Subgroups — C₁₃₉×#36023 #48030619

Order 35584.

1586 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2655×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2627×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2588×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2585×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2569×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2528×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2524×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2524×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2520×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	#2493×C₁₃₉	C₂	1	2	yes	maximal
12	#2484×C₁₃₉	C₂	1	2	yes	maximal
13	#2402×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₂×#398×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2368×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2344×C₁₃₉	C₂	1	2	yes	maximal
17	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2343×C₁₃₉	C₂	1	2	yes	maximal
19	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	#401×C₁₃₉	C₂²	1	2	yes	—
28	#400×C₁₃₉	C₂²	1	2	yes	—
29	#400×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	1	yes	characteristic
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	1	yes	characteristic
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	1	yes	characteristic
48	#398×C₁₃₉	C₂²	1	1	yes	characteristic
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#395×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#387×C₁₃₉	C₂²	1	2	yes	—
57	#387×C₁₃₉	C₂²	1	2	yes	—
58	#387×C₁₃₉	C₂²	1	2	yes	—
59	#387×C₁₃₉	C₂²	1	2	yes	—
60	#387×C₁₃₉	C₂²	1	2	yes	—
61	#387×C₁₃₉	C₂²	1	2	yes	—
62	#387×C₁₃₉	C₂²	1	2	yes	—
63	#387×C₁₃₉	C₂²	1	2	yes	—
64	#387×C₁₃₉	C₂²	1	2	yes	—
65	#387×C₁₃₉	C₂²	1	2	yes	—
66	#387×C₁₃₉	C₂²	1	2	yes	—
67	#387×C₁₃₉	C₂²	1	2	yes	—
68	#387×C₁₃₉	C₂²	1	2	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	—
70	#387×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	2	yes	—
72	#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	#385×C₁₃₉	C₂²	1	2	yes	—
78	#385×C₁₃₉	C₂²	1	2	yes	—
79	#385×C₁₃₉	C₂²	1	2	yes	—
80	#383×C₁₃₉	C₂²	1	2	yes	—
81	#383×C₁₃₉	C₂²	1	2	yes	—
82	#382×C₁₃₉	C₂²	1	2	yes	—
83	#382×C₁₃₉	C₂²	1	2	yes	—
84	#381×C₁₃₉	C₂²	1	2	yes	—
85	#381×C₁₃₉	C₂²	1	2	yes	—
86	#381×C₁₃₉	C₂²	1	2	yes	—
87	#381×C₁₃₉	C₂²	1	2	yes	—
88	#380×C₁₃₉	C₂²	1	1	yes	characteristic
89	#380×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	2	yes	—
97	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	#376×C₁₃₉	C₂²	1	2	yes	—
105	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
114	#117×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	—	2	8	no	—
119	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	1	yes	characteristic
165	#95×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	1	yes	characteristic
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	#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	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₁₃₉	—	2	2	no	—
203	C₂×Q₈×C₁₃₉	—	4	2	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	4	2	no	—
213	C₂²×C₄×C₁₃₉	—	4	2	no	—
214	C₂²×C₄×C₁₃₉	—	4	2	no	—
215	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
216	C₂²×C₄×C₁₃₉	#41	1	4	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	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	2	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	2	no	—
251	C₄⋊C₄×C₁₃₉	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
267	C₄²×C₁₃₉	—	2	4	no	—
268	C₄²×C₁₃₉	—	2	4	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	4	2	no	—
273	C₄²×C₁₃₉	—	4	2	no	—
274	C₄²×C₁₃₉	—	4	2	no	—
275	C₄²×C₁₃₉	—	4	2	no	—
276	C₄²×C₁₃₉	—	4	2	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
280	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
281	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
282	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
