Subgroups — C₁₃₁×#36872 #45722756

Order 33536.

1966 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2849×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#2797×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2763×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2761×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2751×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2736×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2717×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2703×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2693×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#2678×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2670×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#2638×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#2631×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2573×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	#2557×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	#2461×C₁₃₁	C₂	1	2	yes	maximal, complemented
17	#2420×C₁₃₁	C₂	1	2	yes	maximal, complemented
18	#2335×C₁₃₁	C₂	1	2	yes	maximal, complemented
19	C₄×#120×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#120×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
32	#400×C₁₃₁	C₂²	1	2	yes	complemented
33	#400×C₁₃₁	C₂²	1	2	yes	complemented
34	#398×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
35	#397×C₁₃₁	C₂²	1	1	yes	characteristic
36	#397×C₁₃₁	C₂²	1	2	yes	—
37	#397×C₁₃₁	C₂²	1	2	yes	—
38	#397×C₁₃₁	C₂²	1	2	yes	complemented
39	#397×C₁₃₁	C₂²	1	2	yes	complemented
40	#397×C₁₃₁	C₂²	1	2	yes	complemented
41	#397×C₁₃₁	C₂²	1	2	yes	complemented
42	#397×C₁₃₁	C₂²	1	2	yes	complemented
43	#396×C₁₃₁	C₂²	1	2	yes	—
44	#396×C₁₃₁	C₂²	1	2	yes	complemented
45	#395×C₁₃₁	C₂²	1	2	yes	complemented
46	#395×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
47	#394×C₁₃₁	C₂²	1	2	yes	—
48	#394×C₁₃₁	C₂²	1	2	yes	—
49	#394×C₁₃₁	C₂²	1	2	yes	—
50	#394×C₁₃₁	C₂²	1	2	yes	complemented
51	#393×C₁₃₁	C₂²	1	2	yes	—
52	#393×C₁₃₁	C₂²	1	1	yes	characteristic
53	#393×C₁₃₁	C₂²	1	1	yes	characteristic
54	#393×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
55	#392×C₁₃₁	C₂²	1	2	yes	—
56	#392×C₁₃₁	C₂²	1	2	yes	—
57	#392×C₁₃₁	C₂²	1	1	yes	characteristic
58	#392×C₁₃₁	C₂²	1	2	yes	—
59	#392×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
60	#391×C₁₃₁	C₂²	1	2	yes	complemented
61	#390×C₁₃₁	C₂²	1	2	yes	—
62	#390×C₁₃₁	C₂²	1	2	yes	—
63	#390×C₁₃₁	C₂²	1	2	yes	—
64	#390×C₁₃₁	C₂²	1	2	yes	complemented
65	#389×C₁₃₁	C₂²	1	2	yes	complemented
66	#388×C₁₃₁	C₂²	1	2	yes	—
67	#388×C₁₃₁	C₂²	1	2	yes	—
68	#388×C₁₃₁	C₂²	1	2	yes	—
69	#388×C₁₃₁	C₂²	1	2	yes	—
70	#388×C₁₃₁	C₂²	1	2	yes	—
71	#388×C₁₃₁	C₂²	1	2	yes	complemented
72	#388×C₁₃₁	C₂²	1	2	yes	complemented
73	#388×C₁₃₁	C₂²	1	2	yes	complemented
74	#387×C₁₃₁	C₂²	1	2	yes	complemented
75	#387×C₁₃₁	C₂²	1	2	yes	complemented
76	#387×C₁₃₁	C₂²	1	2	yes	complemented
77	#387×C₁₃₁	C₂²	1	2	yes	complemented
78	#387×C₁₃₁	C₂²	1	2	yes	complemented
