Subgroups — C₂×#2071×C₁₃₉ #48018219

Order 35584.

1366 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#102×C₁₃₉	C₂	1	2	yes	maximal
2	C₂×#390×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2071×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂×#336×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
10	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
11	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
14	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
15	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#102×C₁₃₉	—	2	8	no	—
17	C₂×#102×C₁₃₉	C₂²	1	8	yes	—
18	#390×C₁₃₉	—	2	2	no	—
19	#390×C₁₃₉	C₂²	1	4	yes	—
20	#384×C₁₃₉	—	2	2	no	—
21	#384×C₁₃₉	C₂²	1	4	yes	complemented
22	#340×C₁₃₉	C₂²	1	8	yes	complemented
23	#336×C₁₃₉	C₂²	1	4	yes	complemented
24	C₂⁵×C₁₃₉	—	2	1	no	—
25	C₂²×D₄×C₁₃₉	—	2	1	no	—
26	C₂²×D₄×C₁₃₉	—	2	4	no	—
27	C₂²×D₄×C₁₃₉	—	2	4	no	—
28	C₂²×D₄×C₁₃₉	—	2	2	no	—
29	C₂²×D₄×C₁₃₉	D₄	1	4	yes	—
30	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₃₉	—	2	1	no	—
32	C₂³×C₄×C₁₃₉	—	2	2	no	—
33	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃₉	—	2	4	no	—
37	C₂²×C₈×C₁₃₉	—	2	4	no	—
38	C₂²×C₈×C₁₃₉	—	2	4	no	—
39	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
54	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
55	C₂×C₄²×C₁₃₉	—	2	4	no	—
56	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
57	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
58	#102×C₁₃₉	—	2	16	no	—
59	C₂⁴×C₁₃₉	—	2	4	no	—
60	C₂⁴×C₁₃₉	—	2	2	no	—
61	C₂⁴×C₁₃₉	—	4	2	no	—
62	C₂⁴×C₁₃₉	—	4	2	no	—
63	C₂⁴×C₁₃₉	—	4	2	no	—
64	C₂⁴×C₁₃₉	—	4	2	no	—
65	C₂⁴×C₁₃₉	—	4	2	no	—
66	C₂⁴×C₁₃₉	—	4	2	no	—
67	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
68	C₂×D₄×C₁₃₉	—	2	4	no	—
69	C₂×D₄×C₁₃₉	—	2	16	no	—
70	C₂×D₄×C₁₃₉	—	2	4	no	—
71	C₂×D₄×C₁₃₉	—	2	4	no	—
72	C₂×D₄×C₁₃₉	—	2	2	no	—
73	C₂×D₄×C₁₃₉	—	4	2	no	—
74	C₂×D₄×C₁₃₉	—	4	2	no	—
75	C₂×D₄×C₁₃₉	—	4	8	no	—
76	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	2	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	4	no	—
83	C₂²×C₄×C₁₃₉	—	4	4	no	—
84	C₂²×C₄×C₁₃₉	—	4	2	no	—
85	C₂²×C₄×C₁₃₉	—	4	2	no	—
86	C₂²×C₄×C₁₃₉	—	4	4	no	—
87	C₂²×C₄×C₁₃₉	—	4	2	no	—
88	C₂²×C₄×C₁₃₉	—	4	4	no	—
89	C₂²×C₄×C₁₃₉	D₈	1	4	yes	—
90	C₂²×C₄×C₁₃₉	SD₁₆	1	4	yes	—
91	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
96	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
97	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
98	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	4	no	—
104	C₄⋊C₄×C₁₃₉	—	2	4	no	—
105	C₄⋊C₄×C₁₃₉	—	2	4	no	—
106	C₄⋊C₄×C₁₃₉	—	4	8	no	—
107	C₄⋊C₄×C₁₃₉	—	4	4	no	—
108	C₄⋊C₄×C₁₃₉	—	4	2	no	—
109	C₄⋊C₄×C₁₃₉	—	4	8	no	—
110	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
111	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
112	C₄²×C₁₃₉	—	2	4	no	—
113	C₄²×C₁₃₉	—	2	4	no	—
