Subgroups — C₁₃₁×#36813 #45722697

Order 33536.

1688 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2855×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#2799×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2751×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2743×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2740×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2713×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2700×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2694×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#2687×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2652×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2607×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#2589×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2583×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2475×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	#2432×C₁₃₁	C₂	1	1	yes	maximal, characteristic
16	#2406×C₁₃₁	C₂	1	1	yes	maximal, characteristic
17	#2332×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#2313×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#2297×C₁₃₁	C₂	1	1	yes	maximal, characteristic
20	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#125×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂×#123×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#123×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
31	#400×C₁₃₁	C₂²	1	2	yes	—
32	#400×C₁₃₁	C₂²	1	2	yes	—
33	#400×C₁₃₁	C₂²	1	2	yes	—
34	#400×C₁₃₁	C₂²	1	2	yes	—
35	#400×C₁₃₁	C₂²	1	2	yes	—
36	#399×C₁₃₁	C₂²	1	2	yes	—
37	#399×C₁₃₁	C₂²	1	2	yes	—
38	#398×C₁₃₁	C₂²	1	2	yes	—
39	#398×C₁₃₁	C₂²	1	2	yes	—
40	#398×C₁₃₁	C₂²	1	2	yes	—
41	#398×C₁₃₁	C₂²	1	2	yes	—
42	#397×C₁₃₁	C₂²	1	2	yes	—
43	#397×C₁₃₁	C₂²	1	2	yes	—
44	#397×C₁₃₁	C₂²	1	2	yes	—
45	#397×C₁₃₁	C₂²	1	2	yes	—
46	#396×C₁₃₁	C₂²	1	2	yes	—
47	#396×C₁₃₁	C₂²	1	2	yes	—
48	#395×C₁₃₁	C₂²	1	2	yes	—
49	#395×C₁₃₁	C₂²	1	2	yes	—
50	#394×C₁₃₁	C₂²	1	2	yes	—
51	#394×C₁₃₁	C₂²	1	2	yes	—
52	#394×C₁₃₁	C₂²	1	2	yes	—
53	#393×C₁₃₁	C₂²	1	2	yes	—
54	#393×C₁₃₁	C₂²	1	2	yes	—
55	#391×C₁₃₁	C₂²	1	2	yes	—
56	#391×C₁₃₁	C₂²	1	1	yes	characteristic
57	#391×C₁₃₁	C₂²	1	2	yes	—
58	#391×C₁₃₁	C₂²	1	2	yes	—
59	#391×C₁₃₁	C₂²	1	2	yes	—
60	#391×C₁₃₁	C₂²	1	2	yes	—
61	#391×C₁₃₁	C₂²	1	2	yes	—
62	#390×C₁₃₁	C₂²	1	1	yes	characteristic
63	#390×C₁₃₁	C₂²	1	2	yes	—
64	#389×C₁₃₁	C₂²	1	2	yes	—
65	#389×C₁₃₁	C₂²	1	2	yes	—
66	#389×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	#387×C₁₃₁	C₂²	1	2	yes	—
74	#387×C₁₃₁	C₂²	1	2	yes	—
