Subgroups — C₁₃₉×#21201 #48015797

Order 35584.

1638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#417×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×M₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1961×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1960×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1958×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
10	#532×C₁₃₉	—	2	4	no	—
11	#532×C₁₃₉	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#121×C₁₃₉	—	2	2	no	—
16	C₂×C₄×D₄×C₁₃₉	—	2	2	no	—
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
19	#417×C₁₃₉	—	2	16	no	—
20	C₂×#103×C₁₃₉	C₂²	1	8	yes	—
21	C₂×#102×C₁₃₉	C₂²	1	8	yes	—
22	C₄×M₁₆×C₁₃₉	—	2	4	no	—
23	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
25	#382×C₁₃₉	—	2	2	no	—
26	#382×C₁₃₉	C₂²	1	2	yes	—
27	#382×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#95×C₁₃₉	—	2	2	no	—
29	C₂×#41×C₁₃₉	—	2	4	no	—
30	C₂×#41×C₁₃₉	—	2	8	no	—
31	C₂×#41×C₁₃₉	—	2	8	no	—
32	C₂×#41×C₁₃₉	C₂×C₄	1	8	yes	—
33	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₃₉	—	2	2	no	—
35	C₂²×D₄×C₁₃₉	—	2	2	no	—
36	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	—	2	2	no	—
38	C₂³×C₄×C₁₃₉	—	2	2	no	—
39	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₁₃₉	—	2	4	no	—
42	C₂×M₁₆×C₁₃₉	—	2	4	no	—
43	C₂×M₁₆×C₁₃₉	D₄	1	8	yes	complemented
44	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
47	#127×C₁₃₉	—	2	2	no	—
48	#127×C₁₃₉	C₂×C₄	1	4	yes	complemented
49	#124×C₁₃₉	—	2	4	no	—
50	#124×C₁₃₉	C₂×C₄	1	8	yes	complemented
51	#121×C₁₃₉	—	2	16	no	—
52	C₄×D₄×C₁₃₉	—	2	16	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
58	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
61	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
63	#103×C₁₃₉	—	2	16	no	—
64	#102×C₁₃₉	—	2	16	no	—
65	#97×C₁₃₉	—	2	4	no	—
66	C₄×C₈×C₁₃₉	—	2	4	no	—
67	#95×C₁₃₉	—	2	4	no	—
68	#95×C₁₃₉	—	2	4	no	—
69	C₂⁴×C₁₃₉	—	2	2	no	—
70	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
71	#41×C₁₃₉	—	2	32	no	—
72	#41×C₁₃₉	—	4	16	no	—
73	C₂×Q₈×C₁₃₉	—	2	2	no	—
74	C₂×Q₈×C₁₃₉	—	2	4	no	—
75	C₂×Q₈×C₁₃₉	—	2	4	no	—
76	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
77	C₂×D₄×C₁₃₉	—	2	8	no	—
78	C₂×D₄×C₁₃₉	—	2	8	no	—
79	C₂×D₄×C₁₃₉	—	2	4	no	—
80	C₂×D₄×C₁₃₉	—	2	2	no	—
81	C₂×D₄×C₁₃₉	—	2	4	no	—
82	C₂×D₄×C₁₃₉	—	4	8	no	—
83	C₂×D₄×C₁₃₉	—	4	4	no	—
84	C₂×D₄×C₁₃₉	—	4	4	no	—
85	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	8	no	—
88	C₂²×C₄×C₁₃₉	—	2	4	no	—
89	C₂²×C₄×C₁₃₉	—	4	4	no	—
90	C₂²×C₄×C₁₃₉	—	4	4	no	—
91	C₂²×C₄×C₁₃₉	—	4	4	no	—
92	C₂²×C₄×C₁₃₉	—	4	8	no	—
93	C₂²×C₄×C₁₃₉	—	4	4	no	—
94	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
95	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
102	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
103	M₁₆×C₁₃₉	—	2	16	no	—
104	C₂×C₈×C₁₃₉	—	2	4	no	—
105	C₂×C₈×C₁₃₉	—	2	4	no	—
106	C₂×C₈×C₁₃₉	C₂×D₄	1	8	yes	—
107	C₄⋊C₄×C₁₃₉	—	2	8	no	—
108	C₄⋊C₄×C₁₃₉	—	2	8	no	—
109	C₄⋊C₄×C₁₃₉	—	4	4	no	—
110	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
111	C₄²×C₁₃₉	C₂²⋊C₄	1	8	yes	—
112	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
113	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
114	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
115	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
116	C₂³×C₁₃₉	—	2	4	no	—
117	C₂³×C₁₃₉	—	2	4	no	—
118	C₂³×C₁₃₉	—	4	2	no	—
119	C₂³×C₁₃₉	—	4	2	no	—
120	C₂³×C₁₃₉	—	4	8	no	—
121	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
122	C₂³×C₁₃₉	#124	1	2	yes	—
123	C₂³×C₁₃₉	#127	1	2	yes	—
124	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₁₃₉	—	2	8	no	—
126	Q₈×C₁₃₉	—	4	4	no	—
127	D₄×C₁₃₉	—	2	8	no	—
128	D₄×C₁₃₉	—	4	16	no	—
