Subgroups — C₁₃₉×#37298 #48031894

Order 35584.

2618 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2682×C₁₃₉	C₂	1	8	yes	maximal, complemented
4	#2675×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2619×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2566×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2541×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#540×C₁₃₉	—	2	16	no	—
10	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
11	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
12	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
14	C₂×#123×C₁₃₉	C₂²	1	8	yes	—
15	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
16	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
17	C₂×#121×C₁₃₉	C₂²	1	16	yes	—
18	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
23	#396×C₁₃₉	C₂²	1	16	yes	—
24	#394×C₁₃₉	C₂²	1	8	yes	—
25	#392×C₁₃₉	C₂²	1	16	yes	—
26	#392×C₁₃₉	C₂²	1	8	yes	—
27	#390×C₁₃₉	C₂²	1	4	yes	—
28	#390×C₁₃₉	C₂²	1	4	yes	—
29	#390×C₁₃₉	C₂²	1	8	yes	—
30	#389×C₁₃₉	C₂²	1	4	yes	—
31	#385×C₁₃₉	C₂²	1	4	yes	—
32	#385×C₁₃₉	C₂²	1	16	yes	—
33	#384×C₁₃₉	C₂²	1	2	yes	—
34	#382×C₁₃₉	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
36	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
37	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
38	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
39	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
40	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
41	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
44	#127×C₁₃₉	—	2	8	no	—
45	#127×C₁₃₉	—	4	4	no	—
46	#127×C₁₃₉	—	4	4	no	—
47	#125×C₁₃₉	—	2	8	no	—
48	#123×C₁₃₉	—	2	32	no	—
49	#121×C₁₃₉	—	2	16	no	—
50	#121×C₁₃₉	—	2	32	no	—
51	#121×C₁₃₉	—	4	16	no	—
52	#121×C₁₃₉	—	4	32	no	—
53	C₄×D₄×C₁₃₉	—	2	16	no	—
54	#117×C₁₃₉	—	4	2	no	—
55	#117×C₁₃₉	D₄	1	8	yes	complemented
56	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
64	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
65	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
66	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃₉	—	4	2	no	—
69	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
73	#95×C₁₃₉	C₂³	1	8	yes	—
74	#95×C₁₃₉	C₂³	1	8	yes	—
75	C₂⁴×C₁₃₉	C₂⁴	1	8	yes	—
76	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
77	C₂×D₄×C₁₃₉	—	2	16	no	—
78	C₂×D₄×C₁₃₉	—	2	8	no	—
79	C₂×D₄×C₁₃₉	—	2	16	no	—
80	C₂×D₄×C₁₃₉	—	2	8	no	—
81	C₂×D₄×C₁₃₉	—	2	16	no	—
82	C₂×D₄×C₁₃₉	—	2	8	no	—
83	C₂×D₄×C₁₃₉	—	4	16	no	—
84	C₂×D₄×C₁₃₉	—	4	8	no	—
85	C₂×D₄×C₁₃₉	—	4	16	no	—
86	C₂×D₄×C₁₃₉	—	4	16	no	—
87	C₂×D₄×C₁₃₉	—	4	8	no	—
88	C₂×D₄×C₁₃₉	—	4	8	no	—
89	C₂²×C₄×C₁₃₉	—	2	2	no	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	8	no	—
92	C₂²×C₄×C₁₃₉	—	2	16	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	—	4	16	no	—
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₁₃₉	—	2	8	no	—
103	C₄⋊C₄×C₁₃₉	—	2	16	no	—
104	C₄⋊C₄×C₁₃₉	—	2	16	no	—
105	C₄⋊C₄×C₁₃₉	—	4	2	no	—
106	C₄⋊C₄×C₁₃₉	—	4	8	no	—
107	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
108	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
109	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
110	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
111	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₃₉	—	4	16	no	—
113	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
114	C₄²×C₁₃₉	—	2	4	no	—
115	C₄²×C₁₃₉	—	2	4	no	—
116	C₄²×C₁₃₉	—	4	2	no	—
117	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
118	C₂³×C₁₃₉	—	2	1	no	—
119	C₂³×C₁₃₉	—	2	4	no	—
120	C₂³×C₁₃₉	—	2	1	no	—
121	C₂³×C₁₃₉	—	2	8	no	—
122	C₂³×C₁₃₉	—	2	16	no	—
123	C₂³×C₁₃₉	—	2	16	no	—
124	C₂³×C₁₃₉	—	2	8	no	—
125	C₂³×C₁₃₉	—	2	8	no	—
126	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
127	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
128	D₄×C₁₃₉	—	4	16	no	—
129	D₄×C₁₃₉	—	8	16	no	—
130	D₄×C₁₃₉	—	8	16	no	—
131	D₄×C₁₃₉	—	8	16	no	—
132	D₄×C₁₃₉	—	8	16	no	—
