Subgroups — C₁₃₉×#20684 #48015280

Order 35584.

1402 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#408×C₁₃₉	C₂	1	2	yes	maximal
3	#1818×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#1817×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#1729×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1728×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#336×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
10	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
11	C₄×#41×C₁₃₉	—	2	8	no	—
12	C₂×C₄×Q₈×C₁₃₉	C₄	1	2	yes	—
13	C₂×C₄×D₄×C₁₃₉	C₄	1	4	yes	—
14	C₂×C₄×D₄×C₁₃₉	C₄	1	2	yes	—
15	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
19	#408×C₁₃₉	—	2	8	no	—
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	8	yes	—
21	#336×C₁₃₉	C₂²	1	2	yes	—
22	#336×C₁₃₉	C₂²	1	2	yes	—
23	#336×C₁₃₉	C₂²	1	8	yes	—
24	#336×C₁₃₉	C₂²	1	2	yes	—
25	#336×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#41×C₁₃₉	—	2	2	no	—
27	C₂×#41×C₁₃₉	—	2	4	no	—
28	C₂×#41×C₁₃₉	—	2	2	no	—
29	C₂×#41×C₁₃₉	D₄	1	8	yes	—
30	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₃₉	—	2	4	no	—
38	C₂×M₁₆×C₁₃₉	—	2	4	no	—
39	C₂×M₁₆×C₁₃₉	—	2	4	no	—
40	C₂²×C₈×C₁₃₉	—	2	4	no	—
41	C₂²×C₈×C₁₃₉	—	2	4	no	—
42	C₂²×C₈×C₁₃₉	—	2	4	no	—
43	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
44	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
45	C₄×Q₈×C₁₃₉	—	2	8	no	—
46	C₄×D₄×C₁₃₉	—	2	16	no	—
47	C₄×D₄×C₁₃₉	—	2	8	no	—
48	#117×C₁₃₉	—	2	8	no	—
49	#117×C₁₃₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
53	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₃₉	—	2	8	no	—
55	C₂×C₄²×C₁₃₉	—	2	4	no	—
56	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
61	C₂²⋊C₈×C₁₃₉	—	2	16	no	—
62	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
63	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
64	#41×C₁₃₉	—	2	16	no	—
65	#41×C₁₃₉	—	2	16	no	—
66	C₂×Q₈×C₁₃₉	—	2	2	no	—
67	C₂×Q₈×C₁₃₉	—	2	2	no	—
68	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	4	yes	—
69	C₂×D₄×C₁₃₉	—	2	4	no	—
70	C₂×D₄×C₁₃₉	—	2	4	no	—
71	C₂×D₄×C₁₃₉	—	2	2	no	—
72	C₂×D₄×C₁₃₉	—	2	2	no	—
73	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
74	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
75	C₂²×C₄×C₁₃₉	—	2	4	no	—
76	C₂²×C₄×C₁₃₉	—	2	2	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	8	no	—
79	C₂²×C₄×C₁₃₉	—	2	4	no	—
80	C₂²×C₄×C₁₃₉	—	2	4	no	—
81	C₂²×C₄×C₁₃₉	—	2	8	no	—
82	C₂²×C₄×C₁₃₉	—	4	2	no	—
83	C₂²×C₄×C₁₃₉	—	4	4	no	—
84	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
90	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
92	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
93	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
94	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
95	M₁₆×C₁₃₉	—	4	8	no	—
96	C₂×C₈×C₁₃₉	—	2	4	no	—
97	C₂×C₈×C₁₃₉	—	2	4	no	—
98	C₂×C₈×C₁₃₉	—	2	4	no	—
99	C₂×C₈×C₁₃₉	—	2	4	no	—
100	C₂×C₈×C₁₃₉	—	2	4	no	—
101	C₂×C₈×C₁₃₉	—	2	4	no	—
102	C₂×C₈×C₁₃₉	—	4	8	no	—
103	C₄⋊C₄×C₁₃₉	—	2	8	no	—
104	C₄⋊C₄×C₁₃₉	—	2	4	no	—
105	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
106	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
107	C₄²×C₁₃₉	—	2	8	no	—
108	C₄²×C₁₃₉	—	2	4	no	—
109	C₄²×C₁₃₉	—	2	2	no	—
110	C₄²×C₁₃₉	—	2	4	no	—
111	C₄²×C₁₃₉	—	2	2	no	—
112	C₂³×C₁₃₉	—	2	2	no	—
113	C₂³×C₁₃₉	—	2	2	no	—
114	C₂³×C₁₃₉	—	2	2	no	—
115	C₂³×C₁₃₉	—	2	2	no	—
116	C₂³×C₁₃₉	—	2	4	no	—
117	C₂³×C₁₃₉	—	2	4	no	—
118	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
119	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
120	C₂³×C₁₃₉	#117	1	2	yes	—
121	C₂³×C₁₃₉	#117	1	2	yes	—