79	#386×C₁₃₁	C₂²	1	2	yes	—
80	#386×C₁₃₁	C₂²	1	2	yes	—
81	#386×C₁₃₁	C₂²	1	1	yes	characteristic
82	#386×C₁₃₁	C₂²	1	2	yes	—
83	#386×C₁₃₁	C₂²	1	2	yes	—
84	#386×C₁₃₁	C₂²	1	2	yes	—
85	#386×C₁₃₁	C₂²	1	2	yes	—
86	#386×C₁₃₁	C₂²	1	2	yes	complemented
87	#386×C₁₃₁	C₂²	1	2	yes	complemented
88	#385×C₁₃₁	C₂²	1	2	yes	—
89	#385×C₁₃₁	C₂²	1	2	yes	—
90	#385×C₁₃₁	C₂²	1	2	yes	—
91	#385×C₁₃₁	C₂²	1	1	yes	characteristic
92	#385×C₁₃₁	C₂²	1	2	yes	—
93	#385×C₁₃₁	C₂²	1	2	yes	—
94	#383×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
95	#382×C₁₃₁	C₂²	1	2	yes	complemented
96	#381×C₁₃₁	C₂²	1	2	yes	—
97	#381×C₁₃₁	C₂²	1	2	yes	—
98	#381×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
99	#380×C₁₃₁	C₂²	1	2	yes	complemented
100	#380×C₁₃₁	C₂²	1	2	yes	complemented
101	#379×C₁₃₁	C₂²	1	1	yes	characteristic
102	#379×C₁₃₁	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
107	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃₁	—	4	2	no	—
118	C₂³×C₄×C₁₃₁	—	4	4	no	—
119	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
125	#124×C₁₃₁	—	4	2	no	—
126	#124×C₁₃₁	—	4	4	no	—
127	#123×C₁₃₁	—	2	8	no	—
128	#123×C₁₃₁	—	4	4	no	—
129	#123×C₁₃₁	—	4	4	no	—
130	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
131	#121×C₁₃₁	—	4	4	no	—
132	#120×C₁₃₁	—	2	4	no	—
133	#120×C₁₃₁	—	4	4	no	—
134	C₄×D₄×C₁₃₁	—	4	2	no	—
135	C₄×D₄×C₁₃₁	—	4	4	no	—
136	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
183	#95×C₁₃₁	C₂³	1	2	yes	—
184	#95×C₁₃₁	C₂³	1	1	yes	characteristic
185	#95×C₁₃₁	C₂³	1	1	yes	characteristic
186	#95×C₁₃₁	C₂³	1	2	yes	—
187	#95×C₁₃₁	C₂³	1	2	yes	—
188	#95×C₁₃₁	C₂³	1	2	yes	—
189	#95×C₁₃₁	C₂³	1	2	yes	—
190	#95×C₁₃₁	C₂³	1	2	yes	—
191	#95×C₁₃₁	C₂³	1	2	yes	—
192	#95×C₁₃₁	C₂³	1	2	yes	—
193	#95×C₁₃₁	C₂³	1	2	yes	—
194	#95×C₁₃₁	C₂³	1	2	yes	—
195	#95×C₁₃₁	C₂³	1	2	yes	—
196	#95×C₁₃₁	C₂³	1	2	yes	—
197	#95×C₁₃₁	C₂³	1	2	yes	—
198	#95×C₁₃₁	C₂³	1	2	yes	—
199	#95×C₁₃₁	C₂³	1	2	yes	—
200	#95×C₁₃₁	C₂³	1	1	yes	characteristic
201	#95×C₁₃₁	C₂³	1	2	yes	—
202	#95×C₁₃₁	C₂³	1	2	yes	—
203	#95×C₁₃₁	C₂³	1	2	yes	—
204	#95×C₁₃₁	C₂³	1	1	yes	characteristic
205	#95×C₁₃₁	C₂³	1	2	yes	—
206	#95×C₁₃₁	C₂³	1	2	yes	—
207	C₂⁴×C₁₃₁	—	2	2	no	—
208	C₂⁴×C₁₃₁	—	2	4	no	—
209	C₂⁴×C₁₃₁	—	4	1	no	—
210	C₂⁴×C₁₃₁	—	4	2	no	—
211	C₂⁴×C₁₃₁	—	4	1	no	—
212	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
213	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₁₃₁	—	4	1	no	—
217	C₂×Q₈×C₁₃₁	—	4	1	no	—
218	C₂×Q₈×C₁₃₁	—	4	2	no	—
219	C₂×Q₈×C₁₃₁	—	4	2	no	—
220	C₂×D₄×C₁₃₁	—	2	2	no	—
221	C₂×D₄×C₁₃₁	—	2	4	no	—
222	C₂×D₄×C₁₃₁	—	2	4	no	—
223	C₂×D₄×C₁₃₁	—	2	4	no	—
224	C₂×D₄×C₁₃₁	—	2	4	no	—
225	C₂×D₄×C₁₃₁	—	2	4	no	—
226	C₂×D₄×C₁₃₁	—	4	1	no	—
227	C₂×D₄×C₁₃₁	—	4	2	no	—
228	C₂×D₄×C₁₃₁	—	4	1	no	—
229	C₂×D₄×C₁₃₁	—	4	2	no	—
230	C₂×D₄×C₁₃₁	—	4	2	no	—
231	C₂×D₄×C₁₃₁	—	4	2	no	—
232	C₂×D₄×C₁₃₁	—	4	2	no	—
233	C₂×D₄×C₁₃₁	—	4	1	no	—
234	C₂×D₄×C₁₃₁	—	4	2	no	—
235	C₂×D₄×C₁₃₁	—	4	2	no	—
236	C₂×D₄×C₁₃₁	—	4	2	no	—
237	C₂×D₄×C₁₃₁	—	4	2	no	—
238	C₂×D₄×C₁₃₁	—	4	2	no	—
