Subgroups — C₁₃₉×#9087 #48003683

Order 35584.

532 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	#2972×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#440×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#1479×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1478×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1461×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1281×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₁₃₉	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
11	#440×C₁₃₉	—	2	2	no	—
12	#440×C₁₃₉	—	2	2	no	—
13	C₈×D₄×C₁₃₉	—	2	2	no	—
14	C₈×D₄×C₁₃₉	—	2	2	no	—
15	#431×C₁₃₉	C₂²	1	1	yes	characteristic
16	#431×C₁₃₉	C₂²	1	1	yes	characteristic
17	#431×C₁₃₉	C₂²	1	1	yes	characteristic
18	#431×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#107×C₁₃₉	C₄	1	1	yes	characteristic
20	C₂×#103×C₁₃₉	C₄	1	1	yes	characteristic
21	C₂×#102×C₁₃₉	C₄	1	1	yes	characteristic
22	C₂×C₂²⋊C₈×C₁₃₉	—	2	2	no	—
23	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
24	Q₈⋊C₈×C₁₃₉	—	2	2	no	—
25	D₄⋊C₈×C₁₃₉	—	2	2	no	—
26	#324×C₁₃₉	—	2	2	no	—
27	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₉	—	2	1	no	—
30	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
31	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
32	C₂×SD₁₆×C₁₃₉	C₈	1	4	yes	complemented
33	C₂²×C₈×C₁₃₉	—	2	4	no	—
34	C₂²×C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
36	C₄×Q₈×C₁₃₉	—	2	1	no	—
37	C₄×Q₈×C₁₃₉	—	2	1	no	—
38	C₄×Q₈×C₁₃₉	—	2	1	no	—
39	C₄×Q₈×C₁₃₉	—	2	1	no	—
40	C₄×D₄×C₁₃₉	—	2	1	no	—
41	C₄×D₄×C₁₃₉	—	2	1	no	—
42	C₄×D₄×C₁₃₉	D₄	1	2	yes	—
43	C₄×D₄×C₁₃₉	D₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
48	C₂×C₄²×C₁₃₉	—	2	1	no	—
49	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
50	#107×C₁₃₉	—	2	2	no	—
51	C₄⋊C₈×C₁₃₉	—	2	1	no	—
52	C₄⋊C₈×C₁₃₉	—	2	1	no	—
53	C₄⋊C₈×C₁₃₉	—	2	1	no	—
54	C₄⋊C₈×C₁₃₉	—	2	1	no	—
55	#103×C₁₃₉	—	2	2	no	—
56	#102×C₁₃₉	—	2	2	no	—
57	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
58	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
59	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
60	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
61	C₂²⋊C₈×C₁₃₉	D₄	1	2	yes	—
62	#97×C₁₃₉	—	2	1	no	—
63	#97×C₁₃₉	—	2	1	no	—
64	C₄×C₈×C₁₃₉	—	2	1	no	—
65	C₄×C₈×C₁₃₉	—	2	1	no	—
66	C₄×C₈×C₁₃₉	—	2	1	no	—
67	C₄×C₈×C₁₃₉	D₄	1	2	yes	—
68	C₂⁴×C₁₃₉	—	2	1	no	—
69	C₂×Q₈×C₁₃₉	—	2	1	no	—
70	C₂×Q₈×C₁₃₉	—	2	1	no	—
71	C₂×Q₈×C₁₃₉	—	2	1	no	—
72	C₂×Q₈×C₁₃₉	—	2	1	no	—
73	C₂×Q₈×C₁₃₉	—	2	1	no	—
74	C₂×Q₈×C₁₃₉	C₂×C₈	1	2	yes	complemented
75	C₂×D₄×C₁₃₉	—	2	1	no	—
76	C₂×D₄×C₁₃₉	—	2	1	no	—
77	C₂×D₄×C₁₃₉	—	2	1	no	—
78	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
