Subgroups — C₁₃₉×#10712 #48005308

Order 35584.

2038 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₃₉	C₂	1	2	yes	maximal
3	C₂×#336×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	C₂⁴×C₄×C₁₃₉	C₄	1	2	yes	—
5	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
6	C₂³×C₈×C₁₃₉	C₂²	1	4	yes	—
7	C₂²×C₄²×C₁₃₉	—	2	4	no	—
8	C₂²×C₄²×C₁₃₉	—	2	8	no	—
9	C₂²×C₄²×C₁₃₉	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
11	C₂×C₂²⋊C₈×C₁₃₉	—	2	4	no	—
12	C₂×C₂²⋊C₈×C₁₃₉	—	2	4	no	—
13	C₂×C₂²⋊C₈×C₁₃₉	C₄	1	8	yes	complemented
14	#336×C₁₃₉	—	2	8	no	—
15	C₂⁵×C₁₃₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₃₉	—	2	4	no	—
17	C₂³×C₄×C₁₃₉	—	2	4	no	—
18	C₂³×C₄×C₁₃₉	—	2	8	no	—
19	C₂³×C₄×C₁₃₉	—	2	8	no	—
20	C₂³×C₄×C₁₃₉	—	2	4	no	—
21	C₂³×C₄×C₁₃₉	—	2	4	no	—
22	C₂³×C₄×C₁₃₉	C₈	1	8	yes	complemented
23	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
26	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
27	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
28	C₂³×C₄×C₁₃₉	Q₈	1	2	yes	—
29	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₃₉	—	2	4	no	—
31	C₂²×C₈×C₁₃₉	—	2	4	no	—
32	C₂²×C₈×C₁₃₉	—	2	8	no	—
33	C₂²×C₈×C₁₃₉	—	2	8	no	—
34	C₂²×C₈×C₁₃₉	C₂×C₄	1	8	yes	complemented
35	C₂×C₄²×C₁₃₉	—	2	32	no	—
36	C₂×C₄²×C₁₃₉	—	2	4	no	—
37	C₂×C₄²×C₁₃₉	—	2	8	no	—
38	C₂×C₄²×C₁₃₉	—	2	4	no	—
39	C₂×C₄²×C₁₃₉	—	2	4	no	—
40	C₂×C₄²×C₁₃₉	D₄	1	8	yes	—
41	C₂²⋊C₈×C₁₃₉	—	2	16	no	—
42	C₂⁴×C₁₃₉	—	2	2	no	—
43	C₂⁴×C₁₃₉	—	2	2	no	—
44	C₂⁴×C₁₃₉	—	2	4	no	—
45	C₂⁴×C₁₃₉	C₄²	1	2	yes	—
46	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
47	C₂⁴×C₁₃₉	C₄⋊C₄	1	2	yes	—
48	C₂⁴×C₁₃₉	C₂×C₈	1	4	yes	—
49	C₂⁴×C₁₃₉	M₁₆	1	4	yes	—
50	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃₉	—	2	16	no	—
52	C₂²×C₄×C₁₃₉	—	2	32	no	—
53	C₂²×C₄×C₁₃₉	—	2	16	no	—
54	C₂²×C₄×C₁₃₉	—	2	16	no	—
55	C₂²×C₄×C₁₃₉	—	2	2	no	—
56	C₂²×C₄×C₁₃₉	—	2	4	no	—
57	C₂²×C₄×C₁₃₉	—	2	4	no	—
58	C₂²×C₄×C₁₃₉	—	2	2	no	—
59	C₂²×C₄×C₁₃₉	—	2	4	no	—
60	C₂²×C₄×C₁₃₉	—	2	4	no	—
61	C₂²×C₄×C₁₃₉	—	2	32	no	—
62	C₂²×C₄×C₁₃₉	—	2	16	no	—
63	C₂²×C₄×C₁₃₉	—	2	8	no	—
64	C₂²×C₄×C₁₃₉	—	2	8	no	—
65	C₂²×C₄×C₁₃₉	—	2	8	no	—
66	C₂²×C₄×C₁₃₉	—	2	8	no	—
67	C₂²×C₄×C₁₃₉	C₄²	1	2	yes	—
68	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
70	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
71	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
