Subgroups — C₁₃₁×#36837 #45722721

Order 33536.

1534 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2853×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#2788×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2777×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2764×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2757×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2755×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2751×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2724×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2706×C₁₃₁	C₂	1	2	yes	maximal
10	#2654×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2610×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	#2606×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#2599×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2592×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#2577×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	#2470×C₁₃₁	C₂	1	2	yes	maximal, complemented
17	#2337×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#2320×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#2296×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
27	#400×C₁₃₁	C₂²	1	2	yes	—
28	#400×C₁₃₁	C₂²	1	2	yes	—
29	#400×C₁₃₁	C₂²	1	2	yes	—
30	#400×C₁₃₁	C₂²	1	2	yes	—
31	#399×C₁₃₁	C₂²	1	2	yes	—
32	#398×C₁₃₁	C₂²	1	2	yes	—
33	#398×C₁₃₁	C₂²	1	2	yes	—
34	#398×C₁₃₁	C₂²	1	2	yes	—
35	#398×C₁₃₁	C₂²	1	2	yes	—
36	#398×C₁₃₁	C₂²	1	2	yes	—
37	#398×C₁₃₁	C₂²	1	1	yes	characteristic
38	#397×C₁₃₁	C₂²	1	2	yes	—
39	#397×C₁₃₁	C₂²	1	2	yes	—
40	#397×C₁₃₁	C₂²	1	2	yes	—
41	#397×C₁₃₁	C₂²	1	2	yes	—
42	#397×C₁₃₁	C₂²	1	2	yes	—
43	#397×C₁₃₁	C₂²	1	2	yes	—
44	#397×C₁₃₁	C₂²	1	1	yes	characteristic
45	#396×C₁₃₁	C₂²	1	2	yes	—
46	#396×C₁₃₁	C₂²	1	2	yes	—
47	#395×C₁₃₁	C₂²	1	1	yes	characteristic
48	#395×C₁₃₁	C₂²	1	1	yes	characteristic
49	#394×C₁₃₁	C₂²	1	2	yes	—
50	#394×C₁₃₁	C₂²	1	1	yes	characteristic
51	#393×C₁₃₁	C₂²	1	1	yes	characteristic
52	#393×C₁₃₁	C₂²	1	2	yes	—
53	#393×C₁₃₁	C₂²	1	1	yes	characteristic
54	#392×C₁₃₁	C₂²	1	1	yes	characteristic
55	#391×C₁₃₁	C₂²	1	2	yes	—
56	#391×C₁₃₁	C₂²	1	2	yes	—
57	#391×C₁₃₁	C₂²	1	2	yes	—
58	#390×C₁₃₁	C₂²	1	2	yes	—
59	#390×C₁₃₁	C₂²	1	2	yes	—
60	#389×C₁₃₁	C₂²	1	2	yes	—
61	#389×C₁₃₁	C₂²	1	2	yes	—
62	#389×C₁₃₁	C₂²	1	2	yes	—
63	#389×C₁₃₁	C₂²	1	2	yes	—
64	#389×C₁₃₁	C₂²	1	2	yes	—
65	#389×C₁₃₁	C₂²	1	2	yes	—
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	—
72	#388×C₁₃₁	C₂²	1	2	yes	—
73	#388×C₁₃₁	C₂²	1	2	yes	—
74	#388×C₁₃₁	C₂²	1	2	yes	—
75	#388×C₁₃₁	C₂²	1	2	yes	—
76	#387×C₁₃₁	C₂²	1	2	yes	—
77	#387×C₁₃₁	C₂²	1	2	yes	—
