Subgroups — C₁₃₁×#34468 #45720352

Order 33536.

3220 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2377×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2375×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2364×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2358×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2358×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2353×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	D₄×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#2333×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2328×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#2325×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2321×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#2321×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	#2318×C₁₃₁	C₂	1	2	yes	maximal, complemented
17	#2308×C₁₃₁	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#386×C₁₃₁	C₂	1	2	yes	maximal, complemented
20	C₂³×D₄×C₁₃₁	C₂²	1	2	yes	—
21	C₂³×D₄×C₁₃₁	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
23	D₄²×C₁₃₁	C₄	1	16	yes	complemented
24	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#120×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#120×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
42	#390×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
43	#390×C₁₃₁	C₂²	1	2	yes	complemented
44	#390×C₁₃₁	C₂²	1	2	yes	complemented
45	#390×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
46	#390×C₁₃₁	C₂²	1	2	yes	complemented
47	#390×C₁₃₁	C₂²	1	2	yes	complemented
48	#388×C₁₃₁	C₂²	1	2	yes	complemented
49	#388×C₁₃₁	C₂²	1	2	yes	complemented
50	#388×C₁₃₁	C₂²	1	2	yes	complemented
51	#388×C₁₃₁	C₂²	1	2	yes	complemented
52	#388×C₁₃₁	C₂²	1	2	yes	complemented
53	#388×C₁₃₁	C₂²	1	2	yes	complemented
54	#388×C₁₃₁	C₂²	1	2	yes	complemented
55	#388×C₁₃₁	C₂²	1	2	yes	complemented
56	#387×C₁₃₁	C₂²	1	2	yes	complemented
57	#387×C₁₃₁	C₂²	1	2	yes	complemented
58	#387×C₁₃₁	C₂²	1	2	yes	complemented
59	#387×C₁₃₁	C₂²	1	2	yes	complemented
60	#386×C₁₃₁	C₂²	1	2	yes	—
61	#386×C₁₃₁	C₂²	1	2	yes	—
62	#386×C₁₃₁	C₂²	1	2	yes	—
63	#386×C₁₃₁	C₂²	1	2	yes	—
64	#386×C₁₃₁	C₂²	1	2	yes	complemented
65	#386×C₁₃₁	C₂²	1	2	yes	complemented
66	#386×C₁₃₁	C₂²	1	2	yes	complemented
67	#386×C₁₃₁	C₂²	1	2	yes	complemented
68	#386×C₁₃₁	C₂²	1	2	yes	complemented
69	#386×C₁₃₁	C₂²	1	2	yes	complemented
70	#386×C₁₃₁	C₂²	1	2	yes	complemented
71	#386×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
72	#386×C₁₃₁	C₂²	1	2	yes	complemented
73	#386×C₁₃₁	C₂²	1	2	yes	complemented
74	#386×C₁₃₁	C₂²	1	2	yes	complemented
75	#386×C₁₃₁	C₂²	1	2	yes	complemented
76	#386×C₁₃₁	C₂²	1	2	yes	complemented
77	#386×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
78	#386×C₁₃₁	C₂²	1	2	yes	complemented
79	#386×C₁₃₁	C₂²	1	2	yes	complemented
80	#386×C₁₃₁	C₂²	1	2	yes	complemented
81	#386×C₁₃₁	C₂²	1	2	yes	complemented
82	#386×C₁₃₁	C₂²	1	2	yes	complemented
83	#385×C₁₃₁	C₂²	1	2	yes	complemented
84	#385×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
85	#385×C₁₃₁	C₂²	1	2	yes	complemented
86	#385×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
87	#385×C₁₃₁	C₂²	1	2	yes	complemented
88	#383×C₁₃₁	C₂²	1	2	yes	complemented
89	#382×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
90	#381×C₁₃₁	C₂²	1	2	yes	complemented
91	#381×C₁₃₁	C₂²	1	2	yes	complemented
92	#380×C₁₃₁	C₂²	1	2	yes	complemented
93	#380×C₁₃₁	C₂²	1	2	yes	complemented
94	#379×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
95	#379×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
96	#379×C₁₃₁	C₂²	1	2	yes	complemented
97	#379×C₁₃₁	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
105	#376×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
107	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
108	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
109	C₂⁵×C₁₃₁	C₂³	1	2	yes	—
110	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₁	—	4	4	no	—
112	C₂²×D₄×C₁₃₁	—	4	4	no	—
113	C₂²×D₄×C₁₃₁	—	4	4	no	—
114	C₂²×D₄×C₁₃₁	—	4	4	no	—
115	C₂²×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
116	C₂²×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
117	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
120	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃₁	—	4	2	no	—
127	C₂³×C₄×C₁₃₁	—	4	4	no	—
128	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
140	#127×C₁₃₁	C₂×C₄	1	8	yes	complemented
141	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
142	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
