Subgroups — C₁₃₁×#36621 #45722505

Order 33536.

3202 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2854×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2853×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2852×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	#2851×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2850×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2849×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2848×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#2847×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	C₄×#123×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	C₄×#121×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	C₄×#120×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	#2290×C₁₃₁	C₂	1	4	yes	maximal, complemented
17	#2283×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
21	#529×C₁₃₁	—	2	8	no	—
22	C₂×#126×C₁₃₁	C₂²	1	2	yes	complemented
23	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×#117×C₁₃₁	C₂²	1	2	yes	complemented
37	C₂²×C₄²×C₁₃₁	—	2	8	no	—
38	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
39	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
46	#391×C₁₃₁	C₂²	1	2	yes	complemented
47	#390×C₁₃₁	C₂²	1	2	yes	complemented
48	#389×C₁₃₁	C₂²	1	2	yes	complemented
49	#389×C₁₃₁	C₂²	1	2	yes	complemented
50	#388×C₁₃₁	C₂²	1	4	yes	complemented
51	#388×C₁₃₁	C₂²	1	4	yes	complemented
52	#388×C₁₃₁	C₂²	1	4	yes	complemented
53	#388×C₁₃₁	C₂²	1	4	yes	complemented
54	#387×C₁₃₁	C₂²	1	4	yes	complemented
55	#387×C₁₃₁	C₂²	1	4	yes	complemented
56	#387×C₁₃₁	C₂²	1	4	yes	complemented
57	#387×C₁₃₁	C₂²	1	4	yes	complemented
58	#386×C₁₃₁	C₂²	1	4	yes	—
59	#386×C₁₃₁	C₂²	1	4	yes	—
60	#386×C₁₃₁	C₂²	1	4	yes	—
61	#386×C₁₃₁	C₂²	1	2	yes	—
62	#386×C₁₃₁	C₂²	1	4	yes	—
63	#386×C₁₃₁	C₂²	1	2	yes	—
64	#385×C₁₃₁	C₂²	1	4	yes	—
65	#385×C₁₃₁	C₂²	1	4	yes	—
66	#385×C₁₃₁	C₂²	1	4	yes	—
67	#385×C₁₃₁	C₂²	1	2	yes	—
68	#385×C₁₃₁	C₂²	1	2	yes	—
69	#385×C₁₃₁	C₂²	1	4	yes	—
70	#383×C₁₃₁	C₂²	1	2	yes	complemented
71	#382×C₁₃₁	C₂²	1	2	yes	complemented
72	#381×C₁₃₁	C₂²	1	2	yes	—
73	#381×C₁₃₁	C₂²	1	2	yes	—
74	#380×C₁₃₁	C₂²	1	1	yes	characteristic
75	#380×C₁₃₁	C₂²	1	1	yes	characteristic
76	#380×C₁₃₁	C₂²	1	2	yes	—
77	#380×C₁₃₁	C₂²	1	2	yes	—
78	#379×C₁₃₁	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
84	#376×C₁₃₁	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃₁	—	2	4	no	—
91	C₂³×C₄×C₁₃₁	—	2	4	no	—
92	C₂³×C₄×C₁₃₁	—	2	4	no	—
93	C₂³×C₄×C₁₃₁	—	2	4	no	—
94	C₂³×C₄×C₁₃₁	—	2	8	no	—
95	C₂³×C₄×C₁₃₁	—	2	8	no	—
96	C₂³×C₄×C₁₃₁	—	2	4	no	—
97	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
110	#126×C₁₃₁	—	2	8	no	—
111	#125×C₁₃₁	—	2	4	no	—
112	#124×C₁₃₁	—	2	4	no	—
113	#123×C₁₃₁	—	2	8	no	—
114	#123×C₁₃₁	—	2	8	no	—
115	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
