Subgroups — C₁₃₉×#35851 #48030447

Order 35584.

1816 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2667×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2652×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2578×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2575×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2553×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2534×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2522×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2495×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2482×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2480×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2470×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2418×C₁₃₉	C₂	1	2	yes	maximal
13	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2373×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2353×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2273×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	2	yes	complemented
31	#400×C₁₃₉	C₂²	1	2	yes	complemented
32	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	#400×C₁₃₉	C₂²	1	2	yes	complemented
34	#399×C₁₃₉	C₂²	1	2	yes	—
35	#399×C₁₃₉	C₂²	1	2	yes	—
36	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
37	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	#398×C₁₃₉	C₂²	1	2	yes	complemented
39	#398×C₁₃₉	C₂²	1	2	yes	complemented
40	#397×C₁₃₉	C₂²	1	2	yes	—
41	#397×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	complemented
46	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	#396×C₁₃₉	C₂²	1	2	yes	—
48	#396×C₁₃₉	C₂²	1	2	yes	—
49	#394×C₁₃₉	C₂²	1	2	yes	—
50	#394×C₁₃₉	C₂²	1	2	yes	—
51	#394×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	complemented
53	#389×C₁₃₉	C₂²	1	2	yes	complemented
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#389×C₁₃₉	C₂²	1	2	yes	complemented
56	#388×C₁₃₉	C₂²	1	2	yes	—
57	#388×C₁₃₉	C₂²	1	2	yes	—
58	#388×C₁₃₉	C₂²	1	2	yes	—
59	#388×C₁₃₉	C₂²	1	2	yes	—
60	#388×C₁₃₉	C₂²	1	2	yes	—
61	#388×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	complemented
65	#387×C₁₃₉	C₂²	1	2	yes	complemented
66	#387×C₁₃₉	C₂²	1	2	yes	complemented
67	#387×C₁₃₉	C₂²	1	2	yes	complemented
68	#387×C₁₃₉	C₂²	1	2	yes	complemented
69	#387×C₁₃₉	C₂²	1	2	yes	complemented
70	#387×C₁₃₉	C₂²	1	2	yes	complemented
71	#387×C₁₃₉	C₂²	1	2	yes	complemented
72	#386×C₁₃₉	C₂²	1	2	yes	—
73	#386×C₁₃₉	C₂²	1	2	yes	—
74	#386×C₁₃₉	C₂²	1	2	yes	—
75	#385×C₁₃₉	C₂²	1	2	yes	—
76	#385×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	complemented
80	#383×C₁₃₉	C₂²	1	2	yes	complemented
81	#383×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
82	#382×C₁₃₉	C₂²	1	2	yes	complemented
83	#381×C₁₃₉	C₂²	1	1	yes	characteristic
84	#381×C₁₃₉	C₂²	1	1	yes	characteristic
85	#380×C₁₃₉	C₂²	1	2	yes	—
86	#380×C₁₃₉	C₂²	1	1	yes	characteristic
87	#380×C₁₃₉	C₂²	1	2	yes	—
88	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
89	#379×C₁₃₉	C₂²	1	1	yes	characteristic
90	#379×C₁₃₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
92	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
105	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
