Subgroups — C₁₃₉×#36145 #48030741

Order 35584.

2326 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2549×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2543×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2521×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2479×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2478×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2462×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2461×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2443×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2364×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#529×C₁₃₉	—	2	16	no	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
42	#399×C₁₃₉	C₂²	1	2	yes	—
43	#399×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	1	yes	characteristic
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#397×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	1	yes	characteristic
50	#396×C₁₃₉	C₂²	1	2	yes	—
51	#395×C₁₃₉	C₂²	1	2	yes	—
52	#395×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	1	yes	characteristic
55	#392×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#390×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×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	#386×C₁₃₉	C₂²	1	2	yes	—
81	#386×C₁₃₉	C₂²	1	2	yes	—
82	#386×C₁₃₉	C₂²	1	1	yes	characteristic
83	#386×C₁₃₉	C₂²	1	2	yes	—
84	#386×C₁₃₉	C₂²	1	2	yes	—
85	#386×C₁₃₉	C₂²	1	2	yes	—
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#385×C₁₃₉	C₂²	1	1	yes	characteristic
88	#385×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#382×C₁₃₉	C₂²	1	1	yes	characteristic
93	#381×C₁₃₉	C₂²	1	1	yes	characteristic
94	#380×C₁₃₉	C₂²	1	1	yes	characteristic
95	#380×C₁₃₉	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	#126×C₁₃₉	—	2	8	no	—
122	#126×C₁₃₉	—	2	8	no	—
123	#125×C₁₃₉	—	2	8	no	—
124	#124×C₁₃₉	—	2	8	no	—
125	#123×C₁₃₉	—	2	8	no	—
126	#123×C₁₃₉	—	2	8	no	—
127	#123×C₁₃₉	D₄	1	8	yes	complemented
128	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
129	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
130	#121×C₁₃₉	—	2	8	no	—
131	#121×C₁₃₉	—	2	4	no	—
132	C₄×Q₈×C₁₃₉	—	2	8	no	—
133	C₄×D₄×C₁₃₉	—	2	8	no	—
134	C₄×D₄×C₁₃₉	—	2	4	no	—
135	C₄×D₄×C₁₃₉	—	2	8	no	—
136	C₄×D₄×C₁₃₉	—	2	8	no	—
137	#117×C₁₃₉	—	2	8	no	—
138	#117×C₁₃₉	—	2	8	no	—
139	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	—	2	8	no	—
182	C₂×C₄²×C₁₃₉	—	2	4	no	—
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	1	yes	characteristic
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂×Q₈×C₁₃₉	—	2	4	no	—
220	C₂×Q₈×C₁₃₉	—	2	4	no	—
221	C₂×Q₈×C₁₃₉	—	4	2	no	—
222	C₂×D₄×C₁₃₉	—	2	2	no	—
223	C₂×D₄×C₁₃₉	—	2	2	no	—
224	C₂×D₄×C₁₃₉	—	2	4	no	—
225	C₂×D₄×C₁₃₉	—	2	4	no	—
226	C₂×D₄×C₁₃₉	—	2	4	no	—
227	C₂×D₄×C₁₃₉	—	2	4	no	—
228	C₂×D₄×C₁₃₉	—	2	4	no	—
229	C₂×D₄×C₁₃₉	—	2	2	no	—
230	C₂×D₄×C₁₃₉	—	4	2	no	—
231	C₂×D₄×C₁₃₉	—	4	2	no	—
232	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₃₉	—	2	2	no	—
234	C₂²×C₄×C₁₃₉	—	2	2	no	—
235	C₂²×C₄×C₁₃₉	—	2	2	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	4	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	2	4	no	—
240	C₂²×C₄×C₁₃₉	—	2	4	no	—
241	C₂²×C₄×C₁₃₉	—	2	4	no	—
242	C₂²×C₄×C₁₃₉	—	2	4	no	—
