Subgroups — C₁₃₉×#35925 #48030521

Order 35584.

1956 conjugacy classes of subgroups.

The subgroup lattice has 854 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	#2666×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2609×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2598×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2579×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2574×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2573×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2553×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2468×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2468×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2457×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2406×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2392×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2388×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2353×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2349×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2343×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2339×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
33	#399×C₁₃₉	C₂²	1	2	yes	—
34	#398×C₁₃₉	C₂²	1	2	yes	—
35	#398×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	#397×C₁₃₉	C₂²	1	2	yes	—
40	#396×C₁₃₉	C₂²	1	2	yes	—
41	#396×C₁₃₉	C₂²	1	2	yes	—
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#395×C₁₃₉	C₂²	1	2	yes	—
44	#395×C₁₃₉	C₂²	1	1	yes	characteristic
45	#394×C₁₃₉	C₂²	1	2	yes	—
46	#394×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	1	yes	characteristic
48	#394×C₁₃₉	C₂²	1	2	yes	—
49	#394×C₁₃₉	C₂²	1	2	yes	—
50	#393×C₁₃₉	C₂²	1	1	yes	characteristic
51	#392×C₁₃₉	C₂²	1	2	yes	—
52	#392×C₁₃₉	C₂²	1	1	yes	characteristic
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
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	#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	#386×C₁₃₉	C₂²	1	2	yes	—
70	#386×C₁₃₉	C₂²	1	1	yes	characteristic
71	#386×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
80	#385×C₁₃₉	C₂²	1	2	yes	—
81	#385×C₁₃₉	C₂²	1	2	yes	—
82	#385×C₁₃₉	C₂²	1	2	yes	—
83	#383×C₁₃₉	C₂²	1	1	yes	characteristic
84	#383×C₁₃₉	C₂²	1	2	yes	—
85	#382×C₁₃₉	C₂²	1	2	yes	—
86	#382×C₁₃₉	C₂²	1	2	yes	—
87	#381×C₁₃₉	C₂²	1	2	yes	—
88	#381×C₁₃₉	C₂²	1	2	yes	—
89	#381×C₁₃₉	C₂²	1	1	yes	characteristic
90	#380×C₁₃₉	C₂²	1	2	yes	—
91	#380×C₁₃₉	C₂²	1	2	yes	—
92	#380×C₁₃₉	C₂²	1	1	yes	characteristic
93	#380×C₁₃₉	C₂²	1	1	yes	characteristic
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×C₂²⋊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	2	yes	—
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	#376×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
106	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂×#41×C₁₃₉	—	2	4	no	—
108	C₂×#41×C₁₃₉	—	4	4	no	—
109	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	#126×C₁₃₉	—	4	4	no	—
123	#123×C₁₃₉	—	4	4	no	—
124	C₄×D₄×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	—	2	8	no	—
126	C₄×D₄×C₁₃₉	—	4	4	no	—
127	C₄×D₄×C₁₃₉	—	4	4	no	—
128	C₄×D₄×C₁₃₉	—	4	4	no	—
129	#117×C₁₃₉	—	2	8	no	—
130	#117×C₁₃₉	—	2	8	no	—
131	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	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×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×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×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×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	1	yes	characteristic
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	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	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	#95×C₁₃₉	C₂³	1	1	yes	characteristic
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	#41×C₁₃₉	—	4	16	no	—
210	C₂×Q₈×C₁₃₉	—	2	2	no	—
211	C₂×Q₈×C₁₃₉	—	4	2	no	—
212	C₂×D₄×C₁₃₉	—	2	4	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	—	2	4	no	—