143	#120×C₁₃₁	C₂×C₄	1	8	yes	complemented
144	#120×C₁₃₁	C₂×C₄	1	16	yes	complemented
145	#120×C₁₃₁	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₁₃₁	—	4	2	no	—
147	C₄×D₄×C₁₃₁	—	4	2	no	—
148	C₄×D₄×C₁₃₁	—	4	4	no	—
149	C₄×D₄×C₁₃₁	—	4	4	no	—
150	C₄×D₄×C₁₃₁	—	4	4	no	—
151	C₄×D₄×C₁₃₁	—	4	4	no	—
152	C₄×D₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
153	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
161	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
162	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
163	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
164	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
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	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
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	#95×C₁₃₁	C₂³	1	2	yes	—
208	#95×C₁₃₁	C₂³	1	2	yes	—
209	#95×C₁₃₁	C₂³	1	2	yes	—
210	#95×C₁₃₁	C₂³	1	2	yes	—
211	#95×C₁₃₁	C₂³	1	2	yes	—
212	#95×C₁₃₁	C₂³	1	2	yes	—
213	#95×C₁₃₁	C₂³	1	2	yes	—
214	#95×C₁₃₁	C₂³	1	2	yes	—
215	#95×C₁₃₁	C₂³	1	2	yes	—
216	#95×C₁₃₁	C₂³	1	2	yes	—
217	#95×C₁₃₁	C₂³	1	2	yes	—
218	#95×C₁₃₁	C₂³	1	2	yes	—
219	#95×C₁₃₁	C₂³	1	2	yes	—
220	#95×C₁₃₁	C₂³	1	2	yes	—
221	C₂⁴×C₁₃₁	—	2	4	no	—
222	C₂⁴×C₁₃₁	—	2	4	no	—
223	C₂⁴×C₁₃₁	—	2	4	no	—
224	C₂⁴×C₁₃₁	—	2	4	no	—
225	C₂⁴×C₁₃₁	—	4	1	no	—
226	C₂⁴×C₁₃₁	—	4	1	no	—
227	C₂⁴×C₁₃₁	—	4	2	no	—
228	C₂⁴×C₁₃₁	—	4	1	no	—
229	C₂⁴×C₁₃₁	—	4	2	no	—
230	C₂⁴×C₁₃₁	—	4	2	no	—
231	C₂⁴×C₁₃₁	—	4	2	no	—
232	C₂⁴×C₁₃₁	—	4	2	no	—
233	C₂⁴×C₁₃₁	—	4	2	no	—
234	C₂⁴×C₁₃₁	—	4	1	no	—
235	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
236	C₂⁴×C₁₃₁	C₂²×C₄	1	8	yes	—
237	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	complemented
238	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
239	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
240	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
243	C₂×D₄×C₁₃₁	—	2	4	no	—
244	C₂×D₄×C₁₃₁	—	2	4	no	—
245	C₂×D₄×C₁₃₁	—	2	4	no	—
246	C₂×D₄×C₁₃₁	—	2	4	no	—
247	C₂×D₄×C₁₃₁	—	2	4	no	—
248	C₂×D₄×C₁₃₁	—	2	4	no	—
249	C₂×D₄×C₁₃₁	—	4	1	no	—
250	C₂×D₄×C₁₃₁	—	4	1	no	—
251	C₂×D₄×C₁₃₁	—	4	2	no	—
252	C₂×D₄×C₁₃₁	—	4	2	no	—
253	C₂×D₄×C₁₃₁	—	4	2	no	—
254	C₂×D₄×C₁₃₁	—	4	2	no	—
255	C₂×D₄×C₁₃₁	—	4	2	no	—
256	C₂×D₄×C₁₃₁	—	4	2	no	—
257	C₂×D₄×C₁₃₁	—	4	2	no	—
258	C₂×D₄×C₁₃₁	—	4	2	no	—
259	C₂×D₄×C₁₃₁	—	4	1	no	—
260	C₂×D₄×C₁₃₁	—	4	1	no	—
261	C₂×D₄×C₁₃₁	—	4	32	no	—
262	C₂×D₄×C₁₃₁	—	4	32	no	—
263	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
265	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
266	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
268	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
269	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	complemented
270	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
271	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
272	C₂²×C₄×C₁₃₁	—	2	4	no	—
273	C₂²×C₄×C₁₃₁	—	2	4	no	—
274	C₂²×C₄×C₁₃₁	—	2	4	no	—
275	C₂²×C₄×C₁₃₁	—	2	4	no	—
276	C₂²×C₄×C₁₃₁	—	2	4	no	—
277	C₂²×C₄×C₁₃₁	—	2	2	no	—
278	C₂²×C₄×C₁₃₁	—	2	2	no	—
279	C₂²×C₄×C₁₃₁	—	4	2	no	—
280	C₂²×C₄×C₁₃₁	—	4	2	no	—
281	C₂²×C₄×C₁₃₁	—	4	1	no	—
282	C₂²×C₄×C₁₃₁	—	4	2	no	—
283	C₂²×C₄×C₁₃₁	—	4	2	no	—
284	C₂²×C₄×C₁₃₁	—	4	2	no	—
285	C₂²×C₄×C₁₃₁	—	4	2	no	—
286	C₂²×C₄×C₁₃₁	—	4	2	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	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	2	no	—
299	C₂²×C₄×C₁₃₁	—	4	2	no	—
300	C₂²×C₄×C₁₃₁	—	4	2	no	—
301	C₂²×C₄×C₁₃₁	—	4	2	no	—
302	C₂²×C₄×C₁₃₁	—	4	16	no	—
303	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
304	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
305	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₁₃₁	—	4	1	no	—
320	C₄⋊C₄×C₁₃₁	—	4	1	no	—
321	C₄⋊C₄×C₁₃₁	—	4	2	no	—
322	C₄⋊C₄×C₁₃₁	—	4	2	no	—
323	C₄⋊C₄×C₁₃₁	—	4	2	no	—
324	C₄⋊C₄×C₁₃₁	—	4	2	no	—
325	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
326	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
329	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
330	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
331	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
332	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
333	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
334	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
335	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
336	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
338	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