239	C₂×D₄×C₁₃₁	—	4	2	no	—
240	C₂²×C₄×C₁₃₁	—	2	4	no	—
241	C₂²×C₄×C₁₃₁	—	2	4	no	—
242	C₂²×C₄×C₁₃₁	—	2	2	no	—
243	C₂²×C₄×C₁₃₁	—	2	4	no	—
244	C₂²×C₄×C₁₃₁	—	2	4	no	—
245	C₂²×C₄×C₁₃₁	—	2	2	no	—
246	C₂²×C₄×C₁₃₁	—	4	2	no	—
247	C₂²×C₄×C₁₃₁	—	4	2	no	—
248	C₂²×C₄×C₁₃₁	—	4	2	no	—
249	C₂²×C₄×C₁₃₁	—	4	2	no	—
250	C₂²×C₄×C₁₃₁	—	4	1	no	—
251	C₂²×C₄×C₁₃₁	—	4	2	no	—
252	C₂²×C₄×C₁₃₁	—	4	2	no	—
253	C₂²×C₄×C₁₃₁	—	4	2	no	—
254	C₂²×C₄×C₁₃₁	—	4	2	no	—
255	C₂²×C₄×C₁₃₁	—	4	16	no	—
256	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₁₃₁	—	2	4	no	—
272	C₄⋊C₄×C₁₃₁	—	2	4	no	—
273	C₄⋊C₄×C₁₃₁	—	2	4	no	—
274	C₄⋊C₄×C₁₃₁	—	4	2	no	—
275	C₄⋊C₄×C₁₃₁	—	4	2	no	—
276	C₄⋊C₄×C₁₃₁	—	4	2	no	—
277	C₄⋊C₄×C₁₃₁	—	4	2	no	—
278	C₄⋊C₄×C₁₃₁	—	4	1	no	—
279	C₄⋊C₄×C₁₃₁	—	4	2	no	—
280	C₄⋊C₄×C₁₃₁	—	4	1	no	—
281	C₄⋊C₄×C₁₃₁	—	4	2	no	—
282	C₄⋊C₄×C₁₃₁	—	4	2	no	—
283	C₄⋊C₄×C₁₃₁	—	4	2	no	—
284	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
292	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
293	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
294	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
295	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
296	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
298	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
299	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
300	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
302	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
303	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
304	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
305	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
306	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
307	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
310	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
311	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
312	C₂²⋊C₄×C₁₃₁	#41	1	4	yes	—
313	C₄²×C₁₃₁	—	2	2	no	—
314	C₄²×C₁₃₁	—	4	2	no	—
315	C₄²×C₁₃₁	—	4	2	no	—
316	C₄²×C₁₃₁	—	4	2	no	—
317	C₄²×C₁₃₁	—	4	2	no	—
318	C₂³×C₁₃₁	—	2	2	no	—
319	C₂³×C₁₃₁	—	2	1	no	—
320	C₂³×C₁₃₁	—	2	2	no	—
321	C₂³×C₁₃₁	—	2	2	no	—
322	C₂³×C₁₃₁	—	2	2	no	—
323	C₂³×C₁₃₁	—	2	1	no	—
324	C₂³×C₁₃₁	—	2	2	no	—
325	C₂³×C₁₃₁	—	2	2	no	—
326	C₂³×C₁₃₁	—	2	2	no	—
327	C₂³×C₁₃₁	—	2	2	no	—
328	C₂³×C₁₃₁	—	2	2	no	—
329	C₂³×C₁₃₁	—	2	1	no	—
330	C₂³×C₁₃₁	—	2	2	no	—
331	C₂³×C₁₃₁	—	2	2	no	—
332	C₂³×C₁₃₁	—	2	1	no	—
333	C₂³×C₁₃₁	—	2	2	no	—
334	C₂³×C₁₃₁	—	2	2	no	—
335	C₂³×C₁₃₁	—	2	2	no	—
336	C₂³×C₁₃₁	—	2	2	no	—
337	C₂³×C₁₃₁	—	2	2	no	—
338	C₂³×C₁₃₁	—	2	1	no	—
339	C₂³×C₁₃₁	—	2	2	no	—
340	C₂³×C₁₃₁	—	4	4	no	—
341	C₂³×C₁₃₁	—	4	8	no	—
342	C₂³×C₁₃₁	—	4	4	no	—
343	C₂³×C₁₃₁	—	4	8	no	—
344	C₂³×C₁₃₁	—	4	4	no	—
345	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
346	C₂³×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
347	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
348	Q₈×C₁₃₁	—	8	2	no	—
349	Q₈×C₁₃₁	—	8	2	no	—
350	D₄×C₁₃₁	—	4	8	no	—
351	D₄×C₁₃₁	—	4	4	no	—
352	D₄×C₁₃₁	—	8	4	no	—
