Subgroups — C₁₃₉×#35632 #48030228

Order 35584.

1608 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2577×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2575×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2570×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2568×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2530×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2527×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2523×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2517×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2514×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2511×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2505×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2447×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2447×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2327×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2326×C₁₃₉	C₂	1	1	yes	maximal, characteristic
19	#2320×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic
21	#2295×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2295×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	#401×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	2	yes	—
37	#400×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#400×C₁₃₉	C₂²	1	2	yes	—
40	#399×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	2	yes	—
45	#397×C₁₃₉	C₂²	1	2	yes	—
46	#397×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	2	yes	—
48	#393×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	1	yes	characteristic
50	#391×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	1	yes	characteristic
52	#391×C₁₃₉	C₂²	1	1	yes	characteristic
53	#391×C₁₃₉	C₂²	1	1	yes	characteristic
54	#391×C₁₃₉	C₂²	1	1	yes	characteristic
55	#391×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#389×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×C₁₃₉	C₂²	1	1	yes	characteristic
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	2	yes	—
72	#387×C₁₃₉	C₂²	1	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	1	yes	characteristic
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	1	yes	characteristic
86	#387×C₁₃₉	C₂²	1	1	yes	characteristic
87	#387×C₁₃₉	C₂²	1	1	yes	characteristic
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#384×C₁₃₉	C₂²	1	1	yes	characteristic
96	#383×C₁₃₉	C₂²	1	2	yes	—
97	#383×C₁₃₉	C₂²	1	2	yes	—
98	#382×C₁₃₉	C₂²	1	1	yes	characteristic
99	#382×C₁₃₉	C₂²	1	2	yes	—
100	#382×C₁₃₉	C₂²	1	2	yes	—
101	#382×C₁₃₉	C₂²	1	1	yes	characteristic
102	#381×C₁₃₉	C₂²	1	2	yes	—
103	#381×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	2	yes	—
105	#380×C₁₃₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
118	#376×C₁₃₉	C₂²	1	2	yes	—
119	#376×C₁₃₉	C₂²	1	1	yes	characteristic
120	#376×C₁₃₉	C₂²	1	1	yes	characteristic
121	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
131	#124×C₁₃₉	—	2	4	no	—
132	#124×C₁₃₉	—	2	4	no	—
133	C₄×Q₈×C₁₃₉	—	2	4	no	—
134	C₄×Q₈×C₁₃₉	—	2	4	no	—