78	#387×C₁₃₁	C₂²	1	2	yes	—
79	#387×C₁₃₁	C₂²	1	2	yes	—
80	#387×C₁₃₁	C₂²	1	2	yes	—
81	#387×C₁₃₁	C₂²	1	2	yes	—
82	#387×C₁₃₁	C₂²	1	2	yes	—
83	#387×C₁₃₁	C₂²	1	2	yes	—
84	#387×C₁₃₁	C₂²	1	2	yes	—
85	#386×C₁₃₁	C₂²	1	2	yes	—
86	#386×C₁₃₁	C₂²	1	2	yes	—
87	#386×C₁₃₁	C₂²	1	2	yes	—
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	2	yes	—
92	#385×C₁₃₁	C₂²	1	2	yes	—
93	#385×C₁₃₁	C₂²	1	2	yes	—
94	#385×C₁₃₁	C₂²	1	2	yes	—
95	#383×C₁₃₁	C₂²	1	2	yes	—
96	#383×C₁₃₁	C₂²	1	2	yes	—
97	#383×C₁₃₁	C₂²	1	1	yes	characteristic
98	#382×C₁₃₁	C₂²	1	2	yes	—
99	#381×C₁₃₁	C₂²	1	2	yes	—
100	#380×C₁₃₁	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
106	#376×C₁₃₁	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
114	#124×C₁₃₁	—	2	4	no	—
115	#123×C₁₃₁	—	4	4	no	—
116	#123×C₁₃₁	—	4	4	no	—
117	C₄×Q₈×C₁₃₁	—	2	4	no	—
118	#117×C₁₃₁	—	2	4	no	—
119	#117×C₁₃₁	—	4	2	no	—
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
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×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	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	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊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	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₁	—	4	2	no	—
160	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃₁	C₂³	1	2	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	2	yes	—
168	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
170	#95×C₁₃₁	C₂³	1	2	yes	—
171	#95×C₁₃₁	C₂³	1	2	yes	—
172	#95×C₁₃₁	C₂³	1	2	yes	—
173	#95×C₁₃₁	C₂³	1	1	yes	characteristic
174	#95×C₁₃₁	C₂³	1	2	yes	—
175	#95×C₁₃₁	C₂³	1	2	yes	—
176	#95×C₁₃₁	C₂³	1	2	yes	—
177	#95×C₁₃₁	C₂³	1	2	yes	—
178	#95×C₁₃₁	C₂³	1	2	yes	—
179	#95×C₁₃₁	C₂³	1	2	yes	—
180	#95×C₁₃₁	C₂³	1	2	yes	—
181	#95×C₁₃₁	C₂³	1	2	yes	—
182	#95×C₁₃₁	C₂³	1	2	yes	—
183	#95×C₁₃₁	C₂³	1	2	yes	—
184	#95×C₁₃₁	C₂³	1	2	yes	—
185	#95×C₁₃₁	C₂³	1	2	yes	—
186	#95×C₁₃₁	C₂³	1	2	yes	—
187	#95×C₁₃₁	C₂³	1	2	yes	—
188	#95×C₁₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
197	#95×C₁₃₁	C₂³	1	1	yes	characteristic
198	#95×C₁₃₁	C₂³	1	2	yes	—
199	#95×C₁₃₁	C₂³	1	2	yes	—
200	#95×C₁₃₁	C₂³	1	2	yes	—
201	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
202	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₁₃₁	—	2	2	no	—
204	C₂×Q₈×C₁₃₁	—	2	2	no	—
205	C₂×Q₈×C₁₃₁	—	4	2	no	—
206	C₂×Q₈×C₁₃₁	—	4	2	no	—
207	C₂×D₄×C₁₃₁	—	2	4	no	—
208	C₂×D₄×C₁₃₁	—	2	2	no	—
209	C₂×D₄×C₁₃₁	—	4	2	no	—
210	C₂×D₄×C₁₃₁	—	4	2	no	—
211	C₂×D₄×C₁₃₁	—	4	2	no	—
212	C₂²×C₄×C₁₃₁	—	2	2	no	—
213	C₂²×C₄×C₁₃₁	—	2	2	no	—
214	C₂²×C₄×C₁₃₁	—	2	2	no	—
