteristic
181	C₂×C₁₃₉	#3067	1	1	yes	characteristic
182	#19146	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₁₃₉	#19146	1	1	yes	characteristic, direct product factor, Sylow
184	#3147	C₂×C₁₃₉	1	1	yes	characteristic
185	#3103	C₂×C₁₃₉	1	2	yes	complemented
186	C₂×#446	C₂×C₁₃₉	1	1	yes	characteristic, complemented
187	#1690	C₂×C₁₃₉	1	2	yes	complemented
188	#1688	C₂×C₁₃₉	1	2	yes	complemented
189	#1686	C₂×C₁₃₉	1	4	yes	complemented
190	#1564	C₂×C₁₃₉	1	1	yes	characteristic, complemented
191	#1540	C₂×C₁₃₉	1	2	yes	complemented
192	C₂×#135	—	2	1	no	—
193	C₂×#135	—	2	1	no	—
194	#532	C₂²×C₁₃₉	1	2	yes	—
195	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
196	#495	—	2	1	no	—
197	#495	—	2	1	no	—
198	#494	C₂²×C₁₃₉	1	1	yes	characteristic
199	#493	C₂²×C₁₃₉	1	1	yes	characteristic
200	#492	C₂²×C₁₃₉	1	2	yes	—
201	#481	—	2	2	no	—
202	#475	C₂²×C₁₃₉	1	4	yes	—
203	#460	C₂²×C₁₃₉	1	4	yes	—
204	#448	—	2	2	no	—
205	#446	—	2	1	no	—
206	#446	—	2	1	no	—
207	#446	C₂²×C₁₃₉	1	2	yes	—
208	#446	C₂²×C₁₃₉	1	2	yes	—
209	C₄×SD₁₆	—	2	4	no	—
210	#431	C₂²×C₁₃₉	1	2	yes	—
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
213	C₂×#97	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
215	#335	C₂²×C₁₃₉	1	2	yes	—
216	#334	C₂²×C₁₃₉	1	2	yes	—
217	#332	C₂²×C₁₃₉	1	4	yes	—
218	#331	C₂²×C₁₃₉	1	4	yes	—
219	C₂×#41	—	2	2	no	—
220	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
221	#135	—	4	4	no	—
222	#135	—	4	4	no	—
223	C₂×Q₁₆	—	2	1	no	—
224	C₂×Q₁₆	—	2	1	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×SD₁₆	—	2	2	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
232	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
233	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
234	#127	C₂³×C₁₃₉	1	2	yes	—
235	#124	—	2	2	no	—
236	#121	—	2	2	no	—
237	#121	—	2	2	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	D₄×C₁₃₉	1	2	yes	—
241	C₄×Q₈	C₂³×C₁₃₉	1	2	yes	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
248	#106	—	2	4	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	C₂³×C₁₃₉	1	2	yes	—
253	C₄⋊C₈	C₂³×C₁₃₉	1	4	yes	—
254	#103	—	2	4	no	—
255	#102	—	2	4	no	—
256	C₂²⋊C₈	—	2	2	no	—
257	#97	—	2	2	no	—
258	#97	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	D₄×C₁₃₉	1	1	yes	characteristic
261	C₄×C₈	D₄×C₁₃₉	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
264	#41	—	4	4	no	—
265	#41	—	4	4	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
279	C₂²×C₄	#41×C₁₃₉	1	1	yes	characteristic
280	Q₁₆	—	4	2	no	—
281	Q₁₆	—	4	2	no	—
282	SD₁₆	—	4	4	no	—
283	SD₁₆	—	4	8	no	—
284	SD₁₆	—	4	4	no	—
285	D₈	—	4	2	no	—
286	D₈	—	4	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	SD₁₆×C₁₃₉	1	4	yes	complemented
292	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
307	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
308	C₄²	#41×C₁₃₉	1	1	yes	characteristic
309	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
310	C₂³	—	4	2	no	—
311	C₂³	#121×C₁₃₉	1	1	yes	characteristic
312	Q₈	—	2	4	no	—
313	Q₈	—	4	2	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	4	no	—
319	D₄	—	8	2	no	—
320	D₄	—	8	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	4	no	—
329	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
331	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
332	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
333	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
334	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	2	1	no	—
339	C₈	—	4	2	no	—
340	C₈	—	4	4	no	—
341	C₈	C₂×SD₁₆×C₁₃₉	1	2	yes	—
342	C₈	C₂×SD₁₆×C₁₃₉	1	2	yes	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	#460×C₁₃₉	1	2	yes	—
349	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	8	2	no	—
356	C₄	#460×C₁₃₉	1	2	yes	—
357	C₄	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
358	C₄	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
359	C₄	#575×C₁₃₉	1	2	yes	—
360	C₂	—	2	2	no	—
361	C₂	—	16	2	no	—
362	C₂	C₂×#460×C₁₃₉	1	1	yes	characteristic
363	C₂	#3054×C₁₃₉	1	1	yes	characteristic
364	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	#3147×C₁₃₉	C₂
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
2. #3103×C₁₃₉	C₂	semidirect
3. C₂×#446×C₁₃₉	C₂	semidirect
4. #1690×C₁₃₉	C₂	semidirect
5. #1688×C₁₃₉	C₂	semidirect
6. #1686×C₁₃₉	C₂	semidirect
7. #1564×C₁₃₉	C₂	semidirect
8. #1540×C₁₃₉	C₂	semidirect
108. C₂×C₈×C₁₃₉	SD₁₆	semidirect
182. #19146	C₁₃₉	direct (N × H)
183. C₁₃₉	#19146	direct (N × H)
185. #3103	C₂×C₁₃₉	semidirect
186. C₂×#446	C₂×C₁₃₉	semidirect
187. #1690	C₂×C₁₃₉	semidirect
188. #1688	C₂×C₁₃₉	semidirect
189. #1686	C₂×C₁₃₉	semidirect
190. #1564	C₂×C₁₃₉	semidirect
191. #1540	C₂×C₁₃₉	semidirect
291. 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
#3147×C₁₃₉	2
#3103×C₁₃₉	2
C₂×#446×C₁₃₉	2
#1690×C₁₃₉	2
#1688×C₁₃₉	2
#1686×C₁₃₉	2
#1564×C₁₃₉	2
#1540×C₁₃₉	2
#19146	139

Subgroups — C139×#19146 #48013742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#19146 #48013742