129	D₄×C₁₃₉	—	4	16	no	—
130	D₄×C₁₃₉	—	4	4	no	—
131	C₂×C₄×C₁₃₉	—	2	4	no	—
132	C₂×C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	4	8	no	—
135	C₂×C₄×C₁₃₉	—	4	2	no	—
136	C₂×C₄×C₁₃₉	—	4	2	no	—
137	C₂×C₄×C₁₃₉	—	4	16	no	—
138	C₂×C₄×C₁₃₉	—	4	4	no	—
139	C₂×C₄×C₁₃₉	—	4	8	no	—
140	C₂×C₄×C₁₃₉	—	8	8	no	—
141	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
143	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₁₃₉	C₄×D₄	1	8	yes	—
145	C₂×C₄×C₁₃₉	#121	1	8	yes	—
146	C₂×C₄×C₁₃₉	#124	1	2	yes	—
147	C₂×C₄×C₁₃₉	#127	1	2	yes	—
148	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
152	C₈×C₁₃₉	—	2	8	no	—
153	C₂²×C₁₃₉	—	2	4	no	—
154	C₂²×C₁₃₉	—	2	4	no	—
155	C₂²×C₁₃₉	—	2	4	no	—
156	C₂²×C₁₃₉	—	4	8	no	—
157	C₂²×C₁₃₉	—	4	4	no	—
158	C₂²×C₁₃₉	—	8	4	no	—
159	C₂²×C₁₃₉	—	8	4	no	—
160	C₂²×C₁₃₉	#390	1	4	yes	—
161	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
163	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
164	C₂²×C₁₃₉	#575	1	4	yes	—
165	C₄×C₁₃₉	—	2	4	no	—
166	C₄×C₁₃₉	—	2	4	no	—
167	C₄×C₁₃₉	—	4	4	no	—
168	C₄×C₁₃₉	—	8	4	no	—
169	C₄×C₁₃₉	#390	1	4	yes	—
170	C₄×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
171	C₄×C₁₃₉	C₂×#121	1	2	yes	—
172	C₂×C₁₃₉	—	2	4	no	—
173	C₂×C₁₃₉	—	8	4	no	—
174	C₂×C₁₃₉	C₂×#390	1	1	yes	characteristic
175	C₂×C₁₃₉	#2896	1	2	yes	—
176	C₂×C₁₃₉	#3142	1	2	yes	—
177	C₂×C₁₃₉	#3153	1	2	yes	—
178	#21201	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₁₃₉	#21201	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic
181	C₂×#417	C₂×C₁₃₉	1	4	yes	complemented
182	C₂×C₄×M₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
183	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
184	#1961	C₂×C₁₃₉	1	2	yes	complemented
185	#1960	C₂×C₁₃₉	1	2	yes	complemented
186	#1958	C₂×C₁₃₉	1	4	yes	complemented
187	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
188	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
189	#532	—	2	4	no	—
190	#532	C₄×C₁₃₉	1	8	yes	complemented
191	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
192	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
193	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
194	C₂×#121	—	2	2	no	—
195	C₂×C₄×D₄	—	2	2	no	—
196	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
197	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
198	#417	—	2	16	no	—
199	C₂×#103	C₂²×C₁₃₉	1	8	yes	—
200	C₂×#102	C₂²×C₁₃₉	1	8	yes	—
201	C₄×M₁₆	—	2	4	no	—
202	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
203	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
204	#382	—	2	2	no	—
205	#382	C₂²×C₁₃₉	1	2	yes	—
206	#382	C₂²×C₁₃₉	1	2	yes	—
207	C₂×#95	—	2	2	no	—
208	C₂×#41	—	2	4	no	—
209	C₂×#41	—	2	8	no	—
210	C₂×#41	—	2	8	no	—
211	C₂×#41	C₂×C₄×C₁₃₉	1	8	yes	—
212	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
213	C₂²×D₄	—	2	2	no	—
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
216	C₂³×C₄	—	2	2	no	—
217	C₂³×C₄	—	2	2	no	—
218	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
219	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
220	C₂×M₁₆	—	2	4	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	D₄×C₁₃₉	1	8	yes	complemented
223	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
226	#127	—	2	2	no	—
227	#127	C₂×C₄×C₁₃₉	1	4	yes	complemented
228	#124	—	2	4	no	—
229	#124	C₂×C₄×C₁₃₉	1	8	yes	complemented
230	#121	—	2	16	no	—
231	C₄×D₄	—	2	16	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	8	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
236	C₂×C₂²⋊C₄	—	2	4	no	—
237	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
238	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
239	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
