Subgroups — C₁₃₉×#36341 #48030937

Order 35584.

2528 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2853×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2849×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2583×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2579×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2484×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2483×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2478×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2478×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2474×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2470×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2438×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2413×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2412×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2344×C₁₃₉	C₂	1	2	yes	maximal, complemented
20	#2342×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#385×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	#551×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
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	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₃₉	—	2	8	no	—
40	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
45	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
46	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
56	#400×C₁₃₉	C₂²	1	2	yes	complemented
57	#398×C₁₃₉	C₂²	1	2	yes	complemented
58	#398×C₁₃₉	C₂²	1	2	yes	complemented
59	#398×C₁₃₉	C₂²	1	2	yes	complemented
60	#398×C₁₃₉	C₂²	1	2	yes	complemented
61	#397×C₁₃₉	C₂²	1	2	yes	—
62	#397×C₁₃₉	C₂²	1	2	yes	—
63	#397×C₁₃₉	C₂²	1	2	yes	—
64	#396×C₁₃₉	C₂²	1	2	yes	complemented
65	#396×C₁₃₉	C₂²	1	2	yes	complemented
66	#395×C₁₃₉	C₂²	1	2	yes	complemented
67	#394×C₁₃₉	C₂²	1	2	yes	—
68	#391×C₁₃₉	C₂²	1	2	yes	complemented
69	#389×C₁₃₉	C₂²	1	2	yes	complemented
70	#389×C₁₃₉	C₂²	1	2	yes	complemented
71	#389×C₁₃₉	C₂²	1	2	yes	complemented
72	#389×C₁₃₉	C₂²	1	2	yes	complemented
73	#389×C₁₃₉	C₂²	1	2	yes	complemented
74	#389×C₁₃₉	C₂²	1	2	yes	complemented
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	complemented
78	#388×C₁₃₉	C₂²	1	2	yes	complemented
79	#388×C₁₃₉	C₂²	1	2	yes	complemented
80	#388×C₁₃₉	C₂²	1	2	yes	complemented
81	#387×C₁₃₉	C₂²	1	2	yes	complemented
82	#387×C₁₃₉	C₂²	1	2	yes	complemented
83	#387×C₁₃₉	C₂²	1	2	yes	complemented
84	#387×C₁₃₉	C₂²	1	2	yes	complemented
85	#387×C₁₃₉	C₂²	1	2	yes	complemented
86	#387×C₁₃₉	C₂²	1	2	yes	complemented
87	#387×C₁₃₉	C₂²	1	2	yes	complemented
88	#387×C₁₃₉	C₂²	1	2	yes	complemented
89	#386×C₁₃₉	C₂²	1	1	yes	characteristic
90	#386×C₁₃₉	C₂²	1	1	yes	characteristic
91	#386×C₁₃₉	C₂²	1	1	yes	characteristic
92	#386×C₁₃₉	C₂²	1	2	yes	—
93	#386×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	1	yes	characteristic
95	#385×C₁₃₉	C₂²	1	1	yes	characteristic
96	#385×C₁₃₉	C₂²	1	1	yes	characteristic
97	#385×C₁₃₉	C₂²	1	1	yes	characteristic
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#385×C₁₃₉	C₂²	1	1	yes	characteristic
101	#385×C₁₃₉	C₂²	1	1	yes	characteristic
102	#385×C₁₃₉	C₂²	1	1	yes	characteristic
103	#385×C₁₃₉	C₂²	1	1	yes	characteristic
104	#385×C₁₃₉	C₂²	1	1	yes	characteristic
105	#385×C₁₃₉	C₂²	1	2	yes	—
106	#385×C₁₃₉	C₂²	1	2	yes	—
107	#385×C₁₃₉	C₂²	1	2	yes	—
108	#385×C₁₃₉	C₂²	1	2	yes	complemented
109	#381×C₁₃₉	C₂²	1	1	yes	characteristic
