Subgroups — C₁₃₉×#20700 #48015296

Order 35584.

1774 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2280×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1824×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#1823×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1736×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	C₂⁴×C₄×C₁₃₉	—	2	1	no	—
8	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
10	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
12	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₃₉	—	2	4	no	—
15	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	8	yes	complemented
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
19	#407×C₁₃₉	—	2	4	no	—
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
22	#381×C₁₃₉	—	2	1	no	—
23	#380×C₁₃₉	C₂²	1	2	yes	—
24	#380×C₁₃₉	C₂²	1	2	yes	—
25	#379×C₁₃₉	—	2	1	no	—
26	C₄×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
28	#340×C₁₃₉	C₂²	1	16	yes	complemented
29	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₉	—	2	8	no	—
31	C₂³×C₄×C₁₃₉	—	2	8	no	—
32	C₂³×C₄×C₁₃₉	—	2	2	no	—
33	C₂³×C₄×C₁₃₉	—	2	2	no	—
34	C₂³×C₄×C₁₃₉	—	2	2	no	—
35	C₂³×C₄×C₁₃₉	—	4	8	no	—
36	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
41	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₃₉	—	2	4	no	—
45	C₂×M₁₆×C₁₃₉	—	2	8	no	—
46	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
47	#117×C₁₃₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
65	C₂×C₄²×C₁₃₉	—	2	2	no	—
66	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
67	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
68	#95×C₁₃₉	—	2	2	no	—
69	#95×C₁₃₉	—	2	2	no	—
70	C₂⁴×C₁₃₉	—	2	4	no	—
71	C₂⁴×C₁₃₉	—	2	4	no	—
72	C₂⁴×C₁₃₉	—	2	4	no	—
73	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
74	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₉	—	2	4	no	—
78	C₂²×C₄×C₁₃₉	—	2	16	no	—
79	C₂²×C₄×C₁₃₉	—	2	4	no	—
80	C₂²×C₄×C₁₃₉	—	2	4	no	—
81	C₂²×C₄×C₁₃₉	—	2	16	no	—
82	C₂²×C₄×C₁₃₉	—	2	4	no	—
83	C₂²×C₄×C₁₃₉	—	2	4	no	—
84	C₂²×C₄×C₁₃₉	—	2	8	no	—
85	C₂²×C₄×C₁₃₉	—	2	8	no	—
86	C₂²×C₄×C₁₃₉	—	2	8	no	—
87	C₂²×C₄×C₁₃₉	—	2	4	no	—
88	C₂²×C₄×C₁₃₉	—	2	4	no	—
89	C₂²×C₄×C₁₃₉	—	4	8	no	—
90	C₂²×C₄×C₁₃₉	—	4	8	no	—
91	C₂²×C₄×C₁₃₉	—	4	32	no	—
92	C₂²×C₄×C₁₃₉	—	4	8	no	—
93	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
94	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
106	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₁₃₉	—	4	8	no	—
108	C₂×C₈×C₁₃₉	—	2	4	no	—
109	C₂×C₈×C₁₃₉	—	2	8	no	—
110	C₄⋊C₄×C₁₃₉	—	2	8	no	—
111	C₄⋊C₄×C₁₃₉	—	2	8	no	—
112	C₄⋊C₄×C₁₃₉	—	2	8	no	—
113	C₄⋊C₄×C₁₃₉	—	2	4	no	—
114	C₄⋊C₄×C₁₃₉	—	2	8	no	—
115	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
116	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
117	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
118	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
119	C₄²×C₁₃₉	—	4	4	no	—
120	C₂³×C₁₃₉	—	2	32	no	—
121	C₂³×C₁₃₉	—	2	2	no	—
122	C₂³×C₁₃₉	—	2	2	no	—
123	C₂³×C₁₃₉	—	2	2	no	—
124	C₂³×C₁₃₉	—	2	2	no	—
125	C₂³×C₁₃₉	—	2	2	no	—
126	C₂³×C₁₃₉	—	2	2	no	—
127	C₂³×C₁₃₉	—	2	8	no	—
128	C₂³×C₁₃₉	—	2	8	no	—
129	C₂³×C₁₃₉	—	2	8	no	—
130	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂³×C₁₃₉	#123	1	4	yes	—
134	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
