Subgroups — C₂×#2014×C₁₃₉ #48018012

Order 35584.

2726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	C₂²×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2014×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
6	C₂×#336×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₃₉	—	2	2	no	—
9	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
10	C₂²×SD₁₆×C₁₃₉	—	2	8	no	—
11	C₂²×SD₁₆×C₁₃₉	—	2	8	no	—
12	C₂²×SD₁₆×C₁₃₉	—	2	8	no	—
13	C₂²×SD₁₆×C₁₃₉	C₂²	1	8	yes	complemented
14	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#127×C₁₃₉	—	2	8	no	—
16	C₂×#127×C₁₃₉	—	2	2	no	—
17	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#102×C₁₃₉	—	2	8	no	—
21	C₂×#102×C₁₃₉	C₂²	1	8	yes	complemented
22	#391×C₁₃₉	—	2	2	no	—
23	#391×C₁₃₉	C₂²	1	4	yes	complemented
24	C₂×#95×C₁₃₉	—	2	2	no	—
25	#336×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂⁵×C₁₃₉	—	2	2	no	—
27	C₂²×Q₈×C₁₃₉	—	2	1	no	—
28	C₂²×Q₈×C₁₃₉	—	2	2	no	—
29	C₂²×Q₈×C₁₃₉	—	2	4	no	—
30	C₂²×Q₈×C₁₃₉	—	2	4	no	—
31	C₂²×Q₈×C₁₃₉	D₄	1	4	yes	complemented
32	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
33	C₂²×D₄×C₁₃₉	—	2	16	no	—
34	C₂²×D₄×C₁₃₉	—	2	4	no	—
35	C₂²×D₄×C₁₃₉	—	2	4	no	—
36	C₂²×D₄×C₁₃₉	—	2	4	no	—
37	C₂²×D₄×C₁₃₉	—	2	4	no	—
38	C₂²×D₄×C₁₃₉	—	2	2	no	—
39	C₂²×D₄×C₁₃₉	—	2	8	no	—
40	C₂²×D₄×C₁₃₉	—	2	4	no	—
41	C₂²×D₄×C₁₃₉	—	4	8	no	—
42	C₂²×D₄×C₁₃₉	—	4	8	no	—
43	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
44	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃₉	—	2	1	no	—
46	C₂³×C₄×C₁₃₉	—	2	1	no	—
47	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
48	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₃₉	—	2	64	no	—
50	C₂×SD₁₆×C₁₃₉	—	2	16	no	—
51	C₂×SD₁₆×C₁₃₉	—	2	16	no	—
52	C₂×SD₁₆×C₁₃₉	—	2	16	no	—
53	C₂²×C₈×C₁₃₉	—	2	4	no	—
54	C₂²×C₈×C₁₃₉	—	2	4	no	—
55	C₂²×C₈×C₁₃₉	D₄	1	8	yes	complemented
56	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
57	#127×C₁₃₉	—	2	16	no	—
58	#127×C₁₃₉	—	2	16	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃₉	—	2	4	no	—
63	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
64	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
65	#102×C₁₃₉	—	2	16	no	—
66	#95×C₁₃₉	—	2	8	no	—
67	C₂⁴×C₁₃₉	—	2	8	no	—
68	C₂⁴×C₁₃₉	—	2	4	no	—
69	C₂⁴×C₁₃₉	—	4	4	no	—
70	C₂⁴×C₁₃₉	—	4	4	no	—
71	C₂⁴×C₁₃₉	—	4	8	no	—
72	C₂⁴×C₁₃₉	—	4	8	no	—
73	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
74	C₂×Q₈×C₁₃₉	—	2	4	no	—
75	C₂×Q₈×C₁₃₉	—	2	2	no	—
76	C₂×Q₈×C₁₃₉	—	2	16	no	—
77	C₂×Q₈×C₁₃₉	—	2	4	no	—
78	C₂×Q₈×C₁₃₉	—	2	4	no	—
79	C₂×Q₈×C₁₃₉	—	4	2	no	—
