Subgroups — C₁₃₉×#33964 #48028560

Order 35584.

554 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3393×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2250×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2248×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2210×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2208×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2207×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2206×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2183×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2175×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₄×D₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#556×C₁₃₉	—	2	1	no	—
13	#550×C₁₃₉	—	2	1	no	—
14	C₂×SD₃₂×C₁₃₉	C₂²	1	2	yes	—
15	C₂×SD₃₂×C₁₃₉	C₂²	1	2	yes	—
16	C₂×SD₃₂×C₁₃₉	C₂²	1	2	yes	—
17	C₂×D₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×D₁₆×C₁₃₉	C₂²	1	2	yes	—
19	#495×C₁₃₉	C₂²	1	2	yes	—
20	#494×C₁₃₉	C₂²	1	1	yes	characteristic
21	#493×C₁₃₉	C₂²	1	1	yes	characteristic
22	#493×C₁₃₉	C₂²	1	2	yes	—
23	#464×C₁₃₉	—	2	2	no	—
24	#461×C₁₃₉	—	2	1	no	—
25	#459×C₁₃₉	—	2	1	no	—
26	#459×C₁₃₉	—	2	2	no	—
27	C₈×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₄×Q₁₆×C₁₃₉	C₂²	1	2	yes	—
29	C₄×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₄×D₈×C₁₃₉	C₂²	1	2	yes	—
31	C₄×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	#366×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₄⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
35	#358×C₁₃₉	C₂²	1	2	yes	—
36	#357×C₁₃₉	C₂²	1	1	yes	characteristic
37	#357×C₁₃₉	C₂²	1	1	yes	characteristic
38	#357×C₁₃₉	C₂²	1	2	yes	—
39	#346×C₁₃₉	C₂²	1	2	yes	—
40	C₄×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#41×C₁₃₉	—	4	1	no	—
42	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
43	C₂×Q₁₆×C₁₃₉	C₂³	1	2	yes	—
44	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
45	C₂×D₈×C₁₃₉	—	2	1	no	—
46	C₂×D₈×C₁₃₉	—	2	2	no	—
47	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₁₃₉	C₂³	1	2	yes	—
49	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
51	#127×C₁₃₉	—	2	1	no	—
52	#127×C₁₃₉	—	2	2	no	—
53	#126×C₁₃₉	—	4	2	no	—
54	#124×C₁₃₉	—	2	2	no	—
55	C₂²⋊Q₈×C₁₃₉	—	4	1	no	—
56	#121×C₁₃₉	—	4	1	no	—
57	#121×C₁₃₉	—	4	2	no	—
58	C₄×Q₈×C₁₃₉	—	2	2	no	—
59	C₄×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
60	C₄×D₄×C₁₃₉	—	2	1	no	—
61	C₄×D₄×C₁₃₉	—	2	2	no	—
62	C₄×D₄×C₁₃₉	—	2	1	no	—
63	#117×C₁₃₉	—	4	1	no	—
64	SD₃₂×C₁₃₉	—	2	4	no	—
65	SD₃₂×C₁₃₉	—	4	2	no	—
66	SD₃₂×C₁₃₉	—	4	2	no	—
67	D₁₆×C₁₃₉	—	2	2	no	—
68	D₁₆×C₁₃₉	—	4	2	no	—
69	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
70	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
72	#107×C₁₃₉	C₂³	1	1	yes	characteristic
73	#107×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₁₃₉	D₄	1	1	yes	characteristic
75	C₄⋊C₈×C₁₃₉	D₄	1	2	yes	—
76	#103×C₁₃₉	—	2	2	no	—
77	#102×C₁₃₉	—	2	1	no	—
78	#102×C₁₃₉	—	2	2	no	—
