Subgroups — C₁₃₉×#36086 #48030682

Order 35584.

2234 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2637×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2634×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2614×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2604×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2599×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2581×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2498×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	#2484×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2469×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2462×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2462×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2438×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2413×C₁₃₉	C₂	1	2	yes	maximal
18	#2399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2396×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2359×C₁₃₉	C₂	1	2	yes	maximal
22	#2344×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	#2343×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	#552×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	#519×C₁₃₉	—	2	8	no	—
37	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
48	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	#400×C₁₃₉	C₂²	1	1	yes	characteristic
54	#400×C₁₃₉	C₂²	1	1	yes	characteristic
55	#400×C₁₃₉	C₂²	1	1	yes	characteristic
56	#400×C₁₃₉	C₂²	1	2	yes	—
57	#399×C₁₃₉	C₂²	1	1	yes	characteristic
58	#398×C₁₃₉	C₂²	1	1	yes	characteristic
59	#398×C₁₃₉	C₂²	1	1	yes	characteristic
60	#398×C₁₃₉	C₂²	1	1	yes	characteristic
61	#398×C₁₃₉	C₂²	1	2	yes	—
62	#398×C₁₃₉	C₂²	1	2	yes	—
63	#398×C₁₃₉	C₂²	1	2	yes	—
64	#398×C₁₃₉	C₂²	1	2	yes	—
65	#397×C₁₃₉	C₂²	1	1	yes	characteristic
66	#396×C₁₃₉	C₂²	1	2	yes	—
67	#396×C₁₃₉	C₂²	1	2	yes	—
68	#395×C₁₃₉	C₂²	1	1	yes	characteristic
69	#395×C₁₃₉	C₂²	1	1	yes	characteristic
70	#395×C₁₃₉	C₂²	1	1	yes	characteristic
71	#395×C₁₃₉	C₂²	1	1	yes	characteristic
72	#395×C₁₃₉	C₂²	1	2	yes	—
73	#395×C₁₃₉	C₂²	1	1	yes	characteristic
74	#395×C₁₃₉	C₂²	1	1	yes	characteristic
75	#395×C₁₃₉	C₂²	1	2	yes	—
76	#395×C₁₃₉	C₂²	1	2	yes	—
77	#395×C₁₃₉	C₂²	1	2	yes	—
78	#393×C₁₃₉	C₂²	1	1	yes	characteristic
79	#393×C₁₃₉	C₂²	1	1	yes	characteristic
80	#393×C₁₃₉	C₂²	1	2	yes	—
81	#391×C₁₃₉	C₂²	1	2	yes	—
82	#389×C₁₃₉	C₂²	1	2	yes	—
83	#389×C₁₃₉	C₂²	1	2	yes	—
84	#389×C₁₃₉	C₂²	1	2	yes	—
85	#389×C₁₃₉	C₂²	1	2	yes	—
86	#389×C₁₃₉	C₂²	1	2	yes	—
87	#389×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	2	yes	—
89	#388×C₁₃₉	C₂²	1	2	yes	—
90	#388×C₁₃₉	C₂²	1	2	yes	—
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	—
96	#387×C₁₃₉	C₂²	1	2	yes	—
97	#387×C₁₃₉	C₂²	1	2	yes	—
98	#387×C₁₃₉	C₂²	1	2	yes	—