215	C₂²×C₄×C₁₃₁	—	2	4	no	—
216	C₂²×C₄×C₁₃₁	—	4	2	no	—
217	C₂²×C₄×C₁₃₁	—	4	2	no	—
218	C₂²×C₄×C₁₃₁	—	4	2	no	—
219	C₂²×C₄×C₁₃₁	—	4	2	no	—
220	C₂²×C₄×C₁₃₁	—	4	2	no	—
221	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₁₃₁	—	2	2	no	—
239	C₄⋊C₄×C₁₃₁	—	2	2	no	—
240	C₄⋊C₄×C₁₃₁	—	2	2	no	—
241	C₄⋊C₄×C₁₃₁	—	2	4	no	—
242	C₄⋊C₄×C₁₃₁	—	2	4	no	—
243	C₄⋊C₄×C₁₃₁	—	4	2	no	—
244	C₄⋊C₄×C₁₃₁	—	4	2	no	—
245	C₄⋊C₄×C₁₃₁	—	4	2	no	—
246	C₄⋊C₄×C₁₃₁	—	4	2	no	—
247	C₄⋊C₄×C₁₃₁	—	4	2	no	—
248	C₄⋊C₄×C₁₃₁	—	4	2	no	—
249	C₄⋊C₄×C₁₃₁	—	4	2	no	—
250	C₄⋊C₄×C₁₃₁	—	4	2	no	—
251	C₄⋊C₄×C₁₃₁	—	4	2	no	—
252	C₄⋊C₄×C₁₃₁	—	4	2	no	—
253	C₄⋊C₄×C₁₃₁	—	4	2	no	—
254	C₄⋊C₄×C₁₃₁	—	4	2	no	—
255	C₄⋊C₄×C₁₃₁	—	4	2	no	—
256	C₄⋊C₄×C₁₃₁	—	4	2	no	—
257	C₄⋊C₄×C₁₃₁	—	4	2	no	—
258	C₄⋊C₄×C₁₃₁	—	4	2	no	—
259	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
262	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
267	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
268	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
269	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
270	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
271	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
272	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
274	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
275	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
276	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
277	C₄²×C₁₃₁	—	2	2	no	—
278	C₄²×C₁₃₁	—	2	4	no	—
279	C₄²×C₁₃₁	—	4	1	no	—
280	C₄²×C₁₃₁	—	4	1	no	—
281	C₄²×C₁₃₁	—	4	2	no	—
282	C₄²×C₁₃₁	—	4	2	no	—
283	C₄²×C₁₃₁	—	4	2	no	—
284	C₄²×C₁₃₁	—	4	1	no	—
285	C₄²×C₁₃₁	—	4	1	no	—
286	C₄²×C₁₃₁	#41	1	4	yes	—
287	C₂³×C₁₃₁	—	2	1	no	—
288	C₂³×C₁₃₁	—	2	1	no	—
289	C₂³×C₁₃₁	—	2	2	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	H(5,𝔽₂)	1	2	yes	—
299	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
300	Q₈×C₁₃₁	—	4	4	no	—
301	Q₈×C₁₃₁	—	8	2	no	—
302	D₄×C₁₃₁	—	8	2	no	—
303	D₄×C₁₃₁	—	8	4	no	—
304	C₂×C₄×C₁₃₁	—	2	8	no	—
305	C₂×C₄×C₁₃₁	—	2	1	no	—
306	C₂×C₄×C₁₃₁	—	2	1	no	—
307	C₂×C₄×C₁₃₁	—	2	1	no	—
308	C₂×C₄×C₁₃₁	—	2	1	no	—
309	C₂×C₄×C₁₃₁	—	2	2	no	—
310	C₂×C₄×C₁₃₁	—	2	2	no	—
311	C₂×C₄×C₁₃₁	—	2	1	no	—
312	C₂×C₄×C₁₃₁	—	2	1	no	—
313	C₂×C₄×C₁₃₁	—	2	2	no	—
314	C₂×C₄×C₁₃₁	—	2	2	no	—
315	C₂×C₄×C₁₃₁	—	2	2	no	—
316	C₂×C₄×C₁₃₁	—	2	2	no	—
317	C₂×C₄×C₁₃₁	—	2	2	no	—
318	C₂×C₄×C₁₃₁	—	2	2	no	—
319	C₂×C₄×C₁₃₁	—	2	2	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	2	no	—
324	C₂×C₄×C₁₃₁	—	2	2	no	—
325	C₂×C₄×C₁₃₁	—	2	2	no	—
326	C₂×C₄×C₁₃₁	—	2	2	no	—
327	C₂×C₄×C₁₃₁	—	2	2	no	—
328	C₂×C₄×C₁₃₁	—	2	2	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	2	no	—