339	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
340	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
341	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
342	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
343	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
344	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
345	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
346	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
347	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
348	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
349	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
350	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
351	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
352	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
354	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
355	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	complemented
356	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	complemented
357	C₄²×C₁₃₁	—	2	2	no	—
358	C₄²×C₁₃₁	—	4	1	no	—
359	C₄²×C₁₃₁	—	4	2	no	—
360	C₄²×C₁₃₁	—	4	2	no	—
361	C₄²×C₁₃₁	—	4	2	no	—
362	C₄²×C₁₃₁	—	4	2	no	—
363	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	complemented
364	C₂³×C₁₃₁	—	2	2	no	—
365	C₂³×C₁₃₁	—	2	2	no	—
366	C₂³×C₁₃₁	—	2	2	no	—
367	C₂³×C₁₃₁	—	2	2	no	—
368	C₂³×C₁₃₁	—	2	16	no	—
369	C₂³×C₁₃₁	—	2	2	no	—
370	C₂³×C₁₃₁	—	2	2	no	—
371	C₂³×C₁₃₁	—	2	2	no	—
372	C₂³×C₁₃₁	—	2	2	no	—
373	C₂³×C₁₃₁	—	2	2	no	—
374	C₂³×C₁₃₁	—	2	2	no	—
375	C₂³×C₁₃₁	—	2	1	no	—
376	C₂³×C₁₃₁	—	2	1	no	—
377	C₂³×C₁₃₁	—	2	2	no	—
378	C₂³×C₁₃₁	—	2	2	no	—
379	C₂³×C₁₃₁	—	2	2	no	—
380	C₂³×C₁₃₁	—	2	2	no	—
381	C₂³×C₁₃₁	—	2	2	no	—
382	C₂³×C₁₃₁	—	2	2	no	—
383	C₂³×C₁₃₁	—	2	2	no	—
384	C₂³×C₁₃₁	—	2	2	no	—
385	C₂³×C₁₃₁	—	2	1	no	—
386	C₂³×C₁₃₁	—	2	1	no	—
387	C₂³×C₁₃₁	—	2	2	no	—
388	C₂³×C₁₃₁	—	2	2	no	—
389	C₂³×C₁₃₁	—	2	16	no	—
390	C₂³×C₁₃₁	—	4	4	no	—
391	C₂³×C₁₃₁	—	4	8	no	—
392	C₂³×C₁₃₁	—	4	8	no	—
393	C₂³×C₁₃₁	—	4	8	no	—
394	C₂³×C₁₃₁	—	4	4	no	—
395	C₂³×C₁₃₁	—	4	4	no	—
396	C₂³×C₁₃₁	—	4	8	no	—
397	C₂³×C₁₃₁	—	4	4	no	—
398	C₂³×C₁₃₁	—	8	4	no	—
399	C₂³×C₁₃₁	—	8	4	no	—
400	C₂³×C₁₃₁	—	8	4	no	—
401	C₂³×C₁₃₁	—	8	4	no	—
402	C₂³×C₁₃₁	—	8	2	no	—
403	C₂³×C₁₃₁	—	8	4	no	—
404	C₂³×C₁₃₁	—	8	2	no	—
405	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
406	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
407	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
408	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
409	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
410	C₂³×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
411	C₂³×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
412	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
413	D₄×C₁₃₁	—	2	16	no	—
414	D₄×C₁₃₁	—	2	16	no	—
415	D₄×C₁₃₁	—	2	16	no	—
416	D₄×C₁₃₁	—	4	8	no	—
417	D₄×C₁₃₁	—	4	8	no	—
418	D₄×C₁₃₁	—	4	8	no	—
419	D₄×C₁₃₁	—	4	8	no	—
420	D₄×C₁₃₁	—	4	4	no	—
421	D₄×C₁₃₁	—	4	4	no	—
422	C₂×C₄×C₁₃₁	—	2	1	no	—
423	C₂×C₄×C₁₃₁	—	2	2	no	—
424	C₂×C₄×C₁₃₁	—	2	2	no	—
425	C₂×C₄×C₁₃₁	—	2	2	no	—
426	C₂×C₄×C₁₃₁	—	2	2	no	—
427	C₂×C₄×C₁₃₁	—	2	2	no	—
428	C₂×C₄×C₁₃₁	—	2	2	no	—
429	C₂×C₄×C₁₃₁	—	2	2	no	—
430	C₂×C₄×C₁₃₁	—	2	1	no	—
431	C₂×C₄×C₁₃₁	—	2	1	no	—
432	C₂×C₄×C₁₃₁	—	2	2	no	—
433	C₂×C₄×C₁₃₁	—	2	2	no	—
434	C₂×C₄×C₁₃₁	—	2	2	no	—
435	C₂×C₄×C₁₃₁	—	2	2	no	—
436	C₂×C₄×C₁₃₁	—	2	2	no	—
437	C₂×C₄×C₁₃₁	—	2	2	no	—
438	C₂×C₄×C₁₃₁	—	2	2	no	—
439	C₂×C₄×C₁₃₁	—	2	2	no	—
440	C₂×C₄×C₁₃₁	—	2	2	no	—
441	C₂×C₄×C₁₃₁	—	2	2	no	—
442	C₂×C₄×C₁₃₁	—	2	2	no	—
443	C₂×C₄×C₁₃₁	—	2	2	no	—
444	C₂×C₄×C₁₃₁	—	2	2	no	—
445	C₂×C₄×C₁₃₁	—	2	1	no	—
446	C₂×C₄×C₁₃₁	—	2	2	no	—
447	C₂×C₄×C₁₃₁	—	2	2	no	—
448	C₂×C₄×C₁₃₁	—	2	2	no	—
449	C₂×C₄×C₁₃₁	—	2	2	no	—
450	C₂×C₄×C₁₃₁	—	2	2	no	—
451	C₂×C₄×C₁₃₁	—	2	1	no	—
452	C₂×C₄×C₁₃₁	—	2	2	no	—
453	C₂×C₄×C₁₃₁	—	2	2	no	—
454	C₂×C₄×C₁₃₁	—	2	2	no	—
455	C₂×C₄×C₁₃₁	—	4	8	no	—
456	C₂×C₄×C₁₃₁	—	4	8	no	—
457	C₂×C₄×C₁₃₁	—	4	8	no	—
458	C₂×C₄×C₁₃₁	—	4	4	no	—
459	C₂×C₄×C₁₃₁	—	4	8	no	—
460	C₂×C₄×C₁₃₁	—	4	4	no	—
461	C₂×C₄×C₁₃₁	—	8	2	no	—
462	C₂×C₄×C₁₃₁	—	8	4	no	—
463	C₂×C₄×C₁₃₁	—	8	4	no	—
464	C₂×C₄×C₁₃₁	—	8	4	no	—
465	C₂×C₄×C₁₃₁	—	8	4	no	—
466	C₂×C₄×C₁₃₁	—	8	2	no	—
467	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
469	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
470	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
471	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
472	C₂²×C₁₃₁	—	2	4	no	—
473	C₂²×C₁₃₁	—	2	4	no	—
474	C₂²×C₁₃₁	—	2	4	no	—
475	C₂²×C₁₃₁	—	2	4	no	—
476	C₂²×C₁₃₁	—	2	4	no	—
477	C₂²×C₁₃₁	—	2	4	no	—
