Subgroups — C₁₃₉×#10739 #48005335

Order 35584.

1406 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#343×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₃₉	—	2	2	no	—
7	C₂²×M₁₆×C₁₃₉	—	2	1	no	—
8	C₂²×M₁₆×C₁₃₉	—	2	8	no	—
9	C₂²×M₁₆×C₁₃₉	C₄	1	4	yes	complemented
10	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
12	C₂³×C₈×C₁₃₉	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₃₉	C₄	1	2	yes	—
15	#407×C₁₃₉	—	2	2	no	—
16	#407×C₁₃₉	C₄	1	4	yes	complemented
17	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
18	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
19	#380×C₁₃₉	—	2	1	no	—
20	#380×C₁₃₉	—	2	1	no	—
21	#380×C₁₃₉	—	2	1	no	—
22	#380×C₁₃₉	—	2	1	no	—
23	C₂×#95×C₁₃₉	C₄	1	2	yes	—
24	#343×C₁₃₉	—	2	8	no	—
25	C₂⁵×C₁₃₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃₉	—	2	4	no	—
27	C₂³×C₄×C₁₃₉	—	2	4	no	—
28	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₉	Q₈	1	2	yes	—
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₃₉	—	2	16	no	—
40	C₂×M₁₆×C₁₃₉	—	2	8	no	—
41	C₂×M₁₆×C₁₃₉	—	2	4	no	—
42	C₂×M₁₆×C₁₃₉	—	2	2	no	—
43	C₂×M₁₆×C₁₃₉	—	2	4	no	—
44	C₂×M₁₆×C₁₃₉	—	2	16	no	—
45	C₂×M₁₆×C₁₃₉	—	2	2	no	—
46	C₂×M₁₆×C₁₃₉	—	2	4	no	—
47	C₂×M₁₆×C₁₃₉	—	2	4	no	—
48	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
50	C₂×M₁₆×C₁₃₉	D₄	1	8	yes	—
51	C₂²×C₈×C₁₃₉	—	2	8	no	—
52	C₂²×C₈×C₁₃₉	—	2	4	no	—
53	C₂²×C₈×C₁₃₉	—	2	2	no	—
54	C₂²×C₈×C₁₃₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
62	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
63	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
64	#95×C₁₃₉	—	2	2	no	—
65	#95×C₁₃₉	—	2	2	no	—
66	C₂⁴×C₁₃₉	—	2	2	no	—
67	C₂⁴×C₁₃₉	—	2	2	no	—
68	C₂⁴×C₁₃₉	—	2	4	no	—
69	C₂⁴×C₁₃₉	—	4	2	no	—
70	C₂⁴×C₁₃₉	C₄²	1	2	yes	—
71	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂⁴×C₁₃₉	C₄⋊C₄	1	2	yes	—
74	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₉	—	2	4	no	—
76	C₂²×C₄×C₁₃₉	—	2	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	4	no	—
78	C₂²×C₄×C₁₃₉	—	2	8	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	4	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	4	no	—
83	C₂²×C₄×C₁₃₉	—	2	4	no	—
84	C₂²×C₄×C₁₃₉	—	2	8	no	—
85	C₂²×C₄×C₁₃₉	—	2	4	no	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	2	no	—
88	C₂²×C₄×C₁₃₉	—	2	4	no	—
89	C₂²×C₄×C₁₃₉	—	2	8	no	—
90	C₂²×C₄×C₁₃₉	—	4	4	no	—
91	C₂²×C₄×C₁₃₉	—	4	4	no	—
92	C₂²×C₄×C₁₃₉	C₄²	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
112	M₁₆×C₁₃₉	—	2	16	no	—
113	M₁₆×C₁₃₉	—	2	4	no	—
114	M₁₆×C₁₃₉	—	2	8	no	—
115	M₁₆×C₁₃₉	—	2	8	no	—
116	M₁₆×C₁₃₉	—	4	2	no	—
117	M₁₆×C₁₃₉	—	4	2	no	—
118	M₁₆×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
119	C₂×C₈×C₁₃₉	—	2	16	no	—
120	C₂×C₈×C₁₃₉	—	2	4	no	—
121	C₂×C₈×C₁₃₉	—	2	8	no	—
122	C₂×C₈×C₁₃₉	—	2	4	no	—
123	C₂×C₈×C₁₃₉	—	4	4	no	—
124	C₄⋊C₄×C₁₃₉	—	4	2	no	—
125	C₄⋊C₄×C₁₃₉	—	4	4	no	—
126	C₄⋊C₄×C₁₃₉	—	4	2	no	—
127	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
