Subgroups — C₁₃₉×#35641 #48030237

Order 35584.

1538 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2590×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2589×C₁₃₉	C₂	1	2	yes	maximal
3	#2585×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2574×C₁₃₉	C₂	1	2	yes	maximal
5	#2571×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2570×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2522×C₁₃₉	C₂	1	2	yes	maximal
10	#2520×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2511×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2497×C₁₃₉	C₂	1	2	yes	maximal
13	#2442×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2442×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2441×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2439×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2331×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2330×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2314×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
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	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×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	#398×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#396×C₁₃₉	C₂²	1	2	yes	—
45	#395×C₁₃₉	C₂²	1	2	yes	—
46	#393×C₁₃₉	C₂²	1	2	yes	—
47	#391×C₁₃₉	C₂²	1	2	yes	—
48	#391×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	2	yes	—
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	1	yes	characteristic
55	#389×C₁₃₉	C₂²	1	1	yes	characteristic
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	1	yes	characteristic
58	#389×C₁₃₉	C₂²	1	1	yes	characteristic
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	1	yes	characteristic
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic
62	#389×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	1	yes	characteristic
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	1	yes	characteristic
68	#388×C₁₃₉	C₂²	1	1	yes	characteristic
69	#388×C₁₃₉	C₂²	1	1	yes	characteristic
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	1	yes	characteristic
83	#387×C₁₃₉	C₂²	1	1	yes	characteristic
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#384×C₁₃₉	C₂²	1	2	yes	—
92	#384×C₁₃₉	C₂²	1	1	yes	characteristic
93	#384×C₁₃₉	C₂²	1	1	yes	characteristic
94	#382×C₁₃₉	C₂²	1	2	yes	—
95	#382×C₁₃₉	C₂²	1	1	yes	characteristic
96	#382×C₁₃₉	C₂²	1	1	yes	characteristic
97	#382×C₁₃₉	C₂²	1	1	yes	characteristic
98	#382×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	2	yes	—
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
121	#376×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
127	#125×C₁₃₉	—	2	4	no	—
128	#125×C₁₃₉	—	2	4	no	—
129	#125×C₁₃₉	—	2	4	no	—
130	#117×C₁₃₉	—	2	4	no	—
131	#117×C₁₃₉	Q₈	1	8	yes	complemented
132	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×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	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	1	yes	characteristic
199	#95×C₁₃₉	C₂³	1	1	yes	characteristic
200	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	1	yes	characteristic
213	#95×C₁₃₉	C₂³	1	1	yes	characteristic
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	1	yes	characteristic
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	2	yes	—
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	2	yes	—
221	#95×C₁₃₉	C₂³	1	1	yes	characteristic
222	#95×C₁₃₉	C₂³	1	1	yes	characteristic
223	#95×C₁₃₉	C₂³	1	1	yes	characteristic