75	#387×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	1	yes	characteristic
87	#386×C₁₃₁	C₂²	1	2	yes	—
88	#386×C₁₃₁	C₂²	1	1	yes	characteristic
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	#381×C₁₃₁	C₂²	1	2	yes	—
96	#381×C₁₃₁	C₂²	1	2	yes	—
97	#381×C₁₃₁	C₂²	1	2	yes	—
98	#381×C₁₃₁	C₂²	1	1	yes	characteristic
99	#380×C₁₃₁	C₂²	1	2	yes	—
100	#380×C₁₃₁	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
107	C₂×#41×C₁₃₁	—	2	4	no	—
108	C₂×#41×C₁₃₁	—	4	2	no	—
109	C₂×#41×C₁₃₁	—	4	2	no	—
110	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
112	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₁₃₁	—	4	2	no	—
123	#125×C₁₃₁	—	4	4	no	—
124	#124×C₁₃₁	—	4	2	no	—
125	#123×C₁₃₁	—	4	2	no	—
126	#123×C₁₃₁	—	4	2	no	—
127	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
128	C₂²⋊Q₈×C₁₃₁	—	4	4	no	—
129	#117×C₁₃₁	—	4	2	no	—
130	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
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	1	yes	characteristic
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×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	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊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	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃₁	—	4	2	no	—
169	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
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	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	2	yes	—
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	2	yes	—
205	#95×C₁₃₁	C₂³	1	2	yes	—
206	#95×C₁₃₁	C₂³	1	2	yes	—
207	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
208	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
209	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
210	#41×C₁₃₁	—	4	16	no	—
211	C₂×Q₈×C₁₃₁	—	2	2	no	—
212	C₂×Q₈×C₁₃₁	—	2	2	no	—
213	C₂×Q₈×C₁₃₁	—	2	2	no	—
214	C₂×Q₈×C₁₃₁	—	2	4	no	—
215	C₂×Q₈×C₁₃₁	—	4	1	no	—
216	C₂×Q₈×C₁₃₁	—	4	2	no	—
217	C₂×Q₈×C₁₃₁	—	4	1	no	—
218	C₂×Q₈×C₁₃₁	—	4	1	no	—
219	C₂×Q₈×C₁₃₁	—	4	2	no	—
220	C₂×D₄×C₁₃₁	—	2	2	no	—
221	C₂×D₄×C₁₃₁	—	2	2	no	—
222	C₂×D₄×C₁₃₁	—	2	2	no	—
223	C₂×D₄×C₁₃₁	—	2	2	no	—
224	C₂×D₄×C₁₃₁	—	2	2	no	—
225	C₂×D₄×C₁₃₁	—	2	2	no	—
226	C₂×D₄×C₁₃₁	—	4	1	no	—
227	C₂×D₄×C₁₃₁	—	4	1	no	—
228	C₂×D₄×C₁₃₁	—	4	1	no	—
229	C₂²×C₄×C₁₃₁	—	2	2	no	—
230	C₂²×C₄×C₁₃₁	—	2	2	no	—
231	C₂²×C₄×C₁₃₁	—	2	2	no	—
232	C₂²×C₄×C₁₃₁	—	2	2	no	—
233	C₂²×C₄×C₁₃₁	—	2	4	no	—
234	C₂²×C₄×C₁₃₁	—	2	2	no	—
235	C₂²×C₄×C₁₃₁	—	2	2	no	—
236	C₂²×C₄×C₁₃₁	—	2	4	no	—
237	C₂²×C₄×C₁₃₁	—	4	2	no	—
238	C₂²×C₄×C₁₃₁	—	4	2	no	—
239	C₂²×C₄×C₁₃₁	—	4	1	no	—
240	C₂²×C₄×C₁₃₁	—	4	1	no	—
