Subgroups — C₁₃₁×#34411 #45720295

Order 33536.

2766 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2380×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2375×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2366×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2363×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2361×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2358×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2347×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2337×C₁₃₁	C₂	1	4	yes	maximal, complemented
11	#2324×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2321×C₁₃₁	C₂	1	4	yes	maximal, complemented
13	#2311×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#121×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	#2297×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	#535×C₁₃₁	C₄	1	16	yes	complemented
19	C₂×#127×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	complemented
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	complemented
29	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
34	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
35	#391×C₁₃₁	C₂²	1	2	yes	complemented
36	#391×C₁₃₁	C₂²	1	2	yes	complemented
37	#390×C₁₃₁	C₂²	1	2	yes	—
38	#390×C₁₃₁	C₂²	1	2	yes	—
39	#390×C₁₃₁	C₂²	1	2	yes	—
40	#390×C₁₃₁	C₂²	1	2	yes	—
41	#390×C₁₃₁	C₂²	1	4	yes	complemented
42	#390×C₁₃₁	C₂²	1	4	yes	complemented
43	#389×C₁₃₁	C₂²	1	2	yes	complemented
44	#389×C₁₃₁	C₂²	1	2	yes	complemented
45	#388×C₁₃₁	C₂²	1	4	yes	—
46	#388×C₁₃₁	C₂²	1	4	yes	—
47	#388×C₁₃₁	C₂²	1	4	yes	complemented
48	#388×C₁₃₁	C₂²	1	4	yes	complemented
49	#388×C₁₃₁	C₂²	1	4	yes	complemented
50	#388×C₁₃₁	C₂²	1	4	yes	complemented
51	#386×C₁₃₁	C₂²	1	1	yes	characteristic
52	#386×C₁₃₁	C₂²	1	1	yes	characteristic
53	#386×C₁₃₁	C₂²	1	2	yes	—
54	#386×C₁₃₁	C₂²	1	4	yes	—
55	#386×C₁₃₁	C₂²	1	4	yes	—
56	#386×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
57	#386×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
58	#386×C₁₃₁	C₂²	1	4	yes	complemented
59	#386×C₁₃₁	C₂²	1	2	yes	complemented
60	#386×C₁₃₁	C₂²	1	4	yes	complemented
61	#386×C₁₃₁	C₂²	1	4	yes	complemented
62	#386×C₁₃₁	C₂²	1	4	yes	complemented
63	#385×C₁₃₁	C₂²	1	4	yes	complemented
64	#385×C₁₃₁	C₂²	1	4	yes	complemented
65	#383×C₁₃₁	C₂²	1	4	yes	complemented
66	#380×C₁₃₁	C₂²	1	2	yes	—
67	#380×C₁₃₁	C₂²	1	2	yes	complemented
68	#379×C₁₃₁	C₂²	1	4	yes	—
69	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
70	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
71	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
72	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
76	C₂⁵×C₁₃₁	C₂³	1	2	yes	—
77	C₂×#41×C₁₃₁	—	4	2	no	—
78	C₂×#41×C₁₃₁	—	4	2	no	—
79	C₂×#41×C₁₃₁	C₂×C₄	1	8	yes	complemented
80	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃₁	—	4	2	no	—
82	C₂²×D₄×C₁₃₁	—	4	2	no	—
83	C₂²×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
84	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
88	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
89	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
99	#127×C₁₃₁	C₂×C₄	1	16	yes	complemented
100	#124×C₁₃₁	C₂×C₄	1	16	yes	complemented
101	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
102	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
103	#120×C₁₃₁	C₂×C₄	1	16	yes	complemented
104	#120×C₁₃₁	C₂×C₄	1	16	yes	complemented
105	C₄×D₄×C₁₃₁	—	4	4	no	—
106	C₄×D₄×C₁₃₁	—	4	4	no	—
107	C₄×D₄×C₁₃₁	—	4	8	no	—
108	C₄×D₄×C₁₃₁	—	4	8	no	—
109	#117×C₁₃₁	—	4	2	no	—
110	#117×C₁₃₁	—	4	2	no	—
111	#117×C₁₃₁	C₂×C₄	1	8	yes	complemented
112	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₃₁	—	4	8	no	—
121	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₁	—	4	2	no	—
140	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
144	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
147	#95×C₁₃₁	C₂³	1	4	yes	—