128	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
129	C₂³×C₁₃₉	—	2	2	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	2	1	no	—
132	C₂³×C₁₃₉	—	2	2	no	—
133	C₂³×C₁₃₉	—	2	2	no	—
134	C₂³×C₁₃₉	—	2	4	no	—
135	C₂³×C₁₃₉	—	2	4	no	—
136	C₂³×C₁₃₉	—	2	4	no	—
137	C₂³×C₁₃₉	—	2	4	no	—
138	C₂³×C₁₃₉	—	2	2	no	—
139	C₂³×C₁₃₉	—	2	1	no	—
140	C₂³×C₁₃₉	—	2	1	no	—
141	C₂³×C₁₃₉	—	2	2	no	—
142	C₂³×C₁₃₉	—	4	2	no	—
143	C₂³×C₁₃₉	—	4	2	no	—
144	C₂³×C₁₃₉	—	4	8	no	—
145	C₂³×C₁₃₉	—	4	8	no	—
146	C₂³×C₁₃₉	#95	1	2	yes	—
147	C₂³×C₁₃₉	#95	1	2	yes	—
148	C₂³×C₁₃₉	#100	1	2	yes	—
149	C₂³×C₁₃₉	#101	1	2	yes	—
150	C₂³×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
151	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂³×C₁₃₉	C₄×D₄	1	4	yes	—
154	C₂×C₄×C₁₃₉	—	2	4	no	—
155	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
163	C₂×C₄×C₁₃₉	—	2	2	no	—
164	C₂×C₄×C₁₃₉	—	2	4	no	—
165	C₂×C₄×C₁₃₉	—	2	4	no	—
166	C₂×C₄×C₁₃₉	—	2	4	no	—
167	C₂×C₄×C₁₃₉	—	2	4	no	—
168	C₂×C₄×C₁₃₉	—	4	4	no	—
169	C₂×C₄×C₁₃₉	—	4	4	no	—
170	C₂×C₄×C₁₃₉	—	4	4	no	—
171	C₂×C₄×C₁₃₉	—	8	8	no	—
172	C₂×C₄×C₁₃₉	#95	1	2	yes	—
173	C₂×C₄×C₁₃₉	#95	1	2	yes	—
174	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃₉	#117	1	2	yes	—
180	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
181	C₂×C₄×C₁₃₉	#120	1	2	yes	—
182	C₂×C₄×C₁₃₉	#120	1	2	yes	—
183	C₂×C₄×C₁₃₉	#121	1	4	yes	—
184	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
185	C₂×C₄×C₁₃₉	#123	1	2	yes	—
186	C₂×C₄×C₁₃₉	#123	1	2	yes	—
187	C₈×C₁₃₉	—	2	8	no	—
188	C₈×C₁₃₉	—	4	4	no	—
189	C₂²×C₁₃₉	—	2	4	no	—
190	C₂²×C₁₃₉	—	2	4	no	—
191	C₂²×C₁₃₉	—	2	4	no	—
192	C₂²×C₁₃₉	—	2	4	no	—
193	C₂²×C₁₃₉	—	2	2	no	—
194	C₂²×C₁₃₉	—	2	1	no	—
195	C₂²×C₁₃₉	—	2	1	no	—
196	C₂²×C₁₃₉	—	2	2	no	—
197	C₂²×C₁₃₉	—	2	1	no	—
198	C₂²×C₁₃₉	—	2	1	no	—
199	C₂²×C₁₃₉	—	2	2	no	—
200	C₂²×C₁₃₉	—	2	2	no	—
201	C₂²×C₁₃₉	—	2	2	no	—
202	C₂²×C₁₃₉	—	4	8	no	—
203	C₂²×C₁₃₉	—	4	8	no	—
204	C₂²×C₁₃₉	—	4	2	no	—
205	C₂²×C₁₃₉	—	4	2	no	—
206	C₂²×C₁₃₉	#343	1	4	yes	complemented
207	C₂²×C₁₃₉	C₂×#95	1	1	yes	characteristic
208	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
209	C₂²×C₁₃₉	#385	1	2	yes	—
210	C₂²×C₁₃₉	#386	1	2	yes	—
211	C₂²×C₁₃₉	C₂×#100	1	1	yes	characteristic
212	C₂²×C₁₃₉	C₂×#101	1	1	yes	characteristic
213	C₂²×C₁₃₉	#413	1	2	yes	—
214	C₄×C₁₃₉	—	2	2	no	—
215	C₄×C₁₃₉	—	2	2	no	—
216	C₄×C₁₃₉	—	8	4	no	—
217	C₄×C₁₃₉	#379	1	1	yes	characteristic
218	C₄×C₁₃₉	#380	1	2	yes	—
219	C₄×C₁₃₉	#381	1	1	yes	characteristic
220	C₄×C₁₃₉	#385	1	2	yes	—
221	C₄×C₁₃₉	#386	1	2	yes	—
222	C₂×C₁₃₉	—	2	4	no	—
223	C₂×C₁₃₉	—	2	2	no	—
224	C₂×C₁₃₉	—	2	2	no	—
225	C₂×C₁₃₉	—	4	2	no	—
226	C₂×C₁₃₉	C₂²⋊#95	1	1	yes	characteristic
227	C₂×C₁₃₉	C₂×#343	1	1	yes	characteristic
228	C₂×C₁₃₉	#1742	1	1	yes	characteristic
229	C₂×C₁₃₉	#1900	1	2	yes	—
230	C₂×C₁₃₉	#1901	1	2	yes	—
231	#10739	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃₉	#10739	1	1	yes	characteristic, direct product factor, Sylow