241	C₂²×C₄×C₁₃₁	—	4	1	no	—
242	C₂²×C₄×C₁₃₁	—	4	1	no	—
243	C₂²×C₄×C₁₃₁	—	4	1	no	—
244	C₂²×C₄×C₁₃₁	—	4	1	no	—
245	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
246	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₁₃₁	—	2	4	no	—
263	C₄⋊C₄×C₁₃₁	—	2	4	no	—
264	C₄⋊C₄×C₁₃₁	—	2	2	no	—
265	C₄⋊C₄×C₁₃₁	—	2	4	no	—
266	C₄⋊C₄×C₁₃₁	—	2	4	no	—
267	C₄⋊C₄×C₁₃₁	—	2	4	no	—
268	C₄⋊C₄×C₁₃₁	—	2	4	no	—
269	C₄⋊C₄×C₁₃₁	—	2	4	no	—
270	C₄⋊C₄×C₁₃₁	—	4	2	no	—
271	C₄⋊C₄×C₁₃₁	—	4	2	no	—
272	C₄⋊C₄×C₁₃₁	—	4	2	no	—
273	C₄⋊C₄×C₁₃₁	—	4	2	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	2	no	—
279	C₄⋊C₄×C₁₃₁	—	4	2	no	—
280	C₄⋊C₄×C₁₃₁	—	4	2	no	—
281	C₄⋊C₄×C₁₃₁	—	4	2	no	—
282	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₁	—	2	4	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	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
290	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₁	—	4	2	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	1	no	—
296	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
298	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
299	C₄²×C₁₃₁	—	4	1	no	—
300	C₄²×C₁₃₁	—	4	2	no	—
301	C₄²×C₁₃₁	—	4	1	no	—
302	C₄²×C₁₃₁	—	4	2	no	—
303	C₄²×C₁₃₁	—	4	1	no	—
304	C₄²×C₁₃₁	—	4	1	no	—
305	C₄²×C₁₃₁	—	4	1	no	—
306	C₄²×C₁₃₁	—	4	2	no	—
307	C₄²×C₁₃₁	—	4	1	no	—
308	C₂³×C₁₃₁	—	2	1	no	—
309	C₂³×C₁₃₁	—	2	1	no	—
310	C₂³×C₁₃₁	—	2	1	no	—
311	C₂³×C₁₃₁	—	2	1	no	—
312	C₂³×C₁₃₁	—	2	2	no	—
313	C₂³×C₁₃₁	—	2	2	no	—
314	C₂³×C₁₃₁	—	2	2	no	—
315	C₂³×C₁₃₁	—	2	2	no	—
316	C₂³×C₁₃₁	—	2	1	no	—
317	C₂³×C₁₃₁	—	2	1	no	—
318	C₂³×C₁₃₁	—	2	1	no	—
319	C₂³×C₁₃₁	—	2	2	no	—
320	C₂³×C₁₃₁	—	2	2	no	—
321	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
322	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
323	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
324	Q₈×C₁₃₁	—	4	4	no	—
325	Q₈×C₁₃₁	—	8	2	no	—
326	Q₈×C₁₃₁	—	8	4	no	—
327	D₄×C₁₃₁	—	4	4	no	—
328	D₄×C₁₃₁	—	4	4	no	—
329	D₄×C₁₃₁	—	4	4	no	—
330	C₂×C₄×C₁₃₁	—	2	8	no	—
331	C₂×C₄×C₁₃₁	—	2	1	no	—
332	C₂×C₄×C₁₃₁	—	2	2	no	—
333	C₂×C₄×C₁₃₁	—	2	1	no	—
334	C₂×C₄×C₁₃₁	—	2	1	no	—
335	C₂×C₄×C₁₃₁	—	2	1	no	—
336	C₂×C₄×C₁₃₁	—	2	1	no	—
337	C₂×C₄×C₁₃₁	—	2	1	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	1	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	—	2	2	no	—
349	C₂×C₄×C₁₃₁	—	2	2	no	—
350	C₂×C₄×C₁₃₁	—	2	2	no	—
351	C₂×C₄×C₁₃₁	—	2	2	no	—
352	C₂×C₄×C₁₃₁	—	2	2	no	—
353	C₂×C₄×C₁₃₁	—	2	2	no	—
354	C₂×C₄×C₁₃₁	—	2	2	no	—
355	C₂×C₄×C₁₃₁	—	2	1	no	—
356	C₂×C₄×C₁₃₁	—	2	1	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	2	no	—
362	C₂×C₄×C₁₃₁	—	2	2	no	—