135	C₄×Q₈×C₁₃₉	—	2	4	no	—
136	C₄×D₄×C₁₃₉	—	2	4	no	—
137	C₄×D₄×C₁₃₉	—	2	4	no	—
138	C₄×D₄×C₁₃₉	—	2	4	no	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	#95×C₁₃₉	C₂³	1	1	yes	characteristic
191	#95×C₁₃₉	C₂³	1	1	yes	characteristic
192	#95×C₁₃₉	C₂³	1	1	yes	characteristic
193	#95×C₁₃₉	C₂³	1	1	yes	characteristic
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	1	yes	characteristic
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	2	yes	—
217	#95×C₁₃₉	C₂³	1	2	yes	—
218	#95×C₁₃₉	C₂³	1	2	yes	—
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	1	yes	characteristic
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	1	yes	characteristic
223	#95×C₁₃₉	C₂³	1	2	yes	—
224	#95×C₁₃₉	C₂³	1	1	yes	characteristic
225	#95×C₁₃₉	C₂³	1	1	yes	characteristic
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	#95×C₁₃₉	C₂³	1	1	yes	characteristic
229	#95×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	1	yes	characteristic
231	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₁₃₉	—	2	2	no	—
233	C₂×Q₈×C₁₃₉	—	2	2	no	—
234	C₂×Q₈×C₁₃₉	—	2	2	no	—
235	C₂×Q₈×C₁₃₉	—	2	2	no	—
236	C₂×Q₈×C₁₃₉	—	2	2	no	—
237	C₂×Q₈×C₁₃₉	—	2	2	no	—
238	C₂×Q₈×C₁₃₉	—	2	2	no	—
239	C₂×Q₈×C₁₃₉	—	2	2	no	—
240	C₂×Q₈×C₁₃₉	—	4	1	no	—
241	C₂×D₄×C₁₃₉	—	2	2	no	—
242	C₂×D₄×C₁₃₉	—	2	2	no	—
243	C₂×D₄×C₁₃₉	#41	1	4	yes	—
244	C₂²×C₄×C₁₃₉	—	2	4	no	—
245	C₂²×C₄×C₁₃₉	—	2	4	no	—
246	C₂²×C₄×C₁₃₉	—	2	4	no	—
247	C₂²×C₄×C₁₃₉	—	4	2	no	—
248	C₂²×C₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	4	2	no	—
250	C₂²×C₄×C₁₃₉	—	4	2	no	—
251	C₂²×C₄×C₁₃₉	—	4	2	no	—
252	C₂²×C₄×C₁₃₉	—	4	2	no	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₄⋊C₄×C₁₃₉	—	2	2	no	—
276	C₄⋊C₄×C₁₃₉	—	2	2	no	—
277	C₄⋊C₄×C₁₃₉	—	2	2	no	—
278	C₄⋊C₄×C₁₃₉	—	2	2	no	—
279	C₄⋊C₄×C₁₃₉	—	2	2	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	4	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	2	2	no	—
285	C₄⋊C₄×C₁₃₉	—	2	4	no	—
286	C₄⋊C₄×C₁₃₉	—	2	4	no	—
287	C₄⋊C₄×C₁₃₉	—	2	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	1	no	—
289	C₄⋊C₄×C₁₃₉	—	4	1	no	—
290	C₄⋊C₄×C₁₃₉	—	4	1	no	—
291	C₄⋊C₄×C₁₃₉	—	4	1	no	—
292	C₄⋊C₄×C₁₃₉	—	4	2	no	—
293	C₄⋊C₄×C₁₃₉	—	4	2	no	—
294	C₄⋊C₄×C₁₃₉	—	4	1	no	—
295	C₄⋊C₄×C₁₃₉	—	4	2	no	—
296	C₄⋊C₄×C₁₃₉	—	4	2	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
310	C₄²×C₁₃₉	—	2	2	no	—
311	C₄²×C₁₃₉	—	2	2	no	—
312	C₄²×C₁₃₉	—	2	4	no	—
313	C₄²×C₁₃₉	—	2	4	no	—
314	C₄²×C₁₃₉	—	2	2	no	—
315	C₄²×C₁₃₉	—	2	2	no	—
316	C₄²×C₁₃₉	—	2	2	no	—
317	C₄²×C₁₃₉	—	2	2	no	—
318	C₄²×C₁₃₉	—	4	1	no	—
319	C₄²×C₁₃₉	—	4	2	no	—
320	C₄²×C₁₃₉	—	4	2	no	—
321	C₄²×C₁₃₉	—	4	1	no	—
322	C₄²×C₁₃₉	—	4	1	no	—
323	C₄²×C₁₃₉	—	4	2	no	—
324	C₄²×C₁₃₉	#41	1	4	yes	—
325	C₄²×C₁₃₉	#41	1	4	yes	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
333	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
334	Q₈×C₁₃₉	—	4	4	no	—
335	Q₈×C₁₃₉	—	4	4	no	—
336	Q₈×C₁₃₉	—	4	4	no	—
337	D₄×C₁₃₉	—	2	8	no	—