333	C₂×C₄×C₁₃₁	—	2	2	no	—
334	C₂×C₄×C₁₃₁	—	2	2	no	—
335	C₂×C₄×C₁₃₁	—	2	2	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	2	no	—
340	C₂×C₄×C₁₃₁	—	2	2	no	—
341	C₂×C₄×C₁₃₁	—	2	2	no	—
342	C₂×C₄×C₁₃₁	—	2	2	no	—
343	C₂×C₄×C₁₃₁	—	2	2	no	—
344	C₂×C₄×C₁₃₁	—	2	2	no	—
345	C₂×C₄×C₁₃₁	—	2	2	no	—
346	C₂×C₄×C₁₃₁	—	2	2	no	—
347	C₂×C₄×C₁₃₁	—	2	2	no	—
348	C₂×C₄×C₁₃₁	—	4	8	no	—
349	C₂×C₄×C₁₃₁	—	8	4	no	—
350	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
351	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
352	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
353	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
354	C₂²×C₁₃₁	—	2	2	no	—
355	C₂²×C₁₃₁	—	2	4	no	—
356	C₂²×C₁₃₁	—	4	1	no	—
357	C₂²×C₁₃₁	—	4	1	no	—
358	C₂²×C₁₃₁	—	4	2	no	—
359	C₂²×C₁₃₁	—	4	2	no	—
360	C₂²×C₁₃₁	—	4	2	no	—
361	C₂²×C₁₃₁	—	4	2	no	—
362	C₂²×C₁₃₁	—	4	2	no	—
363	C₂²×C₁₃₁	—	4	2	no	—
364	C₂²×C₁₃₁	—	4	2	no	—
365	C₂²×C₁₃₁	—	4	2	no	—
366	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
367	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
369	C₂²×C₁₃₁	#585	1	2	yes	—
370	C₂²×C₁₃₁	#585	1	2	yes	—
371	C₄×C₁₃₁	—	2	2	no	—
372	C₄×C₁₃₁	—	2	2	no	—
373	C₄×C₁₃₁	—	2	2	no	—
374	C₄×C₁₃₁	—	2	2	no	—
375	C₄×C₁₃₁	—	4	1	no	—
376	C₄×C₁₃₁	—	4	2	no	—
377	C₄×C₁₃₁	—	4	2	no	—
378	C₄×C₁₃₁	—	4	1	no	—
379	C₄×C₁₃₁	—	4	2	no	—
380	C₄×C₁₃₁	—	4	2	no	—
381	C₄×C₁₃₁	—	4	2	no	—
382	C₄×C₁₃₁	—	4	2	no	—
383	C₄×C₁₃₁	—	4	2	no	—
384	C₄×C₁₃₁	—	4	2	no	—
385	C₄×C₁₃₁	—	4	2	no	—
386	C₄×C₁₃₁	—	4	2	no	—
387	C₄×C₁₃₁	—	4	2	no	—
388	C₂×C₁₃₁	—	4	2	no	—
389	C₂×C₁₃₁	—	8	2	no	—
390	C₂×C₁₃₁	#3455	1	1	yes	characteristic
391	C₂×C₁₃₁	#3492	1	1	yes	characteristic
392	C₂×C₁₃₁	#3510	1	1	yes	characteristic
393	C₂×C₁₃₁	#3533	1	2	yes	—
394	C₂×C₁₃₁	#3565	1	2	yes	—
395	#36837	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₁₃₁	#36837	1	1	yes	characteristic, direct product factor, Sylow
397	#2853	C₂×C₁₃₁	1	2	yes	complemented
398	#2788	C₂×C₁₃₁	1	2	yes	complemented
399	#2777	C₂×C₁₃₁	1	2	yes	complemented
400	#2764	C₂×C₁₃₁	1	2	yes	complemented
401	#2757	C₂×C₁₃₁	1	2	yes	complemented
402	#2755	C₂×C₁₃₁	1	2	yes	complemented
403	#2751	C₂×C₁₃₁	1	2	yes	complemented
404	#2724	C₂×C₁₃₁	1	2	yes	complemented
405	#2706	C₂×C₁₃₁	1	2	yes	—
406	#2654	C₂×C₁₃₁	1	2	yes	complemented
407	#2610	C₂×C₁₃₁	1	1	yes	characteristic
408	#2606	C₂×C₁₃₁	1	1	yes	characteristic, complemented
409	#2599	C₂×C₁₃₁	1	1	yes	characteristic, complemented
410	#2592	C₂×C₁₃₁	1	1	yes	characteristic, complemented
411	#2577	C₂×C₁₃₁	1	2	yes	complemented
412	#2470	C₂×C₁₃₁	1	2	yes	complemented
413	#2337	C₂×C₁₃₁	1	1	yes	characteristic, complemented
