Subgroups — C₁₃₉×#36201 #48030797

Order 35584.

1702 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2864×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2577×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2530×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2524×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2515×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2507×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2506×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2497×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2496×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2485×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2485×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2468×C₁₃₉	C₂	1	2	yes	maximal
15	#2460×C₁₃₉	C₂	1	2	yes	maximal
16	#2373×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2371×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2346×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2283×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#397×C₁₃₉	C₂²	1	2	yes	—
41	#397×C₁₃₉	C₂²	1	2	yes	—
42	#397×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#394×C₁₃₉	C₂²	1	2	yes	—
45	#394×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	2	yes	—
47	#389×C₁₃₉	C₂²	1	1	yes	characteristic
48	#389×C₁₃₉	C₂²	1	1	yes	characteristic
49	#389×C₁₃₉	C₂²	1	1	yes	characteristic
50	#389×C₁₃₉	C₂²	1	1	yes	characteristic
51	#389×C₁₃₉	C₂²	1	1	yes	characteristic
52	#389×C₁₃₉	C₂²	1	1	yes	characteristic
53	#389×C₁₃₉	C₂²	1	1	yes	characteristic
54	#389×C₁₃₉	C₂²	1	1	yes	characteristic
55	#389×C₁₃₉	C₂²	1	1	yes	characteristic
56	#389×C₁₃₉	C₂²	1	1	yes	characteristic
57	#388×C₁₃₉	C₂²	1	2	yes	—
58	#388×C₁₃₉	C₂²	1	2	yes	—
59	#388×C₁₃₉	C₂²	1	2	yes	—
60	#388×C₁₃₉	C₂²	1	2	yes	—
61	#388×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#387×C₁₃₉	C₂²	1	2	yes	—
65	#387×C₁₃₉	C₂²	1	2	yes	—
66	#387×C₁₃₉	C₂²	1	2	yes	—
67	#387×C₁₃₉	C₂²	1	2	yes	—
68	#387×C₁₃₉	C₂²	1	2	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	—
70	#387×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	2	yes	—
72	#387×C₁₃₉	C₂²	1	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#385×C₁₃₉	C₂²	1	2	yes	—
81	#385×C₁₃₉	C₂²	1	2	yes	—
82	#385×C₁₃₉	C₂²	1	2	yes	—
83	#385×C₁₃₉	C₂²	1	2	yes	—
84	#384×C₁₃₉	C₂²	1	1	yes	characteristic
85	#384×C₁₃₉	C₂²	1	1	yes	characteristic
86	#383×C₁₃₉	C₂²	1	2	yes	—
87	#383×C₁₃₉	C₂²	1	2	yes	—
88	#382×C₁₃₉	C₂²	1	2	yes	—
89	#382×C₁₃₉	C₂²	1	1	yes	characteristic
90	#382×C₁₃₉	C₂²	1	1	yes	characteristic
91	#382×C₁₃₉	C₂²	1	1	yes	characteristic
92	#381×C₁₃₉	C₂²	1	2	yes	—
93	#380×C₁₃₉	C₂²	1	2	yes	—
94	#380×C₁₃₉	C₂²	1	1	yes	characteristic
95	#380×C₁₃₉	C₂²	1	1	yes	characteristic
96	#380×C₁₃₉	C₂²	1	2	yes	—
97	#380×C₁₃₉	C₂²	1	1	yes	characteristic
98	#380×C₁₃₉	C₂²	1	1	yes	characteristic
99	#380×C₁₃₉	C₂²	1	1	yes	characteristic
100	#380×C₁₃₉	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
120	#376×C₁₃₉	C₂²	1	2	yes	—
121	#376×C₁₃₉	C₂²	1	2	yes	—
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	#126×C₁₃₉	—	2	8	no	—
131	#125×C₁₃₉	—	2	8	no	—
132	#125×C₁₃₉	—	2	4	no	—
133	C₄×D₄×C₁₃₉	—	2	4	no	—
134	C₄×D₄×C₁₃₉	—	2	4	no	—
135	C₄×D₄×C₁₃₉	—	2	4	no	—
136	#117×C₁₃₉	—	2	4	no	—
