Subgroups — C₁₃₉×#33779 #48028375

Order 35584.

642 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	#3169×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#495×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2250×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2243×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2210×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2185×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2184×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2163×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₁₃₉	—	2	1	no	—
11	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
12	#532×C₁₃₉	—	2	1	no	—
13	C₂×#124×C₁₃₉	—	2	1	no	—
14	C₂×SD₃₂×C₁₃₉	C₂²	1	4	yes	complemented
15	C₂×D₁₆×C₁₃₉	C₂²	1	4	yes	—
16	#500×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
17	#495×C₁₃₉	—	2	1	no	—
18	#495×C₁₃₉	—	2	1	no	—
19	#495×C₁₃₉	C₂²	1	2	yes	—
20	#495×C₁₃₉	C₂²	1	2	yes	—
21	#493×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	#486×C₁₃₉	—	2	1	no	—
23	#466×C₁₃₉	—	2	1	no	—
24	#466×C₁₃₉	C₂²	1	2	yes	—
25	C₄×D₈×C₁₃₉	—	2	1	no	—
26	C₄×D₈×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₄⋊C₁₆×C₁₃₉	C₂²	1	2	yes	complemented
29	#358×C₁₃₉	C₂²	1	4	yes	complemented
30	#357×C₁₃₉	C₂²	1	4	yes	—
31	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
32	#346×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×#41×C₁₃₉	—	4	1	no	—
34	C₂²×Q₈×C₁₃₉	—	2	1	no	—
35	C₂²×D₄×C₁₃₉	—	2	1	no	—
36	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
37	C₂×Q₁₆×C₁₃₉	—	4	2	no	—
38	C₂×Q₁₆×C₁₃₉	C₂³	1	2	yes	—
39	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
40	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
41	C₂×SD₁₆×C₁₃₉	—	4	4	no	—
42	C₂×D₈×C₁₃₉	—	2	1	no	—
43	C₂×D₈×C₁₃₉	—	2	1	no	—
44	C₂×D₈×C₁₃₉	—	4	2	no	—
45	C₂×D₈×C₁₃₉	C₂³	1	2	yes	—
46	C₂×D₈×C₁₃₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
50	#127×C₁₃₉	—	2	1	no	—
51	#124×C₁₃₉	—	2	2	no	—
52	#124×C₁₃₉	—	2	2	no	—
53	#124×C₁₃₉	—	4	1	no	—
54	#124×C₁₃₉	—	4	1	no	—
55	#124×C₁₃₉	—	4	1	no	—
56	#121×C₁₃₉	—	2	2	no	—
57	#121×C₁₃₉	—	4	1	no	—
58	C₄×D₄×C₁₃₉	—	2	2	no	—
59	C₄×D₄×C₁₃₉	—	4	1	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	4	1	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	4	1	no	—
62	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
63	SD₃₂×C₁₃₉	—	4	4	no	—
64	D₁₆×C₁₃₉	—	4	4	no	—
65	C₂×C₁₆×C₁₃₉	C₂³	1	4	yes	—
66	#107×C₁₃₉	—	2	1	no	—
67	#107×C₁₃₉	C₂³	1	2	yes	—
68	#102×C₁₃₉	—	2	2	no	—
69	#102×C₁₃₉	—	2	2	no	—
70	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
71	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
72	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂⁴×C₁₃₉	—	4	1	no	—
75	#41×C₁₃₉	—	8	4	no	—
76	C₂×Q₈×C₁₃₉	—	2	2	no	—
77	C₂×Q₈×C₁₃₉	—	4	2	no	—
78	C₂×Q₈×C₁₃₉	—	4	2	no	—