353	D₄×C₁₃₁	—	8	4	no	—
354	D₄×C₁₃₁	—	8	4	no	—
355	D₄×C₁₃₁	—	8	4	no	—
356	D₄×C₁₃₁	—	8	2	no	—
357	C₂×C₄×C₁₃₁	—	2	2	no	—
358	C₂×C₄×C₁₃₁	—	2	2	no	—
359	C₂×C₄×C₁₃₁	—	2	2	no	—
360	C₂×C₄×C₁₃₁	—	2	2	no	—
361	C₂×C₄×C₁₃₁	—	2	1	no	—
362	C₂×C₄×C₁₃₁	—	2	2	no	—
363	C₂×C₄×C₁₃₁	—	2	2	no	—
364	C₂×C₄×C₁₃₁	—	2	1	no	—
365	C₂×C₄×C₁₃₁	—	2	1	no	—
366	C₂×C₄×C₁₃₁	—	2	2	no	—
367	C₂×C₄×C₁₃₁	—	2	2	no	—
368	C₂×C₄×C₁₃₁	—	2	2	no	—
369	C₂×C₄×C₁₃₁	—	2	2	no	—
370	C₂×C₄×C₁₃₁	—	2	2	no	—
371	C₂×C₄×C₁₃₁	—	2	2	no	—
372	C₂×C₄×C₁₃₁	—	2	2	no	—
373	C₂×C₄×C₁₃₁	—	2	2	no	—
374	C₂×C₄×C₁₃₁	—	2	2	no	—
375	C₂×C₄×C₁₃₁	—	2	2	no	—
376	C₂×C₄×C₁₃₁	—	2	2	no	—
377	C₂×C₄×C₁₃₁	—	2	1	no	—
378	C₂×C₄×C₁₃₁	—	2	1	no	—
379	C₂×C₄×C₁₃₁	—	2	2	no	—
380	C₂×C₄×C₁₃₁	—	2	2	no	—
381	C₂×C₄×C₁₃₁	—	2	2	no	—
382	C₂×C₄×C₁₃₁	—	2	2	no	—
383	C₂×C₄×C₁₃₁	—	2	2	no	—
384	C₂×C₄×C₁₃₁	—	2	2	no	—
385	C₂×C₄×C₁₃₁	—	2	2	no	—
386	C₂×C₄×C₁₃₁	—	2	2	no	—
387	C₂×C₄×C₁₃₁	—	2	2	no	—
388	C₂×C₄×C₁₃₁	—	2	2	no	—
389	C₂×C₄×C₁₃₁	—	2	2	no	—
390	C₂×C₄×C₁₃₁	—	2	2	no	—
391	C₂×C₄×C₁₃₁	—	2	2	no	—
392	C₂×C₄×C₁₃₁	—	2	2	no	—
393	C₂×C₄×C₁₃₁	—	2	2	no	—
394	C₂×C₄×C₁₃₁	—	2	2	no	—
395	C₂×C₄×C₁₃₁	—	2	1	no	—
396	C₂×C₄×C₁₃₁	—	4	8	no	—
397	C₂×C₄×C₁₃₁	—	4	4	no	—
398	C₂×C₄×C₁₃₁	—	4	8	no	—
399	C₂×C₄×C₁₃₁	—	4	4	no	—
400	C₂×C₄×C₁₃₁	—	8	4	no	—
401	C₂×C₄×C₁₃₁	—	8	2	no	—
402	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
403	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
404	C₂²×C₁₃₁	—	2	2	no	—
405	C₂²×C₁₃₁	—	2	4	no	—
406	C₂²×C₁₃₁	—	2	4	no	—
407	C₂²×C₁₃₁	—	2	4	no	—
408	C₂²×C₁₃₁	—	2	4	no	—
409	C₂²×C₁₃₁	—	4	16	no	—
410	C₂²×C₁₃₁	—	4	2	no	—
411	C₂²×C₁₃₁	—	4	2	no	—
412	C₂²×C₁₃₁	—	4	1	no	—
413	C₂²×C₁₃₁	—	4	2	no	—
414	C₂²×C₁₃₁	—	4	2	no	—
415	C₂²×C₁₃₁	—	4	1	no	—
416	C₂²×C₁₃₁	—	4	2	no	—
417	C₂²×C₁₃₁	—	4	1	no	—
418	C₂²×C₁₃₁	—	4	2	no	—
419	C₂²×C₁₃₁	—	4	2	no	—
420	C₂²×C₁₃₁	—	4	2	no	—
421	C₂²×C₁₃₁	—	4	2	no	—
422	C₂²×C₁₃₁	—	4	1	no	—
423	C₂²×C₁₃₁	—	4	2	no	—
424	C₂²×C₁₃₁	—	4	2	no	—
425	C₂²×C₁₃₁	—	4	2	no	—
426	C₂²×C₁₃₁	—	4	2	no	—
427	C₂²×C₁₃₁	—	4	2	no	—
428	C₂²×C₁₃₁	—	4	1	no	—
429	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
432	C₂²×C₁₃₁	#585	1	1	yes	characteristic
433	C₂²×C₁₃₁	#585	1	2	yes	—
434	C₄×C₁₃₁	—	2	4	no	—
435	C₄×C₁₃₁	—	2	2	no	—
436	C₄×C₁₃₁	—	4	2	no	—
437	C₄×C₁₃₁	—	4	1	no	—
438	C₄×C₁₃₁	—	4	2	no	—
439	C₄×C₁₃₁	—	4	2	no	—
440	C₄×C₁₃₁	—	4	2	no	—
441	C₄×C₁₃₁	—	4	1	no	—
442	C₄×C₁₃₁	—	4	1	no	—
443	C₄×C₁₃₁	—	4	2	no	—
444	C₄×C₁₃₁	—	4	2	no	—
445	C₄×C₁₃₁	—	4	2	no	—
446	C₄×C₁₃₁	—	4	2	no	—
447	C₄×C₁₃₁	—	4	1	no	—
448	C₄×C₁₃₁	—	4	2	no	—
449	C₂×C₁₃₁	—	4	2	no	—
450	C₂×C₁₃₁	—	4	4	no	—
451	C₂×C₁₃₁	—	8	1	no	—
452	C₂×C₁₃₁	—	8	2	no	—
453	C₂×C₁₃₁	#3460	1	1	yes	characteristic
454	C₂×C₁₃₁	#3513	1	2	yes	—
455	C₂×C₁₃₁	#3532	1	1	yes	characteristic
456	C₂×C₁₃₁	#3533	1	2	yes	—
457	C₂×C₁₃₁	#3540	1	1	yes	characteristic
458	#36872	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₁₃₁	#36872	1	1	yes	characteristic, direct product factor, Sylow
460	#2849	C₂×C₁₃₁	1	2	yes	complemented
461	#2797	C₂×C₁₃₁	1	2	yes	complemented
