Subgroups — C₁₃₉×#20852 #48015448

Order 35584.

1314 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#430×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#108×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2879×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#1855×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#1738×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#341×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
10	#568×C₁₃₉	—	2	4	no	—
11	#568×C₁₃₉	—	2	4	no	—
12	C₂×#131×C₁₃₉	—	2	2	no	—
13	C₂×#131×C₁₃₉	—	2	2	no	—
14	C₂²×M₁₆×C₁₃₉	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	#430×C₁₃₉	—	2	4	no	—
22	C₂×#108×C₁₃₉	—	2	4	no	—
23	C₂×#108×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#108×C₁₃₉	C₂²	1	4	yes	—
25	#408×C₁₃₉	—	2	2	no	—
26	#408×C₁₃₉	—	2	2	no	—
27	#408×C₁₃₉	C₄	1	4	yes	—
28	#408×C₁₃₉	C₄	1	4	yes	—
29	#407×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
31	#341×C₁₃₉	C₂²	1	4	yes	—
32	#341×C₁₃₉	C₂²	1	4	yes	—
33	C₂×#41×C₁₃₉	—	2	2	no	—
34	C₂×#41×C₁₃₉	—	2	2	no	—
35	C₂×#41×C₁₃₉	—	2	2	no	—
36	C₂×#41×C₁₃₉	—	2	2	no	—
37	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
38	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
39	C₂×#41×C₁₃₉	D₄	1	2	yes	—
40	C₂×#41×C₁₃₉	D₄	1	2	yes	—
41	C₂²×Q₈×C₁₃₉	Q₈	1	1	yes	characteristic
42	C₂²×D₄×C₁₃₉	Q₈	1	2	yes	—
43	C₂²×D₄×C₁₃₉	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	#131×C₁₃₉	—	2	16	no	—
47	#131×C₁₃₉	—	2	16	no	—
48	C₂×M₁₆×C₁₃₉	—	2	2	no	—
49	C₂×M₁₆×C₁₃₉	—	2	4	no	—
50	C₂×M₁₆×C₁₃₉	—	2	1	no	—
51	C₂×M₁₆×C₁₃₉	—	2	1	no	—
52	C₂×M₁₆×C₁₃₉	—	2	2	no	—
53	C₂×M₁₆×C₁₃₉	—	2	2	no	—
54	C₂×M₁₆×C₁₃₉	—	2	2	no	—
55	C₂×M₁₆×C₁₃₉	—	2	8	no	—
56	C₂×M₁₆×C₁₃₉	—	2	8	no	—
57	C₂×M₁₆×C₁₃₉	—	2	1	no	—
58	C₂×M₁₆×C₁₃₉	—	2	1	no	—
59	C₂×M₁₆×C₁₃₉	—	2	2	no	—
60	C₂×M₁₆×C₁₃₉	—	2	2	no	—
61	C₂×M₁₆×C₁₃₉	—	2	2	no	—
62	C₂×M₁₆×C₁₃₉	—	2	2	no	—
63	C₂×M₁₆×C₁₃₉	C₂×C₄	1	2	yes	—
64	C₂×M₁₆×C₁₃₉	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
66	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
67	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
68	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
69	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
70	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃₉	—	2	2	no	—
72	C₂²×C₈×C₁₃₉	—	2	4	no	—
73	C₂²×C₈×C₁₃₉	—	2	1	no	—
74	C₂²×C₈×C₁₃₉	—	2	1	no	—
75	C₂²×C₈×C₁₃₉	—	2	2	no	—
76	C₂²×C₈×C₁₃₉	—	2	1	no	—
77	C₂²×C₈×C₁₃₉	—	2	1	no	—
78	C₂²×C₈×C₁₃₉	C₂×C₄	1	2	yes	—
79	C₂²×C₈×C₁₃₉	C₂×C₄	1	2	yes	—
80	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
82	#108×C₁₃₉	—	2	8	no	—
83	#108×C₁₃₉	—	2	8	no	—
84	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
85	C₂²⋊C₈×C₁₃₉	C₂×C₄	1	16	yes	—
86	C₂⁴×C₁₃₉	C₂×Q₈	1	2	yes	—
87	C₂⁴×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
88	#41×C₁₃₉	—	2	4	no	—
89	#41×C₁₃₉	—	2	4	no	—
90	#41×C₁₃₉	—	2	4	no	—
91	#41×C₁₃₉	—	2	4	no	—
92	#41×C₁₃₉	—	2	4	no	—
93	#41×C₁₃₉	—	2	4	no	—
94	#41×C₁₃₉	—	2	4	no	—
95	#41×C₁₃₉	—	2	4	no	—
96	C₂×Q₈×C₁₃₉	—	2	2	no	—
97	C₂×Q₈×C₁₃₉	—	2	2	no	—
98	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	2	yes	—
99	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	2	yes	—
100	C₂×D₄×C₁₃₉	—	2	4	no	—
101	C₂×D₄×C₁₃₉	—	2	4	no	—
102	C₂×D₄×C₁₃₉	—	2	2	no	—
103	C₂×D₄×C₁₃₉	—	2	2	no	—
