Subgroups — C₁₃₉×#10776 #48005372

Order 35584.

1394 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#418×C₁₃₉	C₂	1	2	yes	maximal
3	#1742×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1740×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1733×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
8	#518×C₁₃₉	—	2	4	no	—
9	#518×C₁₃₉	—	2	4	no	—
10	C₂×C₄×D₄×C₁₃₉	—	2	2	no	—
11	C₂×C₄×D₄×C₁₃₉	C₄	1	4	yes	complemented
12	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
16	#418×C₁₃₉	—	2	4	no	—
17	#418×C₁₃₉	C₄	1	8	yes	complemented
18	C₂×#102×C₁₃₉	—	2	4	no	—
19	#343×C₁₃₉	—	2	2	no	—
20	#342×C₁₃₉	—	2	2	no	—
21	#339×C₁₃₉	—	2	4	no	—
22	C₂⁵×C₁₃₉	—	2	1	no	—
23	C₂²×D₄×C₁₃₉	—	2	1	no	—
24	C₂²×D₄×C₁₃₉	—	2	2	no	—
25	C₂²×D₄×C₁₃₉	—	2	1	no	—
26	C₂²×D₄×C₁₃₉	—	2	1	no	—
27	C₂²×D₄×C₁₃₉	—	2	2	no	—
28	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
29	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₃₉	D₄	1	4	yes	—
31	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
32	C₂²×D₄×C₁₃₉	Q₈	1	2	yes	—
33	C₂³×C₄×C₁₃₉	—	2	4	no	—
34	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₁₃₉	—	2	2	no	—
36	C₂×M₁₆×C₁₃₉	—	2	2	no	—
37	C₂×M₁₆×C₁₃₉	—	2	2	no	—
38	C₂×M₁₆×C₁₃₉	—	2	2	no	—
39	C₂×M₁₆×C₁₃₉	—	2	2	no	—
40	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	complemented
41	C₂²×C₈×C₁₃₉	—	2	2	no	—
42	C₄×D₄×C₁₃₉	—	2	16	no	—
43	C₄×D₄×C₁₃₉	—	2	8	no	—
44	C₄×D₄×C₁₃₉	—	2	8	no	—
45	#117×C₁₃₉	—	2	2	no	—
46	#117×C₁₃₉	—	2	2	no	—
47	#117×C₁₃₉	—	2	2	no	—
48	#117×C₁₃₉	—	2	2	no	—
49	#117×C₁₃₉	—	2	2	no	—
50	#117×C₁₃₉	—	2	2	no	—
51	#117×C₁₃₉	C₂×C₄	1	4	yes	complemented
52	#117×C₁₃₉	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
57	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃₉	—	2	1	no	—
62	C₂×C₄²×C₁₃₉	—	2	2	no	—
63	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
64	#102×C₁₃₉	—	2	16	no	—
65	C₂⁴×C₁₃₉	—	2	2	no	—
66	C₂⁴×C₁₃₉	—	2	4	no	—
67	C₂⁴×C₁₃₉	—	2	4	no	—
68	C₂⁴×C₁₃₉	—	2	2	no	—
69	C₂⁴×C₁₃₉	—	2	2	no	—
70	C₂⁴×C₁₃₉	—	8	4	no	—
71	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
72	C₂×D₄×C₁₃₉	—	2	2	no	—
73	C₂×D₄×C₁₃₉	—	2	2	no	—
74	C₂×D₄×C₁₃₉	—	2	2	no	—
75	C₂×D₄×C₁₃₉	—	2	4	no	—
76	C₂×D₄×C₁₃₉	—	2	4	no	—
77	C₂×D₄×C₁₃₉	—	2	4	no	—
78	C₂×D₄×C₁₃₉	—	2	4	no	—
79	C₂×D₄×C₁₃₉	—	2	4	no	—
80	C₂×D₄×C₁₃₉	—	2	2	no	—
81	C₂×D₄×C₁₃₉	—	2	4	no	—
82	C₂×D₄×C₁₃₉	—	2	2	no	—
83	C₂×D₄×C₁₃₉	—	2	4	no	—
84	C₂×D₄×C₁₃₉	—	2	4	no	—
85	C₂×D₄×C₁₃₉	C₄²	1	4	yes	—
86	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
87	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
88	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
89	C₂×D₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	16	no	—
92	C₂²×C₄×C₁₃₉	—	4	2	no	—
93	C₂²×C₄×C₁₃₉	—	8	8	no	—
94	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
105	M₁₆×C₁₃₉	—	2	4	no	—
106	M₁₆×C₁₃₉	—	2	4	no	—
107	M₁₆×C₁₃₉	—	4	2	no	—
108	M₁₆×C₁₃₉	—	4	2	no	—
109	C₂×C₈×C₁₃₉	—	2	4	no	—
110	C₂×C₈×C₁₃₉	—	4	2	no	—
111	C₂×C₈×C₁₃₉	—	4	2	no	—
112	C₄⋊C₄×C₁₃₉	—	2	2	no	—
113	C₄⋊C₄×C₁₃₉	—	2	4	no	—
114	C₄⋊C₄×C₁₃₉	—	2	4	no	—
115	C₄⋊C₄×C₁₃₉	—	4	2	no	—
116	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
117	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
118	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
122	C₄²×C₁₃₉	—	2	2	no	—
123	C₄²×C₁₃₉	—	2	2	no	—
124	C₄²×C₁₃₉	—	2	4	no	—
125	C₄²×C₁₃₉	—	2	4	no	—
126	C₄²×C₁₃₉	—	4	2	no	—
127	C₂³×C₁₃₉	—	2	4	no	—
128	C₂³×C₁₃₉	—	2	4	no	—
129	C₂³×C₁₃₉	—	2	4	no	—
130	C₂³×C₁₃₉	—	2	8	no	—
131	C₂³×C₁₃₉	—	2	8	no	—
132	C₂³×C₁₃₉	—	4	2	no	—
133	C₂³×C₁₃₉	—	4	8	no	—
134	C₂³×C₁₃₉	—	8	8	no	—
135	C₂³×C₁₃₉	—	8	8	no	—
136	C₂³×C₁₃₉	—	8	4	no	—