135	C₂³×C₁₃₉	#137	1	4	yes	—
136	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₄×C₁₃₉	—	2	4	no	—
141	C₂×C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₄×C₁₃₉	—	2	4	no	—
143	C₂×C₄×C₁₃₉	—	2	4	no	—
144	C₂×C₄×C₁₃₉	—	2	8	no	—
145	C₂×C₄×C₁₃₉	—	2	8	no	—
146	C₂×C₄×C₁₃₉	—	2	8	no	—
147	C₂×C₄×C₁₃₉	—	4	16	no	—
148	C₂×C₄×C₁₃₉	—	4	16	no	—
149	C₂×C₄×C₁₃₉	—	4	8	no	—
150	C₂×C₄×C₁₃₉	—	4	16	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	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₃₉	#117	1	8	yes	—
158	C₂×C₄×C₁₃₉	#123	1	8	yes	—
159	C₂×C₄×C₁₃₉	#123	1	4	yes	—
160	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
163	C₈×C₁₃₉	—	4	4	no	—
164	C₂²×C₁₃₉	—	2	32	no	—
165	C₂²×C₁₃₉	—	2	8	no	—
166	C₂²×C₁₃₉	—	2	8	no	—
167	C₂²×C₁₃₉	—	2	8	no	—
168	C₂²×C₁₃₉	—	2	2	no	—
169	C₂²×C₁₃₉	—	2	2	no	—
170	C₂²×C₁₃₉	—	2	2	no	—
171	C₂²×C₁₃₉	—	2	2	no	—
172	C₂²×C₁₃₉	—	2	2	no	—
173	C₂²×C₁₃₉	—	2	2	no	—
174	C₂²×C₁₃₉	#381	1	4	yes	—
175	C₂²×C₁₃₉	#418	1	4	yes	—
176	C₂²×C₁₃₉	#419	1	4	yes	—
177	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
179	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
180	C₂²×C₁₃₉	C₂×#137	1	2	yes	—
181	C₄×C₁₃₉	—	2	2	no	—
182	C₄×C₁₃₉	—	2	2	no	—
183	C₄×C₁₃₉	—	4	8	no	—
184	C₄×C₁₃₉	—	8	4	no	—
185	C₄×C₁₃₉	#381	1	4	yes	—
186	C₄×C₁₃₉	C₂×#117	1	2	yes	—
187	C₄×C₁₃₉	C₂×#123	1	2	yes	—
188	C₂×C₁₃₉	—	2	4	no	—
189	C₂×C₁₃₉	—	2	4	no	—
190	C₂×C₁₃₉	—	2	4	no	—
191	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
192	C₂×C₁₃₉	C₂×#418	1	1	yes	characteristic
193	C₂×C₁₃₉	C₂×#419	1	1	yes	characteristic
194	C₂×C₁₃₉	#3092	1	4	yes	—
195	#20700	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₁₃₉	#20700	1	1	yes	characteristic, direct product factor, Sylow
197	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
198	C₂×#407	C₂×C₁₃₉	1	1	yes	characteristic
199	#2280	C₂×C₁₃₉	1	1	yes	characteristic
200	#1824	C₂×C₁₃₉	1	4	yes	complemented
201	#1823	C₂×C₁₃₉	1	4	yes	complemented
202	#1736	C₂×C₁₃₉	1	4	yes	complemented
203	C₂⁴×C₄	—	2	1	no	—
204	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
205	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
206	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
207	C₂²×C₄⋊C₄	—	2	1	no	—
208	C₂²×C₄⋊C₄	—	2	1	no	—
209	C₂²×C₄⋊C₄	—	2	1	no	—
210	C₂²×C₄⋊C₄	—	2	4	no	—
211	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	8	yes	complemented
212	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
213	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
215	#407	—	2	4	no	—
216	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
218	#381	—	2	1	no	—
219	#380	C₂²×C₁₃₉	1	2	yes	—
220	#380	C₂²×C₁₃₉	1	2	yes	—
221	#379	—	2	1	no	—
222	C₄×C₂²⋊C₄	—	2	1	no	—
223	C₄×C₂²⋊C₄	—	2	1	no	—
224	#340	C₂²×C₁₃₉	1	16	yes	complemented
225	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
226	C₂³×C₄	—	2	8	no	—
227	C₂³×C₄	—	2	8	no	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	—	4	8	no	—
232	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
233	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
237	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	—	2	8	no	—
242	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
243	#117	—	2	8	no	—
244	C₂×C₄⋊C₄	—	2	8	no	—
