Subgroups — C₁₃₉×#37218 #48031814

Order 35584.

1770 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2780×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2772×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2727×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2727×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2726×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2714×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2711×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2706×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2705×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2682×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2630×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2558×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2553×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2464×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2334×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#399×C₁₃₉	C₂²	1	2	yes	—
35	#399×C₁₃₉	C₂²	1	2	yes	—
36	#399×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	#397×C₁₃₉	C₂²	1	2	yes	—
41	#397×C₁₃₉	C₂²	1	2	yes	—
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#396×C₁₃₉	C₂²	1	2	yes	—
45	#396×C₁₃₉	C₂²	1	2	yes	—
46	#396×C₁₃₉	C₂²	1	2	yes	—
47	#396×C₁₃₉	C₂²	1	2	yes	—
48	#394×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	#394×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#392×C₁₃₉	C₂²	1	2	yes	—
55	#392×C₁₃₉	C₂²	1	2	yes	—
56	#392×C₁₃₉	C₂²	1	2	yes	—
57	#390×C₁₃₉	C₂²	1	2	yes	—
58	#390×C₁₃₉	C₂²	1	1	yes	characteristic
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#389×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic
73	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	—
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×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	#386×C₁₃₉	C₂²	1	2	yes	—
87	#386×C₁₃₉	C₂²	1	2	yes	—
88	#386×C₁₃₉	C₂²	1	2	yes	—
89	#386×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	#385×C₁₃₉	C₂²	1	2	yes	—
96	#382×C₁₃₉	C₂²	1	2	yes	—
97	#382×C₁₃₉	C₂²	1	1	yes	characteristic
98	#380×C₁₃₉	C₂²	1	1	yes	characteristic
99	#380×C₁₃₉	C₂²	1	2	yes	—
100	#380×C₁₃₉	C₂²	1	1	yes	characteristic
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	#380×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	#126×C₁₃₉	—	2	8	no	—
119	#126×C₁₃₉	—	4	4	no	—
120	#125×C₁₃₉	—	4	2	no	—
121	#125×C₁₃₉	—	4	4	no	—
122	#123×C₁₃₉	—	4	4	no	—
123	#123×C₁₃₉	—	4	4	no	—
124	#123×C₁₃₉	—	4	4	no	—
125	#121×C₁₃₉	—	2	4	no	—
126	#121×C₁₃₉	—	4	2	no	—
127	#121×C₁₃₉	—	4	4	no	—
128	C₄×D₄×C₁₃₉	—	4	2	no	—
129	C₄×D₄×C₁₃₉	—	4	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₉	—	4	2	no	—
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄²×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	#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	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂×D₄×C₁₃₉	—	2	4	no	—
211	C₂×D₄×C₁₃₉	—	2	4	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	2	2	no	—
214	C₂×D₄×C₁₃₉	—	2	2	no	—
215	C₂×D₄×C₁₃₉	—	4	1	no	—
216	C₂×D₄×C₁₃₉	—	4	2	no	—
217	C₂×D₄×C₁₃₉	—	4	1	no	—
218	C₂×D₄×C₁₃₉	—	4	1	no	—
219	C₂×D₄×C₁₃₉	—	4	2	no	—