243	C₂²×C₄×C₁₃₉	—	2	4	no	—
244	C₂²×C₄×C₁₃₉	—	2	4	no	—
245	C₂²×C₄×C₁₃₉	—	2	2	no	—
246	C₂²×C₄×C₁₃₉	—	4	2	no	—
247	C₂²×C₄×C₁₃₉	—	4	2	no	—
248	C₂²×C₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	4	2	no	—
250	C₂²×C₄×C₁₃₉	—	4	2	no	—
251	C₂²×C₄×C₁₃₉	—	4	2	no	—
252	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
253	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	2	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	no	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	2	4	no	—
275	C₄⋊C₄×C₁₃₉	—	2	4	no	—
276	C₄⋊C₄×C₁₃₉	—	2	4	no	—
277	C₄⋊C₄×C₁₃₉	—	2	4	no	—
278	C₄⋊C₄×C₁₃₉	—	2	4	no	—
279	C₄⋊C₄×C₁₃₉	—	2	4	no	—
280	C₄⋊C₄×C₁₃₉	—	2	4	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	2	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	—	4	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
290	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
296	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
310	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
311	C₄²×C₁₃₉	—	2	4	no	—
312	C₄²×C₁₃₉	—	2	4	no	—
313	C₄²×C₁₃₉	—	2	4	no	—
314	C₄²×C₁₃₉	—	2	4	no	—
315	C₄²×C₁₃₉	—	2	4	no	—
316	C₄²×C₁₃₉	—	2	4	no	—
317	C₄²×C₁₃₉	—	2	4	no	—
318	C₄²×C₁₃₉	—	2	4	no	—
319	C₄²×C₁₃₉	—	2	2	no	—
320	C₄²×C₁₃₉	—	4	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	1	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	1	no	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
335	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
336	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
337	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
338	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
339	Q₈×C₁₃₉	—	4	8	no	—
340	D₄×C₁₃₉	—	2	8	no	—
341	D₄×C₁₃₉	—	4	8	no	—
342	D₄×C₁₃₉	—	4	8	no	—
343	D₄×C₁₃₉	—	8	2	no	—
344	C₂×C₄×C₁₃₉	—	2	8	no	—
345	C₂×C₄×C₁₃₉	—	2	8	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	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	—	4	4	no	—
383	C₂×C₄×C₁₃₉	—	4	8	no	—
384	C₂×C₄×C₁₃₉	—	4	8	no	—
385	C₂×C₄×C₁₃₉	—	4	8	no	—
386	C₂×C₄×C₁₃₉	—	4	8	no	—
387	C₂×C₄×C₁₃₉	—	8	2	no	—
388	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
389	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
391	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
392	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
393	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
394	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
395	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
396	C₂²×C₁₃₉	—	2	2	no	—
397	C₂²×C₁₃₉	—	2	4	no	—
398	C₂²×C₁₃₉	—	2	2	no	—
399	C₂²×C₁₃₉	—	2	4	no	—
400	C₂²×C₁₃₉	—	2	2	no	—
401	C₂²×C₁₃₉	—	2	4	no	—
402	C₂²×C₁₃₉	—	4	1	no	—
403	C₂²×C₁₃₉	—	4	1	no	—
404	C₂²×C₁₃₉	—	4	2	no	—
405	C₂²×C₁₃₉	—	4	2	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	—	4	2	no	—
409	C₂²×C₁₃₉	—	4	2	no	—
410	C₂²×C₁₃₉	—	4	2	no	—
411	C₂²×C₁₃₉	—	4	2	no	—
412	C₂²×C₁₃₉	#547	1	4	yes	—
413	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
414	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
415	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
416	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂²×C₁₃₉	#585	1	2	yes	—
418	C₄×C₁₃₉	—	2	4	no	—
419	C₄×C₁₃₉	—	2	4	no	—