478	C₂²×C₁₃₁	—	2	4	no	—
479	C₂²×C₁₃₁	—	2	4	no	—
480	C₂²×C₁₃₁	—	2	4	no	—
481	C₂²×C₁₃₁	—	2	4	no	—
482	C₂²×C₁₃₁	—	2	4	no	—
483	C₂²×C₁₃₁	—	2	4	no	—
484	C₂²×C₁₃₁	—	2	2	no	—
485	C₂²×C₁₃₁	—	2	2	no	—
486	C₂²×C₁₃₁	—	2	4	no	—
487	C₂²×C₁₃₁	—	2	4	no	—
488	C₂²×C₁₃₁	—	4	16	no	—
489	C₂²×C₁₃₁	—	4	1	no	—
490	C₂²×C₁₃₁	—	4	1	no	—
491	C₂²×C₁₃₁	—	4	2	no	—
492	C₂²×C₁₃₁	—	4	2	no	—
493	C₂²×C₁₃₁	—	4	2	no	—
494	C₂²×C₁₃₁	—	4	2	no	—
495	C₂²×C₁₃₁	—	4	2	no	—
496	C₂²×C₁₃₁	—	4	2	no	—
497	C₂²×C₁₃₁	—	4	2	no	—
498	C₂²×C₁₃₁	—	4	2	no	—
499	C₂²×C₁₃₁	—	4	2	no	—
500	C₂²×C₁₃₁	—	4	1	no	—
501	C₂²×C₁₃₁	—	4	1	no	—
502	C₂²×C₁₃₁	—	4	2	no	—
503	C₂²×C₁₃₁	—	8	16	no	—
504	C₂²×C₁₃₁	—	8	8	no	—
505	C₂²×C₁₃₁	#518	1	8	yes	—
506	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
507	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
508	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
509	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂²×C₁₃₁	#585	1	1	yes	characteristic
511	C₄×C₁₃₁	—	2	4	no	—
512	C₄×C₁₃₁	—	2	4	no	—
513	C₄×C₁₃₁	—	2	4	no	—
514	C₄×C₁₃₁	—	2	2	no	—
515	C₄×C₁₃₁	—	2	2	no	—
516	C₄×C₁₃₁	—	4	2	no	—
517	C₄×C₁₃₁	—	4	1	no	—
518	C₄×C₁₃₁	—	4	1	no	—
519	C₄×C₁₃₁	—	4	2	no	—
520	C₄×C₁₃₁	—	4	2	no	—
521	C₄×C₁₃₁	—	4	2	no	—
522	C₄×C₁₃₁	—	4	1	no	—
523	C₄×C₁₃₁	—	4	2	no	—
524	C₄×C₁₃₁	—	4	2	no	—
525	C₂×C₁₃₁	—	2	8	no	—
526	C₂×C₁₃₁	—	4	2	no	—
527	C₂×C₁₃₁	—	4	2	no	—
528	C₂×C₁₃₁	—	4	4	no	—
529	C₂×C₁₃₁	—	4	4	no	—
530	C₂×C₁₃₁	C₂×#518	1	2	yes	—
531	C₂×C₁₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₁₃₁	#3532	1	1	yes	characteristic
533	C₂×C₁₃₁	#3534	1	2	yes	—
534	C₂×C₁₃₁	#3537	1	1	yes	characteristic
535	#34468	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
536	C₁₃₁	#34468	1	1	yes	characteristic, direct product factor, Sylow
537	C₂×D₄²	C₂×C₁₃₁	1	1	yes	characteristic
538	#2380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
539	#2377	C₂×C₁₃₁	1	2	yes	complemented
540	#2375	C₂×C₁₃₁	1	1	yes	characteristic, complemented
541	#2364	C₂×C₁₃₁	1	2	yes	complemented
542	#2358	C₂×C₁₃₁	1	2	yes	complemented
543	#2358	C₂×C₁₃₁	1	1	yes	characteristic, complemented
544	#2353	C₂×C₁₃₁	1	2	yes	complemented
545	D₄×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
546	D₄×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
547	#2333	C₂×C₁₃₁	1	2	yes	complemented
548	#2328	C₂×C₁₃₁	1	1	yes	characteristic, complemented
549	#2325	C₂×C₁₃₁	1	2	yes	complemented
550	#2321	C₂×C₁₃₁	1	2	yes	complemented
551	#2321	C₂×C₁₃₁	1	1	yes	characteristic, complemented
552	#2318	C₂×C₁₃₁	1	2	yes	complemented
553	#2308	C₂×C₁₃₁	1	2	yes	complemented
554	C₄×#120	C₂×C₁₃₁	1	1	yes	characteristic, complemented
555	C₂×#386	C₂×C₁₃₁	1	2	yes	complemented
556	C₂³×D₄	C₂²×C₁₃₁	1	2	yes	—
557	C₂³×D₄	C₂²×C₁₃₁	1	2	yes	—
558	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
559	D₄²	C₄×C₁₃₁	1	16	yes	complemented
560	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
561	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
562	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
563	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
564	C₂×#120	C₂²×C₁₃₁	1	1	yes	characteristic
565	C₂×#120	C₂²×C₁₃₁	1	1	yes	characteristic
566	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
567	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
568	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	complemented
569	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	complemented
570	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	complemented
571	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
572	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	complemented
573	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
574	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
575	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
576	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
577	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
578	#390	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
579	#390	C₂²×C₁₃₁	1	2	yes	complemented
580	#390	C₂²×C₁₃₁	1	2	yes	complemented
581	#390	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
582	#390	C₂²×C₁₃₁	1	2	yes	complemented
583	#390	C₂²×C₁₃₁	1	2	yes	complemented
584	#388	C₂²×C₁₃₁	1	2	yes	complemented
585	#388	C₂²×C₁₃₁	1	2	yes	complemented
586	#388	C₂²×C₁₃₁	1	2	yes	complemented
587	#388	C₂²×C₁₃₁	1	2	yes	complemented
588	#388	C₂²×C₁₃₁	1	2	yes	complemented
589	#388	C₂²×C₁₃₁	1	2	yes	complemented
590	#388	C₂²×C₁₃₁	1	2	yes	complemented
591	#388	C₂²×C₁₃₁	1	2	yes	complemented
