Subgroups — C₁₃₉×#9072 #48003668

Order 35584.

810 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#1797×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊C₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1279×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₁₃₉	—	2	1	no	—
7	C₂×#121×C₁₃₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
9	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
12	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃₉	—	2	1	no	—
14	C₂×C₄×C₈×C₁₃₉	—	2	4	no	—
15	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
16	#390×C₁₃₉	C₄	1	1	yes	characteristic
17	#389×C₁₃₉	C₄	1	1	yes	characteristic
18	#388×C₁₃₉	—	2	1	no	—
19	#386×C₁₃₉	—	2	1	no	—
20	#380×C₁₃₉	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
23	#336×C₁₃₉	—	2	1	no	—
24	D₄⋊C₈×C₁₃₉	—	2	4	no	—
25	C₂²×D₄×C₁₃₉	—	2	1	no	—
26	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃₉	—	2	1	no	—
28	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃₉	—	2	4	no	—
32	C₂²×C₈×C₁₃₉	—	2	4	no	—
33	C₂²×C₈×C₁₃₉	—	2	4	no	—
34	C₂²×C₈×C₁₃₉	—	2	2	no	—
35	C₂²×C₈×C₁₃₉	—	2	2	no	—
36	#121×C₁₃₉	—	2	2	no	—
37	#121×C₁₃₉	C₈	1	4	yes	complemented
38	C₄×D₄×C₁₃₉	—	2	2	no	—
39	C₄×D₄×C₁₃₉	—	2	2	no	—
40	C₄×D₄×C₁₃₉	—	4	2	no	—
41	C₄×D₄×C₁₃₉	—	4	2	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
51	C₂×C₄²×C₁₃₉	—	2	2	no	—
52	C₂×C₄²×C₁₃₉	—	2	2	no	—
53	C₂×C₄²×C₁₃₉	—	2	1	no	—
54	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₁₃₉	—	2	2	no	—
59	C₄⋊C₈×C₁₃₉	—	2	2	no	—
60	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
61	C₄×C₈×C₁₃₉	—	2	4	no	—
62	C₄×C₈×C₁₃₉	—	2	2	no	—
63	C₄×C₈×C₁₃₉	D₄	1	4	yes	complemented
64	#95×C₁₃₉	—	2	1	no	—
65	#95×C₁₃₉	—	2	1	no	—
66	#95×C₁₃₉	—	2	1	no	—
67	C₂⁴×C₁₃₉	—	2	1	no	—
68	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×D₄×C₁₃₉	—	2	4	no	—
70	C₂×D₄×C₁₃₉	—	2	2	no	—
71	C₂×D₄×C₁₃₉	—	2	1	no	—
72	C₂×D₄×C₁₃₉	—	2	2	no	—
73	C₂×D₄×C₁₃₉	—	4	2	no	—
74	C₂×D₄×C₁₃₉	—	4	2	no	—
75	C₂×D₄×C₁₃₉	C₂×C₈	1	2	yes	complemented
76	C₂²×C₄×C₁₃₉	—	2	2	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	2	no	—
79	C₂²×C₄×C₁₃₉	—	2	1	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	—	2	1	no	—
82	C₂²×C₄×C₁₃₉	—	2	2	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	1	no	—
85	C₂²×C₄×C₁₃₉	—	2	1	no	—
86	C₂²×C₄×C₁₃₉	—	2	1	no	—
87	C₂²×C₄×C₁₃₉	—	4	2	no	—
88	C₂²×C₄×C₁₃₉	—	4	1	no	—
89	C₂²×C₄×C₁₃₉	—	4	1	no	—
90	C₂²×C₄×C₁₃₉	—	4	2	no	—
91	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₁₃₉	M₁₆	1	2	yes	—
96	C₂²×C₄×C₁₃₉	D₈	1	2	yes	—
97	C₂²×C₄×C₁₃₉	SD₁₆	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	C₂×D₄	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	—	2	4	no	—
105	C₂×C₈×C₁₃₉	—	4	2	no	—
106	C₂×C₈×C₁₃₉	—	4	2	no	—
107	C₂×C₈×C₁₃₉	—	4	2	no	—
108	C₄⋊C₄×C₁₃₉	—	2	1	no	—