363	C₂×C₄×C₁₃₁	—	2	2	no	—
364	C₂×C₄×C₁₃₁	—	2	2	no	—
365	C₂×C₄×C₁₃₁	—	2	2	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	—	4	4	no	—
376	C₂×C₄×C₁₃₁	—	4	8	no	—
377	C₂×C₄×C₁₃₁	—	4	4	no	—
378	C₂×C₄×C₁₃₁	—	4	4	no	—
379	C₂×C₄×C₁₃₁	—	8	2	no	—
380	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
381	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
382	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	4	yes	—
384	C₂²×C₁₃₁	—	2	2	no	—
385	C₂²×C₁₃₁	—	2	2	no	—
386	C₂²×C₁₃₁	—	2	2	no	—
387	C₂²×C₁₃₁	—	2	2	no	—
388	C₂²×C₁₃₁	—	2	4	no	—
389	C₂²×C₁₃₁	—	4	1	no	—
390	C₂²×C₁₃₁	—	4	1	no	—
391	C₂²×C₁₃₁	—	4	2	no	—
392	C₂²×C₁₃₁	—	4	2	no	—
393	C₂²×C₁₃₁	—	4	2	no	—
394	C₂²×C₁₃₁	—	4	1	no	—
395	C₂²×C₁₃₁	—	4	1	no	—
396	C₂²×C₁₃₁	—	4	1	no	—
397	C₂²×C₁₃₁	—	4	2	no	—
398	C₂²×C₁₃₁	—	4	2	no	—
399	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
403	C₂²×C₁₃₁	#585	1	2	yes	—
404	C₄×C₁₃₁	—	2	2	no	—
405	C₄×C₁₃₁	—	2	2	no	—
406	C₄×C₁₃₁	—	2	2	no	—
407	C₄×C₁₃₁	—	2	4	no	—
408	C₄×C₁₃₁	—	4	2	no	—
409	C₄×C₁₃₁	—	4	2	no	—
410	C₄×C₁₃₁	—	4	1	no	—
411	C₄×C₁₃₁	—	4	2	no	—
412	C₄×C₁₃₁	—	4	2	no	—
413	C₄×C₁₃₁	—	4	2	no	—
414	C₄×C₁₃₁	—	4	2	no	—
415	C₄×C₁₃₁	—	4	2	no	—
416	C₄×C₁₃₁	—	4	2	no	—
417	C₄×C₁₃₁	—	4	2	no	—
418	C₄×C₁₃₁	—	4	2	no	—
419	C₄×C₁₃₁	—	4	2	no	—
420	C₂×C₁₃₁	—	4	2	no	—
421	C₂×C₁₃₁	—	4	2	no	—
422	C₂×C₁₃₁	—	8	1	no	—
423	C₂×C₁₃₁	#3455	1	1	yes	characteristic
424	C₂×C₁₃₁	#3490	1	1	yes	characteristic
425	C₂×C₁₃₁	#3509	1	1	yes	characteristic
426	C₂×C₁₃₁	#3535	1	2	yes	—
427	C₂×C₁₃₁	#3554	1	2	yes	—
428	#36813	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
429	C₁₃₁	#36813	1	1	yes	characteristic, direct product factor, Sylow
430	#2855	C₂×C₁₃₁	1	2	yes	complemented
431	#2799	C₂×C₁₃₁	1	2	yes	complemented
432	#2751	C₂×C₁₃₁	1	2	yes	complemented
433	#2743	C₂×C₁₃₁	1	2	yes	complemented
434	#2740	C₂×C₁₃₁	1	2	yes	complemented
435	#2713	C₂×C₁₃₁	1	2	yes	complemented
436	#2700	C₂×C₁₃₁	1	2	yes	complemented
437	#2694	C₂×C₁₃₁	1	2	yes	complemented
438	#2687	C₂×C₁₃₁	1	2	yes	complemented
439	#2652	C₂×C₁₃₁	1	2	yes	complemented
440	#2607	C₂×C₁₃₁	1	1	yes	characteristic, complemented
441	#2589	C₂×C₁₃₁	1	2	yes	complemented
442	#2583	C₂×C₁₃₁	1	1	yes	characteristic, complemented
443	#2475	C₂×C₁₃₁	1	2	yes	complemented
444	#2432	C₂×C₁₃₁	1	1	yes	characteristic
445	#2406	C₂×C₁₃₁	1	1	yes	characteristic
446	#2332	C₂×C₁₃₁	1	1	yes	characteristic, complemented
447	#2313	C₂×C₁₃₁	1	1	yes	characteristic, complemented
448	#2297	C₂×C₁₃₁	1	1	yes	characteristic
449	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
451	C₂×#125	C₂²×C₁₃₁	1	2	yes	—