99	#387×C₁₃₉	C₂²	1	2	yes	—
100	#387×C₁₃₉	C₂²	1	2	yes	—
101	#387×C₁₃₉	C₂²	1	2	yes	—
102	#387×C₁₃₉	C₂²	1	2	yes	—
103	#387×C₁₃₉	C₂²	1	2	yes	—
104	#387×C₁₃₉	C₂²	1	2	yes	—
105	#387×C₁₃₉	C₂²	1	2	yes	—
106	#386×C₁₃₉	C₂²	1	2	yes	—
107	#385×C₁₃₉	C₂²	1	2	yes	—
108	#385×C₁₃₉	C₂²	1	2	yes	—
109	#385×C₁₃₉	C₂²	1	2	yes	—
110	#383×C₁₃₉	C₂²	1	1	yes	characteristic
111	#382×C₁₃₉	C₂²	1	1	yes	characteristic
112	#381×C₁₃₉	C₂²	1	1	yes	characteristic
113	#381×C₁₃₉	C₂²	1	2	yes	—
114	#381×C₁₃₉	C₂²	1	2	yes	—
115	#380×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
122	#376×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
125	C₂²×Q₈×C₁₃₉	—	2	4	no	—
126	C₂²×Q₈×C₁₃₉	—	2	8	no	—
127	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
130	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	#126×C₁₃₉	—	2	4	no	—
139	#126×C₁₃₉	—	2	4	no	—
140	#125×C₁₃₉	—	2	4	no	—
141	#125×C₁₃₉	—	2	4	no	—
142	#125×C₁₃₉	—	2	4	no	—
143	#123×C₁₃₉	—	2	4	no	—
144	#123×C₁₃₉	—	2	8	no	—
145	#123×C₁₃₉	—	2	4	no	—
146	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
147	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
148	C₄×Q₈×C₁₃₉	—	2	8	no	—
149	C₄×Q₈×C₁₃₉	—	2	8	no	—
150	C₄×Q₈×C₁₃₉	—	2	4	no	—
151	C₄×Q₈×C₁₃₉	—	2	4	no	—
152	C₄×Q₈×C₁₃₉	—	2	4	no	—
153	C₄×Q₈×C₁₃₉	—	2	4	no	—
154	C₄×Q₈×C₁₃₉	—	2	4	no	—
155	C₄×D₄×C₁₃₉	—	2	4	no	—
156	#117×C₁₃₉	—	2	4	no	—
157	#117×C₁₃₉	—	2	8	no	—
158	#117×C₁₃₉	—	2	8	no	—
159	#117×C₁₃₉	—	2	4	no	—
160	#117×C₁₃₉	—	2	4	no	—
161	#117×C₁₃₉	D₄	1	8	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
163	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	#95×C₁₃₉	C₂³	1	2	yes	—
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	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	1	yes	characteristic
234	#95×C₁₃₉	C₂³	1	1	yes	characteristic
235	#95×C₁₃₉	C₂³	1	2	yes	—
236	#95×C₁₃₉	C₂³	1	2	yes	—
237	#95×C₁₃₉	C₂³	1	2	yes	—
238	#95×C₁₃₉	C₂³	1	2	yes	—
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	2	yes	—
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂×Q₈×C₁₃₉	—	2	32	no	—
255	C₂×Q₈×C₁₃₉	—	2	4	no	—
256	C₂×Q₈×C₁₃₉	—	2	2	no	—
257	C₂×Q₈×C₁₃₉	—	2	2	no	—
258	C₂×Q₈×C₁₃₉	—	2	2	no	—
259	C₂×Q₈×C₁₃₉	—	2	4	no	—
260	C₂×Q₈×C₁₃₉	—	2	4	no	—
261	C₂×Q₈×C₁₃₉	—	2	4	no	—
262	C₂×Q₈×C₁₃₉	—	2	4	no	—
263	C₂×Q₈×C₁₃₉	—	2	2	no	—
264	C₂×Q₈×C₁₃₉	—	4	1	no	—
265	C₂×D₄×C₁₃₉	—	2	2	no	—
266	C₂×D₄×C₁₃₉	—	2	4	no	—
267	C₂²×C₄×C₁₃₉	—	2	4	no	—
268	C₂²×C₄×C₁₃₉	—	2	4	no	—
269	C₂²×C₄×C₁₃₉	—	2	4	no	—
270	C₂²×C₄×C₁₃₉	—	2	2	no	—
271	C₂²×C₄×C₁₃₉	—	2	2	no	—
272	C₂²×C₄×C₁₃₉	—	2	4	no	—
273	C₂²×C₄×C₁₃₉	—	2	4	no	—
274	C₂²×C₄×C₁₃₉	—	2	2	no	—
275	C₂²×C₄×C₁₃₉	—	2	2	no	—
276	C₂²×C₄×C₁₃₉	—	2	4	no	—
277	C₂²×C₄×C₁₃₉	—	2	2	no	—
278	C₂²×C₄×C₁₃₉	—	4	1	no	—
279	C₂²×C₄×C₁₃₉	—	4	2	no	—
280	C₂²×C₄×C₁₃₉	—	4	1	no	—