109	C₄⋊C₄×C₁₃₉	—	2	2	no	—
110	C₄⋊C₄×C₁₃₉	—	2	2	no	—
111	C₄⋊C₄×C₁₃₉	—	4	2	no	—
112	C₄⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	complemented
113	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
115	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
117	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
118	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
119	C₄²×C₁₃₉	—	2	2	no	—
120	C₄²×C₁₃₉	—	2	1	no	—
121	C₄²×C₁₃₉	—	2	2	no	—
122	C₄²×C₁₃₉	—	2	1	no	—
123	C₄²×C₁₃₉	—	4	1	no	—
124	C₄²×C₁₃₉	—	4	1	no	—
125	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₃₉	#41	1	2	yes	—
127	C₂³×C₁₃₉	—	2	1	no	—
128	C₂³×C₁₃₉	—	2	1	no	—
129	C₂³×C₁₃₉	—	2	1	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	2	2	no	—
132	C₂³×C₁₃₉	—	4	1	no	—
133	C₂³×C₁₃₉	—	4	1	no	—
134	C₂³×C₁₃₉	—	4	1	no	—
135	C₂³×C₁₃₉	—	4	1	no	—
136	C₂³×C₁₃₉	—	4	1	no	—
137	C₂³×C₁₃₉	—	4	1	no	—
138	C₂³×C₁₃₉	C₂²⋊C₈	1	2	yes	—
139	C₂³×C₁₃₉	#102	1	2	yes	—
140	C₂³×C₁₃₉	#104	1	2	yes	—
141	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	D₄×C₁₃₉	—	2	4	no	—
143	D₄×C₁₃₉	—	4	8	no	—
144	D₄×C₁₃₉	—	4	2	no	—
145	C₂×C₄×C₁₃₉	—	2	4	no	—
146	C₂×C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₄×C₁₃₉	—	2	1	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	2	1	no	—
150	C₂×C₄×C₁₃₉	—	2	1	no	—
151	C₂×C₄×C₁₃₉	—	2	1	no	—
152	C₂×C₄×C₁₃₉	—	2	1	no	—
153	C₂×C₄×C₁₃₉	—	2	1	no	—
154	C₂×C₄×C₁₃₉	—	2	1	no	—
155	C₂×C₄×C₁₃₉	—	2	4	no	—
156	C₂×C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄×C₁₃₉	—	2	2	no	—
160	C₂×C₄×C₁₃₉	—	4	1	no	—
161	C₂×C₄×C₁₃₉	—	4	1	no	—
162	C₂×C₄×C₁₃₉	—	4	1	no	—
163	C₂×C₄×C₁₃₉	—	4	1	no	—
164	C₂×C₄×C₁₃₉	—	4	1	no	—
165	C₂×C₄×C₁₃₉	—	4	1	no	—
166	C₂×C₄×C₁₃₉	—	4	1	no	—
167	C₂×C₄×C₁₃₉	—	4	1	no	—
168	C₂×C₄×C₁₃₉	—	8	2	no	—
169	C₂×C₄×C₁₃₉	—	8	2	no	—
170	C₂×C₄×C₁₃₉	C₂²⋊C₈	1	2	yes	—
171	C₂×C₄×C₁₃₉	#102	1	2	yes	—
172	C₂×C₄×C₁₃₉	#104	1	2	yes	—
173	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₃₉	#121	1	2	yes	—
176	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
177	C₂×C₄×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃₉	C₂×M₁₆	1	1	yes	characteristic
179	C₂×C₄×C₁₃₉	#131	1	2	yes	—
180	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
182	C₂×C₄×C₁₃₉	#135	1	2	yes	—
183	C₈×C₁₃₉	—	2	8	no	—
184	C₈×C₁₃₉	—	8	2	no	—
185	C₂²×C₁₃₉	—	2	2	no	—
186	C₂²×C₁₃₉	—	2	2	no	—
187	C₂²×C₁₃₉	—	2	2	no	—
188	C₂²×C₁₃₉	—	2	2	no	—
189	C₂²×C₁₃₉	—	2	2	no	—
190	C₂²×C₁₃₉	—	2	2	no	—
191	C₂²×C₁₃₉	—	4	2	no	—
192	C₂²×C₁₃₉	—	4	2	no	—
193	C₂²×C₁₃₉	—	4	2	no	—
194	C₂²×C₁₃₉	—	8	1	no	—
195	C₂²×C₁₃₉	—	8	1	no	—
196	C₂²×C₁₃₉	—	8	1	no	—
197	C₂²×C₁₃₉	—	8	1	no	—
198	C₂²×C₁₃₉	D₄⋊C₈	1	4	yes	complemented
199	C₂²×C₁₃₉	#386	1	1	yes	characteristic
200	C₂²×C₁₃₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
201	C₂²×C₁₃₉	#408	1	1	yes	characteristic