122	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
123	Q₈×C₁₃₉	—	2	8	no	—
124	D₄×C₁₃₉	—	2	16	no	—
125	D₄×C₁₃₉	—	2	8	no	—
126	C₂×C₄×C₁₃₉	—	2	2	no	—
127	C₂×C₄×C₁₃₉	—	2	2	no	—
128	C₂×C₄×C₁₃₉	—	2	2	no	—
129	C₂×C₄×C₁₃₉	—	2	2	no	—
130	C₂×C₄×C₁₃₉	—	2	8	no	—
131	C₂×C₄×C₁₃₉	—	2	8	no	—
132	C₂×C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₄×C₁₃₉	—	2	2	no	—
134	C₂×C₄×C₁₃₉	—	2	2	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	2	4	no	—
138	C₂×C₄×C₁₃₉	—	4	8	no	—
139	C₂×C₄×C₁₃₉	—	4	16	no	—
140	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
141	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₁₃₉	#117	1	2	yes	—
143	C₂×C₄×C₁₃₉	#117	1	2	yes	—
144	C₂×C₄×C₁₃₉	#123	1	8	yes	—
145	C₂×C₄×C₁₃₉	#123	1	8	yes	—
146	C₂×C₄×C₁₃₉	#131	1	4	yes	—
147	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
149	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
151	C₈×C₁₃₉	—	4	4	no	—
152	C₈×C₁₃₉	—	4	4	no	—
153	C₂²×C₁₃₉	—	2	4	no	—
154	C₂²×C₁₃₉	—	2	2	no	—
155	C₂²×C₁₃₉	—	2	2	no	—
156	C₂²×C₁₃₉	—	2	4	no	—
157	C₂²×C₁₃₉	—	2	8	no	—
158	C₂²×C₁₃₉	—	2	4	no	—
159	C₂²×C₁₃₉	—	4	2	no	—
160	C₂²×C₁₃₉	—	4	2	no	—
161	C₂²×C₁₃₉	—	4	4	no	—
162	C₂²×C₁₃₉	#381	1	4	yes	—
163	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₁₃₉	C₂×#117	1	1	yes	characteristic
165	C₂²×C₁₃₉	C₂×#117	1	1	yes	characteristic
166	C₂²×C₁₃₉	C₂×#131	1	2	yes	—
167	C₂²×C₁₃₉	#568	1	2	yes	—
168	C₄×C₁₃₉	—	2	4	no	—
169	C₄×C₁₃₉	—	2	4	no	—
170	C₄×C₁₃₉	—	4	2	no	—
171	C₄×C₁₃₉	—	4	4	no	—
172	C₄×C₁₃₉	#381	1	4	yes	—
173	C₄×C₁₃₉	C₂×#123	1	2	yes	—
174	C₄×C₁₃₉	C₂×#123	1	2	yes	—
175	C₂×C₁₃₉	—	2	4	no	—
176	C₂×C₁₃₉	—	4	4	no	—
177	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
178	C₂×C₁₃₉	#2880	1	2	yes	—
179	C₂×C₁₃₉	#2922	1	1	yes	characteristic
180	C₂×C₁₃₉	#2923	1	1	yes	characteristic
181	C₂×C₁₃₉	#2925	1	2	yes	—
182	#20684	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₁₃₉	#20684	1	1	yes	characteristic, direct product factor, Sylow
184	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic
185	C₂×#408	C₂×C₁₃₉	1	2	yes	—
186	#1818	C₂×C₁₃₉	1	4	yes	complemented
187	#1817	C₂×C₁₃₉	1	4	yes	complemented
188	#1729	C₂×C₁₃₉	1	2	yes	complemented
189	#1728	C₂×C₁₃₉	1	1	yes	characteristic, complemented
190	C₂×#336	C₂×C₁₃₉	1	1	yes	characteristic, complemented
191	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
192	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
193	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
194	C₄×#41	—	2	8	no	—
195	C₂×C₄×Q₈	C₄×C₁₃₉	1	2	yes	—
196	C₂×C₄×D₄	C₄×C₁₃₉	1	4	yes	—
197	C₂×C₄×D₄	C₄×C₁₃₉	1	2	yes	—
198	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
199	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
200	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
201	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
202	#408	—	2	8	no	—
203	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	8	yes	—
204	#336	C₂²×C₁₃₉	1	2	yes	—
205	#336	C₂²×C₁₃₉	1	2	yes	—
206	#336	C₂²×C₁₃₉	1	8	yes	—
207	#336	C₂²×C₁₃₉	1	2	yes	—
208	#336	C₂²×C₁₃₉	1	2	yes	—
209	C₂×#41	—	2	2	no	—
210	C₂×#41	—	2	4	no	—
211	C₂×#41	—	2	2	no	—
212	C₂×#41	D₄×C₁₃₉	1	8	yes	—
213	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
214	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
215	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
216	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
217	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
218	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
219	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