245	C₂×C₄⋊C₄	—	2	8	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	C₂²⋊C₈	—	2	4	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	C₂⁴	—	2	4	no	—
267	C₂⁴	—	2	4	no	—
268	C₂⁴	—	2	4	no	—
269	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
270	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
271	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
272	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	16	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	4	32	no	—
286	C₂²×C₄	—	4	8	no	—
287	C₂²×C₄	—	4	8	no	—
288	C₂²×C₄	—	4	8	no	—
289	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
290	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
291	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
301	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
302	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
303	M₁₆	—	4	8	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	4	4	no	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₄²	—	4	4	no	—
316	C₂³	—	2	32	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	2	8	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	8	no	—
326	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
327	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
328	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
329	C₂³	#123×C₁₃₉	1	4	yes	—
330	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
331	C₂³	#137×C₁₃₉	1	4	yes	—
332	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	4	16	no	—
344	C₂×C₄	—	4	16	no	—
345	C₂×C₄	—	4	16	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
353	C₂×C₄	#117×C₁₃₉	1	8	yes	—
354	C₂×C₄	#123×C₁₃₉	1	8	yes	—
355	C₂×C₄	#123×C₁₃₉	1	4	yes	—
356	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
359	C₈	—	4	4	no	—
360	C₂²	—	2	32	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	2	8	no	—
365	C₂²	—	2	8	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	#381×C₁₃₉	1	4	yes	—
371	C₂²	#418×C₁₃₉	1	4	yes	—
372	C₂²	#419×C₁₃₉	1	4	yes	—
373	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
374	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
375	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
376	C₂²	C₂×#137×C₁₃₉	1	2	yes	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	8	no	—
380	C₄	—	8	4	no	—
381	C₄	#381×C₁₃₉	1	4	yes	—
382	C₄	C₂×#117×C₁₃₉	1	2	yes	—
383	C₄	C₂×#123×C₁₃₉	1	2	yes	—
384	C₂	—	2	4	no	—
385	C₂	—	2	4	no	—
386	C₂	—	2	4	no	—
387	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
388	C₂	C₂×#418×C₁₃₉	1	1	yes	characteristic
389	C₂	C₂×#419×C₁₃₉	1	1	yes	characteristic
390	C₂	#3092×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁵×C₁₃₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1824×C₁₃₉	C₂	semidirect
5. #1823×C₁₃₉	C₂	semidirect
6. #1736×C₁₃₉	C₂	semidirect
15. C₂²×C₄⋊C₄×C₁₃₉	C₄	semidirect
28. #340×C₁₃₉	C₂²	semidirect
195. #20700	C₁₃₉	direct (N × H)
196. C₁₃₉	#20700	direct (N × H)
200. #1824	C₂×C₁₃₉	semidirect
201. #1823	C₂×C₁₃₉	semidirect
202. #1736	C₂×C₁₃₉	semidirect
211. C₂²×C₄⋊C₄	C₄×C₁₃₉	semidirect
224. #340	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₃₉	2
C₂×#407×C₁₃₉	2
#2280×C₁₃₉	2
#1824×C₁₃₉	2
#1823×C₁₃₉	2
#1736×C₁₃₉	2
#20700	139

Subgroups — C139×#20700 #48015296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20700 #48015296