Subgroups — C₁₃₉×#8886 #48003482

Order 35584.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1948×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#1844×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1802×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#1296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1279×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
9	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
11	C₂×#106×C₁₃₉	—	2	2	no	—
12	C₂×#106×C₁₃₉	—	2	1	no	—
13	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#102×C₁₃₉	—	2	1	no	—
16	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	#389×C₁₃₉	—	2	1	no	—
18	#385×C₁₃₉	—	2	2	no	—
19	#384×C₁₃₉	C₂²	1	1	yes	characteristic
20	#384×C₁₃₉	C₂²	1	1	yes	characteristic
21	#380×C₁₃₉	—	2	1	no	—
22	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	#340×C₁₃₉	—	2	1	no	—
24	#340×C₁₃₉	—	2	1	no	—
25	D₄⋊C₈×C₁₃₉	C₄	1	4	yes	complemented
26	C₂²×D₄×C₁₃₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃₉	—	2	1	no	—
28	C₂³×C₄×C₁₃₉	—	2	2	no	—
29	C₂²×C₈×C₁₃₉	—	2	1	no	—
30	C₂²×C₈×C₁₃₉	—	2	1	no	—
31	C₂²×C₈×C₁₃₉	—	2	1	no	—
32	C₄×D₄×C₁₃₉	—	2	1	no	—
33	C₄×D₄×C₁₃₉	—	2	1	no	—
34	C₄×D₄×C₁₃₉	—	4	2	no	—
35	C₄×D₄×C₁₃₉	—	4	2	no	—
36	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
37	C₄×D₄×C₁₃₉	Q₈	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
52	C₂×C₄²×C₁₃₉	—	2	1	no	—
53	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
54	#106×C₁₃₉	—	4	2	no	—
55	#106×C₁₃₉	—	4	4	no	—
56	C₄⋊C₈×C₁₃₉	—	2	1	no	—
57	C₄⋊C₈×C₁₃₉	—	2	1	no	—
58	C₄⋊C₈×C₁₃₉	—	2	1	no	—
59	C₄⋊C₈×C₁₃₉	C₂×C₄	1	2	yes	complemented
60	#102×C₁₃₉	—	4	2	no	—
61	C₄×C₈×C₁₃₉	—	2	1	no	—
62	C₄×C₈×C₁₃₉	C₂×C₄	1	2	yes	complemented
63	#95×C₁₃₉	—	2	2	no	—
64	#95×C₁₃₉	—	2	1	no	—
65	C₂⁴×C₁₃₉	—	2	1	no	—
66	C₂×D₄×C₁₃₉	—	2	1	no	—
67	C₂×D₄×C₁₃₉	—	2	1	no	—
68	C₂×D₄×C₁₃₉	—	2	1	no	—
69	C₂×D₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
70	C₂×D₄×C₁₃₉	SD₁₆	1	2	yes	—
71	C₂×D₄×C₁₃₉	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₁₃₉	—	2	1	no	—
73	C₂²×C₄×C₁₃₉	—	2	1	no	—
74	C₂²×C₄×C₁₃₉	—	2	2	no	—
75	C₂²×C₄×C₁₃₉	—	2	2	no	—
76	C₂²×C₄×C₁₃₉	—	2	1	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	4	4	no	—
79	C₂²×C₄×C₁₃₉	—	4	1	no	—
80	C₂²×C₄×C₁₃₉	—	4	1	no	—
81	C₂²×C₄×C₁₃₉	—	4	1	no	—
82	C₂²×C₄×C₁₃₉	—	4	1	no	—
83	C₂²×C₄×C₁₃₉	—	4	4	no	—
84	C₂²×C₄×C₁₃₉	—	4	1	no	—
85	C₂²×C₄×C₁₃₉	—	8	2	no	—
86	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₁₃₉	—	2	2	no	—
90	C₂×C₈×C₁₃₉	—	2	2	no	—
91	C₂×C₈×C₁₃₉	—	2	2	no	—
92	C₂×C₈×C₁₃₉	—	2	2	no	—
93	C₂×C₈×C₁₃₉	—	4	1	no	—
94	C₂×C₈×C₁₃₉	—	4	1	no	—
95	C₂×C₈×C₁₃₉	—	4	1	no	—
96	C₂×C₈×C₁₃₉	—	4	1	no	—
97	C₂×C₈×C₁₃₉	—	4	1	no	—
98	C₄⋊C₄×C₁₃₉	—	2	1	no	—
99	C₄⋊C₄×C₁₃₉	—	2	1	no	—
