Subgroups — C₁₃₉×#36523 #48031119

Order 35584.

1732 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2852×C₁₃₉	C₂	1	2	yes	maximal
3	#2605×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2604×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2564×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2549×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2533×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2532×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2528×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2527×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2488×C₁₃₉	C₂	1	2	yes	maximal
13	#2373×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2368×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2356×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2353×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic
19	C₂×#376×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
28	#401×C₁₃₉	C₂²	1	2	yes	—
29	#400×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	1	yes	characteristic
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#399×C₁₃₉	C₂²	1	1	yes	characteristic
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#397×C₁₃₉	C₂²	1	2	yes	—
38	#395×C₁₃₉	C₂²	1	2	yes	—
39	#395×C₁₃₉	C₂²	1	1	yes	characteristic
40	#393×C₁₃₉	C₂²	1	2	yes	—
41	#393×C₁₃₉	C₂²	1	1	yes	characteristic
42	#391×C₁₃₉	C₂²	1	2	yes	—
43	#391×C₁₃₉	C₂²	1	2	yes	—
44	#391×C₁₃₉	C₂²	1	2	yes	—
45	#391×C₁₃₉	C₂²	1	2	yes	—
46	#391×C₁₃₉	C₂²	1	2	yes	—
47	#389×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	2	yes	—
50	#388×C₁₃₉	C₂²	1	2	yes	—
51	#388×C₁₃₉	C₂²	1	2	yes	—
52	#388×C₁₃₉	C₂²	1	2	yes	—
53	#388×C₁₃₉	C₂²	1	2	yes	—
54	#388×C₁₃₉	C₂²	1	2	yes	—
55	#388×C₁₃₉	C₂²	1	2	yes	—
56	#388×C₁₃₉	C₂²	1	2	yes	—
57	#387×C₁₃₉	C₂²	1	2	yes	—
58	#387×C₁₃₉	C₂²	1	2	yes	—
59	#387×C₁₃₉	C₂²	1	2	yes	—
60	#387×C₁₃₉	C₂²	1	2	yes	—
61	#387×C₁₃₉	C₂²	1	2	yes	—
62	#387×C₁₃₉	C₂²	1	2	yes	—
63	#387×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	#386×C₁₃₉	C₂²	1	1	yes	characteristic
73	#386×C₁₃₉	C₂²	1	2	yes	—
74	#386×C₁₃₉	C₂²	1	2	yes	—
75	#385×C₁₃₉	C₂²	1	2	yes	—
76	#385×C₁₃₉	C₂²	1	2	yes	—
77	#385×C₁₃₉	C₂²	1	1	yes	characteristic
78	#385×C₁₃₉	C₂²	1	2	yes	—
79	#385×C₁₃₉	C₂²	1	2	yes	—
80	#383×C₁₃₉	C₂²	1	2	yes	—
81	#383×C₁₃₉	C₂²	1	1	yes	characteristic
82	#383×C₁₃₉	C₂²	1	2	yes	—
83	#382×C₁₃₉	C₂²	1	2	yes	—
84	#381×C₁₃₉	C₂²	1	1	yes	characteristic
85	#381×C₁₃₉	C₂²	1	1	yes	characteristic
86	#381×C₁₃₉	C₂²	1	2	yes	—
87	#380×C₁₃₉	C₂²	1	1	yes	characteristic
88	#380×C₁₃₉	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
99	#376×C₁₃₉	C₂²	1	2	yes	—
100	#376×C₁₃₉	C₂²	1	2	yes	—
101	#376×C₁₃₉	C₂²	1	2	yes	—
102	#376×C₁₃₉	C₂²	1	2	yes	—
103	#376×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	#126×C₁₃₉	—	2	8	no	—
117	#123×C₁₃₉	—	2	4	no	—
118	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
119	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
120	C₄×Q₈×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	4	no	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₉	—	2	4	no	—
152	C₂×C₄²×C₁₃₉	—	2	8	no	—
153	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	1	yes	characteristic
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	1	yes	characteristic
189	#95×C₁₃₉	C₂³	1	1	yes	characteristic
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	1	yes	characteristic
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	1	yes	characteristic
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