281	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
282	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
283	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₁₃₉	—	2	2	no	—
305	C₄⋊C₄×C₁₃₉	—	2	2	no	—
306	C₄⋊C₄×C₁₃₉	—	2	2	no	—
307	C₄⋊C₄×C₁₃₉	—	2	2	no	—
308	C₄⋊C₄×C₁₃₉	—	2	4	no	—
309	C₄⋊C₄×C₁₃₉	—	2	4	no	—
310	C₄⋊C₄×C₁₃₉	—	2	4	no	—
311	C₄⋊C₄×C₁₃₉	—	2	4	no	—
312	C₄⋊C₄×C₁₃₉	—	2	2	no	—
313	C₄⋊C₄×C₁₃₉	—	2	2	no	—
314	C₄⋊C₄×C₁₃₉	—	2	2	no	—
315	C₄⋊C₄×C₁₃₉	—	2	2	no	—
316	C₄⋊C₄×C₁₃₉	—	2	2	no	—
317	C₄⋊C₄×C₁₃₉	—	2	2	no	—
318	C₄⋊C₄×C₁₃₉	—	2	2	no	—
319	C₄⋊C₄×C₁₃₉	—	2	2	no	—
320	C₄⋊C₄×C₁₃₉	—	2	2	no	—
321	C₄⋊C₄×C₁₃₉	—	2	2	no	—
322	C₄⋊C₄×C₁₃₉	—	2	2	no	—
323	C₄⋊C₄×C₁₃₉	—	2	2	no	—
324	C₄⋊C₄×C₁₃₉	—	2	4	no	—
325	C₄⋊C₄×C₁₃₉	—	2	4	no	—
326	C₄⋊C₄×C₁₃₉	—	2	4	no	—
327	C₄⋊C₄×C₁₃₉	—	2	4	no	—
328	C₄⋊C₄×C₁₃₉	—	2	4	no	—
329	C₄⋊C₄×C₁₃₉	—	2	4	no	—
330	C₄⋊C₄×C₁₃₉	—	2	4	no	—
331	C₄⋊C₄×C₁₃₉	—	2	4	no	—
332	C₄⋊C₄×C₁₃₉	—	2	4	no	—
333	C₄⋊C₄×C₁₃₉	—	4	2	no	—
334	C₄⋊C₄×C₁₃₉	—	4	2	no	—
335	C₄⋊C₄×C₁₃₉	—	4	2	no	—
336	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
337	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
338	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
339	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
340	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
341	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
347	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
348	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
349	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
350	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
351	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
352	C₄²×C₁₃₉	—	2	2	no	—
353	C₄²×C₁₃₉	—	2	4	no	—
354	C₄²×C₁₃₉	—	2	4	no	—
355	C₄²×C₁₃₉	—	2	4	no	—
356	C₄²×C₁₃₉	—	2	4	no	—
357	C₄²×C₁₃₉	—	2	4	no	—
358	C₄²×C₁₃₉	—	2	2	no	—
359	C₄²×C₁₃₉	—	2	2	no	—
360	C₄²×C₁₃₉	—	2	4	no	—
361	C₄²×C₁₃₉	—	4	2	no	—
362	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
363	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
364	C₂³×C₁₃₉	—	2	1	no	—
365	C₂³×C₁₃₉	—	2	2	no	—
366	C₂³×C₁₃₉	—	2	1	no	—
367	C₂³×C₁₃₉	—	2	1	no	—
368	C₂³×C₁₃₉	—	2	2	no	—
369	C₂³×C₁₃₉	—	2	2	no	—
370	C₂³×C₁₃₉	—	2	1	no	—
371	C₂³×C₁₃₉	—	2	1	no	—
372	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
373	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
374	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
375	Q₈×C₁₃₉	—	2	16	no	—
376	Q₈×C₁₃₉	—	2	8	no	—
377	Q₈×C₁₃₉	—	2	8	no	—
378	Q₈×C₁₃₉	—	4	4	no	—
379	D₄×C₁₃₉	—	4	4	no	—
380	C₂×C₄×C₁₃₉	—	2	8	no	—
381	C₂×C₄×C₁₃₉	—	2	16	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	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	2	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	1	no	—
