Subgroups — C₁₃₉×#17518 #48012114

Order 35584.

1020 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3482×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2991×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#131×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1493×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#1489×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#1485×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#1476×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	C₂×#131×C₁₃₉	—	2	1	no	—
9	#557×C₁₃₉	C₄	1	1	yes	characteristic
10	#556×C₁₃₉	C₄	1	3	yes	—
11	#552×C₁₃₉	—	2	3	no	—
12	D₄×Q₈×C₁₃₉	C₄	1	1	yes	characteristic
13	#548×C₁₃₉	—	2	1	no	—
14	#547×C₁₃₉	C₄	1	3	yes	—
15	#533×C₁₃₉	C₂²	1	3	yes	—
16	#529×C₁₃₉	—	2	3	no	—
17	C₄×#41×C₁₃₉	C₂²	1	3	yes	—
18	C₄×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃₉	—	2	1	no	—
20	C₈×Q₈×C₁₃₉	—	2	1	no	—
21	#436×C₁₃₉	—	2	3	no	—
22	#431×C₁₃₉	C₂²	1	3	yes	—
23	#423×C₁₃₉	C₂²	1	3	yes	—
24	#405×C₁₃₉	—	2	3	no	—
25	C₄×M₁₆×C₁₃₉	C₂²	1	3	yes	—
26	C₂×C₄×C₈×C₁₃₉	C₂²	1	3	yes	—
27	Q₈⋊C₈×C₁₃₉	C₂²	1	6	yes	—
28	Q₈⋊C₈×C₁₃₉	C₂²	1	3	yes	—
29	Q₈⋊C₈×C₁₃₉	C₂²	1	3	yes	—
30	D₄⋊C₈×C₁₃₉	C₂²	1	3	yes	—
31	D₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#41×C₁₃₉	C₂×C₄	1	3	yes	—
33	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
34	C₂²×Q₈×C₁₃₉	—	2	1	no	—
35	#131×C₁₃₉	—	2	8	no	—
36	C₂×M₁₆×C₁₃₉	—	2	3	no	—
37	C₂×M₁₆×C₁₃₉	—	2	3	no	—
38	C₂²×C₈×C₁₃₉	—	2	3	no	—
39	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	3	yes	—
40	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	3	yes	—
41	#126×C₁₃₉	—	2	6	no	—
42	#125×C₁₃₉	—	2	3	no	—
43	#125×C₁₃₉	—	2	3	no	—
44	#124×C₁₃₉	—	2	3	no	—
45	#123×C₁₃₉	—	2	6	no	—
46	C₂²⋊Q₈×C₁₃₉	—	2	3	no	—
47	C₂²⋊Q₈×C₁₃₉	—	2	3	no	—
48	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	6	yes	—
49	#121×C₁₃₉	—	2	3	no	—
50	C₄×Q₈×C₁₃₉	—	2	1	no	—
51	C₄×Q₈×C₁₃₉	—	2	3	no	—
52	C₄×Q₈×C₁₃₉	—	2	3	no	—
53	C₄×Q₈×C₁₃₉	C₂×C₄	1	3	yes	—
54	C₄×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₃₉	C₂³	1	3	yes	—
57	C₄×D₄×C₁₃₉	—	2	3	no	—
58	C₄×D₄×C₁₃₉	—	2	3	no	—
59	C₄×D₄×C₁₃₉	C₂×C₄	1	3	yes	—
60	C₄×D₄×C₁₃₉	C₂×C₄	1	3	yes	—
61	C₄×D₄×C₁₃₉	D₄	1	3	yes	—
62	C₄×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	#117×C₁₃₉	—	2	3	no	—
64	#117×C₁₃₉	—	2	3	no	—
65	#117×C₁₃₉	C₂×C₄	1	3	yes	—
66	#117×C₁₃₉	D₄	1	3	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	3	no	—
68	C₂×C₄²×C₁₃₉	—	2	3	no	—
69	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
70	C₄⋊C₈×C₁₃₉	—	2	3	no	—
71	C₄⋊C₈×C₁₃₉	C₂³	1	3	yes	—
72	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂²⋊C₈×C₁₃₉	—	2	3	no	—
74	#97×C₁₃₉	—	2	3	no	—
75	C₄×C₈×C₁₃₉	—	2	3	no	—
76	C₄×C₈×C₁₃₉	—	2	3	no	—
77	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₁₃₉	C₂³	1	3	yes	—
79	#41×C₁₃₉	—	2	4	no	—
80	#41×C₁₃₉	—	2	6	no	—
81	#41×C₁₃₉	—	4	3	no	—
82	C₂×Q₈×C₁₃₉	—	2	3	no	—
83	C₂×Q₈×C₁₃₉	—	4	4	no	—
84	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₃₉	C₂²×C₄	1	3	yes	—
86	C₂×D₄×C₁₃₉	—	2	3	no	—
87	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	3	yes	—