338	C₂×C₄×C₁₃₉	—	2	1	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	1	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	1	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	1	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	1	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	1	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	1	no	—
371	C₂×C₄×C₁₃₉	—	2	1	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	1	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	1	no	—
377	C₂×C₄×C₁₃₉	—	2	1	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	1	no	—
386	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
391	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
396	C₂×C₄×C₁₃₉	—	8	4	no	—
397	C₂×C₄×C₁₃₉	—	8	4	no	—
398	C₂×C₄×C₁₃₉	—	8	4	no	—
399	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
400	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
401	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
402	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
403	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
404	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
405	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
406	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
407	C₂²×C₁₃₉	—	2	4	no	—
408	C₂²×C₁₃₉	—	2	4	no	—
409	C₂²×C₁₃₉	—	2	4	no	—
410	C₂²×C₁₃₉	—	4	2	no	—
411	C₂²×C₁₃₉	—	4	2	no	—
412	C₂²×C₁₃₉	—	4	2	no	—
413	C₂²×C₁₃₉	—	4	2	no	—
414	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
415	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
416	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
418	C₂²×C₁₃₉	#585	1	1	yes	characteristic
419	C₂²×C₁₃₉	#585	1	1	yes	characteristic
420	C₂²×C₁₃₉	#585	1	1	yes	characteristic
421	C₄×C₁₃₉	—	2	2	no	—
422	C₄×C₁₃₉	—	2	2	no	—
423	C₄×C₁₃₉	—	2	2	no	—
424	C₄×C₁₃₉	—	2	2	no	—
425	C₄×C₁₃₉	—	2	2	no	—
426	C₄×C₁₃₉	—	4	2	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	1	no	—
429	C₄×C₁₃₉	—	4	2	no	—
430	C₄×C₁₃₉	—	4	1	no	—
431	C₄×C₁₃₉	—	4	1	no	—
432	C₄×C₁₃₉	—	4	2	no	—
433	C₄×C₁₃₉	—	4	2	no	—
434	C₄×C₁₃₉	—	4	2	no	—
435	C₄×C₁₃₉	—	4	1	no	—
436	C₄×C₁₃₉	—	4	1	no	—
437	C₄×C₁₃₉	—	4	1	no	—
438	C₄×C₁₃₉	—	4	1	no	—
439	C₄×C₁₃₉	—	4	1	no	—
440	C₄×C₁₃₉	—	4	2	no	—
441	C₄×C₁₃₉	—	4	1	no	—
442	C₄×C₁₃₉	#529	1	4	yes	—
443	C₂×C₁₃₉	—	4	4	no	—
444	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
445	C₂×C₁₃₉	#3495	1	1	yes	characteristic
446	C₂×C₁₃₉	#3507	1	1	yes	characteristic
447	C₂×C₁₃₉	#3510	1	1	yes	characteristic
448	C₂×C₁₃₉	#3510	1	1	yes	characteristic
449	C₂×C₁₃₉	#3515	1	1	yes	characteristic
450	C₂×C₁₃₉	#3521	1	1	yes	characteristic
451	#35632	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₁₃₉	#35632	1	1	yes	characteristic, direct product factor, Sylow
453	#2580	C₂×C₁₃₉	1	1	yes	characteristic
454	#2577	C₂×C₁₃₉	1	2	yes	complemented
455	#2575	C₂×C₁₃₉	1	2	yes	complemented
456	#2570	C₂×C₁₃₉	1	1	yes	characteristic, complemented
457	#2568	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	#2547	C₂×C₁₃₉	1	1	yes	characteristic
459	#2530	C₂×C₁₃₉	1	2	yes	complemented
460	#2527	C₂×C₁₃₉	1	2	yes	complemented
461	#2523	C₂×C₁₃₉	1	2	yes	complemented