224	#95×C₁₃₉	C₂³	1	1	yes	characteristic
225	#95×C₁₃₉	C₂³	1	2	yes	—
226	#95×C₁₃₉	C₂³	1	2	yes	—
227	#95×C₁₃₉	C₂³	1	2	yes	—
228	#95×C₁₃₉	C₂³	1	2	yes	—
229	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₁₃₉	—	2	4	no	—
231	C₂×Q₈×C₁₃₉	—	4	2	no	—
232	C₂×Q₈×C₁₃₉	—	4	2	no	—
233	C₂²×C₄×C₁₃₉	—	2	2	no	—
234	C₂²×C₄×C₁₃₉	—	2	2	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	4	2	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	2	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	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	2	2	no	—
271	C₄⋊C₄×C₁₃₉	—	2	2	no	—
272	C₄⋊C₄×C₁₃₉	—	2	2	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	2	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	1	no	—
276	C₄⋊C₄×C₁₃₉	—	4	1	no	—
277	C₄⋊C₄×C₁₃₉	—	4	2	no	—
278	C₄⋊C₄×C₁₃₉	—	4	2	no	—
279	C₄⋊C₄×C₁₃₉	—	4	1	no	—
280	C₄⋊C₄×C₁₃₉	—	4	1	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	—	4	2	no	—
285	C₄⋊C₄×C₁₃₉	—	4	2	no	—
286	C₄⋊C₄×C₁₃₉	—	4	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄⋊C₄×C₁₃₉	—	4	2	no	—
290	C₄⋊C₄×C₁₃₉	—	4	2	no	—
291	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
292	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
293	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
294	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
300	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
302	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
303	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
304	C₄²×C₁₃₉	—	2	4	no	—
305	C₄²×C₁₃₉	—	2	2	no	—
306	C₄²×C₁₃₉	—	2	2	no	—
307	C₄²×C₁₃₉	—	2	2	no	—
308	C₄²×C₁₃₉	—	2	2	no	—
309	C₄²×C₁₃₉	—	4	2	no	—
310	C₄²×C₁₃₉	—	4	2	no	—
311	C₄²×C₁₃₉	—	4	1	no	—
312	C₄²×C₁₃₉	—	4	1	no	—
313	C₄²×C₁₃₉	—	4	1	no	—
314	C₄²×C₁₃₉	—	4	1	no	—
315	C₄²×C₁₃₉	—	4	2	no	—
316	C₄²×C₁₃₉	—	4	2	no	—
317	C₄²×C₁₃₉	—	4	2	no	—
318	C₄²×C₁₃₉	—	4	2	no	—
319	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
320	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
321	C₂³×C₁₃₉	—	2	1	no	—
322	C₂³×C₁₃₉	—	2	1	no	—
323	C₂³×C₁₃₉	—	2	1	no	—
324	C₂³×C₁₃₉	—	2	1	no	—
325	C₂³×C₁₃₉	—	2	1	no	—
326	C₂³×C₁₃₉	—	2	1	no	—
327	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
328	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
329	Q₈×C₁₃₉	—	8	4	no	—
330	C₂×C₄×C₁₃₉	—	2	1	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	1	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	8	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	1	no	—
347	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	1	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
380	C₂×C₄×C₁₃₉	—	2	1	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	1	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	8	4	no	—
388	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
389	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
390	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
391	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
392	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
393	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
394	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
395	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
396	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
397	C₂×C₄×C₁₃₉	C₂×#41	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	C₂³×Q₈	1	1	yes	characteristic
406	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
408	C₂²×C₁₃₉	#585	1	1	yes	characteristic
