Subgroups — C₁₃₉×#32859 #48027455

Order 35584.

708 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	#2860×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2088×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2087×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2067×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2065×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2065×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2054×C₁₃₉	C₂	1	2	yes	maximal
8	#2054×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#1842×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#126×C₁₃₉	—	2	2	no	—
12	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
21	#390×C₁₃₉	C₂²	1	2	yes	—
22	#390×C₁₃₉	C₂²	1	2	yes	—
23	#390×C₁₃₉	C₂²	1	2	yes	—
24	#389×C₁₃₉	C₂²	1	2	yes	—
25	#389×C₁₃₉	C₂²	1	2	yes	—
26	#389×C₁₃₉	C₂²	1	2	yes	—
27	#388×C₁₃₉	—	2	2	no	—
28	#388×C₁₃₉	—	2	2	no	—
29	#388×C₁₃₉	—	2	2	no	—
30	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
31	#340×C₁₃₉	C₂²	1	2	yes	—
32	#340×C₁₃₉	C₂²	1	1	yes	characteristic
33	#340×C₁₃₉	C₂²	1	1	yes	characteristic
34	#340×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂×D₈×C₁₃₉	—	4	2	no	—
37	C₂×D₈×C₁₃₉	—	4	1	no	—
38	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
41	#126×C₁₃₉	—	4	8	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
48	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
55	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
59	#107×C₁₃₉	—	4	1	no	—
60	#106×C₁₃₉	—	4	2	no	—
61	C₄⋊C₈×C₁₃₉	—	4	1	no	—
62	C₄⋊C₈×C₁₃₉	—	4	2	no	—
63	C₄⋊C₈×C₁₃₉	—	4	2	no	—
64	C₄⋊C₈×C₁₃₉	—	4	1	no	—
65	#102×C₁₃₉	—	4	2	no	—
66	#102×C₁₃₉	—	4	2	no	—
67	#102×C₁₃₉	—	4	2	no	—
68	#95×C₁₃₉	—	2	2	no	—
69	#95×C₁₃₉	—	2	2	no	—
70	#95×C₁₃₉	—	2	2	no	—
71	C₂⁴×C₁₃₉	—	2	2	no	—
72	C₂×D₄×C₁₃₉	—	2	2	no	—
73	C₂×D₄×C₁₃₉	—	2	2	no	—
74	C₂×D₄×C₁₃₉	—	2	2	no	—
75	C₂×D₄×C₁₃₉	—	2	2	no	—
76	C₂×D₄×C₁₃₉	—	2	2	no	—
77	C₂×D₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	2	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
86	D₈×C₁₃₉	—	4	4	no	—
87	C₂×C₈×C₁₃₉	—	2	2	no	—
88	C₂×C₈×C₁₃₉	—	2	2	no	—
89	C₂×C₈×C₁₃₉	—	2	2	no	—
90	C₂×C₈×C₁₃₉	—	2	2	no	—
91	C₂×C₈×C₁₃₉	—	2	1	no	—
92	C₂×C₈×C₁₃₉	—	2	2	no	—
93	C₂×C₈×C₁₃₉	—	2	1	no	—
94	C₄⋊C₄×C₁₃₉	—	2	2	no	—
95	C₄⋊C₄×C₁₃₉	—	2	2	no	—
96	C₄⋊C₄×C₁₃₉	—	2	2	no	—
97	C₄⋊C₄×C₁₃₉	—	2	2	no	—
98	C₄⋊C₄×C₁₃₉	—	2	2	no	—
99	C₄⋊C₄×C₁₃₉	—	2	2	no	—
100	C₄⋊C₄×C₁₃₉	—	4	4	no	—
101	C₄⋊C₄×C₁₃₉	—	4	4	no	—
102	C₄⋊C₄×C₁₃₉	—	4	4	no	—
103	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
104	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
105	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
106	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
107	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
108	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
109	C₄²×C₁₃₉	—	2	2	no	—
110	C₄²×C₁₃₉	—	2	4	no	—
111	C₄²×C₁₃₉	—	2	2	no	—
112	C₄²×C₁₃₉	—	2	1	no	—
113	C₄²×C₁₃₉	—	2	2	no	—
114	C₄²×C₁₃₉	—	2	1	no	—
115	C₄²×C₁₃₉	—	4	1	no	—
116	C₂³×C₁₃₉	—	4	2	no	—
117	C₂³×C₁₃₉	—	4	2	no	—
118	C₂³×C₁₃₉	—	4	2	no	—
119	C₂³×C₁₃₉	—	4	2	no	—
120	C₂³×C₁₃₉	—	4	2	no	—
121	C₂³×C₁₃₉	—	4	2	no	—
122	C₂³×C₁₃₉	—	4	2	no	—
123	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
124	D₄×C₁₃₉	—	4	2	no	—