462	#2763	C₂×C₁₃₁	1	1	yes	characteristic, complemented
463	#2761	C₂×C₁₃₁	1	2	yes	complemented
464	#2751	C₂×C₁₃₁	1	2	yes	complemented
465	#2736	C₂×C₁₃₁	1	1	yes	characteristic, complemented
466	#2717	C₂×C₁₃₁	1	2	yes	complemented
467	#2703	C₂×C₁₃₁	1	2	yes	complemented
468	#2693	C₂×C₁₃₁	1	1	yes	characteristic, complemented
469	#2678	C₂×C₁₃₁	1	2	yes	complemented
470	#2670	C₂×C₁₃₁	1	1	yes	characteristic, complemented
471	#2638	C₂×C₁₃₁	1	1	yes	characteristic, complemented
472	#2631	C₂×C₁₃₁	1	1	yes	characteristic, complemented
473	#2573	C₂×C₁₃₁	1	2	yes	complemented
474	#2557	C₂×C₁₃₁	1	2	yes	complemented
475	#2461	C₂×C₁₃₁	1	2	yes	complemented
476	#2420	C₂×C₁₃₁	1	2	yes	complemented
477	#2335	C₂×C₁₃₁	1	2	yes	complemented
478	C₄×#120	C₂×C₁₃₁	1	1	yes	characteristic, complemented
479	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
480	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
481	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
482	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
483	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
484	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
486	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
487	C₂×#120	C₂²×C₁₃₁	1	1	yes	characteristic
488	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
489	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
491	#400	C₂²×C₁₃₁	1	2	yes	complemented
492	#400	C₂²×C₁₃₁	1	2	yes	complemented
493	#398	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
494	#397	C₂²×C₁₃₁	1	2	yes	—
495	#397	C₂²×C₁₃₁	1	1	yes	characteristic
496	#397	C₂²×C₁₃₁	1	2	yes	—
497	#397	C₂²×C₁₃₁	1	2	yes	complemented
498	#397	C₂²×C₁₃₁	1	2	yes	complemented
499	#397	C₂²×C₁₃₁	1	2	yes	complemented
500	#397	C₂²×C₁₃₁	1	2	yes	complemented
501	#397	C₂²×C₁₃₁	1	2	yes	complemented
502	#396	C₂²×C₁₃₁	1	2	yes	—
503	#396	C₂²×C₁₃₁	1	2	yes	complemented
504	#395	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
505	#395	C₂²×C₁₃₁	1	2	yes	complemented
506	#394	C₂²×C₁₃₁	1	2	yes	—
507	#394	C₂²×C₁₃₁	1	2	yes	—
508	#394	C₂²×C₁₃₁	1	2	yes	—
509	#394	C₂²×C₁₃₁	1	2	yes	complemented
510	#393	C₂²×C₁₃₁	1	1	yes	characteristic
511	#393	C₂²×C₁₃₁	1	1	yes	characteristic
512	#393	C₂²×C₁₃₁	1	2	yes	—
513	#393	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
514	#392	C₂²×C₁₃₁	1	1	yes	characteristic
515	#392	C₂²×C₁₃₁	1	2	yes	—
516	#392	C₂²×C₁₃₁	1	2	yes	—
517	#392	C₂²×C₁₃₁	1	2	yes	—
518	#392	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
519	#391	C₂²×C₁₃₁	1	2	yes	complemented
520	#390	C₂²×C₁₃₁	1	2	yes	—
521	#390	C₂²×C₁₃₁	1	2	yes	—
522	#390	C₂²×C₁₃₁	1	2	yes	—
523	#390	C₂²×C₁₃₁	1	2	yes	complemented
524	#389	C₂²×C₁₃₁	1	2	yes	complemented
525	#388	C₂²×C₁₃₁	1	2	yes	—
526	#388	C₂²×C₁₃₁	1	2	yes	—
527	#388	C₂²×C₁₃₁	1	2	yes	—
528	#388	C₂²×C₁₃₁	1	2	yes	—
529	#388	C₂²×C₁₃₁	1	2	yes	—
530	#388	C₂²×C₁₃₁	1	2	yes	complemented
531	#388	C₂²×C₁₃₁	1	2	yes	complemented
532	#388	C₂²×C₁₃₁	1	2	yes	complemented
533	#387	C₂²×C₁₃₁	1	2	yes	complemented
