Subgroups — C₂×#2052×C₁₃₉ #48018125

Order 35584.

1362 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#103×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#101×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2052×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
8	C₂×#343×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#137×C₁₃₉	—	2	2	no	—
12	C₂×#137×C₁₃₉	—	2	4	no	—
13	C₂×#137×C₁₃₉	—	2	4	no	—
14	C₂×#137×C₁₃₉	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₁₃₉	—	2	1	no	—
16	C₂²×SD₁₆×C₁₃₉	—	2	1	no	—
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	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#108×C₁₃₉	—	2	4	no	—
23	C₂×#108×C₁₃₉	C₂²	1	4	yes	complemented
24	#417×C₁₃₉	—	2	2	no	—
25	#417×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#103×C₁₃₉	—	2	1	no	—
27	C₂×#103×C₁₃₉	—	2	2	no	—
28	C₂×#103×C₁₃₉	—	2	2	no	—
29	C₂×#103×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×#102×C₁₃₉	—	2	1	no	—
31	C₂×#101×C₁₃₉	—	2	4	no	—
32	C₂×#101×C₁₃₉	C₂²	1	4	yes	complemented
33	#408×C₁₃₉	—	2	2	no	—
34	#408×C₁₃₉	C₂²	1	4	yes	—
35	C₂×C₂²⋊C₈×C₁₃₉	—	2	2	no	—
36	#343×C₁₃₉	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₃₉	—	2	1	no	—
38	C₂×#41×C₁₃₉	—	2	1	no	—
39	C₂×#41×C₁₃₉	—	2	2	no	—
40	C₂×#41×C₁₃₉	—	2	2	no	—
41	C₂×#41×C₁₃₉	—	2	2	no	—
42	C₂×#41×C₁₃₉	—	2	2	no	—
43	C₂×#41×C₁₃₉	D₄	1	2	yes	—
44	C₂×#41×C₁₃₉	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₃₉	—	2	2	no	—
46	C₂²×Q₈×C₁₃₉	—	2	1	no	—
47	C₂²×Q₈×C₁₃₉	—	2	1	no	—
48	C₂²×Q₈×C₁₃₉	—	2	1	no	—
49	C₂²×Q₈×C₁₃₉	—	2	1	no	—
50	C₂²×Q₈×C₁₃₉	—	2	1	no	—
51	C₂²×Q₈×C₁₃₉	—	2	2	no	—
52	C₂²×Q₈×C₁₃₉	—	2	2	no	—
53	C₂²×Q₈×C₁₃₉	D₄	1	4	yes	—
54	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃₉	—	2	1	no	—
57	C₂²×D₄×C₁₃₉	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃₉	—	2	1	no	—
59	C₂³×C₄×C₁₃₉	—	2	1	no	—
60	C₂³×C₄×C₁₃₉	—	2	1	no	—
61	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	#137×C₁₃₉	—	2	16	no	—
63	#137×C₁₃₉	—	2	8	no	—
64	#137×C₁₃₉	—	2	8	no	—
65	C₂×Q₁₆×C₁₃₉	—	2	8	no	—
66	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
67	C₂×SD₁₆×C₁₃₉	—	2	8	no	—
68	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
69	C₂×M₁₆×C₁₃₉	—	2	2	no	—
70	C₂×M₁₆×C₁₃₉	—	2	1	no	—
71	C₂×M₁₆×C₁₃₉	—	2	1	no	—
72	C₂×M₁₆×C₁₃₉	—	2	1	no	—
73	C₂×M₁₆×C₁₃₉	—	2	2	no	—
74	C₂×M₁₆×C₁₃₉	—	2	2	no	—
75	C₂×M₁₆×C₁₃₉	—	2	2	no	—
76	C₂×M₁₆×C₁₃₉	—	2	2	no	—
77	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