462	#2517	C₂×C₁₃₉	1	2	yes	complemented
463	#2514	C₂×C₁₃₉	1	1	yes	characteristic, complemented
464	#2511	C₂×C₁₃₉	1	1	yes	characteristic, complemented
465	#2505	C₂×C₁₃₉	1	2	yes	complemented
466	#2493	C₂×C₁₃₉	1	2	yes	complemented
467	#2447	C₂×C₁₃₉	1	1	yes	characteristic
468	#2447	C₂×C₁₃₉	1	1	yes	characteristic
469	#2327	C₂×C₁₃₉	1	1	yes	characteristic, complemented
470	#2326	C₂×C₁₃₉	1	1	yes	characteristic
471	#2320	C₂×C₁₃₉	1	1	yes	characteristic, complemented
472	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic
473	#2295	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	#2295	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	#2275	C₂×C₁₃₉	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
477	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
478	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
479	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
485	#401	C₂²×C₁₃₉	1	2	yes	—
486	#400	C₂²×C₁₃₉	1	2	yes	—
487	#400	C₂²×C₁₃₉	1	2	yes	—
488	#400	C₂²×C₁₃₉	1	2	yes	—
489	#400	C₂²×C₁₃₉	1	2	yes	—
490	#400	C₂²×C₁₃₉	1	2	yes	—
491	#400	C₂²×C₁₃₉	1	2	yes	—
492	#399	C₂²×C₁₃₉	1	2	yes	—
493	#398	C₂²×C₁₃₉	1	2	yes	—
494	#397	C₂²×C₁₃₉	1	2	yes	—
495	#397	C₂²×C₁₃₉	1	2	yes	—
496	#397	C₂²×C₁₃₉	1	2	yes	—
497	#397	C₂²×C₁₃₉	1	2	yes	—
498	#397	C₂²×C₁₃₉	1	2	yes	—
499	#397	C₂²×C₁₃₉	1	2	yes	—
500	#393	C₂²×C₁₃₉	1	2	yes	—
501	#391	C₂²×C₁₃₉	1	1	yes	characteristic
502	#391	C₂²×C₁₃₉	1	1	yes	characteristic
503	#391	C₂²×C₁₃₉	1	1	yes	characteristic
504	#391	C₂²×C₁₃₉	1	1	yes	characteristic
505	#391	C₂²×C₁₃₉	1	2	yes	—
506	#391	C₂²×C₁₃₉	1	1	yes	characteristic
507	#391	C₂²×C₁₃₉	1	1	yes	characteristic
508	#391	C₂²×C₁₃₉	1	1	yes	characteristic
509	#391	C₂²×C₁₃₉	1	1	yes	characteristic
510	#391	C₂²×C₁₃₉	1	1	yes	characteristic
511	#391	C₂²×C₁₃₉	1	1	yes	characteristic
512	#390	C₂²×C₁₃₉	1	1	yes	characteristic
513	#390	C₂²×C₁₃₉	1	1	yes	characteristic
514	#389	C₂²×C₁₃₉	1	1	yes	characteristic
515	#389	C₂²×C₁₃₉	1	1	yes	characteristic
516	#389	C₂²×C₁₃₉	1	1	yes	characteristic
517	#389	C₂²×C₁₃₉	1	1	yes	characteristic
518	#389	C₂²×C₁₃₉	1	1	yes	characteristic
519	#389	C₂²×C₁₃₉	1	1	yes	characteristic
520	#388	C₂²×C₁₃₉	1	2	yes	—
521	#388	C₂²×C₁₃₉	1	2	yes	—
522	#388	C₂²×C₁₃₉	1	2	yes	—
523	#388	C₂²×C₁₃₉	1	2	yes	—
524	#387	C₂²×C₁₃₉	1	2	yes	—
525	#387	C₂²×C₁₃₉	1	2	yes	—
526	#387	C₂²×C₁₃₉	1	1	yes	characteristic
527	#387	C₂²×C₁₃₉	1	2	yes	—
528	#387	C₂²×C₁₃₉	1	2	yes	—
529	#387	C₂²×C₁₃₉	1	2	yes	—
530	#387	C₂²×C₁₃₉	1	1	yes	characteristic
531	#387	C₂²×C₁₃₉	1	2	yes	—
532	#387	C₂²×C₁₃₉	1	2	yes	—
533	#387	C₂²×C₁₃₉	1	2	yes	—
534	#387	C₂²×C₁₃₉	1	2	yes	—
535	#387	C₂²×C₁₃₉	1	1	yes	characteristic
536	#387	C₂²×C₁₃₉	1	2	yes	—
537	#387	C₂²×C₁₃₉	1	2	yes	—
538	#387	C₂²×C₁₃₉	1	2	yes	—
539	#387	C₂²×C₁₃₉	1	2	yes	—
540	#387	C₂²×C₁₃₉	1	1	yes	characteristic
541	#385	C₂²×C₁₃₉	1	2	yes	—
542	#385	C₂²×C₁₃₉	1	2	yes	—
543	#385	C₂²×C₁₃₉	1	2	yes	—
544	#385	C₂²×C₁₃₉	1	2	yes	—
545	#385	C₂²×C₁₃₉	1	2	yes	—
546	#385	C₂²×C₁₃₉	1	2	yes	—