137	#117×C₁₃₉	—	2	4	no	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	—	2	4	no	—
180	C₂×C₄²×C₁₃₉	—	2	4	no	—
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	1	yes	characteristic
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	2	yes	—
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	1	yes	characteristic
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	2	yes	—
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	2	yes	—
223	#95×C₁₃₉	C₂³	1	2	yes	—
224	#95×C₁₃₉	C₂³	1	1	yes	characteristic
225	#95×C₁₃₉	C₂³	1	1	yes	characteristic
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	2	yes	—
228	#95×C₁₃₉	C₂³	1	2	yes	—
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂×D₄×C₁₃₉	—	2	2	no	—
235	C₂×D₄×C₁₃₉	—	2	2	no	—
236	C₂×D₄×C₁₃₉	—	2	2	no	—
237	C₂²×C₄×C₁₃₉	—	2	2	no	—
238	C₂²×C₄×C₁₃₉	—	2	2	no	—
239	C₂²×C₄×C₁₃₉	—	2	2	no	—
240	C₂²×C₄×C₁₃₉	—	2	2	no	—
241	C₂²×C₄×C₁₃₉	—	2	2	no	—
242	C₂²×C₄×C₁₃₉	—	2	2	no	—
243	C₂²×C₄×C₁₃₉	—	2	2	no	—
244	C₂²×C₄×C₁₃₉	—	2	2	no	—
245	C₂²×C₄×C₁₃₉	—	2	2	no	—
246	C₂²×C₄×C₁₃₉	—	2	2	no	—
247	C₂²×C₄×C₁₃₉	—	2	2	no	—
248	C₂²×C₄×C₁₃₉	—	2	2	no	—
249	C₂²×C₄×C₁₃₉	—	2	2	no	—
250	C₂²×C₄×C₁₃₉	—	4	1	no	—
251	C₂²×C₄×C₁₃₉	—	4	1	no	—
252	C₂²×C₄×C₁₃₉	—	4	1	no	—
253	C₂²×C₄×C₁₃₉	—	4	1	no	—
254	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₁₃₉	—	2	2	no	—
277	C₄⋊C₄×C₁₃₉	—	2	2	no	—
278	C₄⋊C₄×C₁₃₉	—	2	2	no	—
279	C₄⋊C₄×C₁₃₉	—	2	2	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	4	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄⋊C₄×C₁₃₉	—	2	4	no	—
286	C₄⋊C₄×C₁₃₉	—	2	4	no	—
287	C₄⋊C₄×C₁₃₉	—	2	4	no	—
288	C₄⋊C₄×C₁₃₉	—	2	4	no	—
289	C₄⋊C₄×C₁₃₉	—	2	2	no	—
290	C₄⋊C₄×C₁₃₉	—	2	2	no	—
291	C₄⋊C₄×C₁₃₉	—	2	4	no	—
292	C₄⋊C₄×C₁₃₉	—	2	4	no	—
293	C₄⋊C₄×C₁₃₉	—	2	4	no	—
294	C₄⋊C₄×C₁₃₉	—	2	2	no	—
295	C₄⋊C₄×C₁₃₉	—	2	2	no	—
296	C₄⋊C₄×C₁₃₉	—	4	2	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	2	no	—
299	C₄⋊C₄×C₁₃₉	—	4	2	no	—
300	C₄⋊C₄×C₁₃₉	—	4	2	no	—
301	C₄⋊C₄×C₁₃₉	—	4	2	no	—
302	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
303	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
308	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
309	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
310	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
312	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
314	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
315	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
316	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
317	C₄²×C₁₃₉	—	2	2	no	—
318	C₄²×C₁₃₉	—	2	2	no	—
319	C₄²×C₁₃₉	—	2	2	no	—
320	C₄²×C₁₃₉	—	2	2	no	—
321	C₄²×C₁₃₉	—	2	2	no	—
322	C₄²×C₁₃₉	—	2	2	no	—
323	C₄²×C₁₃₉	—	2	4	no	—
324	C₄²×C₁₃₉	—	2	4	no	—
325	C₄²×C₁₃₉	—	2	2	no	—
326	C₄²×C₁₃₉	—	2	2	no	—
327	C₄²×C₁₃₉	—	2	2	no	—
328	C₄²×C₁₃₉	—	2	4	no	—
329	C₄²×C₁₃₉	—	2	4	no	—
330	C₄²×C₁₃₉	—	2	2	no	—
331	C₄²×C₁₃₉	—	4	1	no	—
332	C₄²×C₁₃₉	—	4	2	no	—
333	C₄²×C₁₃₉	—	4	2	no	—
334	C₄²×C₁₃₉	—	4	1	no	—
335	C₄²×C₁₃₉	#41	1	4	yes	—
336	C₂³×C₁₃₉	—	2	1	no	—
337	C₂³×C₁₃₉	—	2	1	no	—
338	C₂³×C₁₃₉	—	2	1	no	—
339	C₂³×C₁₃₉	—	2	1	no	—
340	C₂³×C₁₃₉	—	2	1	no	—
341	C₂³×C₁₃₉	—	2	1	no	—
342	C₂³×C₁₃₉	—	2	1	no	—
343	C₂³×C₁₃₉	—	2	1	no	—
344	C₂³×C₁₃₉	—	2	1	no	—
345	C₂³×C₁₃₉	—	2	1	no	—
346	C₂³×C₁₃₉	—	2	1	no	—