110	#381×C₁₃₉	C₂²	1	2	yes	—
111	#381×C₁₃₉	C₂²	1	1	yes	characteristic
112	#381×C₁₃₉	C₂²	1	1	yes	characteristic
113	#381×C₁₃₉	C₂²	1	1	yes	characteristic
114	#381×C₁₃₉	C₂²	1	2	yes	—
115	#380×C₁₃₉	C₂²	1	1	yes	characteristic
116	#380×C₁₃₉	C₂²	1	2	yes	—
117	#379×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
120	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃₉	—	2	4	no	—
131	C₂³×C₄×C₁₃₉	—	2	8	no	—
132	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	#126×C₁₃₉	—	2	4	no	—
145	#126×C₁₃₉	—	2	4	no	—
146	#124×C₁₃₉	—	2	4	no	—
147	#123×C₁₃₉	—	2	4	no	—
148	#123×C₁₃₉	—	2	8	no	—
149	#123×C₁₃₉	—	2	4	no	—
150	#123×C₁₃₉	—	2	4	no	—
151	#123×C₁₃₉	—	2	4	no	—
152	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
153	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
154	#120×C₁₃₉	—	2	4	no	—
155	C₄×D₄×C₁₃₉	—	2	4	no	—
156	C₄×D₄×C₁₃₉	—	2	4	no	—
157	#117×C₁₃₉	—	2	4	no	—
158	#117×C₁₃₉	—	2	8	no	—
159	#117×C₁₃₉	—	2	8	no	—
160	#117×C₁₃₉	—	2	8	no	—
161	#117×C₁₃₉	—	2	8	no	—
162	#117×C₁₃₉	—	2	4	no	—
163	#117×C₁₃₉	—	2	4	no	—
164	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
165	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
192	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
193	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
194	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	—
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃₉	—	2	4	no	—
223	C₂×C₄²×C₁₃₉	—	2	4	no	—
224	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	2	yes	—
234	#95×C₁₃₉	C₂³	1	2	yes	—
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	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	#95×C₁₃₉	C₂³	1	2	yes	—
255	C₂⁴×C₁₃₉	—	2	2	no	—
256	C₂⁴×C₁₃₉	—	2	4	no	—
257	C₂⁴×C₁₃₉	—	2	2	no	—
258	C₂⁴×C₁₃₉	—	4	2	no	—
259	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
260	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂×Q₈×C₁₃₉	—	2	2	no	—
265	C₂×Q₈×C₁₃₉	—	4	2	no	—
266	C₂×D₄×C₁₃₉	—	2	2	no	—
267	C₂×D₄×C₁₃₉	—	2	2	no	—
268	C₂×D₄×C₁₃₉	—	2	4	no	—
269	C₂×D₄×C₁₃₉	—	2	2	no	—
270	C₂×D₄×C₁₃₉	—	2	2	no	—
271	C₂×D₄×C₁₃₉	—	2	2	no	—
272	C₂×D₄×C₁₃₉	—	4	2	no	—
273	C₂²×C₄×C₁₃₉	—	2	32	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	4	no	—
278	C₂²×C₄×C₁₃₉	—	2	2	no	—
279	C₂²×C₄×C₁₃₉	—	2	4	no	—
280	C₂²×C₄×C₁₃₉	—	2	2	no	—
281	C₂²×C₄×C₁₃₉	—	2	4	no	—
282	C₂²×C₄×C₁₃₉	—	2	4	no	—
283	C₂²×C₄×C₁₃₉	—	2	4	no	—
284	C₂²×C₄×C₁₃₉	—	2	4	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	2	no	—
287	C₂²×C₄×C₁₃₉	—	2	2	no	—
288	C₂²×C₄×C₁₃₉	—	2	4	no	—
289	C₂²×C₄×C₁₃₉	—	2	4	no	—
290	C₂²×C₄×C₁₃₉	—	2	2	no	—
291	C₂²×C₄×C₁₃₉	—	2	2	no	—
292	C₂²×C₄×C₁₃₉	—	2	2	no	—
293	C₂²×C₄×C₁₃₉	—	2	4	no	—
294	C₂²×C₄×C₁₃₉	—	2	2	no	—
295	C₂²×C₄×C₁₃₉	—	4	2	no	—
296	C₂²×C₄×C₁₃₉	—	4	2	no	—
297	C₂²×C₄×C₁₃₉	—	4	2	no	—
298	C₂²×C₄×C₁₃₉	—	4	2	no	—
299	C₂²×C₄×C₁₃₉	—	4	2	no	—
300	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
301	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
302	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
303	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₁₃₉	—	2	4	no	—
323	C₄⋊C₄×C₁₃₉	—	2	4	no	—
324	C₄⋊C₄×C₁₃₉	—	2	4	no	—
325	C₄⋊C₄×C₁₃₉	—	2	4	no	—
326	C₄⋊C₄×C₁₃₉	—	2	2	no	—
327	C₄⋊C₄×C₁₃₉	—	2	2	no	—
328	C₄⋊C₄×C₁₃₉	—	2	2	no	—
329	C₄⋊C₄×C₁₃₉	—	2	2	no	—
330	C₄⋊C₄×C₁₃₉	—	2	2	no	—
331	C₄⋊C₄×C₁₃₉	—	2	2	no	—
332	C₄⋊C₄×C₁₃₉	—	2	2	no	—
333	C₄⋊C₄×C₁₃₉	—	2	2	no	—
334	C₄⋊C₄×C₁₃₉	—	2	4	no	—
335	C₄⋊C₄×C₁₃₉	—	2	4	no	—