106	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	#126×C₁₃₉	—	2	8	no	—
117	#123×C₁₃₉	—	2	8	no	—
118	#123×C₁₃₉	—	4	2	no	—
119	#120×C₁₃₉	—	4	2	no	—
120	C₄×D₄×C₁₃₉	—	2	4	no	—
121	C₄×D₄×C₁₃₉	—	4	4	no	—
122	#117×C₁₃₉	—	2	4	no	—
123	#117×C₁₃₉	—	4	4	no	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄²×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	1	yes	characteristic
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	1	yes	characteristic
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	1	yes	characteristic
197	#95×C₁₃₉	C₂³	1	1	yes	characteristic
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	1	yes	characteristic
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	1	yes	characteristic
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	C₂⁴×C₁₃₉	—	2	2	no	—
205	C₂⁴×C₁₃₉	—	2	4	no	—
206	C₂⁴×C₁₃₉	—	4	1	no	—
207	C₂⁴×C₁₃₉	—	4	2	no	—
208	C₂⁴×C₁₃₉	—	4	1	no	—
209	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂×D₄×C₁₃₉	—	2	2	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	2	4	no	—
215	C₂×D₄×C₁₃₉	—	2	2	no	—
216	C₂×D₄×C₁₃₉	—	4	1	no	—
217	C₂×D₄×C₁₃₉	—	4	2	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	2	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	—	4	2	no	—
227	C₂²×C₄×C₁₃₉	—	4	1	no	—
228	C₂²×C₄×C₁₃₉	—	4	2	no	—
229	C₂²×C₄×C₁₃₉	—	4	2	no	—
230	C₂²×C₄×C₁₃₉	—	4	2	no	—
231	C₂²×C₄×C₁₃₉	—	4	2	no	—
232	C₂²×C₄×C₁₃₉	—	4	1	no	—
233	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₁₃₉	—	2	2	no	—
251	C₄⋊C₄×C₁₃₉	—	2	2	no	—
252	C₄⋊C₄×C₁₃₉	—	2	2	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	2	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	2	no	—
266	C₄⋊C₄×C₁₃₉	—	4	2	no	—
267	C₄⋊C₄×C₁₃₉	—	4	2	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
283	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
284	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
290	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	—
291	C₄²×C₁₃₉	—	2	4	no	—
292	C₄²×C₁₃₉	—	2	2	no	—
293	C₄²×C₁₃₉	—	2	4	no	—
294	C₄²×C₁₃₉	—	4	2	no	—
295	C₄²×C₁₃₉	—	4	2	no	—
296	C₄²×C₁₃₉	—	4	2	no	—
297	C₄²×C₁₃₉	—	4	2	no	—
298	C₄²×C₁₃₉	—	4	2	no	—
299	C₄²×C₁₃₉	—	4	2	no	—
300	C₂³×C₁₃₉	—	2	8	no	—
301	C₂³×C₁₃₉	—	2	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	2	1	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	1	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	1	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	1	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	8	2	no	—
316	C₂³×C₁₃₉	—	8	2	no	—
317	C₂³×C₁₃₉	—	8	4	no	—
318	C₂³×C₁₃₉	—	8	4	no	—
319	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
320	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
321	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
322	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
323	D₄×C₁₃₉	—	4	4	no	—
324	D₄×C₁₃₉	—	4	8	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	1	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	1	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	4	4	no	—
366	C₂×C₄×C₁₃₉	—	4	8	no	—
367	C₂×C₄×C₁₃₉	—	8	2	no	—
368	C₂×C₄×C₁₃₉	—	8	4	no	—
369	C₂×C₄×C₁₃₉	—	8	4	no	—
370	C₂×C₄×C₁₃₉	—	8	2	no	—