79	C₂×D₄×C₁₃₉	C₂×C₈	1	2	yes	—
80	C₂×D₄×C₁₃₉	M₁₆	1	2	yes	—
81	C₂²×C₄×C₁₃₉	—	2	1	no	—
82	C₂²×C₄×C₁₃₉	—	2	1	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	2	no	—
85	C₂²×C₄×C₁₃₉	—	2	1	no	—
86	C₂²×C₄×C₁₃₉	—	8	2	no	—
87	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₉	#41	1	1	yes	characteristic
90	SD₁₆×C₁₃₉	—	2	8	no	—
91	C₂×C₈×C₁₃₉	—	2	1	no	—
92	C₂×C₈×C₁₃₉	—	2	1	no	—
93	C₂×C₈×C₁₃₉	—	2	1	no	—
94	C₂×C₈×C₁₃₉	—	2	2	no	—
95	C₂×C₈×C₁₃₉	—	2	2	no	—
96	C₂×C₈×C₁₃₉	—	2	1	no	—
97	C₂×C₈×C₁₃₉	—	2	1	no	—
98	C₂×C₈×C₁₃₉	—	4	1	no	—
99	C₂×C₈×C₁₃₉	—	4	1	no	—
100	C₂×C₈×C₁₃₉	—	8	4	no	—
101	C₂×C₈×C₁₃₉	C₂×C₈	1	2	yes	complemented
102	C₄⋊C₄×C₁₃₉	—	2	1	no	—
103	C₄⋊C₄×C₁₃₉	—	2	1	no	—
104	C₄⋊C₄×C₁₃₉	—	2	1	no	—
105	C₄⋊C₄×C₁₃₉	—	4	1	no	—
106	C₄⋊C₄×C₁₃₉	—	4	1	no	—
107	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
108	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
110	C₄²×C₁₃₉	—	4	1	no	—
111	C₄²×C₁₃₉	—	4	1	no	—
112	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₃₉	#41	1	1	yes	characteristic
116	C₂³×C₁₃₉	—	2	2	no	—
117	C₂³×C₁₃₉	—	2	2	no	—
118	C₂³×C₁₃₉	—	2	2	no	—
119	C₂³×C₁₃₉	—	8	1	no	—
120	C₂³×C₁₃₉	—	8	1	no	—
121	C₂³×C₁₃₉	C₄×D₄	1	1	yes	characteristic
122	Q₈×C₁₃₉	—	2	2	no	—
123	Q₈×C₁₃₉	—	2	2	no	—
124	Q₈×C₁₃₉	—	4	1	no	—
125	Q₈×C₁₃₉	—	4	1	no	—
126	D₄×C₁₃₉	—	2	2	no	—
127	D₄×C₁₃₉	—	2	2	no	—
128	D₄×C₁₃₉	—	2	2	no	—
129	D₄×C₁₃₉	C₂²⋊C₈	1	4	yes	—
130	C₂×C₄×C₁₃₉	—	2	2	no	—
131	C₂×C₄×C₁₃₉	—	2	2	no	—
132	C₂×C₄×C₁₃₉	—	4	1	no	—
133	C₂×C₄×C₁₃₉	—	4	1	no	—
134	C₂×C₄×C₁₃₉	—	4	4	no	—
135	C₂×C₄×C₁₃₉	—	4	1	no	—
136	C₂×C₄×C₁₃₉	—	4	1	no	—
137	C₂×C₄×C₁₃₉	—	4	1	no	—
138	C₂×C₄×C₁₃₉	—	8	2	no	—
139	C₂×C₄×C₁₃₉	—	8	1	no	—
140	C₂×C₄×C₁₃₉	—	8	1	no	—
141	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
144	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
145	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
146	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₃₉	#131	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	#131	1	1	yes	characteristic
151	C₈×C₁₃₉	—	2	2	no	—
152	C₈×C₁₃₉	—	4	2	no	—
153	C₈×C₁₃₉	—	4	2	no	—
154	C₈×C₁₃₉	—	4	1	no	—
155	C₈×C₁₃₉	—	8	1	no	—
156	C₈×C₁₃₉	—	8	1	no	—
157	C₂²×C₁₃₉	—	2	1	no	—
158	C₂²×C₁₃₉	—	2	1	no	—
159	C₂²×C₁₃₉	—	2	4	no	—
160	C₂²×C₁₃₉	—	4	2	no	—
161	C₂²×C₁₃₉	—	4	2	no	—
162	C₂²×C₁₃₉	—	8	2	no	—
163	C₂²×C₁₃₉	—	8	2	no	—
164	C₂²×C₁₃₉	#386	1	1	yes	characteristic
165	C₂²×C₁₃₉	C₈×D₄	1	1	yes	characteristic
166	C₂²×C₁₃₉	#435	1	1	yes	characteristic
167	C₄×C₁₃₉	—	2	1	no	—
168	C₄×C₁₃₉	—	2	1	no	—
169	C₄×C₁₃₉	—	2	1	no	—
170	C₄×C₁₃₉	—	2	1	no	—
171	C₄×C₁₃₉	—	4	2	no	—
172	C₄×C₁₃₉	—	4	2	no	—
173	C₄×C₁₃₉	—	8	1	no	—
174	C₄×C₁₃₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