100	C₄⋊C₄×C₁₃₉	—	2	1	no	—
101	C₄⋊C₄×C₁₃₉	—	2	1	no	—
102	C₄⋊C₄×C₁₃₉	—	4	2	no	—
103	C₄⋊C₄×C₁₃₉	—	4	4	no	—
104	C₄⋊C₄×C₁₃₉	—	4	2	no	—
105	C₄⋊C₄×C₁₃₉	—	4	1	no	—
106	C₄⋊C₄×C₁₃₉	—	4	1	no	—
107	C₄⋊C₄×C₁₃₉	—	4	1	no	—
108	C₄⋊C₄×C₁₃₉	—	4	1	no	—
109	C₄⋊C₄×C₁₃₉	—	4	1	no	—
110	C₄⋊C₄×C₁₃₉	—	4	1	no	—
111	C₄⋊C₄×C₁₃₉	—	4	1	no	—
112	C₄⋊C₄×C₁₃₉	—	4	1	no	—
113	C₄⋊C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₁₃₉	SD₁₆	1	2	yes	—
115	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
116	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
118	C₄²×C₁₃₉	—	4	1	no	—
119	C₄²×C₁₃₉	—	4	1	no	—
120	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₁₃₉	#41	1	1	yes	characteristic
123	C₄²×C₁₃₉	#41	1	1	yes	characteristic
124	C₂³×C₁₃₉	—	2	2	no	—
125	C₂³×C₁₃₉	—	2	2	no	—
126	C₂³×C₁₃₉	—	2	2	no	—
127	C₂³×C₁₃₉	—	4	1	no	—
128	C₂³×C₁₃₉	—	4	1	no	—
129	C₂³×C₁₃₉	—	4	1	no	—
130	C₂³×C₁₃₉	—	4	1	no	—
131	C₂³×C₁₃₉	#120	1	1	yes	characteristic
132	D₄×C₁₃₉	—	2	2	no	—
133	D₄×C₁₃₉	—	2	2	no	—
134	D₄×C₁₃₉	—	2	2	no	—
135	D₄×C₁₃₉	#106	1	4	yes	complemented
136	C₂×C₄×C₁₃₉	—	2	1	no	—
137	C₂×C₄×C₁₃₉	—	2	1	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	4	1	no	—
141	C₂×C₄×C₁₃₉	—	4	1	no	—
142	C₂×C₄×C₁₃₉	—	4	1	no	—
143	C₂×C₄×C₁₃₉	—	4	1	no	—
144	C₂×C₄×C₁₃₉	—	4	2	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	2	no	—
148	C₂×C₄×C₁₃₉	—	4	1	no	—
149	C₂×C₄×C₁₃₉	—	4	1	no	—
150	C₂×C₄×C₁₃₉	—	4	2	no	—
151	C₂×C₄×C₁₃₉	—	4	2	no	—
152	C₂×C₄×C₁₃₉	—	4	2	no	—
153	C₂×C₄×C₁₃₉	—	4	1	no	—
154	C₂×C₄×C₁₃₉	—	8	8	no	—
155	C₂×C₄×C₁₃₉	—	8	1	no	—
156	C₂×C₄×C₁₃₉	—	8	1	no	—
157	C₂×C₄×C₁₃₉	—	8	1	no	—
158	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
164	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₃₉	#135	1	1	yes	characteristic
168	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₁₃₉	#137	1	1	yes	characteristic
172	C₈×C₁₃₉	—	2	4	no	—
173	C₈×C₁₃₉	—	4	2	no	—
174	C₈×C₁₃₉	—	8	1	no	—
175	C₂²×C₁₃₉	—	2	4	no	—
176	C₂²×C₁₃₉	—	4	2	no	—
177	C₂²×C₁₃₉	—	4	2	no	—
178	C₂²×C₁₃₉	—	4	2	no	—
179	C₂²×C₁₃₉	—	4	2	no	—
180	C₂²×C₁₃₉	—	4	2	no	—
181	C₂²×C₁₃₉	—	4	2	no	—
182	C₂²×C₁₃₉	#385	1	1	yes	characteristic
183	C₂²×C₁₃₉	#448	1	1	yes	characteristic
184	C₂²×C₁₃₉	#449	1	1	yes	characteristic
185	C₂²×C₁₃₉	#450	1	1	yes	characteristic
186	C₂²×C₁₃₉	#450	1	1	yes	characteristic
187	C₂²×C₁₃₉	#453	1	1	yes	characteristic
188	C₂²×C₁₃₉	#456	1	1	yes	characteristic
189	C₄×C₁₃₉	—	2	1	no	—
190	C₄×C₁₃₉	—	2	1	no	—
191	C₄×C₁₃₉	—	4	2	no	—
192	C₄×C₁₃₉	—	4	2	no	—
193	C₄×C₁₃₉	—	8	2	no	—
194	C₄×C₁₃₉	—	8	1	no	—
195	C₄×C₁₃₉	—	16	1	no	—
196	C₄×C₁₃₉	C₂×#106	1	1	yes	characteristic
197	C₄×C₁₃₉	#428	1	1	yes	characteristic
198	C₄×C₁₃₉	C₄×SD₁₆	1	1	yes	characteristic
199	C₄×C₁₃₉	#442	1	1	yes	characteristic
200	C₄×C₁₃₉	#476	1	1	yes	characteristic
