Subgroups — C₁₃₉×#20745 #48015341

Order 35584.

1222 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#433×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2314×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1825×C₁₃₉	C₂	1	2	yes	maximal
5	#1805×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1803×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1787×C₁₃₉	C₂	1	2	yes	maximal
8	#1763×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₄×#103×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	#519×C₁₃₉	—	2	4	no	—
12	#519×C₁₃₉	C₄	1	8	yes	complemented
13	C₂×C₄×Q₈×C₁₃₉	—	2	2	no	—
14	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#117×C₁₃₉	—	2	2	no	—
17	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
19	#433×C₁₃₉	—	2	4	no	—
20	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	#388×C₁₃₉	—	2	2	no	—
29	#387×C₁₃₉	—	2	2	no	—
30	#384×C₁₃₉	C₂²	1	1	yes	characteristic
31	#382×C₁₃₉	C₂²	1	1	yes	characteristic
32	#380×C₁₃₉	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
34	#340×C₁₃₉	C₂²	1	2	yes	—
35	#340×C₁₃₉	C₂²	1	2	yes	—
36	#340×C₁₃₉	C₂²	1	2	yes	—
37	#340×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₃₉	—	2	4	no	—
39	C₂²×Q₈×C₁₃₉	—	2	4	no	—
40	C₂²×Q₈×C₁₃₉	—	2	1	no	—
41	C₂²×Q₈×C₁₃₉	—	2	2	no	—
42	C₂²×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
43	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃₉	—	2	1	no	—
45	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
48	C₄×Q₈×C₁₃₉	—	2	16	no	—
49	C₄×Q₈×C₁₃₉	—	2	4	no	—
50	C₄×Q₈×C₁₃₉	—	2	4	no	—
51	C₄×Q₈×C₁₃₉	C₂×C₄	1	8	yes	—
52	C₄×Q₈×C₁₃₉	C₂×C₄	1	8	yes	—
53	#117×C₁₃₉	—	2	2	no	—
54	#117×C₁₃₉	—	2	16	no	—
55	#117×C₁₃₉	C₂×C₄	1	4	yes	—
56	#117×C₁₃₉	C₂×C₄	1	4	yes	—
57	#117×C₁₃₉	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃₉	—	2	2	no	—
69	C₂×C₄²×C₁₃₉	—	2	2	no	—
70	C₂×C₄²×C₁₃₉	—	2	1	no	—
71	C₂×C₄²×C₁₃₉	—	2	2	no	—
72	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₁₃₉	—	2	4	no	—
75	#103×C₁₃₉	—	2	4	no	—
76	#103×C₁₃₉	—	2	4	no	—
77	#103×C₁₃₉	—	2	4	no	—
78	#103×C₁₃₉	—	2	4	no	—
79	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
80	#97×C₁₃₉	—	2	2	no	—
81	C₄×C₈×C₁₃₉	—	2	2	no	—
82	#95×C₁₃₉	—	2	2	no	—
83	#95×C₁₃₉	—	2	2	no	—
84	#95×C₁₃₉	—	2	2	no	—
85	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₃₉	—	2	16	no	—
87	C₂×Q₈×C₁₃₉	—	2	4	no	—
88	C₂×Q₈×C₁₃₉	—	2	4	no	—
89	C₂×Q₈×C₁₃₉	—	2	16	no	—
90	C₂×Q₈×C₁₃₉	—	2	4	no	—
91	C₂×Q₈×C₁₃₉	—	2	2	no	—
92	C₂×Q₈×C₁₃₉	—	2	2	no	—
93	C₂×Q₈×C₁₃₉	—	2	2	no	—
94	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
95	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
96	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
97	C₂²×C₄×C₁₃₉	—	2	4	no	—
98	C₂²×C₄×C₁₃₉	—	2	4	no	—
99	C₂²×C₄×C₁₃₉	—	2	4	no	—
100	C₂²×C₄×C₁₃₉	—	2	2	no	—
101	C₂²×C₄×C₁₃₉	—	2	2	no	—
102	C₂²×C₄×C₁₃₉	—	2	2	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	2	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₃₉	—	2	2	no	—
113	C₂×C₈×C₁₃₉	—	2	2	no	—
114	C₂×C₈×C₁₃₉	—	2	2	no	—
115	C₂×C₈×C₁₃₉	—	2	2	no	—
116	C₂×C₈×C₁₃₉	—	2	2	no	—
117	C₂×C₈×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	—	2	8	no	—
119	C₄⋊C₄×C₁₃₉	—	2	8	no	—
120	C₄⋊C₄×C₁₃₉	—	2	2	no	—
121	C₄⋊C₄×C₁₃₉	—	2	2	no	—
122	C₄⋊C₄×C₁₃₉	—	2	2	no	—
123	C₄⋊C₄×C₁₃₉	—	2	2	no	—
124	C₄⋊C₄×C₁₃₉	—	2	2	no	—
125	C₄⋊C₄×C₁₃₉	—	8	2	no	—
126	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
127	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