80	C₂×Q₈×C₁₃₉	—	4	8	no	—
81	C₂×Q₈×C₁₃₉	—	4	2	no	—
82	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	complemented
83	C₂×D₄×C₁₃₉	—	2	32	no	—
84	C₂×D₄×C₁₃₉	—	2	16	no	—
85	C₂×D₄×C₁₃₉	—	2	8	no	—
86	C₂×D₄×C₁₃₉	—	2	16	no	—
87	C₂×D₄×C₁₃₉	—	2	4	no	—
88	C₂×D₄×C₁₃₉	—	2	4	no	—
89	C₂×D₄×C₁₃₉	—	2	4	no	—
90	C₂×D₄×C₁₃₉	—	2	4	no	—
91	C₂×D₄×C₁₃₉	—	2	4	no	—
92	C₂×D₄×C₁₃₉	—	4	16	no	—
93	C₂×D₄×C₁₃₉	—	4	64	no	—
94	C₂×D₄×C₁₃₉	—	4	8	no	—
95	C₂×D₄×C₁₃₉	—	4	8	no	—
96	C₂×D₄×C₁₃₉	—	4	4	no	—
97	C₂×D₄×C₁₃₉	—	4	4	no	—
98	C₂×D₄×C₁₃₉	—	4	16	no	—
99	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
100	C₂²×C₄×C₁₃₉	—	2	4	no	—
101	C₂²×C₄×C₁₃₉	—	2	4	no	—
102	C₂²×C₄×C₁₃₉	—	2	4	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	2	no	—
105	C₂²×C₄×C₁₃₉	—	4	2	no	—
106	C₂²×C₄×C₁₃₉	—	4	2	no	—
107	C₂²×C₄×C₁₃₉	—	4	2	no	—
108	C₂²×C₄×C₁₃₉	—	4	4	no	—
109	C₂²×C₄×C₁₃₉	SD₁₆	1	8	yes	complemented
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
116	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
117	SD₁₆×C₁₃₉	—	2	64	no	—
118	C₂×C₈×C₁₃₉	—	2	16	no	—
119	C₂×C₈×C₁₃₉	—	2	4	no	—
120	C₂×C₈×C₁₃₉	—	2	4	no	—
121	C₂×C₈×C₁₃₉	C₂×D₄	1	8	yes	complemented
122	C₄⋊C₄×C₁₃₉	—	2	4	no	—
123	C₄⋊C₄×C₁₃₉	—	4	2	no	—
124	C₄²×C₁₃₉	—	2	4	no	—
125	C₄²×C₁₃₉	—	2	4	no	—
126	C₂³×C₁₃₉	—	2	8	no	—
127	C₂³×C₁₃₉	—	4	4	no	—
128	C₂³×C₁₃₉	—	4	4	no	—
129	C₂³×C₁₃₉	—	4	8	no	—
130	C₂³×C₁₃₉	—	4	8	no	—
131	C₂³×C₁₃₉	—	4	16	no	—
132	C₂³×C₁₃₉	—	4	32	no	—
133	C₂³×C₁₃₉	—	8	16	no	—
134	C₂³×C₁₃₉	—	8	8	no	—
135	C₂³×C₁₃₉	—	8	8	no	—
136	C₂³×C₁₃₉	#120	1	2	yes	—
137	C₂³×C₁₃₉	#121	1	2	yes	—
138	C₂³×C₁₃₉	#127	1	2	yes	—
139	C₂³×C₁₃₉	C₂×SD₁₆	1	4	yes	—
140	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
141	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₁₃₉	—	2	8	no	—
143	Q₈×C₁₃₉	—	4	4	no	—
144	Q₈×C₁₃₉	—	4	8	no	—
145	D₄×C₁₃₉	—	2	8	no	—
146	D₄×C₁₃₉	—	2	8	no	—
147	D₄×C₁₃₉	—	4	64	no	—
148	D₄×C₁₃₉	—	4	4	no	—
149	D₄×C₁₃₉	—	4	4	no	—
150	D₄×C₁₃₉	—	4	16	no	—
151	C₂×C₄×C₁₃₉	—	2	4	no	—
152	C₂×C₄×C₁₃₉	—	2	4	no	—
153	C₂×C₄×C₁₃₉	—	2	16	no	—
154	C₂×C₄×C₁₃₉	—	2	4	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	—	4	2	no	—
157	C₂×C₄×C₁₃₉	—	4	8	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	—	4	4	no	—
160	C₂×C₄×C₁₃₉	—	8	4	no	—
161	C₂×C₄×C₁₃₉	#120	1	8	yes	—
162	C₂×C₄×C₁₃₉	#120	1	2	yes	—
163	C₂×C₄×C₁₃₉	#121	1	8	yes	—
164	C₂×C₄×C₁₃₉	#121	1	2	yes	—
165	C₂×C₄×C₁₃₉	#127	1	2	yes	—
166	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	8	yes	complemented
167	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