336	C₄⋊C₄×C₁₃₉	—	2	4	no	—
337	C₄⋊C₄×C₁₃₉	—	2	4	no	—
338	C₄⋊C₄×C₁₃₉	—	2	4	no	—
339	C₄⋊C₄×C₁₃₉	—	2	4	no	—
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	4	no	—
342	C₄⋊C₄×C₁₃₉	—	4	2	no	—
343	C₄⋊C₄×C₁₃₉	—	4	2	no	—
344	C₄⋊C₄×C₁₃₉	—	4	2	no	—
345	C₄⋊C₄×C₁₃₉	—	4	2	no	—
346	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
347	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
348	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
350	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
368	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
369	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
370	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
371	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
372	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
373	C₄²×C₁₃₉	—	2	4	no	—
374	C₄²×C₁₃₉	—	2	4	no	—
375	C₄²×C₁₃₉	—	2	4	no	—
376	C₄²×C₁₃₉	—	2	4	no	—
377	C₄²×C₁₃₉	—	2	2	no	—
378	C₄²×C₁₃₉	—	2	2	no	—
379	C₄²×C₁₃₉	—	2	2	no	—
380	C₄²×C₁₃₉	—	2	4	no	—
381	C₄²×C₁₃₉	—	4	2	no	—
382	C₂³×C₁₃₉	—	2	2	no	—
383	C₂³×C₁₃₉	—	2	1	no	—
384	C₂³×C₁₃₉	—	2	1	no	—
385	C₂³×C₁₃₉	—	2	2	no	—
386	C₂³×C₁₃₉	—	2	2	no	—
387	C₂³×C₁₃₉	—	2	8	no	—
388	C₂³×C₁₃₉	—	2	8	no	—
389	C₂³×C₁₃₉	—	2	1	no	—
390	C₂³×C₁₃₉	—	2	2	no	—
391	C₂³×C₁₃₉	—	2	1	no	—
392	C₂³×C₁₃₉	—	2	2	no	—
393	C₂³×C₁₃₉	—	2	1	no	—
394	C₂³×C₁₃₉	—	2	2	no	—
395	C₂³×C₁₃₉	—	2	1	no	—
396	C₂³×C₁₃₉	—	2	1	no	—
397	C₂³×C₁₃₉	—	2	2	no	—
398	C₂³×C₁₃₉	—	4	4	no	—
399	C₂³×C₁₃₉	—	4	8	no	—
400	C₂³×C₁₃₉	—	4	8	no	—
401	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
402	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
403	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
404	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
405	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
406	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
407	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
408	Q₈×C₁₃₉	—	8	2	no	—
409	D₄×C₁₃₉	—	4	4	no	—
410	D₄×C₁₃₉	—	4	4	no	—
411	D₄×C₁₃₉	—	8	2	no	—
412	C₂×C₄×C₁₃₉	—	2	8	no	—
413	C₂×C₄×C₁₃₉	—	2	8	no	—
414	C₂×C₄×C₁₃₉	—	2	16	no	—
415	C₂×C₄×C₁₃₉	—	2	16	no	—
416	C₂×C₄×C₁₃₉	—	2	8	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	1	no	—
421	C₂×C₄×C₁₃₉	—	2	2	no	—
422	C₂×C₄×C₁₃₉	—	2	2	no	—
423	C₂×C₄×C₁₃₉	—	2	2	no	—
424	C₂×C₄×C₁₃₉	—	2	1	no	—
425	C₂×C₄×C₁₃₉	—	2	1	no	—
426	C₂×C₄×C₁₃₉	—	2	2	no	—
427	C₂×C₄×C₁₃₉	—	2	2	no	—
428	C₂×C₄×C₁₃₉	—	2	2	no	—
429	C₂×C₄×C₁₃₉	—	2	1	no	—
430	C₂×C₄×C₁₃₉	—	2	2	no	—
431	C₂×C₄×C₁₃₉	—	2	2	no	—
432	C₂×C₄×C₁₃₉	—	2	1	no	—
433	C₂×C₄×C₁₃₉	—	2	1	no	—
434	C₂×C₄×C₁₃₉	—	2	1	no	—
435	C₂×C₄×C₁₃₉	—	2	1	no	—
436	C₂×C₄×C₁₃₉	—	2	1	no	—
437	C₂×C₄×C₁₃₉	—	2	1	no	—
438	C₂×C₄×C₁₃₉	—	2	2	no	—
439	C₂×C₄×C₁₃₉	—	2	2	no	—
440	C₂×C₄×C₁₃₉	—	2	2	no	—
441	C₂×C₄×C₁₃₉	—	2	2	no	—
442	C₂×C₄×C₁₃₉	—	2	2	no	—
443	C₂×C₄×C₁₃₉	—	2	2	no	—
444	C₂×C₄×C₁₃₉	—	2	2	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	2	2	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	2	2	no	—
449	C₂×C₄×C₁₃₉	—	2	2	no	—
450	C₂×C₄×C₁₃₉	—	2	1	no	—
451	C₂×C₄×C₁₃₉	—	2	2	no	—
452	C₂×C₄×C₁₃₉	—	2	2	no	—
453	C₂×C₄×C₁₃₉	—	2	2	no	—
454	C₂×C₄×C₁₃₉	—	2	2	no	—
455	C₂×C₄×C₁₃₉	—	2	2	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	2	no	—
458	C₂×C₄×C₁₃₉	—	2	2	no	—
459	C₂×C₄×C₁₃₉	—	4	4	no	—
460	C₂×C₄×C₁₃₉	—	4	8	no	—
461	C₂×C₄×C₁₃₉	—	4	4	no	—
462	C₂×C₄×C₁₃₉	—	4	4	no	—
463	C₂×C₄×C₁₃₉	—	4	4	no	—
464	C₂×C₄×C₁₃₉	—	8	2	no	—