79	#102×C₁₃₉	—	2	1	no	—
80	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃₉	C₂³	1	2	yes	—
82	#41×C₁₃₉	—	8	4	no	—
83	C₂×Q₈×C₁₃₉	—	2	2	no	—
84	C₂×Q₈×C₁₃₉	D₈	1	1	yes	characteristic
85	C₂×D₄×C₁₃₉	—	2	1	no	—
86	C₂×D₄×C₁₃₉	—	2	1	no	—
87	C₂×D₄×C₁₃₉	—	2	2	no	—
88	C₂×D₄×C₁₃₉	—	4	2	no	—
89	C₂×D₄×C₁₃₉	—	4	1	no	—
90	C₂×D₄×C₁₃₉	—	4	2	no	—
91	C₂×D₄×C₁₃₉	—	4	1	no	—
92	C₂²×C₄×C₁₃₉	—	4	1	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	—	4	1	no	—
95	Q₁₆×C₁₃₉	—	2	2	no	—
96	Q₁₆×C₁₃₉	—	2	2	no	—
97	Q₁₆×C₁₃₉	—	8	1	no	—
98	SD₁₆×C₁₃₉	—	8	2	no	—
99	D₈×C₁₃₉	—	2	1	no	—
100	D₈×C₁₃₉	—	2	1	no	—
101	D₈×C₁₃₉	—	2	2	no	—
102	D₈×C₁₃₉	—	2	1	no	—
103	D₈×C₁₃₉	—	2	2	no	—
104	D₈×C₁₃₉	—	2	1	no	—
105	D₈×C₁₃₉	—	8	2	no	—
106	D₈×C₁₃₉	—	8	1	no	—
107	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₉	—	2	1	no	—
111	C₄⋊C₄×C₁₃₉	—	2	1	no	—
112	C₄⋊C₄×C₁₃₉	—	4	1	no	—
113	C₄⋊C₄×C₁₃₉	—	4	2	no	—
114	C₄⋊C₄×C₁₃₉	—	4	1	no	—
115	C₄⋊C₄×C₁₃₉	D₈	1	1	yes	characteristic
116	C₄⋊C₄×C₁₃₉	D₈	1	2	yes	—
117	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
119	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
120	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
122	C₄²×C₁₃₉	—	4	2	no	—
123	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
125	C₁₆×C₁₃₉	—	2	2	no	—
126	C₁₆×C₁₃₉	—	2	1	no	—
127	C₁₆×C₁₃₉	#41	1	2	yes	complemented
128	C₂³×C₁₃₉	—	4	1	no	—
129	C₂³×C₁₃₉	—	4	2	no	—
130	C₂³×C₁₃₉	—	4	1	no	—
131	Q₈×C₁₃₉	—	2	2	no	—
132	Q₈×C₁₃₉	—	4	2	no	—
133	Q₈×C₁₃₉	—	4	2	no	—
134	D₄×C₁₃₉	—	4	1	no	—
135	D₄×C₁₃₉	—	4	1	no	—
136	D₄×C₁₃₉	—	4	2	no	—
137	D₄×C₁₃₉	—	4	1	no	—
138	D₄×C₁₃₉	—	4	2	no	—
139	D₄×C₁₃₉	—	4	1	no	—
140	D₄×C₁₃₉	—	8	4	no	—
141	D₄×C₁₃₉	—	8	2	no	—
142	D₄×C₁₃₉	—	16	2	no	—
143	D₄×C₁₃₉	—	16	1	no	—
144	C₂×C₄×C₁₃₉	—	4	1	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	4	1	no	—
147	C₂×C₄×C₁₃₉	—	8	4	no	—
148	C₂×C₄×C₁₃₉	—	8	2	no	—
149	C₂×C₄×C₁₃₉	—	8	2	no	—
150	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₁₃₉	—	2	2	no	—
156	C₈×C₁₃₉	—	2	1	no	—
157	C₈×C₁₃₉	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂²×C₁₃₉	—	8	1	no	—
160	C₂²×C₁₃₉	—	8	2	no	—
161	C₂²×C₁₃₉	—	8	1	no	—
162	C₂²×C₁₃₉	—	8	2	no	—
163	C₂²×C₁₃₉	—	8	1	no	—
164	C₂²×C₁₃₉	—	8	1	no	—
165	C₂²×C₁₃₉	—	8	2	no	—
166	C₂²×C₁₃₉	—	8	1	no	—
167	C₂²×C₁₃₉	—	8	1	no	—
168	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
169	C₄×C₁₃₉	—	2	2	no	—
170	C₄×C₁₃₉	—	2	2	no	—
171	C₄×C₁₃₉	—	2	1	no	—
172	C₄×C₁₃₉	—	8	2	no	—
173	C₄×C₁₃₉	—	8	1	no	—
174	C₄×C₁₃₉	—	8	1	no	—
175	C₄×C₁₃₉	#509	1	2	yes	—
176	C₄×C₁₃₉	#550	1	1	yes	characteristic
177	C₄×C₁₃₉	#576	1	1	yes	characteristic
178	C₂×C₁₃₉	—	16	2	no	—
179	C₂×C₁₃₉	—	16	1	no	—
180	C₂×C₁₃₉	—	16	1	no	—
181	C₂×C₁₃₉	#3391	1	1	yes	characteristic
182	C₂×C₁₃₉	C₂×#509	1	1	yes	characteristic
183	C₂×C₁₃₉	#3416	1	1	yes	characteristic
184	#33964	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃₉	#33964	1	1	yes	characteristic, direct product factor, Sylow