420	C₄×C₁₃₉	—	2	2	no	—
421	C₄×C₁₃₉	—	2	4	no	—
422	C₄×C₁₃₉	—	2	4	no	—
423	C₄×C₁₃₉	—	2	4	no	—
424	C₄×C₁₃₉	—	2	2	no	—
425	C₄×C₁₃₉	—	2	2	no	—
426	C₄×C₁₃₉	—	4	1	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	—	4	2	no	—
430	C₄×C₁₃₉	—	4	2	no	—
431	C₄×C₁₃₉	—	4	2	no	—
432	C₄×C₁₃₉	—	4	1	no	—
433	C₄×C₁₃₉	—	4	2	no	—
434	C₂×C₁₃₉	—	2	4	no	—
435	C₂×C₁₃₉	—	4	2	no	—
436	C₂×C₁₃₉	—	8	2	no	—
437	C₂×C₁₃₉	#3444	1	1	yes	characteristic
438	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
439	C₂×C₁₃₉	D₄×#41	1	2	yes	—
440	C₂×C₁₃₉	#3491	1	1	yes	characteristic
441	C₂×C₁₃₉	#3516	1	2	yes	—
442	#36145	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
443	C₁₃₉	#36145	1	1	yes	characteristic, direct product factor, Sylow
444	C₂×#529	C₂×C₁₃₉	1	2	yes	complemented
445	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2853	C₂×C₁₃₉	1	2	yes	complemented
447	#2549	C₂×C₁₃₉	1	1	yes	characteristic, complemented
448	#2543	C₂×C₁₃₉	1	1	yes	characteristic
449	#2521	C₂×C₁₃₉	1	2	yes	complemented
450	#2519	C₂×C₁₃₉	1	2	yes	complemented
451	#2479	C₂×C₁₃₉	1	2	yes	complemented
452	#2478	C₂×C₁₃₉	1	2	yes	complemented
453	#2462	C₂×C₁₃₉	1	2	yes	complemented
454	#2461	C₂×C₁₃₉	1	2	yes	complemented
455	#2449	C₂×C₁₃₉	1	2	yes	complemented
456	#2443	C₂×C₁₃₉	1	2	yes	complemented
457	#2364	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	#2362	C₂×C₁₃₉	1	2	yes	complemented
459	#2359	C₂×C₁₃₉	1	2	yes	complemented
460	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
461	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
462	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
463	#529	—	2	16	no	—
464	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
465	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
466	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
467	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
469	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
470	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
472	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
473	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
474	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
475	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
476	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
477	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
478	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
480	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
481	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
482	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
483	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
484	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
485	#399	C₂²×C₁₃₉	1	2	yes	—
486	#399	C₂²×C₁₃₉	1	2	yes	—
487	#398	C₂²×C₁₃₉	1	2	yes	—
488	#398	C₂²×C₁₃₉	1	2	yes	—
489	#398	C₂²×C₁₃₉	1	1	yes	characteristic
490	#398	C₂²×C₁₃₉	1	2	yes	—
491	#397	C₂²×C₁₃₉	1	2	yes	—
492	#397	C₂²×C₁₃₉	1	1	yes	characteristic
493	#396	C₂²×C₁₃₉	1	2	yes	—
494	#395	C₂²×C₁₃₉	1	2	yes	—
495	#395	C₂²×C₁₃₉	1	2	yes	—
496	#394	C₂²×C₁₃₉	1	2	yes	—
497	#394	C₂²×C₁₃₉	1	1	yes	characteristic
498	#392	C₂²×C₁₃₉	1	1	yes	characteristic
499	#391	C₂²×C₁₃₉	1	2	yes	—
500	#390	C₂²×C₁₃₉	1	2	yes	—
501	#389	C₂²×C₁₃₉	1	2	yes	—