217	C₂×D₄×C₁₃₉	—	2	4	no	—
218	C₂×D₄×C₁₃₉	—	2	2	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	4	1	no	—
222	C₂×D₄×C₁₃₉	—	4	2	no	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	no	—
226	C₂²×C₄×C₁₃₉	—	2	4	no	—
227	C₂²×C₄×C₁₃₉	—	2	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	4	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	2	2	no	—
233	C₂²×C₄×C₁₃₉	—	4	2	no	—
234	C₂²×C₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	—	4	2	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	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	#41	1	4	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	2	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	4	2	no	—
268	C₄⋊C₄×C₁₃₉	—	4	2	no	—
269	C₄⋊C₄×C₁₃₉	—	4	2	no	—
270	C₄⋊C₄×C₁₃₉	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	2	no	—
272	C₄⋊C₄×C₁₃₉	—	4	2	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
292	C₂²⋊C₄×C₁₃₉	—	4	1	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	C₄²×C₁₃₉	—	2	4	no	—
298	C₄²×C₁₃₉	—	2	4	no	—
299	C₄²×C₁₃₉	—	2	2	no	—
300	C₄²×C₁₃₉	—	4	2	no	—
301	C₄²×C₁₃₉	—	4	2	no	—
302	C₄²×C₁₃₉	—	4	2	no	—
303	C₄²×C₁₃₉	—	4	2	no	—
304	C₄²×C₁₃₉	#41	1	8	yes	complemented
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	1	no	—
316	C₂³×C₁₃₉	—	2	1	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	1	no	—
319	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
320	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
321	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
322	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
323	Q₈×C₁₃₉	—	4	4	no	—
324	D₄×C₁₃₉	—	2	16	no	—
325	D₄×C₁₃₉	—	2	8	no	—
326	D₄×C₁₃₉	—	4	4	no	—
327	D₄×C₁₃₉	—	4	8	no	—
328	C₂×C₄×C₁₃₉	—	2	8	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
337	C₂×C₄×C₁₃₉	—	2	1	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	1	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	2	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	1	no	—
363	C₂×C₄×C₁₃₉	—	2	1	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	—	4	4	no	—
369	C₂×C₄×C₁₃₉	—	4	8	no	—
370	C₂×C₄×C₁₃₉	—	4	8	no	—
371	C₂×C₄×C₁₃₉	—	8	2	no	—
372	C₂×C₄×C₁₃₉	—	8	4	no	—
373	C₂×C₄×C₁₃₉	—	8	4	no	—
374	C₂×C₄×C₁₃₉	—	8	2	no	—
375	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
376	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
377	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
378	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
379	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
380	C₂²×C₁₃₉	—	2	2	no	—
381	C₂²×C₁₃₉	—	2	2	no	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	2	4	no	—
384	C₂²×C₁₃₉	—	2	4	no	—
385	C₂²×C₁₃₉	—	2	4	no	—
386	C₂²×C₁₃₉	—	2	2	no	—
387	C₂²×C₁₃₉	—	2	2	no	—
388	C₂²×C₁₃₉	—	4	2	no	—
389	C₂²×C₁₃₉	—	4	1	no	—
390	C₂²×C₁₃₉	—	4	1	no	—
391	C₂²×C₁₃₉	—	4	2	no	—
392	C₂²×C₁₃₉	—	4	2	no	—
393	C₂²×C₁₃₉	—	4	2	no	—
394	C₂²×C₁₃₉	—	4	2	no	—
395	C₂²×C₁₃₉	—	4	2	no	—
396	C₂²×C₁₃₉	—	4	2	no	—
397	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
399	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
400	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
401	C₂²×C₁₃₉	#585	1	1	yes	characteristic
402	C₄×C₁₃₉	—	2	4	no	—
403	C₄×C₁₃₉	—	2	2	no	—
404	C₄×C₁₃₉	—	2	2	no	—
405	C₄×C₁₃₉	—	2	4	no	—
406	C₄×C₁₃₉	—	2	4	no	—
407	C₄×C₁₃₉	—	4	1	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	—	4	1	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	C₄×C₁₃₉	—	4	2	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₄×C₁₃₉	—	4	2	no	—
417	C₄×C₁₃₉	—	4	1	no	—
418	C₂×C₁₃₉	—	4	2	no	—
419	C₂×C₁₃₉	—	4	4	no	—
420	C₂×C₁₃₉	—	4	2	no	—
421	C₂×C₁₃₉	#3444	1	1	yes	characteristic
422	C₂×C₁₃₉	#3490	1	1	yes	characteristic
423	C₂×C₁₃₉	#3492	1	2	yes	—
424	C₂×C₁₃₉	#3494	1	2	yes	—
425	C₂×C₁₃₉	#3495	1	1	yes	characteristic
426	#35925	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₁₃₉	#35925	1	1	yes	characteristic, direct product factor, Sylow