371	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
372	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
373	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
374	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
375	C₂²×C₁₃₉	—	2	2	no	—
376	C₂²×C₁₃₉	—	2	4	no	—
377	C₂²×C₁₃₉	—	2	2	no	—
378	C₂²×C₁₃₉	—	2	2	no	—
379	C₂²×C₁₃₉	—	2	2	no	—
380	C₂²×C₁₃₉	—	2	4	no	—
381	C₂²×C₁₃₉	—	2	4	no	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	4	1	no	—
384	C₂²×C₁₃₉	—	4	1	no	—
385	C₂²×C₁₃₉	—	4	2	no	—
386	C₂²×C₁₃₉	—	4	2	no	—
387	C₂²×C₁₃₉	—	4	2	no	—
388	C₂²×C₁₃₉	—	4	2	no	—
389	C₂²×C₁₃₉	—	4	2	no	—
390	C₂²×C₁₃₉	—	4	2	no	—
391	C₂²×C₁₃₉	—	4	2	no	—
392	C₂²×C₁₃₉	—	8	8	no	—
393	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
394	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
395	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×C₁₃₉	#585	1	2	yes	—
397	C₂²×C₁₃₉	#585	1	1	yes	characteristic
398	C₄×C₁₃₉	—	2	2	no	—
399	C₄×C₁₃₉	—	2	2	no	—
400	C₄×C₁₃₉	—	2	4	no	—
401	C₄×C₁₃₉	—	2	4	no	—
402	C₄×C₁₃₉	—	4	1	no	—
403	C₄×C₁₃₉	—	4	2	no	—
404	C₄×C₁₃₉	—	4	1	no	—
405	C₄×C₁₃₉	—	4	2	no	—
406	C₄×C₁₃₉	—	4	2	no	—
407	C₄×C₁₃₉	—	4	1	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	—	4	2	no	—
412	C₄×C₁₃₉	—	4	2	no	—
413	C₄×C₁₃₉	—	4	2	no	—
414	C₂×C₁₃₉	—	4	2	no	—
415	C₂×C₁₃₉	—	4	2	no	—
416	C₂×C₁₃₉	—	4	4	no	—
417	C₂×C₁₃₉	#3444	1	1	yes	characteristic
418	C₂×C₁₃₉	#3491	1	1	yes	characteristic
419	C₂×C₁₃₉	#3494	1	1	yes	characteristic
420	C₂×C₁₃₉	#3513	1	2	yes	—
421	C₂×C₁₃₉	#3521	1	2	yes	—
422	#35851	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
423	C₁₃₉	#35851	1	1	yes	characteristic, direct product factor, Sylow
424	#2667	C₂×C₁₃₉	1	1	yes	characteristic, complemented
425	#2652	C₂×C₁₃₉	1	2	yes	complemented
426	#2578	C₂×C₁₃₉	1	2	yes	complemented
427	#2575	C₂×C₁₃₉	1	2	yes	complemented
428	#2553	C₂×C₁₃₉	1	2	yes	complemented
429	#2534	C₂×C₁₃₉	1	1	yes	characteristic
430	#2522	C₂×C₁₃₉	1	2	yes	complemented
431	#2495	C₂×C₁₃₉	1	2	yes	complemented
432	#2482	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	#2480	C₂×C₁₃₉	1	2	yes	complemented
434	#2470	C₂×C₁₃₉	1	2	yes	complemented
435	#2418	C₂×C₁₃₉	1	2	yes	—
436	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
437	#2395	C₂×C₁₃₉	1	2	yes	complemented
438	#2373	C₂×C₁₃₉	1	2	yes	complemented
439	#2359	C₂×C₁₃₉	1	2	yes	complemented
440	#2353	C₂×C₁₃₉	1	1	yes	characteristic, complemented
441	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
442	#2273	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
444	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
445	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
448	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
450	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
451	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
452	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
453	#400	C₂²×C₁₃₉	1	2	yes	complemented
454	#400	C₂²×C₁₃₉	1	2	yes	complemented
455	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
456	#400	C₂²×C₁₃₉	1	2	yes	complemented
457	#399	C₂²×C₁₃₉	1	2	yes	—
458	#399	C₂²×C₁₃₉	1	2	yes	—
459	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
