Subgroups — C₁₃₉×#19358 #48013954

Order 35584.

608 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3218×C₁₃₉	C₂	1	2	yes	maximal
2	C₂×#500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2966×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1694×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1693×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1674×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1673×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1568×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1556×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
11	#529×C₁₃₉	C₂²	1	1	yes	characteristic
12	#500×C₁₃₉	—	2	1	no	—
13	#500×C₁₃₉	—	2	1	no	—
14	#500×C₁₃₉	C₂²	1	2	yes	—
15	#500×C₁₃₉	C₂²	1	2	yes	—
16	#497×C₁₃₉	—	2	2	no	—
17	#491×C₁₃₉	—	2	2	no	—
18	#462×C₁₃₉	C₂²	1	4	yes	—
19	#461×C₁₃₉	C₂²	1	4	yes	—
20	#451×C₁₃₉	—	2	2	no	—
21	#448×C₁₃₉	—	2	2	no	—
22	#446×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₈×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	#436×C₁₃₉	C₂²	1	1	yes	characteristic
25	#435×C₁₃₉	—	2	1	no	—
26	C₈×D₄×C₁₃₉	—	2	1	no	—
27	C₈×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	#433×C₁₃₉	—	2	1	no	—
29	#432×C₁₃₉	C₂²	1	1	yes	characteristic
30	#432×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#107×C₁₃₉	—	2	1	no	—
32	C₂×#107×C₁₃₉	—	2	1	no	—
33	#405×C₁₃₉	—	2	1	no	—
34	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	#335×C₁₃₉	C₂²	1	2	yes	—
36	#334×C₁₃₉	C₂²	1	2	yes	—
37	#332×C₁₃₉	C₂²	1	4	yes	—
38	#332×C₁₃₉	C₂²	1	4	yes	—
39	C₂²×Q₈×C₁₃₉	—	2	2	no	—
40	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
41	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
42	C₂×M₁₆×C₁₃₉	—	2	1	no	—
43	C₂²×C₈×C₁₃₉	—	2	1	no	—
44	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
46	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
47	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
48	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
49	C₄⋊Q₈×C₁₃₉	C₂³	1	4	yes	—
50	#126×C₁₃₉	—	2	1	no	—
51	#125×C₁₃₉	D₄	1	1	yes	characteristic
52	#124×C₁₃₉	D₄	1	1	yes	characteristic
53	#123×C₁₃₉	—	2	1	no	—
54	C₂²⋊Q₈×C₁₃₉	D₄	1	1	yes	characteristic
55	#121×C₁₃₉	D₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₁₃₉	—	2	1	no	—
58	C₄×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
59	#117×C₁₃₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
63	#107×C₁₃₉	—	2	2	no	—
64	#107×C₁₃₉	—	2	2	no	—
65	#107×C₁₃₉	—	2	2	no	—
66	#107×C₁₃₉	—	2	2	no	—
67	C₄⋊C₈×C₁₃₉	—	2	1	no	—
68	C₄⋊C₈×C₁₃₉	—	2	1	no	—
69	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₃₉	C₂³	1	4	yes	—
72	#103×C₁₃₉	—	2	4	no	—
73	#103×C₁₃₉	—	2	4	no	—
74	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
75	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
76	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
77	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
78	#97×C₁₃₉	—	2	1	no	—
79	#97×C₁₃₉	—	2	1	no	—
80	#97×C₁₃₉	—	2	2	no	—
81	C₄×C₈×C₁₃₉	—	2	1	no	—
82	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃₉	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₁₃₉	—	2	4	no	—
87	C₂×Q₈×C₁₃₉	—	4	2	no	—
88	C₂×Q₈×C₁₃₉	—	8	4	no	—
89	C₂×Q₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₃₉	—	2	1	no	—
91	C₂×D₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	—	2	1	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₉	#41	1	1	yes	characteristic
97	Q₁₆×C₁₃₉	—	8	4	no	—
98	SD₁₆×C₁₃₉	—	8	4	no	—
99	M₁₆×C₁₃₉	—	4	2	no	—
100	C₂×C₈×C₁₃₉	—	2	2	no	—
101	C₂×C₈×C₁₃₉	—	2	2	no	—
102	C₂×C₈×C₁₃₉	—	2	1	no	—
103	C₂×C₈×C₁₃₉	—	2	1	no	—
104	C₂×C₈×C₁₃₉	—	2	4	no	—
105	C₂×C₈×C₁₃₉	—	4	2	no	—