283	Q₈×C₁₃₉	—	8	2	no	—
284	C₂×C₄×C₁₃₉	—	2	8	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	2	1	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	1	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	—	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	—	4	4	no	—
330	C₂×C₄×C₁₃₉	—	4	8	no	—
331	C₂×C₄×C₁₃₉	—	4	8	no	—
332	C₂×C₄×C₁₃₉	—	8	2	no	—
333	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
334	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
335	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
336	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
339	C₂²×C₁₃₉	—	2	2	no	—
340	C₂²×C₁₃₉	—	2	4	no	—
341	C₂²×C₁₃₉	—	2	2	no	—
342	C₂²×C₁₃₉	—	2	4	no	—
343	C₂²×C₁₃₉	#529	1	4	yes	—
344	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
348	C₂²×C₁₃₉	#585	1	2	yes	—
349	C₄×C₁₃₉	—	2	2	no	—
350	C₄×C₁₃₉	—	2	2	no	—
351	C₄×C₁₃₉	—	2	2	no	—
352	C₄×C₁₃₉	—	2	2	no	—
353	C₄×C₁₃₉	—	2	4	no	—
354	C₄×C₁₃₉	—	2	4	no	—
355	C₄×C₁₃₉	—	4	2	no	—
356	C₄×C₁₃₉	—	4	2	no	—
357	C₄×C₁₃₉	—	4	1	no	—
358	C₄×C₁₃₉	—	4	1	no	—
359	C₄×C₁₃₉	—	4	2	no	—
360	C₄×C₁₃₉	—	4	2	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	2	no	—
363	C₄×C₁₃₉	—	4	2	no	—
364	C₄×C₁₃₉	—	4	2	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	—	4	2	no	—
367	C₂×C₁₃₉	—	2	4	no	—
368	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
369	C₂×C₁₃₉	#3491	1	1	yes	characteristic
370	C₂×C₁₃₉	#3495	1	2	yes	—
371	C₂×C₁₃₉	#3509	1	1	yes	characteristic
372	C₂×C₁₃₉	#3515	1	2	yes	—
373	#36023	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₁₃₉	#36023	1	1	yes	characteristic, direct product factor, Sylow
375	#2655	C₂×C₁₃₉	1	2	yes	complemented
376	#2627	C₂×C₁₃₉	1	1	yes	characteristic
377	#2588	C₂×C₁₃₉	1	2	yes	complemented
378	#2585	C₂×C₁₃₉	1	2	yes	complemented
379	#2569	C₂×C₁₃₉	1	1	yes	characteristic
380	#2528	C₂×C₁₃₉	1	2	yes	complemented
381	#2524	C₂×C₁₃₉	1	2	yes	complemented
382	#2524	C₂×C₁₃₉	1	2	yes	complemented
383	#2520	C₂×C₁₃₉	1	2	yes	complemented
384	#2503	C₂×C₁₃₉	1	1	yes	characteristic
385	#2493	C₂×C₁₃₉	1	2	yes	—
386	#2484	C₂×C₁₃₉	1	2	yes	—
387	#2402	C₂×C₁₃₉	1	2	yes	complemented
388	C₂×#398	C₂×C₁₃₉	1	1	yes	characteristic
389	#2368	C₂×C₁₃₉	1	1	yes	characteristic
390	#2344	C₂×C₁₃₉	1	2	yes	—
391	#2344	C₂×C₁₃₉	1	1	yes	characteristic
392	#2343	C₂×C₁₃₉	1	2	yes	—
393	#2274	C₂×C₁₃₉	1	1	yes	characteristic
394	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
396	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
398	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
399	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
401	#401	C₂²×C₁₃₉	1	2	yes	—
402	#400	C₂²×C₁₃₉	1	2	yes	—
403	#400	C₂²×C₁₃₉	1	2	yes	—
404	#400	C₂²×C₁₃₉	1	2	yes	—
405	#400	C₂²×C₁₃₉	1	2	yes	—
406	#400	C₂²×C₁₃₉	1	1	yes	characteristic
407	#400	C₂²×C₁₃₉	1	1	yes	characteristic
408	#400	C₂²×C₁₃₉	1	2	yes	—
409	#400	C₂²×C₁₃₉	1	2	yes	—
410	#400	C₂²×C₁₃₉	1	2	yes	—
411	#400	C₂²×C₁₃₉	1	2	yes	—
412	#398	C₂²×C₁₃₉	1	2	yes	—
413	#398	C₂²×C₁₃₉	1	1	yes	characteristic
414	#398	C₂²×C₁₃₉	1	2	yes	—
415	#398	C₂²×C₁₃₉	1	2	yes	—
416	#398	C₂²×C₁₃₉	1	2	yes	—
417	#398	C₂²×C₁₃₉	1	1	yes	characteristic
418	#398	C₂²×C₁₃₉	1	1	yes	characteristic
419	#398	C₂²×C₁₃₉	1	2	yes	—
420	#398	C₂²×C₁₃₉	1	1	yes	characteristic
421	#398	C₂²×C₁₃₉	1	2	yes	—
422	#398	C₂²×C₁₃₉	1	2	yes	—
423	#395	C₂²×C₁₃₉	1	1	yes	characteristic
424	#395	C₂²×C₁₃₉	1	1	yes	characteristic
425	#391	C₂²×C₁₃₉	1	2	yes	—
426	#391	C₂²×C₁₃₉	1	2	yes	—
427	#389	C₂²×C₁₃₉	1	2	yes	—
428	#389	C₂²×C₁₃₉	1	2	yes	—
429	#389	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	#385	C₂²×C₁₃₉	1	2	yes	—
452	#385	C₂²×C₁₃₉	1	2	yes	—
453	#385	C₂²×C₁₃₉	1	2	yes	—
454	#383	C₂²×C₁₃₉	1	2	yes	—
455	#383	C₂²×C₁₃₉	1	2	yes	—
456	#382	C₂²×C₁₃₉	1	2	yes	—
457	#382	C₂²×C₁₃₉	1	2	yes	—
458	#381	C₂²×C₁₃₉	1	2	yes	—
459	#381	C₂²×C₁₃₉	1	2	yes	—
460	#381	C₂²×C₁₃₉	1	2	yes	—
461	#381	C₂²×C₁₃₉	1	2	yes	—
462	#380	C₂²×C₁₃₉	1	1	yes	characteristic
463	#380	C₂²×C₁₃₉	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
