Subgroups — C₁₃₉×#36052 #48030648

Order 35584.

1578 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2667×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2654×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2585×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2579×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2575×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2575×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2526×C₁₃₉	C₂	1	2	yes	maximal
8	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2508×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2484×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2479×C₁₃₉	C₂	1	2	yes	maximal
12	#2475×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2402×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2373×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2371×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2346×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	#400×C₁₃₉	C₂²	1	2	yes	—
27	#400×C₁₃₉	C₂²	1	2	yes	—
28	#400×C₁₃₉	C₂²	1	2	yes	—
29	#400×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	1	yes	characteristic
32	#399×C₁₃₉	C₂²	1	1	yes	characteristic
33	#399×C₁₃₉	C₂²	1	2	yes	—
34	#399×C₁₃₉	C₂²	1	2	yes	—
35	#398×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	1	yes	characteristic
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#397×C₁₃₉	C₂²	1	2	yes	—
43	#397×C₁₃₉	C₂²	1	2	yes	—
44	#397×C₁₃₉	C₂²	1	1	yes	characteristic
45	#396×C₁₃₉	C₂²	1	2	yes	—
46	#396×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	2	yes	—
48	#390×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×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	#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	#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	#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	#386×C₁₃₉	C₂²	1	1	yes	characteristic
77	#386×C₁₃₉	C₂²	1	1	yes	characteristic
78	#385×C₁₃₉	C₂²	1	1	yes	characteristic
79	#385×C₁₃₉	C₂²	1	2	yes	—
80	#385×C₁₃₉	C₂²	1	1	yes	characteristic
81	#385×C₁₃₉	C₂²	1	2	yes	—
82	#382×C₁₃₉	C₂²	1	2	yes	—
83	#382×C₁₃₉	C₂²	1	2	yes	—
84	#382×C₁₃₉	C₂²	1	1	yes	characteristic
85	#381×C₁₃₉	C₂²	1	2	yes	—
86	#381×C₁₃₉	C₂²	1	1	yes	characteristic
87	#381×C₁₃₉	C₂²	1	1	yes	characteristic
88	#380×C₁₃₉	C₂²	1	1	yes	characteristic
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×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	#376×C₁₃₉	C₂²	1	2	yes	—
106	#376×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×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	#126×C₁₃₉	—	2	8	no	—
113	#125×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	4	no	—
115	#117×C₁₃₉	—	2	4	no	—
116	#117×C₁₃₉	—	2	8	no	—
117	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊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	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×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	1	yes	characteristic
172	#95×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	1	yes	characteristic
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	1	yes	characteristic
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	1	yes	characteristic
199	#95×C₁₃₉	C₂³	1	1	yes	characteristic