125	D₄×C₁₃₉	—	4	2	no	—
126	D₄×C₁₃₉	—	4	2	no	—
127	D₄×C₁₃₉	—	4	2	no	—
128	C₂×C₄×C₁₃₉	—	2	2	no	—
129	C₂×C₄×C₁₃₉	—	2	1	no	—
130	C₂×C₄×C₁₃₉	—	2	2	no	—
131	C₂×C₄×C₁₃₉	—	2	1	no	—
132	C₂×C₄×C₁₃₉	—	2	2	no	—
133	C₂×C₄×C₁₃₉	—	2	1	no	—
134	C₂×C₄×C₁₃₉	—	2	2	no	—
135	C₂×C₄×C₁₃₉	—	2	2	no	—
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	4	2	no	—
138	C₂×C₄×C₁₃₉	—	4	2	no	—
139	C₂×C₄×C₁₃₉	—	4	2	no	—
140	C₂×C₄×C₁₃₉	—	4	2	no	—
141	C₂×C₄×C₁₃₉	—	4	2	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	—	4	2	no	—
146	C₂×C₄×C₁₃₉	#135	1	2	yes	—
147	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
148	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
149	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
151	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
152	C₈×C₁₃₉	—	4	2	no	—
153	C₈×C₁₃₉	—	4	1	no	—
154	C₈×C₁₃₉	—	4	1	no	—
155	C₂²×C₁₃₉	—	8	2	no	—
156	C₂²×C₁₃₉	—	8	2	no	—
157	C₂²×C₁₃₉	—	8	2	no	—
158	C₂²×C₁₃₉	—	8	2	no	—
159	C₂²×C₁₃₉	—	8	2	no	—
160	C₂²×C₁₃₉	—	8	2	no	—
161	C₂²×C₁₃₉	—	8	2	no	—
162	C₂²×C₁₃₉	#537	1	2	yes	—
163	C₂²×C₁₃₉	#537	1	1	yes	characteristic
164	C₂²×C₁₃₉	C₂×#135	1	1	yes	characteristic
165	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
166	C₂²×C₁₃₉	#575	1	1	yes	characteristic
167	C₄×C₁₃₉	—	2	4	no	—
168	C₄×C₁₃₉	—	2	2	no	—
169	C₄×C₁₃₉	—	4	2	no	—
170	C₄×C₁₃₉	—	4	1	no	—
171	C₄×C₁₃₉	—	8	2	no	—
172	C₄×C₁₃₉	—	8	2	no	—
173	C₄×C₁₃₉	—	8	2	no	—
174	C₄×C₁₃₉	#560	1	1	yes	characteristic
175	C₄×C₁₃₉	#563	1	2	yes	—
176	C₄×C₁₃₉	#563	1	1	yes	characteristic
177	C₂×C₁₃₉	—	16	2	no	—
178	C₂×C₁₃₉	#2823	1	1	yes	characteristic
179	C₂×C₁₃₉	#3247	1	2	yes	—
180	C₂×C₁₃₉	#3250	1	1	yes	characteristic
181	C₂×C₁₃₉	#3251	1	2	yes	—
182	C₂×C₁₃₉	#3253	1	1	yes	characteristic
183	#32859	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₉	#32859	1	1	yes	characteristic, direct product factor, Sylow
185	#2860	C₂×C₁₃₉	1	2	yes	complemented
186	#2088	C₂×C₁₃₉	1	2	yes	complemented
187	#2087	C₂×C₁₃₉	1	1	yes	characteristic, complemented
188	#2067	C₂×C₁₃₉	1	2	yes	complemented
189	#2065	C₂×C₁₃₉	1	2	yes	complemented
190	#2065	C₂×C₁₃₉	1	2	yes	complemented
191	#2054	C₂×C₁₃₉	1	2	yes	—
192	#2054	C₂×C₁₃₉	1	1	yes	characteristic
193	#1842	C₂×C₁₃₉	1	1	yes	characteristic, complemented
194	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
195	C₂×#126	—	2	2	no	—
196	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
197	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
198	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
202	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
203	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
204	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
205	#390	C₂²×C₁₃₉	1	2	yes	—
206	#390	C₂²×C₁₃₉	1	2	yes	—
207	#390	C₂²×C₁₃₉	1	2	yes	—
208	#389	C₂²×C₁₃₉	1	2	yes	—
209	#389	C₂²×C₁₃₉	1	2	yes	—
210	#389	C₂²×C₁₃₉	1	2	yes	—
211	#388	—	2	2	no	—
212	#388	—	2	2	no	—
213	#388	—	2	2	no	—
214	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
215	#340	C₂²×C₁₃₉	1	2	yes	—
216	#340	C₂²×C₁₃₉	1	1	yes	characteristic
217	#340	C₂²×C₁₃₉	1	1	yes	characteristic
218	#340	C₂²×C₁₃₉	1	2	yes	—
219	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
220	C₂×D₈	—	4	2	no	—
221	C₂×D₈	—	4	1	no	—
222	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