88	C₂×D₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₉	—	2	3	no	—
90	C₂²×C₄×C₁₃₉	—	2	3	no	—
91	C₂²×C₄×C₁₃₉	—	2	1	no	—
92	C₂²×C₄×C₁₃₉	C₂²×C₄	1	3	yes	—
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	3	yes	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	3	yes	—
95	M₁₆×C₁₃₉	—	2	12	no	—
96	M₁₆×C₁₃₉	—	8	3	no	—
97	C₂×C₈×C₁₃₉	—	2	12	no	—
98	C₂×C₈×C₁₃₉	—	2	1	no	—
99	C₂×C₈×C₁₃₉	—	2	3	no	—
100	C₂×C₈×C₁₃₉	—	2	1	no	—
101	C₂×C₈×C₁₃₉	—	2	3	no	—
102	C₄⋊C₄×C₁₃₉	—	2	3	no	—
103	C₄⋊C₄×C₁₃₉	—	2	6	no	—
104	C₄⋊C₄×C₁₃₉	—	2	3	no	—
105	C₄⋊C₄×C₁₃₉	—	2	3	no	—
106	C₄⋊C₄×C₁₃₉	—	2	3	no	—
107	C₄⋊C₄×C₁₃₉	—	2	3	no	—
108	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	3	yes	—
109	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	3	yes	—
110	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
111	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	3	yes	—
112	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
113	C₂²⋊C₄×C₁₃₉	—	2	3	no	—
114	C₂²⋊C₄×C₁₃₉	—	2	3	no	—
115	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
116	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	6	yes	—
117	C₄²×C₁₃₉	—	2	3	no	—
118	C₄²×C₁₃₉	—	2	3	no	—
119	C₄²×C₁₃₉	—	2	3	no	—
120	C₄²×C₁₃₉	C₂²×C₄	1	3	yes	—
121	C₄²×C₁₃₉	C₂×D₄	1	3	yes	—
122	C₄²×C₁₃₉	C₂×D₄	1	3	yes	—
123	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
124	C₂³×C₁₃₉	—	2	1	no	—
125	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
126	Q₈×C₁₃₉	—	2	3	no	—
127	Q₈×C₁₃₉	—	2	3	no	—
128	Q₈×C₁₃₉	—	4	6	no	—
129	Q₈×C₁₃₉	#104	1	4	yes	—
130	D₄×C₁₃₉	—	2	1	no	—
131	D₄×C₁₃₉	—	2	6	no	—
132	D₄×C₁₃₉	—	4	6	no	—
133	D₄×C₁₃₉	#131	1	2	yes	complemented
134	C₂×C₄×C₁₃₉	—	2	3	no	—
135	C₂×C₄×C₁₃₉	—	2	3	no	—
136	C₂×C₄×C₁₃₉	—	2	3	no	—
137	C₂×C₄×C₁₃₉	—	2	3	no	—
138	C₂×C₄×C₁₃₉	—	2	6	no	—
139	C₂×C₄×C₁₃₉	—	2	1	no	—
140	C₂×C₄×C₁₃₉	—	2	3	no	—
141	C₂×C₄×C₁₃₉	—	2	3	no	—
142	C₂×C₄×C₁₃₉	—	4	6	no	—
143	C₂×C₄×C₁₃₉	—	4	1	no	—
144	C₂×C₄×C₁₃₉	—	4	1	no	—
145	C₂×C₄×C₁₃₉	—	4	6	no	—
146	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
147	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
148	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
149	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₁₃₉	—	2	2	no	—
153	C₈×C₁₃₉	—	2	6	no	—
154	C₈×C₁₃₉	—	4	3	no	—
155	C₈×C₁₃₉	—	4	1	no	—
156	C₂²×C₁₃₉	—	2	3	no	—
157	C₂²×C₁₃₉	—	2	2	no	—
158	C₂²×C₁₃₉	—	2	3	no	—
159	C₂²×C₁₃₉	—	2	3	no	—
160	C₂²×C₁₃₉	—	4	1	no	—
161	C₂²×C₁₃₉	—	4	1	no	—
162	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
163	C₄×C₁₃₉	—	2	3	no	—
164	C₄×C₁₃₉	—	2	3	no	—
165	C₄×C₁₃₉	—	2	1	no	—
166	C₄×C₁₃₉	—	4	3	no	—
167	C₄×C₁₃₉	—	4	1	no	—
168	C₄×C₁₃₉	—	4	3	no	—
169	C₄×C₁₃₉	C₂×#104	1	6	yes	—
170	C₄×C₁₃₉	C₂×#131	1	1	yes	characteristic
171	C₄×C₁₃₉	#568	1	1	yes	characteristic
172	C₄×C₁₃₉	#577	1	1	yes	characteristic
173	C₄×C₁₃₉	#578	1	1	yes	characteristic
174	C₂×C₁₃₉	—	4	3	no	—
175	C₂×C₁₃₉	—	4	2	no	—
176	C₂×C₁₃₉	#2880	1	1	yes	characteristic
177	C₂×C₁₃₉	#2898	1	1	yes	characteristic
178	C₂×C₁₃₉	C₂²×#104	1	1	yes	characteristic
179	#17518	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₁₃₉	#17518	1	1	yes	characteristic, direct product factor, Sylow