409	C₂²×C₁₃₉	#585	1	1	yes	characteristic
410	C₂²×C₁₃₉	#585	1	1	yes	characteristic
411	C₂²×C₁₃₉	#585	1	1	yes	characteristic
412	C₄×C₁₃₉	—	2	2	no	—
413	C₄×C₁₃₉	—	2	2	no	—
414	C₄×C₁₃₉	—	2	2	no	—
415	C₄×C₁₃₉	—	2	2	no	—
416	C₄×C₁₃₉	—	2	2	no	—
417	C₄×C₁₃₉	—	2	4	no	—
418	C₄×C₁₃₉	—	2	4	no	—
419	C₄×C₁₃₉	—	4	1	no	—
420	C₄×C₁₃₉	—	4	1	no	—
421	C₄×C₁₃₉	—	4	1	no	—
422	C₄×C₁₃₉	—	4	2	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₄×C₁₃₉	—	4	1	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	1	no	—
427	C₄×C₁₃₉	—	4	1	no	—
428	C₄×C₁₃₉	—	4	1	no	—
429	C₄×C₁₃₉	—	4	1	no	—
430	C₄×C₁₃₉	—	4	2	no	—
431	C₄×C₁₃₉	—	4	2	no	—
432	C₄×C₁₃₉	—	4	2	no	—
433	C₄×C₁₃₉	#533	1	4	yes	—
434	C₂×C₁₃₉	—	4	2	no	—
435	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
436	C₂×C₁₃₉	#3504	1	1	yes	characteristic
437	C₂×C₁₃₉	#3504	1	1	yes	characteristic
438	C₂×C₁₃₉	#3521	1	1	yes	characteristic
439	C₂×C₁₃₉	#3521	1	1	yes	characteristic
440	C₂×C₁₃₉	#3524	1	1	yes	characteristic
441	C₂×C₁₃₉	#3524	1	1	yes	characteristic
442	#35641	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
443	C₁₃₉	#35641	1	1	yes	characteristic, direct product factor, Sylow
444	#2590	C₂×C₁₃₉	1	2	yes	complemented
445	#2589	C₂×C₁₃₉	1	2	yes	—
446	#2585	C₂×C₁₃₉	1	2	yes	complemented
447	#2574	C₂×C₁₃₉	1	2	yes	—
448	#2571	C₂×C₁₃₉	1	1	yes	characteristic, complemented
449	#2570	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
451	#2550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
452	#2522	C₂×C₁₃₉	1	2	yes	—
453	#2520	C₂×C₁₃₉	1	2	yes	complemented
454	#2511	C₂×C₁₃₉	1	2	yes	complemented
455	#2497	C₂×C₁₃₉	1	2	yes	—
456	#2442	C₂×C₁₃₉	1	1	yes	characteristic
457	#2442	C₂×C₁₃₉	1	1	yes	characteristic
458	#2441	C₂×C₁₃₉	1	1	yes	characteristic
459	#2439	C₂×C₁₃₉	1	1	yes	characteristic
460	#2331	C₂×C₁₃₉	1	1	yes	characteristic, complemented
461	#2330	C₂×C₁₃₉	1	1	yes	characteristic, complemented
462	#2314	C₂×C₁₃₉	1	1	yes	characteristic
463	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
464	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
465	#2298	C₂×C₁₃₉	1	1	yes	characteristic
466	#2274	C₂×C₁₃₉	1	1	yes	characteristic
467	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
473	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
474	#400	C₂²×C₁₃₉	1	2	yes	—
475	#400	C₂²×C₁₃₉	1	2	yes	—
476	#400	C₂²×C₁₃₉	1	2	yes	—
477	#400	C₂²×C₁₃₉	1	2	yes	—
478	#400	C₂²×C₁₃₉	1	2	yes	—
479	#399	C₂²×C₁₃₉	1	2	yes	—
480	#398	C₂²×C₁₃₉	1	2	yes	—
481	#398	C₂²×C₁₃₉	1	2	yes	—
482	#398	C₂²×C₁₃₉	1	2	yes	—
483	#398	C₂²×C₁₃₉	1	2	yes	—
484	#398	C₂²×C₁₃₉	1	2	yes	—
485	#398	C₂²×C₁₃₉	1	2	yes	—
486	#396	C₂²×C₁₃₉	1	2	yes	—
487	#396	C₂²×C₁₃₉	1	2	yes	—
488	#395	C₂²×C₁₃₉	1	2	yes	—
489	#393	C₂²×C₁₃₉	1	2	yes	—
490	#391	C₂²×C₁₃₉	1	2	yes	—
491	#391	C₂²×C₁₃₉	1	2	yes	—
492	#391	C₂²×C₁₃₉	1	2	yes	—
493	#391	C₂²×C₁₃₉	1	2	yes	—
494	#389	C₂²×C₁₃₉	1	1	yes	characteristic
495	#389	C₂²×C₁₃₉	1	1	yes	characteristic
496	#389	C₂²×C₁₃₉	1	1	yes	characteristic
497	#389	C₂²×C₁₃₉	1	1	yes	characteristic
498	#389	C₂²×C₁₃₉	1	1	yes	characteristic
499	#389	C₂²×C₁₃₉	1	2	yes	—
500	#389	C₂²×C₁₃₉	1	1	yes	characteristic
501	#389	C₂²×C₁₃₉	1	2	yes	—
502	#389	C₂²×C₁₃₉	1	2	yes	—
503	#389	C₂²×C₁₃₉	1	2	yes	—
504	#389	C₂²×C₁₃₉	1	1	yes	characteristic
505	#389	C₂²×C₁₃₉	1	1	yes	characteristic
506	#389	C₂²×C₁₃₉	1	2	yes	—
507	#389	C₂²×C₁₃₉	1	2	yes	—
508	#388	C₂²×C₁₃₉	1	2	yes	—
509	#388	C₂²×C₁₃₉	1	2	yes	—
510	#388	C₂²×C₁₃₉	1	1	yes	characteristic
511	#388	C₂²×C₁₃₉	1	1	yes	characteristic