78	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
79	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
80	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₃₉	—	2	2	no	—
82	C₂²×C₈×C₁₃₉	—	2	1	no	—
83	C₂²×C₈×C₁₃₉	—	2	2	no	—
84	C₂²×C₈×C₁₃₉	—	2	1	no	—
85	C₂²×C₈×C₁₃₉	—	2	1	no	—
86	C₂²×C₈×C₁₃₉	D₄	1	2	yes	—
87	C₂²×C₈×C₁₃₉	D₄	1	2	yes	—
88	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	#108×C₁₃₉	—	2	8	no	—
96	#103×C₁₃₉	—	2	4	no	—
97	#103×C₁₃₉	—	2	8	no	—
98	#102×C₁₃₉	—	2	4	no	—
99	#101×C₁₃₉	—	2	8	no	—
100	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
101	C₂⁴×C₁₃₉	—	2	1	no	—
102	C₂⁴×C₁₃₉	#41	1	1	yes	characteristic
103	#41×C₁₃₉	—	2	4	no	—
104	#41×C₁₃₉	—	2	4	no	—
105	#41×C₁₃₉	—	2	2	no	—
106	#41×C₁₃₉	—	2	2	no	—
107	#41×C₁₃₉	—	2	2	no	—
108	#41×C₁₃₉	—	2	2	no	—
109	#41×C₁₃₉	—	4	2	no	—
110	#41×C₁₃₉	—	4	2	no	—
111	#41×C₁₃₉	—	4	2	no	—
112	#41×C₁₃₉	—	4	2	no	—
113	C₂×Q₈×C₁₃₉	—	2	1	no	—
114	C₂×Q₈×C₁₃₉	—	2	4	no	—
115	C₂×Q₈×C₁₃₉	—	2	2	no	—
116	C₂×Q₈×C₁₃₉	—	2	4	no	—
117	C₂×Q₈×C₁₃₉	—	2	2	no	—
118	C₂×Q₈×C₁₃₉	—	2	4	no	—
119	C₂×Q₈×C₁₃₉	—	2	4	no	—
120	C₂×Q₈×C₁₃₉	—	2	4	no	—
121	C₂×Q₈×C₁₃₉	—	2	2	no	—
122	C₂×Q₈×C₁₃₉	—	2	2	no	—
123	C₂×Q₈×C₁₃₉	—	2	2	no	—
124	C₂×Q₈×C₁₃₉	—	2	2	no	—
125	C₂×Q₈×C₁₃₉	—	2	2	no	—
126	C₂×Q₈×C₁₃₉	—	4	1	no	—
127	C₂×Q₈×C₁₃₉	—	4	1	no	—
128	C₂×Q₈×C₁₃₉	—	4	2	no	—
129	C₂×Q₈×C₁₃₉	—	4	2	no	—
130	C₂×Q₈×C₁₃₉	—	4	2	no	—
131	C₂×Q₈×C₁₃₉	—	4	2	no	—
132	C₂×Q₈×C₁₃₉	—	4	2	no	—
133	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
134	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₁₃₉	—	2	2	no	—
136	C₂×D₄×C₁₃₉	—	2	2	no	—
137	C₂×D₄×C₁₃₉	—	2	2	no	—
138	C₂×D₄×C₁₃₉	—	2	1	no	—
139	C₂×D₄×C₁₃₉	—	2	2	no	—
140	C₂×D₄×C₁₃₉	—	4	2	no	—
141	C₂×D₄×C₁₃₉	—	4	2	no	—
142	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃₉	—	2	1	no	—
144	C₂²×C₄×C₁₃₉	—	2	4	no	—
145	C₂²×C₄×C₁₃₉	—	2	2	no	—
146	C₂²×C₄×C₁₃₉	—	2	2	no	—
147	C₂²×C₄×C₁₃₉	—	2	2	no	—
148	C₂²×C₄×C₁₃₉	—	2	2	no	—
149	C₂²×C₄×C₁₃₉	—	4	1	no	—
150	C₂²×C₄×C₁₃₉	—	4	1	no	—
151	C₂²×C₄×C₁₃₉	—	4	2	no	—
152	C₂²×C₄×C₁₃₉	—	4	2	no	—
153	C₂²×C₄×C₁₃₉	—	4	2	no	—
154	C₂²×C₄×C₁₃₉	—	4	1	no	—
155	C₂²×C₄×C₁₃₉	—	4	1	no	—
156	C₂²×C₄×C₁₃₉	—	8	2	no	—
157	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
164	C₂²×C₄×C₁₃₉	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₁₃₉	—	2	16	no	—
168	SD₁₆×C₁₃₉	—	2	16	no	—
169	M₁₆×C₁₃₉	—	2	4	no	—
170	M₁₆×C₁₃₉	—	2	2	no	—
171	M₁₆×C₁₃₉	—	2	2	no	—
172	M₁₆×C₁₃₉	—	2	2	no	—
173	M₁₆×C₁₃₉	—	2	2	no	—
174	M₁₆×C₁₃₉	—	2	2	no	—
