Subgroups — C₁₃₉×#29263 #48023859

Order 35584.

798 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	#2331×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2328×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2092×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2023×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1982×C₁₃₉	C₂	1	2	yes	maximal
6	#1949×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1864×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1862×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1832×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
14	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
20	#391×C₁₃₉	—	2	2	no	—
21	#390×C₁₃₉	C₂²	1	2	yes	—
22	#389×C₁₃₉	C₂²	1	2	yes	—
23	#387×C₁₃₉	—	2	2	no	—
24	#386×C₁₃₉	—	2	2	no	—
25	#386×C₁₃₉	—	2	2	no	—
26	#382×C₁₃₉	C₂²	1	1	yes	characteristic
27	#382×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	#376×C₁₃₉	C₂²	1	1	yes	characteristic
30	#340×C₁₃₉	C₂²	1	2	yes	—
31	#340×C₁₃₉	C₂²	1	2	yes	—
32	#336×C₁₃₉	C₂²	1	2	yes	—
33	#336×C₁₃₉	C₂²	1	1	yes	characteristic
34	#336×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×Q₈×C₁₃₉	—	2	1	no	—
36	C₂²×D₄×C₁₃₉	—	2	2	no	—
37	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃₉	—	2	2	no	—
39	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
41	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
42	#127×C₁₃₉	—	2	2	no	—
43	#127×C₁₃₉	Q₈	1	4	yes	complemented
44	C₄×D₄×C₁₃₉	—	4	2	no	—
45	C₄×D₄×C₁₃₉	—	4	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	—	2	2	no	—
55	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
58	#107×C₁₃₉	—	4	2	no	—
59	#106×C₁₃₉	—	4	2	no	—
60	C₄⋊C₈×C₁₃₉	—	2	4	no	—
61	#102×C₁₃₉	—	2	4	no	—
62	#102×C₁₃₉	—	2	4	no	—
63	#102×C₁₃₉	—	4	2	no	—
64	#102×C₁₃₉	—	4	2	no	—
65	#95×C₁₃₉	—	2	2	no	—
66	#95×C₁₃₉	—	2	2	no	—
67	#95×C₁₃₉	—	2	1	no	—
68	#95×C₁₃₉	—	2	1	no	—
69	#95×C₁₃₉	—	2	2	no	—
70	#95×C₁₃₉	D₄	1	2	yes	—
71	#95×C₁₃₉	D₄	1	2	yes	—
72	C₂⁴×C₁₃₉	—	2	2	no	—
73	C₂×Q₈×C₁₃₉	—	2	4	no	—
74	C₂×Q₈×C₁₃₉	—	8	2	no	—
75	C₂×D₄×C₁₃₉	—	2	8	no	—
76	C₂×D₄×C₁₃₉	—	2	2	no	—
77	C₂×D₄×C₁₃₉	—	2	2	no	—
78	C₂×D₄×C₁₃₉	—	2	2	no	—
79	C₂×D₄×C₁₃₉	—	2	2	no	—
80	C₂×D₄×C₁₃₉	—	2	2	no	—
81	C₂×D₄×C₁₃₉	—	8	2	no	—
82	C₂×D₄×C₁₃₉	—	8	2	no	—
83	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
84	C₂²×C₄×C₁₃₉	—	2	2	no	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	4	4	no	—
88	C₂²×C₄×C₁₃₉	—	8	2	no	—
89	C₂²×C₄×C₁₃₉	—	8	2	no	—
90	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₃₉	—	2	2	no	—
96	C₂×C₈×C₁₃₉	—	2	2	no	—
97	C₂×C₈×C₁₃₉	—	2	2	no	—
98	C₂×C₈×C₁₃₉	—	2	2	no	—
99	C₂×C₈×C₁₃₉	—	2	2	no	—
100	C₂×C₈×C₁₃₉	—	2	2	no	—
101	C₄⋊C₄×C₁₃₉	—	2	4	no	—
102	C₄⋊C₄×C₁₃₉	—	2	2	no	—
103	C₄⋊C₄×C₁₃₉	—	2	2	no	—
104	C₄⋊C₄×C₁₃₉	—	2	2	no	—
105	C₄⋊C₄×C₁₃₉	—	2	2	no	—
106	C₄⋊C₄×C₁₃₉	—	2	2	no	—
107	C₄⋊C₄×C₁₃₉	—	8	2	no	—
108	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
109	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
110	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
111	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
112	C₄²×C₁₃₉	—	2	2	no	—