79	C₂×Q₈×C₁₃₉	—	4	1	no	—
80	C₂×Q₈×C₁₃₉	—	4	1	no	—
81	C₂×D₄×C₁₃₉	—	2	2	no	—
82	C₂×D₄×C₁₃₉	—	2	2	no	—
83	C₂×D₄×C₁₃₉	—	4	2	no	—
84	C₂×D₄×C₁₃₉	—	4	2	no	—
85	C₂×D₄×C₁₃₉	—	4	2	no	—
86	C₂×D₄×C₁₃₉	—	4	1	no	—
87	C₂×D₄×C₁₃₉	—	4	1	no	—
88	C₂×D₄×C₁₃₉	—	4	1	no	—
89	C₂²×C₄×C₁₃₉	—	4	1	no	—
90	C₂²×C₄×C₁₃₉	—	4	2	no	—
91	C₂²×C₄×C₁₃₉	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	D₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
94	Q₁₆×C₁₃₉	—	2	4	no	—
95	Q₁₆×C₁₃₉	—	4	2	no	—
96	SD₁₆×C₁₃₉	—	4	4	no	—
97	SD₁₆×C₁₃₉	—	4	4	no	—
98	D₈×C₁₃₉	—	2	4	no	—
99	D₈×C₁₃₉	—	2	4	no	—
100	D₈×C₁₃₉	—	4	2	no	—
101	D₈×C₁₃₉	—	4	2	no	—
102	C₂×C₈×C₁₃₉	—	2	2	no	—
103	C₂×C₈×C₁₃₉	—	2	2	no	—
104	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₁₃₉	—	2	2	no	—
109	C₄⋊C₄×C₁₃₉	—	4	1	no	—
110	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
111	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
114	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
115	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
116	C₄²×C₁₃₉	D₈	1	1	yes	characteristic
117	C₄²×C₁₃₉	D₈	1	1	yes	characteristic
118	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
120	C₁₆×C₁₃₉	—	2	4	no	—
121	C₂³×C₁₃₉	—	4	2	no	—
122	C₂³×C₁₃₉	—	4	2	no	—
123	C₂³×C₁₃₉	—	8	2	no	—
124	C₂³×C₁₃₉	—	8	2	no	—
125	C₂³×C₁₃₉	—	8	2	no	—
126	C₂³×C₁₃₉	C₂×D₈	1	1	yes	characteristic
127	Q₈×C₁₃₉	—	4	2	no	—
128	Q₈×C₁₃₉	—	4	2	no	—
129	Q₈×C₁₃₉	—	8	2	no	—
130	Q₈×C₁₃₉	—	8	2	no	—
131	D₄×C₁₃₉	—	4	2	no	—
132	D₄×C₁₃₉	—	4	2	no	—
133	D₄×C₁₃₉	—	4	2	no	—
134	D₄×C₁₃₉	—	4	2	no	—
135	D₄×C₁₃₉	—	8	2	no	—
136	D₄×C₁₃₉	—	8	2	no	—
137	D₄×C₁₃₉	—	8	2	no	—
138	D₄×C₁₃₉	—	8	4	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	2	1	no	—
141	C₂×C₄×C₁₃₉	—	2	1	no	—
142	C₂×C₄×C₁₃₉	—	4	1	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	—	8	2	no	—
147	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
153	C₈×C₁₃₉	—	2	1	no	—
154	C₈×C₁₃₉	—	2	1	no	—
155	C₈×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
156	C₈×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
157	C₂²×C₁₃₉	—	2	1	no	—
158	C₂²×C₁₃₉	—	2	1	no	—
159	C₂²×C₁₃₉	—	8	2	no	—
160	C₂²×C₁₃₉	—	8	2	no	—
161	C₂²×C₁₃₉	—	8	2	no	—
162	C₂²×C₁₃₉	—	8	2	no	—
163	C₂²×C₁₃₉	—	8	2	no	—
164	C₂²×C₁₃₉	—	8	2	no	—
165	C₂²×C₁₃₉	—	16	4	no	—
166	C₂²×C₁₃₉	#509	1	2	yes	—
167	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
168	C₄×C₁₃₉	—	2	1	no	—
169	C₄×C₁₃₉	—	2	1	no	—
170	C₄×C₁₃₉	—	2	1	no	—
171	C₄×C₁₃₉	—	2	1	no	—
172	C₄×C₁₃₉	—	2	1	no	—
173	C₄×C₁₃₉	—	8	2	no	—
174	C₄×C₁₃₉	—	8	2	no	—
175	C₄×C₁₃₉	#535	1	1	yes	characteristic
176	C₄×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₁₃₉	—	2	2	no	—
178	C₂×C₁₃₉	—	16	2	no	—
179	C₂×C₁₃₉	—	16	2	no	—
180	C₂×C₁₃₉	#3205	1	1	yes	characteristic
181	C₂×C₁₃₉	C₂×#509	1	1	yes	characteristic
182	C₂×C₁₃₉	#3414	1	1	yes	characteristic