465	C₂×C₄×C₁₃₉	—	8	2	no	—
466	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
471	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
472	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
473	C₂²×C₁₃₉	—	2	2	no	—
474	C₂²×C₁₃₉	—	2	2	no	—
475	C₂²×C₁₃₉	—	2	4	no	—
476	C₂²×C₁₃₉	—	2	4	no	—
477	C₂²×C₁₃₉	—	2	2	no	—
478	C₂²×C₁₃₉	—	2	2	no	—
479	C₂²×C₁₃₉	—	2	4	no	—
480	C₂²×C₁₃₉	—	2	4	no	—
481	C₂²×C₁₃₉	—	2	2	no	—
482	C₂²×C₁₃₉	—	2	2	no	—
483	C₂²×C₁₃₉	—	2	2	no	—
484	C₂²×C₁₃₉	—	4	16	no	—
485	C₂²×C₁₃₉	—	4	2	no	—
486	C₂²×C₁₃₉	—	4	2	no	—
487	C₂²×C₁₃₉	—	4	1	no	—
488	C₂²×C₁₃₉	—	4	1	no	—
489	C₂²×C₁₃₉	—	4	2	no	—
490	C₂²×C₁₃₉	—	4	1	no	—
491	C₂²×C₁₃₉	—	4	2	no	—
492	C₂²×C₁₃₉	#525	1	4	yes	—
493	C₂²×C₁₃₉	#547	1	4	yes	—
494	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
495	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
496	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
497	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
498	C₂²×C₁₃₉	#585	1	2	yes	—
499	C₄×C₁₃₉	—	2	4	no	—
500	C₄×C₁₃₉	—	2	4	no	—
501	C₄×C₁₃₉	—	2	2	no	—
502	C₄×C₁₃₉	—	2	2	no	—
503	C₄×C₁₃₉	—	2	4	no	—
504	C₄×C₁₃₉	—	2	2	no	—
505	C₄×C₁₃₉	—	2	2	no	—
506	C₄×C₁₃₉	—	4	1	no	—
507	C₄×C₁₃₉	—	4	1	no	—
508	C₄×C₁₃₉	—	4	1	no	—
509	C₄×C₁₃₉	—	4	2	no	—
510	C₄×C₁₃₉	—	4	1	no	—
511	C₄×C₁₃₉	—	4	2	no	—
512	C₄×C₁₃₉	—	4	2	no	—
513	C₄×C₁₃₉	—	4	2	no	—
514	C₄×C₁₃₉	—	4	1	no	—
515	C₄×C₁₃₉	—	4	1	no	—
516	C₄×C₁₃₉	—	4	1	no	—
517	C₄×C₁₃₉	—	4	2	no	—
518	C₂×C₁₃₉	—	2	4	no	—
519	C₂×C₁₃₉	—	2	4	no	—
520	C₂×C₁₃₉	—	4	2	no	—
521	C₂×C₁₃₉	—	8	1	no	—
522	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
523	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
524	C₂×C₁₃₉	#3475	1	2	yes	—
525	C₂×C₁₃₉	#3485	1	1	yes	characteristic
526	C₂×C₁₃₉	#3495	1	2	yes	—
527	#36341	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
528	C₁₃₉	#36341	1	1	yes	characteristic, direct product factor, Sylow
529	C₂×#551	C₂×C₁₃₉	1	1	yes	characteristic
530	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
531	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
532	#2853	C₂×C₁₃₉	1	1	yes	characteristic, complemented
533	#2849	C₂×C₁₃₉	1	1	yes	characteristic
534	#2583	C₂×C₁₃₉	1	1	yes	characteristic, complemented
535	#2579	C₂×C₁₃₉	1	1	yes	characteristic, complemented
536	#2484	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	#2483	C₂×C₁₃₉	1	1	yes	characteristic, complemented
538	#2478	C₂×C₁₃₉	1	2	yes	complemented
539	#2478	C₂×C₁₃₉	1	2	yes	complemented
540	#2474	C₂×C₁₃₉	1	2	yes	complemented
541	#2470	C₂×C₁₃₉	1	2	yes	complemented
542	#2438	C₂×C₁₃₉	1	2	yes	complemented
543	#2413	C₂×C₁₃₉	1	2	yes	complemented
544	#2413	C₂×C₁₃₉	1	1	yes	characteristic, complemented
545	#2412	C₂×C₁₃₉	1	1	yes	characteristic
546	#2359	C₂×C₁₃₉	1	2	yes	complemented
547	#2344	C₂×C₁₃₉	1	2	yes	complemented
548	#2342	C₂×C₁₃₉	1	1	yes	characteristic, complemented
549	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
550	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
551	C₂×#385	C₂×C₁₃₉	1	1	yes	characteristic, complemented
552	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
553	#551	—	2	8	no	—
554	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
555	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
556	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
557	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
558	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