452	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
453	C₂×#123	C₂²×C₁₃₁	1	1	yes	characteristic
454	C₂×#123	C₂²×C₁₃₁	1	1	yes	characteristic
455	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
457	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
458	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
459	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
460	#400	C₂²×C₁₃₁	1	2	yes	—
461	#400	C₂²×C₁₃₁	1	2	yes	—
462	#400	C₂²×C₁₃₁	1	2	yes	—
463	#400	C₂²×C₁₃₁	1	2	yes	—
464	#400	C₂²×C₁₃₁	1	2	yes	—
465	#399	C₂²×C₁₃₁	1	2	yes	—
466	#399	C₂²×C₁₃₁	1	2	yes	—
467	#398	C₂²×C₁₃₁	1	2	yes	—
468	#398	C₂²×C₁₃₁	1	2	yes	—
469	#398	C₂²×C₁₃₁	1	2	yes	—
470	#398	C₂²×C₁₃₁	1	2	yes	—
471	#397	C₂²×C₁₃₁	1	2	yes	—
472	#397	C₂²×C₁₃₁	1	2	yes	—
473	#397	C₂²×C₁₃₁	1	2	yes	—
474	#397	C₂²×C₁₃₁	1	2	yes	—
475	#396	C₂²×C₁₃₁	1	2	yes	—
476	#396	C₂²×C₁₃₁	1	2	yes	—
477	#395	C₂²×C₁₃₁	1	2	yes	—
478	#395	C₂²×C₁₃₁	1	2	yes	—
479	#394	C₂²×C₁₃₁	1	2	yes	—
480	#394	C₂²×C₁₃₁	1	2	yes	—
481	#394	C₂²×C₁₃₁	1	2	yes	—
482	#393	C₂²×C₁₃₁	1	2	yes	—
483	#393	C₂²×C₁₃₁	1	2	yes	—
484	#391	C₂²×C₁₃₁	1	2	yes	—
485	#391	C₂²×C₁₃₁	1	2	yes	—
486	#391	C₂²×C₁₃₁	1	2	yes	—
487	#391	C₂²×C₁₃₁	1	2	yes	—
488	#391	C₂²×C₁₃₁	1	2	yes	—
489	#391	C₂²×C₁₃₁	1	1	yes	characteristic
490	#391	C₂²×C₁₃₁	1	2	yes	—
491	#390	C₂²×C₁₃₁	1	1	yes	characteristic
492	#390	C₂²×C₁₃₁	1	2	yes	—
493	#389	C₂²×C₁₃₁	1	2	yes	—
494	#389	C₂²×C₁₃₁	1	2	yes	—
495	#389	C₂²×C₁₃₁	1	2	yes	—
496	#388	C₂²×C₁₃₁	1	2	yes	—
497	#388	C₂²×C₁₃₁	1	2	yes	—
498	#388	C₂²×C₁₃₁	1	2	yes	—
499	#388	C₂²×C₁₃₁	1	2	yes	—
500	#388	C₂²×C₁₃₁	1	2	yes	—
501	#388	C₂²×C₁₃₁	1	2	yes	—
502	#387	C₂²×C₁₃₁	1	2	yes	—
503	#387	C₂²×C₁₃₁	1	2	yes	—
504	#387	C₂²×C₁₃₁	1	2	yes	—
505	#387	C₂²×C₁₃₁	1	2	yes	—
506	#387	C₂²×C₁₃₁	1	2	yes	—
507	#387	C₂²×C₁₃₁	1	2	yes	—
508	#387	C₂²×C₁₃₁	1	2	yes	—
509	#387	C₂²×C₁₃₁	1	2	yes	—
510	#387	C₂²×C₁₃₁	1	2	yes	—
511	#387	C₂²×C₁₃₁	1	2	yes	—
512	#387	C₂²×C₁₃₁	1	2	yes	—
513	#387	C₂²×C₁₃₁	1	2	yes	—
514	#386	C₂²×C₁₃₁	1	1	yes	characteristic
515	#386	C₂²×C₁₃₁	1	1	yes	characteristic
516	#386	C₂²×C₁₃₁	1	2	yes	—
517	#386	C₂²×C₁₃₁	1	2	yes	—
518	#385	C₂²×C₁₃₁	1	2	yes	—
519	#385	C₂²×C₁₃₁	1	2	yes	—
520	#385	C₂²×C₁₃₁	1	2	yes	—
521	#385	C₂²×C₁₃₁	1	2	yes	—
522	#385	C₂²×C₁₃₁	1	2	yes	—
523	#385	C₂²×C₁₃₁	1	2	yes	—
524	#381	C₂²×C₁₃₁	1	2	yes	—
525	#381	C₂²×C₁₃₁	1	1	yes	characteristic
526	#381	C₂²×C₁₃₁	1	2	yes	—
527	#381	C₂²×C₁₃₁	1	2	yes	—
528	#380	C₂²×C₁₃₁	1	2	yes	—
529	#380	C₂²×C₁₃₁	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
532	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