106	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₉	—	2	1	no	—
111	C₄⋊C₄×C₁₃₉	—	2	1	no	—
112	C₄⋊C₄×C₁₃₉	—	2	1	no	—
113	C₄⋊C₄×C₁₃₉	—	2	1	no	—
114	C₄⋊C₄×C₁₃₉	—	2	4	no	—
115	C₄⋊C₄×C₁₃₉	—	2	4	no	—
116	C₄⋊C₄×C₁₃₉	—	4	2	no	—
117	C₄⋊C₄×C₁₃₉	—	4	2	no	—
118	C₄⋊C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
119	C₄⋊C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
120	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
121	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
122	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
123	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
124	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
125	C₄²×C₁₃₉	—	2	1	no	—
126	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃₉	#41	1	1	yes	characteristic
129	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	#121	1	1	yes	characteristic
132	Q₈×C₁₃₉	—	2	2	no	—
133	Q₈×C₁₃₉	—	4	4	no	—
134	Q₈×C₁₃₉	—	4	4	no	—
135	Q₈×C₁₃₉	—	8	4	no	—
136	D₄×C₁₃₉	—	2	2	no	—
137	D₄×C₁₃₉	—	4	2	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	1	no	—
140	C₂×C₄×C₁₃₉	—	2	1	no	—
141	C₂×C₄×C₁₃₉	—	2	2	no	—
142	C₂×C₄×C₁₃₉	—	2	1	no	—
143	C₂×C₄×C₁₃₉	—	2	1	no	—
144	C₂×C₄×C₁₃₉	—	2	1	no	—
145	C₂×C₄×C₁₃₉	—	4	1	no	—
146	C₂×C₄×C₁₃₉	—	4	1	no	—
147	C₂×C₄×C₁₃₉	—	4	4	no	—
148	C₂×C₄×C₁₃₉	—	8	4	no	—
149	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
155	C₈×C₁₃₉	—	2	1	no	—
156	C₈×C₁₃₉	—	2	1	no	—
157	C₈×C₁₃₉	—	4	1	no	—
158	C₈×C₁₃₉	—	4	1	no	—
159	C₈×C₁₃₉	—	4	4	no	—
160	C₈×C₁₃₉	#137	1	2	yes	—
161	C₈×C₁₃₉	#137	1	2	yes	—
162	C₂²×C₁₃₉	—	2	1	no	—
163	C₂²×C₁₃₉	—	2	1	no	—
164	C₂²×C₁₃₉	—	4	1	no	—
165	C₂²×C₁₃₉	—	4	1	no	—
166	C₂²×C₁₃₉	—	4	1	no	—
167	C₂²×C₁₃₉	#473	1	2	yes	—
168	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
169	C₄×C₁₃₉	—	2	1	no	—
170	C₄×C₁₃₉	—	2	1	no	—
171	C₄×C₁₃₉	—	2	1	no	—
172	C₄×C₁₃₉	—	2	1	no	—
173	C₄×C₁₃₉	—	4	1	no	—
174	C₄×C₁₃₉	—	4	1	no	—
175	C₄×C₁₃₉	—	4	1	no	—
176	C₄×C₁₃₉	—	8	4	no	—
177	C₄×C₁₃₉	C₂×#137	1	1	yes	characteristic
178	C₄×C₁₃₉	C₂×#137	1	1	yes	characteristic
179	C₄×C₁₃₉	#576	1	2	yes	—
180	C₂×C₁₃₉	—	2	2	no	—
181	C₂×C₁₃₉	—	8	1	no	—
182	C₂×C₁₃₉	#3039	1	1	yes	characteristic
183	C₂×C₁₃₉	#3058	1	1	yes	characteristic
184	C₂×C₁₃₉	C₂×#473	1	1	yes	characteristic
185	#19358	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₉	#19358	1	1	yes	characteristic, direct product factor, Sylow
187	#3218	C₂×C₁₃₉	1	2	yes	—
188	C₂×#500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
189	#2966	C₂×C₁₃₉	1	1	yes	characteristic
190	#1694	C₂×C₁₃₉	1	2	yes	complemented
191	#1693	C₂×C₁₃₉	1	2	yes	complemented
192	#1674	C₂×C₁₃₉	1	2	yes	complemented
193	#1673	C₂×C₁₃₉	1	2	yes	complemented
194	#1568	C₂×C₁₃₉	1	1	yes	characteristic, complemented
195	#1556	C₂×C₁₃₉	1	2	yes	complemented
196	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
197	#529	C₂²×C₁₃₉	1	1	yes	characteristic
198	#500	—	2	1	no	—
199	#500	—	2	1	no	—
200	#500	C₂²×C₁₃₉	1	2	yes	—
201	#500	C₂²×C₁₃₉	1	2	yes	—
202	#497	—	2	2	no	—
203	#491	—	2	2	no	—
204	#462	C₂²×C₁₃₉	1	4	yes	—
205	#461	C₂²×C₁₃₉	1	4	yes	—
206	#451	—	2	2	no	—
207	#448	—	2	2	no	—
208	#446	C₂²×C₁₃₉	1	1	yes	characteristic
209	C₈×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
210	#436	C₂²×C₁₃₉	1	1	yes	characteristic
211	#435	—	2	1	no	—
212	C₈×D₄	—	2	1	no	—
213	C₈×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
214	#433	—	2	1	no	—
215	#432	C₂²×C₁₃₉	1	1	yes	characteristic
216	#432	C₂²×C₁₃₉	1	2	yes	—
217	C₂×#107	—	2	1	no	—
218	C₂×#107	—	2	1	no	—
219	#405	—	2	1	no	—
220	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
221	#335	C₂²×C₁₃₉	1	2	yes	—
222	#334	C₂²×C₁₃₉	1	2	yes	—
223	#332	C₂²×C₁₃₉	1	4	yes	—