534	#387	C₂²×C₁₃₁	1	2	yes	complemented
535	#387	C₂²×C₁₃₁	1	2	yes	complemented
536	#387	C₂²×C₁₃₁	1	2	yes	complemented
537	#387	C₂²×C₁₃₁	1	2	yes	complemented
538	#386	C₂²×C₁₃₁	1	2	yes	—
539	#386	C₂²×C₁₃₁	1	2	yes	—
540	#386	C₂²×C₁₃₁	1	2	yes	—
541	#386	C₂²×C₁₃₁	1	2	yes	—
542	#386	C₂²×C₁₃₁	1	2	yes	—
543	#386	C₂²×C₁₃₁	1	2	yes	—
544	#386	C₂²×C₁₃₁	1	1	yes	characteristic
545	#386	C₂²×C₁₃₁	1	2	yes	complemented
546	#386	C₂²×C₁₃₁	1	2	yes	complemented
547	#385	C₂²×C₁₃₁	1	2	yes	—
548	#385	C₂²×C₁₃₁	1	2	yes	—
549	#385	C₂²×C₁₃₁	1	2	yes	—
550	#385	C₂²×C₁₃₁	1	2	yes	—
551	#385	C₂²×C₁₃₁	1	1	yes	characteristic
552	#385	C₂²×C₁₃₁	1	2	yes	—
553	#383	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
554	#382	C₂²×C₁₃₁	1	2	yes	complemented
555	#381	C₂²×C₁₃₁	1	2	yes	—
556	#381	C₂²×C₁₃₁	1	2	yes	—
557	#381	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
558	#380	C₂²×C₁₃₁	1	2	yes	complemented
559	#380	C₂²×C₁₃₁	1	2	yes	complemented
560	#379	C₂²×C₁₃₁	1	2	yes	—
561	#379	C₂²×C₁₃₁	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
563	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
564	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
565	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
566	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
568	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
570	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
572	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
573	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
574	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
575	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
576	C₂³×C₄	—	4	2	no	—
577	C₂³×C₄	—	4	4	no	—
578	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
579	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
582	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
583	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
584	#124	—	4	2	no	—
585	#124	—	4	4	no	—
586	#123	—	2	8	no	—
587	#123	—	4	4	no	—
588	#123	—	4	4	no	—
589	C₂²⋊Q₈	—	4	2	no	—
590	#121	—	4	4	no	—
591	#120	—	2	4	no	—
592	#120	—	4	4	no	—
593	C₄×D₄	—	4	2	no	—
594	C₄×D₄	—	4	4	no	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
639	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
640	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
641	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
642	#95	C₂³×C₁₃₁	1	2	yes	—
643	#95	C₂³×C₁₃₁	1	2	yes	—
644	#95	C₂³×C₁₃₁	1	2	yes	—
645	#95	C₂³×C₁₃₁	1	2	yes	—
646	#95	C₂³×C₁₃₁	1	2	yes	—
647	#95	C₂³×C₁₃₁	1	2	yes	—
648	#95	C₂³×C₁₃₁	1	2	yes	—
649	#95	C₂³×C₁₃₁	1	1	yes	characteristic
650	#95	C₂³×C₁₃₁	1	2	yes	—
651	#95	C₂³×C₁₃₁	1	2	yes	—
652	#95	C₂³×C₁₃₁	1	2	yes	—
653	#95	C₂³×C₁₃₁	1	2	yes	—
654	#95	C₂³×C₁₃₁	1	2	yes	—
655	#95	C₂³×C₁₃₁	1	2	yes	—
656	#95	C₂³×C₁₃₁	1	1	yes	characteristic
657	#95	C₂³×C₁₃₁	1	2	yes	—
658	#95	C₂³×C₁₃₁	1	2	yes	—
659	#95	C₂³×C₁₃₁	1	1	yes	characteristic
660	#95	C₂³×C₁₃₁	1	1	yes	characteristic