202	C₂²×C₁₃₉	C₂×#102	1	1	yes	characteristic
203	C₂²×C₁₃₉	#416	1	1	yes	characteristic
204	C₂²×C₁₃₉	C₂×#104	1	1	yes	characteristic
205	C₂²×C₁₃₉	C₂×#104	1	1	yes	characteristic
206	C₄×C₁₃₉	—	2	2	no	—
207	C₄×C₁₃₉	—	2	2	no	—
208	C₄×C₁₃₉	—	2	1	no	—
209	C₄×C₁₃₉	—	2	2	no	—
210	C₄×C₁₃₉	—	2	1	no	—
211	C₄×C₁₃₉	—	4	2	no	—
212	C₄×C₁₃₉	—	8	1	no	—
213	C₄×C₁₃₉	—	8	1	no	—
214	C₄×C₁₃₉	C₈×D₄	1	2	yes	—
215	C₄×C₁₃₉	#435	1	2	yes	—
216	C₄×C₁₃₉	#465	1	2	yes	—
217	C₄×C₁₃₉	#466	1	2	yes	—
218	C₂×C₁₃₉	—	2	4	no	—
219	C₂×C₁₃₉	—	8	2	no	—
220	C₂×C₁₃₉	C₂×D₄⋊C₈	1	1	yes	characteristic
221	C₂×C₁₃₉	#1476	1	1	yes	characteristic
222	C₂×C₁₃₉	#1492	1	1	yes	characteristic
223	C₂×C₁₃₉	#1494	1	1	yes	characteristic
224	C₂×C₁₃₉	#1869	1	1	yes	characteristic
225	C₂×C₁₃₉	#1893	1	1	yes	characteristic
226	C₂×C₁₃₉	#1896	1	1	yes	characteristic
227	#9072	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₁₃₉	#9072	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×C₄×C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
230	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic
231	#1797	C₂×C₁₃₉	1	1	yes	characteristic, complemented
232	C₂×D₄⋊C₈	C₂×C₁₃₉	1	2	yes	complemented
233	#1279	C₂×C₁₃₉	1	2	yes	complemented
234	C₂³×C₈	—	2	1	no	—
235	C₂×#121	C₄×C₁₃₉	1	1	yes	characteristic
236	C₂×C₄×D₄	—	2	1	no	—
237	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
240	C₂×C₂²⋊C₈	—	2	1	no	—
241	C₂×C₄×C₈	—	2	1	no	—
242	C₂×C₄×C₈	—	2	4	no	—
243	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
244	#390	C₄×C₁₃₉	1	1	yes	characteristic
245	#389	C₄×C₁₃₉	1	1	yes	characteristic
246	#388	—	2	1	no	—
247	#386	—	2	1	no	—
248	#380	C₄×C₁₃₉	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	—	2	1	no	—
251	#336	—	2	1	no	—
252	D₄⋊C₈	—	2	4	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
259	C₂²×C₈	—	2	4	no	—
260	C₂²×C₈	—	2	4	no	—
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	#121	—	2	2	no	—
265	#121	C₈×C₁₃₉	1	4	yes	complemented
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	—	4	2	no	—
269	C₄×D₄	—	4	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	4	2	no	—
289	C₄×C₈	—	2	4	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	D₄×C₁₃₉	1	4	yes	complemented
292	#95	—	2	1	no	—
293	#95	—	2	1	no	—
294	#95	—	2	1	no	—
295	C₂⁴	—	2	1	no	—
296	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	C₂×C₈×C₁₃₉	1	2	yes	complemented
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
320	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
321	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₈×C₁₃₉	1	2	yes	—
323	C₂²×C₄	M₁₆×C₁₃₉	1	2	yes	—
324	C₂²×C₄	D₈×C₁₃₉	1	2	yes	—
325	C₂²×C₄	SD₁₆×C₁₃₉	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
329	C₂×C₈	—	2	16	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	4	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	complemented