347	C₂³×C₁₃₉	—	2	1	no	—
348	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
350	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
351	D₄×C₁₃₉	—	2	8	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	1	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	1	no	—
363	C₂×C₄×C₁₃₉	—	2	1	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	8	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	1	no	—
371	C₂×C₄×C₁₃₉	—	2	1	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	1	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	1	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	1	no	—
393	C₂×C₄×C₁₃₉	—	2	2	no	—
394	C₂×C₄×C₁₃₉	—	2	2	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	1	no	—
397	C₂×C₄×C₁₃₉	—	2	1	no	—
398	C₂×C₄×C₁₃₉	—	2	1	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	2	no	—
401	C₂×C₄×C₁₃₉	—	2	2	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	2	no	—
404	C₂×C₄×C₁₃₉	—	2	1	no	—
405	C₂×C₄×C₁₃₉	—	4	4	no	—
406	C₂×C₄×C₁₃₉	—	4	4	no	—
407	C₂×C₄×C₁₃₉	—	4	4	no	—
408	C₂×C₄×C₁₃₉	—	4	4	no	—
409	C₂×C₄×C₁₃₉	—	4	4	no	—
410	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
411	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
412	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
413	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
414	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
415	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
416	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
417	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
418	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
419	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
420	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
421	C₂²×C₁₃₉	—	2	2	no	—
422	C₂²×C₁₃₉	—	2	2	no	—
423	C₂²×C₁₃₉	—	2	2	no	—
424	C₂²×C₁₃₉	—	2	2	no	—
425	C₂²×C₁₃₉	—	2	2	no	—
426	C₂²×C₁₃₉	—	2	2	no	—
427	C₂²×C₁₃₉	—	4	1	no	—
428	C₂²×C₁₃₉	—	4	1	no	—
429	C₂²×C₁₃₉	—	4	1	no	—
430	C₂²×C₁₃₉	—	4	1	no	—
431	C₂²×C₁₃₉	—	4	1	no	—
432	C₂²×C₁₃₉	—	4	1	no	—
433	C₂²×C₁₃₉	—	4	1	no	—
434	C₂²×C₁₃₉	—	4	1	no	—
435	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
439	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂²×C₁₃₉	#585	1	1	yes	characteristic
441	C₂²×C₁₃₉	#585	1	1	yes	characteristic
442	C₄×C₁₃₉	—	2	2	no	—
443	C₄×C₁₃₉	—	2	2	no	—
444	C₄×C₁₃₉	—	2	2	no	—
445	C₄×C₁₃₉	—	2	2	no	—
446	C₄×C₁₃₉	—	2	2	no	—
447	C₄×C₁₃₉	—	2	2	no	—
448	C₄×C₁₃₉	—	2	2	no	—
449	C₄×C₁₃₉	—	2	2	no	—
450	C₄×C₁₃₉	—	4	2	no	—
451	C₄×C₁₃₉	—	4	2	no	—
452	C₄×C₁₃₉	—	4	1	no	—
453	C₄×C₁₃₉	—	4	2	no	—
454	C₄×C₁₃₉	—	4	2	no	—
455	C₄×C₁₃₉	—	4	1	no	—
456	C₄×C₁₃₉	—	4	1	no	—
457	C₄×C₁₃₉	—	4	2	no	—
458	C₄×C₁₃₉	—	4	2	no	—
459	C₄×C₁₃₉	—	4	2	no	—
460	C₄×C₁₃₉	—	4	1	no	—
461	C₄×C₁₃₉	—	4	2	no	—
462	C₄×C₁₃₉	#552	1	4	yes	—
463	C₂×C₁₃₉	—	4	2	no	—
464	C₂×C₁₃₉	—	4	2	no	—
465	C₂×C₁₃₉	#3444	1	1	yes	characteristic
466	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
467	C₂×C₁₃₉	#3475	1	1	yes	characteristic
468	C₂×C₁₃₉	#3475	1	1	yes	characteristic
469	C₂×C₁₃₉	#3512	1	1	yes	characteristic
470	C₂×C₁₃₉	#3515	1	1	yes	characteristic
471	C₂×C₁₃₉	#3518	1	1	yes	characteristic
472	#36201	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
473	C₁₃₉	#36201	1	1	yes	characteristic, direct product factor, Sylow