592	#387	C₂²×C₁₃₁	1	2	yes	complemented
593	#387	C₂²×C₁₃₁	1	2	yes	complemented
594	#387	C₂²×C₁₃₁	1	2	yes	complemented
595	#387	C₂²×C₁₃₁	1	2	yes	complemented
596	#386	C₂²×C₁₃₁	1	2	yes	—
597	#386	C₂²×C₁₃₁	1	2	yes	—
598	#386	C₂²×C₁₃₁	1	2	yes	—
599	#386	C₂²×C₁₃₁	1	2	yes	—
600	#386	C₂²×C₁₃₁	1	2	yes	complemented
601	#386	C₂²×C₁₃₁	1	2	yes	complemented
602	#386	C₂²×C₁₃₁	1	2	yes	complemented
603	#386	C₂²×C₁₃₁	1	2	yes	complemented
604	#386	C₂²×C₁₃₁	1	2	yes	complemented
605	#386	C₂²×C₁₃₁	1	2	yes	complemented
606	#386	C₂²×C₁₃₁	1	2	yes	complemented
607	#386	C₂²×C₁₃₁	1	2	yes	complemented
608	#386	C₂²×C₁₃₁	1	2	yes	complemented
609	#386	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
610	#386	C₂²×C₁₃₁	1	2	yes	complemented
611	#386	C₂²×C₁₃₁	1	2	yes	complemented
612	#386	C₂²×C₁₃₁	1	2	yes	complemented
613	#386	C₂²×C₁₃₁	1	2	yes	complemented
614	#386	C₂²×C₁₃₁	1	2	yes	complemented
615	#386	C₂²×C₁₃₁	1	2	yes	complemented
616	#386	C₂²×C₁₃₁	1	2	yes	complemented
617	#386	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
618	#386	C₂²×C₁₃₁	1	2	yes	complemented
619	#385	C₂²×C₁₃₁	1	2	yes	complemented
620	#385	C₂²×C₁₃₁	1	2	yes	complemented
621	#385	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
622	#385	C₂²×C₁₃₁	1	2	yes	complemented
623	#385	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
624	#383	C₂²×C₁₃₁	1	2	yes	complemented
625	#382	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
626	#381	C₂²×C₁₃₁	1	2	yes	complemented
627	#381	C₂²×C₁₃₁	1	2	yes	complemented
628	#380	C₂²×C₁₃₁	1	2	yes	complemented
629	#380	C₂²×C₁₃₁	1	2	yes	complemented
630	#379	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
631	#379	C₂²×C₁₃₁	1	2	yes	complemented
632	#379	C₂²×C₁₃₁	1	2	yes	complemented
633	#379	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
634	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
635	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
636	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
637	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
638	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
639	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
640	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
641	#376	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
642	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
643	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
644	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
645	C₂⁵	C₂³×C₁₃₁	1	2	yes	—
646	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
647	C₂²×D₄	—	4	4	no	—
648	C₂²×D₄	—	4	4	no	—
649	C₂²×D₄	—	4	4	no	—
650	C₂²×D₄	—	4	4	no	—
651	C₂²×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
652	C₂²×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
653	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
654	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
655	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
656	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
658	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
659	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
660	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
661	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
662	C₂³×C₄	—	4	2	no	—
663	C₂³×C₄	—	4	4	no	—
664	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
665	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
666	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
667	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
668	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
669	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
671	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
672	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
673	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
674	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
675	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
676	#127	C₂×C₄×C₁₃₁	1	8	yes	complemented
677	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
678	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
679	#120	C₂×C₄×C₁₃₁	1	8	yes	complemented
680	#120	C₂×C₄×C₁₃₁	1	16	yes	complemented
681	#120	C₂×C₄×C₁₃₁	1	8	yes	complemented
682	C₄×D₄	—	4	2	no	—
683	C₄×D₄	—	4	2	no	—
684	C₄×D₄	—	4	4	no	—
685	C₄×D₄	—	4	4	no	—
686	C₄×D₄	—	4	4	no	—
687	C₄×D₄	—	4	4	no	—
688	C₄×D₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
689	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
696	C₂×C₂²⋊C₄	—	4	2	no	—
697	C₂×C₂²⋊C₄	—	4	4	no	—