200	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₂×D₄×C₁₃₉	—	2	2	no	—
203	C₂×D₄×C₁₃₉	—	2	2	no	—
204	C₂×D₄×C₁₃₉	—	4	1	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	4	2	no	—
210	C₂²×C₄×C₁₃₉	—	4	2	no	—
211	C₂²×C₄×C₁₃₉	—	4	2	no	—
212	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	2	no	—
233	C₄⋊C₄×C₁₃₉	—	2	2	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	4	2	no	—
245	C₄⋊C₄×C₁₃₉	—	4	2	no	—
246	C₄⋊C₄×C₁₃₉	—	4	2	no	—
247	C₄⋊C₄×C₁₃₉	—	4	2	no	—
248	C₄⋊C₄×C₁₃₉	—	4	2	no	—
249	C₄⋊C₄×C₁₃₉	—	4	2	no	—
250	C₄⋊C₄×C₁₃₉	—	4	2	no	—
251	C₄⋊C₄×C₁₃₉	—	4	2	no	—
252	C₄⋊C₄×C₁₃₉	—	4	2	no	—
253	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
268	C₄²×C₁₃₉	—	2	4	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	2	no	—
272	C₄²×C₁₃₉	—	2	4	no	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₄²×C₁₃₉	—	2	4	no	—
275	C₄²×C₁₃₉	—	4	2	no	—
276	C₄²×C₁₃₉	—	4	2	no	—
277	C₄²×C₁₃₉	—	4	2	no	—
278	C₄²×C₁₃₉	—	4	2	no	—
279	C₄²×C₁₃₉	—	4	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	1	no	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	1	no	—
286	C₂³×C₁₃₉	—	2	1	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
290	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
291	D₄×C₁₃₉	—	4	4	no	—
292	C₂×C₄×C₁₃₉	—	2	8	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	1	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	1	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	2	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	2	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	2	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	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	4	4	no	—
335	C₂×C₄×C₁₃₉	—	8	2	no	—
336	C₂×C₄×C₁₃₉	—	8	2	no	—
337	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
338	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
340	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
342	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
343	C₂²×C₁₃₉	—	2	2	no	—
344	C₂²×C₁₃₉	—	2	2	no	—
345	C₂²×C₁₃₉	—	2	2	no	—
346	C₂²×C₁₃₉	—	4	2	no	—
347	C₂²×C₁₃₉	—	4	2	no	—
348	C₂²×C₁₃₉	—	4	1	no	—
349	C₂²×C₁₃₉	—	4	1	no	—
350	C₂²×C₁₃₉	—	4	1	no	—
351	C₂²×C₁₃₉	—	4	2	no	—
352	C₂²×C₁₃₉	—	4	2	no	—
353	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
354	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
355	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂²×C₁₃₉	#585	1	2	yes	—
357	C₂²×C₁₃₉	#585	1	1	yes	characteristic
358	C₄×C₁₃₉	—	2	4	no	—
359	C₄×C₁₃₉	—	2	2	no	—
360	C₄×C₁₃₉	—	2	2	no	—
361	C₄×C₁₃₉	—	2	2	no	—
362	C₄×C₁₃₉	—	2	4	no	—
363	C₄×C₁₃₉	—	2	4	no	—
364	C₄×C₁₃₉	—	4	1	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	—	4	1	no	—
367	C₄×C₁₃₉	—	4	2	no	—
368	C₄×C₁₃₉	—	4	2	no	—
369	C₄×C₁₃₉	—	4	2	no	—
370	C₄×C₁₃₉	—	4	2	no	—
371	C₄×C₁₃₉	—	4	2	no	—
372	C₄×C₁₃₉	—	4	2	no	—
373	C₄×C₁₃₉	—	4	2	no	—
374	C₄×C₁₃₉	—	4	2	no	—
375	C₂×C₁₃₉	—	4	2	no	—
376	C₂×C₁₃₉	—	8	1	no	—
377	C₂×C₁₃₉	#3444	1	1	yes	characteristic
378	C₂×C₁₃₉	#3491	1	1	yes	characteristic
379	C₂×C₁₃₉	#3495	1	1	yes	characteristic
380	C₂×C₁₃₉	#3515	1	2	yes	—
381	C₂×C₁₃₉	#3524	1	2	yes	—
382	#36052	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₁₃₉	#36052	1	1	yes	characteristic, direct product factor, Sylow
