Subgroups — C₁₃₉×#10746 #48005342

Order 35584.

1246 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#413×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#344×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1728×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
7	#568×C₁₃₉	—	2	2	no	—
8	#568×C₁₃₉	—	2	4	no	—
9	#568×C₁₃₉	C₄	1	4	yes	complemented
10	C₂×#131×C₁₃₉	—	2	4	no	—
11	C₂²×M₁₆×C₁₃₉	—	2	2	no	—
12	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
14	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
16	#413×C₁₃₉	—	2	2	no	—
17	#413×C₁₃₉	C₄	1	4	yes	complemented
18	C₂×#101×C₁₃₉	—	2	1	no	—
19	C₂×#100×C₁₃₉	—	2	1	no	—
20	#391×C₁₃₉	—	2	1	no	—
21	#390×C₁₃₉	—	2	1	no	—
22	#386×C₁₃₉	C₄	1	4	yes	—
23	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
24	#344×C₁₃₉	—	2	4	no	—
25	#336×C₁₃₉	—	2	4	no	—
26	C₂×#41×C₁₃₉	—	2	2	no	—
27	C₂×#41×C₁₃₉	—	2	2	no	—
28	C₂×#41×C₁₃₉	—	2	2	no	—
29	C₂×#41×C₁₃₉	—	2	2	no	—
30	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
31	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
32	C₂×#41×C₁₃₉	D₄	1	2	yes	—
33	C₂×#41×C₁₃₉	Q₈	1	2	yes	—
34	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₃₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
39	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
40	#131×C₁₃₉	—	2	16	no	—
41	#131×C₁₃₉	—	2	16	no	—
42	C₂×M₁₆×C₁₃₉	—	2	4	no	—
43	C₂×M₁₆×C₁₃₉	—	2	8	no	—
44	C₂×M₁₆×C₁₃₉	—	2	8	no	—
45	C₂×M₁₆×C₁₃₉	—	2	2	no	—
46	C₂×M₁₆×C₁₃₉	—	2	2	no	—
47	C₂×M₁₆×C₁₃₉	—	2	2	no	—
48	C₂×M₁₆×C₁₃₉	—	2	2	no	—
49	C₂×M₁₆×C₁₃₉	—	2	2	no	—
50	C₂×M₁₆×C₁₃₉	—	2	2	no	—
51	C₂×M₁₆×C₁₃₉	—	2	2	no	—
52	C₂×M₁₆×C₁₃₉	—	2	2	no	—
53	C₂×M₁₆×C₁₃₉	—	2	2	no	—
54	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
55	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
56	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
57	C₂²×C₈×C₁₃₉	—	2	4	no	—
58	C₂²×C₈×C₁₃₉	—	2	2	no	—
59	C₂²×C₈×C₁₃₉	D₄	1	4	yes	—
60	#117×C₁₃₉	—	2	2	no	—
61	#117×C₁₃₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₃₉	—	2	2	no	—
66	C₂×C₄²×C₁₃₉	—	2	1	no	—
67	C₂×C₄²×C₁₃₉	—	2	1	no	—
68	C₂×C₄²×C₁₃₉	—	2	1	no	—
69	C₂×C₄²×C₁₃₉	—	2	2	no	—
70	#101×C₁₃₉	—	2	4	no	—
71	#100×C₁₃₉	—	2	4	no	—
72	#95×C₁₃₉	—	2	4	no	—
73	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
74	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
75	#41×C₁₃₉	—	2	4	no	—
76	#41×C₁₃₉	—	2	4	no	—
77	#41×C₁₃₉	—	2	4	no	—
78	#41×C₁₃₉	—	2	4	no	—
79	#41×C₁₃₉	—	2	4	no	—
80	#41×C₁₃₉	—	2	4	no	—
81	#41×C₁₃₉	—	2	4	no	—
82	#41×C₁₃₉	—	2	4	no	—
83	C₂×Q₈×C₁₃₉	—	2	2	no	—
84	C₂×Q₈×C₁₃₉	—	2	2	no	—
85	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	2	yes	—
86	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	2	yes	—
87	C₂×D₄×C₁₃₉	—	2	4	no	—
88	C₂×D₄×C₁₃₉	—	2	4	no	—
89	C₂×D₄×C₁₃₉	—	2	2	no	—
90	C₂×D₄×C₁₃₉	—	2	2	no	—
91	C₂×D₄×C₁₃₉	C₄²	1	4	yes	—
92	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
93	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
94	C₂×D₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	2	4	no	—
101	C₂²×C₄×C₁₃₉	—	2	2	no	—
102	C₂²×C₄×C₁₃₉	—	4	4	no	—
103	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
106	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
115	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
116	M₁₆×C₁₃₉	—	2	16	no	—
117	M₁₆×C₁₃₉	—	2	4	no	—
118	M₁₆×C₁₃₉	—	2	4	no	—
119	M₁₆×C₁₃₉	—	2	4	no	—
120	M₁₆×C₁₃₉	—	2	4	no	—
121	M₁₆×C₁₃₉	—	2	4	no	—
122	M₁₆×C₁₃₉	—	2	4	no	—
123	M₁₆×C₁₃₉	—	4	2	no	—
124	M₁₆×C₁₃₉	—	4	2	no	—
125	C₂×C₈×C₁₃₉	—	2	16	no	—
126	C₂×C₈×C₁₃₉	—	2	4	no	—
127	C₂×C₈×C₁₃₉	—	2	4	no	—
128	C₂×C₈×C₁₃₉	—	2	4	no	—
129	C₂×C₈×C₁₃₉	—	4	2	no	—
130	C₂×C₈×C₁₃₉	—	4	2	no	—
131	C₂×C₈×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
132	C₄⋊C₄×C₁₃₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
135	C₄²×C₁₃₉	—	4	1	no	—
136	C₄²×C₁₃₉	—	4	1	no	—
137	C₄²×C₁₃₉	—	4	2	no	—
138	C₄²×C₁₃₉	—	4	1	no	—
139	C₄²×C₁₃₉	—	4	1	no	—
140	C₂³×C₁₃₉	—	2	2	no	—
141	C₂³×C₁₃₉	—	2	2	no	—
142	C₂³×C₁₃₉	—	4	2	no	—
143	C₂³×C₁₃₉	—	4	4	no	—