512	#388	C₂²×C₁₃₉	1	1	yes	characteristic
513	#388	C₂²×C₁₃₉	1	1	yes	characteristic
514	#387	C₂²×C₁₃₉	1	2	yes	—
515	#387	C₂²×C₁₃₉	1	2	yes	—
516	#387	C₂²×C₁₃₉	1	2	yes	—
517	#387	C₂²×C₁₃₉	1	2	yes	—
518	#387	C₂²×C₁₃₉	1	2	yes	—
519	#387	C₂²×C₁₃₉	1	2	yes	—
520	#387	C₂²×C₁₃₉	1	2	yes	—
521	#387	C₂²×C₁₃₉	1	2	yes	—
522	#387	C₂²×C₁₃₉	1	2	yes	—
523	#387	C₂²×C₁₃₉	1	1	yes	characteristic
524	#387	C₂²×C₁₃₉	1	2	yes	—
525	#387	C₂²×C₁₃₉	1	2	yes	—
526	#387	C₂²×C₁₃₉	1	2	yes	—
527	#387	C₂²×C₁₃₉	1	2	yes	—
528	#387	C₂²×C₁₃₉	1	1	yes	characteristic
529	#387	C₂²×C₁₃₉	1	2	yes	—
530	#387	C₂²×C₁₃₉	1	1	yes	characteristic
531	#387	C₂²×C₁₃₉	1	1	yes	characteristic
532	#385	C₂²×C₁₃₉	1	2	yes	—
533	#385	C₂²×C₁₃₉	1	2	yes	—
534	#384	C₂²×C₁₃₉	1	1	yes	characteristic
535	#384	C₂²×C₁₃₉	1	1	yes	characteristic
536	#384	C₂²×C₁₃₉	1	2	yes	—
537	#382	C₂²×C₁₃₉	1	1	yes	characteristic
538	#382	C₂²×C₁₃₉	1	1	yes	characteristic
539	#382	C₂²×C₁₃₉	1	1	yes	characteristic
540	#382	C₂²×C₁₃₉	1	2	yes	—
541	#382	C₂²×C₁₃₉	1	1	yes	characteristic
542	#380	C₂²×C₁₃₉	1	1	yes	characteristic
543	#380	C₂²×C₁₃₉	1	1	yes	characteristic
544	#380	C₂²×C₁₃₉	1	2	yes	—
545	#380	C₂²×C₁₃₉	1	2	yes	—
546	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
547	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
548	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
549	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
550	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
554	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
555	C₄×C₄⋊C₄	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×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
559	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
562	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
564	#376	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
567	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₄⋊Q₈	—	2	4	no	—
570	#125	—	2	4	no	—
571	#125	—	2	4	no	—
572	#125	—	2	4	no	—
573	#117	—	2	4	no	—
574	#117	Q₈×C₁₃₉	1	8	yes	complemented
575	C₂×C₄⋊C₄	—	2	4	no	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
636	#95	C₂³×C₁₃₉	1	1	yes	characteristic
637	#95	C₂³×C₁₃₉	1	1	yes	characteristic
638	#95	C₂³×C₁₃₉	1	1	yes	characteristic
639	#95	C₂³×C₁₃₉	1	1	yes	characteristic
640	#95	C₂³×C₁₃₉	1	2	yes	—
641	#95	C₂³×C₁₃₉	1	2	yes	—
642	#95	C₂³×C₁₃₉	1	2	yes	—
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	1	yes	characteristic
645	#95	C₂³×C₁₃₉	1	1	yes	characteristic
646	#95	C₂³×C₁₃₉	1	1	yes	characteristic
647	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
658	#95	C₂³×C₁₃₉	1	1	yes	characteristic
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	1	yes	characteristic
661	#95	C₂³×C₁₃₉	1	1	yes	characteristic
662	#95	C₂³×C₁₃₉	1	2	yes	—
663	#95	C₂³×C₁₃₉	1	2	yes	—
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	2	yes	—
666	#95	C₂³×C₁₃₉	1	2	yes	—
667	#95	C₂³×C₁₃₉	1	2	yes	—
668	#95	C₂³×C₁₃₉	1	2	yes	—
669	#95	C₂³×C₁₃₉	1	2	yes	—
670	#95	C₂³×C₁₃₉	1	2	yes	—
671	#95	C₂³×C₁₃₉	1	2	yes	—
672	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	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	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	4	1	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	1	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
735	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
736	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
737	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	4	1	no	—
