Subgroups — C₁₃₉×#21190 #48015786

Order 35584.

2010 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	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#407×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1955×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1954×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₃₉	C₄	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃₉	—	2	4	no	—
12	C₂×C₄×D₄×C₁₃₉	—	2	4	no	—
13	C₂×C₄×D₄×C₁₃₉	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₃₉	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₃₉	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
20	#423×C₁₃₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	complemented
23	#407×C₁₃₉	—	2	16	no	—
24	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	16	yes	complemented
25	C₄×M₁₆×C₁₃₉	—	2	4	no	—
26	C₂×#97×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂⁵×C₁₃₉	C₂×C₄	1	2	yes	—
29	C₂²×D₄×C₁₃₉	—	2	8	no	—
30	C₂²×D₄×C₁₃₉	—	2	4	no	—
31	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₃₉	—	2	8	no	—
34	C₂³×C₄×C₁₃₉	—	2	4	no	—
35	C₂³×C₄×C₁₃₉	—	2	4	no	—
36	C₂³×C₄×C₁₃₉	—	2	8	no	—
37	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₃₉	—	2	4	no	—
44	C₂×M₁₆×C₁₃₉	—	2	4	no	—
45	C₂×M₁₆×C₁₃₉	—	2	8	no	—
46	C₂×M₁₆×C₁₃₉	—	2	4	no	—
47	C₂×M₁₆×C₁₃₉	D₄	1	8	yes	complemented
48	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
49	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
50	C₄×D₄×C₁₃₉	—	2	8	no	—
51	C₄×D₄×C₁₃₉	—	2	8	no	—
52	C₄×D₄×C₁₃₉	—	2	4	no	—
53	C₄×D₄×C₁₃₉	—	2	4	no	—
54	C₄×D₄×C₁₃₉	—	2	4	no	—
55	C₄×D₄×C₁₃₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
61	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
65	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
66	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₁₃₉	—	2	4	no	—
69	C₄⋊C₈×C₁₃₉	—	2	4	no	—
70	C₂²⋊C₈×C₁₃₉	—	2	32	no	—
71	#97×C₁₃₉	—	2	4	no	—
72	C₄×C₈×C₁₃₉	—	2	4	no	—
73	C₂⁴×C₁₃₉	—	2	4	no	—
74	C₂⁴×C₁₃₉	—	2	8	no	—
75	C₂⁴×C₁₃₉	—	2	8	no	—
76	C₂⁴×C₁₃₉	—	4	4	no	—
77	C₂⁴×C₁₃₉	C₂²×C₄	1	4	yes	—
78	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₃₉	—	2	32	no	—
80	C₂×D₄×C₁₃₉	—	2	8	no	—
81	C₂×D₄×C₁₃₉	—	2	4	no	—
82	C₂×D₄×C₁₃₉	—	2	4	no	—
83	C₂×D₄×C₁₃₉	—	2	4	no	—
84	C₂×D₄×C₁₃₉	M₁₆	1	8	yes	complemented
85	C₂²×C₄×C₁₃₉	—	2	4	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	2	8	no	—
88	C₂²×C₄×C₁₃₉	—	2	8	no	—
89	C₂²×C₄×C₁₃₉	—	2	16	no	—
90	C₂²×C₄×C₁₃₉	—	2	8	no	—
91	C₂²×C₄×C₁₃₉	—	2	4	no	—
92	C₂²×C₄×C₁₃₉	—	2	4	no	—
93	C₂²×C₄×C₁₃₉	—	2	8	no	—
94	C₂²×C₄×C₁₃₉	—	4	2	no	—
95	C₂²×C₄×C₁₃₉	—	4	16	no	—
96	C₂²×C₄×C₁₃₉	—	4	8	no	—
97	C₂²×C₄×C₁₃₉	—	4	8	no	—
98	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₃₉	—	2	16	no	—
112	M₁₆×C₁₃₉	—	4	8	no	—
113	C₂×C₈×C₁₃₉	—	2	4	no	—
114	C₂×C₈×C₁₃₉	—	2	4	no	—
115	C₂×C₈×C₁₃₉	—	2	8	no	—
116	C₂×C₈×C₁₃₉	—	2	4	no	—
117	C₂×C₈×C₁₃₉	C₂×D₄	1	8	yes	complemented
118	C₄⋊C₄×C₁₃₉	—	2	4	no	—
119	C₄⋊C₄×C₁₃₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
121	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
122	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
123	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
127	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
128	C₂³×C₁₃₉	—	2	2	no	—
129	C₂³×C₁₃₉	—	2	2	no	—
130	C₂³×C₁₃₉	—	2	16	no	—
131	C₂³×C₁₃₉	—	2	4	no	—
132	C₂³×C₁₃₉	—	2	8	no	—
133	C₂³×C₁₃₉	—	2	4	no	—
134	C₂³×C₁₃₉	—	2	8	no	—
135	C₂³×C₁₃₉	—	4	32	no	—
136	C₂³×C₁₃₉	—	4	8	no	—
137	C₂³×C₁₃₉	—	4	8	no	—
138	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₁₃₉	C₄×D₄	1	4	yes	—
140	C₂³×C₁₃₉	C₂×M₁₆	1	8	yes	—
141	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
142	D₄×C₁₃₉	—	2	16	no	—
143	D₄×C₁₃₉	—	2	16	no	—
144	C₂×C₄×C₁₃₉	—	2	2	no	—
145	C₂×C₄×C₁₃₉	—	2	2	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	8	no	—
148	C₂×C₄×C₁₃₉	—	2	4	no	—
149	C₂×C₄×C₁₃₉	—	2	8	no	—
150	C₂×C₄×C₁₃₉	—	4	4	no	—
151	C₂×C₄×C₁₃₉	—	4	8	no	—