559	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
560	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
561	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
564	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
567	C₂×#117	—	2	8	no	—
568	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
570	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
571	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
572	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
573	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
574	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
577	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
578	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
580	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
583	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
584	#400	C₂²×C₁₃₉	1	2	yes	complemented
585	#398	C₂²×C₁₃₉	1	2	yes	complemented
586	#398	C₂²×C₁₃₉	1	2	yes	complemented
587	#398	C₂²×C₁₃₉	1	2	yes	complemented
588	#398	C₂²×C₁₃₉	1	2	yes	complemented
589	#397	C₂²×C₁₃₉	1	2	yes	—
590	#397	C₂²×C₁₃₉	1	2	yes	—
591	#397	C₂²×C₁₃₉	1	2	yes	—
592	#396	C₂²×C₁₃₉	1	2	yes	complemented
593	#396	C₂²×C₁₃₉	1	2	yes	complemented
594	#395	C₂²×C₁₃₉	1	2	yes	complemented
595	#394	C₂²×C₁₃₉	1	2	yes	—
596	#391	C₂²×C₁₃₉	1	2	yes	complemented
597	#389	C₂²×C₁₃₉	1	2	yes	complemented
598	#389	C₂²×C₁₃₉	1	2	yes	complemented
599	#389	C₂²×C₁₃₉	1	2	yes	complemented
600	#389	C₂²×C₁₃₉	1	2	yes	complemented
601	#389	C₂²×C₁₃₉	1	2	yes	complemented
602	#389	C₂²×C₁₃₉	1	2	yes	complemented
603	#388	C₂²×C₁₃₉	1	2	yes	—
604	#388	C₂²×C₁₃₉	1	2	yes	—
605	#388	C₂²×C₁₃₉	1	2	yes	complemented
606	#388	C₂²×C₁₃₉	1	2	yes	complemented
607	#388	C₂²×C₁₃₉	1	2	yes	complemented
608	#388	C₂²×C₁₃₉	1	2	yes	complemented
609	#387	C₂²×C₁₃₉	1	2	yes	complemented
610	#387	C₂²×C₁₃₉	1	2	yes	complemented
611	#387	C₂²×C₁₃₉	1	2	yes	complemented
612	#387	C₂²×C₁₃₉	1	2	yes	complemented
613	#387	C₂²×C₁₃₉	1	2	yes	complemented
614	#387	C₂²×C₁₃₉	1	2	yes	complemented
615	#387	C₂²×C₁₃₉	1	2	yes	complemented
616	#387	C₂²×C₁₃₉	1	2	yes	complemented
617	#386	C₂²×C₁₃₉	1	1	yes	characteristic
618	#386	C₂²×C₁₃₉	1	1	yes	characteristic
619	#386	C₂²×C₁₃₉	1	1	yes	characteristic
620	#386	C₂²×C₁₃₉	1	2	yes	—
621	#386	C₂²×C₁₃₉	1	2	yes	—
622	#385	C₂²×C₁₃₉	1	1	yes	characteristic
623	#385	C₂²×C₁₃₉	1	1	yes	characteristic
624	#385	C₂²×C₁₃₉	1	1	yes	characteristic
625	#385	C₂²×C₁₃₉	1	1	yes	characteristic
626	#385	C₂²×C₁₃₉	1	1	yes	characteristic
627	#385	C₂²×C₁₃₉	1	1	yes	characteristic
628	#385	C₂²×C₁₃₉	1	1	yes	characteristic
629	#385	C₂²×C₁₃₉	1	2	yes	—
630	#385	C₂²×C₁₃₉	1	1	yes	characteristic
631	#385	C₂²×C₁₃₉	1	2	yes	—
632	#385	C₂²×C₁₃₉	1	2	yes	—
633	#385	C₂²×C₁₃₉	1	2	yes	—
634	#385	C₂²×C₁₃₉	1	2	yes	—
635	#385	C₂²×C₁₃₉	1	1	yes	characteristic
636	#385	C₂²×C₁₃₉	1	2	yes	complemented
637	#381	C₂²×C₁₃₉	1	2	yes	—
638	#381	C₂²×C₁₃₉	1	1	yes	characteristic
639	#381	C₂²×C₁₃₉	1	1	yes	characteristic
640	#381	C₂²×C₁₃₉	1	1	yes	characteristic
641	#381	C₂²×C₁₃₉	1	2	yes	—
642	#381	C₂²×C₁₃₉	1	1	yes	characteristic
643	#380	C₂²×C₁₃₉	1	1	yes	characteristic
644	#380	C₂²×C₁₃₉	1	2	yes	—
645	#379	C₂²×C₁₃₉	1	1	yes	characteristic
646	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
647	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
648	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