116	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
117	#121×C₁₃₁	—	2	4	no	—
118	#121×C₁₃₁	—	2	8	no	—
119	#120×C₁₃₁	—	2	8	no	—
120	C₄×Q₈×C₁₃₁	—	2	4	no	—
121	C₄×D₄×C₁₃₁	—	2	8	no	—
122	C₄×D₄×C₁₃₁	—	2	16	no	—
123	C₄×D₄×C₁₃₁	—	2	4	no	—
124	#117×C₁₃₁	—	2	8	no	—
125	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₁	—	2	4	no	—
150	C₂×C₄²×C₁₃₁	—	2	4	no	—
151	C₂×C₄²×C₁₃₁	—	2	4	no	—
152	C₂×C₄²×C₁₃₁	—	2	8	no	—
153	C₂×C₄²×C₁₃₁	—	2	8	no	—
154	C₂×C₄²×C₁₃₁	—	2	8	no	—
155	C₂×C₄²×C₁₃₁	—	2	8	no	—
156	C₂×C₄²×C₁₃₁	D₄	1	8	yes	complemented
157	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
165	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
169	#95×C₁₃₁	C₂³	1	2	yes	—
170	#95×C₁₃₁	C₂³	1	4	yes	—
171	#95×C₁₃₁	C₂³	1	4	yes	—
172	#95×C₁₃₁	C₂³	1	4	yes	—
173	#95×C₁₃₁	C₂³	1	4	yes	—
174	#95×C₁₃₁	C₂³	1	4	yes	—
175	#95×C₁₃₁	C₂³	1	4	yes	—
176	#95×C₁₃₁	C₂³	1	4	yes	—
177	#95×C₁₃₁	C₂³	1	4	yes	—
178	#95×C₁₃₁	C₂³	1	2	yes	—
179	#95×C₁₃₁	C₂³	1	4	yes	—
180	C₂⁴×C₁₃₁	—	2	2	no	—
181	C₂⁴×C₁₃₁	—	2	4	no	—
182	C₂⁴×C₁₃₁	—	2	4	no	—
183	C₂⁴×C₁₃₁	—	2	2	no	—
184	C₂⁴×C₁₃₁	#41	1	4	yes	—
185	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
186	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
187	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
188	C₂×Q₈×C₁₃₁	—	2	2	no	—
189	C₂×Q₈×C₁₃₁	—	2	4	no	—
190	C₂×D₄×C₁₃₁	—	2	4	no	—
191	C₂×D₄×C₁₃₁	—	2	8	no	—
192	C₂×D₄×C₁₃₁	—	2	4	no	—
193	C₂×D₄×C₁₃₁	—	2	8	no	—
194	C₂×D₄×C₁₃₁	—	2	8	no	—
195	C₂×D₄×C₁₃₁	—	2	4	no	—
196	C₂×D₄×C₁₃₁	—	2	2	no	—
197	C₂×D₄×C₁₃₁	—	2	4	no	—
198	C₂²×C₄×C₁₃₁	—	2	32	no	—
199	C₂²×C₄×C₁₃₁	—	2	32	no	—
200	C₂²×C₄×C₁₃₁	—	2	32	no	—
201	C₂²×C₄×C₁₃₁	—	2	2	no	—
202	C₂²×C₄×C₁₃₁	—	2	2	no	—
203	C₂²×C₄×C₁₃₁	—	2	2	no	—
204	C₂²×C₄×C₁₃₁	—	2	4	no	—
205	C₂²×C₄×C₁₃₁	—	2	4	no	—
206	C₂²×C₄×C₁₃₁	—	2	4	no	—
207	C₂²×C₄×C₁₃₁	—	2	4	no	—
208	C₂²×C₄×C₁₃₁	—	2	2	no	—
209	C₂²×C₄×C₁₃₁	—	2	2	no	—
210	C₂²×C₄×C₁₃₁	—	2	2	no	—
211	C₂²×C₄×C₁₃₁	—	2	4	no	—
212	C₂²×C₄×C₁₃₁	—	2	4	no	—
213	C₂²×C₄×C₁₃₁	—	2	4	no	—
214	C₂²×C₄×C₁₃₁	—	2	4	no	—
215	C₂²×C₄×C₁₃₁	—	2	4	no	—
216	C₂²×C₄×C₁₃₁	—	2	4	no	—
217	C₂²×C₄×C₁₃₁	—	2	4	no	—
218	C₂²×C₄×C₁₃₁	—	2	4	no	—
219	C₂²×C₄×C₁₃₁	—	2	4	no	—
220	C₂²×C₄×C₁₃₁	—	2	4	no	—
221	C₂²×C₄×C₁₃₁	—	2	4	no	—
222	C₂²×C₄×C₁₃₁	—	2	4	no	—
223	C₂²×C₄×C₁₃₁	—	2	4	no	—
224	C₂²×C₄×C₁₃₁	—	2	4	no	—
225	C₂²×C₄×C₁₃₁	—	2	4	no	—
226	C₂²×C₄×C₁₃₁	—	2	4	no	—
227	C₂²×C₄×C₁₃₁	—	2	4	no	—
228	C₂²×C₄×C₁₃₁	—	2	8	no	—
229	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₁₃₁	#41	1	8	yes	—
233	C₂²×C₄×C₁₃₁	#41	1	8	yes	—
234	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
235	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₁₃₁	—	2	4	no	—
250	C₄⋊C₄×C₁₃₁	—	2	4	no	—
251	C₄⋊C₄×C₁₃₁	—	2	2	no	—
252	C₄⋊C₄×C₁₃₁	—	2	4	no	—
253	C₄⋊C₄×C₁₃₁	—	2	2	no	—
254	C₄⋊C₄×C₁₃₁	—	2	4	no	—