394	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	1	no	—
401	C₂×C₄×C₁₃₉	—	2	1	no	—
402	C₂×C₄×C₁₃₉	—	2	1	no	—
403	C₂×C₄×C₁₃₉	—	2	1	no	—
404	C₂×C₄×C₁₃₉	—	2	1	no	—
405	C₂×C₄×C₁₃₉	—	2	1	no	—
406	C₂×C₄×C₁₃₉	—	2	2	no	—
407	C₂×C₄×C₁₃₉	—	2	2	no	—
408	C₂×C₄×C₁₃₉	—	2	2	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	2	2	no	—
411	C₂×C₄×C₁₃₉	—	2	2	no	—
412	C₂×C₄×C₁₃₉	—	2	2	no	—
413	C₂×C₄×C₁₃₉	—	2	2	no	—
414	C₂×C₄×C₁₃₉	—	2	2	no	—
415	C₂×C₄×C₁₃₉	—	2	2	no	—
416	C₂×C₄×C₁₃₉	—	2	2	no	—
417	C₂×C₄×C₁₃₉	—	2	2	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	2	1	no	—
420	C₂×C₄×C₁₃₉	—	2	2	no	—
421	C₂×C₄×C₁₃₉	—	2	1	no	—
422	C₂×C₄×C₁₃₉	—	2	2	no	—
423	C₂×C₄×C₁₃₉	—	2	2	no	—
424	C₂×C₄×C₁₃₉	—	2	2	no	—
425	C₂×C₄×C₁₃₉	—	2	1	no	—
426	C₂×C₄×C₁₃₉	—	2	1	no	—
427	C₂×C₄×C₁₃₉	—	4	4	no	—
428	C₂×C₄×C₁₃₉	—	4	4	no	—
429	C₂×C₄×C₁₃₉	—	4	8	no	—
430	C₂×C₄×C₁₃₉	—	4	4	no	—
431	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
438	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
439	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
440	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
441	C₂²×C₁₃₉	—	2	2	no	—
442	C₂²×C₁₃₉	—	2	4	no	—
443	C₂²×C₁₃₉	—	2	2	no	—
444	C₂²×C₁₃₉	—	2	4	no	—
445	C₂²×C₁₃₉	—	4	1	no	—
446	C₂²×C₁₃₉	—	4	1	no	—
447	C₂²×C₁₃₉	—	4	2	no	—
448	C₂²×C₁₃₉	—	4	1	no	—
449	C₂²×C₁₃₉	—	4	2	no	—
450	C₂²×C₁₃₉	#525	1	4	yes	—
451	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
452	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
453	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
455	C₂²×C₁₃₉	#585	1	1	yes	characteristic
456	C₄×C₁₃₉	—	2	2	no	—
457	C₄×C₁₃₉	—	2	2	no	—
458	C₄×C₁₃₉	—	2	4	no	—
459	C₄×C₁₃₉	—	2	4	no	—
460	C₄×C₁₃₉	—	2	2	no	—
461	C₄×C₁₃₉	—	2	2	no	—
462	C₄×C₁₃₉	—	2	2	no	—
463	C₄×C₁₃₉	—	2	4	no	—
464	C₄×C₁₃₉	—	2	2	no	—
465	C₄×C₁₃₉	—	2	2	no	—
466	C₄×C₁₃₉	—	4	1	no	—
467	C₄×C₁₃₉	—	4	1	no	—
468	C₄×C₁₃₉	—	4	1	no	—
469	C₄×C₁₃₉	—	4	2	no	—
470	C₄×C₁₃₉	—	4	1	no	—
471	C₄×C₁₃₉	—	4	1	no	—
472	C₄×C₁₃₉	—	4	2	no	—
473	C₄×C₁₃₉	—	4	2	no	—
474	C₄×C₁₃₉	—	4	2	no	—
475	C₄×C₁₃₉	—	4	1	no	—
476	C₄×C₁₃₉	—	4	2	no	—
477	C₂×C₁₃₉	—	2	4	no	—
478	C₂×C₁₃₉	—	8	1	no	—
479	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
480	C₂×C₁₃₉	#3489	1	1	yes	characteristic
481	C₂×C₁₃₉	#3495	1	2	yes	—
482	C₂×C₁₃₉	#3499	1	1	yes	characteristic
483	C₂×C₁₃₉	#3509	1	2	yes	—
484	#36086	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
485	C₁₃₉	#36086	1	1	yes	characteristic, direct product factor, Sylow
486	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic
487	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
488	#2637	C₂×C₁₃₉	1	1	yes	characteristic, complemented
489	#2634	C₂×C₁₃₉	1	1	yes	characteristic, complemented
490	#2614	C₂×C₁₃₉	1	1	yes	characteristic
491	#2604	C₂×C₁₃₉	1	1	yes	characteristic, complemented