175	M₁₆×C₁₃₉	—	4	2	no	—
176	M₁₆×C₁₃₉	—	4	2	no	—
177	M₁₆×C₁₃₉	C₂×D₄	1	4	yes	—
178	C₂×C₈×C₁₃₉	—	2	4	no	—
179	C₂×C₈×C₁₃₉	—	2	4	no	—
180	C₂×C₈×C₁₃₉	—	2	4	no	—
181	C₂×C₈×C₁₃₉	—	2	2	no	—
182	C₂×C₈×C₁₃₉	—	2	2	no	—
183	C₂×C₈×C₁₃₉	—	2	2	no	—
184	C₂×C₈×C₁₃₉	—	2	2	no	—
185	C₂×C₈×C₁₃₉	—	2	2	no	—
186	C₂×C₈×C₁₃₉	—	4	2	no	—
187	C₂×C₈×C₁₃₉	—	4	2	no	—
188	C₂×C₈×C₁₃₉	C₂×D₄	1	4	yes	—
189	C₄⋊C₄×C₁₃₉	—	2	2	no	—
190	C₄⋊C₄×C₁₃₉	—	2	2	no	—
191	C₄⋊C₄×C₁₃₉	—	4	1	no	—
192	C₄⋊C₄×C₁₃₉	—	4	1	no	—
193	C₂³×C₁₃₉	—	2	2	no	—
194	C₂³×C₁₃₉	—	2	2	no	—
195	C₂³×C₁₃₉	—	2	2	no	—
196	C₂³×C₁₃₉	—	4	2	no	—
197	C₂³×C₁₃₉	—	4	2	no	—
198	C₂³×C₁₃₉	—	4	2	no	—
199	C₂³×C₁₃₉	#121	1	1	yes	characteristic
200	C₂³×C₁₃₉	#121	1	1	yes	characteristic
201	C₂³×C₁₃₉	#123	1	2	yes	—
202	C₂³×C₁₃₉	#124	1	2	yes	—
203	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
204	Q₈×C₁₃₉	—	2	4	no	—
205	Q₈×C₁₃₉	—	2	2	no	—
206	Q₈×C₁₃₉	—	2	4	no	—
207	Q₈×C₁₃₉	—	2	2	no	—
208	Q₈×C₁₃₉	—	4	2	no	—
209	Q₈×C₁₃₉	—	4	2	no	—
210	Q₈×C₁₃₉	—	4	4	no	—
211	Q₈×C₁₃₉	—	4	4	no	—
212	Q₈×C₁₃₉	—	4	2	no	—
213	D₄×C₁₃₉	—	2	2	no	—
214	D₄×C₁₃₉	—	2	2	no	—
215	D₄×C₁₃₉	—	4	2	no	—
216	D₄×C₁₃₉	—	4	2	no	—
217	D₄×C₁₃₉	—	4	4	no	—
218	D₄×C₁₃₉	—	4	2	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	4	no	—
221	C₂×C₄×C₁₃₉	—	4	2	no	—
222	C₂×C₄×C₁₃₉	—	4	2	no	—
223	C₂×C₄×C₁₃₉	—	4	2	no	—
224	C₂×C₄×C₁₃₉	—	4	4	no	—
225	C₂×C₄×C₁₃₉	—	4	4	no	—
226	C₂×C₄×C₁₃₉	—	4	2	no	—
227	C₂×C₄×C₁₃₉	—	4	2	no	—
228	C₂×C₄×C₁₃₉	—	4	4	no	—
229	C₂×C₄×C₁₃₉	—	4	2	no	—
230	C₂×C₄×C₁₃₉	—	8	2	no	—
231	C₂×C₄×C₁₃₉	—	8	2	no	—
232	C₂×C₄×C₁₃₉	—	8	2	no	—
233	C₂×C₄×C₁₃₉	#120	1	2	yes	—
234	C₂×C₄×C₁₃₉	#120	1	2	yes	—
235	C₂×C₄×C₁₃₉	#121	1	2	yes	—
236	C₂×C₄×C₁₃₉	#121	1	2	yes	—
237	C₂×C₄×C₁₃₉	#121	1	2	yes	—
238	C₂×C₄×C₁₃₉	#121	1	2	yes	—
239	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₃₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₃₉	#123	1	2	yes	—
242	C₂×C₄×C₁₃₉	#123	1	2	yes	—
243	C₂×C₄×C₁₃₉	#123	1	2	yes	—
244	C₂×C₄×C₁₃₉	#124	1	2	yes	—
245	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
251	C₈×C₁₃₉	—	2	4	no	—
252	C₈×C₁₃₉	—	2	4	no	—
253	C₈×C₁₃₉	—	4	2	no	—
254	C₈×C₁₃₉	—	4	2	no	—
255	C₂²×C₁₃₉	—	2	4	no	—
256	C₂²×C₁₃₉	—	2	4	no	—
257	C₂²×C₁₃₉	—	2	1	no	—
258	C₂²×C₁₃₉	—	2	1	no	—
259	C₂²×C₁₃₉	—	2	1	no	—
260	C₂²×C₁₃₉	—	2	1	no	—
261	C₂²×C₁₃₉	—	4	2	no	—
262	C₂²×C₁₃₉	—	4	2	no	—
263	C₂²×C₁₃₉	—	4	2	no	—
264	C₂²×C₁₃₉	—	8	4	no	—
265	C₂²×C₁₃₉	#394	1	2	yes	—
266	C₂²×C₁₃₉	#394	1	2	yes	—
267	C₂²×C₁₃₉	#471	1	2	yes	—