414	#2320	C₂×C₁₃₁	1	1	yes	characteristic, complemented
415	#2296	C₂×C₁₃₁	1	1	yes	characteristic, complemented
416	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
417	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
418	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
419	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
420	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
421	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
422	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
423	#400	C₂²×C₁₃₁	1	2	yes	—
424	#400	C₂²×C₁₃₁	1	2	yes	—
425	#400	C₂²×C₁₃₁	1	2	yes	—
426	#400	C₂²×C₁₃₁	1	2	yes	—
427	#399	C₂²×C₁₃₁	1	2	yes	—
428	#398	C₂²×C₁₃₁	1	2	yes	—
429	#398	C₂²×C₁₃₁	1	1	yes	characteristic
430	#398	C₂²×C₁₃₁	1	2	yes	—
431	#398	C₂²×C₁₃₁	1	2	yes	—
432	#398	C₂²×C₁₃₁	1	2	yes	—
433	#398	C₂²×C₁₃₁	1	2	yes	—
434	#397	C₂²×C₁₃₁	1	2	yes	—
435	#397	C₂²×C₁₃₁	1	2	yes	—
436	#397	C₂²×C₁₃₁	1	2	yes	—
437	#397	C₂²×C₁₃₁	1	1	yes	characteristic
438	#397	C₂²×C₁₃₁	1	2	yes	—
439	#397	C₂²×C₁₃₁	1	2	yes	—
440	#397	C₂²×C₁₃₁	1	2	yes	—
441	#396	C₂²×C₁₃₁	1	2	yes	—
442	#396	C₂²×C₁₃₁	1	2	yes	—
443	#395	C₂²×C₁₃₁	1	1	yes	characteristic
444	#395	C₂²×C₁₃₁	1	1	yes	characteristic
445	#394	C₂²×C₁₃₁	1	1	yes	characteristic
446	#394	C₂²×C₁₃₁	1	2	yes	—
447	#393	C₂²×C₁₃₁	1	2	yes	—
448	#393	C₂²×C₁₃₁	1	1	yes	characteristic
449	#393	C₂²×C₁₃₁	1	1	yes	characteristic
450	#392	C₂²×C₁₃₁	1	1	yes	characteristic
451	#391	C₂²×C₁₃₁	1	2	yes	—
452	#391	C₂²×C₁₃₁	1	2	yes	—
453	#391	C₂²×C₁₃₁	1	2	yes	—
454	#390	C₂²×C₁₃₁	1	2	yes	—
455	#390	C₂²×C₁₃₁	1	2	yes	—
456	#389	C₂²×C₁₃₁	1	2	yes	—
457	#389	C₂²×C₁₃₁	1	2	yes	—
458	#389	C₂²×C₁₃₁	1	2	yes	—
459	#389	C₂²×C₁₃₁	1	2	yes	—
460	#389	C₂²×C₁₃₁	1	2	yes	—
461	#389	C₂²×C₁₃₁	1	2	yes	—
462	#388	C₂²×C₁₃₁	1	2	yes	—
463	#388	C₂²×C₁₃₁	1	2	yes	—
464	#388	C₂²×C₁₃₁	1	2	yes	—
465	#388	C₂²×C₁₃₁	1	2	yes	—
466	#388	C₂²×C₁₃₁	1	2	yes	—
467	#388	C₂²×C₁₃₁	1	2	yes	—
468	#388	C₂²×C₁₃₁	1	2	yes	—
469	#388	C₂²×C₁₃₁	1	2	yes	—
470	#388	C₂²×C₁₃₁	1	2	yes	—
471	#388	C₂²×C₁₃₁	1	2	yes	—
472	#387	C₂²×C₁₃₁	1	2	yes	—
473	#387	C₂²×C₁₃₁	1	2	yes	—
474	#387	C₂²×C₁₃₁	1	2	yes	—
475	#387	C₂²×C₁₃₁	1	2	yes	—
476	#387	C₂²×C₁₃₁	1	2	yes	—
477	#387	C₂²×C₁₃₁	1	2	yes	—
478	#387	C₂²×C₁₃₁	1	2	yes	—
479	#387	C₂²×C₁₃₁	1	2	yes	—
480	#387	C₂²×C₁₃₁	1	2	yes	—
481	#386	C₂²×C₁₃₁	1	2	yes	—
482	#386	C₂²×C₁₃₁	1	2	yes	—
483	#386	C₂²×C₁₃₁	1	2	yes	—
484	#385	C₂²×C₁₃₁	1	2	yes	—
485	#385	C₂²×C₁₃₁	1	2	yes	—
486	#385	C₂²×C₁₃₁	1	2	yes	—
487	#385	C₂²×C₁₃₁	1	2	yes	—
488	#385	C₂²×C₁₃₁	1	2	yes	—
489	#385	C₂²×C₁₃₁	1	2	yes	—
490	#385	C₂²×C₁₃₁	1	2	yes	—