73	C₂²×C₄×C₁₃₉	C₂×C₈	1	8	yes	—
74	C₂²×C₄×C₁₃₉	M₁₆	1	8	yes	—
75	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
79	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
81	C₂×C₈×C₁₃₉	—	2	8	no	—
82	C₂×C₈×C₁₃₉	—	2	16	no	—
83	C₂×C₈×C₁₃₉	—	4	4	no	—
84	C₂×C₈×C₁₃₉	—	4	8	no	—
85	C₂×C₈×C₁₃₉	—	4	4	no	—
86	C₄²×C₁₃₉	—	2	16	no	—
87	C₄²×C₁₃₉	—	2	16	no	—
88	C₂³×C₁₃₉	—	2	4	no	—
89	C₂³×C₁₃₉	—	2	2	no	—
90	C₂³×C₁₃₉	—	2	4	no	—
91	C₂³×C₁₃₉	—	2	2	no	—
92	C₂³×C₁₃₉	—	2	4	no	—
93	C₂³×C₁₃₉	—	2	8	no	—
94	C₂³×C₁₃₉	—	2	4	no	—
95	C₂³×C₁₃₉	—	2	8	no	—
96	C₂³×C₁₃₉	—	2	4	no	—
97	C₂³×C₁₃₉	—	2	8	no	—
98	C₂³×C₁₃₉	—	2	8	no	—
99	C₂³×C₁₃₉	#95	1	4	yes	—
100	C₂³×C₁₃₉	C₄×C₈	1	4	yes	—
101	C₂³×C₁₃₉	#97	1	4	yes	—
102	C₂³×C₁₃₉	C₂²⋊C₈	1	8	yes	—
103	C₂³×C₁₃₉	C₄⋊C₈	1	8	yes	—
104	C₂³×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
105	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
107	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂³×C₁₃₉	#117	1	2	yes	—
109	C₂³×C₁₃₉	C₂²×C₈	1	2	yes	—
110	C₂³×C₁₃₉	C₂×M₁₆	1	2	yes	—
111	C₂³×C₁₃₉	C₂×M₁₆	1	4	yes	—
112	C₂×C₄×C₁₃₉	—	2	64	no	—
113	C₂×C₄×C₁₃₉	—	2	4	no	—
114	C₂×C₄×C₁₃₉	—	2	2	no	—
115	C₂×C₄×C₁₃₉	—	2	8	no	—
116	C₂×C₄×C₁₃₉	—	2	4	no	—
117	C₂×C₄×C₁₃₉	—	2	2	no	—
118	C₂×C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄×C₁₃₉	—	2	8	no	—
120	C₂×C₄×C₁₃₉	—	2	8	no	—
121	C₂×C₄×C₁₃₉	—	2	8	no	—
122	C₂×C₄×C₁₃₉	—	2	8	no	—
123	C₂×C₄×C₁₃₉	—	2	16	no	—
124	C₂×C₄×C₁₃₉	—	2	16	no	—
125	C₂×C₄×C₁₃₉	#95	1	4	yes	—
126	C₂×C₄×C₁₃₉	C₂²⋊C₈	1	16	yes	complemented
127	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₁₃₉	C₄×D₄	1	8	yes	—
130	C₂×C₄×C₁₃₉	#120	1	4	yes	—
131	C₂×C₄×C₁₃₉	#121	1	4	yes	—
132	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
133	C₂×C₄×C₁₃₉	#123	1	4	yes	—
134	C₈×C₁₃₉	—	4	8	no	—
135	C₂²×C₁₃₉	—	2	16	no	—
136	C₂²×C₁₃₉	—	2	8	no	—
137	C₂²×C₁₃₉	—	2	4	no	—
138	C₂²×C₁₃₉	—	2	4	no	—
139	C₂²×C₁₃₉	—	2	8	no	—
140	C₂²×C₁₃₉	—	2	8	no	—
141	C₂²×C₁₃₉	—	2	8	no	—
142	C₂²×C₁₃₉	#336	1	8	yes	complemented
143	C₂²×C₁₃₉	C₂×#95	1	1	yes	characteristic
144	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
145	C₂²×C₁₃₉	#379	1	1	yes	characteristic
146	C₂²×C₁₃₉	#380	1	2	yes	—
147	C₂²×C₁₃₉	#381	1	1	yes	characteristic
148	C₂²×C₁₃₉	C₂×C₄×C₈	1	1	yes	characteristic
149	C₂²×C₁₃₉	C₂×#97	1	1	yes	characteristic
150	C₂²×C₁₃₉	C₄×M₁₆	1	2	yes	—