137	C₂³×C₁₃₉	—	8	4	no	—
138	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
140	C₂³×C₁₃₉	#120	1	2	yes	—
141	C₂³×C₁₃₉	#121	1	1	yes	characteristic
142	C₂³×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
143	D₄×C₁₃₉	—	2	4	no	—
144	D₄×C₁₃₉	—	2	4	no	—
145	D₄×C₁₃₉	—	2	4	no	—
146	D₄×C₁₃₉	—	2	8	no	—
147	D₄×C₁₃₉	—	2	8	no	—
148	D₄×C₁₃₉	#95	1	8	yes	—
149	C₂×C₄×C₁₃₉	—	2	4	no	—
150	C₂×C₄×C₁₃₉	—	2	4	no	—
151	C₂×C₄×C₁₃₉	—	4	4	no	—
152	C₂×C₄×C₁₃₉	—	4	4	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	—	8	16	no	—
155	C₂×C₄×C₁₃₉	—	8	4	no	—
156	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₃₉	#117	1	1	yes	characteristic
163	C₂×C₄×C₁₃₉	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₁₃₉	#120	1	2	yes	—
168	C₂×C₄×C₁₃₉	#121	1	2	yes	—
169	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃₉	#123	1	2	yes	—
173	C₂×C₄×C₁₃₉	#123	1	2	yes	—
174	C₈×C₁₃₉	—	4	4	no	—
175	C₂²×C₁₃₉	—	2	2	no	—
176	C₂²×C₁₃₉	—	2	4	no	—
177	C₂²×C₁₃₉	—	2	8	no	—
178	C₂²×C₁₃₉	—	4	2	no	—
179	C₂²×C₁₃₉	—	4	1	no	—
180	C₂²×C₁₃₉	—	4	1	no	—
181	C₂²×C₁₃₉	—	4	8	no	—
182	C₂²×C₁₃₉	—	4	8	no	—
183	C₂²×C₁₃₉	—	4	8	no	—
184	C₂²×C₁₃₉	—	8	8	no	—
185	C₂²×C₁₃₉	—	8	8	no	—
186	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₁₃₉	#379	1	1	yes	characteristic
188	C₂²×C₁₃₉	#380	1	1	yes	characteristic
189	C₂²×C₁₃₉	#385	1	2	yes	—
190	C₂²×C₁₃₉	#386	1	2	yes	—
191	C₄×C₁₃₉	—	4	4	no	—
192	C₄×C₁₃₉	—	4	4	no	—
193	C₄×C₁₃₉	—	8	4	no	—
194	C₄×C₁₃₉	C₂×#95	1	1	yes	characteristic
195	C₄×C₁₃₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
196	C₄×C₁₃₉	#380	1	1	yes	characteristic
197	C₄×C₁₃₉	#381	1	1	yes	characteristic
198	C₄×C₁₃₉	#385	1	2	yes	—
199	C₄×C₁₃₉	#386	1	2	yes	—
200	C₂×C₁₃₉	—	2	2	no	—
201	C₂×C₁₃₉	—	2	1	no	—
202	C₂×C₁₃₉	—	2	1	no	—
203	C₂×C₁₃₉	—	2	2	no	—
204	C₂×C₁₃₉	—	4	8	no	—
205	C₂×C₁₃₉	C₂²⋊#95	1	1	yes	characteristic
206	C₂×C₁₃₉	#1795	1	2	yes	—
207	#10776	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₉	#10776	1	1	yes	characteristic, direct product factor, Sylow
209	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic
210	C₂×#418	C₂×C₁₃₉	1	2	yes	—
211	#1742	C₂×C₁₃₉	1	1	yes	characteristic, complemented
212	#1740	C₂×C₁₃₉	1	1	yes	characteristic, complemented
213	#1733	C₂×C₁₃₉	1	2	yes	complemented
214	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
216	#518	—	2	4	no	—
217	#518	—	2	4	no	—
218	C₂×C₄×D₄	—	2	2	no	—
219	C₂×C₄×D₄	C₄×C₁₃₉	1	4	yes	complemented
220	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
221	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
223	C₂²×C₂²⋊C₄	—	2	2	no	—
224	#418	—	2	4	no	—
225	#418	C₄×C₁₃₉	1	8	yes	complemented
226	C₂×#102	—	2	4	no	—
227	#343	—	2	2	no	—
228	#342	—	2	2	no	—
229	#339	—	2	4	no	—
230	C₂⁵	—	2	1	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
237	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
238	C₂²×D₄	D₄×C₁₃₉	1	4	yes	—
239	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
240	C₂²×D₄	Q₈×C₁₃₉	1	2	yes	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	complemented
249	C₂²×C₈	—	2	2	no	—
250	C₄×D₄	—	2	16	no	—
251	C₄×D₄	—	2	8	no	—
252	C₄×D₄	—	2	8	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	—	2	2	no	—
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#117	C₂×C₄×C₁₃₉	1	4	yes	complemented
260	#117	D₄×C₁₃₉	1	4	yes	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
263	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	16	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
272	#102	—	2	16	no	—
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	2	no	—
277	C₂⁴	—	2	2	no	—
278	C₂⁴	—	8	4	no	—