220	C₂×M₁₆	—	2	4	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	2	4	no	—
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
227	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
228	C₄×Q₈	—	2	8	no	—
229	C₄×D₄	—	2	16	no	—
230	C₄×D₄	—	2	8	no	—
231	#117	—	2	8	no	—
232	#117	—	2	4	no	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
237	C₂×C₄²	—	2	8	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
240	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
241	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
243	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
244	C₂²⋊C₈	—	2	16	no	—
245	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
246	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
247	#41	—	2	16	no	—
248	#41	—	2	16	no	—
249	C₂×Q₈	—	2	2	no	—
250	C₂×Q₈	—	2	2	no	—
251	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	4	yes	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
257	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
274	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
275	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
276	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
277	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
278	M₁₆	—	4	8	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	4	8	no	—
286	C₄⋊C₄	—	2	8	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₂²⋊C₄	—	2	8	no	—
289	C₂²⋊C₄	—	2	4	no	—
290	C₄²	—	2	8	no	—
291	C₄²	—	2	4	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	4	no	—
301	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
302	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
303	C₂³	#117×C₁₃₉	1	2	yes	—
304	C₂³	#117×C₁₃₉	1	2	yes	—
305	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
306	Q₈	—	2	8	no	—
307	D₄	—	2	16	no	—
308	D₄	—	2	8	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
325	C₂×C₄	#117×C₁₃₉	1	2	yes	—
326	C₂×C₄	#117×C₁₃₉	1	2	yes	—
327	C₂×C₄	#123×C₁₃₉	1	8	yes	—
328	C₂×C₄	#123×C₁₃₉	1	8	yes	—
329	C₂×C₄	#131×C₁₃₉	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
331	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
332	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
334	C₈	—	4	4	no	—
335	C₈	—	4	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	4	no	—
345	C₂²	#381×C₁₃₉	1	4	yes	—
346	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
347	C₂²	C₂×#117×C₁₃₉	1	1	yes	characteristic
348	C₂²	C₂×#117×C₁₃₉	1	1	yes	characteristic
349	C₂²	C₂×#131×C₁₃₉	1	2	yes	—
350	C₂²	#568×C₁₃₉	1	2	yes	—
351	C₄	—	2	4	no	—
352	C₄	—	2	4	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	4	no	—
355	C₄	#381×C₁₃₉	1	4	yes	—
356	C₄	C₂×#123×C₁₃₉	1	2	yes	—
357	C₄	C₂×#123×C₁₃₉	1	2	yes	—
358	C₂	—	2	4	no	—
359	C₂	—	4	4	no	—
360	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
361	C₂	#2880×C₁₃₉	1	2	yes	—
362	C₂	#2922×C₁₃₉	1	1	yes	characteristic
363	C₂	#2923×C₁₃₉	1	1	yes	characteristic
364	C₂	#2925×C₁₃₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #1818×C₁₃₉	C₂	semidirect
4. #1817×C₁₃₉	C₂	semidirect
5. #1729×C₁₃₉	C₂	semidirect
6. #1728×C₁₃₉	C₂	semidirect
7. C₂×#336×C₁₃₉	C₂	semidirect
182. #20684	C₁₃₉	direct (N × H)
183. C₁₃₉	#20684	direct (N × H)
186. #1818	C₂×C₁₃₉	semidirect
187. #1817	C₂×C₁₃₉	semidirect
188. #1729	C₂×C₁₃₉	semidirect
189. #1728	C₂×C₁₃₉	semidirect
190. C₂×#336	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×C₄×#41×C₁₃₉	2
C₂×#408×C₁₃₉	2
#1818×C₁₃₉	2
#1817×C₁₃₉	2
#1729×C₁₃₉	2
#1728×C₁₃₉	2
C₂×#336×C₁₃₉	2
#20684	139

Subgroups — C139×#20684 #48015280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20684 #48015280