255	C₄⋊C₄×C₁₃₁	—	2	8	no	—
256	C₄⋊C₄×C₁₃₁	—	2	4	no	—
257	C₄⋊C₄×C₁₃₁	—	2	4	no	—
258	C₄⋊C₄×C₁₃₁	—	2	8	no	—
259	C₄⋊C₄×C₁₃₁	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
262	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
264	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
265	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
271	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
272	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
273	C₄²×C₁₃₁	—	2	4	no	—
274	C₄²×C₁₃₁	—	2	4	no	—
275	C₄²×C₁₃₁	—	2	4	no	—
276	C₄²×C₁₃₁	—	2	4	no	—
277	C₄²×C₁₃₁	—	2	4	no	—
278	C₄²×C₁₃₁	—	2	4	no	—
279	C₄²×C₁₃₁	—	2	4	no	—
280	C₄²×C₁₃₁	—	2	8	no	—
281	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
282	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
283	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
284	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
285	C₂³×C₁₃₁	—	2	8	no	—
286	C₂³×C₁₃₁	—	2	8	no	—
287	C₂³×C₁₃₁	—	2	16	no	—
288	C₂³×C₁₃₁	—	2	8	no	—
289	C₂³×C₁₃₁	—	2	16	no	—
290	C₂³×C₁₃₁	—	2	2	no	—
291	C₂³×C₁₃₁	—	2	2	no	—
292	C₂³×C₁₃₁	—	2	2	no	—
293	C₂³×C₁₃₁	—	2	2	no	—
294	C₂³×C₁₃₁	—	2	2	no	—
295	C₂³×C₁₃₁	—	2	2	no	—
296	C₂³×C₁₃₁	—	2	2	no	—
297	C₂³×C₁₃₁	—	2	2	no	—
298	C₂³×C₁₃₁	—	2	4	no	—
299	C₂³×C₁₃₁	—	2	4	no	—
300	C₂³×C₁₃₁	—	2	2	no	—
301	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
302	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
303	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
304	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
305	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
306	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
307	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
308	Q₈×C₁₃₁	—	4	4	no	—
309	D₄×C₁₃₁	—	4	8	no	—
310	D₄×C₁₃₁	—	4	16	no	—
311	D₄×C₁₃₁	—	4	4	no	—
312	C₂×C₄×C₁₃₁	—	2	16	no	—
313	C₂×C₄×C₁₃₁	—	2	16	no	—
314	C₂×C₄×C₁₃₁	—	2	16	no	—
315	C₂×C₄×C₁₃₁	—	2	16	no	—
316	C₂×C₄×C₁₃₁	—	2	8	no	—
317	C₂×C₄×C₁₃₁	—	2	8	no	—
318	C₂×C₄×C₁₃₁	—	2	8	no	—
319	C₂×C₄×C₁₃₁	—	2	8	no	—
320	C₂×C₄×C₁₃₁	—	2	2	no	—
321	C₂×C₄×C₁₃₁	—	2	2	no	—
322	C₂×C₄×C₁₃₁	—	2	2	no	—
323	C₂×C₄×C₁₃₁	—	2	1	no	—
324	C₂×C₄×C₁₃₁	—	2	1	no	—
325	C₂×C₄×C₁₃₁	—	2	2	no	—
326	C₂×C₄×C₁₃₁	—	2	2	no	—
327	C₂×C₄×C₁₃₁	—	2	1	no	—
328	C₂×C₄×C₁₃₁	—	2	1	no	—
329	C₂×C₄×C₁₃₁	—	2	2	no	—
330	C₂×C₄×C₁₃₁	—	2	2	no	—
331	C₂×C₄×C₁₃₁	—	2	2	no	—
332	C₂×C₄×C₁₃₁	—	2	8	no	—
333	C₂×C₄×C₁₃₁	—	2	8	no	—
334	C₂×C₄×C₁₃₁	—	2	16	no	—
335	C₂×C₄×C₁₃₁	—	2	16	no	—
336	C₂×C₄×C₁₃₁	—	2	2	no	—
337	C₂×C₄×C₁₃₁	—	2	2	no	—
338	C₂×C₄×C₁₃₁	—	2	2	no	—
339	C₂×C₄×C₁₃₁	—	2	4	no	—
340	C₂×C₄×C₁₃₁	—	2	4	no	—
341	C₂×C₄×C₁₃₁	—	2	4	no	—
342	C₂×C₄×C₁₃₁	—	2	2	no	—
343	C₂×C₄×C₁₃₁	—	2	4	no	—
344	C₂×C₄×C₁₃₁	—	2	4	no	—
345	C₂×C₄×C₁₃₁	—	2	4	no	—
346	C₂×C₄×C₁₃₁	—	2	4	no	—
347	C₂×C₄×C₁₃₁	—	2	4	no	—