113	C₄²×C₁₃₉	—	2	2	no	—
114	C₄²×C₁₃₉	—	8	2	no	—
115	C₄²×C₁₃₉	C₂×Q₈	1	2	yes	—
116	C₄²×C₁₃₉	#41	1	2	yes	—
117	C₂³×C₁₃₉	—	2	4	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	—	4	2	no	—
124	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₁₃₉	—	8	4	no	—
126	D₄×C₁₃₉	—	2	4	no	—
127	D₄×C₁₃₉	—	2	4	no	—
128	D₄×C₁₃₉	—	4	2	no	—
129	D₄×C₁₃₉	—	4	2	no	—
130	D₄×C₁₃₉	—	8	8	no	—
131	C₂×C₄×C₁₃₉	—	2	2	no	—
132	C₂×C₄×C₁₃₉	—	2	2	no	—
133	C₂×C₄×C₁₃₉	—	2	1	no	—
134	C₂×C₄×C₁₃₉	—	2	1	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	2	2	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	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	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	2	no	—
148	C₂×C₄×C₁₃₉	—	4	2	no	—
149	C₂×C₄×C₁₃₉	—	8	8	no	—
150	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
153	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
155	C₈×C₁₃₉	—	4	2	no	—
156	C₈×C₁₃₉	—	4	2	no	—
157	C₂²×C₁₃₉	—	4	4	no	—
158	C₂²×C₁₃₉	—	4	4	no	—
159	C₂²×C₁₃₉	—	4	4	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	C₂×C₂²⋊Q₈	1	1	yes	characteristic
165	C₂²×C₁₃₉	#525	1	1	yes	characteristic
166	C₂²×C₁₃₉	#535	1	1	yes	characteristic
167	C₂²×C₁₃₉	#576	1	2	yes	—
168	C₂²×C₁₃₉	#577	1	2	yes	—
169	C₄×C₁₃₉	—	2	4	no	—
170	C₄×C₁₃₉	—	4	1	no	—
171	C₄×C₁₃₉	—	4	4	no	—
172	C₄×C₁₃₉	—	4	1	no	—
173	C₄×C₁₃₉	—	4	2	no	—
174	C₄×C₁₃₉	—	8	2	no	—
175	C₄×C₁₃₉	—	8	2	no	—
176	C₄×C₁₃₉	#554	1	2	yes	—
177	C₄×C₁₃₉	#559	1	2	yes	—
178	C₂×C₁₃₉	—	8	4	no	—
179	C₂×C₁₃₉	#2580	1	1	yes	characteristic
180	C₂×C₁₃₉	#3081	1	2	yes	—
181	C₂×C₁₃₉	#3122	1	1	yes	characteristic
182	C₂×C₁₃₉	#3126	1	1	yes	characteristic
183	C₂×C₁₃₉	#3224	1	2	yes	—
184	#29263	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃₉	#29263	1	1	yes	characteristic, direct product factor, Sylow
186	#2331	C₂×C₁₃₉	1	1	yes	characteristic, complemented
187	#2328	C₂×C₁₃₉	1	1	yes	characteristic
188	#2092	C₂×C₁₃₉	1	2	yes	complemented
189	#2023	C₂×C₁₃₉	1	2	yes	complemented
190	#1982	C₂×C₁₃₉	1	2	yes	—
191	#1949	C₂×C₁₃₉	1	2	yes	complemented
192	#1864	C₂×C₁₃₉	1	2	yes	complemented
193	#1862	C₂×C₁₃₉	1	2	yes	complemented
194	#1832	C₂×C₁₃₉	1	1	yes	characteristic, complemented
195	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
196	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
198	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
199	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
201	C₂×#102	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	#391	—	2	2	no	—
206	#390	C₂²×C₁₃₉	1	2	yes	—
207	#389	C₂²×C₁₃₉	1	2	yes	—
208	#387	—	2	2	no	—
209	#386	—	2	2	no	—
210	#386	—	2	2	no	—
211	#382	C₂²×C₁₃₉	1	1	yes	characteristic
212	#382	C₂²×C₁₃₉	1	1	yes	characteristic
213	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
214	#376	C₂²×C₁₃₉	1	1	yes	characteristic
215	#340	C₂²×C₁₃₉	1	2	yes	—
216	#340	C₂²×C₁₃₉	1	2	yes	—
217	#336	C₂²×C₁₃₉	1	2	yes	—
218	#336	C₂²×C₁₃₉	1	1	yes	characteristic
219	#336	C₂²×C₁₃₉	1	1	yes	characteristic
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
226	C₄⋊Q₈	—	2	4	no	—
227	#127	—	2	2	no	—
228	#127	Q₈×C₁₃₉	1	4	yes	complemented