186	#3393	C₂×C₁₃₉	1	1	yes	characteristic, complemented
187	#3391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
188	#2250	C₂×C₁₃₉	1	2	yes	complemented
189	#2248	C₂×C₁₃₉	1	1	yes	characteristic, complemented
190	#2210	C₂×C₁₃₉	1	2	yes	complemented
191	#2208	C₂×C₁₃₉	1	1	yes	characteristic, complemented
192	#2207	C₂×C₁₃₉	1	2	yes	complemented
193	#2206	C₂×C₁₃₉	1	1	yes	characteristic, complemented
194	#2183	C₂×C₁₃₉	1	1	yes	characteristic, complemented
195	#2175	C₂×C₁₃₉	1	2	yes	complemented
196	C₄×D₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
197	#556	—	2	1	no	—
198	#550	—	2	1	no	—
199	C₂×SD₃₂	C₂²×C₁₃₉	1	2	yes	—
200	C₂×SD₃₂	C₂²×C₁₃₉	1	2	yes	—
201	C₂×SD₃₂	C₂²×C₁₃₉	1	2	yes	—
202	C₂×D₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
203	C₂×D₁₆	C₂²×C₁₃₉	1	2	yes	—
204	#495	C₂²×C₁₃₉	1	2	yes	—
205	#494	C₂²×C₁₃₉	1	1	yes	characteristic
206	#493	C₂²×C₁₃₉	1	1	yes	characteristic
207	#493	C₂²×C₁₃₉	1	2	yes	—
208	#464	—	2	2	no	—
209	#461	—	2	1	no	—
210	#459	—	2	1	no	—
211	#459	—	2	2	no	—
212	C₈×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
213	C₄×Q₁₆	C₂²×C₁₃₉	1	2	yes	—
214	C₄×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
215	C₄×D₈	C₂²×C₁₃₉	1	2	yes	—
216	C₄×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
217	#366	C₂²×C₁₃₉	1	1	yes	characteristic
218	C₄⋊C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
219	C₄⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
220	#358	C₂²×C₁₃₉	1	2	yes	—
221	#357	C₂²×C₁₃₉	1	1	yes	characteristic
222	#357	C₂²×C₁₃₉	1	1	yes	characteristic
223	#357	C₂²×C₁₃₉	1	2	yes	—
224	#346	C₂²×C₁₃₉	1	2	yes	—
225	C₄×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
226	C₂×#41	—	4	1	no	—
227	C₂×Q₁₆	—	2	1	no	—
228	C₂×Q₁₆	C₂³×C₁₃₉	1	2	yes	—
229	C₂×SD₁₆	—	2	2	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
233	C₂×D₈	C₂³×C₁₃₉	1	2	yes	—
234	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
235	C₄⋊Q₈	—	2	1	no	—
236	#127	—	2	1	no	—
237	#127	—	2	2	no	—
238	#126	—	4	2	no	—
239	#124	—	2	2	no	—
240	C₂²⋊Q₈	—	4	1	no	—
241	#121	—	4	1	no	—
242	#121	—	4	2	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	1	no	—
248	#117	—	4	1	no	—
249	SD₃₂	—	2	4	no	—
250	SD₃₂	—	4	2	no	—
251	SD₃₂	—	4	2	no	—
252	D₁₆	—	2	2	no	—
253	D₁₆	—	4	2	no	—
254	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
255	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
256	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
257	#107	C₂³×C₁₃₉	1	1	yes	characteristic
258	#107	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₄⋊C₈	D₄×C₁₃₉	1	1	yes	characteristic
260	C₄⋊C₈	D₄×C₁₃₉	1	2	yes	—
261	#103	—	2	2	no	—
262	#102	—	2	1	no	—
263	#102	—	2	2	no	—
264	#102	—	2	1	no	—
265	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₁₃₉	1	2	yes	—
267	#41	—	8	4	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	D₈×C₁₃₉	1	1	yes	characteristic
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	1	no	—