203	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂×Q₈×C₁₃₉	—	2	4	no	—
205	C₂×Q₈×C₁₃₉	—	2	4	no	—
206	C₂×Q₈×C₁₃₉	—	2	2	no	—
207	C₂×Q₈×C₁₃₉	—	4	2	no	—
208	C₂×Q₈×C₁₃₉	—	4	2	no	—
209	C₂×D₄×C₁₃₉	—	2	2	no	—
210	C₂×D₄×C₁₃₉	—	2	2	no	—
211	C₂×D₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	2	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	2	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	2	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	2	no	—
222	C₂²×C₄×C₁₃₉	—	4	2	no	—
223	C₂²×C₄×C₁₃₉	—	4	2	no	—
224	C₂²×C₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	2	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
266	C₂²⋊C₄×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	—	4	2	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
272	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₄²×C₁₃₉	—	2	4	no	—
275	C₄²×C₁₃₉	—	2	4	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	—	2	4	no	—
278	C₄²×C₁₃₉	—	2	2	no	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	4	no	—
281	C₄²×C₁₃₉	—	4	2	no	—
282	C₄²×C₁₃₉	—	4	2	no	—
283	C₄²×C₁₃₉	—	4	2	no	—
284	C₄²×C₁₃₉	#41	1	8	yes	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	1	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
293	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
294	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
295	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
296	Q₈×C₁₃₉	—	4	8	no	—
297	Q₈×C₁₃₉	—	8	2	no	—
298	D₄×C₁₃₉	—	4	4	no	—
299	C₂×C₄×C₁₃₉	—	2	8	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	4	4	no	—
342	C₂×C₄×C₁₃₉	—	4	8	no	—
343	C₂×C₄×C₁₃₉	—	4	8	no	—
344	C₂×C₄×C₁₃₉	—	4	4	no	—
345	C₂×C₄×C₁₃₉	—	8	2	no	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
350	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
351	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
352	C₂²×C₁₃₉	—	2	2	no	—
353	C₂²×C₁₃₉	—	2	4	no	—
354	C₂²×C₁₃₉	—	2	2	no	—
355	C₂²×C₁₃₉	—	2	4	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	1	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	1	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	#556	1	4	yes	—
362	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
364	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
366	C₂²×C₁₃₉	#585	1	2	yes	—
367	C₄×C₁₃₉	—	2	4	no	—
368	C₄×C₁₃₉	—	2	4	no	—
369	C₄×C₁₃₉	—	2	4	no	—
370	C₄×C₁₃₉	—	2	2	no	—
371	C₄×C₁₃₉	—	2	2	no	—
372	C₄×C₁₃₉	—	2	4	no	—
373	C₄×C₁₃₉	—	4	1	no	—
374	C₄×C₁₃₉	—	4	2	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	1	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	1	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₂×C₁₃₉	—	2	4	no	—
385	C₂×C₁₃₉	—	8	1	no	—
386	C₂×C₁₃₉	#3444	1	1	yes	characteristic
387	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
388	C₂×C₁₃₉	#3475	1	2	yes	—
389	C₂×C₁₃₉	#3491	1	1	yes	characteristic
390	C₂×C₁₃₉	#3495	1	2	yes	—
391	#36523	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₁₃₉	#36523	1	1	yes	characteristic, direct product factor, Sylow
393	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2852	C₂×C₁₃₉	1	2	yes	—
395	#2605	C₂×C₁₃₉	1	2	yes	complemented
396	#2604	C₂×C₁₃₉	1	2	yes	complemented
397	#2564	C₂×C₁₃₉	1	1	yes	characteristic
398	#2549	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2533	C₂×C₁₃₉	1	2	yes	complemented
400	#2532	C₂×C₁₃₉	1	2	yes	complemented
401	#2528	C₂×C₁₃₉	1	2	yes	complemented
402	#2527	C₂×C₁₃₉	1	2	yes	complemented
403	#2493	C₂×C₁₃₉	1	2	yes	complemented