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	2	1	no	—
135	C₂×C₄×C₁₃₉	—	2	8	no	—
136	C₂×C₄×C₁₃₉	—	2	4	no	—
137	C₂×C₄×C₁₃₉	—	2	1	no	—
138	C₂×C₄×C₁₃₉	—	2	8	no	—
139	C₂×C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₄×C₁₃₉	—	2	4	no	—
141	C₂×C₄×C₁₃₉	—	2	16	no	—
142	C₂×C₄×C₁₃₉	—	2	8	no	—
143	C₂×C₄×C₁₃₉	—	4	8	no	—
144	C₂×C₄×C₁₃₉	—	8	16	no	—
145	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
146	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
147	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	8	yes	—
149	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
150	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
151	C₂²×C₁₃₉	—	2	2	no	—
152	C₂²×C₁₃₉	—	2	4	no	—
153	C₂²×C₁₃₉	—	4	2	no	—
154	C₂²×C₁₃₉	—	4	2	no	—
155	C₂²×C₁₃₉	—	4	8	no	—
156	C₂²×C₁₃₉	—	4	8	no	—
157	C₂²×C₁₃₉	—	4	8	no	—
158	C₂²×C₁₃₉	—	4	16	no	—
159	C₂²×C₁₃₉	—	4	16	no	—
160	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
161	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	4	yes	—
163	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
164	C₄×C₁₃₉	—	2	2	no	—
165	C₄×C₁₃₉	—	2	8	no	—
166	C₄×C₁₃₉	—	2	8	no	—
167	C₄×C₁₃₉	—	4	8	no	—
168	C₄×C₁₃₉	—	4	4	no	—
169	C₄×C₁₃₉	#537	1	4	yes	—
170	C₂×C₁₃₉	—	4	2	no	—
171	C₂×C₁₃₉	—	8	8	no	—
172	C₂×C₁₃₉	C₂×#537	1	1	yes	characteristic
173	C₂×C₁₃₉	#3498	1	2	yes	—
174	C₂×C₁₃₉	#3537	1	2	yes	—
175	C₂×C₁₃₉	#3548	1	2	yes	—
176	#37298	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃₉	#37298	1	1	yes	characteristic, direct product factor, Sylow
178	C₂×#540	C₂×C₁₃₉	1	2	yes	complemented
179	#2856	C₂×C₁₃₉	1	2	yes	complemented
180	#2682	C₂×C₁₃₉	1	8	yes	complemented
181	#2675	C₂×C₁₃₉	1	8	yes	complemented
182	#2619	C₂×C₁₃₉	1	2	yes	complemented
183	#2566	C₂×C₁₃₉	1	4	yes	complemented
184	#2541	C₂×C₁₃₉	1	4	yes	complemented
185	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
186	#540	—	2	16	no	—
187	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
188	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
189	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
190	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
191	C₂×#123	C₂²×C₁₃₉	1	8	yes	—
192	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
193	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
194	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
195	C₂×#121	C₂²×C₁₃₉	1	16	yes	—
196	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
197	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
198	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
199	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
200	#396	C₂²×C₁₃₉	1	16	yes	—
201	#394	C₂²×C₁₃₉	1	8	yes	—
202	#392	C₂²×C₁₃₉	1	8	yes	—
203	#392	C₂²×C₁₃₉	1	16	yes	—
204	#390	C₂²×C₁₃₉	1	4	yes	—
205	#390	C₂²×C₁₃₉	1	4	yes	—
206	#390	C₂²×C₁₃₉	1	8	yes	—
207	#389	C₂²×C₁₃₉	1	4	yes	—
208	#385	C₂²×C₁₃₉	1	16	yes	—
209	#385	C₂²×C₁₃₉	1	4	yes	—
210	#384	C₂²×C₁₃₉	1	2	yes	—
211	#382	C₂²×C₁₃₉	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
213	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
214	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
215	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
216	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
217	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
218	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
219	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
221	#127	—	2	8	no	—
222	#127	—	4	4	no	—
223	#127	—	4	4	no	—
224	#125	—	2	8	no	—
225	#123	—	2	32	no	—
226	#121	—	2	16	no	—
227	#121	—	2	32	no	—
228	#121	—	4	16	no	—
229	#121	—	4	32	no	—
230	C₄×D₄	—	2	16	no	—
231	#117	—	4	2	no	—
232	#117	D₄×C₁₃₉	1	8	yes	complemented
233	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
234	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
239	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
240	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
241	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
