Subgroups — C₁₃₉×#36013 #48030609

Order 35584.

1710 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2652×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2626×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2575×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2573×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2569×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2527×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2523×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2517×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2515×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2483×C₁₃₉	C₂	1	2	yes	maximal
13	#2401×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₂×#397×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2368×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2343×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2342×C₁₃₉	C₂	1	2	yes	maximal
19	#2273×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
27	#401×C₁₃₉	C₂²	1	2	yes	complemented
28	#400×C₁₃₉	C₂²	1	2	yes	complemented
29	#400×C₁₃₉	C₂²	1	2	yes	complemented
30	#400×C₁₃₉	C₂²	1	2	yes	complemented
31	#400×C₁₃₉	C₂²	1	2	yes	complemented
32	#400×C₁₃₉	C₂²	1	2	yes	complemented
33	#400×C₁₃₉	C₂²	1	2	yes	complemented
34	#399×C₁₃₉	C₂²	1	1	yes	characteristic
35	#399×C₁₃₉	C₂²	1	1	yes	characteristic
36	#398×C₁₃₉	C₂²	1	2	yes	complemented
37	#397×C₁₃₉	C₂²	1	1	yes	characteristic
38	#397×C₁₃₉	C₂²	1	2	yes	—
39	#397×C₁₃₉	C₂²	1	2	yes	—
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	1	yes	characteristic
45	#397×C₁₃₉	C₂²	1	1	yes	characteristic
46	#397×C₁₃₉	C₂²	1	1	yes	characteristic
47	#396×C₁₃₉	C₂²	1	2	yes	—
48	#396×C₁₃₉	C₂²	1	2	yes	—
49	#393×C₁₃₉	C₂²	1	1	yes	characteristic
50	#393×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	2	yes	complemented
52	#391×C₁₃₉	C₂²	1	2	yes	complemented
53	#389×C₁₃₉	C₂²	1	2	yes	complemented
54	#388×C₁₃₉	C₂²	1	2	yes	—
55	#388×C₁₃₉	C₂²	1	2	yes	—
56	#388×C₁₃₉	C₂²	1	2	yes	—
57	#388×C₁₃₉	C₂²	1	2	yes	—
58	#387×C₁₃₉	C₂²	1	2	yes	complemented
59	#387×C₁₃₉	C₂²	1	2	yes	complemented
60	#387×C₁₃₉	C₂²	1	2	yes	complemented
61	#387×C₁₃₉	C₂²	1	2	yes	complemented
62	#387×C₁₃₉	C₂²	1	2	yes	complemented
63	#387×C₁₃₉	C₂²	1	2	yes	complemented
64	#387×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	#385×C₁₃₉	C₂²	1	2	yes	—
72	#385×C₁₃₉	C₂²	1	2	yes	—
73	#385×C₁₃₉	C₂²	1	2	yes	—
74	#385×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	#383×C₁₃₉	C₂²	1	2	yes	complemented
79	#383×C₁₃₉	C₂²	1	2	yes	complemented
80	#382×C₁₃₉	C₂²	1	2	yes	complemented
81	#382×C₁₃₉	C₂²	1	2	yes	complemented
82	#381×C₁₃₉	C₂²	1	2	yes	—
83	#381×C₁₃₉	C₂²	1	2	yes	—
84	#381×C₁₃₉	C₂²	1	2	yes	—
85	#381×C₁₃₉	C₂²	1	2	yes	—
86	#381×C₁₃₉	C₂²	1	2	yes	—
87	#380×C₁₃₉	C₂²	1	2	yes	—
88	#380×C₁₃₉	C₂²	1	1	yes	characteristic
89	#379×C₁₃₉	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
91	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
92	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	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	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	#376×C₁₃₉	C₂²	1	2	yes	complemented
105	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
116	#117×C₁₃₉	—	2	8	no	—
117	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
135	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	1	yes	characteristic
169	#95×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	1	yes	characteristic