404	#2488	C₂×C₁₃₉	1	2	yes	—
405	#2373	C₂×C₁₃₉	1	2	yes	complemented
406	#2368	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	#2356	C₂×C₁₃₉	1	2	yes	complemented
408	#2353	C₂×C₁₃₉	1	1	yes	characteristic
409	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	complemented
410	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic
411	C₂×#376	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
417	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
419	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
420	#401	C₂²×C₁₃₉	1	2	yes	—
421	#400	C₂²×C₁₃₉	1	1	yes	characteristic
422	#400	C₂²×C₁₃₉	1	2	yes	—
423	#400	C₂²×C₁₃₉	1	2	yes	—
424	#400	C₂²×C₁₃₉	1	2	yes	—
425	#400	C₂²×C₁₃₉	1	2	yes	—
426	#400	C₂²×C₁₃₉	1	2	yes	—
427	#399	C₂²×C₁₃₉	1	1	yes	characteristic
428	#398	C₂²×C₁₃₉	1	2	yes	—
429	#397	C₂²×C₁₃₉	1	2	yes	—
430	#395	C₂²×C₁₃₉	1	1	yes	characteristic
431	#395	C₂²×C₁₃₉	1	2	yes	—
432	#393	C₂²×C₁₃₉	1	1	yes	characteristic
433	#393	C₂²×C₁₃₉	1	2	yes	—
434	#391	C₂²×C₁₃₉	1	2	yes	—
435	#391	C₂²×C₁₃₉	1	2	yes	—
436	#391	C₂²×C₁₃₉	1	2	yes	—
437	#391	C₂²×C₁₃₉	1	2	yes	—
438	#391	C₂²×C₁₃₉	1	2	yes	—
439	#389	C₂²×C₁₃₉	1	2	yes	—
440	#389	C₂²×C₁₃₉	1	2	yes	—
441	#389	C₂²×C₁₃₉	1	2	yes	—
442	#388	C₂²×C₁₃₉	1	2	yes	—
443	#388	C₂²×C₁₃₉	1	2	yes	—
444	#388	C₂²×C₁₃₉	1	2	yes	—
445	#388	C₂²×C₁₃₉	1	2	yes	—
446	#388	C₂²×C₁₃₉	1	2	yes	—
447	#388	C₂²×C₁₃₉	1	2	yes	—
448	#388	C₂²×C₁₃₉	1	2	yes	—
449	#387	C₂²×C₁₃₉	1	2	yes	—
450	#387	C₂²×C₁₃₉	1	2	yes	—
451	#387	C₂²×C₁₃₉	1	2	yes	—
452	#387	C₂²×C₁₃₉	1	2	yes	—
453	#387	C₂²×C₁₃₉	1	2	yes	—
454	#387	C₂²×C₁₃₉	1	2	yes	—
455	#387	C₂²×C₁₃₉	1	2	yes	—
456	#387	C₂²×C₁₃₉	1	2	yes	—
457	#387	C₂²×C₁₃₉	1	2	yes	—
458	#387	C₂²×C₁₃₉	1	2	yes	—
459	#387	C₂²×C₁₃₉	1	2	yes	—
460	#387	C₂²×C₁₃₉	1	2	yes	—
461	#387	C₂²×C₁₃₉	1	2	yes	—
462	#387	C₂²×C₁₃₉	1	2	yes	—
463	#387	C₂²×C₁₃₉	1	2	yes	—
464	#386	C₂²×C₁₃₉	1	2	yes	—
465	#386	C₂²×C₁₃₉	1	1	yes	characteristic
466	#386	C₂²×C₁₃₉	1	2	yes	—
467	#385	C₂²×C₁₃₉	1	2	yes	—
468	#385	C₂²×C₁₃₉	1	2	yes	—
469	#385	C₂²×C₁₃₉	1	2	yes	—
470	#385	C₂²×C₁₃₉	1	2	yes	—
471	#385	C₂²×C₁₃₉	1	1	yes	characteristic
472	#383	C₂²×C₁₃₉	1	2	yes	—
473	#383	C₂²×C₁₃₉	1	1	yes	characteristic
474	#383	C₂²×C₁₃₉	1	2	yes	—
475	#382	C₂²×C₁₃₉	1	2	yes	—
476	#381	C₂²×C₁₃₉	1	2	yes	—
477	#381	C₂²×C₁₃₉	1	1	yes	characteristic
478	#381	C₂²×C₁₃₉	1	1	yes	characteristic
479	#380	C₂²×C₁₃₉	1	2	yes	—
480	#380	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
491	#376	C₂²×C₁₃₉	1	2	yes	—
492	#376	C₂²×C₁₃₉	1	1	yes	characteristic
493	#376	C₂²×C₁₃₉	1	2	yes	—
494	#376	C₂²×C₁₃₉	1	2	yes	—
495	#376	C₂²×C₁₃₉	1	2	yes	—
496	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
498	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
499	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
500	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
508	#126	—	2	8	no	—
509	#123	—	2	4	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	—	2	8	no	—
512	C₄×Q₈	—	2	8	no	—
513	C₄×D₄	—	2	4	no	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₄²	—	2	4	no	—
544	C₂×C₄²	—	2	8	no	—
545	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	1	yes	characteristic
558	#95	C₂³×C₁₃₉	1	1	yes	characteristic
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	2	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	1	yes	characteristic
564	#95	C₂³×C₁₃₉	1	2	yes	—
565	#95	C₂³×C₁₃₉	1	1	yes	characteristic
566	#95	C₂³×C₁₃₉	1	2	yes	—
567	#95	C₂³×C₁₃₉	1	1	yes	characteristic
568	#95	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	1	yes	characteristic