279	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	C₄²×C₁₃₉	1	4	yes	—
294	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
295	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
296	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
297	C₂×D₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	16	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	8	8	no	—
302	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
310	C₂²×C₄	#41×C₁₃₉	1	1	yes	characteristic
311	C₂²×C₄	#41×C₁₃₉	1	1	yes	characteristic
312	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	4	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	4	2	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
325	C₂²⋊C₄	—	2	16	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	4	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	8	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	8	8	no	—
343	C₂³	—	8	8	no	—
344	C₂³	—	8	4	no	—
345	C₂³	—	8	4	no	—
346	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
347	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
348	C₂³	#120×C₁₃₉	1	2	yes	—
349	C₂³	#121×C₁₃₉	1	1	yes	characteristic
350	C₂³	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
351	D₄	—	2	4	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	4	no	—
354	D₄	—	2	8	no	—
355	D₄	—	2	8	no	—
356	D₄	#95×C₁₃₉	1	8	yes	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	8	16	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
370	C₂×C₄	#117×C₁₃₉	1	1	yes	characteristic
371	C₂×C₄	#117×C₁₃₉	1	1	yes	characteristic
372	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
373	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
374	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
375	C₂×C₄	#120×C₁₃₉	1	2	yes	—
376	C₂×C₄	#121×C₁₃₉	1	2	yes	—
377	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
378	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
379	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
380	C₂×C₄	#123×C₁₃₉	1	2	yes	—
381	C₂×C₄	#123×C₁₃₉	1	2	yes	—
382	C₈	—	4	4	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	4	8	no	—
392	C₂²	—	8	8	no	—
393	C₂²	—	8	8	no	—
394	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
395	C₂²	#379×C₁₃₉	1	1	yes	characteristic
396	C₂²	#380×C₁₃₉	1	1	yes	characteristic
397	C₂²	#385×C₁₃₉	1	2	yes	—
398	C₂²	#386×C₁₃₉	1	2	yes	—
399	C₄	—	4	4	no	—
400	C₄	—	4	4	no	—
401	C₄	—	8	4	no	—
402	C₄	C₂×#95×C₁₃₉	1	1	yes	characteristic
403	C₄	C₄×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
404	C₄	#380×C₁₃₉	1	1	yes	characteristic
405	C₄	#381×C₁₃₉	1	1	yes	characteristic
406	C₄	#385×C₁₃₉	1	2	yes	—
407	C₄	#386×C₁₃₉	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	2	no	—
412	C₂	—	4	8	no	—
413	C₂	C₂²⋊#95×C₁₃₉	1	1	yes	characteristic
414	C₂	#1795×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₉	#379
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1742×C₁₃₉	C₂	semidirect
4. #1740×C₁₃₉	C₂	semidirect
5. #1733×C₁₃₉	C₂	semidirect
11. C₂×C₄×D₄×C₁₃₉	C₄	semidirect
17. #418×C₁₃₉	C₄	semidirect
40. C₂×M₁₆×C₁₃₉	C₂×C₄	semidirect
51. #117×C₁₃₉	C₂×C₄	semidirect
207. #10776	C₁₃₉	direct (N × H)
208. C₁₃₉	#10776	direct (N × H)
211. #1742	C₂×C₁₃₉	semidirect
212. #1740	C₂×C₁₃₉	semidirect
213. #1733	C₂×C₁₃₉	semidirect
219. C₂×C₄×D₄	C₄×C₁₃₉	semidirect
225. #418	C₄×C₁₃₉	semidirect
248. C₂×M₁₆	C₂×C₄×C₁₃₉	semidirect
259. #117	C₂×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×#518×C₁₃₉	2
C₂×#418×C₁₃₉	2
#1742×C₁₃₉	2
#1740×C₁₃₉	2
#1733×C₁₃₉	2
#10776	139

Subgroups — C139×#10776 #48005372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10776 #48005372