740	C₂²⋊C₄	—	4	1	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	1	no	—
743	C₂²⋊C₄	—	4	1	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
746	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	4	2	no	—
753	C₄²	—	4	2	no	—
754	C₄²	—	4	1	no	—
755	C₄²	—	4	1	no	—
756	C₄²	—	4	1	no	—
757	C₄²	—	4	1	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	2	no	—
761	C₄²	—	4	2	no	—
762	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
763	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
771	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
772	Q₈	—	8	4	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	8	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	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	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	8	4	no	—
831	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
832	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
833	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
834	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
835	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
836	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
837	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
838	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
839	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
840	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
849	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
850	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
851	C₂²	#585×C₁₃₉	1	1	yes	characteristic
852	C₂²	#585×C₁₃₉	1	1	yes	characteristic
853	C₂²	#585×C₁₃₉	1	1	yes	characteristic
854	C₂²	#585×C₁₃₉	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	4	no	—
861	C₄	—	2	4	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	#533×C₁₃₉	1	4	yes	—
877	C₂	—	4	2	no	—
878	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
879	C₂	#3504×C₁₃₉	1	1	yes	characteristic
880	C₂	#3504×C₁₃₉	1	1	yes	characteristic
881	C₂	#3521×C₁₃₉	1	1	yes	characteristic
882	C₂	#3521×C₁₃₉	1	1	yes	characteristic
883	C₂	#3524×C₁₃₉	1	1	yes	characteristic
884	C₂	#3524×C₁₃₉	1	1	yes	characteristic

	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. #2590×C₁₃₉	C₂	semidirect
3. #2585×C₁₃₉	C₂	semidirect
5. #2571×C₁₃₉	C₂	semidirect
6. #2570×C₁₃₉	C₂	semidirect
7. #2552×C₁₃₉	C₂	semidirect
8. #2550×C₁₃₉	C₂	semidirect
10. #2520×C₁₃₉	C₂	semidirect
11. #2511×C₁₃₉	C₂	semidirect
17. #2331×C₁₃₉	C₂	semidirect
18. #2330×C₁₃₉	C₂	semidirect
20. C₄×#125×C₁₃₉	C₂	semidirect
21. C₄×#125×C₁₃₉	C₂	semidirect
131. #117×C₁₃₉	Q₈	semidirect
442. #35641	C₁₃₉	direct (N × H)
443. C₁₃₉	#35641	direct (N × H)
444. #2590	C₂×C₁₃₉	semidirect
446. #2585	C₂×C₁₃₉	semidirect
448. #2571	C₂×C₁₃₉	semidirect
449. #2570	C₂×C₁₃₉	semidirect
450. #2552	C₂×C₁₃₉	semidirect
451. #2550	C₂×C₁₃₉	semidirect
453. #2520	C₂×C₁₃₉	semidirect
454. #2511	C₂×C₁₃₉	semidirect
460. #2331	C₂×C₁₃₉	semidirect
461. #2330	C₂×C₁₃₉	semidirect
463. C₄×#125	C₂×C₁₃₉	semidirect
464. C₄×#125	C₂×C₁₃₉	semidirect
574. #117	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2590×C₁₃₉	2
#2589×C₁₃₉	2
#2585×C₁₃₉	2
#2574×C₁₃₉	2
#2571×C₁₃₉	2
#2570×C₁₃₉	2
#2552×C₁₃₉	2
#2550×C₁₃₉	2
#2522×C₁₃₉	2
#2520×C₁₃₉	2
#2511×C₁₃₉	2
#2497×C₁₃₉	2
#2442×C₁₃₉	2
#2441×C₁₃₉	2
#2439×C₁₃₉	2
#2331×C₁₃₉	2
#2330×C₁₃₉	2
#2314×C₁₃₉	2
C₄×#125×C₁₃₉	2
#2298×C₁₃₉	2
#2274×C₁₃₉	2
#35641	139

Subgroups — C139×#35641 #48030237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35641 #48030237