175	C₄×C₁₃₉	#408	1	1	yes	characteristic
176	C₄×C₁₃₉	C₈×D₄	1	1	yes	characteristic
177	C₄×C₁₃₉	#435	1	1	yes	characteristic
178	C₂×C₁₃₉	—	2	1	no	—
179	C₂×C₁₃₉	—	2	1	no	—
180	C₂×C₁₃₉	—	4	4	no	—
181	C₂×C₁₃₉	#1869	1	1	yes	characteristic
182	C₂×C₁₃₉	#1902	1	1	yes	characteristic
183	C₂×C₁₃₉	#1904	1	1	yes	characteristic
184	#9087	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃₉	#9087	1	1	yes	characteristic, direct product factor, Sylow
186	#2972	C₂×C₁₃₉	1	1	yes	characteristic
187	C₂×#440	C₂×C₁₃₉	1	1	yes	characteristic
188	#1479	C₂×C₁₃₉	1	1	yes	characteristic, complemented
189	#1478	C₂×C₁₃₉	1	1	yes	characteristic
190	#1461	C₂×C₁₃₉	1	1	yes	characteristic, complemented
191	#1281	C₂×C₁₃₉	1	1	yes	characteristic, complemented
192	#1275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
193	C₂²×SD₁₆	C₄×C₁₃₉	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
196	#440	—	2	2	no	—
197	#440	—	2	2	no	—
198	C₈×D₄	—	2	2	no	—
199	C₈×D₄	—	2	2	no	—
200	#431	C₂²×C₁₃₉	1	1	yes	characteristic
201	#431	C₂²×C₁₃₉	1	1	yes	characteristic
202	#431	C₂²×C₁₃₉	1	1	yes	characteristic
203	#431	C₂²×C₁₃₉	1	1	yes	characteristic
204	C₂×#107	C₄×C₁₃₉	1	1	yes	characteristic
205	C₂×#103	C₄×C₁₃₉	1	1	yes	characteristic
206	C₂×#102	C₄×C₁₃₉	1	1	yes	characteristic
207	C₂×C₂²⋊C₈	—	2	2	no	—
208	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
209	Q₈⋊C₈	—	2	2	no	—
210	D₄⋊C₈	—	2	2	no	—
211	#324	—	2	2	no	—
212	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
213	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
214	C₂³×C₄	—	2	1	no	—
215	C₂×SD₁₆	—	2	2	no	—
216	C₂×SD₁₆	—	2	2	no	—
217	C₂×SD₁₆	C₈×C₁₃₉	1	4	yes	complemented
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
220	C₂²×C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	D₄×C₁₃₉	1	2	yes	—
228	C₄×D₄	D₄×C₁₃₉	1	2	yes	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
235	#107	—	2	2	no	—
236	C₄⋊C₈	—	2	1	no	—
237	C₄⋊C₈	—	2	1	no	—
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	—	2	1	no	—
240	#103	—	2	2	no	—
241	#102	—	2	2	no	—
242	C₂²⋊C₈	—	2	4	no	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	C₂²⋊C₈	—	2	1	no	—
246	C₂²⋊C₈	D₄×C₁₃₉	1	2	yes	—
247	#97	—	2	1	no	—
248	#97	—	2	1	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	D₄×C₁₃₉	1	2	yes	—
253	C₂⁴	—	2	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	—	2	1	no	—
259	C₂×Q₈	C₂×C₈×C₁₃₉	1	2	yes	complemented
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
264	C₂×D₄	C₂×C₈×C₁₃₉	1	2	yes	—
265	C₂×D₄	M₁₆×C₁₃₉	1	2	yes	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	8	2	no	—
272	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
274	C₂²×C₄	#41×C₁₃₉	1	1	yes	characteristic