144	C₂³×C₁₃₉	#95	1	4	yes	—
145	C₂³×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
146	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
149	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
150	Q₈×C₁₃₉	—	2	4	no	—
151	Q₈×C₁₃₉	—	2	4	no	—
152	D₄×C₁₃₉	—	2	8	no	—
153	D₄×C₁₃₉	—	2	8	no	—
154	D₄×C₁₃₉	—	2	4	no	—
155	D₄×C₁₃₉	—	2	4	no	—
156	C₂×C₄×C₁₃₉	—	2	2	no	—
157	C₂×C₄×C₁₃₉	—	2	2	no	—
158	C₂×C₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄×C₁₃₉	—	2	4	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	—	2	8	no	—
164	C₂×C₄×C₁₃₉	—	4	2	no	—
165	C₂×C₄×C₁₃₉	—	4	4	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	4	4	no	—
168	C₂×C₄×C₁₃₉	—	4	2	no	—
169	C₂×C₄×C₁₃₉	#95	1	4	yes	—
170	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃₉	#117	1	2	yes	—
176	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₃₉	#120	1	2	yes	—
180	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
181	C₂×C₄×C₁₃₉	#121	1	2	yes	—
182	C₂×C₄×C₁₃₉	#121	1	2	yes	—
183	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
186	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₃₉	#123	1	2	yes	—
188	C₈×C₁₃₉	—	2	8	no	—
189	C₈×C₁₃₉	—	4	4	no	—
190	C₂²×C₁₃₉	—	2	2	no	—
191	C₂²×C₁₃₉	—	2	4	no	—
192	C₂²×C₁₃₉	—	2	4	no	—
193	C₂²×C₁₃₉	—	4	1	no	—
194	C₂²×C₁₃₉	—	4	1	no	—
195	C₂²×C₁₃₉	—	4	2	no	—
196	C₂²×C₁₃₉	—	4	4	no	—
197	C₂²×C₁₃₉	—	4	4	no	—
198	C₂²×C₁₃₉	—	8	2	no	—
199	C₂²×C₁₃₉	C₂×#95	1	1	yes	characteristic
200	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
201	C₂²×C₁₃₉	#385	1	2	yes	—
202	C₂²×C₁₃₉	#386	1	1	yes	characteristic
203	C₂²×C₁₃₉	#386	1	1	yes	characteristic
204	C₄×C₁₃₉	—	2	4	no	—
205	C₄×C₁₃₉	—	4	4	no	—
206	C₄×C₁₃₉	—	8	2	no	—
207	C₄×C₁₃₉	#379	1	1	yes	characteristic
208	C₄×C₁₃₉	#380	1	2	yes	—
209	C₄×C₁₃₉	#381	1	1	yes	characteristic
210	C₄×C₁₃₉	#385	1	1	yes	characteristic
211	C₄×C₁₃₉	#385	1	1	yes	characteristic
212	C₄×C₁₃₉	#386	1	2	yes	—
213	C₂×C₁₃₉	—	2	1	no	—
214	C₂×C₁₃₉	—	2	1	no	—
215	C₂×C₁₃₉	—	2	2	no	—
216	C₂×C₁₃₉	—	2	2	no	—
217	C₂×C₁₃₉	—	4	4	no	—
218	C₂×C₁₃₉	C₂²⋊#95	1	1	yes	characteristic
219	C₂×C₁₃₉	#1891	1	2	yes	—
220	#10746	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₁₃₉	#10746	1	1	yes	characteristic, direct product factor, Sylow
222	C₂×#568	C₂×C₁₃₉	1	1	yes	characteristic
223	C₂×#413	C₂×C₁₃₉	1	1	yes	characteristic
224	#2297	C₂×C₁₃₉	1	1	yes	characteristic
225	C₂×#344	C₂×C₁₃₉	1	2	yes	complemented
226	#1728	C₂×C₁₃₉	1	2	yes	complemented
227	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
228	#568	—	2	2	no	—
229	#568	—	2	4	no	—
230	#568	C₄×C₁₃₉	1	4	yes	complemented
231	C₂×#131	—	2	4	no	—
232	C₂²×M₁₆	—	2	2	no	—
233	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
234	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
235	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
236	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
237	#413	—	2	2	no	—
238	#413	C₄×C₁₃₉	1	4	yes	complemented
239	C₂×#101	—	2	1	no	—
240	C₂×#100	—	2	1	no	—
241	#391	—	2	1	no	—
242	#390	—	2	1	no	—
243	#386	C₄×C₁₃₉	1	4	yes	—
244	C₄×C₂²⋊C₄	—	2	2	no	—
245	#344	—	2	4	no	—
246	#336	—	2	4	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	—	2	2	no	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
252	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
253	C₂×#41	D₄×C₁₃₉	1	2	yes	—
254	C₂×#41	Q₈×C₁₃₉	1	2	yes	—
255	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
256	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
257	C₂²×D₄	D₄×C₁₃₉	1	1	yes	characteristic
258	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
259	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
261	#131	—	2	16	no	—
262	#131	—	2	16	no	—
263	C₂×M₁₆	—	2	4	no	—
264	C₂×M₁₆	—	2	8	no	—
265	C₂×M₁₆	—	2	8	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
276	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
277	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
278	C₂²×C₈	—	2	4	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	D₄×C₁₃₉	1	4	yes	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	2	no	—