189	#95×C₁₃₉	C₂³	1	1	yes	characteristic
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	C₂⁴×C₁₃₉	—	2	2	no	—
202	C₂⁴×C₁₃₉	—	2	2	no	—
203	C₂⁴×C₁₃₉	—	4	2	no	—
204	C₂⁴×C₁₃₉	—	4	2	no	—
205	C₂⁴×C₁₃₉	#41	1	4	yes	—
206	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
208	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂×Q₈×C₁₃₉	—	2	2	no	—
210	C₂×Q₈×C₁₃₉	—	4	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	2	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	2	no	—
219	C₂²×C₄×C₁₃₉	—	4	2	no	—
220	C₂²×C₄×C₁₃₉	—	4	2	no	—
221	C₂²×C₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	—	4	2	no	—
223	C₂²×C₄×C₁₃₉	—	4	2	no	—
224	C₂²×C₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	2	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	4	2	no	—
251	C₄⋊C₄×C₁₃₉	—	4	2	no	—
252	C₄⋊C₄×C₁₃₉	—	4	2	no	—
253	C₄⋊C₄×C₁₃₉	—	4	2	no	—
254	C₄⋊C₄×C₁₃₉	—	4	2	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	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	2	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
278	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	4	no	—
281	C₄²×C₁₃₉	—	4	2	no	—
282	C₄²×C₁₃₉	—	4	2	no	—
283	C₄²×C₁₃₉	—	4	2	no	—
284	C₄²×C₁₃₉	—	4	2	no	—
285	C₄²×C₁₃₉	—	4	2	no	—
286	C₄²×C₁₃₉	—	4	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	1	no	—
291	C₂³×C₁₃₉	—	2	1	no	—
292	C₂³×C₁₃₉	—	2	1	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	8	no	—
298	C₂³×C₁₃₉	—	4	8	no	—
299	C₂³×C₁₃₉	—	8	2	no	—
300	C₂³×C₁₃₉	—	8	2	no	—
301	C₂³×C₁₃₉	—	8	4	no	—
302	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
303	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
304	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
305	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
306	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
307	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
308	Q₈×C₁₃₉	—	8	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	1	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	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	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	2	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	—	4	4	no	—
351	C₂×C₄×C₁₃₉	—	4	8	no	—
352	C₂×C₄×C₁₃₉	—	8	4	no	—
353	C₂×C₄×C₁₃₉	—	8	4	no	—
354	C₂×C₄×C₁₃₉	—	8	4	no	—
355	C₂×C₄×C₁₃₉	—	8	2	no	—
356	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
357	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
358	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
359	C₂²×C₁₃₉	—	2	2	no	—
360	C₂²×C₁₃₉	—	2	4	no	—
361	C₂²×C₁₃₉	—	2	2	no	—
362	C₂²×C₁₃₉	—	2	4	no	—
363	C₂²×C₁₃₉	—	2	2	no	—
364	C₂²×C₁₃₉	—	2	2	no	—
365	C₂²×C₁₃₉	—	2	4	no	—
366	C₂²×C₁₃₉	—	2	4	no	—
367	C₂²×C₁₃₉	—	4	1	no	—
368	C₂²×C₁₃₉	—	4	1	no	—
369	C₂²×C₁₃₉	—	4	1	no	—
370	C₂²×C₁₃₉	—	4	1	no	—
371	C₂²×C₁₃₉	—	4	2	no	—
372	C₂²×C₁₃₉	—	4	2	no	—
373	C₂²×C₁₃₉	—	8	8	no	—
374	C₂²×C₁₃₉	#529	1	4	yes	—
375	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
377	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
378	C₂²×C₁₃₉	#585	1	2	yes	—
379	C₂²×C₁₃₉	#585	1	2	yes	—
380	C₄×C₁₃₉	—	2	2	no	—
381	C₄×C₁₃₉	—	2	2	no	—
382	C₄×C₁₃₉	—	2	4	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₄×C₁₃₉	—	4	2	no	—
385	C₄×C₁₃₉	—	4	2	no	—
386	C₄×C₁₃₉	—	4	2	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	—	4	2	no	—
389	C₄×C₁₃₉	—	4	2	no	—
390	C₄×C₁₃₉	—	4	2	no	—
391	C₄×C₁₃₉	—	4	1	no	—
392	C₄×C₁₃₉	—	4	1	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	—	4	2	no	—