280	Q₁₆	—	2	2	no	—
281	Q₁₆	—	2	2	no	—
282	Q₁₆	—	8	1	no	—
283	SD₁₆	—	8	2	no	—
284	D₈	—	2	1	no	—
285	D₈	—	2	1	no	—
286	D₈	—	2	2	no	—
287	D₈	—	2	1	no	—
288	D₈	—	2	2	no	—
289	D₈	—	2	1	no	—
290	D₈	—	8	2	no	—
291	D₈	—	8	1	no	—
292	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
294	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	D₈×C₁₃₉	1	1	yes	characteristic
301	C₄⋊C₄	D₈×C₁₃₉	1	2	yes	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₄²	—	4	2	no	—
308	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
310	C₁₆	—	2	2	no	—
311	C₁₆	—	2	1	no	—
312	C₁₆	#41×C₁₃₉	1	2	yes	complemented
313	C₂³	—	4	1	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	1	no	—
316	Q₈	—	2	2	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	D₄	—	4	1	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	2	no	—
324	D₄	—	4	1	no	—
325	D₄	—	8	4	no	—
326	D₄	—	8	2	no	—
327	D₄	—	16	2	no	—
328	D₄	—	16	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	8	4	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
336	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
338	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	2	1	no	—
342	C₈	C₂×#41×C₁₃₉	1	1	yes	characteristic
343	C₈	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
344	C₂²	—	8	1	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	1	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	1	no	—
357	C₄	—	8	2	no	—
358	C₄	—	8	1	no	—
359	C₄	—	8	1	no	—
360	C₄	#509×C₁₃₉	1	2	yes	—
361	C₄	#550×C₁₃₉	1	1	yes	characteristic
362	C₄	#576×C₁₃₉	1	1	yes	characteristic
363	C₂	—	16	2	no	—
364	C₂	—	16	1	no	—
365	C₂	—	16	1	no	—
366	C₂	#3391×C₁₃₉	1	1	yes	characteristic
367	C₂	C₂×#509×C₁₃₉	1	1	yes	characteristic
368	C₂	#3416×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 ◁ C₄×Q₈×C₁₃₉ ◁ C₈×Q₈×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3393×C₁₃₉	C₂	semidirect
2. #3391×C₁₃₉	C₂	semidirect
3. #2250×C₁₃₉	C₂	semidirect
4. #2248×C₁₃₉	C₂	semidirect
5. #2210×C₁₃₉	C₂	semidirect
6. #2208×C₁₃₉	C₂	semidirect
7. #2207×C₁₃₉	C₂	semidirect
8. #2206×C₁₃₉	C₂	semidirect
9. #2183×C₁₃₉	C₂	semidirect
10. #2175×C₁₃₉	C₂	semidirect
11. C₄×D₁₆×C₁₃₉	C₂	semidirect
127. C₁₆×C₁₃₉	#41	semidirect
184. #33964	C₁₃₉	direct (N × H)
185. C₁₃₉	#33964	direct (N × H)
186. #3393	C₂×C₁₃₉	semidirect
187. #3391	C₂×C₁₃₉	semidirect
188. #2250	C₂×C₁₃₉	semidirect
189. #2248	C₂×C₁₃₉	semidirect
190. #2210	C₂×C₁₃₉	semidirect
191. #2208	C₂×C₁₃₉	semidirect
192. #2207	C₂×C₁₃₉	semidirect
193. #2206	C₂×C₁₃₉	semidirect
194. #2183	C₂×C₁₃₉	semidirect
195. #2175	C₂×C₁₃₉	semidirect
196. C₄×D₁₆	C₂×C₁₃₉	semidirect
312. C₁₆	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3393×C₁₃₉	2
#3391×C₁₃₉	2
#2250×C₁₃₉	2
#2248×C₁₃₉	2
#2210×C₁₃₉	2
#2208×C₁₃₉	2
#2207×C₁₃₉	2
#2206×C₁₃₉	2
#2183×C₁₃₉	2
#2175×C₁₃₉	2
C₄×D₁₆×C₁₃₉	2
#33964	139

Subgroups — C139×#33964 #48028560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33964 #48028560