Subgroups — C₁₃₉×#21220 #48015816

Order 35584.

1454 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2905×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#413×C₁₃₉	C₂	1	2	yes	maximal
4	C₂²×#101×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2873×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1967×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1966×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
12	#536×C₁₃₉	—	2	4	no	—
13	#536×C₁₃₉	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#123×C₁₃₉	C₄	1	4	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₄	1	4	yes	—
18	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
19	#424×C₁₃₉	—	2	4	no	—
20	#423×C₁₃₉	C₂²	1	4	yes	—
21	#413×C₁₃₉	—	2	8	no	—
22	C₂×#101×C₁₃₉	—	2	8	no	—
23	C₂×#101×C₁₃₉	C₂²	1	8	yes	—
24	C₂×#101×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#100×C₁₃₉	C₂²	1	4	yes	—
26	#405×C₁₃₉	—	2	4	no	—
27	C₄×M₁₆×C₁₃₉	C₂²	1	4	yes	—
28	C₂×#41×C₁₃₉	—	2	4	no	—
29	C₂×#41×C₁₃₉	—	2	2	no	—
30	C₂×#41×C₁₃₉	—	2	2	no	—
31	C₂×#41×C₁₃₉	—	2	4	no	—
32	C₂²×Q₈×C₁₃₉	—	2	4	no	—
33	C₂²×Q₈×C₁₃₉	—	2	2	no	—
34	C₂²×Q₈×C₁₃₉	—	2	2	no	—
35	C₂²×Q₈×C₁₃₉	—	2	4	no	—
36	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
37	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
38	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
40	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₃₉	—	2	2	no	—
45	C₂×M₁₆×C₁₃₉	—	2	4	no	—
46	C₂×M₁₆×C₁₃₉	—	2	2	no	—
47	C₂×M₁₆×C₁₃₉	—	2	4	no	—
48	C₂×M₁₆×C₁₃₉	—	2	4	no	—
49	C₂×M₁₆×C₁₃₉	D₄	1	8	yes	—
50	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
51	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
52	C₂²×C₈×C₁₃₉	—	2	2	no	—
53	C₂²×C₈×C₁₃₉	—	2	2	no	—
54	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
55	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
56	#124×C₁₃₉	—	2	4	no	—
57	#124×C₁₃₉	—	2	4	no	—
58	#123×C₁₃₉	—	2	16	no	—
59	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
60	#117×C₁₃₉	D₄	1	4	yes	—
61	#117×C₁₃₉	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
65	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
67	C₄⋊C₈×C₁₃₉	—	2	8	no	—
68	#101×C₁₃₉	—	2	16	no	—
69	#101×C₁₃₉	—	2	8	no	—
70	#100×C₁₃₉	—	2	8	no	—
71	#97×C₁₃₉	—	2	4	no	—
72	C₄×C₈×C₁₃₉	—	2	4	no	—
73	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
75	#41×C₁₃₉	—	4	4	no	—
76	#41×C₁₃₉	—	4	4	no	—
77	#41×C₁₃₉	—	4	4	no	—
78	#41×C₁₃₉	—	4	4	no	—
79	C₂×Q₈×C₁₃₉	—	2	4	no	—
80	C₂×Q₈×C₁₃₉	—	2	8	no	—
81	C₂×Q₈×C₁₃₉	—	2	4	no	—
82	C₂×Q₈×C₁₃₉	—	2	2	no	—
83	C₂×Q₈×C₁₃₉	—	2	2	no	—
84	C₂×Q₈×C₁₃₉	—	2	2	no	—
85	C₂×Q₈×C₁₃₉	—	2	1	no	—
86	C₂×Q₈×C₁₃₉	—	2	1	no	—
87	C₂×Q₈×C₁₃₉	—	2	4	no	—
88	C₂×Q₈×C₁₃₉	—	2	2	no	—
89	C₂×Q₈×C₁₃₉	—	4	4	no	—
90	C₂×Q₈×C₁₃₉	—	4	4	no	—
91	C₂×Q₈×C₁₃₉	—	4	4	no	—
92	C₂×Q₈×C₁₃₉	—	4	4	no	—
93	C₂×D₄×C₁₃₉	—	2	4	no	—
94	C₂×D₄×C₁₃₉	—	2	8	no	—
95	C₂×D₄×C₁₃₉	—	2	2	no	—
96	C₂×D₄×C₁₃₉	—	2	1	no	—
97	C₂×D₄×C₁₃₉	—	2	1	no	—
98	C₂×D₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	4	no	—
100	C₂²×C₄×C₁₃₉	—	2	8	no	—
101	C₂²×C₄×C₁₃₉	—	2	4	no	—
102	C₂²×C₄×C₁₃₉	—	2	8	no	—
103	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₁₃₉	—	2	8	no	—
113	M₁₆×C₁₃₉	—	2	4	no	—
114	M₁₆×C₁₃₉	—	2	4	no	—
115	M₁₆×C₁₃₉	—	2	4	no	—
116	M₁₆×C₁₃₉	—	4	4	no	—
117	M₁₆×C₁₃₉	C₂×D₄	1	8	yes	—
118	C₂×C₈×C₁₃₉	—	2	8	no	—
119	C₂×C₈×C₁₃₉	—	2	4	no	—
120	C₂×C₈×C₁₃₉	—	2	4	no	—
121	C₂×C₈×C₁₃₉	—	4	4	no	—
122	C₄⋊C₄×C₁₃₉	—	2	16	no	—
123	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
124	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