268	C₂²×C₁₃₉	#473	1	2	yes	—
269	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
270	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
271	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
272	C₄×C₁₃₉	—	4	2	no	—
273	C₄×C₁₃₉	—	4	4	no	—
274	C₄×C₁₃₉	—	8	2	no	—
275	C₄×C₁₃₉	#394	1	2	yes	—
276	C₄×C₁₃₉	#394	1	2	yes	—
277	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
278	C₄×C₁₃₉	C₂×#121	1	1	yes	characteristic
279	C₄×C₁₃₉	C₂×#121	1	1	yes	characteristic
280	C₄×C₁₃₉	C₂×#123	1	1	yes	characteristic
281	C₂×C₁₃₉	—	2	1	no	—
282	C₂×C₁₃₉	—	2	1	no	—
283	C₂×C₁₃₉	—	2	2	no	—
284	C₂×C₁₃₉	—	8	2	no	—
285	C₂×C₁₃₉	#2052	1	4	yes	direct product factor
286	C₂×C₁₃₉	C₂×#394	1	1	yes	characteristic
287	C₂×C₁₃₉	C₂×#471	1	1	yes	characteristic
288	C₂×C₁₃₉	C₂×#473	1	1	yes	characteristic
289	C₂×#2052	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₁₃₉	C₂×#2052	1	1	yes	characteristic, direct product factor, Sylow
291	C₂²×#137	C₂×C₁₃₉	1	1	yes	characteristic
292	C₂²×#108	C₂×C₁₃₉	1	1	yes	characteristic, complemented
293	C₂×#417	C₂×C₁₃₉	1	1	yes	characteristic
294	C₂²×#103	C₂×C₁₃₉	1	1	yes	characteristic, complemented
295	C₂²×#101	C₂×C₁₃₉	1	1	yes	characteristic, complemented
296	C₂×#408	C₂×C₁₃₉	1	1	yes	characteristic
297	#2052	C₂×C₁₃₉	1	8	yes	direct product factor
298	C₂×#343	C₂×C₁₃₉	1	1	yes	characteristic, complemented
299	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
300	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
301	C₂×#137	—	2	2	no	—
302	C₂×#137	—	2	4	no	—
303	C₂×#137	—	2	4	no	—
304	C₂×#137	C₂²×C₁₃₉	1	4	yes	—
305	C₂²×Q₁₆	—	2	1	no	—
306	C₂²×SD₁₆	—	2	1	no	—
307	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
308	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
309	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
312	C₂×#108	—	2	4	no	—
313	C₂×#108	C₂²×C₁₃₉	1	4	yes	complemented
314	#417	—	2	2	no	—
315	#417	C₂²×C₁₃₉	1	4	yes	—
316	C₂×#103	—	2	1	no	—
317	C₂×#103	—	2	2	no	—
318	C₂×#103	—	2	2	no	—
319	C₂×#103	C₂²×C₁₃₉	1	4	yes	complemented
320	C₂×#102	—	2	1	no	—
321	C₂×#101	—	2	4	no	—
322	C₂×#101	C₂²×C₁₃₉	1	4	yes	complemented
323	#408	—	2	2	no	—
324	#408	C₂²×C₁₃₉	1	4	yes	—
325	C₂×C₂²⋊C₈	—	2	2	no	—
326	#343	C₂²×C₁₃₉	1	4	yes	complemented
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	1	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	D₄×C₁₃₉	1	2	yes	—
334	C₂×#41	C₂³×C₁₃₉	1	2	yes	—
335	C₂²×Q₈	—	2	2	no	—