698	C₂×C₂²⋊C₄	—	4	4	no	—
699	C₂×C₂²⋊C₄	—	4	4	no	—
700	C₂×C₂²⋊C₄	—	4	4	no	—
701	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
734	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
735	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
736	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
737	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
739	#95	C₂³×C₁₃₁	1	2	yes	—
740	#95	C₂³×C₁₃₁	1	2	yes	—
741	#95	C₂³×C₁₃₁	1	2	yes	—
742	#95	C₂³×C₁₃₁	1	2	yes	—
743	#95	C₂³×C₁₃₁	1	2	yes	—
744	#95	C₂³×C₁₃₁	1	2	yes	—
745	#95	C₂³×C₁₃₁	1	2	yes	—
746	#95	C₂³×C₁₃₁	1	2	yes	—
747	#95	C₂³×C₁₃₁	1	2	yes	—
748	#95	C₂³×C₁₃₁	1	2	yes	—
749	#95	C₂³×C₁₃₁	1	2	yes	—
750	#95	C₂³×C₁₃₁	1	2	yes	—
751	#95	C₂³×C₁₃₁	1	2	yes	—
752	#95	C₂³×C₁₃₁	1	2	yes	—
753	#95	C₂³×C₁₃₁	1	2	yes	—
754	#95	C₂³×C₁₃₁	1	2	yes	—
755	#95	C₂³×C₁₃₁	1	2	yes	—
756	#95	C₂³×C₁₃₁	1	2	yes	—
757	C₂⁴	—	2	4	no	—
758	C₂⁴	—	2	4	no	—
759	C₂⁴	—	2	4	no	—
760	C₂⁴	—	2	4	no	—
761	C₂⁴	—	4	1	no	—
762	C₂⁴	—	4	1	no	—
763	C₂⁴	—	4	2	no	—
764	C₂⁴	—	4	1	no	—
765	C₂⁴	—	4	2	no	—
766	C₂⁴	—	4	2	no	—
767	C₂⁴	—	4	2	no	—
768	C₂⁴	—	4	2	no	—
769	C₂⁴	—	4	2	no	—
770	C₂⁴	—	4	1	no	—
771	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
772	C₂⁴	C₂²×C₄×C₁₃₁	1	8	yes	—
773	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	complemented
774	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
775	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
776	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
777	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
778	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	4	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	1	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	—	4	32	no	—
798	C₂×D₄	—	4	32	no	—
799	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
800	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
801	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
802	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
803	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
804	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
805	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	complemented
806	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
807	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	4	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	16	no	—
839	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
840	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
841	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
855	C₄⋊C₄	—	4	1	no	—
856	C₄⋊C₄	—	4	1	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	—	4	2	no	—
859	C₄⋊C₄	—	4	2	no	—
860	C₄⋊C₄	—	4	2	no	—
861	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	1	no	—
881	C₂²⋊C₄	—	4	1	no	—
882	C₂²⋊C₄	—	4	1	no	—
883	C₂²⋊C₄	—	4	1	no	—
884	C₂²⋊C₄	—	4	2	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	4	2	no	—
888	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
891	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	complemented
892	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	complemented
893	C₄²	—	2	2	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	2	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	complemented
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	16	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	16	no	—
926	C₂³	—	4	4	no	—
927	C₂³	—	4	8	no	—
928	C₂³	—	4	8	no	—
929	C₂³	—	4	8	no	—
930	C₂³	—	4	4	no	—
931	C₂³	—	4	4	no	—
932	C₂³	—	4	8	no	—
933	C₂³	—	4	4	no	—
934	C₂³	—	8	4	no	—
935	C₂³	—	8	4	no	—
936	C₂³	—	8	4	no	—
937	C₂³	—	8	4	no	—
938	C₂³	—	8	2	no	—
939	C₂³	—	8	4	no	—
940	C₂³	—	8	2	no	—
941	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
942	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
943	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
944	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
945	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
946	C₂³	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
947	C₂³	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
948	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
949	D₄	—	2	16	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	4	8	no	—
953	D₄	—	4	8	no	—
954	D₄	—	4	8	no	—
955	D₄	—	4	8	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	4	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	—	4	8	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	—	8	4	no	—
1000	C₂×C₄	—	8	4	no	—
1001	C₂×C₄	—	8	4	no	—
1002	C₂×C₄	—	8	2	no	—