104	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
105	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
106	C₂×D₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
107	C₂×D₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
108	C₂²×C₄×C₁₃₉	—	2	2	no	—
109	C₂²×C₄×C₁₃₉	—	2	2	no	—
110	C₂²×C₄×C₁₃₉	—	2	2	no	—
111	C₂²×C₄×C₁₃₉	—	2	2	no	—
112	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
121	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
123	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
125	M₁₆×C₁₃₉	—	2	16	no	—
126	M₁₆×C₁₃₉	—	2	4	no	—
127	M₁₆×C₁₃₉	—	2	4	no	—
128	M₁₆×C₁₃₉	—	2	4	no	—
129	M₁₆×C₁₃₉	—	2	4	no	—
130	M₁₆×C₁₃₉	—	2	2	no	—
131	M₁₆×C₁₃₉	—	2	2	no	—
132	M₁₆×C₁₃₉	—	2	2	no	—
133	M₁₆×C₁₃₉	—	2	2	no	—
134	M₁₆×C₁₃₉	—	2	2	no	—
135	M₁₆×C₁₃₉	—	2	2	no	—
136	M₁₆×C₁₃₉	—	4	2	no	—
137	M₁₆×C₁₃₉	—	4	2	no	—
138	M₁₆×C₁₃₉	C₂×D₄	1	4	yes	—
139	M₁₆×C₁₃₉	C₂×D₄	1	4	yes	—
140	C₂×C₈×C₁₃₉	—	2	16	no	—
141	C₂×C₈×C₁₃₉	—	2	4	no	—
142	C₂×C₈×C₁₃₉	—	2	4	no	—
143	C₂×C₈×C₁₃₉	—	2	4	no	—
144	C₂×C₈×C₁₃₉	—	2	4	no	—
145	C₂×C₈×C₁₃₉	—	2	2	no	—
146	C₂×C₈×C₁₃₉	—	2	2	no	—
147	C₂×C₈×C₁₃₉	—	2	2	no	—
148	C₂×C₈×C₁₃₉	—	2	2	no	—
149	C₂×C₈×C₁₃₉	—	2	2	no	—
150	C₂×C₈×C₁₃₉	—	2	2	no	—
151	C₂×C₈×C₁₃₉	—	2	2	no	—
152	C₂×C₈×C₁₃₉	—	2	2	no	—
153	C₂×C₈×C₁₃₉	—	4	2	no	—
154	C₂×C₈×C₁₃₉	—	4	2	no	—
155	C₂×C₈×C₁₃₉	C₂²×C₄	1	4	yes	—
156	C₂×C₈×C₁₃₉	C₂²×C₄	1	4	yes	—
157	C₂³×C₁₃₉	—	2	2	no	—
158	C₂³×C₁₃₉	—	2	2	no	—
159	C₂³×C₁₃₉	—	4	2	no	—
160	C₂³×C₁₃₉	—	4	4	no	—
161	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
162	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂³×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
165	C₂³×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
166	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
167	Q₈×C₁₃₉	—	2	4	no	—
168	Q₈×C₁₃₉	—	2	4	no	—
169	D₄×C₁₃₉	—	2	8	no	—
170	D₄×C₁₃₉	—	2	8	no	—
171	D₄×C₁₃₉	—	2	4	no	—
172	D₄×C₁₃₉	—	2	4	no	—
173	C₂×C₄×C₁₃₉	—	2	2	no	—
174	C₂×C₄×C₁₃₉	—	2	2	no	—
175	C₂×C₄×C₁₃₉	—	2	4	no	—
176	C₂×C₄×C₁₃₉	—	2	4	no	—
177	C₂×C₄×C₁₃₉	—	2	4	no	—
178	C₂×C₄×C₁₃₉	—	2	4	no	—
179	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
180	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₃₉	#120	1	2	yes	—
187	C₂×C₄×C₁₃₉	#120	1	2	yes	—
188	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₁₃₉	#123	1	2	yes	—
191	C₂×C₄×C₁₃₉	#123	1	2	yes	—
192	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
198	C₈×C₁₃₉	—	2	4	no	—
199	C₈×C₁₃₉	—	2	4	no	—
200	C₈×C₁₃₉	—	2	4	no	—
201	C₈×C₁₃₉	—	2	4	no	—
202	C₈×C₁₃₉	—	4	2	no	—
203	C₈×C₁₃₉	—	4	2	no	—
204	C₂²×C₁₃₉	—	2	2	no	—
205	C₂²×C₁₃₉	—	2	2	no	—
206	C₂²×C₁₃₉	—	2	2	no	—
207	C₂²×C₁₃₉	—	2	8	no	—
208	C₂²×C₁₃₉	—	2	4	no	—
209	C₂²×C₁₃₉	—	4	2	no	—
210	C₂²×C₁₃₉	—	4	2	no	—
211	C₂²×C₁₃₉	—	8	2	no	—
212	C₂²×C₁₃₉	—	8	2	no	—
213	C₂²×C₁₃₉	#385	1	2	yes	—
214	C₂²×C₁₃₉	#385	1	2	yes	—
215	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
217	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
218	C₄×C₁₃₉	—	2	4	no	—
219	C₄×C₁₃₉	#385	1	2	yes	—
220	C₄×C₁₃₉	#385	1	2	yes	—
221	C₄×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
222	C₄×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
223	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
224	C₄×C₁₃₉	C₂×#123	1	1	yes	characteristic
225	C₂×C₁₃₉	—	2	1	no	—