661	#95	C₂³×C₁₃₁	1	2	yes	—
662	#95	C₂³×C₁₃₁	1	2	yes	—
663	#95	C₂³×C₁₃₁	1	2	yes	—
664	#95	C₂³×C₁₃₁	1	2	yes	—
665	#95	C₂³×C₁₃₁	1	2	yes	—
666	C₂⁴	—	2	2	no	—
667	C₂⁴	—	2	4	no	—
668	C₂⁴	—	4	1	no	—
669	C₂⁴	—	4	2	no	—
670	C₂⁴	—	4	1	no	—
671	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
672	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
673	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
674	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
675	C₂×Q₈	—	4	1	no	—
676	C₂×Q₈	—	4	1	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	16	no	—
715	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	4	1	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	—	4	1	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	#41×C₁₃₁	1	4	yes	—
772	C₄²	—	2	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	8	no	—
802	C₂³	—	4	4	no	—
803	C₂³	—	4	4	no	—
804	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
805	C₂³	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
806	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
807	Q₈	—	8	2	no	—
808	Q₈	—	8	2	no	—
809	D₄	—	4	8	no	—
810	D₄	—	4	4	no	—
811	D₄	—	8	4	no	—
812	D₄	—	8	4	no	—
813	D₄	—	8	4	no	—
814	D₄	—	8	4	no	—
815	D₄	—	8	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	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	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	8	4	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
862	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
863	C₂²	—	2	4	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	4	16	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
889	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
890	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
891	C₂²	#585×C₁₃₁	1	2	yes	—
892	C₂²	#585×C₁₃₁	1	1	yes	characteristic
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₂	—	4	4	no	—
909	C₂	—	4	2	no	—
910	C₂	—	8	2	no	—
911	C₂	—	8	1	no	—
912	C₂	#3460×C₁₃₁	1	1	yes	characteristic
913	C₂	#3513×C₁₃₁	1	2	yes	—
914	C₂	#3532×C₁₃₁	1	1	yes	characteristic
915	C₂	#3533×C₁₃₁	1	2	yes	—
916	C₂	#3540×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2849×C₁₃₁	C₂	semidirect
2. #2797×C₁₃₁	C₂	semidirect
3. #2763×C₁₃₁	C₂	semidirect
4. #2761×C₁₃₁	C₂	semidirect
5. #2751×C₁₃₁	C₂	semidirect
6. #2736×C₁₃₁	C₂	semidirect
7. #2717×C₁₃₁	C₂	semidirect
8. #2703×C₁₃₁	C₂	semidirect
9. #2693×C₁₃₁	C₂	semidirect
10. #2678×C₁₃₁	C₂	semidirect
11. #2670×C₁₃₁	C₂	semidirect
12. #2638×C₁₃₁	C₂	semidirect
13. #2631×C₁₃₁	C₂	semidirect
14. #2573×C₁₃₁	C₂	semidirect
15. #2557×C₁₃₁	C₂	semidirect
16. #2461×C₁₃₁	C₂	semidirect
17. #2420×C₁₃₁	C₂	semidirect
18. #2335×C₁₃₁	C₂	semidirect
19. C₄×#120×C₁₃₁	C₂	semidirect
22. C₂×#124×C₁₃₁	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
32. #400×C₁₃₁	C₂²	semidirect
33. #400×C₁₃₁	C₂²	semidirect
34. #398×C₁₃₁	C₂²	semidirect
38. #397×C₁₃₁	C₂²	semidirect
39. #397×C₁₃₁	C₂²	semidirect
40. #397×C₁₃₁	C₂²	semidirect
41. #397×C₁₃₁	C₂²	semidirect
