Subgroups — C₁₃₉×#20896 #48015492

Order 35584.

1898 conjugacy classes of subgroups.

The subgroup lattice has 400 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, complemented
2	C₂×#525×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#408×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	C₂×#407×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1870×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#1729×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₉	—	2	4	no	—
10	C₂²×M₁₆×C₁₃₉	—	2	8	no	—
11	C₂²×M₁₆×C₁₃₉	C₂²	1	4	yes	—
12	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
14	#525×C₁₃₉	—	2	4	no	—
15	#525×C₁₃₉	—	2	4	no	—
16	C₂×#123×C₁₃₉	C₄	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₄	1	2	yes	—
18	C₂×#121×C₁₃₉	C₄	1	2	yes	—
19	C₂×#120×C₁₃₉	C₄	1	2	yes	—
20	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	#408×C₁₃₉	—	2	8	no	—
23	#407×C₁₃₉	—	2	4	no	—
24	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	8	yes	complemented
26	#336×C₁₃₉	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₃₉	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₃₉	—	2	4	no	—
37	C₂³×C₄×C₁₃₉	—	2	4	no	—
38	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
41	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
42	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₃₉	—	2	32	no	—
46	C₂×M₁₆×C₁₃₉	—	2	8	no	—
47	C₂×M₁₆×C₁₃₉	—	2	4	no	—
48	C₂×M₁₆×C₁₃₉	—	2	4	no	—
49	C₂×M₁₆×C₁₃₉	—	2	4	no	—
50	C₂×M₁₆×C₁₃₉	—	2	16	no	—
51	C₂²×C₈×C₁₃₉	—	2	4	no	—
52	C₂²×C₈×C₁₃₉	—	2	4	no	—
53	C₂²×C₈×C₁₃₉	D₄	1	8	yes	complemented
54	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
55	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
56	#123×C₁₃₉	—	2	8	no	—
57	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
58	#121×C₁₃₉	—	2	8	no	—
59	#120×C₁₃₉	—	2	8	no	—
60	C₄×D₄×C₁₃₉	—	2	8	no	—
61	C₄×D₄×C₁₃₉	—	2	8	no	—
62	#117×C₁₃₉	—	2	2	no	—
63	#117×C₁₃₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
66	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
68	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
70	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
71	C₂²⋊C₈×C₁₃₉	—	2	16	no	—
72	C₂⁴×C₁₃₉	—	2	4	no	—
73	C₂⁴×C₁₃₉	—	4	4	no	—
74	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
75	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
76	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
77	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
78	#41×C₁₃₉	—	4	4	no	—
79	#41×C₁₃₉	—	4	8	no	—
80	#41×C₁₃₉	—	4	4	no	—
81	C₂×Q₈×C₁₃₉	—	2	2	no	—
82	C₂×Q₈×C₁₃₉	—	2	4	no	—
83	C₂×D₄×C₁₃₉	—	2	8	no	—
84	C₂×D₄×C₁₃₉	—	2	4	no	—
85	C₂×D₄×C₁₃₉	—	2	8	no	—
86	C₂×D₄×C₁₃₉	—	2	2	no	—
87	C₂×D₄×C₁₃₉	—	2	4	no	—
88	C₂×D₄×C₁₃₉	—	4	8	no	—
89	C₂²×C₄×C₁₃₉	—	2	4	no	—
90	C₂²×C₄×C₁₃₉	—	2	8	no	—
91	C₂²×C₄×C₁₃₉	—	2	8	no	—
92	C₂²×C₄×C₁₃₉	—	2	16	no	—
93	C₂²×C₄×C₁₃₉	—	2	8	no	—
94	C₂²×C₄×C₁₃₉	—	2	4	no	—
95	C₂²×C₄×C₁₃₉	—	2	4	no	—
96	C₂²×C₄×C₁₃₉	—	2	4	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	4	no	—
100	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
101	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	4	yes	—
111	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
113	M₁₆×C₁₃₉	—	2	32	no	—
114	M₁₆×C₁₃₉	—	4	8	no	—
115	C₂×C₈×C₁₃₉	—	2	16	no	—
116	C₂×C₈×C₁₃₉	—	2	4	no	—
117	C₂×C₈×C₁₃₉	—	2	4	no	—
118	C₂×C₈×C₁₃₉	—	2	4	no	—
119	C₂×C₈×C₁₃₉	—	2	4	no	—
120	C₂×C₈×C₁₃₉	—	2	4	no	—
121	C₂×C₈×C₁₃₉	C₂×D₄	1	8	yes	—
122	C₄⋊C₄×C₁₃₉	—	2	4	no	—
123	C₄⋊C₄×C₁₃₉	—	2	8	no	—
124	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
126	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
127	C₄²×C₁₃₉	—	2	2	no	—
128	C₄²×C₁₃₉	—	2	2	no	—
129	C₂³×C₁₃₉	—	2	4	no	—
130	C₂³×C₁₃₉	—	2	4	no	—
131	C₂³×C₁₃₉	—	2	4	no	—
132	C₂³×C₁₃₉	—	2	4	no	—
133	C₂³×C₁₃₉	—	2	8	no	—