275	SD₁₆	—	2	8	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	8	4	no	—
286	C₂×C₈	C₂×C₈×C₁₃₉	1	2	yes	complemented
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₄²	—	4	1	no	—
296	C₄²	—	4	1	no	—
297	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
300	C₄²	#41×C₁₃₉	1	1	yes	characteristic
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	8	1	no	—
305	C₂³	—	8	1	no	—
306	C₂³	C₄×D₄×C₁₃₉	1	1	yes	characteristic
307	Q₈	—	2	2	no	—
308	Q₈	—	2	2	no	—
309	Q₈	—	4	1	no	—
310	Q₈	—	4	1	no	—
311	D₄	—	2	2	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	2	no	—
314	D₄	C₂²⋊C₈×C₁₃₉	1	4	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	—	8	1	no	—
325	C₂×C₄	—	8	1	no	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
327	C₂×C₄	C₄×D₄×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
329	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
331	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
333	C₂×C₄	C₂×M₁₆×C₁₃₉	1	1	yes	characteristic
334	C₂×C₄	#131×C₁₃₉	1	1	yes	characteristic
335	C₂×C₄	#131×C₁₃₉	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	4	2	no	—
338	C₈	—	4	2	no	—
339	C₈	—	4	1	no	—
340	C₈	—	8	1	no	—
341	C₈	—	8	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	#386×C₁₃₉	1	1	yes	characteristic
350	C₂²	C₈×D₄×C₁₃₉	1	1	yes	characteristic
351	C₂²	#435×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	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	8	1	no	—
359	C₄	C₂×C₂²⋊C₈×C₁₃₉	1	1	yes	characteristic
360	C₄	#408×C₁₃₉	1	1	yes	characteristic
361	C₄	C₈×D₄×C₁₃₉	1	1	yes	characteristic
362	C₄	#435×C₁₃₉	1	1	yes	characteristic
363	C₂	—	2	1	no	—
364	C₂	—	2	1	no	—
365	C₂	—	4	4	no	—
366	C₂	#1869×C₁₃₉	1	1	yes	characteristic
367	C₂	#1902×C₁₃₉	1	1	yes	characteristic
368	C₂	#1904×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	#386
commutator	C₂×C₄	C₂²×C₈×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1479×C₁₃₉	C₂	semidirect
5. #1461×C₁₃₉	C₂	semidirect
6. #1281×C₁₃₉	C₂	semidirect
7. #1275×C₁₃₉	C₂	semidirect
32. C₂×SD₁₆×C₁₃₉	C₈	semidirect
74. C₂×Q₈×C₁₃₉	C₂×C₈	semidirect
101. C₂×C₈×C₁₃₉	C₂×C₈	semidirect
184. #9087	C₁₃₉	direct (N × H)
185. C₁₃₉	#9087	direct (N × H)
188. #1479	C₂×C₁₃₉	semidirect
190. #1461	C₂×C₁₃₉	semidirect
191. #1281	C₂×C₁₃₉	semidirect
192. #1275	C₂×C₁₃₉	semidirect
217. C₂×SD₁₆	C₈×C₁₃₉	semidirect
259. C₂×Q₈	C₂×C₈×C₁₃₉	semidirect
286. C₂×C₈	C₂×C₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2972×C₁₃₉	2
C₂×#440×C₁₃₉	2
#1479×C₁₃₉	2
#1478×C₁₃₉	2
#1461×C₁₃₉	2
#1281×C₁₃₉	2
#1275×C₁₃₉	2
#9087	139

Subgroups — C139×#9087 #48003683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#9087 #48003683