201	C₄×C₁₃₉	#478	1	1	yes	characteristic
202	C₄×C₁₃₉	#481	1	1	yes	characteristic
203	C₄×C₁₃₉	#483	1	1	yes	characteristic
204	C₂×C₁₃₉	—	4	4	no	—
205	C₂×C₁₃₉	#1622	1	1	yes	characteristic
206	C₂×C₁₃₉	#1629	1	1	yes	characteristic
207	C₂×C₁₃₉	#1651	1	1	yes	characteristic
208	C₂×C₁₃₉	#1654	1	1	yes	characteristic
209	C₂×C₁₃₉	#1853	1	1	yes	characteristic
210	C₂×C₁₃₉	#1859	1	1	yes	characteristic
211	C₂×C₁₃₉	#1864	1	1	yes	characteristic
212	#8886	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₁₃₉	#8886	1	1	yes	characteristic, direct product factor, Sylow
214	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
215	#1948	C₂×C₁₃₉	1	1	yes	characteristic, complemented
216	#1844	C₂×C₁₃₉	1	1	yes	characteristic, complemented
217	#1802	C₂×C₁₃₉	1	1	yes	characteristic
218	C₂×D₄⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic
219	#1296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
220	#1279	C₂×C₁₃₉	1	1	yes	characteristic, complemented
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	—	2	1	no	—
224	C₂×#106	—	2	2	no	—
225	C₂×#106	—	2	1	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
228	C₂×#102	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
230	#389	—	2	1	no	—
231	#385	—	2	2	no	—
232	#384	C₂²×C₁₃₉	1	1	yes	characteristic
233	#384	C₂²×C₁₃₉	1	1	yes	characteristic
234	#380	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
236	#340	—	2	1	no	—
237	#340	—	2	1	no	—
238	D₄⋊C₈	C₄×C₁₃₉	1	4	yes	complemented
239	C₂²×D₄	D₄×C₁₃₉	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	2	2	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	4	2	no	—
248	C₄×D₄	—	4	2	no	—
249	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
250	C₄×D₄	Q₈×C₁₃₉	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	4	2	no	—
258	C₂×C₄⋊C₄	—	4	2	no	—
259	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
267	#106	—	4	2	no	—
268	#106	—	4	4	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	C₂×C₄×C₁₃₉	1	2	yes	complemented
273	#102	—	4	2	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	C₂×C₄×C₁₃₉	1	2	yes	complemented
276	#95	—	2	2	no	—
277	#95	—	2	1	no	—
278	C₂⁴	—	2	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
283	C₂×D₄	SD₁₆×C₁₃₉	1	2	yes	—
284	C₂×D₄	SD₁₆×C₁₃₉	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	8	2	no	—
299	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
327	C₄⋊C₄	SD₁₆×C₁₃₉	1	2	yes	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
334	C₄²	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
335	C₄²	#41×C₁₃₉	1	1	yes	characteristic
336	C₄²	#41×C₁₃₉	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	#120×C₁₃₉	1	1	yes	characteristic
345	D₄	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	#106×C₁₃₉	1	4	yes	complemented