171	C₈×C₁₃₉	—	2	8	no	—
172	C₂²×C₁₃₉	—	4	8	no	—
173	C₂²×C₁₃₉	—	4	16	no	—
174	C₂²×C₁₃₉	—	8	4	no	—
175	C₂²×C₁₃₉	—	8	4	no	—
176	C₂²×C₁₃₉	—	8	8	no	—
177	C₂²×C₁₃₉	—	8	32	no	—
178	C₂²×C₁₃₉	#392	1	4	yes	—
179	C₂²×C₁₃₉	#450	1	8	yes	—
180	C₂²×C₁₃₉	#460	1	8	yes	—
181	C₂²×C₁₃₉	#492	1	4	yes	—
182	C₂²×C₁₃₉	#496	1	4	yes	—
183	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
184	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
185	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
186	C₂²×C₁₃₉	C₂²×SD₁₆	1	2	yes	—
187	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
188	C₄×C₁₃₉	—	2	8	no	—
189	C₄×C₁₃₉	—	4	4	no	—
190	C₄×C₁₃₉	—	8	2	no	—
191	C₄×C₁₃₉	#392	1	4	yes	—
192	C₄×C₁₃₉	C₂×#120	1	2	yes	—
193	C₄×C₁₃₉	C₂×#121	1	2	yes	—
194	C₂×C₁₃₉	—	8	8	no	—
195	C₂×C₁₃₉	#2014	1	8	yes	direct product factor
196	C₂×C₁₃₉	C₂×#392	1	1	yes	characteristic
197	C₂×C₁₃₉	C₂×#450	1	2	yes	—
198	C₂×C₁₃₉	C₂×#460	1	2	yes	—
199	C₂×C₁₃₉	C₂×#492	1	1	yes	characteristic
200	C₂×C₁₃₉	C₂×#496	1	1	yes	characteristic
201	C₂×#2014	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₁₃₉	C₂×#2014	1	1	yes	characteristic, direct product factor, Sylow
203	C₂³×SD₁₆	C₂×C₁₃₉	1	2	yes	complemented
204	C₂²×#127	C₂×C₁₃₉	1	1	yes	characteristic
205	C₂²×#102	C₂×C₁₃₉	1	2	yes	complemented
206	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	#2014	C₂×C₁₃₉	1	8	yes	direct product factor
208	C₂×#336	C₂×C₁₃₉	1	1	yes	characteristic, complemented
209	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
210	C₂³×D₄	—	2	2	no	—
211	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
212	C₂²×SD₁₆	—	2	8	no	—
213	C₂²×SD₁₆	—	2	8	no	—
214	C₂²×SD₁₆	—	2	8	no	—
215	C₂²×SD₁₆	C₂²×C₁₃₉	1	8	yes	complemented
216	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
217	C₂×#127	—	2	8	no	—
218	C₂×#127	—	2	2	no	—
219	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
221	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂×#102	—	2	8	no	—
223	C₂×#102	C₂²×C₁₃₉	1	8	yes	complemented
224	#391	—	2	2	no	—
225	#391	C₂²×C₁₃₉	1	4	yes	complemented
226	C₂×#95	—	2	2	no	—
227	#336	C₂²×C₁₃₉	1	4	yes	complemented
228	C₂⁵	—	2	2	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×Q₈	—	2	4	no	—
232	C₂²×Q₈	—	2	4	no	—
233	C₂²×Q₈	D₄×C₁₃₉	1	4	yes	complemented
234	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
235	C₂²×D₄	—	2	16	no	—
236	C₂²×D₄	—	2	4	no	—
237	C₂²×D₄	—	2	4	no	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	8	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	4	8	no	—