547	#384	C₂²×C₁₃₉	1	1	yes	characteristic
548	#383	C₂²×C₁₃₉	1	2	yes	—
549	#383	C₂²×C₁₃₉	1	2	yes	—
550	#382	C₂²×C₁₃₉	1	2	yes	—
551	#382	C₂²×C₁₃₉	1	1	yes	characteristic
552	#382	C₂²×C₁₃₉	1	1	yes	characteristic
553	#382	C₂²×C₁₃₉	1	2	yes	—
554	#381	C₂²×C₁₃₉	1	2	yes	—
555	#381	C₂²×C₁₃₉	1	2	yes	—
556	#380	C₂²×C₁₃₉	1	2	yes	—
557	#380	C₂²×C₁₃₉	1	2	yes	—
558	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
560	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
561	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
568	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
569	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
570	#376	C₂²×C₁₃₉	1	1	yes	characteristic
571	#376	C₂²×C₁₃₉	1	1	yes	characteristic
572	#376	C₂²×C₁₃₉	1	2	yes	—
573	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
574	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₄⋊Q₈	—	2	4	no	—
583	#124	—	2	4	no	—
584	#124	—	2	4	no	—
585	C₄×Q₈	—	2	4	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×Q₈	—	2	4	no	—
588	C₄×D₄	—	2	4	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	4	no	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
642	#95	C₂³×C₁₃₉	1	1	yes	characteristic
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	2	yes	—
646	#95	C₂³×C₁₃₉	1	1	yes	characteristic
647	#95	C₂³×C₁₃₉	1	1	yes	characteristic
648	#95	C₂³×C₁₃₉	1	1	yes	characteristic
649	#95	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	1	yes	characteristic
652	#95	C₂³×C₁₃₉	1	1	yes	characteristic
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	1	yes	characteristic
656	#95	C₂³×C₁₃₉	1	1	yes	characteristic
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	2	yes	—
661	#95	C₂³×C₁₃₉	1	2	yes	—
662	#95	C₂³×C₁₃₉	1	1	yes	characteristic
663	#95	C₂³×C₁₃₉	1	1	yes	characteristic
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	1	yes	characteristic
666	#95	C₂³×C₁₃₉	1	1	yes	characteristic
667	#95	C₂³×C₁₃₉	1	1	yes	characteristic
668	#95	C₂³×C₁₃₉	1	1	yes	characteristic
669	#95	C₂³×C₁₃₉	1	2	yes	—
670	#95	C₂³×C₁₃₉	1	2	yes	—
671	#95	C₂³×C₁₃₉	1	2	yes	—
672	#95	C₂³×C₁₃₉	1	2	yes	—
673	#95	C₂³×C₁₃₉	1	2	yes	—
674	#95	C₂³×C₁₃₉	1	2	yes	—
675	#95	C₂³×C₁₃₉	1	2	yes	—
676	#95	C₂³×C₁₃₉	1	2	yes	—
677	#95	C₂³×C₁₃₉	1	2	yes	—
678	#95	C₂³×C₁₃₉	1	2	yes	—
679	#95	C₂³×C₁₃₉	1	2	yes	—
680	#95	C₂³×C₁₃₉	1	2	yes	—
681	#95	C₂³×C₁₃₉	1	2	yes	—
682	#95	C₂³×C₁₃₉	1	2	yes	—
683	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	4	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	#41×C₁₃₉	1	4	yes	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	—	4	1	no	—
743	C₄⋊C₄	—	4	1	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	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	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	4	1	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	1	no	—
774	C₄²	—	4	1	no	—
775	C₄²	—	4	2	no	—
776	C₄²	#41×C₁₃₉	1	4	yes	—
777	C₄²	#41×C₁₃₉	1	4	yes	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
785	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