134	C₂³×C₁₃₉	—	2	2	no	—
135	C₂³×C₁₃₉	—	2	4	no	—
136	C₂³×C₁₃₉	—	2	8	no	—
137	C₂³×C₁₃₉	—	4	8	no	—
138	C₂³×C₁₃₉	—	4	16	no	—
139	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
140	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₁₃₉	C₄×D₄	1	4	yes	—
142	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
143	Q₈×C₁₃₉	—	4	4	no	—
144	D₄×C₁₃₉	—	4	16	no	—
145	D₄×C₁₃₉	—	4	8	no	—
146	D₄×C₁₃₉	—	4	4	no	—
147	C₂×C₄×C₁₃₉	—	2	4	no	—
148	C₂×C₄×C₁₃₉	—	2	8	no	—
149	C₂×C₄×C₁₃₉	—	2	4	no	—
150	C₂×C₄×C₁₃₉	—	2	8	no	—
151	C₂×C₄×C₁₃₉	—	2	4	no	—
152	C₂×C₄×C₁₃₉	—	2	16	no	—
153	C₂×C₄×C₁₃₉	—	2	4	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	2	4	no	—
156	C₂×C₄×C₁₃₉	—	2	8	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	4	4	no	—
159	C₂×C₄×C₁₃₉	—	4	2	no	—
160	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
161	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₁₃₉	#120	1	4	yes	—
164	C₂×C₄×C₁₃₉	#121	1	8	yes	—
165	C₂×C₄×C₁₃₉	#123	1	4	yes	—
166	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
170	C₈×C₁₃₉	—	2	8	no	—
171	C₈×C₁₃₉	—	4	4	no	—
172	C₂²×C₁₃₉	—	2	4	no	—
173	C₂²×C₁₃₉	—	2	8	no	—
174	C₂²×C₁₃₉	—	2	4	no	—
175	C₂²×C₁₃₉	—	2	4	no	—
176	C₂²×C₁₃₉	—	2	4	no	—
177	C₂²×C₁₃₉	—	4	16	no	—
178	C₂²×C₁₃₉	—	4	8	no	—
179	C₂²×C₁₃₉	—	4	4	no	—
180	C₂²×C₁₃₉	—	4	8	no	—
181	C₂²×C₁₃₉	—	4	2	no	—
182	C₂²×C₁₃₉	#386	1	4	yes	—
183	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
185	C₂²×C₁₃₉	#568	1	4	yes	—
186	C₄×C₁₃₉	—	2	4	no	—
187	C₄×C₁₃₉	—	4	4	no	—
188	C₄×C₁₃₉	—	4	2	no	—
189	C₄×C₁₃₉	#386	1	4	yes	—
190	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
191	C₄×C₁₃₉	C₂×#121	1	2	yes	—
192	C₄×C₁₃₉	C₂×#123	1	1	yes	characteristic
193	C₂×C₁₃₉	—	2	4	no	—
194	C₂×C₁₃₉	—	4	4	no	—
195	C₂×C₁₃₉	—	8	2	no	—
196	C₂×C₁₃₉	C₂×#386	1	1	yes	characteristic
197	C₂×C₁₃₉	#2879	1	2	yes	—
198	C₂×C₁₃₉	#2930	1	4	yes	—
199	#20896	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₁₃₉	#20896	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³×M₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
202	C₂×#525	C₂×C₁₃₉	1	1	yes	characteristic
203	C₂×#408	C₂×C₁₃₉	1	2	yes	complemented
204	C₂×#407	C₂×C₁₃₉	1	1	yes	characteristic, complemented
205	#1870	C₂×C₁₃₉	1	8	yes	complemented
206	#1729	C₂×C₁₃₉	1	2	yes	complemented
207	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
208	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
209	C₂²×M₁₆	—	2	4	no	—
210	C₂²×M₁₆	—	2	8	no	—
211	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
212	C₂²×M₁₆	C₂²×C₁₃₉	1	4	yes	—
213	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
214	#525	—	2	4	no	—
215	#525	—	2	4	no	—
216	C₂×#123	C₄×C₁₃₉	1	2	yes	—
217	C₂×C₂²⋊Q₈	C₄×C₁₃₉	1	2	yes	—
218	C₂×#121	C₄×C₁₃₉	1	2	yes	—
219	C₂×#120	C₄×C₁₃₉	1	2	yes	—
220	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
221	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
222	#408	—	2	8	no	—
223	#407	—	2	4	no	—
224	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	8	yes	complemented
226	#336	C₂²×C₁₃₉	1	8	yes	complemented
227	C₂⁵	C₂×C₄×C₁₃₉	1	1	yes	characteristic
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	2	4	no	—
232	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
233	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
234	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
235	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
236	C₂³×C₄	—	2	4	no	—
237	C₂³×C₄	—	2	4	no	—
238	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
239	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
240	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
241	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
242	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
243	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
245	C₂×M₁₆	—	2	32	no	—
