Subgroups — C₁₃₉×#37146 #48031742

Order 35584.

1316 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2863×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2810×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2806×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2805×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2805×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2794×C₁₃₉	C₂	1	2	yes	maximal
8	#2791×C₁₃₉	C₂	1	2	yes	maximal
9	#2776×C₁₃₉	C₂	1	2	yes	maximal
10	#2774×C₁₃₉	C₂	1	2	yes	maximal
11	#2767×C₁₃₉	C₂	1	2	yes	maximal
12	#2762×C₁₃₉	C₂	1	2	yes	maximal
13	#2634×C₁₃₉	C₂	1	2	yes	maximal
14	#2590×C₁₃₉	C₂	1	2	yes	maximal
15	#2588×C₁₃₉	C₂	1	2	yes	maximal
16	#2533×C₁₃₉	C₂	1	2	yes	maximal
17	#2528×C₁₃₉	C₂	1	2	yes	maximal
18	#2336×C₁₃₉	C₂	1	2	yes	maximal
19	#2295×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	#401×C₁₃₉	C₂²	1	2	yes	—
23	#400×C₁₃₉	C₂²	1	2	yes	—
24	#400×C₁₃₉	C₂²	1	2	yes	—
25	#400×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#395×C₁₃₉	C₂²	1	2	yes	—
44	#395×C₁₃₉	C₂²	1	2	yes	—
45	#395×C₁₃₉	C₂²	1	2	yes	—
46	#391×C₁₃₉	C₂²	1	1	yes	characteristic
47	#391×C₁₃₉	C₂²	1	1	yes	characteristic
48	#391×C₁₃₉	C₂²	1	1	yes	characteristic
49	#391×C₁₃₉	C₂²	1	2	yes	—
50	#391×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	1	yes	characteristic
52	#389×C₁₃₉	C₂²	1	1	yes	characteristic
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	1	yes	characteristic
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	1	yes	characteristic
59	#389×C₁₃₉	C₂²	1	1	yes	characteristic
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×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	2	yes	—
66	#389×C₁₃₉	C₂²	1	1	yes	characteristic
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	#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	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#387×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#384×C₁₃₉	C₂²	1	1	yes	characteristic
96	#384×C₁₃₉	C₂²	1	1	yes	characteristic
97	#383×C₁₃₉	C₂²	1	2	yes	—
98	#383×C₁₃₉	C₂²	1	2	yes	—
99	#382×C₁₃₉	C₂²	1	2	yes	—
100	#382×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	#376×C₁₃₉	C₂²	1	2	yes	—
106	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	#125×C₁₃₉	—	2	8	no	—
110	C₄×Q₈×C₁₃₉	—	2	4	no	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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×C₄²×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	#95×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
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	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	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	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	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	C₂×Q₈×C₁₃₉	—	2	2	no	—
197	C₂×Q₈×C₁₃₉	—	2	2	no	—
198	C₂×Q₈×C₁₃₉	—	4	1	no	—
199	C₂×Q₈×C₁₃₉	—	4	1	no	—
200	C₂×Q₈×C₁₃₉	—	4	1	no	—
201	C₂×Q₈×C₁₃₉	—	4	1	no	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₄×C₁₃₉	—	2	2	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	4	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	2	no	—