226	C₂×C₁₃₉	—	2	1	no	—
227	C₂×C₁₃₉	—	2	2	no	—
228	C₂×C₁₃₉	—	2	2	no	—
229	C₂×C₁₃₉	—	4	4	no	—
230	C₂×C₁₃₉	C₂×#385	1	1	yes	characteristic
231	C₂×C₁₃₉	#2916	1	2	yes	—
232	#20852	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₁₃₉	#20852	1	1	yes	characteristic, direct product factor, Sylow
234	C₂×#568	C₂×C₁₃₉	1	1	yes	characteristic
235	C₂×#430	C₂×C₁₃₉	1	1	yes	characteristic, complemented
236	C₂²×#108	C₂×C₁₃₉	1	1	yes	characteristic, complemented
237	#2879	C₂×C₁₃₉	1	1	yes	characteristic
238	C₂×#408	C₂×C₁₃₉	1	1	yes	characteristic
239	#1855	C₂×C₁₃₉	1	8	yes	complemented
240	#1738	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	C₂×#341	C₂×C₁₃₉	1	1	yes	characteristic, complemented
242	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
243	#568	—	2	4	no	—
244	#568	—	2	4	no	—
245	C₂×#131	—	2	2	no	—
246	C₂×#131	—	2	2	no	—
247	C₂²×M₁₆	C₂²×C₁₃₉	1	4	yes	—
248	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
254	#430	—	2	4	no	—
255	C₂×#108	—	2	4	no	—
256	C₂×#108	C₂²×C₁₃₉	1	4	yes	—
257	C₂×#108	C₂²×C₁₃₉	1	4	yes	—
258	#408	—	2	2	no	—
259	#408	—	2	2	no	—
260	#408	C₄×C₁₃₉	1	4	yes	—
261	#408	C₄×C₁₃₉	1	4	yes	—
262	#407	C₂²×C₁₃₉	1	4	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
264	#341	C₂²×C₁₃₉	1	4	yes	—
265	#341	C₂²×C₁₃₉	1	4	yes	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
271	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
272	C₂×#41	D₄×C₁₃₉	1	2	yes	—
273	C₂×#41	D₄×C₁₃₉	1	2	yes	—
274	C₂²×Q₈	Q₈×C₁₃₉	1	1	yes	characteristic
275	C₂²×D₄	Q₈×C₁₃₉	1	2	yes	—
276	C₂²×D₄	Q₈×C₁₃₉	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
278	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
279	#131	—	2	16	no	—
280	#131	—	2	16	no	—
281	C₂×M₁₆	—	2	4	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	8	no	—
289	C₂×M₁₆	—	2	8	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	C₂×C₄×C₁₃₉	1	2	yes	—
297	C₂×M₁₆	C₂×C₄×C₁₃₉	1	2	yes	—
298	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
299	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
300	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
301	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
302	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
303	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	2	4	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	C₂×C₄×C₁₃₉	1	2	yes	—
312	C₂²×C₈	C₂×C₄×C₁₃₉	1	2	yes	—
313	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
314	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
315	#108	—	2	8	no	—
316	#108	—	2	8	no	—
317	C₂²⋊C₈	—	2	8	no	—
318	C₂²⋊C₈	C₂×C₄×C₁₃₉	1	16	yes	—
319	C₂⁴	C₂×Q₈×C₁₃₉	1	2	yes	—
320	C₂⁴	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	2	yes	—
332	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	2	yes	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
338	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
339	C₂×D₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
340	C₂×D₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
346	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
353	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
354	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
355	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