225	#126	—	4	8	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
231	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
239	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
242	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
243	#107	—	4	1	no	—
244	#106	—	4	2	no	—
245	C₄⋊C₈	—	4	1	no	—
246	C₄⋊C₈	—	4	2	no	—
247	C₄⋊C₈	—	4	2	no	—
248	C₄⋊C₈	—	4	1	no	—
249	#102	—	4	2	no	—
250	#102	—	4	2	no	—
251	#102	—	4	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	C₂⁴	—	2	2	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
270	D₈	—	4	4	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	1	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	4	4	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₂²⋊C₄	—	4	4	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₂²⋊C₄	—	4	4	no	—
290	C₂²⋊C₄	—	4	4	no	—
291	C₂²⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	4	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	4	1	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	2	no	—
307	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
308	D₄	—	4	2	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	2	no	—
311	D₄	—	4	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	#135×C₁₃₉	1	2	yes	—
331	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
332	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
333	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
334	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
335	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
336	C₈	—	4	1	no	—
337	C₈	—	4	2	no	—
338	C₈	—	4	1	no	—
339	C₂²	—	8	2	no	—
340	C₂²	—	8	2	no	—
341	C₂²	—	8	2	no	—
342	C₂²	—	8	2	no	—
343	C₂²	—	8	2	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	#537×C₁₃₉	1	2	yes	—
347	C₂²	#537×C₁₃₉	1	1	yes	characteristic
348	C₂²	C₂×#135×C₁₃₉	1	1	yes	characteristic
349	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
350	C₂²	#575×C₁₃₉	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	1	no	—
355	C₄	—	8	2	no	—
356	C₄	—	8	2	no	—
357	C₄	—	8	2	no	—
358	C₄	#560×C₁₃₉	1	1	yes	characteristic
359	C₄	#563×C₁₃₉	1	2	yes	—
360	C₄	#563×C₁₃₉	1	1	yes	characteristic
361	C₂	—	16	2	no	—
362	C₂	#2823×C₁₃₉	1	1	yes	characteristic
363	C₂	#3247×C₁₃₉	1	2	yes	—
364	C₂	#3250×C₁₃₉	1	1	yes	characteristic
365	C₂	#3251×C₁₃₉	1	2	yes	—
366	C₂	#3253×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×D₈×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₄³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2860×C₁₃₉	C₂	semidirect
2. #2088×C₁₃₉	C₂	semidirect
3. #2087×C₁₃₉	C₂	semidirect
4. #2067×C₁₃₉	C₂	semidirect
5. #2065×C₁₃₉	C₂	semidirect
6. #2065×C₁₃₉	C₂	semidirect
9. #1842×C₁₃₉	C₂	semidirect
183. #32859	C₁₃₉	direct (N × H)
184. C₁₃₉	#32859	direct (N × H)
185. #2860	C₂×C₁₃₉	semidirect
186. #2088	C₂×C₁₃₉	semidirect
187. #2087	C₂×C₁₃₉	semidirect
188. #2067	C₂×C₁₃₉	semidirect
189. #2065	C₂×C₁₃₉	semidirect
190. #2065	C₂×C₁₃₉	semidirect
193. #1842	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₉	2
#2088×C₁₃₉	2
#2087×C₁₃₉	2
#2067×C₁₃₉	2
#2065×C₁₃₉	2
#2054×C₁₃₉	2
#1842×C₁₃₉	2
#32859	139

Subgroups — C139×#32859 #48027455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#32859 #48027455