152	C₂×C₄×C₁₃₉	—	4	8	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	—	4	4	no	—
155	C₂×C₄×C₁₃₉	—	4	16	no	—
156	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
162	C₂×C₄×C₁₃₉	#121	1	8	yes	—
163	C₂×C₄×C₁₃₉	#124	1	4	yes	—
164	C₂×C₄×C₁₃₉	#127	1	4	yes	—
165	C₂×C₄×C₁₃₉	C₂×M₁₆	1	4	yes	—
166	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
170	C₈×C₁₃₉	—	2	8	no	—
171	C₈×C₁₃₉	—	4	4	no	—
172	C₂²×C₁₃₉	—	2	2	no	—
173	C₂²×C₁₃₉	—	2	2	no	—
174	C₂²×C₁₃₉	—	2	8	no	—
175	C₂²×C₁₃₉	—	2	8	no	—
176	C₂²×C₁₃₉	—	2	16	no	—
177	C₂²×C₁₃₉	—	4	32	no	—
178	C₂²×C₁₃₉	—	4	4	no	—
179	C₂²×C₁₃₉	—	4	8	no	—
180	C₂²×C₁₃₉	—	4	4	no	—
181	C₂²×C₁₃₉	#390	1	4	yes	—
182	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
184	C₂²×C₁₃₉	C₂²×M₁₆	1	2	yes	—
185	C₂²×C₁₃₉	#568	1	2	yes	—
186	C₄×C₁₃₉	—	2	2	no	—
187	C₄×C₁₃₉	—	2	2	no	—
188	C₄×C₁₃₉	—	2	2	no	—
189	C₄×C₁₃₉	—	4	4	no	—
190	C₄×C₁₃₉	#390	1	4	yes	—
191	C₄×C₁₃₉	#407	1	4	yes	complemented
192	C₄×C₁₃₉	C₂×#121	1	2	yes	—
193	C₄×C₁₃₉	C₂×#124	1	1	yes	characteristic
194	C₄×C₁₃₉	C₂×#127	1	1	yes	characteristic
195	C₂×C₁₃₉	—	2	4	no	—
196	C₂×C₁₃₉	—	4	8	no	—
197	C₂×C₁₃₉	C₂×#390	1	1	yes	characteristic
198	C₂×C₁₃₉	C₂×#407	1	1	yes	characteristic
199	C₂×C₁₃₉	#2879	1	1	yes	characteristic
200	C₂×C₁₃₉	D₄×M₁₆	1	4	yes	—
201	#21190	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₁₃₉	#21190	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic
204	C₂×#423	C₂×C₁₃₉	1	1	yes	characteristic, complemented
205	C₂×#407	C₂×C₁₃₉	1	4	yes	complemented
206	C₂×C₄×M₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	#1955	C₂×C₁₃₉	1	4	yes	complemented
208	#1954	C₂×C₁₃₉	1	4	yes	complemented
209	C₂³×D₄	C₄×C₁₃₉	1	1	yes	characteristic
210	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
211	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
212	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
213	C₂×C₄×D₄	—	2	4	no	—
214	C₂×C₄×D₄	—	2	4	no	—
215	C₂×C₄×D₄	C₄×C₁₃₉	1	2	yes	—
216	C₂×C₄×D₄	C₄×C₁₃₉	1	2	yes	—
217	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
218	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
219	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	1	yes	characteristic
220	C₂²×C₂²⋊C₄	C₄×C₁₃₉	1	2	yes	—
221	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
222	#423	—	2	4	no	—
223	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	complemented
224	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	complemented
225	#407	—	2	16	no	—
226	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	16	yes	complemented
227	C₄×M₁₆	—	2	4	no	—
228	C₂×#97	C₂²×C₁₃₉	1	2	yes	complemented
229	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	complemented
230	C₂⁵	C₂×C₄×C₁₃₉	1	2	yes	—
231	C₂²×D₄	—	2	8	no	—
232	C₂²×D₄	—	2	4	no	—
233	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
234	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	4	no	—
237	C₂³×C₄	—	2	8	no	—
238	C₂³×C₄	—	2	8	no	—
239	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
240	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
241	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
242	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
244	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	8	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	D₄×C₁₃₉	1	8	yes	complemented
250	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
251	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
252	C₄×D₄	—	2	8	no	—
253	C₄×D₄	—	2	8	no	—
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	8	no	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
264	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
267	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
268	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
270	C₄⋊C₈	—	2	4	no	—
271	C₄⋊C₈	—	2	4	no	—
272	C₂²⋊C₈	—	2	32	no	—
273	#97	—	2	4	no	—
274	C₄×C₈	—	2	4	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	8	no	—