336	C₂²×Q₈	—	2	1	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	—	2	2	no	—
340	C₂²×Q₈	—	2	1	no	—
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×Q₈	—	2	2	no	—
343	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
344	C₂²×Q₈	D₄×C₁₃₉	1	4	yes	—
345	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	D₄×C₁₃₉	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
352	#137	—	2	16	no	—
353	#137	—	2	8	no	—
354	#137	—	2	8	no	—
355	C₂×Q₁₆	—	2	8	no	—
356	C₂×Q₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	8	no	—
358	C₂×SD₁₆	—	2	4	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
368	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
369	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
370	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
371	C₂²×C₈	—	2	2	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	D₄×C₁₃₉	1	2	yes	—
377	C₂²×C₈	D₄×C₁₃₉	1	2	yes	—
378	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
385	#108	—	2	8	no	—
386	#103	—	2	4	no	—
387	#103	—	2	8	no	—
388	#102	—	2	4	no	—
389	#101	—	2	8	no	—
390	C₂²⋊C₈	—	2	8	no	—
391	C₂⁴	—	2	1	no	—
392	C₂⁴	#41×C₁₃₉	1	1	yes	characteristic
393	#41	—	2	4	no	—
394	#41	—	2	4	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	4	2	no	—
400	#41	—	4	2	no	—
401	#41	—	4	2	no	—
402	#41	—	4	2	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	4	1	no	—
417	C₂×Q₈	—	4	1	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
424	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	8	2	no	—
447	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
453	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
454	C₂²×C₄	#41×C₁₃₉	1	1	yes	characteristic
455	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
457	Q₁₆	—	2	16	no	—
458	SD₁₆	—	2	16	no	—
459	M₁₆	—	2	4	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	4	2	no	—
466	M₁₆	—	4	2	no	—
467	M₁₆	C₂×D₄×C₁₃₉	1	4	yes	—
468	C₂×C₈	—	2	4	no	—
469	C₂×C₈	—	2	4	no	—
470	C₂×C₈	—	2	4	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	2	no	—
477	C₂×C₈	—	4	2	no	—
478	C₂×C₈	C₂×D₄×C₁₃₉	1	4	yes	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	#121×C₁₃₉	1	1	yes	characteristic
490	C₂³	#121×C₁₃₉	1	1	yes	characteristic
491	C₂³	#123×C₁₃₉	1	2	yes	—
492	C₂³	#124×C₁₃₉	1	2	yes	—
493	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
494	Q₈	—	2	4	no	—
495	Q₈	—	2	2	no	—
496	Q₈	—	2	4	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	4	no	—
501	Q₈	—	4	4	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	#120×C₁₃₉	1	2	yes	—