1003	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
1004	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
1005	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
1006	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
1007	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	4	no	—
1019	C₂²	—	2	4	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	4	no	—
1024	C₂²	—	4	16	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	8	16	no	—
1040	C₂²	—	8	8	no	—
1041	C₂²	#518×C₁₃₁	1	8	yes	—
1042	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
1043	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
1044	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1045	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
1046	C₂²	#585×C₁₃₁	1	1	yes	characteristic
1047	C₄	—	2	2	no	—
1048	C₄	—	2	4	no	—
1049	C₄	—	2	4	no	—
1050	C₄	—	2	4	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₂	—	2	8	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	4	4	no	—
1064	C₂	—	4	2	no	—
1065	C₂	—	4	4	no	—
1066	C₂	C₂×#518×C₁₃₁	1	2	yes	—
1067	C₂	C₄×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
1068	C₂	#3532×C₁₃₁	1	1	yes	characteristic
1069	C₂	#3534×C₁₃₁	1	2	yes	—
1070	C₂	#3537×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×D₄²×C₁₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2380×C₁₃₁	C₂	semidirect
3. #2377×C₁₃₁	C₂	semidirect
4. #2375×C₁₃₁	C₂	semidirect
5. #2364×C₁₃₁	C₂	semidirect
6. #2358×C₁₃₁	C₂	semidirect
7. #2358×C₁₃₁	C₂	semidirect
8. #2353×C₁₃₁	C₂	semidirect
9. D₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
10. D₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
11. #2333×C₁₃₁	C₂	semidirect
12. #2328×C₁₃₁	C₂	semidirect
13. #2325×C₁₃₁	C₂	semidirect
14. #2321×C₁₃₁	C₂	semidirect
15. #2321×C₁₃₁	C₂	semidirect
16. #2318×C₁₃₁	C₂	semidirect
17. #2308×C₁₃₁	C₂	semidirect
18. C₄×#120×C₁₃₁	C₂	semidirect
19. C₂×#386×C₁₃₁	C₂	semidirect
22. C₂⁴×C₄×C₁₃₁	C₂²	semidirect
23. D₄²×C₁₃₁	C₄	semidirect
31. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
42. #390×C₁₃₁	C₂²	semidirect
43. #390×C₁₃₁	C₂²	semidirect
44. #390×C₁₃₁	C₂²	semidirect
45. #390×C₁₃₁	C₂²	semidirect
46. #390×C₁₃₁	C₂²	semidirect
47. #390×C₁₃₁	C₂²	semidirect
48. #388×C₁₃₁	C₂²	semidirect
49. #388×C₁₃₁	C₂²	semidirect
50. #388×C₁₃₁	C₂²	semidirect
51. #388×C₁₃₁	C₂²	semidirect
52. #388×C₁₃₁	C₂²	semidirect
53. #388×C₁₃₁	C₂²	semidirect
54. #388×C₁₃₁	C₂²	semidirect
55. #388×C₁₃₁	C₂²	semidirect
56. #387×C₁₃₁	C₂²	semidirect
57. #387×C₁₃₁	C₂²	semidirect
58. #387×C₁₃₁	C₂²	semidirect
59. #387×C₁₃₁	C₂²	semidirect
64. #386×C₁₃₁	C₂²	semidirect
65. #386×C₁₃₁	C₂²	semidirect
66. #386×C₁₃₁	C₂²	semidirect
67. #386×C₁₃₁	C₂²	semidirect
68. #386×C₁₃₁	C₂²	semidirect
69. #386×C₁₃₁	C₂²	semidirect
70. #386×C₁₃₁	C₂²	semidirect
71. #386×C₁₃₁	C₂²	semidirect
72. #386×C₁₃₁	C₂²	semidirect
73. #386×C₁₃₁	C₂²	semidirect
74. #386×C₁₃₁	C₂²	semidirect
75. #386×C₁₃₁	C₂²	semidirect
76. #386×C₁₃₁	C₂²	semidirect
77. #386×C₁₃₁	C₂²	semidirect
78. #386×C₁₃₁	C₂²	semidirect
79. #386×C₁₃₁	C₂²	semidirect
80. #386×C₁₃₁	C₂²	semidirect
81. #386×C₁₃₁	C₂²	semidirect
82. #386×C₁₃₁	C₂²	semidirect
83. #385×C₁₃₁	C₂²	semidirect
84. #385×C₁₃₁	C₂²	semidirect
85. #385×C₁₃₁	C₂²	semidirect
86. #385×C₁₃₁	C₂²	semidirect
87. #385×C₁₃₁	C₂²	semidirect
88. #383×C₁₃₁	C₂²	semidirect
89. #382×C₁₃₁	C₂²	semidirect
90. #381×C₁₃₁	C₂²	semidirect
91. #381×C₁₃₁	C₂²	semidirect
92. #380×C₁₃₁	C₂²	semidirect
93. #380×C₁₃₁	C₂²	semidirect
94. #379×C₁₃₁	C₂²	semidirect
95. #379×C₁₃₁	C₂²	semidirect
96. #379×C₁₃₁	C₂²	semidirect
97. #379×C₁₃₁	C₂²	semidirect
98. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
99. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
105. #376×C₁₃₁	C₂²	semidirect
106. C₂×#95×C₁₃₁	C₂²	semidirect
107. C₂×#95×C₁₃₁	C₂²	semidirect
115. C₂²×D₄×C₁₃₁	C₂×C₄	semidirect
116. C₂²×D₄×C₁₃₁	C₂×C₄	semidirect
140. #127×C₁₃₁	C₂×C₄	semidirect
141. #121×C₁₃₁	C₂×C₄	semidirect
142. #121×C₁₃₁	C₂×C₄	semidirect
143. #120×C₁₃₁	C₂×C₄	semidirect
144. #120×C₁₃₁	C₂×C₄	semidirect
145. #120×C₁₃₁	C₂×C₄	semidirect
152. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
237. C₂⁴×C₁₃₁	C₂²×C₄	semidirect
269. C₂×D₄×C₁₃₁	C₂²×C₄	semidirect
270. C₂×D₄×C₁₃₁	C₂²×C₄	semidirect
271. C₂×D₄×C₁₃₁	C₂²×C₄	semidirect
304. C₂²×C₄×C₁₃₁	C₂²×C₄	semidirect
325. C₄⋊C₄×C₁₃₁	C₂²×C₄	semidirect
354. C₂²⋊C₄×C₁₃₁	C₂²×C₄	semidirect
355. C₂²⋊C₄×C₁₃₁	C₂²×C₄	semidirect
356. C₂²⋊C₄×C₁₃₁	C₂²×C₄	semidirect
363. C₄²×C₁₃₁	C₂²×C₄	semidirect
535. #34468	C₁₃₁	direct (N × H)