244	C₂²×D₄	—	4	8	no	—
245	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
246	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	—	2	1	no	—
249	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
250	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
251	C₂×SD₁₆	—	2	64	no	—
252	C₂×SD₁₆	—	2	16	no	—
253	C₂×SD₁₆	—	2	16	no	—
254	C₂×SD₁₆	—	2	16	no	—
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	—	2	4	no	—
257	C₂²×C₈	D₄×C₁₃₉	1	8	yes	complemented
258	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
259	#127	—	2	16	no	—
260	#127	—	2	16	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
267	#102	—	2	16	no	—
268	#95	—	2	8	no	—
269	C₂⁴	—	2	8	no	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	—	4	4	no	—
272	C₂⁴	—	4	4	no	—
273	C₂⁴	—	4	8	no	—
274	C₂⁴	—	4	8	no	—
275	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	16	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	4	8	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	complemented
285	C₂×D₄	—	2	32	no	—
286	C₂×D₄	—	2	16	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	4	64	no	—
295	C₂×D₄	—	4	16	no	—
296	C₂×D₄	—	4	8	no	—
297	C₂×D₄	—	4	8	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	—	4	16	no	—
301	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	SD₁₆×C₁₃₉	1	8	yes	complemented
312	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
317	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
319	SD₁₆	—	2	64	no	—
320	C₂×C₈	—	2	16	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	C₂×D₄×C₁₃₉	1	8	yes	complemented
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	4	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	4	32	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	8	no	—
333	C₂³	—	4	8	no	—
334	C₂³	—	4	16	no	—
335	C₂³	—	8	16	no	—
336	C₂³	—	8	8	no	—
337	C₂³	—	8	8	no	—
338	C₂³	#120×C₁₃₉	1	2	yes	—
339	C₂³	#121×C₁₃₉	1	2	yes	—
340	C₂³	#127×C₁₃₉	1	2	yes	—
341	C₂³	C₂×SD₁₆×C₁₃₉	1	4	yes	—
342	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	4	8	no	—
347	D₄	—	2	8	no	—
348	D₄	—	2	8	no	—
349	D₄	—	4	64	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	16	no	—
353	C₂×C₄	—	2	16	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	#120×C₁₃₉	1	8	yes	—
364	C₂×C₄	#120×C₁₃₉	1	2	yes	—
365	C₂×C₄	#121×C₁₃₉	1	8	yes	—
366	C₂×C₄	#121×C₁₃₉	1	2	yes	—
367	C₂×C₄	#127×C₁₃₉	1	2	yes	—
368	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	8	yes	complemented
369	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