649	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
650	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
651	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
652	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
653	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
654	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
656	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂³×C₄	—	2	4	no	—
659	C₂³×C₄	—	2	8	no	—
660	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
661	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
662	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
664	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
666	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
668	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
671	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
672	#126	—	2	4	no	—
673	#126	—	2	4	no	—
674	#124	—	2	4	no	—
675	#123	—	2	4	no	—
676	#123	—	2	8	no	—
677	#123	—	2	4	no	—
678	#123	—	2	4	no	—
679	#123	—	2	4	no	—
680	C₂²⋊Q₈	—	2	4	no	—
681	C₂²⋊Q₈	—	2	4	no	—
682	#120	—	2	4	no	—
683	C₄×D₄	—	2	4	no	—
684	C₄×D₄	—	2	4	no	—
685	#117	—	2	4	no	—
686	#117	—	2	8	no	—
687	#117	—	2	8	no	—
688	#117	—	2	8	no	—
689	#117	—	2	8	no	—
690	#117	—	2	4	no	—
691	#117	—	2	4	no	—
692	C₂×C₄⋊C₄	—	2	4	no	—
693	C₂×C₄⋊C₄	—	2	4	no	—
694	C₂×C₄⋊C₄	—	2	8	no	—
695	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
719	C₂×C₂²⋊C₄	—	2	4	no	—
720	C₂×C₂²⋊C₄	—	2	4	no	—
721	C₂×C₂²⋊C₄	—	2	4	no	—
722	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
733	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
749	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
750	C₂×C₄²	—	2	4	no	—
751	C₂×C₄²	—	2	4	no	—
752	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
754	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
756	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
757	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
760	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
761	#95	C₂³×C₁₃₉	1	2	yes	—
762	#95	C₂³×C₁₃₉	1	2	yes	—
763	#95	C₂³×C₁₃₉	1	2	yes	—
764	#95	C₂³×C₁₃₉	1	2	yes	—
765	#95	C₂³×C₁₃₉	1	2	yes	—
766	#95	C₂³×C₁₃₉	1	2	yes	—
767	#95	C₂³×C₁₃₉	1	2	yes	—
768	#95	C₂³×C₁₃₉	1	2	yes	—
769	#95	C₂³×C₁₃₉	1	2	yes	—
770	#95	C₂³×C₁₃₉	1	2	yes	—
771	#95	C₂³×C₁₃₉	1	2	yes	—
772	#95	C₂³×C₁₃₉	1	2	yes	—
773	#95	C₂³×C₁₃₉	1	2	yes	—
774	#95	C₂³×C₁₃₉	1	2	yes	—
775	#95	C₂³×C₁₃₉	1	2	yes	—
776	#95	C₂³×C₁₃₉	1	2	yes	—
777	#95	C₂³×C₁₃₉	1	2	yes	—
778	#95	C₂³×C₁₃₉	1	2	yes	—
779	#95	C₂³×C₁₃₉	1	2	yes	—
780	#95	C₂³×C₁₃₉	1	2	yes	—
781	#95	C₂³×C₁₃₉	1	2	yes	—
782	#95	C₂³×C₁₃₉	1	2	yes	—
783	C₂⁴	—	2	2	no	—
784	C₂⁴	—	2	4	no	—
785	C₂⁴	—	2	2	no	—
786	C₂⁴	—	4	2	no	—
787	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
788	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
789	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
790	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
791	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	4	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	4	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂²×C₄	—	2	32	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	4	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	4	no	—
817	C₂²×C₄	—	2	4	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	4	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
829	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