183	#33779	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₉	#33779	1	1	yes	characteristic, direct product factor, Sylow
185	#3169	C₂×C₁₃₉	1	1	yes	characteristic, complemented
186	C₂×#495	C₂×C₁₃₉	1	1	yes	characteristic, complemented
187	#2250	C₂×C₁₃₉	1	2	yes	complemented
188	#2243	C₂×C₁₃₉	1	2	yes	complemented
189	#2210	C₂×C₁₃₉	1	4	yes	complemented
190	#2185	C₂×C₁₃₉	1	2	yes	complemented
191	#2184	C₂×C₁₃₉	1	2	yes	complemented
192	#2163	C₂×C₁₃₉	1	1	yes	characteristic, complemented
193	C₂²×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
194	C₂²×SD₁₆	—	2	1	no	—
195	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
196	#532	—	2	1	no	—
197	C₂×#124	—	2	1	no	—
198	C₂×SD₃₂	C₂²×C₁₃₉	1	4	yes	complemented
199	C₂×D₁₆	C₂²×C₁₃₉	1	4	yes	—
200	#500	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
201	#495	—	2	1	no	—
202	#495	—	2	1	no	—
203	#495	C₂²×C₁₃₉	1	2	yes	—
204	#495	C₂²×C₁₃₉	1	2	yes	—
205	#493	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
206	#486	—	2	1	no	—
207	#466	—	2	1	no	—
208	#466	C₂²×C₁₃₉	1	2	yes	—
209	C₄×D₈	—	2	1	no	—
210	C₄×D₈	C₂²×C₁₃₉	1	2	yes	complemented
211	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
212	C₄⋊C₁₆	C₂²×C₁₃₉	1	2	yes	complemented
213	#358	C₂²×C₁₃₉	1	4	yes	complemented
214	#357	C₂²×C₁₃₉	1	4	yes	—
215	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
216	#346	C₂²×C₁₃₉	1	2	yes	complemented
217	C₂×#41	—	4	1	no	—
218	C₂²×Q₈	—	2	1	no	—
219	C₂²×D₄	—	2	1	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	—	4	2	no	—
222	C₂×Q₁₆	C₂³×C₁₃₉	1	2	yes	—
223	C₂×SD₁₆	—	2	2	no	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	4	4	no	—
226	C₂×D₈	—	2	1	no	—
227	C₂×D₈	—	2	1	no	—
228	C₂×D₈	—	4	2	no	—
229	C₂×D₈	C₂³×C₁₃₉	1	2	yes	—
230	C₂×D₈	C₂³×C₁₃₉	1	2	yes	—
231	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
233	C₄⋊Q₈	—	2	1	no	—
234	#127	—	2	1	no	—
235	#124	—	2	2	no	—
236	#124	—	2	2	no	—
237	#124	—	4	1	no	—
238	#124	—	4	1	no	—
239	#124	—	4	1	no	—
240	#121	—	2	2	no	—
241	#121	—	4	1	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	4	1	no	—
244	C₂×C₂²⋊C₄	—	4	1	no	—
245	C₂×C₂²⋊C₄	—	4	1	no	—
246	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
247	SD₃₂	—	4	4	no	—
248	D₁₆	—	4	4	no	—
249	C₂×C₁₆	C₂³×C₁₃₉	1	4	yes	—
250	#107	—	2	1	no	—
251	#107	C₂³×C₁₃₉	1	2	yes	—
252	#102	—	2	2	no	—
253	#102	—	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	—	4	1	no	—
259	#41	—	8	4	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	D₈×C₁₃₉	1	1	yes	characteristic
276	C₂²×C₄	D₈×C₁₃₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
278	Q₁₆	—	2	4	no	—
279	Q₁₆	—	4	2	no	—
280	SD₁₆	—	4	4	no	—
281	SD₁₆	—	4	4	no	—
282	D₈	—	2	4	no	—
283	D₈	—	2	4	no	—
284	D₈	—	4	2	no	—
285	D₈	—	4	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
289	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