114	C₂³×C₁₃₉	—	2	4	no	—
115	C₂³×C₁₃₉	—	4	2	no	—
116	C₂³×C₁₃₉	—	4	2	no	—
117	C₂³×C₁₃₉	—	4	2	no	—
118	C₂³×C₁₃₉	—	4	2	no	—
119	C₂³×C₁₃₉	—	4	2	no	—
120	C₂³×C₁₃₉	—	4	2	no	—
121	C₂³×C₁₃₉	—	4	8	no	—
122	C₂³×C₁₃₉	—	4	8	no	—
123	C₂³×C₁₃₉	—	4	8	no	—
124	C₂³×C₁₃₉	—	8	4	no	—
125	C₂³×C₁₃₉	—	8	4	no	—
126	C₂³×C₁₃₉	—	8	4	no	—
127	C₂³×C₁₃₉	—	8	4	no	—
128	C₂³×C₁₃₉	#121	1	2	yes	—
129	C₂³×C₁₃₉	#123	1	2	yes	—
130	C₂³×C₁₃₉	#124	1	2	yes	—
131	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
132	C₂³×C₁₃₉	C₂×SD₁₆	1	2	yes	—
133	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
134	C₂³×C₁₃₉	#137	1	2	yes	—
135	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₁₃₉	—	2	8	no	—
137	D₄×C₁₃₉	—	4	4	no	—
138	D₄×C₁₃₉	—	4	8	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	2	2	no	—
142	C₂×C₄×C₁₃₉	—	2	2	no	—
143	C₂×C₄×C₁₃₉	—	2	8	no	—
144	C₂×C₄×C₁₃₉	—	2	8	no	—
145	C₂×C₄×C₁₃₉	—	4	4	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	2	no	—
148	C₂×C₄×C₁₃₉	—	4	4	no	—
149	C₂×C₄×C₁₃₉	—	4	2	no	—
150	C₂×C₄×C₁₃₉	—	4	4	no	—
151	C₂×C₄×C₁₃₉	—	8	8	no	—
152	C₂×C₄×C₁₃₉	—	8	4	no	—
153	C₂×C₄×C₁₃₉	#121	1	2	yes	—
154	C₂×C₄×C₁₃₉	#123	1	8	yes	—
155	C₂×C₄×C₁₃₉	#123	1	2	yes	—
156	C₂×C₄×C₁₃₉	#124	1	2	yes	—
157	C₂×C₄×C₁₃₉	#126	1	8	yes	—
158	C₂×C₄×C₁₃₉	C₂×D₈	1	4	yes	—
159	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	4	yes	—
160	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
162	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
163	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
164	C₈×C₁₃₉	—	4	4	no	—
165	C₂²×C₁₃₉	—	4	4	no	—
166	C₂²×C₁₃₉	—	4	4	no	—
167	C₂²×C₁₃₉	—	4	4	no	—
168	C₂²×C₁₃₉	—	8	2	no	—
169	C₂²×C₁₃₉	—	8	2	no	—
170	C₂²×C₁₃₉	—	8	16	no	—
171	C₂²×C₁₃₉	—	8	2	no	—
172	C₂²×C₁₃₉	—	8	2	no	—
173	C₂²×C₁₃₉	#397	1	4	yes	—
174	C₂²×C₁₃₉	#459	1	4	yes	—
175	C₂²×C₁₃₉	#461	1	4	yes	—
176	C₂²×C₁₃₉	#480	1	4	yes	—
177	C₂²×C₁₃₉	#481	1	4	yes	—
178	C₂²×C₁₃₉	#486	1	4	yes	—
179	C₂²×C₁₃₉	#489	1	4	yes	—
180	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
181	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
182	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
183	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
184	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
185	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
187	C₄×C₁₃₉	—	2	4	no	—
188	C₄×C₁₃₉	—	2	4	no	—
189	C₄×C₁₃₉	—	8	2	no	—
190	C₄×C₁₃₉	—	8	4	no	—
191	C₄×C₁₃₉	#397	1	4	yes	—
192	C₄×C₁₃₉	C₂×#123	1	2	yes	—
193	C₄×C₁₃₉	C₂×#126	1	2	yes	—
194	C₂×C₁₃₉	—	8	4	no	—
195	C₂×C₁₃₉	#2071	1	8	yes	direct product factor
196	C₂×C₁₃₉	C₂×#397	1	1	yes	characteristic
197	C₂×C₁₃₉	C₂×#459	1	1	yes	characteristic
198	C₂×C₁₃₉	C₂×#461	1	1	yes	characteristic
199	C₂×C₁₃₉	C₂×#480	1	1	yes	characteristic
200	C₂×C₁₃₉	C₂×#481	1	1	yes	characteristic
201	C₂×C₁₃₉	C₂×#486	1	1	yes	characteristic