830	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
831	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
850	C₄⋊C₄	—	2	4	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	4	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	4	no	—
870	C₄⋊C₄	—	4	2	no	—
871	C₄⋊C₄	—	4	2	no	—
872	C₄⋊C₄	—	4	2	no	—
873	C₄⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
897	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
898	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
899	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
900	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
901	C₄²	—	2	4	no	—
902	C₄²	—	2	4	no	—
903	C₄²	—	2	4	no	—
904	C₄²	—	2	4	no	—
905	C₄²	—	2	2	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	4	no	—
909	C₄²	—	4	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	8	no	—
916	C₂³	—	2	8	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	4	4	no	—
927	C₂³	—	4	8	no	—
928	C₂³	—	4	8	no	—
929	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
930	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
931	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
932	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
933	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
934	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
935	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
936	Q₈	—	8	2	no	—
937	D₄	—	4	4	no	—
938	D₄	—	4	4	no	—
939	D₄	—	8	2	no	—
940	C₂×C₄	—	2	8	no	—
941	C₂×C₄	—	2	8	no	—
942	C₂×C₄	—	2	16	no	—
943	C₂×C₄	—	2	16	no	—
944	C₂×C₄	—	2	8	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	4	8	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	8	2	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
995	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
996	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
997	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
998	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
999	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1000	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	4	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	4	16	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	#525×C₁₃₉	1	4	yes	—
1021	C₂²	#547×C₁₃₉	1	4	yes	—
1022	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1023	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
1024	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1025	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1026	C₂²	#585×C₁₃₉	1	2	yes	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	4	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	2	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₂	—	2	4	no	—
1047	C₂	—	2	4	no	—
1048	C₂	—	4	2	no	—
1049	C₂	—	8	1	no	—
1050	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1051	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
1052	C₂	#3475×C₁₃₉	1	2	yes	—
1053	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1054	C₂	#3495×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#120×C₁₃₉	C₂²
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. C₂²×#117×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2853×C₁₃₉	C₂	semidirect
6. #2583×C₁₃₉	C₂	semidirect
7. #2579×C₁₃₉	C₂	semidirect
8. #2484×C₁₃₉	C₂	semidirect
9. #2483×C₁₃₉	C₂	semidirect
10. #2478×C₁₃₉	C₂	semidirect
11. #2478×C₁₃₉	C₂	semidirect