371	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
372	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
373	C₈	—	2	8	no	—
374	C₂²	—	4	8	no	—
375	C₂²	—	4	16	no	—
376	C₂²	—	8	8	no	—
377	C₂²	—	8	32	no	—
378	C₂²	—	8	4	no	—
379	C₂²	—	8	4	no	—
380	C₂²	#392×C₁₃₉	1	4	yes	—
381	C₂²	#450×C₁₃₉	1	8	yes	—
382	C₂²	#460×C₁₃₉	1	8	yes	—
383	C₂²	#492×C₁₃₉	1	4	yes	—
384	C₂²	#496×C₁₃₉	1	4	yes	—
385	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
386	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
387	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
388	C₂²	C₂²×SD₁₆×C₁₃₉	1	2	yes	—
389	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
390	C₄	—	2	8	no	—
391	C₄	—	4	4	no	—
392	C₄	—	8	2	no	—
393	C₄	#392×C₁₃₉	1	4	yes	—
394	C₄	C₂×#120×C₁₃₉	1	2	yes	—
395	C₄	C₂×#121×C₁₃₉	1	2	yes	—
396	C₂	—	8	8	no	—
397	C₂	#2014×C₁₃₉	1	8	yes	direct product factor
398	C₂	C₂×#392×C₁₃₉	1	1	yes	characteristic
399	C₂	C₂×#450×C₁₃₉	1	2	yes	—
400	C₂	C₂×#460×C₁₃₉	1	2	yes	—
401	C₂	C₂×#492×C₁₃₉	1	1	yes	characteristic
402	C₂	C₂×#496×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×#127×C₁₃₉	C₂
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
1. C₂³×SD₁₆×C₁₃₉	C₂	semidirect
3. C₂²×#102×C₁₃₉	C₂	semidirect
4. C₂×#391×C₁₃₉	C₂	semidirect
5. #2014×C₁₃₉	C₂	direct (N × H)
6. C₂×#336×C₁₃₉	C₂	semidirect
13. C₂²×SD₁₆×C₁₃₉	C₂²	semidirect
21. C₂×#102×C₁₃₉	C₂²	semidirect
23. #391×C₁₃₉	C₂²	semidirect
25. #336×C₁₃₉	C₂²	semidirect
31. C₂²×Q₈×C₁₃₉	D₄	semidirect
55. C₂²×C₈×C₁₃₉	D₄	semidirect
82. C₂×Q₈×C₁₃₉	C₂×D₄	semidirect
109. C₂²×C₄×C₁₃₉	SD₁₆	semidirect
121. C₂×C₈×C₁₃₉	C₂×D₄	semidirect
166. C₂×C₄×C₁₃₉	C₂×SD₁₆	semidirect
195. C₂×C₁₃₉	#2014	direct (N × H)
201. C₂×#2014	C₁₃₉	direct (N × H)
202. C₁₃₉	C₂×#2014	direct (N × H)
203. C₂³×SD₁₆	C₂×C₁₃₉	semidirect
205. C₂²×#102	C₂×C₁₃₉	semidirect
206. C₂×#391	C₂×C₁₃₉	semidirect
207. #2014	C₂×C₁₃₉	direct (N × H)
208. C₂×#336	C₂×C₁₃₉	semidirect
215. C₂²×SD₁₆	C₂²×C₁₃₉	semidirect
223. C₂×#102	C₂²×C₁₃₉	semidirect
225. #391	C₂²×C₁₃₉	semidirect
227. #336	C₂²×C₁₃₉	semidirect
233. C₂²×Q₈	D₄×C₁₃₉	semidirect
257. C₂²×C₈	D₄×C₁₃₉	semidirect
284. C₂×Q₈	C₂×D₄×C₁₃₉	semidirect
311. C₂²×C₄	SD₁₆×C₁₃₉	semidirect
323. C₂×C₈	C₂×D₄×C₁₃₉	semidirect
368. C₂×C₄	C₂×SD₁₆×C₁₃₉	semidirect
397. C₂	#2014×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
C₂³×SD₁₆×C₁₃₉	2
C₂²×#127×C₁₃₉	2
C₂²×#102×C₁₃₉	2
C₂×#391×C₁₃₉	2
#2014×C₁₃₉	2
C₂×#336×C₁₃₉	2
C₂×#2014	139

Subgroups — C2×#2014×C139 #48018012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2014×C₁₃₉ #48018012