348	C₂×C₄×C₁₃₁	—	2	2	no	—
349	C₂×C₄×C₁₃₁	—	4	8	no	—
350	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
357	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
358	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
359	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
360	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
361	C₂²×C₁₃₁	—	2	32	no	—
362	C₂²×C₁₃₁	—	2	2	no	—
363	C₂²×C₁₃₁	—	2	2	no	—
364	C₂²×C₁₃₁	—	2	4	no	—
365	C₂²×C₁₃₁	—	2	4	no	—
366	C₂²×C₁₃₁	—	2	4	no	—
367	C₂²×C₁₃₁	—	2	4	no	—
368	C₂²×C₁₃₁	—	2	4	no	—
369	C₂²×C₁₃₁	—	2	4	no	—
370	C₂²×C₁₃₁	—	2	4	no	—
371	C₂²×C₁₃₁	—	2	4	no	—
372	C₂²×C₁₃₁	—	4	2	no	—
373	C₂²×C₁₃₁	—	4	2	no	—
374	C₂²×C₁₃₁	—	4	2	no	—
375	C₂²×C₁₃₁	—	4	4	no	—
376	C₂²×C₁₃₁	—	4	4	no	—
377	C₂²×C₁₃₁	#525	1	4	yes	—
378	C₂²×C₁₃₁	#529	1	8	yes	complemented
379	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
380	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
381	C₂²×C₁₃₁	C₂²×#41	1	2	yes	—
382	C₂²×C₁₃₁	C₂²×#41	1	2	yes	—
383	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
384	C₄×C₁₃₁	—	2	2	no	—
385	C₄×C₁₃₁	—	2	2	no	—
386	C₄×C₁₃₁	—	2	2	no	—
387	C₄×C₁₃₁	—	2	2	no	—
388	C₄×C₁₃₁	—	2	4	no	—
389	C₄×C₁₃₁	—	2	4	no	—
390	C₄×C₁₃₁	—	2	4	no	—
391	C₄×C₁₃₁	—	4	2	no	—
392	C₄×C₁₃₁	—	4	2	no	—
393	C₄×C₁₃₁	—	4	2	no	—
394	C₄×C₁₃₁	—	4	4	no	—
395	C₄×C₁₃₁	—	4	4	no	—
396	C₄×C₁₃₁	#525	1	4	yes	—
397	C₄×C₁₃₁	#525	1	4	yes	—
398	C₂×C₁₃₁	—	2	4	no	—
399	C₂×C₁₃₁	—	2	8	no	—
400	C₂×C₁₃₁	—	8	2	no	—
401	C₂×C₁₃₁	C₂×#525	1	1	yes	characteristic
402	C₂×C₁₃₁	C₂×#525	1	1	yes	characteristic
403	C₂×C₁₃₁	C₂×#525	1	1	yes	characteristic
404	C₂×C₁₃₁	C₂×#529	1	2	yes	—
405	C₂×C₁₃₁	#3444	1	2	yes	—
406	#36621	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₁₃₁	#36621	1	1	yes	characteristic, direct product factor, Sylow
408	C₂×#529	C₂×C₁₃₁	1	1	yes	characteristic, complemented
409	C₂³×C₄²	C₂×C₁₃₁	1	1	yes	characteristic, complemented
410	#2855	C₂×C₁₃₁	1	1	yes	characteristic, complemented
411	#2854	C₂×C₁₃₁	1	1	yes	characteristic, complemented
412	#2853	C₂×C₁₃₁	1	2	yes	complemented
413	#2852	C₂×C₁₃₁	1	4	yes	complemented
414	#2851	C₂×C₁₃₁	1	2	yes	complemented
415	#2850	C₂×C₁₃₁	1	2	yes	complemented
416	#2849	C₂×C₁₃₁	1	2	yes	complemented
417	#2848	C₂×C₁₃₁	1	1	yes	characteristic, complemented
418	#2847	C₂×C₁₃₁	1	1	yes	characteristic
419	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	2	yes	complemented
420	C₄×#123	C₂×C₁₃₁	1	2	yes	complemented
421	C₄×#121	C₂×C₁₃₁	1	2	yes	complemented
422	C₄×#120	C₂×C₁₃₁	1	2	yes	complemented
423	#2290	C₂×C₁₃₁	1	4	yes	complemented
424	#2283	C₂×C₁₃₁	1	1	yes	characteristic, complemented
425	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
426	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
427	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