460	#398	C₂²×C₁₃₉	1	2	yes	complemented
461	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
462	#398	C₂²×C₁₃₉	1	2	yes	complemented
463	#397	C₂²×C₁₃₉	1	2	yes	—
464	#397	C₂²×C₁₃₉	1	2	yes	—
465	#397	C₂²×C₁₃₉	1	2	yes	—
466	#397	C₂²×C₁₃₉	1	2	yes	—
467	#397	C₂²×C₁₃₉	1	2	yes	—
468	#397	C₂²×C₁₃₉	1	2	yes	complemented
469	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
470	#396	C₂²×C₁₃₉	1	2	yes	—
471	#396	C₂²×C₁₃₉	1	2	yes	—
472	#394	C₂²×C₁₃₉	1	2	yes	—
473	#394	C₂²×C₁₃₉	1	2	yes	—
474	#394	C₂²×C₁₃₉	1	2	yes	—
475	#389	C₂²×C₁₃₉	1	2	yes	complemented
476	#389	C₂²×C₁₃₉	1	2	yes	complemented
477	#389	C₂²×C₁₃₉	1	2	yes	complemented
478	#389	C₂²×C₁₃₉	1	2	yes	complemented
479	#388	C₂²×C₁₃₉	1	2	yes	—
480	#388	C₂²×C₁₃₉	1	2	yes	—
481	#388	C₂²×C₁₃₉	1	2	yes	—
482	#388	C₂²×C₁₃₉	1	2	yes	—
483	#388	C₂²×C₁₃₉	1	2	yes	—
484	#388	C₂²×C₁₃₉	1	2	yes	—
485	#388	C₂²×C₁₃₉	1	2	yes	—
486	#388	C₂²×C₁₃₉	1	2	yes	—
487	#388	C₂²×C₁₃₉	1	2	yes	complemented
488	#387	C₂²×C₁₃₉	1	2	yes	complemented
489	#387	C₂²×C₁₃₉	1	2	yes	complemented
490	#387	C₂²×C₁₃₉	1	2	yes	complemented
491	#387	C₂²×C₁₃₉	1	2	yes	complemented
492	#387	C₂²×C₁₃₉	1	2	yes	complemented
493	#387	C₂²×C₁₃₉	1	2	yes	complemented
494	#387	C₂²×C₁₃₉	1	2	yes	complemented
495	#386	C₂²×C₁₃₉	1	2	yes	—
496	#386	C₂²×C₁₃₉	1	2	yes	—
497	#386	C₂²×C₁₃₉	1	2	yes	—
498	#385	C₂²×C₁₃₉	1	2	yes	—
499	#385	C₂²×C₁₃₉	1	2	yes	—
500	#385	C₂²×C₁₃₉	1	2	yes	—
501	#385	C₂²×C₁₃₉	1	2	yes	—
502	#385	C₂²×C₁₃₉	1	2	yes	complemented
503	#383	C₂²×C₁₃₉	1	2	yes	complemented
504	#383	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
505	#382	C₂²×C₁₃₉	1	2	yes	complemented
506	#381	C₂²×C₁₃₉	1	1	yes	characteristic
507	#381	C₂²×C₁₃₉	1	1	yes	characteristic
508	#380	C₂²×C₁₃₉	1	1	yes	characteristic
509	#380	C₂²×C₁₃₉	1	2	yes	—
510	#380	C₂²×C₁₃₉	1	2	yes	—
511	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
512	#379	C₂²×C₁₃₉	1	2	yes	—
513	#379	C₂²×C₁₃₉	1	1	yes	characteristic
514	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
515	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
516	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
517	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
518	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
521	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
525	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
527	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
528	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
529	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
530	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	#126	—	2	8	no	—
540	#123	—	2	8	no	—
541	#123	—	4	2	no	—
542	#120	—	4	2	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	—	4	4	no	—
545	#117	—	2	4	no	—
546	#117	—	4	4	no	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	8	no	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
599	#95	C₂³×C₁₃₉	1	1	yes	characteristic
600	#95	C₂³×C₁₃₉	1	1	yes	characteristic
601	#95	C₂³×C₁₃₉	1	2	yes	—
602	#95	C₂³×C₁₃₉	1	1	yes	characteristic
603	#95	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	1	yes	characteristic
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	#95	C₂³×C₁₃₉	1	1	yes	characteristic