395	C₄×C₁₃₉	—	4	2	no	—
396	C₂×C₁₃₉	—	2	4	no	—
397	C₂×C₁₃₉	—	4	2	no	—
398	C₂×C₁₃₉	—	4	2	no	—
399	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
400	C₂×C₁₃₉	#3491	1	1	yes	characteristic
401	C₂×C₁₃₉	#3491	1	2	yes	—
402	C₂×C₁₃₉	#3510	1	1	yes	characteristic
403	C₂×C₁₃₉	#3521	1	2	yes	—
404	#36013	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₁₃₉	#36013	1	1	yes	characteristic, direct product factor, Sylow
406	#2652	C₂×C₁₃₉	1	2	yes	complemented
407	#2626	C₂×C₁₃₉	1	1	yes	characteristic
408	#2575	C₂×C₁₃₉	1	2	yes	complemented
409	#2573	C₂×C₁₃₉	1	2	yes	complemented
410	#2569	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	#2527	C₂×C₁₃₉	1	2	yes	complemented
412	#2523	C₂×C₁₃₉	1	2	yes	complemented
413	#2517	C₂×C₁₃₉	1	2	yes	complemented
414	#2515	C₂×C₁₃₉	1	2	yes	complemented
415	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	#2493	C₂×C₁₃₉	1	2	yes	complemented
417	#2483	C₂×C₁₃₉	1	2	yes	—
418	#2401	C₂×C₁₃₉	1	2	yes	complemented
419	C₂×#397	C₂×C₁₃₉	1	1	yes	characteristic
420	#2368	C₂×C₁₃₉	1	1	yes	characteristic, complemented
421	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
422	#2343	C₂×C₁₃₉	1	2	yes	complemented
423	#2342	C₂×C₁₃₉	1	2	yes	—
424	#2273	C₂×C₁₃₉	1	1	yes	characteristic
425	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
427	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
430	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
432	#401	C₂²×C₁₃₉	1	2	yes	complemented
433	#400	C₂²×C₁₃₉	1	2	yes	complemented
434	#400	C₂²×C₁₃₉	1	2	yes	complemented
435	#400	C₂²×C₁₃₉	1	2	yes	complemented
436	#400	C₂²×C₁₃₉	1	2	yes	complemented
437	#400	C₂²×C₁₃₉	1	2	yes	complemented
438	#400	C₂²×C₁₃₉	1	2	yes	complemented
439	#399	C₂²×C₁₃₉	1	1	yes	characteristic
440	#399	C₂²×C₁₃₉	1	1	yes	characteristic
441	#398	C₂²×C₁₃₉	1	2	yes	complemented
442	#397	C₂²×C₁₃₉	1	1	yes	characteristic
443	#397	C₂²×C₁₃₉	1	2	yes	—
444	#397	C₂²×C₁₃₉	1	1	yes	characteristic
445	#397	C₂²×C₁₃₉	1	1	yes	characteristic
446	#397	C₂²×C₁₃₉	1	1	yes	characteristic
447	#397	C₂²×C₁₃₉	1	2	yes	—
448	#397	C₂²×C₁₃₉	1	2	yes	—
449	#397	C₂²×C₁₃₉	1	2	yes	—
450	#397	C₂²×C₁₃₉	1	2	yes	—
451	#397	C₂²×C₁₃₉	1	2	yes	—
452	#396	C₂²×C₁₃₉	1	2	yes	—
453	#396	C₂²×C₁₃₉	1	2	yes	—
454	#393	C₂²×C₁₃₉	1	1	yes	characteristic
455	#393	C₂²×C₁₃₉	1	1	yes	characteristic
456	#391	C₂²×C₁₃₉	1	2	yes	complemented
457	#391	C₂²×C₁₃₉	1	2	yes	complemented
458	#389	C₂²×C₁₃₉	1	2	yes	complemented
459	#388	C₂²×C₁₃₉	1	2	yes	—
460	#388	C₂²×C₁₃₉	1	2	yes	—
461	#388	C₂²×C₁₃₉	1	2	yes	—
462	#388	C₂²×C₁₃₉	1	2	yes	—
463	#387	C₂²×C₁₃₉	1	2	yes	complemented
464	#387	C₂²×C₁₃₉	1	2	yes	complemented
465	#387	C₂²×C₁₃₉	1	2	yes	complemented
466	#387	C₂²×C₁₃₉	1	2	yes	complemented
467	#387	C₂²×C₁₃₉	1	2	yes	complemented
468	#387	C₂²×C₁₃₉	1	2	yes	complemented
469	#387	C₂²×C₁₃₉	1	2	yes	complemented
470	#387	C₂²×C₁₃₉	1	2	yes	complemented
471	#387	C₂²×C₁₃₉	1	2	yes	complemented
472	#387	C₂²×C₁₃₉	1	2	yes	complemented
473	#387	C₂²×C₁₃₉	1	2	yes	complemented
474	#387	C₂²×C₁₃₉	1	2	yes	complemented
475	#387	C₂²×C₁₃₉	1	2	yes	complemented
476	#385	C₂²×C₁₃₉	1	2	yes	—
477	#385	C₂²×C₁₃₉	1	2	yes	—
478	#385	C₂²×C₁₃₉	1	2	yes	—
479	#385	C₂²×C₁₃₉	1	2	yes	—
480	#385	C₂²×C₁₃₉	1	2	yes	—
481	#385	C₂²×C₁₃₉	1	2	yes	—
482	#385	C₂²×C₁₃₉	1	2	yes	—
483	#383	C₂²×C₁₃₉	1	2	yes	complemented
484	#383	C₂²×C₁₃₉	1	2	yes	complemented
485	#382	C₂²×C₁₃₉	1	2	yes	complemented
486	#382	C₂²×C₁₃₉	1	2	yes	complemented
487	#381	C₂²×C₁₃₉	1	2	yes	—
488	#381	C₂²×C₁₃₉	1	2	yes	—