384	#2667	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	#2654	C₂×C₁₃₉	1	2	yes	complemented
386	#2585	C₂×C₁₃₉	1	2	yes	complemented
387	#2579	C₂×C₁₃₉	1	1	yes	characteristic
388	#2575	C₂×C₁₃₉	1	2	yes	complemented
389	#2575	C₂×C₁₃₉	1	2	yes	complemented
390	#2526	C₂×C₁₃₉	1	2	yes	—
391	#2519	C₂×C₁₃₉	1	2	yes	complemented
392	#2508	C₂×C₁₃₉	1	2	yes	complemented
393	#2484	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2479	C₂×C₁₃₉	1	2	yes	—
395	#2475	C₂×C₁₃₉	1	2	yes	complemented
396	#2402	C₂×C₁₃₉	1	2	yes	complemented
397	#2395	C₂×C₁₃₉	1	1	yes	characteristic
398	#2373	C₂×C₁₃₉	1	2	yes	complemented
399	#2371	C₂×C₁₃₉	1	2	yes	complemented
400	#2357	C₂×C₁₃₉	1	1	yes	characteristic
401	#2346	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
404	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
406	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
407	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
408	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
409	#400	C₂²×C₁₃₉	1	2	yes	—
410	#400	C₂²×C₁₃₉	1	2	yes	—
411	#400	C₂²×C₁₃₉	1	2	yes	—
412	#400	C₂²×C₁₃₉	1	2	yes	—
413	#400	C₂²×C₁₃₉	1	1	yes	characteristic
414	#400	C₂²×C₁₃₉	1	2	yes	—
415	#399	C₂²×C₁₃₉	1	2	yes	—
416	#399	C₂²×C₁₃₉	1	2	yes	—
417	#399	C₂²×C₁₃₉	1	1	yes	characteristic
418	#398	C₂²×C₁₃₉	1	2	yes	—
419	#398	C₂²×C₁₃₉	1	1	yes	characteristic
420	#398	C₂²×C₁₃₉	1	2	yes	—
421	#398	C₂²×C₁₃₉	1	2	yes	—
422	#398	C₂²×C₁₃₉	1	2	yes	—
423	#398	C₂²×C₁₃₉	1	2	yes	—
424	#398	C₂²×C₁₃₉	1	2	yes	—
425	#397	C₂²×C₁₃₉	1	2	yes	—
426	#397	C₂²×C₁₃₉	1	2	yes	—
427	#397	C₂²×C₁₃₉	1	1	yes	characteristic
428	#396	C₂²×C₁₃₉	1	2	yes	—
429	#396	C₂²×C₁₃₉	1	2	yes	—
430	#394	C₂²×C₁₃₉	1	2	yes	—
431	#390	C₂²×C₁₃₉	1	2	yes	—
432	#389	C₂²×C₁₃₉	1	2	yes	—
433	#389	C₂²×C₁₃₉	1	2	yes	—
434	#389	C₂²×C₁₃₉	1	2	yes	—
435	#389	C₂²×C₁₃₉	1	2	yes	—
436	#389	C₂²×C₁₃₉	1	2	yes	—
437	#388	C₂²×C₁₃₉	1	2	yes	—
438	#388	C₂²×C₁₃₉	1	2	yes	—
439	#388	C₂²×C₁₃₉	1	2	yes	—
440	#388	C₂²×C₁₃₉	1	2	yes	—
441	#388	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	#387	C₂²×C₁₃₉	1	2	yes	—
447	#387	C₂²×C₁₃₉	1	2	yes	—
448	#387	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	#386	C₂²×C₁₃₉	1	1	yes	characteristic
460	#386	C₂²×C₁₃₉	1	1	yes	characteristic
461	#385	C₂²×C₁₃₉	1	1	yes	characteristic
462	#385	C₂²×C₁₃₉	1	2	yes	—
463	#385	C₂²×C₁₃₉	1	1	yes	characteristic
464	#385	C₂²×C₁₃₉	1	2	yes	—
465	#382	C₂²×C₁₃₉	1	2	yes	—
466	#382	C₂²×C₁₃₉	1	2	yes	—
467	#382	C₂²×C₁₃₉	1	1	yes	characteristic
468	#381	C₂²×C₁₃₉	1	1	yes	characteristic
469	#381	C₂²×C₁₃₉	1	2	yes	—
470	#381	C₂²×C₁₃₉	1	1	yes	characteristic
471	#380	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
477	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
478	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
488	#376	C₂²×C₁₃₉	1	2	yes	—
489	#376	C₂²×C₁₃₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	#126	—	2	8	no	—
496	#125	—	2	8	no	—
497	C₄×D₄	—	2	4	no	—
498	#117	—	2	4	no	—
499	#117	—	2	8	no	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₄²	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
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	#95	C₂³×C₁₃₉	1	1	yes	characteristic
552	#95	C₂³×C₁₃₉	1	2	yes	—
553	#95	C₂³×C₁₃₉	1	2	yes	—
554	#95	C₂³×C₁₃₉	1	2	yes	—
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	2	yes	—