502	#389	C₂²×C₁₃₉	1	2	yes	—
503	#389	C₂²×C₁₃₉	1	2	yes	—
504	#389	C₂²×C₁₃₉	1	2	yes	—
505	#388	C₂²×C₁₃₉	1	2	yes	—
506	#388	C₂²×C₁₃₉	1	2	yes	—
507	#388	C₂²×C₁₃₉	1	2	yes	—
508	#388	C₂²×C₁₃₉	1	2	yes	—
509	#388	C₂²×C₁₃₉	1	2	yes	—
510	#388	C₂²×C₁₃₉	1	2	yes	—
511	#388	C₂²×C₁₃₉	1	2	yes	—
512	#388	C₂²×C₁₃₉	1	2	yes	—
513	#388	C₂²×C₁₃₉	1	2	yes	—
514	#388	C₂²×C₁₃₉	1	2	yes	—
515	#387	C₂²×C₁₃₉	1	2	yes	—
516	#387	C₂²×C₁₃₉	1	2	yes	—
517	#387	C₂²×C₁₃₉	1	2	yes	—
518	#387	C₂²×C₁₃₉	1	2	yes	—
519	#387	C₂²×C₁₃₉	1	2	yes	—
520	#387	C₂²×C₁₃₉	1	2	yes	—
521	#387	C₂²×C₁₃₉	1	2	yes	—
522	#387	C₂²×C₁₃₉	1	2	yes	—
523	#386	C₂²×C₁₃₉	1	2	yes	—
524	#386	C₂²×C₁₃₉	1	2	yes	—
525	#386	C₂²×C₁₃₉	1	2	yes	—
526	#386	C₂²×C₁₃₉	1	2	yes	—
527	#386	C₂²×C₁₃₉	1	2	yes	—
528	#386	C₂²×C₁₃₉	1	1	yes	characteristic
529	#385	C₂²×C₁₃₉	1	2	yes	—
530	#385	C₂²×C₁₃₉	1	2	yes	—
531	#385	C₂²×C₁₃₉	1	2	yes	—
532	#385	C₂²×C₁₃₉	1	2	yes	—
533	#385	C₂²×C₁₃₉	1	2	yes	—
534	#385	C₂²×C₁₃₉	1	1	yes	characteristic
535	#382	C₂²×C₁₃₉	1	1	yes	characteristic
536	#381	C₂²×C₁₃₉	1	1	yes	characteristic
537	#380	C₂²×C₁₃₉	1	1	yes	characteristic
538	#380	C₂²×C₁₃₉	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
542	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
543	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
544	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
548	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
549	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
550	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
552	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
564	#126	—	2	8	no	—
565	#126	—	2	8	no	—
566	#125	—	2	8	no	—
567	#124	—	2	8	no	—
568	#123	—	2	8	no	—
569	#123	—	2	8	no	—
570	#123	D₄×C₁₃₉	1	8	yes	complemented
571	C₂²⋊Q₈	—	2	8	no	—
572	C₂²⋊Q₈	—	2	8	no	—
573	#121	—	2	8	no	—
574	#121	—	2	4	no	—
575	C₄×Q₈	—	2	8	no	—
576	C₄×D₄	—	2	8	no	—
577	C₄×D₄	—	2	4	no	—
578	C₄×D₄	—	2	8	no	—
579	C₄×D₄	—	2	8	no	—
580	#117	—	2	8	no	—
581	#117	—	2	8	no	—
582	C₂×C₄⋊C₄	—	2	8	no	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄²	—	2	8	no	—
625	C₂×C₄²	—	2	4	no	—
626	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
636	#95	C₂³×C₁₃₉	1	1	yes	characteristic
637	#95	C₂³×C₁₃₉	1	1	yes	characteristic
638	#95	C₂³×C₁₃₉	1	2	yes	—
639	#95	C₂³×C₁₃₉	1	2	yes	—
640	#95	C₂³×C₁₃₉	1	1	yes	characteristic
641	#95	C₂³×C₁₃₉	1	1	yes	characteristic
642	#95	C₂³×C₁₃₉	1	1	yes	characteristic
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	2	yes	—
646	#95	C₂³×C₁₃₉	1	2	yes	—
647	#95	C₂³×C₁₃₉	1	2	yes	—
648	#95	C₂³×C₁₃₉	1	1	yes	characteristic
649	#95	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
660	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
661	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
662	C₂×Q₈	—	2	4	no	—
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
696	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
697	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
733	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
753	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	4	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
778	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
779	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