291	#101	—	2	4	no	—
292	#100	—	2	4	no	—
293	#95	—	2	4	no	—
294	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
295	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	2	yes	—
307	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	2	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	C₄²×C₁₃₉	1	4	yes	—
313	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
314	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
315	C₂×D₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
325	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
326	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
327	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
334	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
335	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
336	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
337	M₁₆	—	2	16	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	—	2	4	no	—
342	M₁₆	—	2	4	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	16	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	4	8	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	2	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	#95×C₁₃₉	1	4	yes	—
366	C₂³	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
367	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
368	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
369	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
370	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	2	8	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#95×C₁₃₉	1	4	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
393	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
394	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
395	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
396	C₂×C₄	#117×C₁₃₉	1	2	yes	—
397	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
398	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
399	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
401	C₂×C₄	#120×C₁₃₉	1	2	yes	—
402	C₂×C₄	#121×C₁₃₉	1	2	yes	—
403	C₂×C₄	#121×C₁₃₉	1	2	yes	—
404	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
405	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
406	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
407	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
408	C₂×C₄	#123×C₁₃₉	1	2	yes	—
409	C₈	—	2	8	no	—
410	C₈	—	4	4	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	2	no	—
420	C₂²	C₂×#95×C₁₃₉	1	1	yes	characteristic
421	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
422	C₂²	#385×C₁₃₉	1	2	yes	—
423	C₂²	#386×C₁₃₉	1	1	yes	characteristic
424	C₂²	#386×C₁₃₉	1	1	yes	characteristic
425	C₄	—	2	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	2	no	—
428	C₄	#379×C₁₃₉	1	1	yes	characteristic
429	C₄	#380×C₁₃₉	1	2	yes	—
430	C₄	#381×C₁₃₉	1	1	yes	characteristic
431	C₄	#385×C₁₃₉	1	1	yes	characteristic
432	C₄	#385×C₁₃₉	1	1	yes	characteristic
433	C₄	#386×C₁₃₉	1	2	yes	—
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	2	no	—
437	C₂	—	2	2	no	—
438	C₂	—	4	4	no	—
439	C₂	C₂²⋊#95×C₁₃₉	1	1	yes	characteristic
440	C₂	#1891×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₉	#120
commutator	C₂³	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	#386
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#344×C₁₃₉	C₂	semidirect
5. #1728×C₁₃₉	C₂	semidirect
9. #568×C₁₃₉	C₄	semidirect
17. #413×C₁₃₉	C₄	semidirect
131. C₂×C₈×C₁₃₉	C₂²⋊C₄	semidirect
220. #10746	C₁₃₉	direct (N × H)
221. C₁₃₉	#10746	direct (N × H)
225. C₂×#344	C₂×C₁₃₉	semidirect
226. #1728	C₂×C₁₃₉	semidirect
230. #568	C₄×C₁₃₉	semidirect
238. #413	C₄×C₁₃₉	semidirect
352. C₂×C₈	C₂²⋊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×#568×C₁₃₉	2
C₂×#413×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#344×C₁₃₉	2
#1728×C₁₃₉	2
#10746	139

Subgroups — C139×#10746 #48005342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10746 #48005342