202	C₂×C₁₃₉	C₂×#489	1	1	yes	characteristic
203	C₂×#2071	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₉	C₂×#2071	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×#102	C₂×C₁₃₉	1	2	yes	—
206	C₂×#390	C₂×C₁₃₉	1	1	yes	characteristic
207	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic, complemented
208	#2071	C₂×C₁₃₉	1	8	yes	direct product factor
209	C₂×#340	C₂×C₁₃₉	1	2	yes	complemented
210	C₂×#336	C₂×C₁₃₉	1	1	yes	characteristic, complemented
211	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
212	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
213	C₂²×C₄⋊C₄	—	2	1	no	—
214	C₂²×C₄⋊C₄	—	2	1	no	—
215	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄	—	2	1	no	—
218	C₂²×C₂²⋊C₄	—	2	1	no	—
219	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
220	C₂×#102	—	2	8	no	—
221	C₂×#102	C₂²×C₁₃₉	1	8	yes	—
222	#390	—	2	2	no	—
223	#390	C₂²×C₁₃₉	1	4	yes	—
224	#384	—	2	2	no	—
225	#384	C₂²×C₁₃₉	1	4	yes	complemented
226	#340	C₂²×C₁₃₉	1	8	yes	complemented
227	#336	C₂²×C₁₃₉	1	4	yes	complemented
228	C₂⁵	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	4	no	—
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	D₄×C₁₃₉	1	4	yes	—
234	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
240	C₂²×C₈	—	2	4	no	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	—	2	4	no	—
243	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	4	4	no	—
252	C₂×C₄⋊C₄	—	4	4	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
255	C₂×C₂²⋊C₄	—	2	4	no	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	4	4	no	—
258	C₂×C₂²⋊C₄	—	4	4	no	—
259	C₂×C₄²	—	2	4	no	—
260	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
262	#102	—	2	16	no	—
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	2	2	no	—
265	C₂⁴	—	4	2	no	—
266	C₂⁴	—	4	2	no	—
267	C₂⁴	—	4	2	no	—
268	C₂⁴	—	4	2	no	—
269	C₂⁴	—	4	2	no	—
270	C₂⁴	—	4	2	no	—
271	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	16	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	8	no	—
280	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	D₈×C₁₃₉	1	4	yes	—
294	C₂²×C₄	SD₁₆×C₁₃₉	1	4	yes	—
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	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
299	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
300	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
301	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
302	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	4	8	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	8	no	—
314	C₂²⋊C₄	—	4	8	no	—
315	C₂²⋊C₄	—	4	8	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	4	8	no	—
320	C₂³	—	4	8	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	—	8	4	no	—
331	C₂³	—	8	4	no	—
332	C₂³	#121×C₁₃₉	1	2	yes	—
333	C₂³	#123×C₁₃₉	1	2	yes	—
334	C₂³	#124×C₁₃₉	1	2	yes	—