181	#3482	C₂×C₁₃₉	1	1	yes	characteristic
182	#2991	C₂×C₁₃₉	1	1	yes	characteristic, complemented
183	C₄×#131	C₂×C₁₃₉	1	1	yes	characteristic, complemented
184	#1493	C₂×C₁₃₉	1	3	yes	complemented
185	#1489	C₂×C₁₃₉	1	3	yes	complemented
186	#1485	C₂×C₁₃₉	1	3	yes	complemented
187	#1476	C₂×C₁₃₉	1	3	yes	complemented
188	C₂×#131	—	2	1	no	—
189	#557	C₄×C₁₃₉	1	1	yes	characteristic
190	#556	C₄×C₁₃₉	1	3	yes	—
191	#552	—	2	3	no	—
192	D₄×Q₈	C₄×C₁₃₉	1	1	yes	characteristic
193	#548	—	2	1	no	—
194	#547	C₄×C₁₃₉	1	3	yes	—
195	#533	C₂²×C₁₃₉	1	3	yes	—
196	#529	—	2	3	no	—
197	C₄×#41	C₂²×C₁₃₉	1	3	yes	—
198	C₄×#41	C₂²×C₁₃₉	1	1	yes	characteristic
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₈×Q₈	—	2	1	no	—
201	#436	—	2	3	no	—
202	#431	C₂²×C₁₃₉	1	3	yes	—
203	#423	C₂²×C₁₃₉	1	3	yes	—
204	#405	—	2	3	no	—
205	C₄×M₁₆	C₂²×C₁₃₉	1	3	yes	—
206	C₂×C₄×C₈	C₂²×C₁₃₉	1	3	yes	—
207	Q₈⋊C₈	C₂²×C₁₃₉	1	3	yes	—
208	Q₈⋊C₈	C₂²×C₁₃₉	1	3	yes	—
209	Q₈⋊C₈	C₂²×C₁₃₉	1	6	yes	—
210	D₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
211	D₄⋊C₈	C₂²×C₁₃₉	1	3	yes	—
212	C₂×#41	C₂×C₄×C₁₃₉	1	3	yes	—
213	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
214	C₂²×Q₈	—	2	1	no	—
215	#131	—	2	8	no	—
216	C₂×M₁₆	—	2	3	no	—
217	C₂×M₁₆	—	2	3	no	—
218	C₂²×C₈	—	2	3	no	—
219	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	3	yes	—
220	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	3	yes	—
221	#126	—	2	6	no	—
222	#125	—	2	3	no	—
223	#125	—	2	3	no	—
224	#124	—	2	3	no	—
225	#123	—	2	6	no	—
226	C₂²⋊Q₈	—	2	3	no	—
227	C₂²⋊Q₈	—	2	3	no	—
228	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	6	yes	—
229	#121	—	2	3	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	3	no	—
232	C₄×Q₈	—	2	3	no	—
233	C₄×Q₈	C₂×C₄×C₁₃₉	1	3	yes	—
234	C₄×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
235	C₄×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
236	C₄×Q₈	C₂³×C₁₃₉	1	3	yes	—
237	C₄×D₄	—	2	3	no	—
238	C₄×D₄	—	2	3	no	—
239	C₄×D₄	C₂×C₄×C₁₃₉	1	3	yes	—
240	C₄×D₄	C₂×C₄×C₁₃₉	1	3	yes	—
241	C₄×D₄	D₄×C₁₃₉	1	3	yes	—
242	C₄×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
243	#117	—	2	3	no	—
244	#117	—	2	3	no	—
245	#117	C₂×C₄×C₁₃₉	1	3	yes	—
246	#117	D₄×C₁₃₉	1	3	yes	—
247	C₂×C₄⋊C₄	—	2	3	no	—
248	C₂×C₄²	—	2	3	no	—
249	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
250	C₄⋊C₈	—	2	3	no	—
251	C₄⋊C₈	C₂³×C₁₃₉	1	3	yes	—
252	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
253	C₂²⋊C₈	—	2	3	no	—
254	#97	—	2	3	no	—
255	C₄×C₈	—	2	3	no	—
256	C₄×C₈	—	2	3	no	—
257	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
258	C₄×C₈	C₂³×C₁₃₉	1	3	yes	—
259	#41	—	2	4	no	—
260	#41	—	2	6	no	—
261	#41	—	4	3	no	—
262	C₂×Q₈	—	2	3	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
265	C₂×Q₈	C₂²×C₄×C₁₃₉	1	3	yes	—
266	C₂×D₄	—	2	3	no	—
267	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	3	yes	—
268	C₂×D₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
269	C₂²×C₄	—	2	3	no	—
270	C₂²×C₄	—	2	3	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	C₂²×C₄×C₁₃₉	1	3	yes	—
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	3	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃₉	1	3	yes	—