428	#529	—	2	8	no	—
429	C₂×#126	C₂²×C₁₃₁	1	2	yes	complemented
430	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
431	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
432	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
433	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
434	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
435	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
436	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
437	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
438	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
439	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
440	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
442	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
443	C₂×#117	C₂²×C₁₃₁	1	2	yes	complemented
444	C₂²×C₄²	—	2	8	no	—
445	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
446	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
447	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
448	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
449	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
450	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
451	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
452	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
453	#391	C₂²×C₁₃₁	1	2	yes	complemented
454	#390	C₂²×C₁₃₁	1	2	yes	complemented
455	#389	C₂²×C₁₃₁	1	2	yes	complemented
456	#389	C₂²×C₁₃₁	1	2	yes	complemented
457	#388	C₂²×C₁₃₁	1	4	yes	complemented
458	#388	C₂²×C₁₃₁	1	4	yes	complemented
459	#388	C₂²×C₁₃₁	1	4	yes	complemented
460	#388	C₂²×C₁₃₁	1	4	yes	complemented
461	#387	C₂²×C₁₃₁	1	4	yes	complemented
462	#387	C₂²×C₁₃₁	1	4	yes	complemented
463	#387	C₂²×C₁₃₁	1	4	yes	complemented
464	#387	C₂²×C₁₃₁	1	4	yes	complemented
465	#386	C₂²×C₁₃₁	1	4	yes	—
466	#386	C₂²×C₁₃₁	1	2	yes	—
467	#386	C₂²×C₁₃₁	1	4	yes	—
468	#386	C₂²×C₁₃₁	1	4	yes	—
469	#386	C₂²×C₁₃₁	1	4	yes	—
470	#386	C₂²×C₁₃₁	1	2	yes	—
471	#385	C₂²×C₁₃₁	1	4	yes	—
472	#385	C₂²×C₁₃₁	1	2	yes	—
473	#385	C₂²×C₁₃₁	1	4	yes	—
474	#385	C₂²×C₁₃₁	1	4	yes	—
475	#385	C₂²×C₁₃₁	1	4	yes	—
476	#385	C₂²×C₁₃₁	1	2	yes	—
477	#383	C₂²×C₁₃₁	1	2	yes	complemented
478	#382	C₂²×C₁₃₁	1	2	yes	complemented
479	#381	C₂²×C₁₃₁	1	2	yes	—
480	#381	C₂²×C₁₃₁	1	2	yes	—
481	#380	C₂²×C₁₃₁	1	2	yes	—
482	#380	C₂²×C₁₃₁	1	1	yes	characteristic
483	#380	C₂²×C₁₃₁	1	2	yes	—
484	#380	C₂²×C₁₃₁	1	1	yes	characteristic
485	#379	C₂²×C₁₃₁	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
487	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
488	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
491	#376	C₂²×C₁₃₁	1	2	yes	complemented
492	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
496	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	—	2	4	no	—
499	C₂³×C₄	—	2	4	no	—