474	#2864	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
476	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
477	#2577	C₂×C₁₃₉	1	2	yes	complemented
478	#2530	C₂×C₁₃₉	1	2	yes	complemented
479	#2524	C₂×C₁₃₉	1	2	yes	complemented
480	#2515	C₂×C₁₃₉	1	2	yes	complemented
481	#2507	C₂×C₁₃₉	1	1	yes	characteristic, complemented
482	#2506	C₂×C₁₃₉	1	1	yes	characteristic, complemented
483	#2497	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	#2496	C₂×C₁₃₉	1	1	yes	characteristic, complemented
485	#2485	C₂×C₁₃₉	1	1	yes	characteristic
486	#2485	C₂×C₁₃₉	1	1	yes	characteristic
487	#2468	C₂×C₁₃₉	1	2	yes	—
488	#2460	C₂×C₁₃₉	1	2	yes	—
489	#2373	C₂×C₁₃₉	1	2	yes	complemented
490	#2371	C₂×C₁₃₉	1	2	yes	complemented
491	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
492	#2346	C₂×C₁₃₉	1	1	yes	characteristic, complemented
493	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
494	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
495	#2283	C₂×C₁₃₉	1	1	yes	characteristic, complemented
496	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
497	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
498	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
499	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
500	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
503	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
504	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
505	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
506	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
507	#400	C₂²×C₁₃₉	1	2	yes	—
508	#400	C₂²×C₁₃₉	1	2	yes	—
509	#400	C₂²×C₁₃₉	1	2	yes	—
510	#398	C₂²×C₁₃₉	1	2	yes	—
511	#398	C₂²×C₁₃₉	1	2	yes	—
512	#398	C₂²×C₁₃₉	1	2	yes	—
513	#397	C₂²×C₁₃₉	1	2	yes	—
514	#397	C₂²×C₁₃₉	1	2	yes	—
515	#397	C₂²×C₁₃₉	1	2	yes	—
516	#396	C₂²×C₁₃₉	1	2	yes	—
517	#394	C₂²×C₁₃₉	1	2	yes	—
518	#394	C₂²×C₁₃₉	1	2	yes	—
519	#389	C₂²×C₁₃₉	1	1	yes	characteristic
520	#389	C₂²×C₁₃₉	1	1	yes	characteristic
521	#389	C₂²×C₁₃₉	1	1	yes	characteristic
522	#389	C₂²×C₁₃₉	1	1	yes	characteristic
523	#389	C₂²×C₁₃₉	1	1	yes	characteristic
524	#389	C₂²×C₁₃₉	1	1	yes	characteristic
525	#389	C₂²×C₁₃₉	1	1	yes	characteristic
526	#389	C₂²×C₁₃₉	1	1	yes	characteristic
527	#389	C₂²×C₁₃₉	1	1	yes	characteristic
528	#389	C₂²×C₁₃₉	1	1	yes	characteristic
529	#389	C₂²×C₁₃₉	1	2	yes	—
530	#388	C₂²×C₁₃₉	1	2	yes	—
531	#388	C₂²×C₁₃₉	1	2	yes	—
532	#388	C₂²×C₁₃₉	1	2	yes	—
533	#388	C₂²×C₁₃₉	1	2	yes	—
534	#388	C₂²×C₁₃₉	1	2	yes	—
535	#388	C₂²×C₁₃₉	1	2	yes	—
536	#388	C₂²×C₁₃₉	1	2	yes	—
537	#387	C₂²×C₁₃₉	1	2	yes	—
538	#387	C₂²×C₁₃₉	1	2	yes	—
539	#387	C₂²×C₁₃₉	1	2	yes	—
540	#387	C₂²×C₁₃₉	1	2	yes	—
541	#387	C₂²×C₁₃₉	1	2	yes	—
542	#387	C₂²×C₁₃₉	1	2	yes	—
543	#387	C₂²×C₁₃₉	1	2	yes	—
544	#387	C₂²×C₁₃₉	1	2	yes	—
545	#387	C₂²×C₁₃₉	1	2	yes	—
546	#387	C₂²×C₁₃₉	1	2	yes	—
547	#387	C₂²×C₁₃₉	1	2	yes	—
548	#387	C₂²×C₁₃₉	1	2	yes	—
549	#387	C₂²×C₁₃₉	1	2	yes	—
550	#387	C₂²×C₁₃₉	1	2	yes	—
551	#387	C₂²×C₁₃₉	1	2	yes	—
552	#387	C₂²×C₁₃₉	1	2	yes	—
553	#385	C₂²×C₁₃₉	1	2	yes	—
554	#385	C₂²×C₁₃₉	1	2	yes	—
555	#385	C₂²×C₁₃₉	1	2	yes	—
556	#385	C₂²×C₁₃₉	1	2	yes	—
557	#384	C₂²×C₁₃₉	1	1	yes	characteristic
558	#384	C₂²×C₁₃₉	1	1	yes	characteristic