42. #397×C₁₃₁	C₂²	semidirect
44. #396×C₁₃₁	C₂²	semidirect
45. #395×C₁₃₁	C₂²	semidirect
46. #395×C₁₃₁	C₂²	semidirect
50. #394×C₁₃₁	C₂²	semidirect
54. #393×C₁₃₁	C₂²	semidirect
59. #392×C₁₃₁	C₂²	semidirect
60. #391×C₁₃₁	C₂²	semidirect
64. #390×C₁₃₁	C₂²	semidirect
65. #389×C₁₃₁	C₂²	semidirect
71. #388×C₁₃₁	C₂²	semidirect
72. #388×C₁₃₁	C₂²	semidirect
73. #388×C₁₃₁	C₂²	semidirect
74. #387×C₁₃₁	C₂²	semidirect
75. #387×C₁₃₁	C₂²	semidirect
76. #387×C₁₃₁	C₂²	semidirect
77. #387×C₁₃₁	C₂²	semidirect
78. #387×C₁₃₁	C₂²	semidirect
86. #386×C₁₃₁	C₂²	semidirect
87. #386×C₁₃₁	C₂²	semidirect
94. #383×C₁₃₁	C₂²	semidirect
95. #382×C₁₃₁	C₂²	semidirect
98. #381×C₁₃₁	C₂²	semidirect
99. #380×C₁₃₁	C₂²	semidirect
100. #380×C₁₃₁	C₂²	semidirect
103. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
458. #36872	C₁₃₁	direct (N × H)
459. C₁₃₁	#36872	direct (N × H)
460. #2849	C₂×C₁₃₁	semidirect
461. #2797	C₂×C₁₃₁	semidirect
462. #2763	C₂×C₁₃₁	semidirect
463. #2761	C₂×C₁₃₁	semidirect
464. #2751	C₂×C₁₃₁	semidirect
465. #2736	C₂×C₁₃₁	semidirect
466. #2717	C₂×C₁₃₁	semidirect
467. #2703	C₂×C₁₃₁	semidirect
468. #2693	C₂×C₁₃₁	semidirect
469. #2678	C₂×C₁₃₁	semidirect
470. #2670	C₂×C₁₃₁	semidirect
471. #2638	C₂×C₁₃₁	semidirect
472. #2631	C₂×C₁₃₁	semidirect
473. #2573	C₂×C₁₃₁	semidirect
474. #2557	C₂×C₁₃₁	semidirect
475. #2461	C₂×C₁₃₁	semidirect
476. #2420	C₂×C₁₃₁	semidirect
477. #2335	C₂×C₁₃₁	semidirect
478. C₄×#120	C₂×C₁₃₁	semidirect
481. C₂×#124	C₂²×C₁₃₁	semidirect
485. C₂×C₂²⋊Q₈	C₂²×C₁₃₁	semidirect
491. #400	C₂²×C₁₃₁	semidirect
492. #400	C₂²×C₁₃₁	semidirect
493. #398	C₂²×C₁₃₁	semidirect
497. #397	C₂²×C₁₃₁	semidirect
498. #397	C₂²×C₁₃₁	semidirect
499. #397	C₂²×C₁₃₁	semidirect
500. #397	C₂²×C₁₃₁	semidirect
501. #397	C₂²×C₁₃₁	semidirect
503. #396	C₂²×C₁₃₁	semidirect
504. #395	C₂²×C₁₃₁	semidirect
505. #395	C₂²×C₁₃₁	semidirect
509. #394	C₂²×C₁₃₁	semidirect
513. #393	C₂²×C₁₃₁	semidirect
518. #392	C₂²×C₁₃₁	semidirect
519. #391	C₂²×C₁₃₁	semidirect
523. #390	C₂²×C₁₃₁	semidirect
524. #389	C₂²×C₁₃₁	semidirect
530. #388	C₂²×C₁₃₁	semidirect
531. #388	C₂²×C₁₃₁	semidirect
532. #388	C₂²×C₁₃₁	semidirect
533. #387	C₂²×C₁₃₁	semidirect
534. #387	C₂²×C₁₃₁	semidirect
535. #387	C₂²×C₁₃₁	semidirect
536. #387	C₂²×C₁₃₁	semidirect
537. #387	C₂²×C₁₃₁	semidirect
545. #386	C₂²×C₁₃₁	semidirect
546. #386	C₂²×C₁₃₁	semidirect
553. #383	C₂²×C₁₃₁	semidirect
554. #382	C₂²×C₁₃₁	semidirect
557. #381	C₂²×C₁₃₁	semidirect
558. #380	C₂²×C₁₃₁	semidirect
559. #380	C₂²×C₁₃₁	semidirect
562. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
565. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2849×C₁₃₁	2
#2797×C₁₃₁	2
#2763×C₁₃₁	2
#2761×C₁₃₁	2
#2751×C₁₃₁	2
#2736×C₁₃₁	2
#2717×C₁₃₁	2
#2703×C₁₃₁	2
#2693×C₁₃₁	2
#2678×C₁₃₁	2
#2670×C₁₃₁	2
#2638×C₁₃₁	2
#2631×C₁₃₁	2
#2573×C₁₃₁	2
#2557×C₁₃₁	2
#2461×C₁₃₁	2
#2420×C₁₃₁	2
#2335×C₁₃₁	2
C₄×#120×C₁₃₁	2
#36872	131

Subgroups — C131×#36872 #45722756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#36872 #45722756