500	C₂³×C₄	—	2	4	no	—
501	C₂³×C₄	—	2	8	no	—
502	C₂³×C₄	—	2	8	no	—
503	C₂³×C₄	—	2	4	no	—
504	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
508	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
509	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
510	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
511	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
515	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
516	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
517	#126	—	2	8	no	—
518	#125	—	2	4	no	—
519	#124	—	2	4	no	—
520	#123	—	2	8	no	—
521	#123	—	2	8	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	8	no	—
524	#121	—	2	4	no	—
525	#121	—	2	8	no	—
526	#120	—	2	8	no	—
527	C₄×Q₈	—	2	4	no	—
528	C₄×D₄	—	2	8	no	—
529	C₄×D₄	—	2	16	no	—
530	C₄×D₄	—	2	4	no	—
531	#117	—	2	8	no	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
556	C₂×C₄²	—	2	4	no	—
557	C₂×C₄²	—	2	4	no	—
558	C₂×C₄²	—	2	4	no	—
559	C₂×C₄²	—	2	8	no	—
560	C₂×C₄²	—	2	8	no	—
561	C₂×C₄²	—	2	8	no	—
562	C₂×C₄²	—	2	8	no	—
563	C₂×C₄²	D₄×C₁₃₁	1	8	yes	complemented
564	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
566	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
567	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
571	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
576	#95	C₂³×C₁₃₁	1	2	yes	—
577	#95	C₂³×C₁₃₁	1	2	yes	—
578	#95	C₂³×C₁₃₁	1	4	yes	—
579	#95	C₂³×C₁₃₁	1	4	yes	—
580	#95	C₂³×C₁₃₁	1	4	yes	—
581	#95	C₂³×C₁₃₁	1	4	yes	—
582	#95	C₂³×C₁₃₁	1	4	yes	—
583	#95	C₂³×C₁₃₁	1	4	yes	—
584	#95	C₂³×C₁₃₁	1	4	yes	—
585	#95	C₂³×C₁₃₁	1	4	yes	—
586	#95	C₂³×C₁₃₁	1	4	yes	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	4	no	—
589	C₂⁴	—	2	4	no	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	#41×C₁₃₁	1	4	yes	—
592	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
593	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
594	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	8	no	—
601	C₂×D₄	—	2	8	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂²×C₄	—	2	32	no	—
606	C₂²×C₄	—	2	32	no	—
607	C₂²×C₄	—	2	32	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
637	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
638	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
639	C₂²×C₄	#41×C₁₃₁	1	8	yes	—
640	C₂²×C₄	#41×C₁₃₁	1	8	yes	—
641	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
642	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
643	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
644	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	8	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	8	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	8	no	—
688	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
689	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