786	Q₈	—	4	4	no	—
787	Q₈	—	4	4	no	—
788	Q₈	—	4	4	no	—
789	D₄	—	2	8	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	—	8	4	no	—
850	C₂×C₄	—	8	4	no	—
851	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
852	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
853	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
854	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
855	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
856	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
857	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
858	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
859	C₂²	—	2	4	no	—
860	C₂²	—	2	4	no	—
861	C₂²	—	2	4	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
867	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
868	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
869	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
870	C₂²	#585×C₁₃₉	1	1	yes	characteristic
871	C₂²	#585×C₁₃₉	1	1	yes	characteristic
872	C₂²	#585×C₁₃₉	1	1	yes	characteristic
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	#529×C₁₃₉	1	4	yes	—
895	C₂	—	4	4	no	—
896	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
897	C₂	#3495×C₁₃₉	1	1	yes	characteristic
898	C₂	#3507×C₁₃₉	1	1	yes	characteristic
899	C₂	#3510×C₁₃₉	1	1	yes	characteristic
900	C₂	#3510×C₁₃₉	1	1	yes	characteristic
901	C₂	#3515×C₁₃₉	1	1	yes	characteristic
902	C₂	#3521×C₁₃₉	1	1	yes	characteristic

	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. #2577×C₁₃₉	C₂	semidirect
3. #2575×C₁₃₉	C₂	semidirect
4. #2570×C₁₃₉	C₂	semidirect
5. #2568×C₁₃₉	C₂	semidirect
7. #2530×C₁₃₉	C₂	semidirect
8. #2527×C₁₃₉	C₂	semidirect
9. #2523×C₁₃₉	C₂	semidirect
10. #2517×C₁₃₉	C₂	semidirect
11. #2514×C₁₃₉	C₂	semidirect
12. #2511×C₁₃₉	C₂	semidirect
13. #2505×C₁₃₉	C₂	semidirect
14. #2493×C₁₃₉	C₂	semidirect
17. #2327×C₁₃₉	C₂	semidirect
19. #2320×C₁₃₉	C₂	semidirect
21. #2295×C₁₃₉	C₂	semidirect
22. #2295×C₁₃₉	C₂	semidirect
451. #35632	C₁₃₉	direct (N × H)
452. C₁₃₉	#35632	direct (N × H)
454. #2577	C₂×C₁₃₉	semidirect
455. #2575	C₂×C₁₃₉	semidirect
456. #2570	C₂×C₁₃₉	semidirect
457. #2568	C₂×C₁₃₉	semidirect
459. #2530	C₂×C₁₃₉	semidirect
460. #2527	C₂×C₁₃₉	semidirect
461. #2523	C₂×C₁₃₉	semidirect
462. #2517	C₂×C₁₃₉	semidirect
463. #2514	C₂×C₁₃₉	semidirect
464. #2511	C₂×C₁₃₉	semidirect
465. #2505	C₂×C₁₃₉	semidirect
466. #2493	C₂×C₁₃₉	semidirect
469. #2327	C₂×C₁₃₉	semidirect
471. #2320	C₂×C₁₃₉	semidirect
473. #2295	C₂×C₁₃₉	semidirect
474. #2295	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2580×C₁₃₉	2
#2577×C₁₃₉	2
#2575×C₁₃₉	2
#2570×C₁₃₉	2
#2568×C₁₃₉	2
#2547×C₁₃₉	2
#2530×C₁₃₉	2
#2527×C₁₃₉	2
#2523×C₁₃₉	2
#2517×C₁₃₉	2
#2514×C₁₃₉	2
#2511×C₁₃₉	2
#2505×C₁₃₉	2
#2493×C₁₃₉	2
#2447×C₁₃₉	2
#2327×C₁₃₉	2
#2326×C₁₃₉	2
#2320×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2295×C₁₃₉	2
#2275×C₁₃₉	2
#35632	139

Subgroups — C139×#35632 #48030228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35632 #48030228