128	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
130	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
131	C₄²×C₁₃₉	—	2	8	no	—
132	C₄²×C₁₃₉	—	2	8	no	—
133	C₄²×C₁₃₉	—	2	4	no	—
134	C₄²×C₁₃₉	—	8	2	no	—
135	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
139	C₂³×C₁₃₉	—	2	1	no	—
140	C₂³×C₁₃₉	—	2	1	no	—
141	C₂³×C₁₃₉	—	2	2	no	—
142	C₂³×C₁₃₉	—	2	2	no	—
143	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₃₉	—	2	16	no	—
146	Q₈×C₁₃₉	—	2	4	no	—
147	Q₈×C₁₃₉	—	2	4	no	—
148	Q₈×C₁₃₉	—	2	4	no	—
149	Q₈×C₁₃₉	#117	1	8	yes	—
150	C₂×C₄×C₁₃₉	—	2	16	no	—
151	C₂×C₄×C₁₃₉	—	2	4	no	—
152	C₂×C₄×C₁₃₉	—	2	4	no	—
153	C₂×C₄×C₁₃₉	—	2	4	no	—
154	C₂×C₄×C₁₃₉	—	2	1	no	—
155	C₂×C₄×C₁₃₉	—	2	1	no	—
156	C₂×C₄×C₁₃₉	—	2	2	no	—
157	C₂×C₄×C₁₃₉	—	2	2	no	—
158	C₂×C₄×C₁₃₉	—	2	2	no	—
159	C₂×C₄×C₁₃₉	—	2	2	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	2	4	no	—
162	C₂×C₄×C₁₃₉	—	2	4	no	—
163	C₂×C₄×C₁₃₉	—	4	2	no	—
164	C₂×C₄×C₁₃₉	—	4	2	no	—
165	C₂×C₄×C₁₃₉	—	4	2	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	4	2	no	—
168	C₂×C₄×C₁₃₉	—	4	2	no	—
169	C₂×C₄×C₁₃₉	—	4	2	no	—
170	C₂×C₄×C₁₃₉	—	4	2	no	—
171	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
172	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
173	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
177	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
178	C₈×C₁₃₉	—	4	2	no	—
179	C₈×C₁₃₉	—	4	2	no	—
180	C₂²×C₁₃₉	—	2	4	no	—
181	C₂²×C₁₃₉	—	2	2	no	—
182	C₂²×C₁₃₉	—	4	2	no	—
183	C₂²×C₁₃₉	—	4	1	no	—
184	C₂²×C₁₃₉	—	4	1	no	—
185	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₁₃₉	#525	1	1	yes	characteristic
187	C₂²×C₁₃₉	#525	1	1	yes	characteristic
188	C₂²×C₁₃₉	#577	1	2	yes	—
189	C₂²×C₁₃₉	#578	1	2	yes	—
190	C₄×C₁₃₉	—	2	4	no	—
191	C₄×C₁₃₉	—	2	4	no	—
192	C₄×C₁₃₉	—	2	8	no	—
193	C₄×C₁₃₉	—	2	2	no	—
194	C₄×C₁₃₉	—	4	4	no	—
195	C₄×C₁₃₉	—	8	2	no	—
196	C₄×C₁₃₉	—	8	2	no	—
197	C₄×C₁₃₉	C₂×#117	1	2	yes	—
198	C₄×C₁₃₉	#525	1	2	yes	—
199	C₂×C₁₃₉	—	4	2	no	—
200	C₂×C₁₃₉	#2280	1	1	yes	characteristic
201	C₂×C₁₃₉	#2898	1	2	yes	—
202	C₂×C₁₃₉	#3121	1	2	yes	—
203	C₂×C₁₃₉	#3126	1	1	yes	characteristic
204	C₂×C₁₃₉	#3127	1	1	yes	characteristic
205	#20745	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₁₃₉	#20745	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic
208	C₂×#433	C₂×C₁₃₉	1	1	yes	characteristic
209	#2314	C₂×C₁₃₉	1	1	yes	characteristic
210	#1825	C₂×C₁₃₉	1	2	yes	—
211	#1805	C₂×C₁₃₉	1	2	yes	complemented
212	#1803	C₂×C₁₃₉	1	2	yes	complemented
213	#1787	C₂×C₁₃₉	1	2	yes	—
214	#1763	C₂×C₁₃₉	1	2	yes	complemented
215	C₄×#103	C₂×C₁₃₉	1	2	yes	complemented
216	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
217	#519	—	2	4	no	—
218	#519	C₄×C₁₃₉	1	8	yes	complemented
219	C₂×C₄×Q₈	—	2	2	no	—
220	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
221	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
222	C₂×#117	—	2	2	no	—
223	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
225	#433	—	2	4	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
227	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
228	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
229	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
230	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
232	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
234	#388	—	2	2	no	—
235	#387	—	2	2	no	—
236	#384	C₂²×C₁₃₉	1	1	yes	characteristic