489	#381	C₂²×C₁₃₉	1	2	yes	—
490	#381	C₂²×C₁₃₉	1	2	yes	—
491	#381	C₂²×C₁₃₉	1	2	yes	—
492	#380	C₂²×C₁₃₉	1	2	yes	—
493	#380	C₂²×C₁₃₉	1	1	yes	characteristic
494	#379	C₂²×C₁₃₉	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
496	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
497	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
498	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
499	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
506	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
508	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
509	#376	C₂²×C₁₃₉	1	2	yes	complemented
510	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
511	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
512	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂²⋊Q₈	—	2	4	no	—
521	#117	—	2	8	no	—
522	C₂×C₄⋊C₄	—	2	4	no	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	—	2	8	no	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	1	yes	characteristic
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	1	yes	characteristic
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	2	yes	—
579	#95	C₂³×C₁₃₉	1	2	yes	—
580	#95	C₂³×C₁₃₉	1	2	yes	—
581	#95	C₂³×C₁₃₉	1	2	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	#95	C₂³×C₁₃₉	1	1	yes	characteristic
596	#95	C₂³×C₁₃₉	1	1	yes	characteristic
597	#95	C₂³×C₁₃₉	1	2	yes	—
598	#95	C₂³×C₁₃₉	1	2	yes	—
599	#95	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	2	yes	—
601	#95	C₂³×C₁₃₉	1	2	yes	—
602	#95	C₂³×C₁₃₉	1	2	yes	—
603	#95	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	C₂⁴	—	2	2	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	4	2	no	—
609	C₂⁴	—	4	2	no	—
610	C₂⁴	#41×C₁₃₉	1	4	yes	—
611	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
612	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
613	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
614	C₂×Q₈	—	2	2	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	4	2	no	—
688	C₄²	—	4	2	no	—
689	C₄²	—	4	2	no	—
690	C₄²	—	4	2	no	—
691	C₄²	—	4	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	8	no	—
703	C₂³	—	4	8	no	—
704	C₂³	—	8	2	no	—
705	C₂³	—	8	2	no	—
706	C₂³	—	8	4	no	—
707	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
708	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
709	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
710	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
711	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
712	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
713	Q₈	—	8	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	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	2	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	4	no	—
760	C₂×C₄	—	8	2	no	—
761	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
762	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
763	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	8	8	no	—
779	C₂²	#529×C₁₃₉	1	4	yes	—
780	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
781	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
782	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
783	C₂²	#585×C₁₃₉	1	2	yes	—
784	C₂²	#585×C₁₃₉	1	2	yes	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	4	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₂	—	2	4	no	—
802	C₂	—	4	2	no	—
803	C₂	—	4	2	no	—
804	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
805	C₂	#3491×C₁₃₉	1	1	yes	characteristic