232	C₄⋊C₄×C₁₃₉	—	2	2	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	4	1	no	—
237	C₄⋊C₄×C₁₃₉	—	4	2	no	—
238	C₄⋊C₄×C₁₃₉	—	4	2	no	—
239	C₄⋊C₄×C₁₃₉	—	4	1	no	—
240	C₄⋊C₄×C₁₃₉	—	4	1	no	—
241	C₄⋊C₄×C₁₃₉	—	4	1	no	—
242	C₄⋊C₄×C₁₃₉	—	4	1	no	—
243	C₄⋊C₄×C₁₃₉	—	4	1	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	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	2	2	no	—
255	C₄²×C₁₃₉	—	2	2	no	—
256	C₄²×C₁₃₉	—	2	2	no	—
257	C₄²×C₁₃₉	—	4	1	no	—
258	C₄²×C₁₃₉	—	4	2	no	—
259	C₄²×C₁₃₉	—	4	1	no	—
260	C₄²×C₁₃₉	—	4	1	no	—
261	C₄²×C₁₃₉	—	4	2	no	—
262	C₄²×C₁₃₉	—	4	2	no	—
263	C₄²×C₁₃₉	—	4	2	no	—
264	C₄²×C₁₃₉	—	4	2	no	—
265	C₄²×C₁₃₉	#41	1	4	yes	—
266	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
267	Q₈×C₁₃₉	—	4	4	no	—
268	Q₈×C₁₃₉	—	8	2	no	—
269	C₂×C₄×C₁₃₉	—	2	1	no	—
270	C₂×C₄×C₁₃₉	—	2	1	no	—
271	C₂×C₄×C₁₃₉	—	2	1	no	—
272	C₂×C₄×C₁₃₉	—	2	1	no	—
273	C₂×C₄×C₁₃₉	—	2	1	no	—
274	C₂×C₄×C₁₃₉	—	2	1	no	—
275	C₂×C₄×C₁₃₉	—	2	1	no	—
276	C₂×C₄×C₁₃₉	—	2	1	no	—
277	C₂×C₄×C₁₃₉	—	2	1	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	1	no	—
280	C₂×C₄×C₁₃₉	—	2	1	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	1	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	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	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	1	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	2	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	C₂×#41	1	2	yes	—
321	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
323	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
324	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
325	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
326	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
328	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	C₂²×C₁₃₉	#585	1	1	yes	characteristic
331	C₂²×C₁₃₉	#585	1	1	yes	characteristic
332	C₂²×C₁₃₉	#585	1	1	yes	characteristic
333	C₄×C₁₃₉	—	2	2	no	—
334	C₄×C₁₃₉	—	2	2	no	—
335	C₄×C₁₃₉	—	2	2	no	—
336	C₄×C₁₃₉	—	2	2	no	—
337	C₄×C₁₃₉	—	2	2	no	—
338	C₄×C₁₃₉	—	2	2	no	—
339	C₄×C₁₃₉	—	4	2	no	—
340	C₄×C₁₃₉	—	4	2	no	—
341	C₄×C₁₃₉	—	4	2	no	—
342	C₄×C₁₃₉	—	4	2	no	—
343	C₄×C₁₃₉	—	4	2	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	2	no	—
346	C₄×C₁₃₉	—	4	2	no	—
347	C₄×C₁₃₉	—	4	1	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	2	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₂×C₁₃₉	#3455	1	1	yes	characteristic
353	C₂×C₁₃₉	#3507	1	1	yes	characteristic
354	C₂×C₁₃₉	#3509	1	1	yes	characteristic
355	C₂×C₁₃₉	#3553	1	1	yes	characteristic
356	C₂×C₁₃₉	#3555	1	1	yes	characteristic
357	C₂×C₁₃₉	#3563	1	1	yes	characteristic
358	C₂×C₁₃₉	#3564	1	1	yes	characteristic
359	#37146	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₁₃₉	#37146	1	1	yes	characteristic, direct product factor, Sylow
361	#2863	C₂×C₁₃₉	1	1	yes	characteristic
362	#2859	C₂×C₁₃₉	1	1	yes	characteristic
363	#2810	C₂×C₁₃₉	1	1	yes	characteristic
364	#2806	C₂×C₁₃₉	1	1	yes	characteristic
365	#2805	C₂×C₁₃₉	1	1	yes	characteristic
366	#2805	C₂×C₁₃₉	1	1	yes	characteristic
367	#2794	C₂×C₁₃₉	1	2	yes	—
368	#2791	C₂×C₁₃₉	1	2	yes	—
369	#2776	C₂×C₁₃₉	1	2	yes	—
370	#2774	C₂×C₁₃₉	1	2	yes	—
