Subgroups — C₁₃₉×#21195 #48015791

Order 35584.

1662 conjugacy classes of subgroups.

The subgroup lattice has 356 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×#416×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄×C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1958×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1957×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1956×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
9	C₂³×C₈×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	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
19	#416×C₁₃₉	—	2	16	no	—
20	C₂×#103×C₁₃₉	C₂²	1	8	yes	—
21	C₂×#102×C₁₃₉	C₂²	1	8	yes	—
22	C₂×C₄×C₈×C₁₃₉	—	2	4	no	—
23	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
25	#384×C₁₃₉	C₂²	1	2	yes	—
26	#382×C₁₃₉	C₂²	1	2	yes	—
27	#380×C₁₃₉	—	2	2	no	—
28	C₄×C₄⋊C₄×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	D₄	1	2	yes	—
39	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₉	—	2	4	no	—
41	C₂²×C₈×C₁₃₉	—	2	4	no	—
42	C₂²×C₈×C₁₃₉	D₄	1	8	yes	complemented
43	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
44	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
45	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
46	#127×C₁₃₉	—	2	2	no	—
47	#127×C₁₃₉	C₂×C₄	1	4	yes	—
48	#124×C₁₃₉	—	2	4	no	—
49	#124×C₁₃₉	C₂×C₄	1	8	yes	—
50	#121×C₁₃₉	—	2	16	no	—
51	C₄×D₄×C₁₃₉	—	2	16	no	—
52	#117×C₁₃₉	—	2	8	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄²×C₁₃₉	—	2	2	no	—
59	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
62	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
64	#103×C₁₃₉	—	2	16	no	—
65	#102×C₁₃₉	—	2	16	no	—
66	C₄×C₈×C₁₃₉	—	2	4	no	—
67	C₄×C₈×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	4	no	—
83	C₂×D₄×C₁₃₉	—	4	4	no	—
84	C₂×D₄×C₁₃₉	—	4	8	no	—
85	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₃₉	—	2	8	no	—
87	C₂²×C₄×C₁₃₉	—	2	2	no	—
88	C₂²×C₄×C₁₃₉	—	2	8	no	—
89	C₂²×C₄×C₁₃₉	—	2	4	no	—
90	C₂²×C₄×C₁₃₉	—	4	4	no	—
91	C₂²×C₄×C₁₃₉	—	4	4	no	—
92	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
93	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
100	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₃₉	—	2	16	no	—
102	C₂×C₈×C₁₃₉	—	2	4	no	—
103	C₂×C₈×C₁₃₉	—	2	4	no	—
104	C₂×C₈×C₁₃₉	C₂×D₄	1	8	yes	—
105	C₄⋊C₄×C₁₃₉	—	2	8	no	—
106	C₄⋊C₄×C₁₃₉	—	2	8	no	—
107	C₄⋊C₄×C₁₃₉	—	4	8	no	—
108	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
109	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
110	C₄²×C₁₃₉	—	4	4	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	4	no	—
130	D₄×C₁₃₉	—	4	16	no	—
131	C₂×C₄×C₁₃₉	—	2	4	no	—
132	C₂×C₄×C₁₃₉	—	2	16	no	—
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	4	2	no	—
135	C₂×C₄×C₁₃₉	—	4	2	no	—
136	C₂×C₄×C₁₃₉	—	4	16	no	—
137	C₂×C₄×C₁₃₉	—	4	4	no	—
138	C₂×C₄×C₁₃₉	—	4	8	no	—
139	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
140	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₁₃₉	C₄×D₄	1	8	yes	—
143	C₂×C₄×C₁₃₉	#121	1	8	yes	—
144	C₂×C₄×C₁₃₉	#124	1	2	yes	—
145	C₂×C₄×C₁₃₉	#127	1	2	yes	—
146	C₂×C₄×C₁₃₉	#135	1	8	yes	—
147	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
149	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
151	C₈×C₁₃₉	—	2	8	no	—