559	#383	C₂²×C₁₃₉	1	2	yes	—
560	#383	C₂²×C₁₃₉	1	2	yes	—
561	#382	C₂²×C₁₃₉	1	1	yes	characteristic
562	#382	C₂²×C₁₃₉	1	1	yes	characteristic
563	#382	C₂²×C₁₃₉	1	1	yes	characteristic
564	#382	C₂²×C₁₃₉	1	2	yes	—
565	#381	C₂²×C₁₃₉	1	2	yes	—
566	#380	C₂²×C₁₃₉	1	2	yes	—
567	#380	C₂²×C₁₃₉	1	1	yes	characteristic
568	#380	C₂²×C₁₃₉	1	1	yes	characteristic
569	#380	C₂²×C₁₃₉	1	1	yes	characteristic
570	#380	C₂²×C₁₃₉	1	1	yes	characteristic
571	#380	C₂²×C₁₃₉	1	2	yes	—
572	#380	C₂²×C₁₃₉	1	1	yes	characteristic
573	#380	C₂²×C₁₃₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
575	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
578	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
580	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
584	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
586	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
588	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
590	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
592	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
593	#376	C₂²×C₁₃₉	1	2	yes	—
594	#376	C₂²×C₁₃₉	1	2	yes	—
595	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
603	#126	—	2	8	no	—
604	#125	—	2	8	no	—
605	#125	—	2	4	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	4	no	—
609	#117	—	2	4	no	—
610	#117	—	2	4	no	—
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
652	C₂×C₄²	—	2	4	no	—
653	C₂×C₄²	—	2	4	no	—
654	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
656	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
660	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
661	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
671	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
672	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
673	#95	C₂³×C₁₃₉	1	1	yes	characteristic
674	#95	C₂³×C₁₃₉	1	2	yes	—
675	#95	C₂³×C₁₃₉	1	2	yes	—
676	#95	C₂³×C₁₃₉	1	2	yes	—
677	#95	C₂³×C₁₃₉	1	2	yes	—
678	#95	C₂³×C₁₃₉	1	2	yes	—
679	#95	C₂³×C₁₃₉	1	2	yes	—
680	#95	C₂³×C₁₃₉	1	2	yes	—
681	#95	C₂³×C₁₃₉	1	1	yes	characteristic
682	#95	C₂³×C₁₃₉	1	1	yes	characteristic
683	#95	C₂³×C₁₃₉	1	1	yes	characteristic
684	#95	C₂³×C₁₃₉	1	1	yes	characteristic
685	#95	C₂³×C₁₃₉	1	1	yes	characteristic
686	#95	C₂³×C₁₃₉	1	2	yes	—
687	#95	C₂³×C₁₃₉	1	2	yes	—
688	#95	C₂³×C₁₃₉	1	2	yes	—
689	#95	C₂³×C₁₃₉	1	2	yes	—
690	#95	C₂³×C₁₃₉	1	2	yes	—
691	#95	C₂³×C₁₃₉	1	2	yes	—
692	#95	C₂³×C₁₃₉	1	2	yes	—
693	#95	C₂³×C₁₃₉	1	2	yes	—
694	#95	C₂³×C₁₃₉	1	2	yes	—
695	#95	C₂³×C₁₃₉	1	2	yes	—
696	#95	C₂³×C₁₃₉	1	2	yes	—
697	#95	C₂³×C₁₃₉	1	2	yes	—
698	#95	C₂³×C₁₃₉	1	2	yes	—
699	#95	C₂³×C₁₃₉	1	2	yes	—
700	#95	C₂³×C₁₃₉	1	2	yes	—
701	#95	C₂³×C₁₃₉	1	2	yes	—
702	#95	C₂³×C₁₃₉	1	2	yes	—
703	#95	C₂³×C₁₃₉	1	2	yes	—
704	#95	C₂³×C₁₃₉	1	2	yes	—
705	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
706	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	4	1	no	—
724	C₂²×C₄	—	4	1	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
728	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	4	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	4	no	—
802	C₄²	—	2	4	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	4	1	no	—
805	C₄²	—	4	2	no	—
806	C₄²	—	4	2	no	—
807	C₄²	—	4	1	no	—