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	1	yes	characteristic
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	2	yes	—
614	#95	C₂³×C₁₃₉	1	2	yes	—
615	#95	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	2	yes	—
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	2	yes	—
621	#95	C₂³×C₁₃₉	1	2	yes	—
622	#95	C₂³×C₁₃₉	1	2	yes	—
623	#95	C₂³×C₁₃₉	1	2	yes	—
624	#95	C₂³×C₁₃₉	1	2	yes	—
625	#95	C₂³×C₁₃₉	1	2	yes	—
626	#95	C₂³×C₁₃₉	1	2	yes	—
627	C₂⁴	—	2	2	no	—
628	C₂⁴	—	2	4	no	—
629	C₂⁴	—	4	1	no	—
630	C₂⁴	—	4	2	no	—
631	C₂⁴	—	4	1	no	—
632	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
633	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	4	1	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	1	no	—
656	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
657	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	1	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	1	no	—
713	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	4	2	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	4	2	no	—
720	C₄²	—	4	2	no	—
721	C₄²	—	4	2	no	—
722	C₄²	—	4	2	no	—
723	C₂³	—	2	8	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	8	2	no	—
739	C₂³	—	8	2	no	—
740	C₂³	—	8	4	no	—
741	C₂³	—	8	4	no	—
742	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
743	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
744	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
745	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
746	D₄	—	4	4	no	—
747	D₄	—	4	8	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	8	2	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	—	8	4	no	—
793	C₂×C₄	—	8	2	no	—
794	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
795	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
796	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
797	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	8	8	no	—
816	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
817	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
818	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
819	C₂²	#585×C₁₃₉	1	2	yes	—
820	C₂²	#585×C₁₃₉	1	1	yes	characteristic
821	C₄	—	2	2	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	4	no	—
824	C₄	—	2	4	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₂	—	4	2	no	—
838	C₂	—	4	4	no	—
839	C₂	—	4	2	no	—
840	C₂	#3444×C₁₃₉	1	1	yes	characteristic
841	C₂	#3491×C₁₃₉	1	1	yes	characteristic
842	C₂	#3494×C₁₃₉	1	1	yes	characteristic
843	C₂	#3513×C₁₃₉	1	2	yes	—
844	C₂	#3521×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
1. #2667×C₁₃₉	C₂	semidirect
2. #2652×C₁₃₉	C₂	semidirect
3. #2578×C₁₃₉	C₂	semidirect
4. #2575×C₁₃₉	C₂	semidirect
5. #2553×C₁₃₉	C₂	semidirect
7. #2522×C₁₃₉	C₂	semidirect
8. #2495×C₁₃₉	C₂	semidirect
9. #2482×C₁₃₉	C₂	semidirect
10. #2480×C₁₃₉	C₂	semidirect
11. #2470×C₁₃₉	C₂	semidirect
13. #2395×C₁₃₉	C₂	semidirect
14. #2395×C₁₃₉	C₂	semidirect
15. #2373×C₁₃₉	C₂	semidirect
16. #2359×C₁₃₉	C₂	semidirect
17. #2353×C₁₃₉	C₂	semidirect
18. #2347×C₁₃₉	C₂	semidirect
19. #2273×C₁₃₉	C₂	semidirect
27. C₂×#117×C₁₃₉	C₂²	semidirect
30. #400×C₁₃₉	C₂²	semidirect