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
354	C₄²	#41×C₁₃₉	1	2	yes	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	C₂²⋊C₈×C₁₃₉	1	2	yes	—
367	C₂³	#102×C₁₃₉	1	2	yes	—
368	C₂³	#104×C₁₃₉	1	2	yes	—
369	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
370	D₄	—	2	4	no	—
371	D₄	—	4	8	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	C₂²⋊C₈×C₁₃₉	1	2	yes	—
399	C₂×C₄	#102×C₁₃₉	1	2	yes	—
400	C₂×C₄	#104×C₁₃₉	1	2	yes	—
401	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
402	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
403	C₂×C₄	#121×C₁₃₉	1	2	yes	—
404	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄	C₂×M₁₆×C₁₃₉	1	1	yes	characteristic
407	C₂×C₄	#131×C₁₃₉	1	2	yes	—
408	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
409	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
410	C₂×C₄	#135×C₁₃₉	1	2	yes	—
411	C₈	—	2	8	no	—
412	C₈	—	8	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	D₄⋊C₈×C₁₃₉	1	4	yes	complemented
427	C₂²	#386×C₁₃₉	1	1	yes	characteristic
428	C₂²	C₂×C₂²⋊C₈×C₁₃₉	1	1	yes	characteristic
429	C₂²	#408×C₁₃₉	1	1	yes	characteristic
430	C₂²	C₂×#102×C₁₃₉	1	1	yes	characteristic
431	C₂²	#416×C₁₃₉	1	1	yes	characteristic
432	C₂²	C₂×#104×C₁₃₉	1	1	yes	characteristic
433	C₂²	C₂×#104×C₁₃₉	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	C₈×D₄×C₁₃₉	1	2	yes	—
443	C₄	#435×C₁₃₉	1	2	yes	—
444	C₄	#465×C₁₃₉	1	2	yes	—
445	C₄	#466×C₁₃₉	1	2	yes	—
446	C₂	—	2	4	no	—
447	C₂	—	8	2	no	—
448	C₂	C₂×D₄⋊C₈×C₁₃₉	1	1	yes	characteristic
449	C₂	#1476×C₁₃₉	1	1	yes	characteristic
450	C₂	#1492×C₁₃₉	1	1	yes	characteristic
451	C₂	#1494×C₁₃₉	1	1	yes	characteristic
452	C₂	#1869×C₁₃₉	1	1	yes	characteristic
453	C₂	#1893×C₁₃₉	1	1	yes	characteristic
454	C₂	#1896×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₁₃₉	C₄
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
1. C₂²×C₄×C₈×C₁₃₉	C₂	semidirect
3. #1797×C₁₃₉	C₂	semidirect
4. C₂×D₄⋊C₈×C₁₃₉	C₂	semidirect
5. #1279×C₁₃₉	C₂	semidirect
37. #121×C₁₃₉	C₈	semidirect
63. C₄×C₈×C₁₃₉	D₄	semidirect
75. C₂×D₄×C₁₃₉	C₂×C₈	semidirect
112. C₄⋊C₄×C₁₃₉	C₂×C₈	semidirect
198. C₂²×C₁₃₉	D₄⋊C₈	semidirect
227. #9072	C₁₃₉	direct (N × H)
228. C₁₃₉	#9072	direct (N × H)
229. C₂²×C₄×C₈	C₂×C₁₃₉	semidirect
231. #1797	C₂×C₁₃₉	semidirect
232. C₂×D₄⋊C₈	C₂×C₁₃₉	semidirect
233. #1279	C₂×C₁₃₉	semidirect
265. #121	C₈×C₁₃₉	semidirect
291. C₄×C₈	D₄×C₁₃₉	semidirect
303. C₂×D₄	C₂×C₈×C₁₃₉	semidirect
340. C₄⋊C₄	C₂×C₈×C₁₃₉	semidirect
426. C₂²	D₄⋊C₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₈×C₁₃₉	2
C₄×#121×C₁₃₉	2
#1797×C₁₃₉	2
C₂×D₄⋊C₈×C₁₃₉	2
#1279×C₁₃₉	2
#9072	139

Subgroups — C139×#9072 #48003668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#9072 #48003668