240	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
242	#103	—	2	16	no	—
243	#102	—	2	16	no	—
244	#97	—	2	4	no	—
245	C₄×C₈	—	2	4	no	—
246	#95	—	2	4	no	—
247	#95	—	2	4	no	—
248	C₂⁴	—	2	2	no	—
249	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
250	#41	—	2	32	no	—
251	#41	—	4	16	no	—
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
256	C₂×D₄	—	2	8	no	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	4	8	no	—
262	C₂×D₄	—	4	4	no	—
263	C₂×D₄	—	4	4	no	—
264	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
280	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
282	M₁₆	—	2	16	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	C₂×D₄×C₁₃₉	1	8	yes	—
286	C₄⋊C₄	—	2	8	no	—
287	C₄⋊C₄	—	2	8	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₂²⋊C₄	—	2	16	no	—
290	C₄²	C₂²⋊C₄×C₁₃₉	1	8	yes	—
291	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
292	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
293	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
294	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	2	no	—
299	C₂³	—	4	8	no	—
300	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
301	C₂³	#124×C₁₃₉	1	2	yes	—
302	C₂³	#127×C₁₃₉	1	2	yes	—
303	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
304	Q₈	—	2	8	no	—
305	Q₈	—	4	4	no	—
306	D₄	—	2	8	no	—
307	D₄	—	4	16	no	—
308	D₄	—	4	16	no	—
309	D₄	—	4	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	16	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	—	8	8	no	—
320	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
321	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
322	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
323	C₂×C₄	C₄×D₄×C₁₃₉	1	8	yes	—
324	C₂×C₄	#121×C₁₃₉	1	8	yes	—
325	C₂×C₄	#124×C₁₃₉	1	2	yes	—
326	C₂×C₄	#127×C₁₃₉	1	2	yes	—
327	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
329	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
331	C₈	—	2	8	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	8	4	no	—
338	C₂²	—	8	4	no	—
339	C₂²	#390×C₁₃₉	1	4	yes	—
340	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
341	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
342	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
343	C₂²	#575×C₁₃₉	1	4	yes	—
344	C₄	—	2	4	no	—
345	C₄	—	2	4	no	—
346	C₄	—	4	4	no	—
347	C₄	—	8	4	no	—
348	C₄	#390×C₁₃₉	1	4	yes	—
349	C₄	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
350	C₄	C₂×#121×C₁₃₉	1	2	yes	—
351	C₂	—	2	4	no	—
352	C₂	—	8	4	no	—
353	C₂	C₂×#390×C₁₃₉	1	1	yes	characteristic
354	C₂	#2896×C₁₃₉	1	2	yes	—
355	C₂	#3142×C₁₃₉	1	2	yes	—
356	C₂	#3153×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#532×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#417×C₁₃₉	C₂	semidirect
3. C₂×C₄×M₁₆×C₁₃₉	C₂	semidirect
4. C₂×#382×C₁₃₉	C₂	semidirect
5. #1961×C₁₃₉	C₂	semidirect
6. #1960×C₁₃₉	C₂	semidirect
7. #1958×C₁₃₉	C₂	semidirect
11. #532×C₁₃₉	C₄	semidirect
43. C₂×M₁₆×C₁₃₉	D₄	semidirect
46. C₄⋊Q₈×C₁₃₉	C₂×C₄	semidirect
48. #127×C₁₃₉	C₂×C₄	semidirect
50. #124×C₁₃₉	C₂×C₄	semidirect
178. #21201	C₁₃₉	direct (N × H)
179. C₁₃₉	#21201	direct (N × H)
181. C₂×#417	C₂×C₁₃₉	semidirect
182. C₂×C₄×M₁₆	C₂×C₁₃₉	semidirect
183. C₂×#382	C₂×C₁₃₉	semidirect
184. #1961	C₂×C₁₃₉	semidirect
185. #1960	C₂×C₁₃₉	semidirect
186. #1958	C₂×C₁₃₉	semidirect
190. #532	C₄×C₁₃₉	semidirect
222. C₂×M₁₆	D₄×C₁₃₉	semidirect
225. C₄⋊Q₈	C₂×C₄×C₁₃₉	semidirect
227. #127	C₂×C₄×C₁₃₉	semidirect
229. #124	C₂×C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₃₉	2
C₂×#417×C₁₃₉	2
C₂×C₄×M₁₆×C₁₃₉	2
C₂×#382×C₁₃₉	2
#1961×C₁₃₉	2
#1960×C₁₃₉	2
#1958×C₁₃₉	2
#21201	139

Subgroups — C139×#21201 #48015797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21201 #48015797