31. #400×C₁₃₉	C₂²	semidirect
32. #400×C₁₃₉	C₂²	semidirect
33. #400×C₁₃₉	C₂²	semidirect
36. #399×C₁₃₉	C₂²	semidirect
37. #398×C₁₃₉	C₂²	semidirect
38. #398×C₁₃₉	C₂²	semidirect
39. #398×C₁₃₉	C₂²	semidirect
45. #397×C₁₃₉	C₂²	semidirect
46. #397×C₁₃₉	C₂²	semidirect
52. #389×C₁₃₉	C₂²	semidirect
53. #389×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
64. #388×C₁₃₉	C₂²	semidirect
65. #387×C₁₃₉	C₂²	semidirect
66. #387×C₁₃₉	C₂²	semidirect
67. #387×C₁₃₉	C₂²	semidirect
68. #387×C₁₃₉	C₂²	semidirect
69. #387×C₁₃₉	C₂²	semidirect
70. #387×C₁₃₉	C₂²	semidirect
71. #387×C₁₃₉	C₂²	semidirect
79. #385×C₁₃₉	C₂²	semidirect
80. #383×C₁₃₉	C₂²	semidirect
81. #383×C₁₃₉	C₂²	semidirect
82. #382×C₁₃₉	C₂²	semidirect
88. #380×C₁₃₉	C₂²	semidirect
91. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
92. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
105. #376×C₁₃₉	C₂²	semidirect
106. C₂×#95×C₁₃₉	C₂²	semidirect
422. #35851	C₁₃₉	direct (N × H)
423. C₁₃₉	#35851	direct (N × H)
424. #2667	C₂×C₁₃₉	semidirect
425. #2652	C₂×C₁₃₉	semidirect
426. #2578	C₂×C₁₃₉	semidirect
427. #2575	C₂×C₁₃₉	semidirect
428. #2553	C₂×C₁₃₉	semidirect
430. #2522	C₂×C₁₃₉	semidirect
431. #2495	C₂×C₁₃₉	semidirect
432. #2482	C₂×C₁₃₉	semidirect
433. #2480	C₂×C₁₃₉	semidirect
434. #2470	C₂×C₁₃₉	semidirect
436. #2395	C₂×C₁₃₉	semidirect
437. #2395	C₂×C₁₃₉	semidirect
438. #2373	C₂×C₁₃₉	semidirect
439. #2359	C₂×C₁₃₉	semidirect
440. #2353	C₂×C₁₃₉	semidirect
441. #2347	C₂×C₁₃₉	semidirect
442. #2273	C₂×C₁₃₉	semidirect
450. C₂×#117	C₂²×C₁₃₉	semidirect
453. #400	C₂²×C₁₃₉	semidirect
454. #400	C₂²×C₁₃₉	semidirect
455. #400	C₂²×C₁₃₉	semidirect
456. #400	C₂²×C₁₃₉	semidirect
459. #399	C₂²×C₁₃₉	semidirect
460. #398	C₂²×C₁₃₉	semidirect
461. #398	C₂²×C₁₃₉	semidirect
462. #398	C₂²×C₁₃₉	semidirect
468. #397	C₂²×C₁₃₉	semidirect
469. #397	C₂²×C₁₃₉	semidirect
475. #389	C₂²×C₁₃₉	semidirect
476. #389	C₂²×C₁₃₉	semidirect
477. #389	C₂²×C₁₃₉	semidirect
478. #389	C₂²×C₁₃₉	semidirect
487. #388	C₂²×C₁₃₉	semidirect
488. #387	C₂²×C₁₃₉	semidirect
489. #387	C₂²×C₁₃₉	semidirect
490. #387	C₂²×C₁₃₉	semidirect
491. #387	C₂²×C₁₃₉	semidirect
492. #387	C₂²×C₁₃₉	semidirect
493. #387	C₂²×C₁₃₉	semidirect
494. #387	C₂²×C₁₃₉	semidirect
502. #385	C₂²×C₁₃₉	semidirect
503. #383	C₂²×C₁₃₉	semidirect
504. #383	C₂²×C₁₃₉	semidirect
505. #382	C₂²×C₁₃₉	semidirect
511. #380	C₂²×C₁₃₉	semidirect
514. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
515. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
516. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
517. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
526. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
527. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
528. #376	C₂²×C₁₃₉	semidirect
529. C₂×#95	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2667×C₁₃₉	2
#2652×C₁₃₉	2
#2578×C₁₃₉	2
#2575×C₁₃₉	2
#2553×C₁₃₉	2
#2534×C₁₃₉	2
#2522×C₁₃₉	2
#2495×C₁₃₉	2
#2482×C₁₃₉	2
#2480×C₁₃₉	2
#2470×C₁₃₉	2
#2418×C₁₃₉	2
#2395×C₁₃₉	2
#2373×C₁₃₉	2
#2359×C₁₃₉	2
#2353×C₁₃₉	2
#2347×C₁₃₉	2
#2273×C₁₃₉	2
#35851	139

Subgroups — C139×#35851 #48030447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35851 #48030447