428	#2667	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#2666	C₂×C₁₃₉	1	2	yes	complemented
430	#2609	C₂×C₁₃₉	1	2	yes	complemented
431	#2598	C₂×C₁₃₉	1	2	yes	complemented
432	#2579	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	#2574	C₂×C₁₃₉	1	2	yes	complemented
434	#2573	C₂×C₁₃₉	1	2	yes	complemented
435	#2553	C₂×C₁₃₉	1	2	yes	complemented
436	#2468	C₂×C₁₃₉	1	2	yes	complemented
437	#2468	C₂×C₁₃₉	1	2	yes	complemented
438	#2457	C₂×C₁₃₉	1	2	yes	complemented
439	#2406	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	#2392	C₂×C₁₃₉	1	2	yes	complemented
441	#2388	C₂×C₁₃₉	1	1	yes	characteristic
442	#2353	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	#2349	C₂×C₁₃₉	1	2	yes	complemented
444	#2343	C₂×C₁₃₉	1	2	yes	complemented
445	#2339	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
448	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
452	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
453	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
455	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
456	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
457	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
458	#400	C₂²×C₁₃₉	1	2	yes	—
459	#400	C₂²×C₁₃₉	1	2	yes	—
460	#399	C₂²×C₁₃₉	1	2	yes	—
461	#398	C₂²×C₁₃₉	1	2	yes	—
462	#398	C₂²×C₁₃₉	1	2	yes	—
463	#398	C₂²×C₁₃₉	1	2	yes	—
464	#398	C₂²×C₁₃₉	1	2	yes	—
465	#398	C₂²×C₁₃₉	1	2	yes	—
466	#397	C₂²×C₁₃₉	1	2	yes	—
467	#396	C₂²×C₁₃₉	1	2	yes	—
468	#396	C₂²×C₁₃₉	1	2	yes	—
469	#396	C₂²×C₁₃₉	1	2	yes	—
470	#395	C₂²×C₁₃₉	1	2	yes	—
471	#395	C₂²×C₁₃₉	1	1	yes	characteristic
472	#394	C₂²×C₁₃₉	1	2	yes	—
473	#394	C₂²×C₁₃₉	1	2	yes	—
474	#394	C₂²×C₁₃₉	1	1	yes	characteristic
475	#394	C₂²×C₁₃₉	1	2	yes	—
476	#394	C₂²×C₁₃₉	1	2	yes	—
477	#393	C₂²×C₁₃₉	1	1	yes	characteristic
478	#392	C₂²×C₁₃₉	1	2	yes	—
479	#392	C₂²×C₁₃₉	1	1	yes	characteristic
480	#391	C₂²×C₁₃₉	1	2	yes	—
481	#389	C₂²×C₁₃₉	1	2	yes	—
482	#389	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	—
488	#388	C₂²×C₁₃₉	1	2	yes	—
489	#387	C₂²×C₁₃₉	1	2	yes	—
490	#387	C₂²×C₁₃₉	1	2	yes	—
491	#387	C₂²×C₁₃₉	1	2	yes	—
492	#387	C₂²×C₁₃₉	1	2	yes	—
493	#387	C₂²×C₁₃₉	1	2	yes	—
494	#387	C₂²×C₁₃₉	1	2	yes	—
495	#387	C₂²×C₁₃₉	1	2	yes	—
496	#386	C₂²×C₁₃₉	1	1	yes	characteristic
497	#386	C₂²×C₁₃₉	1	1	yes	characteristic
498	#386	C₂²×C₁₃₉	1	2	yes	—
499	#386	C₂²×C₁₃₉	1	2	yes	—
500	#386	C₂²×C₁₃₉	1	2	yes	—
501	#386	C₂²×C₁₃₉	1	2	yes	—
502	#385	C₂²×C₁₃₉	1	2	yes	—
503	#385	C₂²×C₁₃₉	1	2	yes	—
504	#385	C₂²×C₁₃₉	1	2	yes	—
505	#385	C₂²×C₁₃₉	1	1	yes	characteristic
506	#385	C₂²×C₁₃₉	1	1	yes	characteristic
507	#385	C₂²×C₁₃₉	1	2	yes	—
508	#385	C₂²×C₁₃₉	1	2	yes	—
509	#385	C₂²×C₁₃₉	1	2	yes	—
510	#383	C₂²×C₁₃₉	1	1	yes	characteristic
511	#383	C₂²×C₁₃₉	1	2	yes	—
512	#382	C₂²×C₁₃₉	1	2	yes	—
513	#382	C₂²×C₁₃₉	1	2	yes	—
514	#381	C₂²×C₁₃₉	1	2	yes	—
515	#381	C₂²×C₁₃₉	1	2	yes	—
516	#381	C₂²×C₁₃₉	1	1	yes	characteristic
517	#380	C₂²×C₁₃₉	1	2	yes	—
518	#380	C₂²×C₁₃₉	1	1	yes	characteristic
519	#380	C₂²×C₁₃₉	1	2	yes	—
520	#380	C₂²×C₁₃₉	1	1	yes	characteristic
521	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
528	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
529	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
531	#376	C₂²×C₁₃₉	1	1	yes	characteristic
532	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
533	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
534	C₂×#41	—	2	4	no	—
535	C₂×#41	—	4	4	no	—
536	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	#126	—	4	4	no	—
550	#123	—	4	4	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	—	4	4	no	—
554	C₄×D₄	—	4	4	no	—
555	C₄×D₄	—	4	4	no	—
556	#117	—	2	8	no	—
557	#117	—	2	8	no	—
558	C₂×C₄⋊C₄	—	2	4	no	—
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×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	1	yes	characteristic
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	2	yes	—
609	#95	C₂³×C₁₃₉	1	1	yes	characteristic