371	#2767	C₂×C₁₃₉	1	2	yes	—
372	#2762	C₂×C₁₃₉	1	2	yes	—
373	#2634	C₂×C₁₃₉	1	2	yes	—
374	#2590	C₂×C₁₃₉	1	2	yes	—
375	#2588	C₂×C₁₃₉	1	2	yes	—
376	#2533	C₂×C₁₃₉	1	2	yes	—
377	#2528	C₂×C₁₃₉	1	2	yes	—
378	#2336	C₂×C₁₃₉	1	2	yes	—
379	#2295	C₂×C₁₃₉	1	1	yes	characteristic
380	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
381	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
382	#401	C₂²×C₁₃₉	1	2	yes	—
383	#400	C₂²×C₁₃₉	1	2	yes	—
384	#400	C₂²×C₁₃₉	1	2	yes	—
385	#400	C₂²×C₁₃₉	1	2	yes	—
386	#400	C₂²×C₁₃₉	1	2	yes	—
387	#400	C₂²×C₁₃₉	1	2	yes	—
388	#400	C₂²×C₁₃₉	1	2	yes	—
389	#400	C₂²×C₁₃₉	1	2	yes	—
390	#400	C₂²×C₁₃₉	1	2	yes	—
391	#400	C₂²×C₁₃₉	1	2	yes	—
392	#400	C₂²×C₁₃₉	1	2	yes	—
393	#400	C₂²×C₁₃₉	1	2	yes	—
394	#400	C₂²×C₁₃₉	1	2	yes	—
395	#400	C₂²×C₁₃₉	1	2	yes	—
396	#398	C₂²×C₁₃₉	1	2	yes	—
397	#398	C₂²×C₁₃₉	1	2	yes	—
398	#398	C₂²×C₁₃₉	1	2	yes	—
399	#398	C₂²×C₁₃₉	1	2	yes	—
400	#398	C₂²×C₁₃₉	1	2	yes	—
401	#398	C₂²×C₁₃₉	1	2	yes	—
402	#398	C₂²×C₁₃₉	1	2	yes	—
403	#395	C₂²×C₁₃₉	1	2	yes	—
404	#395	C₂²×C₁₃₉	1	2	yes	—
405	#395	C₂²×C₁₃₉	1	2	yes	—
406	#391	C₂²×C₁₃₉	1	1	yes	characteristic
407	#391	C₂²×C₁₃₉	1	2	yes	—
408	#391	C₂²×C₁₃₉	1	1	yes	characteristic
409	#391	C₂²×C₁₃₉	1	1	yes	characteristic
410	#391	C₂²×C₁₃₉	1	1	yes	characteristic
411	#391	C₂²×C₁₃₉	1	1	yes	characteristic
412	#389	C₂²×C₁₃₉	1	2	yes	—
413	#389	C₂²×C₁₃₉	1	1	yes	characteristic
414	#389	C₂²×C₁₃₉	1	2	yes	—
415	#389	C₂²×C₁₃₉	1	2	yes	—
416	#389	C₂²×C₁₃₉	1	2	yes	—
417	#389	C₂²×C₁₃₉	1	2	yes	—
418	#389	C₂²×C₁₃₉	1	1	yes	characteristic
419	#389	C₂²×C₁₃₉	1	1	yes	characteristic
420	#389	C₂²×C₁₃₉	1	1	yes	characteristic
421	#389	C₂²×C₁₃₉	1	1	yes	characteristic
422	#389	C₂²×C₁₃₉	1	1	yes	characteristic
423	#389	C₂²×C₁₃₉	1	1	yes	characteristic
424	#389	C₂²×C₁₃₉	1	1	yes	characteristic
425	#389	C₂²×C₁₃₉	1	2	yes	—
426	#389	C₂²×C₁₃₉	1	1	yes	characteristic
427	#387	C₂²×C₁₃₉	1	2	yes	—
428	#387	C₂²×C₁₃₉	1	2	yes	—
429	#387	C₂²×C₁₃₉	1	2	yes	—
430	#387	C₂²×C₁₃₉	1	2	yes	—
431	#387	C₂²×C₁₃₉	1	2	yes	—
432	#387	C₂²×C₁₃₉	1	2	yes	—
433	#387	C₂²×C₁₃₉	1	2	yes	—
434	#387	C₂²×C₁₃₉	1	2	yes	—
435	#387	C₂²×C₁₃₉	1	2	yes	—
436	#387	C₂²×C₁₃₉	1	2	yes	—
437	#387	C₂²×C₁₃₉	1	2	yes	—
438	#387	C₂²×C₁₃₉	1	2	yes	—
439	#387	C₂²×C₁₃₉	1	2	yes	—
440	#387	C₂²×C₁₃₉	1	2	yes	—
441	#387	C₂²×C₁₃₉	1	2	yes	—
442	#387	C₂²×C₁₃₉	1	2	yes	—
443	#387	C₂²×C₁₃₉	1	2	yes	—
444	#387	C₂²×C₁₃₉	1	2	yes	—
445	#387	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	#384	C₂²×C₁₃₉	1	1	yes	characteristic
456	#384	C₂²×C₁₃₉	1	1	yes	characteristic
457	#383	C₂²×C₁₃₉	1	2	yes	—
458	#383	C₂²×C₁₃₉	1	2	yes	—
459	#382	C₂²×C₁₃₉	1	2	yes	—
460	#382	C₂²×C₁₃₉	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
465	#376	C₂²×C₁₃₉	1	2	yes	—
466	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
469	#125	—	2	8	no	—
470	C₄×Q₈	—	2	4	no	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
516	#95	C₂³×C₁₃₉	1	2	yes	—
517	#95	C₂³×C₁₃₉	1	2	yes	—
518	#95	C₂³×C₁₃₉	1	2	yes	—
519	#95	C₂³×C₁₃₉	1	2	yes	—
520	#95	C₂³×C₁₃₉	1	2	yes	—
521	#95	C₂³×C₁₃₉	1	2	yes	—
522	#95	C₂³×C₁₃₉	1	2	yes	—
523	#95	C₂³×C₁₃₉	1	2	yes	—
524	#95	C₂³×C₁₃₉	1	2	yes	—
525	#95	C₂³×C₁₃₉	1	2	yes	—