151	C₂²×C₁₃₉	C₂×C₂²⋊C₈	1	4	yes	—
152	C₂²×C₁₃₉	C₂×C₂²⋊C₈	1	2	yes	—
153	C₂²×C₁₃₉	#407	1	4	yes	—
154	C₂²×C₁₃₉	#407	1	2	yes	—
155	C₂²×C₁₃₉	C₂×C₄⋊C₈	1	2	yes	—
156	C₂²×C₁₃₉	#423	1	2	yes	—
157	C₂²×C₁₃₉	#431	1	4	yes	—
158	C₂²×C₁₃₉	#432	1	4	yes	—
159	C₄×C₁₃₉	—	2	4	no	—
160	C₄×C₁₃₉	—	2	16	no	—
161	C₄×C₁₃₉	#385	1	4	yes	—
162	C₄×C₁₃₉	#386	1	4	yes	—
163	C₂×C₁₃₉	—	2	8	no	—
164	C₂×C₁₃₉	C₂²⋊#95	1	1	yes	characteristic
165	C₂×C₁₃₉	C₂×#336	1	1	yes	characteristic
166	C₂×C₁₃₉	#1728	1	1	yes	characteristic
167	C₂×C₁₃₉	C₄×C₂²⋊C₈	1	2	yes	—
168	C₂×C₁₃₉	#1749	1	2	yes	—
169	C₂×C₁₃₉	#1779	1	2	yes	—
170	C₂×C₁₃₉	#1797	1	4	yes	—
171	C₂×C₁₃₉	#1817	1	2	yes	—
172	#10712	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₁₃₉	#10712	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³×C₄²	C₂×C₁₃₉	1	1	yes	characteristic
175	C₂²×C₂²⋊C₈	C₂×C₁₃₉	1	2	yes	—
176	C₂×#336	C₂×C₁₃₉	1	4	yes	complemented
177	C₂⁴×C₄	C₄×C₁₃₉	1	2	yes	—
178	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
179	C₂³×C₈	C₂²×C₁₃₉	1	4	yes	—
180	C₂²×C₄²	—	2	4	no	—
181	C₂²×C₄²	—	2	8	no	—
182	C₂²×C₄²	C₄×C₁₃₉	1	2	yes	—
183	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
184	C₂×C₂²⋊C₈	—	2	4	no	—
185	C₂×C₂²⋊C₈	—	2	4	no	—
186	C₂×C₂²⋊C₈	C₄×C₁₃₉	1	8	yes	complemented
187	#336	—	2	8	no	—
188	C₂⁵	C₂×C₄×C₁₃₉	1	1	yes	characteristic
189	C₂³×C₄	—	2	4	no	—
190	C₂³×C₄	—	2	4	no	—
191	C₂³×C₄	—	2	8	no	—
192	C₂³×C₄	—	2	8	no	—
193	C₂³×C₄	—	2	4	no	—
194	C₂³×C₄	—	2	4	no	—
195	C₂³×C₄	C₈×C₁₃₉	1	8	yes	complemented
196	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
197	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
198	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
199	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
200	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
201	C₂³×C₄	Q₈×C₁₃₉	1	2	yes	—
202	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
203	C₂²×C₈	—	2	8	no	—
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	—	2	8	no	—
207	C₂²×C₈	C₂×C₄×C₁₃₉	1	8	yes	complemented
208	C₂×C₄²	—	2	32	no	—
209	C₂×C₄²	—	2	4	no	—
210	C₂×C₄²	—	2	8	no	—
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	—	2	4	no	—
213	C₂×C₄²	D₄×C₁₃₉	1	8	yes	—
214	C₂²⋊C₈	—	2	16	no	—
215	C₂⁴	—	2	2	no	—
216	C₂⁴	—	2	2	no	—
217	C₂⁴	—	2	4	no	—
218	C₂⁴	C₄²×C₁₃₉	1	2	yes	—
219	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