533	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
534	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
535	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
536	C₂×#41	—	2	4	no	—
537	C₂×#41	—	4	2	no	—
538	C₂×#41	—	4	2	no	—
539	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
540	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
542	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
547	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
551	C₄⋊Q₈	—	4	2	no	—
552	#125	—	4	4	no	—
553	#124	—	4	2	no	—
554	#123	—	4	2	no	—
555	#123	—	4	2	no	—
556	C₂²⋊Q₈	—	2	4	no	—
557	C₂²⋊Q₈	—	4	4	no	—
558	#117	—	4	2	no	—
559	C₂×C₄⋊C₄	—	2	4	no	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
597	C₂×C₄²	—	4	2	no	—
598	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
602	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
606	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
607	#95	C₂³×C₁₃₁	1	2	yes	—
608	#95	C₂³×C₁₃₁	1	2	yes	—
609	#95	C₂³×C₁₃₁	1	2	yes	—
610	#95	C₂³×C₁₃₁	1	2	yes	—
611	#95	C₂³×C₁₃₁	1	2	yes	—
612	#95	C₂³×C₁₃₁	1	2	yes	—
613	#95	C₂³×C₁₃₁	1	2	yes	—
614	#95	C₂³×C₁₃₁	1	2	yes	—
615	#95	C₂³×C₁₃₁	1	2	yes	—
616	#95	C₂³×C₁₃₁	1	2	yes	—
617	#95	C₂³×C₁₃₁	1	2	yes	—
618	#95	C₂³×C₁₃₁	1	2	yes	—
619	#95	C₂³×C₁₃₁	1	2	yes	—
620	#95	C₂³×C₁₃₁	1	2	yes	—
621	#95	C₂³×C₁₃₁	1	2	yes	—
622	#95	C₂³×C₁₃₁	1	2	yes	—
623	#95	C₂³×C₁₃₁	1	2	yes	—
624	#95	C₂³×C₁₃₁	1	2	yes	—
625	#95	C₂³×C₁₃₁	1	2	yes	—
626	#95	C₂³×C₁₃₁	1	2	yes	—
627	#95	C₂³×C₁₃₁	1	2	yes	—
628	#95	C₂³×C₁₃₁	1	2	yes	—
629	#95	C₂³×C₁₃₁	1	2	yes	—
630	#95	C₂³×C₁₃₁	1	2	yes	—
631	#95	C₂³×C₁₃₁	1	2	yes	—
632	#95	C₂³×C₁₃₁	1	2	yes	—
633	#95	C₂³×C₁₃₁	1	2	yes	—
634	#95	C₂³×C₁₃₁	1	2	yes	—
635	#95	C₂³×C₁₃₁	1	2	yes	—
636	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
637	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
638	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
639	#41	—	4	16	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	4	1	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂×Q₈	—	4	1	no	—
647	C₂×Q₈	—	4	1	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	4	1	no	—
656	C₂×D₄	—	4	1	no	—
657	C₂×D₄	—	4	1	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
675	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	1	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	1	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₄²	—	4	1	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	1	no	—
731	C₄²	—	4	2	no	—
732	C₄²	—	4	1	no	—
733	C₄²	—	4	1	no	—
734	C₄²	—	4	1	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