233	C₂³×M₁₆	C₂×C₁₃₉	1	1	yes	characteristic
234	C₂×#407	C₂×C₁₃₉	1	1	yes	characteristic
235	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
236	C₂×#343	C₂×C₁₃₉	1	4	yes	complemented
237	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
238	C₂²×M₁₆	—	2	2	no	—
239	C₂²×M₁₆	—	2	1	no	—
240	C₂²×M₁₆	—	2	8	no	—
241	C₂²×M₁₆	C₄×C₁₃₉	1	4	yes	complemented
242	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
243	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
244	C₂³×C₈	—	2	1	no	—
245	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
246	C₂²×C₂²⋊C₄	C₄×C₁₃₉	1	2	yes	—
247	#407	—	2	2	no	—
248	#407	C₄×C₁₃₉	1	4	yes	complemented
249	C₂×C₂²⋊C₈	—	2	1	no	—
250	C₂×C₂²⋊C₈	—	2	1	no	—
251	#380	—	2	1	no	—
252	#380	—	2	1	no	—
253	#380	—	2	1	no	—
254	#380	—	2	1	no	—
255	C₂×#95	C₄×C₁₃₉	1	2	yes	—
256	#343	—	2	8	no	—
257	C₂⁵	C₂×C₄×C₁₃₉	1	1	yes	characteristic
258	C₂³×C₄	—	2	4	no	—
259	C₂³×C₄	—	2	4	no	—
260	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
261	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
262	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
263	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
264	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
265	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
266	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
267	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
268	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
269	C₂³×C₄	Q₈×C₁₃₉	1	2	yes	—
270	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
271	C₂×M₁₆	—	2	16	no	—
272	C₂×M₁₆	—	2	8	no	—
273	C₂×M₁₆	—	2	4	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	4	no	—
276	C₂×M₁₆	—	2	16	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
281	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
282	C₂×M₁₆	D₄×C₁₃₉	1	8	yes	—
283	C₂²×C₈	—	2	8	no	—
284	C₂²×C₈	—	2	4	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₈	—	2	4	no	—
295	C₂²⋊C₈	—	2	4	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₂⁴	—	2	2	no	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	4	2	no	—
302	C₂⁴	C₄²×C₁₃₉	1	2	yes	—
303	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
304	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
305	C₂⁴	C₄⋊C₄×C₁₃₉	1	2	yes	—
306	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	C₄²×C₁₃₉	1	2	yes	—
325	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
327	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
328	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
329	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
330	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
331	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
332	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
333	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
334	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