224	#332	C₂²×C₁₃₉	1	4	yes	—
225	C₂²×Q₈	—	2	2	no	—
226	C₂×Q₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
231	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	C₂³×C₁₃₉	1	4	yes	—
236	#126	—	2	1	no	—
237	#125	D₄×C₁₃₉	1	1	yes	characteristic
238	#124	D₄×C₁₃₉	1	1	yes	characteristic
239	#123	—	2	1	no	—
240	C₂²⋊Q₈	D₄×C₁₃₉	1	1	yes	characteristic
241	#121	D₄×C₁₃₉	1	1	yes	characteristic
242	C₄×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
245	#117	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
249	#107	—	2	2	no	—
250	#107	—	2	2	no	—
251	#107	—	2	2	no	—
252	#107	—	2	2	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
256	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
257	C₄⋊C₈	C₂³×C₁₃₉	1	4	yes	—
258	#103	—	2	4	no	—
259	#103	—	2	4	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	1	no	—
263	C₂²⋊C₈	—	2	1	no	—
264	#97	—	2	1	no	—
265	#97	—	2	1	no	—
266	#97	—	2	2	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	D₄×C₁₃₉	1	1	yes	characteristic
269	C₄×C₈	D₄×C₁₃₉	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	8	4	no	—
275	C₂×Q₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
282	C₂²×C₄	#41×C₁₃₉	1	1	yes	characteristic
283	Q₁₆	—	8	4	no	—
284	SD₁₆	—	8	4	no	—
285	M₁₆	—	4	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
305	C₄⋊C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
306	C₂²⋊C₄	—	2	1	no	—
307	C₂²⋊C₄	—	2	1	no	—
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	2	1	no	—
310	C₂²⋊C₄	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
313	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
314	C₄²	#41×C₁₃₉	1	1	yes	characteristic
315	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
316	C₂³	—	2	1	no	—
317	C₂³	#121×C₁₃₉	1	1	yes	characteristic
318	Q₈	—	2	2	no	—
319	Q₈	—	4	4	no	—
320	Q₈	—	4	4	no	—
321	Q₈	—	8	4	no	—
322	D₄	—	2	2	no	—
323	D₄	—	4	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	8	4	no	—
335	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
336	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
337	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	2	1	no	—
343	C₈	—	4	1	no	—
344	C₈	—	4	1	no	—
345	C₈	—	4	4	no	—
346	C₈	#137×C₁₃₉	1	2	yes	—
347	C₈	#137×C₁₃₉	1	2	yes	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	4	1	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	#473×C₁₃₉	1	2	yes	—
354	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	8	4	no	—
363	C₄	C₂×#137×C₁₃₉	1	1	yes	characteristic
364	C₄	C₂×#137×C₁₃₉	1	1	yes	characteristic
365	C₄	#576×C₁₃₉	1	2	yes	—
366	C₂	—	2	2	no	—
367	C₂	—	8	1	no	—
368	C₂	#3039×C₁₃₉	1	1	yes	characteristic
369	C₂	#3058×C₁₃₉	1	1	yes	characteristic
370	C₂	C₂×#473×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
prime radical	#121×C₁₃₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ 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
2. C₂×#500×C₁₃₉	C₂	semidirect
4. #1694×C₁₃₉	C₂	semidirect
5. #1693×C₁₃₉	C₂	semidirect
6. #1674×C₁₃₉	C₂	semidirect
7. #1673×C₁₃₉	C₂	semidirect
8. #1568×C₁₃₉	C₂	semidirect
9. #1556×C₁₃₉	C₂	semidirect
185. #19358	C₁₃₉	direct (N × H)
186. C₁₃₉	#19358	direct (N × H)
188. C₂×#500	C₂×C₁₃₉	semidirect
190. #1694	C₂×C₁₃₉	semidirect
191. #1693	C₂×C₁₃₉	semidirect
192. #1674	C₂×C₁₃₉	semidirect
193. #1673	C₂×C₁₃₉	semidirect
194. #1568	C₂×C₁₃₉	semidirect
195. #1556	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3218×C₁₃₉	2
C₂×#500×C₁₃₉	2
#2966×C₁₃₉	2
#1694×C₁₃₉	2
#1693×C₁₃₉	2
#1674×C₁₃₉	2
#1673×C₁₃₉	2
#1568×C₁₃₉	2
#1556×C₁₃₉	2
#19358	139

Subgroups — C139×#19358 #48013954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#19358 #48013954