491	#383	C₂²×C₁₃₁	1	2	yes	—
492	#383	C₂²×C₁₃₁	1	2	yes	—
493	#383	C₂²×C₁₃₁	1	1	yes	characteristic
494	#382	C₂²×C₁₃₁	1	2	yes	—
495	#381	C₂²×C₁₃₁	1	2	yes	—
496	#380	C₂²×C₁₃₁	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
500	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
502	#376	C₂²×C₁₃₁	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
504	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
506	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
509	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
510	#124	—	2	4	no	—
511	#123	—	4	4	no	—
512	#123	—	4	4	no	—
513	C₄×Q₈	—	2	4	no	—
514	#117	—	2	4	no	—
515	#117	—	4	2	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
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	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	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	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	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	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
555	C₂×C₄²	—	4	2	no	—
556	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
558	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
566	#95	C₂³×C₁₃₁	1	1	yes	characteristic
567	#95	C₂³×C₁₃₁	1	1	yes	characteristic
568	#95	C₂³×C₁₃₁	1	2	yes	—
569	#95	C₂³×C₁₃₁	1	2	yes	—
570	#95	C₂³×C₁₃₁	1	2	yes	—
571	#95	C₂³×C₁₃₁	1	2	yes	—
572	#95	C₂³×C₁₃₁	1	2	yes	—
573	#95	C₂³×C₁₃₁	1	2	yes	—
574	#95	C₂³×C₁₃₁	1	2	yes	—
575	#95	C₂³×C₁₃₁	1	2	yes	—
576	#95	C₂³×C₁₃₁	1	2	yes	—
577	#95	C₂³×C₁₃₁	1	2	yes	—
578	#95	C₂³×C₁₃₁	1	2	yes	—
579	#95	C₂³×C₁₃₁	1	2	yes	—
580	#95	C₂³×C₁₃₁	1	2	yes	—
581	#95	C₂³×C₁₃₁	1	2	yes	—
582	#95	C₂³×C₁₃₁	1	1	yes	characteristic
583	#95	C₂³×C₁₃₁	1	2	yes	—
584	#95	C₂³×C₁₃₁	1	2	yes	—
585	#95	C₂³×C₁₃₁	1	2	yes	—
586	#95	C₂³×C₁₃₁	1	2	yes	—
587	#95	C₂³×C₁₃₁	1	1	yes	characteristic
588	#95	C₂³×C₁₃₁	1	2	yes	—
589	#95	C₂³×C₁₃₁	1	2	yes	—
590	#95	C₂³×C₁₃₁	1	2	yes	—
591	#95	C₂³×C₁₃₁	1	2	yes	—
592	#95	C₂³×C₁₃₁	1	2	yes	—
593	#95	C₂³×C₁₃₁	1	2	yes	—
594	#95	C₂³×C₁₃₁	1	2	yes	—
595	#95	C₂³×C₁₃₁	1	2	yes	—
596	#95	C₂³×C₁₃₁	1	2	yes	—
597	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
598	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	4	2	no	—
602	C₂×Q₈	—	4	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	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	—	4	2	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	4	1	no	—
676	C₄²	—	4	1	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	—	4	2	no	—
680	C₄²	—	4	1	no	—
681	C₄²	—	4	1	no	—
682	C₄²	#41×C₁₃₁	1	4	yes	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