751	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
752	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
753	Q₈	—	4	4	no	—
754	Q₈	—	8	4	no	—
755	Q₈	—	8	2	no	—
756	D₄	—	4	4	no	—
757	D₄	—	4	4	no	—
758	D₄	—	4	4	no	—
759	C₂×C₄	—	2	8	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
810	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
811	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
812	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	4	yes	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
829	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
830	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
831	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	2	yes	—
832	C₂²	#585×C₁₃₁	1	2	yes	—
833	C₄	—	2	4	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	2	no	—
851	C₂	—	8	1	no	—
852	C₂	#3455×C₁₃₁	1	1	yes	characteristic
853	C₂	#3490×C₁₃₁	1	1	yes	characteristic
854	C₂	#3509×C₁₃₁	1	1	yes	characteristic
855	C₂	#3535×C₁₃₁	1	2	yes	—
856	C₂	#3554×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂²×#41×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. #2855×C₁₃₁	C₂	semidirect
2. #2799×C₁₃₁	C₂	semidirect
3. #2751×C₁₃₁	C₂	semidirect
4. #2743×C₁₃₁	C₂	semidirect
5. #2740×C₁₃₁	C₂	semidirect
6. #2713×C₁₃₁	C₂	semidirect
7. #2700×C₁₃₁	C₂	semidirect
8. #2694×C₁₃₁	C₂	semidirect
9. #2687×C₁₃₁	C₂	semidirect
10. #2652×C₁₃₁	C₂	semidirect
11. #2607×C₁₃₁	C₂	semidirect
12. #2589×C₁₃₁	C₂	semidirect
13. #2583×C₁₃₁	C₂	semidirect
14. #2475×C₁₃₁	C₂	semidirect
17. #2332×C₁₃₁	C₂	semidirect
18. #2313×C₁₃₁	C₂	semidirect
428. #36813	C₁₃₁	direct (N × H)
429. C₁₃₁	#36813	direct (N × H)
430. #2855	C₂×C₁₃₁	semidirect
431. #2799	C₂×C₁₃₁	semidirect
432. #2751	C₂×C₁₃₁	semidirect
433. #2743	C₂×C₁₃₁	semidirect
434. #2740	C₂×C₁₃₁	semidirect
435. #2713	C₂×C₁₃₁	semidirect
436. #2700	C₂×C₁₃₁	semidirect
437. #2694	C₂×C₁₃₁	semidirect
438. #2687	C₂×C₁₃₁	semidirect
439. #2652	C₂×C₁₃₁	semidirect
440. #2607	C₂×C₁₃₁	semidirect
441. #2589	C₂×C₁₃₁	semidirect
442. #2583	C₂×C₁₃₁	semidirect
443. #2475	C₂×C₁₃₁	semidirect
446. #2332	C₂×C₁₃₁	semidirect
447. #2313	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2855×C₁₃₁	2
#2799×C₁₃₁	2
#2751×C₁₃₁	2
#2743×C₁₃₁	2
#2740×C₁₃₁	2
#2713×C₁₃₁	2
#2700×C₁₃₁	2
#2694×C₁₃₁	2
#2687×C₁₃₁	2
#2652×C₁₃₁	2
#2607×C₁₃₁	2
#2589×C₁₃₁	2
#2583×C₁₃₁	2
#2475×C₁₃₁	2
#2432×C₁₃₁	2
#2406×C₁₃₁	2
#2332×C₁₃₁	2
#2313×C₁₃₁	2
#2297×C₁₃₁	2
#36813	131

Subgroups — C131×#36813 #45722697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#36813 #45722697