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
372	C₂×C₄	C₄×D₄×C₁₃₉	1	1	yes	characteristic
373	C₂×C₄	C₄×D₄×C₁₃₉	1	1	yes	characteristic
374	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
375	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
376	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
377	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
378	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
379	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
380	C₂×C₄	#135×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
383	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
384	C₂×C₄	#137×C₁₃₉	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	4	2	no	—
387	C₈	—	8	1	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	#385×C₁₃₉	1	1	yes	characteristic
396	C₂²	#448×C₁₃₉	1	1	yes	characteristic
397	C₂²	#449×C₁₃₉	1	1	yes	characteristic
398	C₂²	#450×C₁₃₉	1	1	yes	characteristic
399	C₂²	#450×C₁₃₉	1	1	yes	characteristic
400	C₂²	#453×C₁₃₉	1	1	yes	characteristic
401	C₂²	#456×C₁₃₉	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	8	2	no	—
407	C₄	—	8	1	no	—
408	C₄	—	16	1	no	—
409	C₄	C₂×#106×C₁₃₉	1	1	yes	characteristic
410	C₄	#428×C₁₃₉	1	1	yes	characteristic
411	C₄	C₄×SD₁₆×C₁₃₉	1	1	yes	characteristic
412	C₄	#442×C₁₃₉	1	1	yes	characteristic
413	C₄	#476×C₁₃₉	1	1	yes	characteristic
414	C₄	#478×C₁₃₉	1	1	yes	characteristic
415	C₄	#481×C₁₃₉	1	1	yes	characteristic
416	C₄	#483×C₁₃₉	1	1	yes	characteristic
417	C₂	—	4	4	no	—
418	C₂	#1622×C₁₃₉	1	1	yes	characteristic
419	C₂	#1629×C₁₃₉	1	1	yes	characteristic
420	C₂	#1651×C₁₃₉	1	1	yes	characteristic
421	C₂	#1654×C₁₃₉	1	1	yes	characteristic
422	C₂	#1853×C₁₃₉	1	1	yes	characteristic
423	C₂	#1859×C₁₃₉	1	1	yes	characteristic
424	C₂	#1864×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	#120
commutator	C₄²	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #1948×C₁₃₉	C₂	semidirect
3. #1844×C₁₃₉	C₂	semidirect
6. #1296×C₁₃₉	C₂	semidirect
7. #1279×C₁₃₉	C₂	semidirect
25. D₄⋊C₈×C₁₃₉	C₄	semidirect
59. C₄⋊C₈×C₁₃₉	C₂×C₄	semidirect
62. C₄×C₈×C₁₃₉	C₂×C₄	semidirect
135. D₄×C₁₃₉	#106	semidirect
212. #8886	C₁₃₉	direct (N × H)
213. C₁₃₉	#8886	direct (N × H)
215. #1948	C₂×C₁₃₉	semidirect
216. #1844	C₂×C₁₃₉	semidirect
219. #1296	C₂×C₁₃₉	semidirect
220. #1279	C₂×C₁₃₉	semidirect
238. D₄⋊C₈	C₄×C₁₃₉	semidirect
272. C₄⋊C₈	C₂×C₄×C₁₃₉	semidirect
275. C₄×C₈	C₂×C₄×C₁₃₉	semidirect
348. D₄	#106×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₄⋊C₄×C₁₃₉	2
#1948×C₁₃₉	2
#1844×C₁₃₉	2
#1802×C₁₃₉	2
C₂×D₄⋊C₈×C₁₃₉	2
#1296×C₁₃₉	2
#1279×C₁₃₉	2
#8886	139

Subgroups — C139×#8886 #48003482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#8886 #48003482