220	C₂⁴	C₄⋊C₄×C₁₃₉	1	2	yes	—
221	C₂⁴	C₂×C₈×C₁₃₉	1	4	yes	—
222	C₂⁴	M₁₆×C₁₃₉	1	4	yes	—
223	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
224	C₂²×C₄	—	2	16	no	—
225	C₂²×C₄	—	2	32	no	—
226	C₂²×C₄	—	2	16	no	—
227	C₂²×C₄	—	2	16	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	32	no	—
235	C₂²×C₄	—	2	16	no	—
236	C₂²×C₄	—	2	8	no	—
237	C₂²×C₄	—	2	8	no	—
238	C₂²×C₄	—	2	8	no	—
239	C₂²×C₄	—	2	8	no	—
240	C₂²×C₄	C₄²×C₁₃₉	1	2	yes	—
241	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
242	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
243	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
244	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
245	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
246	C₂²×C₄	C₂×C₈×C₁₃₉	1	8	yes	—
247	C₂²×C₄	M₁₆×C₁₃₉	1	8	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
249	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
250	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
251	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
252	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
253	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
254	C₂×C₈	—	2	8	no	—
255	C₂×C₈	—	2	16	no	—
256	C₂×C₈	—	4	4	no	—
257	C₂×C₈	—	4	8	no	—
258	C₂×C₈	—	4	4	no	—
259	C₄²	—	2	16	no	—
260	C₄²	—	2	16	no	—
261	C₂³	—	2	4	no	—
262	C₂³	—	2	8	no	—
263	C₂³	—	2	4	no	—
264	C₂³	—	2	8	no	—
265	C₂³	—	2	4	no	—
266	C₂³	—	2	8	no	—
267	C₂³	—	2	8	no	—
268	C₂³	—	2	4	no	—
269	C₂³	—	2	2	no	—
270	C₂³	—	2	4	no	—
271	C₂³	—	2	2	no	—
272	C₂³	#95×C₁₃₉	1	4	yes	—
273	C₂³	C₄×C₈×C₁₃₉	1	4	yes	—
274	C₂³	#97×C₁₃₉	1	4	yes	—
275	C₂³	C₂²⋊C₈×C₁₃₉	1	8	yes	—
276	C₂³	C₄⋊C₈×C₁₃₉	1	8	yes	—
277	C₂³	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
278	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
279	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
280	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
281	C₂³	#117×C₁₃₉	1	2	yes	—
282	C₂³	C₂²×C₈×C₁₃₉	1	2	yes	—
283	C₂³	C₂×M₁₆×C₁₃₉	1	2	yes	—
284	C₂³	C₂×M₁₆×C₁₃₉	1	4	yes	—
285	C₂×C₄	—	2	64	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	8	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	16	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	#95×C₁₃₉	1	4	yes	—
299	C₂×C₄	C₂²⋊C₈×C₁₃₉	1	16	yes	complemented
300	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