152	C₂²×C₁₃₉	—	2	4	no	—
153	C₂²×C₁₃₉	—	2	4	no	—
154	C₂²×C₁₃₉	—	2	4	no	—
155	C₂²×C₁₃₉	—	4	8	no	—
156	C₂²×C₁₃₉	—	4	4	no	—
157	C₂²×C₁₃₉	—	8	4	no	—
158	C₂²×C₁₃₉	—	8	4	no	—
159	C₂²×C₁₃₉	#390	1	4	yes	—
160	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
163	C₂²×C₁₃₉	C₂×#135	1	4	yes	—
164	C₄×C₁₃₉	—	2	4	no	—
165	C₄×C₁₃₉	—	4	4	no	—
166	C₄×C₁₃₉	—	8	4	no	—
167	C₄×C₁₃₉	#390	1	4	yes	—
168	C₄×C₁₃₉	#416	1	8	yes	complemented
169	C₄×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
170	C₄×C₁₃₉	C₂×#121	1	2	yes	—
171	C₂×C₁₃₉	—	2	4	no	—
172	C₂×C₁₃₉	—	8	4	no	—
173	C₂×C₁₃₉	C₂×#390	1	1	yes	characteristic
174	C₂×C₁₃₉	C₂×#416	1	2	yes	—
175	C₂×C₁₃₉	#3131	1	2	yes	—
176	C₂×C₁₃₉	#3147	1	2	yes	—
177	#21195	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₃₉	#21195	1	1	yes	characteristic, direct product factor, Sylow
179	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic
180	C₂×#416	C₂×C₁₃₉	1	4	yes	complemented
181	C₂²×C₄×C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
182	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
183	#1958	C₂×C₁₃₉	1	4	yes	complemented
184	#1957	C₂×C₁₃₉	1	2	yes	complemented
185	#1956	C₂×C₁₃₉	1	2	yes	complemented
186	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
187	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
188	#532	—	2	4	no	—
189	#532	C₄×C₁₃₉	1	8	yes	complemented
190	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
191	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
192	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
193	C₂×#121	—	2	2	no	—
194	C₂×C₄×D₄	—	2	2	no	—
195	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
196	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
197	#416	—	2	16	no	—
198	C₂×#103	C₂²×C₁₃₉	1	8	yes	—
199	C₂×#102	C₂²×C₁₃₉	1	8	yes	—
200	C₂×C₄×C₈	—	2	4	no	—
201	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
203	#384	C₂²×C₁₃₉	1	2	yes	—
204	#382	C₂²×C₁₃₉	1	2	yes	—
205	#380	—	2	2	no	—
206	C₄×C₄⋊C₄	—	2	2	no	—
207	C₂×#41	—	2	4	no	—
208	C₂×#41	—	2	8	no	—
209	C₂×#41	—	2	8	no	—
210	C₂×#41	C₂×C₄×C₁₃₉	1	8	yes	—
211	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	—	2	2	no	—
214	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
215	C₂³×C₄	—	2	2	no	—
216	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	D₄×C₁₃₉	1	8	yes	complemented
221	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
222	C₄⋊Q₈	—	2	2	no	—
223	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
224	#127	—	2	2	no	—
225	#127	C₂×C₄×C₁₃₉	1	4	yes	—
226	#124	—	2	4	no	—
227	#124	C₂×C₄×C₁₃₉	1	8	yes	—
228	#121	—	2	16	no	—
229	C₄×D₄	—	2	16	no	—
230	#117	—	2	8	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₄²	—	2	2	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	C₄×C₈	—	2	4	no	—
245	C₄×C₈	—	2	4	no	—
246	#95	—	2	4	no	—
247	C₂⁴	—	2	2	no	—
248	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
249	#41	—	2	32	no	—
250	#41	—	4	16	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	2	4	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
255	C₂×D₄	—	2	8	no	—
256	C₂×D₄	—	2	8	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	4	4	no	—
261	C₂×D₄	—	4	4	no	—
262	C₂×D₄	—	4	8	no	—
263	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