806	C₂	#3491×C₁₃₉	1	2	yes	—
807	C₂	#3510×C₁₃₉	1	1	yes	characteristic
808	C₂	#3521×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂³
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. #2652×C₁₃₉	C₂	semidirect
3. #2575×C₁₃₉	C₂	semidirect
4. #2573×C₁₃₉	C₂	semidirect
5. #2569×C₁₃₉	C₂	semidirect
6. #2527×C₁₃₉	C₂	semidirect
7. #2523×C₁₃₉	C₂	semidirect
8. #2517×C₁₃₉	C₂	semidirect
9. #2515×C₁₃₉	C₂	semidirect
10. #2503×C₁₃₉	C₂	semidirect
11. #2493×C₁₃₉	C₂	semidirect
13. #2401×C₁₃₉	C₂	semidirect
15. #2368×C₁₃₉	C₂	semidirect
16. #2344×C₁₃₉	C₂	semidirect
17. #2343×C₁₃₉	C₂	semidirect
27. #401×C₁₃₉	C₂²	semidirect
28. #400×C₁₃₉	C₂²	semidirect
29. #400×C₁₃₉	C₂²	semidirect
30. #400×C₁₃₉	C₂²	semidirect
31. #400×C₁₃₉	C₂²	semidirect
32. #400×C₁₃₉	C₂²	semidirect
33. #400×C₁₃₉	C₂²	semidirect
36. #398×C₁₃₉	C₂²	semidirect
51. #391×C₁₃₉	C₂²	semidirect
52. #391×C₁₃₉	C₂²	semidirect
53. #389×C₁₃₉	C₂²	semidirect
58. #387×C₁₃₉	C₂²	semidirect
59. #387×C₁₃₉	C₂²	semidirect
60. #387×C₁₃₉	C₂²	semidirect
61. #387×C₁₃₉	C₂²	semidirect
62. #387×C₁₃₉	C₂²	semidirect
63. #387×C₁₃₉	C₂²	semidirect
64. #387×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
78. #383×C₁₃₉	C₂²	semidirect
79. #383×C₁₃₉	C₂²	semidirect
80. #382×C₁₃₉	C₂²	semidirect
81. #382×C₁₃₉	C₂²	semidirect
90. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
91. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
92. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
104. #376×C₁₃₉	C₂²	semidirect
404. #36013	C₁₃₉	direct (N × H)
405. C₁₃₉	#36013	direct (N × H)
406. #2652	C₂×C₁₃₉	semidirect
408. #2575	C₂×C₁₃₉	semidirect
409. #2573	C₂×C₁₃₉	semidirect
410. #2569	C₂×C₁₃₉	semidirect
411. #2527	C₂×C₁₃₉	semidirect
412. #2523	C₂×C₁₃₉	semidirect
413. #2517	C₂×C₁₃₉	semidirect
414. #2515	C₂×C₁₃₉	semidirect
415. #2503	C₂×C₁₃₉	semidirect
416. #2493	C₂×C₁₃₉	semidirect
418. #2401	C₂×C₁₃₉	semidirect
420. #2368	C₂×C₁₃₉	semidirect
421. #2344	C₂×C₁₃₉	semidirect
422. #2343	C₂×C₁₃₉	semidirect
432. #401	C₂²×C₁₃₉	semidirect
433. #400	C₂²×C₁₃₉	semidirect
434. #400	C₂²×C₁₃₉	semidirect
435. #400	C₂²×C₁₃₉	semidirect
436. #400	C₂²×C₁₃₉	semidirect
437. #400	C₂²×C₁₃₉	semidirect
438. #400	C₂²×C₁₃₉	semidirect
441. #398	C₂²×C₁₃₉	semidirect
456. #391	C₂²×C₁₃₉	semidirect
457. #391	C₂²×C₁₃₉	semidirect
458. #389	C₂²×C₁₃₉	semidirect
463. #387	C₂²×C₁₃₉	semidirect
464. #387	C₂²×C₁₃₉	semidirect
465. #387	C₂²×C₁₃₉	semidirect
466. #387	C₂²×C₁₃₉	semidirect
467. #387	C₂²×C₁₃₉	semidirect
468. #387	C₂²×C₁₃₉	semidirect
469. #387	C₂²×C₁₃₉	semidirect
470. #387	C₂²×C₁₃₉	semidirect
471. #387	C₂²×C₁₃₉	semidirect
472. #387	C₂²×C₁₃₉	semidirect
473. #387	C₂²×C₁₃₉	semidirect
474. #387	C₂²×C₁₃₉	semidirect
475. #387	C₂²×C₁₃₉	semidirect
483. #383	C₂²×C₁₃₉	semidirect
484. #383	C₂²×C₁₃₉	semidirect
485. #382	C₂²×C₁₃₉	semidirect
486. #382	C₂²×C₁₃₉	semidirect
495. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
496. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
497. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
509. #376	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2652×C₁₃₉	2
#2626×C₁₃₉	2
#2575×C₁₃₉	2
#2573×C₁₃₉	2
#2569×C₁₃₉	2
#2527×C₁₃₉	2
#2523×C₁₃₉	2
#2517×C₁₃₉	2
#2515×C₁₃₉	2
#2503×C₁₃₉	2
#2493×C₁₃₉	2
#2483×C₁₃₉	2
#2401×C₁₃₉	2
C₂×#397×C₁₃₉	2
#2368×C₁₃₉	2
#2344×C₁₃₉	2
#2343×C₁₃₉	2
#2342×C₁₃₉	2
#2273×C₁₃₉	2
#36013	139

Subgroups — C139×#36013 #48030609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36013 #48030609