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	2	yes	—
579	#95	C₂³×C₁₃₉	1	2	yes	—
580	#95	C₂³×C₁₃₉	1	2	yes	—
581	#95	C₂³×C₁₃₉	1	2	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
595	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	4	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	4	2	no	—
600	C₂×Q₈	—	4	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	4	2	no	—
674	C₄²	—	4	2	no	—
675	C₄²	—	4	2	no	—
676	C₄²	#41×C₁₃₉	1	8	yes	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	2	no	—
684	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
685	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
686	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
687	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
688	Q₈	—	4	8	no	—
689	Q₈	—	8	2	no	—
690	D₄	—	4	4	no	—
691	C₂×C₄	—	2	8	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	4	8	no	—
735	C₂×C₄	—	4	8	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	2	no	—
738	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
739	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
740	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
741	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
742	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
743	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	2	no	—
753	C₂²	#556×C₁₃₉	1	4	yes	—
754	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
755	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
756	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
757	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
758	C₂²	#585×C₁₃₉	1	2	yes	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	4	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	4	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₂	—	2	4	no	—
777	C₂	—	8	1	no	—
778	C₂	#3444×C₁₃₉	1	1	yes	characteristic
779	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
780	C₂	#3475×C₁₃₉	1	2	yes	—
781	C₂	#3491×C₁₃₉	1	1	yes	characteristic
782	C₂	#3495×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
1. #2855×C₁₃₉	C₂	semidirect
3. #2605×C₁₃₉	C₂	semidirect
4. #2604×C₁₃₉	C₂	semidirect
6. #2549×C₁₃₉	C₂	semidirect
7. #2533×C₁₃₉	C₂	semidirect
8. #2532×C₁₃₉	C₂	semidirect
9. #2528×C₁₃₉	C₂	semidirect
10. #2527×C₁₃₉	C₂	semidirect
11. #2493×C₁₃₉	C₂	semidirect
13. #2373×C₁₃₉	C₂	semidirect
14. #2368×C₁₃₉	C₂	semidirect
15. #2356×C₁₃₉	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
19. C₂×#376×C₁₃₉	C₂	semidirect
391. #36523	C₁₃₉	direct (N × H)
392. C₁₃₉	#36523	direct (N × H)
393. #2855	C₂×C₁₃₉	semidirect
395. #2605	C₂×C₁₃₉	semidirect
396. #2604	C₂×C₁₃₉	semidirect
398. #2549	C₂×C₁₃₉	semidirect
399. #2533	C₂×C₁₃₉	semidirect
400. #2532	C₂×C₁₃₉	semidirect
401. #2528	C₂×C₁₃₉	semidirect
402. #2527	C₂×C₁₃₉	semidirect
403. #2493	C₂×C₁₃₉	semidirect
405. #2373	C₂×C₁₃₉	semidirect
406. #2368	C₂×C₁₃₉	semidirect
407. #2356	C₂×C₁₃₉	semidirect
409. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
411. C₂×#376	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2855×C₁₃₉	2
#2852×C₁₃₉	2
#2605×C₁₃₉	2
#2604×C₁₃₉	2
#2564×C₁₃₉	2
#2549×C₁₃₉	2
#2533×C₁₃₉	2
#2532×C₁₃₉	2
#2528×C₁₃₉	2
#2527×C₁₃₉	2
#2493×C₁₃₉	2
#2488×C₁₃₉	2
#2373×C₁₃₉	2
#2368×C₁₃₉	2
#2356×C₁₃₉	2
#2353×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄×#123×C₁₃₉	2
C₂×#376×C₁₃₉	2
#36523	139

Subgroups — C139×#36523 #48031119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36523 #48031119