524	C₂×C₄	#120×C₁₃₉	1	2	yes	—
525	C₂×C₄	#121×C₁₃₉	1	2	yes	—
526	C₂×C₄	#121×C₁₃₉	1	2	yes	—
527	C₂×C₄	#121×C₁₃₉	1	2	yes	—
528	C₂×C₄	#121×C₁₃₉	1	2	yes	—
529	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄	#121×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄	#123×C₁₃₉	1	2	yes	—
532	C₂×C₄	#123×C₁₃₉	1	2	yes	—
533	C₂×C₄	#123×C₁₃₉	1	2	yes	—
534	C₂×C₄	#124×C₁₃₉	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
540	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	2	4	no	—
543	C₈	—	4	2	no	—
544	C₈	—	4	2	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	4	no	—
555	C₂²	#394×C₁₃₉	1	2	yes	—
556	C₂²	#394×C₁₃₉	1	2	yes	—
557	C₂²	#471×C₁₃₉	1	2	yes	—
558	C₂²	#473×C₁₃₉	1	2	yes	—
559	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
560	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
561	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	8	2	no	—
565	C₄	#394×C₁₃₉	1	2	yes	—
566	C₄	#394×C₁₃₉	1	2	yes	—
567	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
568	C₄	C₂×#121×C₁₃₉	1	1	yes	characteristic
569	C₄	C₂×#121×C₁₃₉	1	1	yes	characteristic
570	C₄	C₂×#123×C₁₃₉	1	1	yes	characteristic
571	C₂	—	2	1	no	—
572	C₂	—	2	1	no	—
573	C₂	—	2	2	no	—
574	C₂	—	8	2	no	—
575	C₂	#2052×C₁₃₉	1	4	yes	direct product factor
576	C₂	C₂×#394×C₁₃₉	1	1	yes	characteristic
577	C₂	C₂×#471×C₁₃₉	1	1	yes	characteristic
578	C₂	C₂×#473×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₁₃₉	C₂	semidirect
4. C₂²×#103×C₁₃₉	C₂	semidirect
5. C₂²×#101×C₁₃₉	C₂	semidirect
7. #2052×C₁₃₉	C₂	direct (N × H)
8. C₂×#343×C₁₃₉	C₂	semidirect
23. C₂×#108×C₁₃₉	C₂²	semidirect
29. C₂×#103×C₁₃₉	C₂²	semidirect
32. C₂×#101×C₁₃₉	C₂²	semidirect
36. #343×C₁₃₉	C₂²	semidirect
285. C₂×C₁₃₉	#2052	direct (N × H)
289. C₂×#2052	C₁₃₉	direct (N × H)
290. C₁₃₉	C₂×#2052	direct (N × H)
292. C₂²×#108	C₂×C₁₃₉	semidirect
294. C₂²×#103	C₂×C₁₃₉	semidirect
295. C₂²×#101	C₂×C₁₃₉	semidirect
297. #2052	C₂×C₁₃₉	direct (N × H)
298. C₂×#343	C₂×C₁₃₉	semidirect
313. C₂×#108	C₂²×C₁₃₉	semidirect
319. C₂×#103	C₂²×C₁₃₉	semidirect
322. C₂×#101	C₂²×C₁₃₉	semidirect
326. #343	C₂²×C₁₃₉	semidirect
575. C₂	#2052×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
C₂²×#137×C₁₃₉	2
C₂²×#108×C₁₃₉	2
C₂×#417×C₁₃₉	2
C₂²×#103×C₁₃₉	2
C₂²×#101×C₁₃₉	2
C₂×#408×C₁₃₉	2
#2052×C₁₃₉	2
C₂×#343×C₁₃₉	2
C₂×#2052	139

Subgroups — C2×#2052×C139 #48018125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2052×C₁₃₉ #48018125