526	#95	C₂³×C₁₃₉	1	2	yes	—
527	#95	C₂³×C₁₃₉	1	2	yes	—
528	#95	C₂³×C₁₃₉	1	2	yes	—
529	#95	C₂³×C₁₃₉	1	2	yes	—
530	#95	C₂³×C₁₃₉	1	2	yes	—
531	#95	C₂³×C₁₃₉	1	2	yes	—
532	#95	C₂³×C₁₃₉	1	2	yes	—
533	#95	C₂³×C₁₃₉	1	2	yes	—
534	#95	C₂³×C₁₃₉	1	2	yes	—
535	#95	C₂³×C₁₃₉	1	2	yes	—
536	#95	C₂³×C₁₃₉	1	2	yes	—
537	#95	C₂³×C₁₃₉	1	2	yes	—
538	#95	C₂³×C₁₃₉	1	2	yes	—
539	#95	C₂³×C₁₃₉	1	2	yes	—
540	#95	C₂³×C₁₃₉	1	2	yes	—
541	#95	C₂³×C₁₃₉	1	2	yes	—
542	#95	C₂³×C₁₃₉	1	2	yes	—
543	#95	C₂³×C₁₃₉	1	2	yes	—
544	#95	C₂³×C₁₃₉	1	2	yes	—
545	#95	C₂³×C₁₃₉	1	2	yes	—
546	#95	C₂³×C₁₃₉	1	2	yes	—
547	#95	C₂³×C₁₃₉	1	2	yes	—
548	#95	C₂³×C₁₃₉	1	2	yes	—
549	#95	C₂³×C₁₃₉	1	2	yes	—
550	#95	C₂³×C₁₃₉	1	2	yes	—
551	#95	C₂³×C₁₃₉	1	2	yes	—
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	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	4	1	no	—
559	C₂×Q₈	—	4	1	no	—
560	C₂×Q₈	—	4	1	no	—
561	C₂×Q₈	—	4	1	no	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	4	1	no	—
597	C₄⋊C₄	—	4	2	no	—
598	C₄⋊C₄	—	4	2	no	—
599	C₄⋊C₄	—	4	1	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₄⋊C₄	—	4	1	no	—
603	C₄⋊C₄	—	4	1	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	2	no	—
617	C₄²	—	4	1	no	—
618	C₄²	—	4	2	no	—
619	C₄²	—	4	1	no	—
620	C₄²	—	4	1	no	—
621	C₄²	—	4	2	no	—
622	C₄²	—	4	2	no	—
623	C₄²	—	4	2	no	—
624	C₄²	—	4	2	no	—
625	C₄²	#41×C₁₃₉	1	4	yes	—
626	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
627	Q₈	—	4	4	no	—
628	Q₈	—	8	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
681	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
682	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
683	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
684	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
685	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
686	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
687	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
688	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
689	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
690	C₂²	#585×C₁₃₉	1	1	yes	characteristic
691	C₂²	#585×C₁₃₉	1	1	yes	characteristic
692	C₂²	#585×C₁₃₉	1	1	yes	characteristic
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	2	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₂	#3455×C₁₃₉	1	1	yes	characteristic
713	C₂	#3507×C₁₃₉	1	1	yes	characteristic
714	C₂	#3509×C₁₃₉	1	1	yes	characteristic
715	C₂	#3553×C₁₃₉	1	1	yes	characteristic
716	C₂	#3555×C₁₃₉	1	1	yes	characteristic
717	C₂	#3563×C₁₃₉	1	1	yes	characteristic
718	C₂	#3564×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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
359. #37146	C₁₃₉	direct (N × H)
360. C₁₃₉	#37146	direct (N × H)

Maximal subgroups

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

subgroup	index
#2863×C₁₃₉	2
#2859×C₁₃₉	2
#2810×C₁₃₉	2
#2806×C₁₃₉	2
#2805×C₁₃₉	2
#2794×C₁₃₉	2
#2791×C₁₃₉	2
#2776×C₁₃₉	2
#2774×C₁₃₉	2
#2767×C₁₃₉	2
#2762×C₁₃₉	2
#2634×C₁₃₉	2
#2590×C₁₃₉	2
#2588×C₁₃₉	2
#2533×C₁₃₉	2
#2528×C₁₃₉	2
#2336×C₁₃₉	2
#2295×C₁₃₉	2
#37146	139

Subgroups — C139×#37146 #48031742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37146 #48031742