536. C₁₃₁	#34468	direct (N × H)
538. #2380	C₂×C₁₃₁	semidirect
539. #2377	C₂×C₁₃₁	semidirect
540. #2375	C₂×C₁₃₁	semidirect
541. #2364	C₂×C₁₃₁	semidirect
542. #2358	C₂×C₁₃₁	semidirect
543. #2358	C₂×C₁₃₁	semidirect
544. #2353	C₂×C₁₃₁	semidirect
545. D₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
546. D₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
547. #2333	C₂×C₁₃₁	semidirect
548. #2328	C₂×C₁₃₁	semidirect
549. #2325	C₂×C₁₃₁	semidirect
550. #2321	C₂×C₁₃₁	semidirect
551. #2321	C₂×C₁₃₁	semidirect
552. #2318	C₂×C₁₃₁	semidirect
553. #2308	C₂×C₁₃₁	semidirect
554. C₄×#120	C₂×C₁₃₁	semidirect
555. C₂×#386	C₂×C₁₃₁	semidirect
558. C₂⁴×C₄	C₂²×C₁₃₁	semidirect
559. D₄²	C₄×C₁₃₁	semidirect
567. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
568. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
569. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
570. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
571. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
572. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
573. C₂²×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
574. C₂²×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
575. C₂²×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
576. C₂²×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
577. C₂²×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
578. #390	C₂²×C₁₃₁	semidirect
579. #390	C₂²×C₁₃₁	semidirect
580. #390	C₂²×C₁₃₁	semidirect
581. #390	C₂²×C₁₃₁	semidirect
582. #390	C₂²×C₁₃₁	semidirect
583. #390	C₂²×C₁₃₁	semidirect
584. #388	C₂²×C₁₃₁	semidirect
585. #388	C₂²×C₁₃₁	semidirect
586. #388	C₂²×C₁₃₁	semidirect
587. #388	C₂²×C₁₃₁	semidirect
588. #388	C₂²×C₁₃₁	semidirect
589. #388	C₂²×C₁₃₁	semidirect
590. #388	C₂²×C₁₃₁	semidirect
591. #388	C₂²×C₁₃₁	semidirect
592. #387	C₂²×C₁₃₁	semidirect
593. #387	C₂²×C₁₃₁	semidirect
594. #387	C₂²×C₁₃₁	semidirect
595. #387	C₂²×C₁₃₁	semidirect
600. #386	C₂²×C₁₃₁	semidirect
601. #386	C₂²×C₁₃₁	semidirect
602. #386	C₂²×C₁₃₁	semidirect
603. #386	C₂²×C₁₃₁	semidirect
604. #386	C₂²×C₁₃₁	semidirect
605. #386	C₂²×C₁₃₁	semidirect
606. #386	C₂²×C₁₃₁	semidirect
607. #386	C₂²×C₁₃₁	semidirect
608. #386	C₂²×C₁₃₁	semidirect
609. #386	C₂²×C₁₃₁	semidirect
610. #386	C₂²×C₁₃₁	semidirect
611. #386	C₂²×C₁₃₁	semidirect
612. #386	C₂²×C₁₃₁	semidirect
613. #386	C₂²×C₁₃₁	semidirect
614. #386	C₂²×C₁₃₁	semidirect
615. #386	C₂²×C₁₃₁	semidirect
616. #386	C₂²×C₁₃₁	semidirect
617. #386	C₂²×C₁₃₁	semidirect
618. #386	C₂²×C₁₃₁	semidirect
619. #385	C₂²×C₁₃₁	semidirect
620. #385	C₂²×C₁₃₁	semidirect
621. #385	C₂²×C₁₃₁	semidirect
622. #385	C₂²×C₁₃₁	semidirect
623. #385	C₂²×C₁₃₁	semidirect
624. #383	C₂²×C₁₃₁	semidirect
625. #382	C₂²×C₁₃₁	semidirect
626. #381	C₂²×C₁₃₁	semidirect
627. #381	C₂²×C₁₃₁	semidirect
628. #380	C₂²×C₁₃₁	semidirect
629. #380	C₂²×C₁₃₁	semidirect
630. #379	C₂²×C₁₃₁	semidirect
631. #379	C₂²×C₁₃₁	semidirect
632. #379	C₂²×C₁₃₁	semidirect
633. #379	C₂²×C₁₃₁	semidirect
634. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
635. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
636. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
637. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
638. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
639. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
640. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
641. #376	C₂²×C₁₃₁	semidirect
642. C₂×#95	C₂²×C₁₃₁	semidirect
643. C₂×#95	C₂²×C₁₃₁	semidirect
651. C₂²×D₄	C₂×C₄×C₁₃₁	semidirect
652. C₂²×D₄	C₂×C₄×C₁₃₁	semidirect
676. #127	C₂×C₄×C₁₃₁	semidirect
677. #121	C₂×C₄×C₁₃₁	semidirect
678. #121	C₂×C₄×C₁₃₁	semidirect
679. #120	C₂×C₄×C₁₃₁	semidirect
680. #120	C₂×C₄×C₁₃₁	semidirect
681. #120	C₂×C₄×C₁₃₁	semidirect
688. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
773. C₂⁴	C₂²×C₄×C₁₃₁	semidirect
805. C₂×D₄	C₂²×C₄×C₁₃₁	semidirect
806. C₂×D₄	C₂²×C₄×C₁₃₁	semidirect
807. C₂×D₄	C₂²×C₄×C₁₃₁	semidirect
840. C₂²×C₄	C₂²×C₄×C₁₃₁	semidirect
861. C₄⋊C₄	C₂²×C₄×C₁₃₁	semidirect
890. C₂²⋊C₄	C₂²×C₄×C₁₃₁	semidirect
891. C₂²⋊C₄	C₂²×C₄×C₁₃₁	semidirect
892. C₂²⋊C₄	C₂²×C₄×C₁₃₁	semidirect
899. C₄²	C₂²×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₃₁	2
#2380×C₁₃₁	2
#2377×C₁₃₁	2
#2375×C₁₃₁	2
#2364×C₁₃₁	2
#2358×C₁₃₁	2
#2353×C₁₃₁	2
D₄×C₂²⋊C₄×C₁₃₁	2
#2333×C₁₃₁	2
#2328×C₁₃₁	2
#2325×C₁₃₁	2
#2321×C₁₃₁	2
#2318×C₁₃₁	2
#2308×C₁₃₁	2
C₄×#120×C₁₃₁	2
C₂×#386×C₁₃₁	2
#34468	131

Subgroups — C131×#34468 #45720352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34468 #45720352