492	#2599	C₂×C₁₃₉	1	1	yes	characteristic, complemented
493	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
494	#2581	C₂×C₁₃₉	1	1	yes	characteristic, complemented
495	#2498	C₂×C₁₃₉	1	1	yes	characteristic
496	#2484	C₂×C₁₃₉	1	1	yes	characteristic, complemented
497	#2469	C₂×C₁₃₉	1	2	yes	complemented
498	#2465	C₂×C₁₃₉	1	2	yes	complemented
499	#2462	C₂×C₁₃₉	1	2	yes	complemented
500	#2462	C₂×C₁₃₉	1	2	yes	complemented
501	#2438	C₂×C₁₃₉	1	2	yes	complemented
502	#2413	C₂×C₁₃₉	1	2	yes	—
503	#2399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
504	#2396	C₂×C₁₃₉	1	1	yes	characteristic, complemented
505	C₂×#395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
506	#2359	C₂×C₁₃₉	1	2	yes	—
507	#2344	C₂×C₁₃₉	1	2	yes	complemented
508	#2343	C₂×C₁₃₉	1	1	yes	characteristic, complemented
509	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
510	#552	—	2	8	no	—
511	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
512	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
513	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
514	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
515	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
516	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
517	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
518	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
519	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
520	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
521	#519	—	2	8	no	—
522	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
528	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
529	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
530	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
531	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
532	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
533	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
534	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
535	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
536	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
537	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
538	#400	C₂²×C₁₃₉	1	1	yes	characteristic
539	#400	C₂²×C₁₃₉	1	1	yes	characteristic
540	#400	C₂²×C₁₃₉	1	1	yes	characteristic
541	#400	C₂²×C₁₃₉	1	2	yes	—
542	#399	C₂²×C₁₃₉	1	1	yes	characteristic
543	#398	C₂²×C₁₃₉	1	1	yes	characteristic
544	#398	C₂²×C₁₃₉	1	1	yes	characteristic
545	#398	C₂²×C₁₃₉	1	1	yes	characteristic
546	#398	C₂²×C₁₃₉	1	2	yes	—
547	#398	C₂²×C₁₃₉	1	2	yes	—
548	#398	C₂²×C₁₃₉	1	2	yes	—
549	#398	C₂²×C₁₃₉	1	2	yes	—
550	#397	C₂²×C₁₃₉	1	1	yes	characteristic
551	#396	C₂²×C₁₃₉	1	2	yes	—
552	#396	C₂²×C₁₃₉	1	2	yes	—
553	#395	C₂²×C₁₃₉	1	1	yes	characteristic