244	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
245	C₂×C₄²	—	4	2	no	—
246	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
247	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
250	#95	C₂³×C₁₃₉	1	8	yes	—
251	#95	C₂³×C₁₃₉	1	8	yes	—
252	C₂⁴	C₂⁴×C₁₃₉	1	8	yes	—
253	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	—	2	8	no	—
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	16	no	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	4	16	no	—
261	C₂×D₄	—	4	8	no	—
262	C₂×D₄	—	4	16	no	—
263	C₂×D₄	—	4	16	no	—
264	C₂×D₄	—	4	8	no	—
265	C₂×D₄	—	4	8	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	16	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	16	no	—
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
273	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
274	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
275	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
276	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
277	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	16	no	—
281	C₄⋊C₄	—	2	16	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	8	no	—
284	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
285	C₂²⋊C₄	—	2	16	no	—
286	C₂²⋊C₄	—	2	16	no	—
287	C₂²⋊C₄	—	2	32	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	4	16	no	—
290	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
291	C₄²	—	2	4	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	4	2	no	—
294	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	8	no	—
299	C₂³	—	2	16	no	—
300	C₂³	—	2	16	no	—
301	C₂³	—	2	8	no	—
302	C₂³	—	2	8	no	—
303	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
304	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
305	D₄	—	4	16	no	—
306	D₄	—	8	16	no	—
307	D₄	—	8	16	no	—
308	D₄	—	8	16	no	—
309	D₄	—	8	16	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	16	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	4	8	no	—
321	C₂×C₄	—	8	16	no	—
322	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
323	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
324	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
325	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	8	yes	—
326	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
327	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	4	2	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	16	no	—
333	C₂²	—	4	16	no	—
334	C₂²	—	4	8	no	—
335	C₂²	—	4	8	no	—
336	C₂²	—	4	8	no	—
337	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
338	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
339	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	4	yes	—
340	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
341	C₄	—	2	8	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	8	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	#537×C₁₃₉	1	4	yes	—
347	C₂	—	4	2	no	—
348	C₂	—	8	8	no	—
349	C₂	C₂×#537×C₁₃₉	1	1	yes	characteristic
350	C₂	#3498×C₁₃₉	1	2	yes	—
351	C₂	#3537×C₁₃₉	1	2	yes	—
352	C₂	#3548×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#540×C₁₃₉	C₂	semidirect
2. #2856×C₁₃₉	C₂	semidirect
3. #2682×C₁₃₉	C₂	semidirect
4. #2675×C₁₃₉	C₂	semidirect
5. #2619×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2541×C₁₃₉	C₂	semidirect
8. #2296×C₁₃₉	C₂	semidirect
55. #117×C₁₃₉	D₄	semidirect
176. #37298	C₁₃₉	direct (N × H)
177. C₁₃₉	#37298	direct (N × H)
178. C₂×#540	C₂×C₁₃₉	semidirect
179. #2856	C₂×C₁₃₉	semidirect
180. #2682	C₂×C₁₃₉	semidirect
181. #2675	C₂×C₁₃₉	semidirect
182. #2619	C₂×C₁₃₉	semidirect
183. #2566	C₂×C₁₃₉	semidirect
184. #2541	C₂×C₁₃₉	semidirect
185. #2296	C₂×C₁₃₉	semidirect
232. #117	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₁₃₉	2
#2856×C₁₃₉	2
#2682×C₁₃₉	2
#2675×C₁₃₉	2
#2619×C₁₃₉	2
#2566×C₁₃₉	2
#2541×C₁₃₉	2
#2296×C₁₃₉	2
#37298	139

Subgroups — C139×#37298 #48031894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37298 #48031894