220	C₂×D₄×C₁₃₉	—	4	2	no	—
221	C₂×D₄×C₁₃₉	—	4	2	no	—
222	C₂×D₄×C₁₃₉	—	4	2	no	—
223	C₂×D₄×C₁₃₉	—	4	2	no	—
224	C₂×D₄×C₁₃₉	—	4	2	no	—
225	C₂×D₄×C₁₃₉	—	4	1	no	—
226	C₂×D₄×C₁₃₉	—	4	2	no	—
227	C₂×D₄×C₁₃₉	—	4	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	2	no	—
229	C₂²×C₄×C₁₃₉	—	2	2	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	2	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	4	1	no	—
235	C₂²×C₄×C₁₃₉	—	4	1	no	—
236	C₂²×C₄×C₁₃₉	—	4	1	no	—
237	C₂²×C₄×C₁₃₉	—	4	1	no	—
238	C₂²×C₄×C₁₃₉	—	4	2	no	—
239	C₂²×C₄×C₁₃₉	—	4	2	no	—
240	C₂²×C₄×C₁₃₉	—	4	2	no	—
241	C₂²×C₄×C₁₃₉	—	4	2	no	—
242	C₂²×C₄×C₁₃₉	—	4	2	no	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	4	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	4	no	—
263	C₄⋊C₄×C₁₃₉	—	2	2	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	2	no	—
267	C₄⋊C₄×C₁₃₉	—	2	2	no	—
268	C₄⋊C₄×C₁₃₉	—	4	1	no	—
269	C₄⋊C₄×C₁₃₉	—	4	1	no	—
270	C₄⋊C₄×C₁₃₉	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	2	no	—
272	C₄⋊C₄×C₁₃₉	—	4	1	no	—
273	C₄⋊C₄×C₁₃₉	—	4	1	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₄⋊C₄×C₁₃₉	—	4	1	no	—
278	C₄⋊C₄×C₁₃₉	—	4	1	no	—
279	C₄⋊C₄×C₁₃₉	—	4	2	no	—
280	C₄⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄⋊C₄×C₁₃₉	—	4	2	no	—
282	C₄⋊C₄×C₁₃₉	—	4	2	no	—
283	C₄⋊C₄×C₁₃₉	—	4	2	no	—
284	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
294	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
295	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
304	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
305	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
306	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
307	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
309	C₄²×C₁₃₉	—	2	4	no	—
310	C₄²×C₁₃₉	—	2	2	no	—
311	C₄²×C₁₃₉	—	2	2	no	—
312	C₄²×C₁₃₉	—	4	1	no	—
313	C₄²×C₁₃₉	—	4	1	no	—
314	C₄²×C₁₃₉	—	4	2	no	—
315	C₄²×C₁₃₉	—	4	2	no	—
316	C₄²×C₁₃₉	—	4	2	no	—
317	C₂³×C₁₃₉	—	2	1	no	—
318	C₂³×C₁₃₉	—	2	1	no	—
319	C₂³×C₁₃₉	—	2	1	no	—
320	C₂³×C₁₃₉	—	2	1	no	—
321	C₂³×C₁₃₉	—	2	1	no	—
322	C₂³×C₁₃₉	—	2	1	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
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	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	—	2	2	no	—
335	C₂³×C₁₃₉	—	2	2	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
338	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
339	D₄×C₁₃₉	—	4	8	no	—
340	D₄×C₁₃₉	—	4	4	no	—
341	D₄×C₁₃₉	—	8	2	no	—
342	D₄×C₁₃₉	—	8	4	no	—
343	D₄×C₁₃₉	—	8	4	no	—
344	D₄×C₁₃₉	—	8	4	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	1	no	—
347	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	1	no	—
378	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	4	4	no	—
389	C₂×C₄×C₁₃₉	—	4	4	no	—
390	C₂×C₄×C₁₃₉	—	4	4	no	—
391	C₂×C₄×C₁₃₉	—	8	4	no	—
392	C₂×C₄×C₁₃₉	—	8	4	no	—
393	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
394	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
395	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
398	C₂²×C₁₃₉	—	2	2	no	—
399	C₂²×C₁₃₉	—	2	2	no	—
400	C₂²×C₁₃₉	—	2	2	no	—
401	C₂²×C₁₃₉	—	4	1	no	—
402	C₂²×C₁₃₉	—	4	1	no	—
403	C₂²×C₁₃₉	—	4	1	no	—
404	C₂²×C₁₃₉	—	4	1	no	—
405	C₂²×C₁₃₉	—	4	2	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	—	4	2	no	—