278	C₂⁴	—	4	4	no	—
279	C₂⁴	C₂²×C₄×C₁₃₉	1	4	yes	—
280	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
281	C₂×D₄	—	2	32	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	M₁₆×C₁₃₉	1	8	yes	complemented
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	16	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	16	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
301	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
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	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
311	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
313	M₁₆	—	2	16	no	—
314	M₁₆	—	4	8	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	8	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	C₂×D₄×C₁₃₉	1	8	yes	complemented
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
325	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
326	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
327	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
328	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
329	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	16	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	4	32	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	8	no	—
340	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
341	C₂³	C₄×D₄×C₁₃₉	1	4	yes	—
342	C₂³	C₂×M₁₆×C₁₃₉	1	8	yes	—
343	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
344	D₄	—	2	16	no	—
345	D₄	—	2	16	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	16	no	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
364	C₂×C₄	#121×C₁₃₉	1	8	yes	—
365	C₂×C₄	#124×C₁₃₉	1	4	yes	—
366	C₂×C₄	#127×C₁₃₉	1	4	yes	—
367	C₂×C₄	C₂×M₁₆×C₁₃₉	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
372	C₈	—	2	8	no	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	2	16	no	—
379	C₂²	—	4	32	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	8	no	—
383	C₂²	#390×C₁₃₉	1	4	yes	—
384	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
385	C₂²	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
386	C₂²	C₂²×M₁₆×C₁₃₉	1	2	yes	—
387	C₂²	#568×C₁₃₉	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	#390×C₁₃₉	1	4	yes	—
393	C₄	#407×C₁₃₉	1	4	yes	complemented
394	C₄	C₂×#121×C₁₃₉	1	2	yes	—
395	C₄	C₂×#124×C₁₃₉	1	1	yes	characteristic
396	C₄	C₂×#127×C₁₃₉	1	1	yes	characteristic
397	C₂	—	2	4	no	—
398	C₂	—	4	8	no	—
399	C₂	C₂×#390×C₁₃₉	1	1	yes	characteristic
400	C₂	C₂×#407×C₁₃₉	1	1	yes	characteristic
401	C₂	#2879×C₁₃₉	1	1	yes	characteristic
402	C₂	D₄×M₁₆×C₁₃₉	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#423×C₁₃₉	C₂	semidirect
3. C₂×#407×C₁₃₉	C₂	semidirect
4. C₂×C₄×M₁₆×C₁₃₉	C₂	semidirect
5. #1955×C₁₃₉	C₂	semidirect
6. #1954×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
22. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
24. C₂×C₂²⋊C₈×C₁₃₉	C₂²	semidirect
26. C₂×#97×C₁₃₉	C₂²	semidirect
27. C₂×C₄×C₈×C₁₃₉	C₂²	semidirect
47. C₂×M₁₆×C₁₃₉	D₄	semidirect
84. C₂×D₄×C₁₃₉	M₁₆	semidirect
117. C₂×C₈×C₁₃₉	C₂×D₄	semidirect
191. C₄×C₁₃₉	#407	semidirect
201. #21190	C₁₃₉	direct (N × H)
202. C₁₃₉	#21190	direct (N × H)
204. C₂×#423	C₂×C₁₃₉	semidirect
205. C₂×#407	C₂×C₁₃₉	semidirect
206. C₂×C₄×M₁₆	C₂×C₁₃₉	semidirect
207. #1955	C₂×C₁₃₉	semidirect
208. #1954	C₂×C₁₃₉	semidirect
223. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
224. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
226. C₂×C₂²⋊C₈	C₂²×C₁₃₉	semidirect
228. C₂×#97	C₂²×C₁₃₉	semidirect
229. C₂×C₄×C₈	C₂²×C₁₃₉	semidirect
249. C₂×M₁₆	D₄×C₁₃₉	semidirect
286. C₂×D₄	M₁₆×C₁₃₉	semidirect
319. C₂×C₈	C₂×D₄×C₁₃₉	semidirect
393. C₄	#407×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₃₉	2
C₂×#423×C₁₃₉	2
C₂×#407×C₁₃₉	2
C₂×C₄×M₁₆×C₁₃₉	2
#1955×C₁₃₉	2
#1954×C₁₃₉	2
#21190	139

Subgroups — C139×#21190 #48015786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21190 #48015786