12. #2474×C₁₃₉	C₂	semidirect
13. #2470×C₁₃₉	C₂	semidirect
14. #2438×C₁₃₉	C₂	semidirect
15. #2413×C₁₃₉	C₂	semidirect
16. #2413×C₁₃₉	C₂	semidirect
18. #2359×C₁₃₉	C₂	semidirect
19. #2344×C₁₃₉	C₂	semidirect
20. #2342×C₁₃₉	C₂	semidirect
21. C₄×#123×C₁₃₉	C₂	semidirect
22. #2296×C₁₃₉	C₂	semidirect
23. C₂×#385×C₁₃₉	C₂	semidirect
56. #400×C₁₃₉	C₂²	semidirect
57. #398×C₁₃₉	C₂²	semidirect
58. #398×C₁₃₉	C₂²	semidirect
59. #398×C₁₃₉	C₂²	semidirect
60. #398×C₁₃₉	C₂²	semidirect
64. #396×C₁₃₉	C₂²	semidirect
65. #396×C₁₃₉	C₂²	semidirect
66. #395×C₁₃₉	C₂²	semidirect
68. #391×C₁₃₉	C₂²	semidirect
69. #389×C₁₃₉	C₂²	semidirect
70. #389×C₁₃₉	C₂²	semidirect
71. #389×C₁₃₉	C₂²	semidirect
72. #389×C₁₃₉	C₂²	semidirect
73. #389×C₁₃₉	C₂²	semidirect
74. #389×C₁₃₉	C₂²	semidirect
77. #388×C₁₃₉	C₂²	semidirect
78. #388×C₁₃₉	C₂²	semidirect
79. #388×C₁₃₉	C₂²	semidirect
80. #388×C₁₃₉	C₂²	semidirect
81. #387×C₁₃₉	C₂²	semidirect
82. #387×C₁₃₉	C₂²	semidirect
83. #387×C₁₃₉	C₂²	semidirect
84. #387×C₁₃₉	C₂²	semidirect
85. #387×C₁₃₉	C₂²	semidirect
86. #387×C₁₃₉	C₂²	semidirect
87. #387×C₁₃₉	C₂²	semidirect
88. #387×C₁₃₉	C₂²	semidirect
108. #385×C₁₃₉	C₂²	semidirect
118. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
527. #36341	C₁₃₉	direct (N × H)
528. C₁₃₉	#36341	direct (N × H)
530. C₂²×#117	C₂×C₁₃₉	semidirect
531. #2855	C₂×C₁₃₉	semidirect
532. #2853	C₂×C₁₃₉	semidirect
534. #2583	C₂×C₁₃₉	semidirect
535. #2579	C₂×C₁₃₉	semidirect
536. #2484	C₂×C₁₃₉	semidirect
537. #2483	C₂×C₁₃₉	semidirect
538. #2478	C₂×C₁₃₉	semidirect
539. #2478	C₂×C₁₃₉	semidirect
540. #2474	C₂×C₁₃₉	semidirect
541. #2470	C₂×C₁₃₉	semidirect
542. #2438	C₂×C₁₃₉	semidirect
543. #2413	C₂×C₁₃₉	semidirect
544. #2413	C₂×C₁₃₉	semidirect
546. #2359	C₂×C₁₃₉	semidirect
547. #2344	C₂×C₁₃₉	semidirect
548. #2342	C₂×C₁₃₉	semidirect
549. C₄×#123	C₂×C₁₃₉	semidirect
550. #2296	C₂×C₁₃₉	semidirect
551. C₂×#385	C₂×C₁₃₉	semidirect
584. #400	C₂²×C₁₃₉	semidirect
585. #398	C₂²×C₁₃₉	semidirect
586. #398	C₂²×C₁₃₉	semidirect
587. #398	C₂²×C₁₃₉	semidirect
588. #398	C₂²×C₁₃₉	semidirect
592. #396	C₂²×C₁₃₉	semidirect
593. #396	C₂²×C₁₃₉	semidirect
594. #395	C₂²×C₁₃₉	semidirect
596. #391	C₂²×C₁₃₉	semidirect
597. #389	C₂²×C₁₃₉	semidirect
598. #389	C₂²×C₁₃₉	semidirect
599. #389	C₂²×C₁₃₉	semidirect
600. #389	C₂²×C₁₃₉	semidirect
601. #389	C₂²×C₁₃₉	semidirect
602. #389	C₂²×C₁₃₉	semidirect
605. #388	C₂²×C₁₃₉	semidirect
606. #388	C₂²×C₁₃₉	semidirect
607. #388	C₂²×C₁₃₉	semidirect
608. #388	C₂²×C₁₃₉	semidirect
609. #387	C₂²×C₁₃₉	semidirect
610. #387	C₂²×C₁₃₉	semidirect
611. #387	C₂²×C₁₃₉	semidirect
612. #387	C₂²×C₁₃₉	semidirect
613. #387	C₂²×C₁₃₉	semidirect
614. #387	C₂²×C₁₃₉	semidirect
615. #387	C₂²×C₁₃₉	semidirect
616. #387	C₂²×C₁₃₉	semidirect
636. #385	C₂²×C₁₃₉	semidirect
646. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
647. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
648. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
651. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551×C₁₃₉	2
C₂²×#117×C₁₃₉	2
#2855×C₁₃₉	2
#2853×C₁₃₉	2
#2849×C₁₃₉	2
#2583×C₁₃₉	2
#2579×C₁₃₉	2
#2484×C₁₃₉	2
#2483×C₁₃₉	2
#2478×C₁₃₉	2
#2474×C₁₃₉	2
#2470×C₁₃₉	2
#2438×C₁₃₉	2
#2413×C₁₃₉	2
#2412×C₁₃₉	2
#2359×C₁₃₉	2
#2344×C₁₃₉	2
#2342×C₁₃₉	2
C₄×#123×C₁₃₉	2
#2296×C₁₃₉	2
C₂×#385×C₁₃₉	2
#36341	139

Subgroups — C139×#36341 #48030937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36341 #48030937