690	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
691	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
692	C₂³	—	2	8	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	16	no	—
695	C₂³	—	2	8	no	—
696	C₂³	—	2	16	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
709	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
710	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
711	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
712	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
713	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
714	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
715	Q₈	—	4	4	no	—
716	D₄	—	4	8	no	—
717	D₄	—	4	16	no	—
718	D₄	—	4	4	no	—
719	C₂×C₄	—	2	16	no	—
720	C₂×C₄	—	2	16	no	—
721	C₂×C₄	—	2	16	no	—
722	C₂×C₄	—	2	16	no	—
723	C₂×C₄	—	2	8	no	—
724	C₂×C₄	—	2	8	no	—
725	C₂×C₄	—	2	8	no	—
726	C₂×C₄	—	2	8	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	8	no	—
741	C₂×C₄	—	2	16	no	—
742	C₂×C₄	—	2	16	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
758	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
763	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
764	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
765	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
766	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
767	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
768	C₂²	—	2	32	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	4	no	—
784	C₂²	#525×C₁₃₁	1	4	yes	—
785	C₂²	#529×C₁₃₁	1	8	yes	complemented
786	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
787	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
788	C₂²	C₂²×#41×C₁₃₁	1	2	yes	—
789	C₂²	C₂²×#41×C₁₃₁	1	2	yes	—
790	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	4	no	—
796	C₄	—	2	4	no	—
797	C₄	—	2	4	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	4	no	—
802	C₄	—	4	4	no	—
803	C₄	#525×C₁₃₁	1	4	yes	—
804	C₄	#525×C₁₃₁	1	4	yes	—
805	C₂	—	2	4	no	—
806	C₂	—	2	8	no	—
807	C₂	—	8	2	no	—
808	C₂	C₂×#525×C₁₃₁	1	1	yes	characteristic
809	C₂	C₂×#525×C₁₃₁	1	1	yes	characteristic
810	C₂	C₂×#525×C₁₃₁	1	1	yes	characteristic
811	C₂	C₂×#529×C₁₃₁	1	2	yes	—
812	C₂	#3444×C₁₃₁	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
socle	C₂³×C₁₃₁	C₂⁵
prime radical	#2847×C₁₃₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#529×C₁₃₁	C₂	semidirect
2. C₂³×C₄²×C₁₃₁	C₂	semidirect
3. #2855×C₁₃₁	C₂	semidirect
4. #2854×C₁₃₁	C₂	semidirect
5. #2853×C₁₃₁	C₂	semidirect
6. #2852×C₁₃₁	C₂	semidirect
7. #2851×C₁₃₁	C₂	semidirect
8. #2850×C₁₃₁	C₂	semidirect
9. #2849×C₁₃₁	C₂	semidirect
10. #2848×C₁₃₁	C₂	semidirect
12. C₄×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
13. C₄×#123×C₁₃₁	C₂	semidirect
14. C₄×#121×C₁₃₁	C₂	semidirect