237	#382	C₂²×C₁₃₉	1	1	yes	characteristic
238	#380	C₂²×C₁₃₉	1	2	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
240	#340	C₂²×C₁₃₉	1	2	yes	—
241	#340	C₂²×C₁₃₉	1	2	yes	—
242	#340	C₂²×C₁₃₉	1	2	yes	—
243	#340	C₂²×C₁₃₉	1	2	yes	—
244	C₂²×Q₈	—	2	4	no	—
245	C₂²×Q₈	—	2	4	no	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	—	2	2	no	—
248	C₂²×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
249	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
253	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
254	C₄×Q₈	—	2	16	no	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	C₂×C₄×C₁₃₉	1	8	yes	—
258	C₄×Q₈	C₂×C₄×C₁₃₉	1	8	yes	—
259	#117	—	2	2	no	—
260	#117	—	2	16	no	—
261	#117	C₂×C₄×C₁₃₉	1	4	yes	—
262	#117	C₂×C₄×C₁₃₉	1	4	yes	—
263	#117	D₄×C₁₃₉	1	4	yes	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
280	C₄⋊C₈	—	2	4	no	—
281	#103	—	2	4	no	—
282	#103	—	2	4	no	—
283	#103	—	2	4	no	—
284	#103	—	2	4	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	#97	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
292	C₂×Q₈	—	2	16	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	16	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
301	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
302	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	8	2	no	—
332	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
333	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	8	2	no	—
336	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
337	C₄²	—	2	8	no	—
338	C₄²	—	2	8	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	8	2	no	—
341	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
342	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
343	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
344	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
350	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
351	Q₈	—	2	16	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	2	4	no	—
355	Q₈	#117×C₁₃₉	1	8	yes	—
356	C₂×C₄	—	2	16	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
380	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
383	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
392	C₂²	#525×C₁₃₉	1	1	yes	characteristic
393	C₂²	#525×C₁₃₉	1	1	yes	characteristic
394	C₂²	#577×C₁₃₉	1	2	yes	—
395	C₂²	#578×C₁₃₉	1	2	yes	—
396	C₄	—	2	8	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	4	4	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₂×#117×C₁₃₉	1	2	yes	—
404	C₄	#525×C₁₃₉	1	2	yes	—
405	C₂	—	4	2	no	—
406	C₂	#2280×C₁₃₉	1	1	yes	characteristic
407	C₂	#2898×C₁₃₉	1	2	yes	—
408	C₂	#3121×C₁₃₉	1	2	yes	—
409	C₂	#3126×C₁₃₉	1	1	yes	characteristic
410	C₂	#3127×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×#117×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. #1805×C₁₃₉	C₂	semidirect
6. #1803×C₁₃₉	C₂	semidirect
8. #1763×C₁₃₉	C₂	semidirect
9. C₄×#103×C₁₃₉	C₂	semidirect
12. #519×C₁₃₉	C₄	semidirect
205. #20745	C₁₃₉	direct (N × H)
206. C₁₃₉	#20745	direct (N × H)
211. #1805	C₂×C₁₃₉	semidirect
212. #1803	C₂×C₁₃₉	semidirect
214. #1763	C₂×C₁₃₉	semidirect
215. C₄×#103	C₂×C₁₃₉	semidirect
218. #519	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×#519×C₁₃₉	2
C₂×#433×C₁₃₉	2
#2314×C₁₃₉	2
#1825×C₁₃₉	2
#1805×C₁₃₉	2
#1803×C₁₃₉	2
#1787×C₁₃₉	2
#1763×C₁₃₉	2
C₄×#103×C₁₃₉	2
#20745	139

Subgroups — C139×#20745 #48015341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20745 #48015341