125	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
126	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
127	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
128	C₂³×C₁₃₉	—	2	2	no	—
129	C₂³×C₁₃₉	—	2	4	no	—
130	C₂³×C₁₃₉	—	4	2	no	—
131	C₂³×C₁₃₉	—	4	4	no	—
132	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂³×C₁₃₉	C₄×D₄	1	4	yes	—
134	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
135	Q₈×C₁₃₉	—	4	4	no	—
136	Q₈×C₁₃₉	—	4	2	no	—
137	Q₈×C₁₃₉	—	4	2	no	—
138	Q₈×C₁₃₉	—	4	1	no	—
139	Q₈×C₁₃₉	—	4	2	no	—
140	Q₈×C₁₃₉	—	4	1	no	—
141	Q₈×C₁₃₉	—	4	8	no	—
142	D₄×C₁₃₉	—	4	8	no	—
143	D₄×C₁₃₉	—	4	2	no	—
144	D₄×C₁₃₉	—	4	1	no	—
145	D₄×C₁₃₉	—	4	1	no	—
146	C₂×C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₄×C₁₃₉	—	2	2	no	—
148	C₂×C₄×C₁₃₉	—	2	4	no	—
149	C₂×C₄×C₁₃₉	—	2	8	no	—
150	C₂×C₄×C₁₃₉	—	4	4	no	—
151	C₂×C₄×C₁₃₉	—	4	8	no	—
152	C₂×C₄×C₁₃₉	—	4	8	no	—
153	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	—
154	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
156	C₂×C₄×C₁₃₉	#121	1	4	yes	—
157	C₂×C₄×C₁₃₉	#121	1	4	yes	—
158	C₂×C₄×C₁₃₉	#124	1	4	yes	—
159	C₂×C₄×C₁₃₉	#127	1	4	yes	—
160	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
164	C₈×C₁₃₉	—	2	8	no	—
165	C₈×C₁₃₉	—	4	4	no	—
166	C₂²×C₁₃₉	—	2	2	no	—
167	C₂²×C₁₃₉	—	2	4	no	—
168	C₂²×C₁₃₉	—	4	4	no	—
169	C₂²×C₁₃₉	—	4	4	no	—
170	C₂²×C₁₃₉	—	4	2	no	—
171	C₂²×C₁₃₉	—	8	4	no	—
172	C₂²×C₁₃₉	#390	1	4	yes	—
173	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
175	C₄×C₁₃₉	—	2	8	no	—
176	C₄×C₁₃₉	—	4	2	no	—
177	C₄×C₁₃₉	—	4	4	no	—
178	C₄×C₁₃₉	#390	1	4	yes	—
179	C₄×C₁₃₉	C₂×#121	1	2	yes	—
180	C₄×C₁₃₉	C₂×#124	1	1	yes	characteristic
181	C₄×C₁₃₉	C₂×#127	1	1	yes	characteristic
182	C₂×C₁₃₉	—	2	2	no	—
183	C₂×C₁₃₉	—	2	4	no	—
184	C₂×C₁₃₉	—	8	2	no	—
185	C₂×C₁₃₉	C₂×#390	1	1	yes	characteristic
186	C₂×C₁₃₉	#2889	1	2	yes	—
187	#21220	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₉	#21220	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#536	C₂×C₁₃₉	1	1	yes	characteristic
190	#2905	C₂×C₁₃₉	1	1	yes	characteristic, complemented
191	C₂×#413	C₂×C₁₃₉	1	2	yes	—
192	C₂²×#101	C₂×C₁₃₉	1	2	yes	complemented
193	#2873	C₂×C₁₃₉	1	1	yes	characteristic, complemented
194	#1967	C₂×C₁₃₉	1	4	yes	complemented
195	#1966	C₂×C₁₃₉	1	4	yes	complemented
196	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
197	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
198	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
199	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
200	#536	—	2	4	no	—
201	#536	—	2	4	no	—
202	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
203	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
204	C₂×#123	C₄×C₁₃₉	1	4	yes	—
205	C₂×C₂²⋊Q₈	C₄×C₁₃₉	1	4	yes	—
206	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
207	#424	—	2	4	no	—
208	#423	C₂²×C₁₃₉	1	4	yes	—
209	#413	—	2	8	no	—
210	C₂×#101	—	2	8	no	—
211	C₂×#101	C₂²×C₁₃₉	1	8	yes	—
212	C₂×#101	C₂²×C₁₃₉	1	4	yes	—
213	C₂×#100	C₂²×C₁₃₉	1	4	yes	—
214	#405	—	2	4	no	—
215	C₄×M₁₆	C₂²×C₁₃₉	1	4	yes	—
216	C₂×#41	—	2	2	no	—
217	C₂×#41	—	2	2	no	—
218	C₂×#41	—	2	4	no	—
219	C₂×#41	—	2	4	no	—
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	—	2	4	no	—
223	C₂²×Q₈	—	2	4	no	—
224	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
225	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
226	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
227	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
228	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
230	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