554	#395	C₂²×C₁₃₉	1	1	yes	characteristic
555	#395	C₂²×C₁₃₉	1	1	yes	characteristic
556	#395	C₂²×C₁₃₉	1	1	yes	characteristic
557	#395	C₂²×C₁₃₉	1	2	yes	—
558	#395	C₂²×C₁₃₉	1	1	yes	characteristic
559	#395	C₂²×C₁₃₉	1	1	yes	characteristic
560	#395	C₂²×C₁₃₉	1	2	yes	—
561	#395	C₂²×C₁₃₉	1	2	yes	—
562	#395	C₂²×C₁₃₉	1	2	yes	—
563	#393	C₂²×C₁₃₉	1	1	yes	characteristic
564	#393	C₂²×C₁₃₉	1	1	yes	characteristic
565	#393	C₂²×C₁₃₉	1	2	yes	—
566	#391	C₂²×C₁₃₉	1	2	yes	—
567	#389	C₂²×C₁₃₉	1	2	yes	—
568	#389	C₂²×C₁₃₉	1	2	yes	—
569	#389	C₂²×C₁₃₉	1	2	yes	—
570	#389	C₂²×C₁₃₉	1	2	yes	—
571	#389	C₂²×C₁₃₉	1	2	yes	—
572	#389	C₂²×C₁₃₉	1	2	yes	—
573	#388	C₂²×C₁₃₉	1	2	yes	—
574	#388	C₂²×C₁₃₉	1	2	yes	—
575	#388	C₂²×C₁₃₉	1	2	yes	—
576	#388	C₂²×C₁₃₉	1	2	yes	—
577	#388	C₂²×C₁₃₉	1	2	yes	—
578	#387	C₂²×C₁₃₉	1	2	yes	—
579	#387	C₂²×C₁₃₉	1	2	yes	—
580	#387	C₂²×C₁₃₉	1	2	yes	—
581	#387	C₂²×C₁₃₉	1	2	yes	—
582	#387	C₂²×C₁₃₉	1	2	yes	—
583	#387	C₂²×C₁₃₉	1	2	yes	—
584	#387	C₂²×C₁₃₉	1	2	yes	—
585	#387	C₂²×C₁₃₉	1	2	yes	—
586	#387	C₂²×C₁₃₉	1	2	yes	—
587	#387	C₂²×C₁₃₉	1	2	yes	—
588	#387	C₂²×C₁₃₉	1	2	yes	—
589	#387	C₂²×C₁₃₉	1	2	yes	—
590	#387	C₂²×C₁₃₉	1	2	yes	—
591	#386	C₂²×C₁₃₉	1	2	yes	—
592	#385	C₂²×C₁₃₉	1	2	yes	—
593	#385	C₂²×C₁₃₉	1	2	yes	—
594	#385	C₂²×C₁₃₉	1	2	yes	—
595	#383	C₂²×C₁₃₉	1	1	yes	characteristic
596	#382	C₂²×C₁₃₉	1	1	yes	characteristic
597	#381	C₂²×C₁₃₉	1	1	yes	characteristic
598	#381	C₂²×C₁₃₉	1	2	yes	—
599	#381	C₂²×C₁₃₉	1	2	yes	—
600	#380	C₂²×C₁₃₉	1	2	yes	—
601	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
603	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
604	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
605	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
606	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
607	#376	C₂²×C₁₃₉	1	1	yes	characteristic
608	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
609	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
610	C₂²×Q₈	—	2	4	no	—
611	C₂²×Q₈	—	2	8	no	—
612	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
615	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
623	#126	—	2	4	no	—
624	#126	—	2	4	no	—
625	#125	—	2	4	no	—
626	#125	—	2	4	no	—
627	#125	—	2	4	no	—
628	#123	—	2	4	no	—
629	#123	—	2	8	no	—
630	#123	—	2	4	no	—
631	C₂²⋊Q₈	—	2	4	no	—
632	C₂²⋊Q₈	—	2	4	no	—
633	C₄×Q₈	—	2	8	no	—
634	C₄×Q₈	—	2	8	no	—
635	C₄×Q₈	—	2	4	no	—
636	C₄×Q₈	—	2	4	no	—
637	C₄×Q₈	—	2	4	no	—
638	C₄×Q₈	—	2	4	no	—
639	C₄×Q₈	—	2	4	no	—
640	C₄×D₄	—	2	4	no	—
641	#117	—	2	4	no	—
642	#117	—	2	8	no	—
643	#117	—	2	8	no	—
644	#117	—	2	4	no	—
645	#117	—	2	4	no	—
646	#117	D₄×C₁₃₉	1	8	yes	—
647	C₂×C₄⋊C₄	—	2	4	no	—
648	C₂×C₄⋊C₄	—	2	8	no	—
649	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
699	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