409	C₂²×C₁₃₉	—	4	2	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	—	4	2	no	—
415	C₂²×C₁₃₉	—	4	2	no	—
416	C₂²×C₁₃₉	—	4	2	no	—
417	C₂²×C₁₃₉	—	4	2	no	—
418	C₂²×C₁₃₉	—	4	2	no	—
419	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
420	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
424	C₂²×C₁₃₉	#585	1	1	yes	characteristic
425	C₂²×C₁₃₉	#585	1	1	yes	characteristic
426	C₄×C₁₃₉	—	2	2	no	—
427	C₄×C₁₃₉	—	2	4	no	—
428	C₄×C₁₃₉	—	2	2	no	—
429	C₄×C₁₃₉	—	2	2	no	—
430	C₄×C₁₃₉	—	2	2	no	—
431	C₄×C₁₃₉	—	4	2	no	—
432	C₄×C₁₃₉	—	4	1	no	—
433	C₄×C₁₃₉	—	4	2	no	—
434	C₄×C₁₃₉	—	4	2	no	—
435	C₄×C₁₃₉	—	4	2	no	—
436	C₄×C₁₃₉	—	4	2	no	—
437	C₄×C₁₃₉	—	4	1	no	—
438	C₄×C₁₃₉	—	4	2	no	—
439	C₄×C₁₃₉	—	4	2	no	—
440	C₄×C₁₃₉	—	4	2	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₂×C₁₃₉	—	4	2	no	—
443	C₂×C₁₃₉	—	8	2	no	—
444	C₂×C₁₃₉	—	8	2	no	—
445	C₂×C₁₃₉	#3460	1	1	yes	characteristic
446	C₂×C₁₃₉	#3517	1	1	yes	characteristic
447	C₂×C₁₃₉	#3520	1	1	yes	characteristic
448	C₂×C₁₃₉	#3534	1	1	yes	characteristic
449	C₂×C₁₃₉	#3536	1	1	yes	characteristic
450	C₂×C₁₃₉	#3546	1	1	yes	characteristic
451	C₂×C₁₃₉	#3553	1	1	yes	characteristic
452	#37218	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₁₃₉	#37218	1	1	yes	characteristic, direct product factor, Sylow
454	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
455	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
456	#2780	C₂×C₁₃₉	1	2	yes	complemented
457	#2772	C₂×C₁₃₉	1	2	yes	complemented
458	#2727	C₂×C₁₃₉	1	1	yes	characteristic, complemented
459	#2727	C₂×C₁₃₉	1	1	yes	characteristic, complemented
460	#2726	C₂×C₁₃₉	1	1	yes	characteristic, complemented
461	#2714	C₂×C₁₃₉	1	2	yes	complemented
462	#2711	C₂×C₁₃₉	1	2	yes	complemented
463	#2706	C₂×C₁₃₉	1	2	yes	complemented
464	#2705	C₂×C₁₃₉	1	2	yes	complemented
465	#2682	C₂×C₁₃₉	1	1	yes	characteristic, complemented
466	#2630	C₂×C₁₃₉	1	2	yes	complemented
467	#2558	C₂×C₁₃₉	1	2	yes	complemented
468	#2553	C₂×C₁₃₉	1	2	yes	complemented
469	#2464	C₂×C₁₃₉	1	2	yes	complemented
470	#2454	C₂×C₁₃₉	1	2	yes	complemented
471	#2334	C₂×C₁₃₉	1	2	yes	complemented
472	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
473	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
474	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
475	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
476	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
477	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
478	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
479	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
480	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
483	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
485	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
486	#400	C₂²×C₁₃₉	1	2	yes	—
487	#399	C₂²×C₁₃₉	1	2	yes	—
488	#399	C₂²×C₁₃₉	1	2	yes	—
489	#399	C₂²×C₁₃₉	1	2	yes	—
490	#398	C₂²×C₁₃₉	1	2	yes	—
491	#398	C₂²×C₁₃₉	1	2	yes	—
492	#398	C₂²×C₁₃₉	1	2	yes	—
493	#397	C₂²×C₁₃₉	1	2	yes	—
494	#397	C₂²×C₁₃₉	1	2	yes	—
495	#396	C₂²×C₁₃₉	1	2	yes	—
496	#396	C₂²×C₁₃₉	1	2	yes	—
497	#396	C₂²×C₁₃₉	1	2	yes	—
498	#396	C₂²×C₁₃₉	1	2	yes	—
499	#396	C₂²×C₁₃₉	1	2	yes	—
500	#396	C₂²×C₁₃₉	1	2	yes	—