559	#95	C₂³×C₁₃₉	1	1	yes	characteristic
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	1	yes	characteristic
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	2	yes	—
564	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
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	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
584	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	1	no	—
649	C₂²⋊C₄	—	4	1	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	4	2	no	—
659	C₄²	—	4	2	no	—
660	C₄²	—	4	2	no	—
661	C₄²	—	4	2	no	—
662	C₄²	—	4	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	1	no	—
672	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
673	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
674	D₄	—	4	4	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	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	1	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	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	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	2	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
721	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
722	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
723	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
724	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
725	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
737	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
738	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
739	C₂²	#585×C₁₃₉	1	2	yes	—
740	C₂²	#585×C₁₃₉	1	1	yes	characteristic
741	C₄	—	2	4	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	4	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₂	—	4	2	no	—
759	C₂	—	8	1	no	—
760	C₂	#3444×C₁₃₉	1	1	yes	characteristic
761	C₂	#3491×C₁₃₉	1	1	yes	characteristic
762	C₂	#3495×C₁₃₉	1	1	yes	characteristic
763	C₂	#3515×C₁₃₉	1	2	yes	—
764	C₂	#3524×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. #2667×C₁₃₉	C₂	semidirect
2. #2654×C₁₃₉	C₂	semidirect
3. #2585×C₁₃₉	C₂	semidirect
5. #2575×C₁₃₉	C₂	semidirect
6. #2575×C₁₃₉	C₂	semidirect
8. #2519×C₁₃₉	C₂	semidirect
9. #2508×C₁₃₉	C₂	semidirect
10. #2484×C₁₃₉	C₂	semidirect
12. #2475×C₁₃₉	C₂	semidirect
13. #2402×C₁₃₉	C₂	semidirect
15. #2373×C₁₃₉	C₂	semidirect
16. #2371×C₁₃₉	C₂	semidirect
18. #2346×C₁₃₉	C₂	semidirect
19. #2274×C₁₃₉	C₂	semidirect
382. #36052	C₁₃₉	direct (N × H)
383. C₁₃₉	#36052	direct (N × H)
384. #2667	C₂×C₁₃₉	semidirect
385. #2654	C₂×C₁₃₉	semidirect
386. #2585	C₂×C₁₃₉	semidirect
388. #2575	C₂×C₁₃₉	semidirect
389. #2575	C₂×C₁₃₉	semidirect
391. #2519	C₂×C₁₃₉	semidirect
392. #2508	C₂×C₁₃₉	semidirect
393. #2484	C₂×C₁₃₉	semidirect
395. #2475	C₂×C₁₃₉	semidirect
396. #2402	C₂×C₁₃₉	semidirect
398. #2373	C₂×C₁₃₉	semidirect
399. #2371	C₂×C₁₃₉	semidirect
401. #2346	C₂×C₁₃₉	semidirect
402. #2274	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2667×C₁₃₉	2
#2654×C₁₃₉	2
#2585×C₁₃₉	2
#2579×C₁₃₉	2
#2575×C₁₃₉	2
#2526×C₁₃₉	2
#2519×C₁₃₉	2
#2508×C₁₃₉	2
#2484×C₁₃₉	2
#2479×C₁₃₉	2
#2475×C₁₃₉	2
#2402×C₁₃₉	2
#2395×C₁₃₉	2
#2373×C₁₃₉	2
#2371×C₁₃₉	2
#2357×C₁₃₉	2
#2346×C₁₃₉	2
#2274×C₁₃₉	2
#36052	139

Subgroups — C139×#36052 #48030648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36052 #48030648