700	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
701	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
702	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
703	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
706	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
707	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
709	#95	C₂³×C₁₃₉	1	1	yes	characteristic
710	#95	C₂³×C₁₃₉	1	2	yes	—
711	#95	C₂³×C₁₃₉	1	1	yes	characteristic
712	#95	C₂³×C₁₃₉	1	2	yes	—
713	#95	C₂³×C₁₃₉	1	2	yes	—
714	#95	C₂³×C₁₃₉	1	2	yes	—
715	#95	C₂³×C₁₃₉	1	2	yes	—
716	#95	C₂³×C₁₃₉	1	1	yes	characteristic
717	#95	C₂³×C₁₃₉	1	2	yes	—
718	#95	C₂³×C₁₃₉	1	2	yes	—
719	#95	C₂³×C₁₃₉	1	2	yes	—
720	#95	C₂³×C₁₃₉	1	2	yes	—
721	#95	C₂³×C₁₃₉	1	1	yes	characteristic
722	#95	C₂³×C₁₃₉	1	2	yes	—
723	#95	C₂³×C₁₃₉	1	2	yes	—
724	#95	C₂³×C₁₃₉	1	2	yes	—
725	#95	C₂³×C₁₃₉	1	2	yes	—
726	#95	C₂³×C₁₃₉	1	2	yes	—
727	#95	C₂³×C₁₃₉	1	2	yes	—
728	#95	C₂³×C₁₃₉	1	2	yes	—
729	#95	C₂³×C₁₃₉	1	2	yes	—
730	#95	C₂³×C₁₃₉	1	2	yes	—
731	#95	C₂³×C₁₃₉	1	2	yes	—
732	#95	C₂³×C₁₃₉	1	2	yes	—
733	#95	C₂³×C₁₃₉	1	2	yes	—
734	#95	C₂³×C₁₃₉	1	2	yes	—
735	#95	C₂³×C₁₃₉	1	2	yes	—
736	#95	C₂³×C₁₃₉	1	2	yes	—
737	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
738	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
739	C₂×Q₈	—	2	32	no	—
740	C₂×Q₈	—	2	4	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	4	no	—
745	C₂×Q₈	—	2	4	no	—
746	C₂×Q₈	—	2	4	no	—
747	C₂×Q₈	—	2	4	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	—	4	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
767	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
768	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	4	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	4	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
822	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
836	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	4	no	—
839	C₄²	—	2	4	no	—
840	C₄²	—	2	4	no	—
841	C₄²	—	2	4	no	—
842	C₄²	—	2	4	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	4	no	—
846	C₄²	—	4	2	no	—
847	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
848	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
858	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
859	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
860	Q₈	—	2	16	no	—
861	Q₈	—	2	8	no	—
862	Q₈	—	2	8	no	—
863	Q₈	—	4	4	no	—
864	D₄	—	4	4	no	—
865	C₂×C₄	—	2	8	no	—
866	C₂×C₄	—	2	16	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	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	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
917	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
918	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