229	C₄×D₄	—	4	2	no	—
230	C₄×D₄	—	4	2	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
243	#107	—	4	2	no	—
244	#106	—	4	2	no	—
245	C₄⋊C₈	—	2	4	no	—
246	#102	—	2	4	no	—
247	#102	—	2	4	no	—
248	#102	—	4	2	no	—
249	#102	—	4	2	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	1	no	—
253	#95	—	2	1	no	—
254	#95	—	2	2	no	—
255	#95	D₄×C₁₃₉	1	2	yes	—
256	#95	D₄×C₁₃₉	1	2	yes	—
257	C₂⁴	—	2	2	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	8	2	no	—
260	C₂×D₄	—	2	8	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	8	2	no	—
267	C₂×D₄	—	8	2	no	—
268	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	—	8	2	no	—
274	C₂²×C₄	—	8	2	no	—
275	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	8	2	no	—
293	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
294	C₂²⋊C₄	—	4	4	no	—
295	C₂²⋊C₄	—	8	2	no	—
296	C₂²⋊C₄	—	8	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	8	2	no	—
300	C₄²	C₂×Q₈×C₁₃₉	1	2	yes	—
301	C₄²	#41×C₁₃₉	1	2	yes	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
310	Q₈	—	8	4	no	—
311	D₄	—	2	4	no	—
312	D₄	—	2	4	no	—
313	D₄	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	8	8	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	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	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	8	no	—
335	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
336	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
338	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
339	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
350	C₂²	#525×C₁₃₉	1	1	yes	characteristic
351	C₂²	#535×C₁₃₉	1	1	yes	characteristic
352	C₂²	#576×C₁₃₉	1	2	yes	—
353	C₂²	#577×C₁₃₉	1	2	yes	—
354	C₄	—	2	4	no	—
355	C₄	—	4	1	no	—
356	C₄	—	4	4	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	2	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	#554×C₁₃₉	1	2	yes	—
362	C₄	#559×C₁₃₉	1	2	yes	—
363	C₂	—	8	4	no	—
364	C₂	#2580×C₁₃₉	1	1	yes	characteristic
365	C₂	#3081×C₁₃₉	1	2	yes	—
366	C₂	#3122×C₁₃₉	1	1	yes	characteristic
367	C₂	#3126×C₁₃₉	1	1	yes	characteristic
368	C₂	#3224×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#127×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ #376×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2331×C₁₃₉	C₂	semidirect
3. #2092×C₁₃₉	C₂	semidirect
4. #2023×C₁₃₉	C₂	semidirect
6. #1949×C₁₃₉	C₂	semidirect
7. #1864×C₁₃₉	C₂	semidirect
8. #1862×C₁₃₉	C₂	semidirect
9. #1832×C₁₃₉	C₂	semidirect
43. #127×C₁₃₉	Q₈	semidirect
184. #29263	C₁₃₉	direct (N × H)
185. C₁₃₉	#29263	direct (N × H)
186. #2331	C₂×C₁₃₉	semidirect
188. #2092	C₂×C₁₃₉	semidirect
189. #2023	C₂×C₁₃₉	semidirect
191. #1949	C₂×C₁₃₉	semidirect
192. #1864	C₂×C₁₃₉	semidirect
193. #1862	C₂×C₁₃₉	semidirect
194. #1832	C₂×C₁₃₉	semidirect
228. #127	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2331×C₁₃₉	2
#2328×C₁₃₉	2
#2092×C₁₃₉	2
#2023×C₁₃₉	2
#1982×C₁₃₉	2
#1949×C₁₃₉	2
#1864×C₁₃₉	2
#1862×C₁₃₉	2
#1832×C₁₃₉	2
#29263	139

Subgroups — C139×#29263 #48023859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29263 #48023859