501	#394	C₂²×C₁₃₉	1	2	yes	—
502	#394	C₂²×C₁₃₉	1	2	yes	—
503	#394	C₂²×C₁₃₉	1	2	yes	—
504	#394	C₂²×C₁₃₉	1	2	yes	—
505	#394	C₂²×C₁₃₉	1	2	yes	—
506	#394	C₂²×C₁₃₉	1	2	yes	—
507	#392	C₂²×C₁₃₉	1	2	yes	—
508	#392	C₂²×C₁₃₉	1	2	yes	—
509	#392	C₂²×C₁₃₉	1	2	yes	—
510	#390	C₂²×C₁₃₉	1	1	yes	characteristic
511	#390	C₂²×C₁₃₉	1	1	yes	characteristic
512	#390	C₂²×C₁₃₉	1	1	yes	characteristic
513	#390	C₂²×C₁₃₉	1	2	yes	—
514	#390	C₂²×C₁₃₉	1	2	yes	—
515	#390	C₂²×C₁₃₉	1	2	yes	—
516	#390	C₂²×C₁₃₉	1	2	yes	—
517	#389	C₂²×C₁₃₉	1	2	yes	—
518	#389	C₂²×C₁₃₉	1	2	yes	—
519	#389	C₂²×C₁₃₉	1	1	yes	characteristic
520	#389	C₂²×C₁₃₉	1	1	yes	characteristic
521	#389	C₂²×C₁₃₉	1	1	yes	characteristic
522	#389	C₂²×C₁₃₉	1	1	yes	characteristic
523	#389	C₂²×C₁₃₉	1	2	yes	—
524	#389	C₂²×C₁₃₉	1	2	yes	—
525	#389	C₂²×C₁₃₉	1	1	yes	characteristic
526	#388	C₂²×C₁₃₉	1	2	yes	—
527	#388	C₂²×C₁₃₉	1	2	yes	—
528	#388	C₂²×C₁₃₉	1	2	yes	—
529	#388	C₂²×C₁₃₉	1	2	yes	—
530	#388	C₂²×C₁₃₉	1	2	yes	—
531	#388	C₂²×C₁₃₉	1	2	yes	—
532	#388	C₂²×C₁₃₉	1	2	yes	—
533	#388	C₂²×C₁₃₉	1	2	yes	—
534	#387	C₂²×C₁₃₉	1	2	yes	—
535	#387	C₂²×C₁₃₉	1	2	yes	—
536	#387	C₂²×C₁₃₉	1	2	yes	—
537	#387	C₂²×C₁₃₉	1	2	yes	—
538	#387	C₂²×C₁₃₉	1	2	yes	—
539	#386	C₂²×C₁₃₉	1	2	yes	—
540	#386	C₂²×C₁₃₉	1	2	yes	—
541	#386	C₂²×C₁₃₉	1	2	yes	—
542	#386	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	#385	C₂²×C₁₃₉	1	2	yes	—
548	#385	C₂²×C₁₃₉	1	2	yes	—
549	#382	C₂²×C₁₃₉	1	2	yes	—
550	#382	C₂²×C₁₃₉	1	1	yes	characteristic
551	#380	C₂²×C₁₃₉	1	1	yes	characteristic
552	#380	C₂²×C₁₃₉	1	1	yes	characteristic
553	#380	C₂²×C₁₃₉	1	1	yes	characteristic
554	#380	C₂²×C₁₃₉	1	2	yes	—
555	#380	C₂²×C₁₃₉	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
560	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
571	#126	—	2	8	no	—
572	#126	—	4	4	no	—
573	#125	—	4	2	no	—
574	#125	—	4	4	no	—
575	#123	—	4	4	no	—
576	#123	—	4	4	no	—
577	#123	—	4	4	no	—
578	#121	—	2	4	no	—
579	#121	—	4	2	no	—
580	#121	—	4	4	no	—
581	C₄×D₄	—	4	2	no	—
582	C₄×D₄	—	4	4	no	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₂²⋊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×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄²	—	4	2	no	—
634	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	2	yes	—
647	#95	C₂³×C₁₃₉	1	2	yes	—
648	#95	C₂³×C₁₃₉	1	2	yes	—
649	#95	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
661	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
662	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	4	1	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	1	no	—
671	C₂×D₄	—	4	1	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	4	1	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	4	1	no	—
688	C₂²×C₄	—	4	1	no	—
689	C₂²×C₄	—	4	1	no	—
690	C₂²×C₄	—	4	1	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	4	1	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	4	1	no	—
766	C₄²	—	4	1	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
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	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
791	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
792	D₄	—	4	8	no	—
793	D₄	—	4	4	no	—
794	D₄	—	8	2	no	—
795	D₄	—	8	4	no	—