301	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
302	C₂×C₄	C₄×D₄×C₁₃₉	1	8	yes	—
303	C₂×C₄	#120×C₁₃₉	1	4	yes	—
304	C₂×C₄	#121×C₁₃₉	1	4	yes	—
305	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
306	C₂×C₄	#123×C₁₃₉	1	4	yes	—
307	C₈	—	4	8	no	—
308	C₂²	—	2	8	no	—
309	C₂²	—	2	8	no	—
310	C₂²	—	2	8	no	—
311	C₂²	—	2	16	no	—
312	C₂²	—	2	8	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	4	no	—
315	C₂²	#336×C₁₃₉	1	8	yes	complemented
316	C₂²	C₂×#95×C₁₃₉	1	1	yes	characteristic
317	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
318	C₂²	#379×C₁₃₉	1	1	yes	characteristic
319	C₂²	#380×C₁₃₉	1	2	yes	—
320	C₂²	#381×C₁₃₉	1	1	yes	characteristic
321	C₂²	C₂×C₄×C₈×C₁₃₉	1	1	yes	characteristic
322	C₂²	C₂×#97×C₁₃₉	1	1	yes	characteristic
323	C₂²	C₄×M₁₆×C₁₃₉	1	2	yes	—
324	C₂²	C₂×C₂²⋊C₈×C₁₃₉	1	4	yes	—
325	C₂²	C₂×C₂²⋊C₈×C₁₃₉	1	2	yes	—
326	C₂²	#407×C₁₃₉	1	4	yes	—
327	C₂²	#407×C₁₃₉	1	2	yes	—
328	C₂²	C₂×C₄⋊C₈×C₁₃₉	1	2	yes	—
329	C₂²	#423×C₁₃₉	1	2	yes	—
330	C₂²	#431×C₁₃₉	1	4	yes	—
331	C₂²	#432×C₁₃₉	1	4	yes	—
332	C₄	—	2	16	no	—
333	C₄	—	2	4	no	—
334	C₄	#385×C₁₃₉	1	4	yes	—
335	C₄	#386×C₁₃₉	1	4	yes	—
336	C₂	—	2	8	no	—
337	C₂	C₂²⋊#95×C₁₃₉	1	1	yes	characteristic
338	C₂	C₂×#336×C₁₃₉	1	1	yes	characteristic
339	C₂	#1728×C₁₃₉	1	1	yes	characteristic
340	C₂	C₄×C₂²⋊C₈×C₁₃₉	1	2	yes	—
341	C₂	#1749×C₁₃₉	1	2	yes	—
342	C₂	#1779×C₁₃₉	1	2	yes	—
343	C₂	#1797×C₁₃₉	1	4	yes	—
344	C₂	#1817×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃₉	C₂³
commutator	C₂²	C₂×C₄×C₈×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂⁴×C₁₃₉	C₂²×C₄
prime radical	C₂⁵×C₁₃₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#336×C₁₃₉	C₂	semidirect
13. C₂×C₂²⋊C₈×C₁₃₉	C₄	semidirect
22. C₂³×C₄×C₁₃₉	C₈	semidirect
34. C₂²×C₈×C₁₃₉	C₂×C₄	semidirect
126. C₂×C₄×C₁₃₉	C₂²⋊C₈	semidirect
142. C₂²×C₁₃₉	#336	semidirect
172. #10712	C₁₃₉	direct (N × H)
173. C₁₃₉	#10712	direct (N × H)
176. C₂×#336	C₂×C₁₃₉	semidirect
186. C₂×C₂²⋊C₈	C₄×C₁₃₉	semidirect
195. C₂³×C₄	C₈×C₁₃₉	semidirect
207. C₂²×C₈	C₂×C₄×C₁₃₉	semidirect
299. C₂×C₄	C₂²⋊C₈×C₁₃₉	semidirect
315. C₂²	#336×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₁₃₉	2
C₂²×C₂²⋊C₈×C₁₃₉	2
C₂×#336×C₁₃₉	2
#10712	139

Subgroups — C139×#10712 #48005308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10712 #48005308