15. C₄×#120×C₁₃₁	C₂	semidirect
16. #2290×C₁₃₁	C₂	semidirect
17. #2283×C₁₃₁	C₂	semidirect
22. C₂×#126×C₁₃₁	C₂²	semidirect
23. C₂×#125×C₁₃₁	C₂²	semidirect
24. C₂×#124×C₁₃₁	C₂²	semidirect
32. C₂×C₄×Q₈×C₁₃₁	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
36. C₂×#117×C₁₃₁	C₂²	semidirect
46. #391×C₁₃₁	C₂²	semidirect
47. #390×C₁₃₁	C₂²	semidirect
48. #389×C₁₃₁	C₂²	semidirect
49. #389×C₁₃₁	C₂²	semidirect
50. #388×C₁₃₁	C₂²	semidirect
51. #388×C₁₃₁	C₂²	semidirect
52. #388×C₁₃₁	C₂²	semidirect
53. #388×C₁₃₁	C₂²	semidirect
54. #387×C₁₃₁	C₂²	semidirect
55. #387×C₁₃₁	C₂²	semidirect
56. #387×C₁₃₁	C₂²	semidirect
57. #387×C₁₃₁	C₂²	semidirect
70. #383×C₁₃₁	C₂²	semidirect
71. #382×C₁₃₁	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
84. #376×C₁₃₁	C₂²	semidirect
156. C₂×C₄²×C₁₃₁	D₄	semidirect
378. C₂²×C₁₃₁	#529	semidirect
406. #36621	C₁₃₁	direct (N × H)
407. C₁₃₁	#36621	direct (N × H)
408. C₂×#529	C₂×C₁₃₁	semidirect
409. C₂³×C₄²	C₂×C₁₃₁	semidirect
410. #2855	C₂×C₁₃₁	semidirect
411. #2854	C₂×C₁₃₁	semidirect
412. #2853	C₂×C₁₃₁	semidirect
413. #2852	C₂×C₁₃₁	semidirect
414. #2851	C₂×C₁₃₁	semidirect
415. #2850	C₂×C₁₃₁	semidirect
416. #2849	C₂×C₁₃₁	semidirect
417. #2848	C₂×C₁₃₁	semidirect
419. C₄×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
420. C₄×#123	C₂×C₁₃₁	semidirect
421. C₄×#121	C₂×C₁₃₁	semidirect
422. C₄×#120	C₂×C₁₃₁	semidirect
423. #2290	C₂×C₁₃₁	semidirect
424. #2283	C₂×C₁₃₁	semidirect
429. C₂×#126	C₂²×C₁₃₁	semidirect
430. C₂×#125	C₂²×C₁₃₁	semidirect
431. C₂×#124	C₂²×C₁₃₁	semidirect
439. C₂×C₄×Q₈	C₂²×C₁₃₁	semidirect
442. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
443. C₂×#117	C₂²×C₁₃₁	semidirect
453. #391	C₂²×C₁₃₁	semidirect
454. #390	C₂²×C₁₃₁	semidirect
455. #389	C₂²×C₁₃₁	semidirect
456. #389	C₂²×C₁₃₁	semidirect
457. #388	C₂²×C₁₃₁	semidirect
458. #388	C₂²×C₁₃₁	semidirect
459. #388	C₂²×C₁₃₁	semidirect
460. #388	C₂²×C₁₃₁	semidirect
461. #387	C₂²×C₁₃₁	semidirect
462. #387	C₂²×C₁₃₁	semidirect
463. #387	C₂²×C₁₃₁	semidirect
464. #387	C₂²×C₁₃₁	semidirect
477. #383	C₂²×C₁₃₁	semidirect
478. #382	C₂²×C₁₃₁	semidirect
486. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
487. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
490. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
491. #376	C₂²×C₁₃₁	semidirect
563. C₂×C₄²	D₄×C₁₃₁	semidirect
785. C₂²	#529×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₃₁	2
C₂³×C₄²×C₁₃₁	2
#2855×C₁₃₁	2
#2854×C₁₃₁	2
#2853×C₁₃₁	2
#2852×C₁₃₁	2
#2851×C₁₃₁	2
#2850×C₁₃₁	2
#2849×C₁₃₁	2
#2848×C₁₃₁	2
#2847×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
C₄×#123×C₁₃₁	2
C₄×#121×C₁₃₁	2
C₄×#120×C₁₃₁	2
#2290×C₁₃₁	2
#2283×C₁₃₁	2
#36621	131

Subgroups — C131×#36621 #45722505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#36621 #45722505