695	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
696	Q₈	—	4	4	no	—
697	Q₈	—	8	2	no	—
698	D₄	—	8	2	no	—
699	D₄	—	8	4	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	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	2	no	—
728	C₂×C₄	—	2	2	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	—	4	8	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
747	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
748	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
749	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
763	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
764	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
765	C₂²	#585×C₁₃₁	1	2	yes	—
766	C₂²	#585×C₁₃₁	1	2	yes	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	2	no	—
784	C₂	—	4	2	no	—
785	C₂	—	8	2	no	—
786	C₂	#3455×C₁₃₁	1	1	yes	characteristic
787	C₂	#3492×C₁₃₁	1	1	yes	characteristic
788	C₂	#3510×C₁₃₁	1	1	yes	characteristic
789	C₂	#3533×C₁₃₁	1	2	yes	—
790	C₂	#3565×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	#392×C₁₃₁	C₂²
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. #2853×C₁₃₁	C₂	semidirect
2. #2788×C₁₃₁	C₂	semidirect
3. #2777×C₁₃₁	C₂	semidirect
4. #2764×C₁₃₁	C₂	semidirect
5. #2757×C₁₃₁	C₂	semidirect
6. #2755×C₁₃₁	C₂	semidirect
7. #2751×C₁₃₁	C₂	semidirect
8. #2724×C₁₃₁	C₂	semidirect
10. #2654×C₁₃₁	C₂	semidirect
12. #2606×C₁₃₁	C₂	semidirect
13. #2599×C₁₃₁	C₂	semidirect
14. #2592×C₁₃₁	C₂	semidirect
15. #2577×C₁₃₁	C₂	semidirect
16. #2470×C₁₃₁	C₂	semidirect
17. #2337×C₁₃₁	C₂	semidirect
18. #2320×C₁₃₁	C₂	semidirect
19. #2296×C₁₃₁	C₂	semidirect
395. #36837	C₁₃₁	direct (N × H)
396. C₁₃₁	#36837	direct (N × H)
397. #2853	C₂×C₁₃₁	semidirect
398. #2788	C₂×C₁₃₁	semidirect
399. #2777	C₂×C₁₃₁	semidirect
400. #2764	C₂×C₁₃₁	semidirect
401. #2757	C₂×C₁₃₁	semidirect
402. #2755	C₂×C₁₃₁	semidirect
403. #2751	C₂×C₁₃₁	semidirect
404. #2724	C₂×C₁₃₁	semidirect
406. #2654	C₂×C₁₃₁	semidirect
408. #2606	C₂×C₁₃₁	semidirect
409. #2599	C₂×C₁₃₁	semidirect
410. #2592	C₂×C₁₃₁	semidirect
411. #2577	C₂×C₁₃₁	semidirect
412. #2470	C₂×C₁₃₁	semidirect
413. #2337	C₂×C₁₃₁	semidirect
414. #2320	C₂×C₁₃₁	semidirect
415. #2296	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2853×C₁₃₁	2
#2788×C₁₃₁	2
#2777×C₁₃₁	2
#2764×C₁₃₁	2
#2757×C₁₃₁	2
#2755×C₁₃₁	2
#2751×C₁₃₁	2
#2724×C₁₃₁	2
#2706×C₁₃₁	2
#2654×C₁₃₁	2
#2610×C₁₃₁	2
#2606×C₁₃₁	2
#2599×C₁₃₁	2
#2592×C₁₃₁	2
#2577×C₁₃₁	2
#2470×C₁₃₁	2
#2337×C₁₃₁	2
#2320×C₁₃₁	2
#2296×C₁₃₁	2
#36837	131

Subgroups — C131×#36837 #45722721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#36837 #45722721