335	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
342	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
343	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
344	M₁₆	—	2	16	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	8	no	—
347	M₁₆	—	2	8	no	—
348	M₁₆	—	4	2	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
351	C₂×C₈	—	2	16	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	8	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	4	4	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	8	no	—
378	C₂³	#95×C₁₃₉	1	2	yes	—
379	C₂³	#95×C₁₃₉	1	2	yes	—
380	C₂³	#100×C₁₃₉	1	2	yes	—
381	C₂³	#101×C₁₃₉	1	2	yes	—
382	C₂³	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
383	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
384	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
385	C₂³	C₄×D₄×C₁₃₉	1	4	yes	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	8	8	no	—
404	C₂×C₄	#95×C₁₃₉	1	2	yes	—
405	C₂×C₄	#95×C₁₃₉	1	2	yes	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
408	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
411	C₂×C₄	#117×C₁₃₉	1	2	yes	—
412	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
413	C₂×C₄	#120×C₁₃₉	1	2	yes	—
414	C₂×C₄	#120×C₁₃₉	1	2	yes	—
415	C₂×C₄	#121×C₁₃₉	1	4	yes	—
416	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
417	C₂×C₄	#123×C₁₃₉	1	2	yes	—
418	C₂×C₄	#123×C₁₃₉	1	2	yes	—
419	C₈	—	2	8	no	—
420	C₈	—	4	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	#343×C₁₃₉	1	4	yes	complemented
439	C₂²	C₂×#95×C₁₃₉	1	1	yes	characteristic
440	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
441	C₂²	#385×C₁₃₉	1	2	yes	—
442	C₂²	#386×C₁₃₉	1	2	yes	—
443	C₂²	C₂×#100×C₁₃₉	1	1	yes	characteristic
444	C₂²	C₂×#101×C₁₃₉	1	1	yes	characteristic
445	C₂²	#413×C₁₃₉	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	8	4	no	—
449	C₄	#379×C₁₃₉	1	1	yes	characteristic
450	C₄	#380×C₁₃₉	1	2	yes	—
451	C₄	#381×C₁₃₉	1	1	yes	characteristic
452	C₄	#385×C₁₃₉	1	2	yes	—
453	C₄	#386×C₁₃₉	1	2	yes	—
454	C₂	—	2	4	no	—
455	C₂	—	2	2	no	—
456	C₂	—	2	2	no	—
457	C₂	—	4	2	no	—
458	C₂	C₂²⋊#95×C₁₃₉	1	1	yes	characteristic
459	C₂	C₂×#343×C₁₃₉	1	1	yes	characteristic
460	C₂	#1742×C₁₃₉	1	1	yes	characteristic
461	C₂	#1900×C₁₃₉	1	2	yes	—
462	C₂	#1901×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#343×C₁₃₉	C₂	semidirect
9. C₂²×M₁₆×C₁₃₉	C₄	semidirect
16. #407×C₁₃₉	C₄	semidirect
118. M₁₆×C₁₃₉	C₂²⋊C₄	semidirect
206. C₂²×C₁₃₉	#343	semidirect
231. #10739	C₁₃₉	direct (N × H)
232. C₁₃₉	#10739	direct (N × H)
236. C₂×#343	C₂×C₁₃₉	semidirect
241. C₂²×M₁₆	C₄×C₁₃₉	semidirect
248. #407	C₄×C₁₃₉	semidirect
350. M₁₆	C₂²⋊C₄×C₁₃₉	semidirect
438. C₂²	#343×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₃₉	2
C₂×#407×C₁₃₉	2
C₂×#380×C₁₃₉	2
C₂×#343×C₁₃₉	2
#10739	139

Subgroups — C139×#10739 #48005335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10739 #48005335