291	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	D₈×C₁₃₉	1	1	yes	characteristic
301	C₄²	D₈×C₁₃₉	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
303	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
304	C₁₆	—	2	4	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	8	2	no	—
308	C₂³	—	8	2	no	—
309	C₂³	—	8	2	no	—
310	C₂³	C₂×D₈×C₁₃₉	1	1	yes	characteristic
311	Q₈	—	4	2	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	8	2	no	—
314	Q₈	—	8	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	D₄	—	8	2	no	—
320	D₄	—	8	2	no	—
321	D₄	—	8	2	no	—
322	D₄	—	8	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
332	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
333	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
334	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
335	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	2	1	no	—
339	C₈	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
340	C₈	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	8	2	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	16	4	no	—
350	C₂²	#509×C₁₃₉	1	2	yes	—
351	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	8	2	no	—
358	C₄	—	8	2	no	—
359	C₄	#535×C₁₃₉	1	1	yes	characteristic
360	C₄	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
361	C₂	—	2	2	no	—
362	C₂	—	16	2	no	—
363	C₂	—	16	2	no	—
364	C₂	#3205×C₁₃₉	1	1	yes	characteristic
365	C₂	C₂×#509×C₁₃₉	1	1	yes	characteristic
366	C₂	#3414×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ C₂×C₄×C₈×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3169×C₁₃₉	C₂	semidirect
2. C₂×#495×C₁₃₉	C₂	semidirect
3. #2250×C₁₃₉	C₂	semidirect
4. #2243×C₁₃₉	C₂	semidirect
5. #2210×C₁₃₉	C₂	semidirect
6. #2185×C₁₃₉	C₂	semidirect
7. #2184×C₁₃₉	C₂	semidirect
8. #2163×C₁₃₉	C₂	semidirect
14. C₂×SD₃₂×C₁₃₉	C₂²	semidirect
16. #500×C₁₃₉	C₂²	semidirect
21. #493×C₁₃₉	C₂²	semidirect
26. C₄×D₈×C₁₃₉	C₂²	semidirect
28. C₄⋊C₁₆×C₁₃₉	C₂²	semidirect
29. #358×C₁₃₉	C₂²	semidirect
32. #346×C₁₃₉	C₂²	semidirect
183. #33779	C₁₃₉	direct (N × H)
184. C₁₃₉	#33779	direct (N × H)
185. #3169	C₂×C₁₃₉	semidirect
186. C₂×#495	C₂×C₁₃₉	semidirect
187. #2250	C₂×C₁₃₉	semidirect
188. #2243	C₂×C₁₃₉	semidirect
189. #2210	C₂×C₁₃₉	semidirect
190. #2185	C₂×C₁₃₉	semidirect
191. #2184	C₂×C₁₃₉	semidirect
192. #2163	C₂×C₁₃₉	semidirect
198. C₂×SD₃₂	C₂²×C₁₃₉	semidirect
200. #500	C₂²×C₁₃₉	semidirect
205. #493	C₂²×C₁₃₉	semidirect
210. C₄×D₈	C₂²×C₁₃₉	semidirect
212. C₄⋊C₁₆	C₂²×C₁₃₉	semidirect
213. #358	C₂²×C₁₃₉	semidirect
216. #346	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3169×C₁₃₉	2
C₂×#495×C₁₃₉	2
#2250×C₁₃₉	2
#2243×C₁₃₉	2
#2210×C₁₃₉	2
#2185×C₁₃₉	2
#2184×C₁₃₉	2
#2163×C₁₃₉	2
#33779	139

Subgroups — C139×#33779 #48028375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33779 #48028375