246	C₂×M₁₆	—	2	8	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	—	2	16	no	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	D₄×C₁₃₉	1	8	yes	complemented
254	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
255	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
256	#123	—	2	8	no	—
257	C₂²⋊Q₈	—	2	8	no	—
258	#121	—	2	8	no	—
259	#120	—	2	8	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	8	no	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
269	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
270	C₂²⋊C₈	—	2	8	no	—
271	C₂²⋊C₈	—	2	16	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	4	4	no	—
274	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
275	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
276	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
277	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
278	#41	—	4	4	no	—
279	#41	—	4	8	no	—
280	#41	—	4	4	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	4	8	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	16	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
301	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
311	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
313	M₁₆	—	2	32	no	—
314	M₁₆	—	4	8	no	—
315	C₂×C₈	—	2	16	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	C₂×D₄×C₁₃₉	1	8	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	8	no	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	8	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	4	8	no	—
338	C₂³	—	4	16	no	—
339	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
340	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
341	C₂³	C₄×D₄×C₁₃₉	1	4	yes	—
342	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
343	Q₈	—	4	4	no	—
344	D₄	—	4	16	no	—
345	D₄	—	4	8	no	—
346	D₄	—	4	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
362	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
363	C₂×C₄	#120×C₁₃₉	1	4	yes	—
364	C₂×C₄	#121×C₁₃₉	1	8	yes	—
365	C₂×C₄	#123×C₁₃₉	1	4	yes	—
366	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
370	C₈	—	2	8	no	—
371	C₈	—	4	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	8	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	16	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	8	no	—
382	C₂²	#386×C₁₃₉	1	4	yes	—
383	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
384	C₂²	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
385	C₂²	#568×C₁₃₉	1	4	yes	—
386	C₄	—	2	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	4	no	—
389	C₄	#386×C₁₃₉	1	4	yes	—
390	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
391	C₄	C₂×#121×C₁₃₉	1	2	yes	—
392	C₄	C₂×#123×C₁₃₉	1	1	yes	characteristic
393	C₂	—	2	4	no	—
394	C₂	—	4	4	no	—
395	C₂	—	8	2	no	—
396	C₂	C₂×#386×C₁₃₉	1	1	yes	characteristic
397	C₂	#2879×C₁₃₉	1	2	yes	—
398	C₂	#2930×C₁₃₉	1	4	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	C₂×#525×C₁₃₉	C₂
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
1. C₂³×M₁₆×C₁₃₉	C₂	semidirect
3. C₂×#408×C₁₃₉	C₂	semidirect
4. C₂×#407×C₁₃₉	C₂	semidirect
5. #1870×C₁₃₉	C₂	semidirect
6. #1729×C₁₃₉	C₂	semidirect
25. C₂×C₂²⋊C₈×C₁₃₉	C₂²	semidirect
26. #336×C₁₃₉	C₂²	semidirect
53. C₂²×C₈×C₁₃₉	D₄	semidirect
199. #20896	C₁₃₉	direct (N × H)
200. C₁₃₉	#20896	direct (N × H)
201. C₂³×M₁₆	C₂×C₁₃₉	semidirect
203. C₂×#408	C₂×C₁₃₉	semidirect
204. C₂×#407	C₂×C₁₃₉	semidirect
205. #1870	C₂×C₁₃₉	semidirect
206. #1729	C₂×C₁₃₉	semidirect
225. C₂×C₂²⋊C₈	C₂²×C₁₃₉	semidirect
226. #336	C₂²×C₁₃₉	semidirect
253. C₂²×C₈	D₄×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×#525×C₁₃₉	2
C₂×#408×C₁₃₉	2
C₂×#407×C₁₃₉	2
#1870×C₁₃₉	2
#1729×C₁₃₉	2
#20896	139

Subgroups — C139×#20896 #48015492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20896 #48015492