356	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
358	M₁₆	—	2	16	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	4	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	4	2	no	—
370	M₁₆	—	4	2	no	—
371	M₁₆	C₂×D₄×C₁₃₉	1	4	yes	—
372	M₁₆	C₂×D₄×C₁₃₉	1	4	yes	—
373	C₂×C₈	—	2	16	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	4	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	2	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	C₂²×C₄×C₁₃₉	1	4	yes	—
389	C₂×C₈	C₂²×C₄×C₁₃₉	1	4	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
395	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
396	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
397	C₂³	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
398	C₂³	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
399	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	2	4	no	—
402	D₄	—	2	8	no	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
413	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
414	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
415	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
416	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
417	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
418	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
419	C₂×C₄	#120×C₁₃₉	1	2	yes	—
420	C₂×C₄	#120×C₁₃₉	1	2	yes	—
421	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
422	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
423	C₂×C₄	#123×C₁₃₉	1	2	yes	—
424	C₂×C₄	#123×C₁₃₉	1	2	yes	—
425	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
426	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
431	C₈	—	2	4	no	—
432	C₈	—	2	4	no	—
433	C₈	—	2	4	no	—
434	C₈	—	2	4	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	8	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	#385×C₁₃₉	1	2	yes	—
447	C₂²	#385×C₁₃₉	1	2	yes	—
448	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
449	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
450	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	#385×C₁₃₉	1	2	yes	—
453	C₄	#385×C₁₃₉	1	2	yes	—
454	C₄	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
455	C₄	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
456	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
457	C₄	C₂×#123×C₁₃₉	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	2	no	—
461	C₂	—	2	2	no	—
462	C₂	—	4	4	no	—
463	C₂	C₂×#385×C₁₃₉	1	1	yes	characteristic
464	C₂	#2916×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₄⋊C₄
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂²×#41×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#430×C₁₃₉	C₂	semidirect
3. C₂²×#108×C₁₃₉	C₂	semidirect
6. #1855×C₁₃₉	C₂	semidirect
7. #1738×C₁₃₉	C₂	semidirect
8. C₂×#341×C₁₃₉	C₂	semidirect
232. #20852	C₁₃₉	direct (N × H)
233. C₁₃₉	#20852	direct (N × H)
235. C₂×#430	C₂×C₁₃₉	semidirect
236. C₂²×#108	C₂×C₁₃₉	semidirect
239. #1855	C₂×C₁₃₉	semidirect
240. #1738	C₂×C₁₃₉	semidirect
241. C₂×#341	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#568×C₁₃₉	2
C₂×#430×C₁₃₉	2
C₂²×#108×C₁₃₉	2
#2879×C₁₃₉	2
C₂×#408×C₁₃₉	2
#1855×C₁₃₉	2
#1738×C₁₃₉	2
C₂×#341×C₁₃₉	2
#20852	139

Subgroups — C139×#20852 #48015448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20852 #48015448