264	C₂²×C₄	—	2	8	no	—
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	C₂²⋊C₄×C₁₃₉	1	8	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
277	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
279	C₂×C₈	—	2	16	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	C₂×D₄×C₁₃₉	1	8	yes	—
283	C₄⋊C₄	—	2	8	no	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	4	8	no	—
286	C₂²⋊C₄	—	2	16	no	—
287	C₂²⋊C₄	—	4	4	no	—
288	C₄²	—	4	4	no	—
289	C₄²	C₂²⋊C₄×C₁₃₉	1	8	yes	—
290	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
291	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
292	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
293	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	8	no	—
299	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
300	C₂³	#124×C₁₃₉	1	2	yes	—
301	C₂³	#127×C₁₃₉	1	2	yes	—
302	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
303	Q₈	—	2	8	no	—
304	Q₈	—	4	4	no	—
305	D₄	—	2	8	no	—
306	D₄	—	4	16	no	—
307	D₄	—	4	16	no	—
308	D₄	—	4	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	16	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	16	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
318	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
319	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
320	C₂×C₄	C₄×D₄×C₁₃₉	1	8	yes	—
321	C₂×C₄	#121×C₁₃₉	1	8	yes	—
322	C₂×C₄	#124×C₁₃₉	1	2	yes	—
323	C₂×C₄	#127×C₁₃₉	1	2	yes	—
324	C₂×C₄	#135×C₁₃₉	1	8	yes	—
325	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
327	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
329	C₈	—	2	8	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	4	8	no	—
335	C₂²	—	8	4	no	—
336	C₂²	—	8	4	no	—
337	C₂²	#390×C₁₃₉	1	4	yes	—
338	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
339	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
340	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
341	C₂²	C₂×#135×C₁₃₉	1	4	yes	—
342	C₄	—	2	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	8	4	no	—
345	C₄	#390×C₁₃₉	1	4	yes	—
346	C₄	#416×C₁₃₉	1	8	yes	complemented
347	C₄	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
348	C₄	C₂×#121×C₁₃₉	1	2	yes	—
349	C₂	—	2	4	no	—
350	C₂	—	8	4	no	—
351	C₂	C₂×#390×C₁₃₉	1	1	yes	characteristic
352	C₂	C₂×#416×C₁₃₉	1	2	yes	—
353	C₂	#3131×C₁₃₉	1	2	yes	—
354	C₂	#3147×C₁₃₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#416×C₁₃₉	C₂	semidirect
3. C₂²×C₄×C₈×C₁₃₉	C₂	semidirect
4. #2285×C₁₃₉	C₂	semidirect
5. #1958×C₁₃₉	C₂	semidirect
6. #1957×C₁₃₉	C₂	semidirect
7. #1956×C₁₃₉	C₂	semidirect
11. #532×C₁₃₉	C₄	semidirect
42. C₂²×C₈×C₁₃₉	D₄	semidirect
168. C₄×C₁₃₉	#416	semidirect
177. #21195	C₁₃₉	direct (N × H)
178. C₁₃₉	#21195	direct (N × H)
180. C₂×#416	C₂×C₁₃₉	semidirect
181. C₂²×C₄×C₈	C₂×C₁₃₉	semidirect
182. #2285	C₂×C₁₃₉	semidirect
183. #1958	C₂×C₁₃₉	semidirect
184. #1957	C₂×C₁₃₉	semidirect
185. #1956	C₂×C₁₃₉	semidirect
189. #532	C₄×C₁₃₉	semidirect
220. C₂²×C₈	D₄×C₁₃₉	semidirect
346. C₄	#416×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×#416×C₁₃₉	2
C₂²×C₄×C₈×C₁₃₉	2
#2285×C₁₃₉	2
#1958×C₁₃₉	2
#1957×C₁₃₉	2
#1956×C₁₃₉	2
#21195	139

Subgroups — C139×#21195 #48015791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21195 #48015791