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	1	yes	characteristic
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	2	yes	—
614	#95	C₂³×C₁₃₉	1	1	yes	characteristic
615	#95	C₂³×C₁₃₉	1	1	yes	characteristic
616	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	#95	C₂³×C₁₃₉	1	2	yes	—
631	#95	C₂³×C₁₃₉	1	2	yes	—
632	#95	C₂³×C₁₃₉	1	2	yes	—
633	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
634	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
636	#41	—	4	16	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	4	2	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	1	no	—
719	C₂²⋊C₄	—	4	1	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	4	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	2	no	—
731	C₄²	#41×C₁₃₉	1	8	yes	complemented
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	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	1	no	—
746	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
747	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
748	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
749	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
750	Q₈	—	4	4	no	—
751	D₄	—	2	8	no	—
752	D₄	—	2	16	no	—
753	D₄	—	4	8	no	—
754	D₄	—	4	4	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	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	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	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	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
803	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
804	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
805	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
806	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
825	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
826	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
827	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
828	C₂²	#585×C₁₃₉	1	1	yes	characteristic
829	C₄	—	2	4	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₂	—	4	2	no	—
846	C₂	—	4	4	no	—
847	C₂	—	4	2	no	—
848	C₂	#3444×C₁₃₉	1	1	yes	characteristic
849	C₂	#3490×C₁₃₉	1	1	yes	characteristic
850	C₂	#3492×C₁₃₉	1	2	yes	—
851	C₂	#3494×C₁₃₉	1	2	yes	—
852	C₂	#3495×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2388×C₁₃₉	C₂
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. #2666×C₁₃₉	C₂	semidirect
3. #2609×C₁₃₉	C₂	semidirect
4. #2598×C₁₃₉	C₂	semidirect
5. #2579×C₁₃₉	C₂	semidirect
6. #2574×C₁₃₉	C₂	semidirect
7. #2573×C₁₃₉	C₂	semidirect
8. #2553×C₁₃₉	C₂	semidirect
9. #2468×C₁₃₉	C₂	semidirect
10. #2468×C₁₃₉	C₂	semidirect
11. #2457×C₁₃₉	C₂	semidirect
12. #2406×C₁₃₉	C₂	semidirect
13. #2392×C₁₃₉	C₂	semidirect
15. #2353×C₁₃₉	C₂	semidirect
16. #2349×C₁₃₉	C₂	semidirect
17. #2343×C₁₃₉	C₂	semidirect
18. #2339×C₁₃₉	C₂	semidirect
19. #2274×C₁₃₉	C₂	semidirect
304. C₄²×C₁₃₉	#41	semidirect
426. #35925	C₁₃₉	direct (N × H)
427. C₁₃₉	#35925	direct (N × H)
428. #2667	C₂×C₁₃₉	semidirect
429. #2666	C₂×C₁₃₉	semidirect
430. #2609	C₂×C₁₃₉	semidirect
431. #2598	C₂×C₁₃₉	semidirect
432. #2579	C₂×C₁₃₉	semidirect
433. #2574	C₂×C₁₃₉	semidirect
434. #2573	C₂×C₁₃₉	semidirect
435. #2553	C₂×C₁₃₉	semidirect
436. #2468	C₂×C₁₃₉	semidirect
437. #2468	C₂×C₁₃₉	semidirect
438. #2457	C₂×C₁₃₉	semidirect
439. #2406	C₂×C₁₃₉	semidirect
440. #2392	C₂×C₁₃₉	semidirect
442. #2353	C₂×C₁₃₉	semidirect
443. #2349	C₂×C₁₃₉	semidirect
444. #2343	C₂×C₁₃₉	semidirect
445. #2339	C₂×C₁₃₉	semidirect
446. #2274	C₂×C₁₃₉	semidirect
731. C₄²	#41×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
#2666×C₁₃₉	2
#2609×C₁₃₉	2
#2598×C₁₃₉	2
#2579×C₁₃₉	2
#2574×C₁₃₉	2
#2573×C₁₃₉	2
#2553×C₁₃₉	2
#2468×C₁₃₉	2
#2457×C₁₃₉	2
#2406×C₁₃₉	2
#2392×C₁₃₉	2
#2388×C₁₃₉	2
#2353×C₁₃₉	2
#2349×C₁₃₉	2
#2343×C₁₃₉	2
#2339×C₁₃₉	2
#2274×C₁₃₉	2
#35925	139

Subgroups — C139×#35925 #48030521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35925 #48030521