275	M₁₆	—	2	12	no	—
276	M₁₆	—	8	3	no	—
277	C₂×C₈	—	2	12	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	3	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	3	no	—
282	C₄⋊C₄	—	2	3	no	—
283	C₄⋊C₄	—	2	6	no	—
284	C₄⋊C₄	—	2	3	no	—
285	C₄⋊C₄	—	2	3	no	—
286	C₄⋊C₄	—	2	3	no	—
287	C₄⋊C₄	—	2	3	no	—
288	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	3	yes	—
289	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	3	yes	—
290	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	3	yes	—
292	C₂²⋊C₄	—	2	6	no	—
293	C₂²⋊C₄	—	2	3	no	—
294	C₂²⋊C₄	—	2	3	no	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	6	yes	—
297	C₄²	—	2	3	no	—
298	C₄²	—	2	3	no	—
299	C₄²	—	2	3	no	—
300	C₄²	C₂²×C₄×C₁₃₉	1	3	yes	—
301	C₄²	C₂×D₄×C₁₃₉	1	3	yes	—
302	C₄²	C₂×D₄×C₁₃₉	1	3	yes	—
303	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
304	C₂³	—	2	1	no	—
305	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
306	Q₈	—	2	3	no	—
307	Q₈	—	2	3	no	—
308	Q₈	—	4	6	no	—
309	Q₈	#104×C₁₃₉	1	4	yes	—
310	D₄	—	2	6	no	—
311	D₄	—	2	1	no	—
312	D₄	—	4	6	no	—
313	D₄	#131×C₁₃₉	1	2	yes	complemented
314	C₂×C₄	—	2	6	no	—
315	C₂×C₄	—	2	3	no	—
316	C₂×C₄	—	2	3	no	—
317	C₂×C₄	—	2	3	no	—
318	C₂×C₄	—	2	3	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	2	3	no	—
322	C₂×C₄	—	4	6	no	—
323	C₂×C₄	—	4	6	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
329	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	—	2	6	no	—
334	C₈	—	4	3	no	—
335	C₈	—	4	1	no	—
336	C₂²	—	2	3	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	3	no	—
339	C₂²	—	2	3	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	1	no	—
342	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
343	C₄	—	2	3	no	—
344	C₄	—	2	3	no	—
345	C₄	—	2	1	no	—
346	C₄	—	4	3	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	3	no	—
349	C₄	C₂×#104×C₁₃₉	1	6	yes	—
350	C₄	C₂×#131×C₁₃₉	1	1	yes	characteristic
351	C₄	#568×C₁₃₉	1	1	yes	characteristic
352	C₄	#577×C₁₃₉	1	1	yes	characteristic
353	C₄	#578×C₁₃₉	1	1	yes	characteristic
354	C₂	—	4	3	no	—
355	C₂	—	4	2	no	—
356	C₂	#2880×C₁₃₉	1	1	yes	characteristic
357	C₂	#2898×C₁₃₉	1	1	yes	characteristic
358	C₂	C₂²×#104×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
prime radical	#3482×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₄×#41×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2991×C₁₃₉	C₂	semidirect
3. C₄×#131×C₁₃₉	C₂	semidirect
4. #1493×C₁₃₉	C₂	semidirect
5. #1489×C₁₃₉	C₂	semidirect
6. #1485×C₁₃₉	C₂	semidirect
7. #1476×C₁₃₉	C₂	semidirect
133. D₄×C₁₃₉	#131	semidirect
179. #17518	C₁₃₉	direct (N × H)
180. C₁₃₉	#17518	direct (N × H)
182. #2991	C₂×C₁₃₉	semidirect
183. C₄×#131	C₂×C₁₃₉	semidirect
184. #1493	C₂×C₁₃₉	semidirect
185. #1489	C₂×C₁₃₉	semidirect
186. #1485	C₂×C₁₃₉	semidirect
187. #1476	C₂×C₁₃₉	semidirect
313. D₄	#131×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3482×C₁₃₉	2
#2991×C₁₃₉	2
C₄×#131×C₁₃₉	2
#1493×C₁₃₉	2
#1489×C₁₃₉	2
#1485×C₁₃₉	2
#1476×C₁₃₉	2
#17518	139

Subgroups — C139×#17518 #48012114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#17518 #48012114