780	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
781	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
782	Q₈	—	4	8	no	—
783	D₄	—	2	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	8	no	—
786	D₄	—	8	2	no	—
787	C₂×C₄	—	2	8	no	—
788	C₂×C₄	—	2	8	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	8	no	—
827	C₂×C₄	—	4	8	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
832	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
834	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
835	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
836	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
837	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
838	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	#547×C₁₃₉	1	4	yes	—
856	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
857	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
858	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
859	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
860	C₂²	#585×C₁₃₉	1	2	yes	—
861	C₄	—	2	4	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	4	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₂	—	2	4	no	—
878	C₂	—	4	2	no	—
879	C₂	—	8	2	no	—
880	C₂	#3444×C₁₃₉	1	1	yes	characteristic
881	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
882	C₂	D₄×#41×C₁₃₉	1	2	yes	—
883	C₂	#3491×C₁₃₉	1	1	yes	characteristic
884	C₂	#3516×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2543×C₁₃₉	C₂
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. C₂×#529×C₁₃₉	C₂	semidirect
2. #2854×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2549×C₁₃₉	C₂	semidirect
6. #2521×C₁₃₉	C₂	semidirect
7. #2519×C₁₃₉	C₂	semidirect
8. #2479×C₁₃₉	C₂	semidirect
9. #2478×C₁₃₉	C₂	semidirect
10. #2462×C₁₃₉	C₂	semidirect
11. #2461×C₁₃₉	C₂	semidirect
12. #2449×C₁₃₉	C₂	semidirect
13. #2443×C₁₃₉	C₂	semidirect
14. #2364×C₁₃₉	C₂	semidirect
15. #2362×C₁₃₉	C₂	semidirect
16. #2359×C₁₃₉	C₂	semidirect
17. #2349×C₁₃₉	C₂	semidirect
18. C₄×#123×C₁₃₉	C₂	semidirect
19. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
127. #123×C₁₃₉	D₄	semidirect
442. #36145	C₁₃₉	direct (N × H)
443. C₁₃₉	#36145	direct (N × H)
444. C₂×#529	C₂×C₁₃₉	semidirect
445. #2854	C₂×C₁₃₉	semidirect
446. #2853	C₂×C₁₃₉	semidirect
447. #2549	C₂×C₁₃₉	semidirect
449. #2521	C₂×C₁₃₉	semidirect
450. #2519	C₂×C₁₃₉	semidirect
451. #2479	C₂×C₁₃₉	semidirect
452. #2478	C₂×C₁₃₉	semidirect
453. #2462	C₂×C₁₃₉	semidirect
454. #2461	C₂×C₁₃₉	semidirect
455. #2449	C₂×C₁₃₉	semidirect
456. #2443	C₂×C₁₃₉	semidirect
457. #2364	C₂×C₁₃₉	semidirect
458. #2362	C₂×C₁₃₉	semidirect
459. #2359	C₂×C₁₃₉	semidirect
460. #2349	C₂×C₁₃₉	semidirect
461. C₄×#123	C₂×C₁₃₉	semidirect
462. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
570. #123	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₃₉	2
#2854×C₁₃₉	2
#2853×C₁₃₉	2
#2549×C₁₃₉	2
#2543×C₁₃₉	2
#2521×C₁₃₉	2
#2519×C₁₃₉	2
#2479×C₁₃₉	2
#2478×C₁₃₉	2
#2462×C₁₃₉	2
#2461×C₁₃₉	2
#2449×C₁₃₉	2
#2443×C₁₃₉	2
#2364×C₁₃₉	2
#2362×C₁₃₉	2
#2359×C₁₃₉	2
#2349×C₁₃₉	2
C₄×#123×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#36145	139

Subgroups — C139×#36145 #48030741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36145 #48030741