335	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
336	C₂³	C₂×SD₁₆×C₁₃₉	1	2	yes	—
337	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
338	C₂³	#137×C₁₃₉	1	2	yes	—
339	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
340	D₄	—	2	8	no	—
341	D₄	—	4	8	no	—
342	D₄	—	4	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	8	8	no	—
356	C₂×C₄	—	8	4	no	—
357	C₂×C₄	#121×C₁₃₉	1	2	yes	—
358	C₂×C₄	#123×C₁₃₉	1	2	yes	—
359	C₂×C₄	#123×C₁₃₉	1	8	yes	—
360	C₂×C₄	#124×C₁₃₉	1	2	yes	—
361	C₂×C₄	#126×C₁₃₉	1	8	yes	—
362	C₂×C₄	C₂×D₈×C₁₃₉	1	4	yes	—
363	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	4	yes	—
364	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
366	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
367	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	16	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	#397×C₁₃₉	1	4	yes	—
378	C₂²	#459×C₁₃₉	1	4	yes	—
379	C₂²	#461×C₁₃₉	1	4	yes	—
380	C₂²	#480×C₁₃₉	1	4	yes	—
381	C₂²	#481×C₁₃₉	1	4	yes	—
382	C₂²	#486×C₁₃₉	1	4	yes	—
383	C₂²	#489×C₁₃₉	1	4	yes	—
384	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
385	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
386	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
387	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
388	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
389	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
390	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	8	4	no	—
394	C₄	—	8	2	no	—
395	C₄	#397×C₁₃₉	1	4	yes	—
396	C₄	C₂×#123×C₁₃₉	1	2	yes	—
397	C₄	C₂×#126×C₁₃₉	1	2	yes	—
398	C₂	—	8	4	no	—
399	C₂	#2071×C₁₃₉	1	8	yes	direct product factor
400	C₂	C₂×#397×C₁₃₉	1	1	yes	characteristic
401	C₂	C₂×#459×C₁₃₉	1	1	yes	characteristic
402	C₂	C₂×#461×C₁₃₉	1	1	yes	characteristic
403	C₂	C₂×#480×C₁₃₉	1	1	yes	characteristic
404	C₂	C₂×#481×C₁₃₉	1	1	yes	characteristic
405	C₂	C₂×#486×C₁₃₉	1	1	yes	characteristic
406	C₂	C₂×#489×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#384×C₁₃₉	C₂	semidirect
4. #2071×C₁₃₉	C₂	direct (N × H)
5. C₂×#340×C₁₃₉	C₂	semidirect
6. C₂×#336×C₁₃₉	C₂	semidirect
21. #384×C₁₃₉	C₂²	semidirect
22. #340×C₁₃₉	C₂²	semidirect
23. #336×C₁₃₉	C₂²	semidirect
195. C₂×C₁₃₉	#2071	direct (N × H)
203. C₂×#2071	C₁₃₉	direct (N × H)
204. C₁₃₉	C₂×#2071	direct (N × H)
207. C₂×#384	C₂×C₁₃₉	semidirect
208. #2071	C₂×C₁₃₉	direct (N × H)
209. C₂×#340	C₂×C₁₃₉	semidirect
210. C₂×#336	C₂×C₁₃₉	semidirect
225. #384	C₂²×C₁₃₉	semidirect
226. #340	C₂²×C₁₃₉	semidirect
227. #336	C₂²×C₁₃₉	semidirect
399. C₂	#2071×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#102×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₂×#384×C₁₃₉	2
#2071×C₁₃₉	2
C₂×#340×C₁₃₉	2
C₂×#336×C₁₃₉	2
C₂×#2071	139

Subgroups — C2×#2071×C139 #48018219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2071×C₁₃₉ #48018219