796	D₄	—	8	4	no	—
797	D₄	—	8	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	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	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	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	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	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	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	8	4	no	—
845	C₂×C₄	—	8	4	no	—
846	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
847	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
848	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
849	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
850	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
873	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
874	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
875	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
876	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
877	C₂²	#585×C₁₃₉	1	1	yes	characteristic
878	C₂²	#585×C₁₃₉	1	1	yes	characteristic
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	4	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₂	—	4	2	no	—
896	C₂	—	8	2	no	—
897	C₂	—	8	2	no	—
898	C₂	#3460×C₁₃₉	1	1	yes	characteristic
899	C₂	#3517×C₁₃₉	1	1	yes	characteristic
900	C₂	#3520×C₁₃₉	1	1	yes	characteristic
901	C₂	#3534×C₁₃₉	1	1	yes	characteristic
902	C₂	#3536×C₁₃₉	1	1	yes	characteristic
903	C₂	#3546×C₁₃₉	1	1	yes	characteristic
904	C₂	#3553×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	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
1. #2854×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
3. #2780×C₁₃₉	C₂	semidirect
4. #2772×C₁₃₉	C₂	semidirect
5. #2727×C₁₃₉	C₂	semidirect
6. #2727×C₁₃₉	C₂	semidirect
7. #2726×C₁₃₉	C₂	semidirect
8. #2714×C₁₃₉	C₂	semidirect
9. #2711×C₁₃₉	C₂	semidirect
10. #2706×C₁₃₉	C₂	semidirect
11. #2705×C₁₃₉	C₂	semidirect
12. #2682×C₁₃₉	C₂	semidirect
13. #2630×C₁₃₉	C₂	semidirect
14. #2558×C₁₃₉	C₂	semidirect
15. #2553×C₁₃₉	C₂	semidirect
16. #2464×C₁₃₉	C₂	semidirect
17. #2454×C₁₃₉	C₂	semidirect
18. #2334×C₁₃₉	C₂	semidirect
19. C₄×#121×C₁₃₉	C₂	semidirect
452. #37218	C₁₃₉	direct (N × H)
453. C₁₃₉	#37218	direct (N × H)
454. #2854	C₂×C₁₃₉	semidirect
455. #2851	C₂×C₁₃₉	semidirect
456. #2780	C₂×C₁₃₉	semidirect
457. #2772	C₂×C₁₃₉	semidirect
458. #2727	C₂×C₁₃₉	semidirect
459. #2727	C₂×C₁₃₉	semidirect
460. #2726	C₂×C₁₃₉	semidirect
461. #2714	C₂×C₁₃₉	semidirect
462. #2711	C₂×C₁₃₉	semidirect
463. #2706	C₂×C₁₃₉	semidirect
464. #2705	C₂×C₁₃₉	semidirect
465. #2682	C₂×C₁₃₉	semidirect
466. #2630	C₂×C₁₃₉	semidirect
467. #2558	C₂×C₁₃₉	semidirect
468. #2553	C₂×C₁₃₉	semidirect
469. #2464	C₂×C₁₃₉	semidirect
470. #2454	C₂×C₁₃₉	semidirect
471. #2334	C₂×C₁₃₉	semidirect
472. C₄×#121	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2854×C₁₃₉	2
#2851×C₁₃₉	2
#2780×C₁₃₉	2
#2772×C₁₃₉	2
#2727×C₁₃₉	2
#2726×C₁₃₉	2
#2714×C₁₃₉	2
#2711×C₁₃₉	2
#2706×C₁₃₉	2
#2705×C₁₃₉	2
#2682×C₁₃₉	2
#2630×C₁₃₉	2
#2558×C₁₃₉	2
#2553×C₁₃₉	2
#2464×C₁₃₉	2
#2454×C₁₃₉	2
#2334×C₁₃₉	2
C₄×#121×C₁₃₉	2
#37218	139

Subgroups — C139×#37218 #48031814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37218 #48031814