919	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
920	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
921	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
922	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
923	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
924	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
925	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	4	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	2	no	—
935	C₂²	#525×C₁₃₉	1	4	yes	—
936	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
937	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
938	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
939	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
940	C₂²	#585×C₁₃₉	1	1	yes	characteristic
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	2	no	—
962	C₂	—	2	4	no	—
963	C₂	—	8	1	no	—
964	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
965	C₂	#3489×C₁₃₉	1	1	yes	characteristic
966	C₂	#3495×C₁₃₉	1	2	yes	—
967	C₂	#3499×C₁₃₉	1	1	yes	characteristic
968	C₂	#3509×C₁₃₉	1	2	yes	—

	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
2. C₂×#519×C₁₃₉	C₂	semidirect
3. #2637×C₁₃₉	C₂	semidirect
4. #2634×C₁₃₉	C₂	semidirect
6. #2604×C₁₃₉	C₂	semidirect
7. #2599×C₁₃₉	C₂	semidirect
8. #2584×C₁₃₉	C₂	semidirect
9. #2581×C₁₃₉	C₂	semidirect
11. #2484×C₁₃₉	C₂	semidirect
12. #2469×C₁₃₉	C₂	semidirect
13. #2465×C₁₃₉	C₂	semidirect
14. #2462×C₁₃₉	C₂	semidirect
15. #2462×C₁₃₉	C₂	semidirect
16. #2438×C₁₃₉	C₂	semidirect
18. #2399×C₁₃₉	C₂	semidirect
19. #2396×C₁₃₉	C₂	semidirect
20. C₂×#395×C₁₃₉	C₂	semidirect
22. #2344×C₁₃₉	C₂	semidirect
23. #2343×C₁₃₉	C₂	semidirect
484. #36086	C₁₃₉	direct (N × H)
485. C₁₃₉	#36086	direct (N × H)
487. C₂×#519	C₂×C₁₃₉	semidirect
488. #2637	C₂×C₁₃₉	semidirect
489. #2634	C₂×C₁₃₉	semidirect
491. #2604	C₂×C₁₃₉	semidirect
492. #2599	C₂×C₁₃₉	semidirect
493. #2584	C₂×C₁₃₉	semidirect
494. #2581	C₂×C₁₃₉	semidirect
496. #2484	C₂×C₁₃₉	semidirect
497. #2469	C₂×C₁₃₉	semidirect
498. #2465	C₂×C₁₃₉	semidirect
499. #2462	C₂×C₁₃₉	semidirect
500. #2462	C₂×C₁₃₉	semidirect
501. #2438	C₂×C₁₃₉	semidirect
503. #2399	C₂×C₁₃₉	semidirect
504. #2396	C₂×C₁₃₉	semidirect
505. C₂×#395	C₂×C₁₃₉	semidirect
507. #2344	C₂×C₁₃₉	semidirect
508. #2343	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×#552×C₁₃₉	2
C₂×#519×C₁₃₉	2
#2637×C₁₃₉	2
#2634×C₁₃₉	2
#2614×C₁₃₉	2
#2604×C₁₃₉	2
#2599×C₁₃₉	2
#2584×C₁₃₉	2
#2581×C₁₃₉	2
#2498×C₁₃₉	2
#2484×C₁₃₉	2
#2469×C₁₃₉	2
#2465×C₁₃₉	2
#2462×C₁₃₉	2
#2438×C₁₃₉	2
#2413×C₁₃₉	2
#2399×C₁₃₉	2
#2396×C₁₃₉	2
C₂×#395×C₁₃₉	2
#2359×C₁₃₉	2
#2344×C₁₃₉	2
#2343×C₁₃₉	2
#36086	139

Subgroups — C139×#36086 #48030682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36086 #48030682