808	C₄²	#41×C₁₃₉	1	4	yes	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
822	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
823	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
824	D₄	—	2	8	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
884	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
885	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
886	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
887	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
888	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
889	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
890	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
891	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
892	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
893	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
909	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
910	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
911	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
912	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
913	C₂²	#585×C₁₃₉	1	1	yes	characteristic
914	C₂²	#585×C₁₃₉	1	1	yes	characteristic
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	2	no	—
935	C₄	#552×C₁₃₉	1	4	yes	—
936	C₂	—	4	2	no	—
937	C₂	—	4	2	no	—
938	C₂	#3444×C₁₃₉	1	1	yes	characteristic
939	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic
940	C₂	#3475×C₁₃₉	1	1	yes	characteristic
941	C₂	#3475×C₁₃₉	1	1	yes	characteristic
942	C₂	#3512×C₁₃₉	1	1	yes	characteristic
943	C₂	#3515×C₁₃₉	1	1	yes	characteristic
944	C₂	#3518×C₁₃₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #2864×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
3. #2851×C₁₃₉	C₂	semidirect
4. #2577×C₁₃₉	C₂	semidirect
5. #2530×C₁₃₉	C₂	semidirect
6. #2524×C₁₃₉	C₂	semidirect
7. #2515×C₁₃₉	C₂	semidirect
8. #2507×C₁₃₉	C₂	semidirect
9. #2506×C₁₃₉	C₂	semidirect
10. #2497×C₁₃₉	C₂	semidirect
11. #2496×C₁₃₉	C₂	semidirect
16. #2373×C₁₃₉	C₂	semidirect
17. #2371×C₁₃₉	C₂	semidirect
18. #2347×C₁₃₉	C₂	semidirect
19. #2346×C₁₃₉	C₂	semidirect
20. C₄×#125×C₁₃₉	C₂	semidirect
21. #2285×C₁₃₉	C₂	semidirect
22. #2283×C₁₃₉	C₂	semidirect
472. #36201	C₁₃₉	direct (N × H)
473. C₁₃₉	#36201	direct (N × H)
474. #2864	C₂×C₁₃₉	semidirect
475. #2851	C₂×C₁₃₉	semidirect
476. #2851	C₂×C₁₃₉	semidirect
477. #2577	C₂×C₁₃₉	semidirect
478. #2530	C₂×C₁₃₉	semidirect
479. #2524	C₂×C₁₃₉	semidirect
480. #2515	C₂×C₁₃₉	semidirect
481. #2507	C₂×C₁₃₉	semidirect
482. #2506	C₂×C₁₃₉	semidirect
483. #2497	C₂×C₁₃₉	semidirect
484. #2496	C₂×C₁₃₉	semidirect
489. #2373	C₂×C₁₃₉	semidirect
490. #2371	C₂×C₁₃₉	semidirect
491. #2347	C₂×C₁₃₉	semidirect
492. #2346	C₂×C₁₃₉	semidirect
493. C₄×#125	C₂×C₁₃₉	semidirect
494. #2285	C₂×C₁₃₉	semidirect
495. #2283	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2864×C₁₃₉	2
#2851×C₁₃₉	2
#2577×C₁₃₉	2
#2530×C₁₃₉	2
#2524×C₁₃₉	2
#2515×C₁₃₉	2
#2507×C₁₃₉	2
#2506×C₁₃₉	2
#2497×C₁₃₉	2
#2496×C₁₃₉	2
#2485×C₁₃₉	2
#2468×C₁₃₉	2
#2460×C₁₃₉	2
#2373×C₁₃₉	2
#2371×C₁₃₉	2
#2347×C₁₃₉	2
#2346×C₁₃₉	2
C₄×#125×C₁₃₉	2
#2285×C₁₃₉	2
#2283×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36201	139

Subgroups — C139×#36201 #48030797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36201 #48030797