474	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
478	#376	C₂²×C₁₃₉	1	2	yes	—
479	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
480	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
481	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂²⋊Q₈	—	2	4	no	—
488	#117	—	2	4	no	—
489	#117	—	2	4	no	—
490	#117	—	2	8	no	—
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	—	2	8	no	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
536	#95	C₂³×C₁₃₉	1	2	yes	—
537	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
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	#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	2	yes	—
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	1	yes	characteristic
562	#95	C₂³×C₁₃₉	1	1	yes	characteristic
563	#95	C₂³×C₁₃₉	1	2	yes	—
564	#95	C₂³×C₁₃₉	1	2	yes	—
565	#95	C₂³×C₁₃₉	1	2	yes	—
566	#95	C₂³×C₁₃₉	1	2	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
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	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
590	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
591	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	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	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	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	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	4	2	no	—
649	C₄²	—	4	2	no	—
650	C₄²	—	4	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
654	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
655	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
656	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
657	Q₈	—	8	2	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	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	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	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	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
708	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
709	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
710	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
711	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
712	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	4	no	—
717	C₂²	#529×C₁₃₉	1	4	yes	—
718	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
719	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
720	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
721	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
722	C₂²	#585×C₁₃₉	1	2	yes	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	4	no	—
728	C₄	—	2	4	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₂	—	2	4	no	—
742	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
743	C₂	#3491×C₁₃₉	1	1	yes	characteristic
744	C₂	#3495×C₁₃₉	1	2	yes	—
745	C₂	#3509×C₁₃₉	1	1	yes	characteristic
746	C₂	#3515×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂⁴
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. #2655×C₁₃₉	C₂	semidirect
3. #2588×C₁₃₉	C₂	semidirect
4. #2585×C₁₃₉	C₂	semidirect
6. #2528×C₁₃₉	C₂	semidirect
7. #2524×C₁₃₉	C₂	semidirect
8. #2524×C₁₃₉	C₂	semidirect
9. #2520×C₁₃₉	C₂	semidirect
13. #2402×C₁₃₉	C₂	semidirect
373. #36023	C₁₃₉	direct (N × H)
374. C₁₃₉	#36023	direct (N × H)
375. #2655	C₂×C₁₃₉	semidirect
377. #2588	C₂×C₁₃₉	semidirect
378. #2585	C₂×C₁₃₉	semidirect
380. #2528	C₂×C₁₃₉	semidirect
381. #2524	C₂×C₁₃₉	semidirect
382. #2524	C₂×C₁₃₉	semidirect
383. #2520	C₂×C₁₃₉	semidirect
387. #2402	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2655×C₁₃₉	2
#2627×C₁₃₉	2
#2588×C₁₃₉	2
#2585×C₁₃₉	2
#2569×C₁₃₉	2
#2528×C₁₃₉	2
#2524×C₁₃₉	2
#2520×C₁₃₉	2
#2503×C₁₃₉	2
#2493×C₁₃₉	2
#2484×C₁₃₉	2
#2402×C₁₃₉	2
C₂×#398×C₁₃₉	2
#2368×C₁₃₉	2
#2344×C₁₃₉	2
#2343×C₁₃₉	2
#2274×C₁₃₉	2
#36023	139

Subgroups — C139×#36023 #48030619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36023 #48030619