231	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	—	2	4	no	—
237	C₂×M₁₆	D₄×C₁₃₉	1	8	yes	—
238	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
239	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	4	no	—
243	C₄⋊Q₈	—	2	4	no	—
244	#124	—	2	4	no	—
245	#124	—	2	4	no	—
246	#123	—	2	16	no	—
247	C₂²⋊Q₈	—	2	16	no	—
248	#117	D₄×C₁₃₉	1	4	yes	—
249	#117	D₄×C₁₃₉	1	4	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
254	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
255	C₄⋊C₈	—	2	8	no	—
256	#101	—	2	16	no	—
257	#101	—	2	8	no	—
258	#100	—	2	8	no	—
259	#97	—	2	4	no	—
260	C₄×C₈	—	2	4	no	—
261	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
262	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
263	#41	—	4	4	no	—
264	#41	—	4	4	no	—
265	#41	—	4	4	no	—
266	#41	—	4	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	4	4	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
298	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
299	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
300	M₁₆	—	2	8	no	—
301	M₁₆	—	2	4	no	—
302	M₁₆	—	2	4	no	—
303	M₁₆	—	2	4	no	—
304	M₁₆	—	4	4	no	—
305	M₁₆	C₂×D₄×C₁₃₉	1	8	yes	—
306	C₂×C₈	—	2	8	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	4	4	no	—
310	C₄⋊C₄	—	2	16	no	—
311	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
314	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
315	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	4	no	—
320	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
321	C₂³	C₄×D₄×C₁₃₉	1	4	yes	—
322	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
323	Q₈	—	4	4	no	—
324	Q₈	—	4	2	no	—
325	Q₈	—	4	2	no	—
326	Q₈	—	4	1	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	4	1	no	—
329	Q₈	—	4	8	no	—
330	D₄	—	4	8	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
343	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
344	C₂×C₄	#121×C₁₃₉	1	4	yes	—
345	C₂×C₄	#121×C₁₃₉	1	4	yes	—
346	C₂×C₄	#124×C₁₃₉	1	4	yes	—
347	C₂×C₄	#127×C₁₃₉	1	4	yes	—
348	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
350	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
351	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
352	C₈	—	2	8	no	—
353	C₈	—	4	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	4	4	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	#390×C₁₃₉	1	4	yes	—
361	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
362	C₂²	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
363	C₄	—	2	8	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	4	no	—
366	C₄	#390×C₁₃₉	1	4	yes	—
367	C₄	C₂×#121×C₁₃₉	1	2	yes	—
368	C₄	C₂×#124×C₁₃₉	1	1	yes	characteristic
369	C₄	C₂×#127×C₁₃₉	1	1	yes	characteristic
370	C₂	—	2	2	no	—
371	C₂	—	2	4	no	—
372	C₂	—	8	2	no	—
373	C₂	C₂×#390×C₁₃₉	1	1	yes	characteristic
374	C₂	#2889×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×#117×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2905×C₁₃₉	C₂	semidirect
4. C₂²×#101×C₁₃₉	C₂	semidirect
5. #2873×C₁₃₉	C₂	semidirect
6. #1967×C₁₃₉	C₂	semidirect
7. #1966×C₁₃₉	C₂	semidirect
187. #21220	C₁₃₉	direct (N × H)
188. C₁₃₉	#21220	direct (N × H)
190. #2905	C₂×C₁₃₉	semidirect
192. C₂²×#101	C₂×C₁₃₉	semidirect
193. #2873	C₂×C₁₃₉	semidirect
194. #1967	C₂×C₁₃₉	semidirect
195. #1966	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₁₃₉	2
#2905×C₁₃₉	2
C₂×#413×C₁₃₉	2
C₂²×#101×C₁₃₉	2
#2873×C₁₃₉	2
#1967×C₁₃₉	2
#1966×C₁₃₉	2
#21220	139

Subgroups — C139×#21220 #48015816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21220 #48015816