148	#95×C₁₃₁	C₂³	1	4	yes	—
149	#95×C₁₃₁	C₂³	1	4	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	2	yes	—
152	#95×C₁₃₁	C₂³	1	4	yes	—
153	#95×C₁₃₁	C₂³	1	2	yes	—
154	#95×C₁₃₁	C₂³	1	2	yes	—
155	#95×C₁₃₁	C₂³	1	2	yes	—
156	#95×C₁₃₁	C₂³	1	4	yes	—
157	C₂⁴×C₁₃₁	—	4	4	no	—
158	C₂⁴×C₁₃₁	—	4	2	no	—
159	C₂⁴×C₁₃₁	—	4	2	no	—
160	C₂⁴×C₁₃₁	—	4	4	no	—
161	C₂⁴×C₁₃₁	C₂²×C₄	1	8	yes	—
162	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₁₃₁	C₂⁴	1	4	yes	—
164	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
166	#41×C₁₃₁	—	4	16	no	—
167	C₂×Q₈×C₁₃₁	—	4	1	no	—
168	C₂×Q₈×C₁₃₁	—	4	1	no	—
169	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₁₃₁	—	2	4	no	—
171	C₂×D₄×C₁₃₁	—	2	4	no	—
172	C₂×D₄×C₁₃₁	—	4	16	no	—
173	C₂×D₄×C₁₃₁	—	4	4	no	—
174	C₂×D₄×C₁₃₁	—	4	4	no	—
175	C₂×D₄×C₁₃₁	—	4	2	no	—
176	C₂×D₄×C₁₃₁	—	4	2	no	—
177	C₂×D₄×C₁₃₁	—	4	4	no	—
178	C₂×D₄×C₁₃₁	—	4	4	no	—
179	C₂×D₄×C₁₃₁	—	4	1	no	—
180	C₂×D₄×C₁₃₁	—	4	1	no	—
181	C₂×D₄×C₁₃₁	—	4	1	no	—
182	C₂×D₄×C₁₃₁	—	4	1	no	—
183	C₂×D₄×C₁₃₁	—	4	1	no	—
184	C₂×D₄×C₁₃₁	—	4	1	no	—
185	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
186	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
187	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
188	C₂×D₄×C₁₃₁	C₂²×C₄	1	16	yes	—
189	C₂×D₄×C₁₃₁	C₂²×C₄	1	16	yes	—
190	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
191	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₁₃₁	—	2	2	no	—
193	C₂²×C₄×C₁₃₁	—	2	2	no	—
194	C₂²×C₄×C₁₃₁	—	2	2	no	—
195	C₂²×C₄×C₁₃₁	—	2	2	no	—
196	C₂²×C₄×C₁₃₁	—	2	2	no	—
197	C₂²×C₄×C₁₃₁	—	2	2	no	—
198	C₂²×C₄×C₁₃₁	—	2	4	no	—
199	C₂²×C₄×C₁₃₁	—	2	8	no	—
200	C₂²×C₄×C₁₃₁	—	4	1	no	—
201	C₂²×C₄×C₁₃₁	—	4	1	no	—
202	C₂²×C₄×C₁₃₁	—	4	2	no	—
203	C₂²×C₄×C₁₃₁	—	4	4	no	—
204	C₂²×C₄×C₁₃₁	—	4	2	no	—
205	C₂²×C₄×C₁₃₁	—	4	4	no	—
206	C₂²×C₄×C₁₃₁	—	4	4	no	—
207	C₂²×C₄×C₁₃₁	—	4	4	no	—
208	C₂²×C₄×C₁₃₁	—	4	4	no	—
209	C₂²×C₄×C₁₃₁	—	4	4	no	—
210	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
211	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
212	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
213	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
224	C₄⋊C₄×C₁₃₁	—	2	4	no	—
225	C₄⋊C₄×C₁₃₁	—	2	4	no	—
226	C₄⋊C₄×C₁₃₁	—	2	8	no	—
227	C₄⋊C₄×C₁₃₁	—	4	2	no	—
228	C₄⋊C₄×C₁₃₁	—	4	4	no	—
229	C₄⋊C₄×C₁₃₁	—	4	2	no	—
230	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
231	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
232	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
233	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
234	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
236	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
237	C₂²⋊C₄×C₁₃₁	—	4	4	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	2	no	—
242	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
243	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
244	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
245	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
246	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
247	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
248	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
249	C₄²×C₁₃₁	—	2	4	no	—
250	C₄²×C₁₃₁	—	2	4	no	—
251	C₄²×C₁₃₁	—	4	2	no	—
252	C₄²×C₁₃₁	—	4	2	no	—
253	C₄²×C₁₃₁	—	4	4	no	—
254	C₄²×C₁₃₁	—	4	4	no	—
255	C₄²×C₁₃₁	C₂²×C₄	1	8	yes	—
256	C₂³×C₁₃₁	—	2	2	no	—
257	C₂³×C₁₃₁	—	2	4	no	—
258	C₂³×C₁₃₁	—	2	2	no	—
259	C₂³×C₁₃₁	—	2	1	no	—
260	C₂³×C₁₃₁	—	2	1	no	—
261	C₂³×C₁₃₁	—	2	2	no	—
262	C₂³×C₁₃₁	—	2	4	no	—
263	C₂³×C₁₃₁	—	2	4	no	—
264	C₂³×C₁₃₁	—	2	4	no	—
265	C₂³×C₁₃₁	—	2	1	no	—
266	C₂³×C₁₃₁	—	2	1	no	—
267	C₂³×C₁₃₁	—	2	1	no	—
268	C₂³×C₁₃₁	—	2	1	no	—
269	C₂³×C₁₃₁	—	2	2	no	—
270	C₂³×C₁₃₁	—	2	4	no	—
271	C₂³×C₁₃₁	—	2	2	no	—
272	C₂³×C₁₃₁	—	2	2	no	—
273	C₂³×C₁₃₁	—	2	4	no	—
274	C₂³×C₁₃₁	—	4	8	no	—
275	C₂³×C₁₃₁	—	4	16	no	—
276	C₂³×C₁₃₁	—	8	4	no	—
277	C₂³×C₁₃₁	—	8	4	no	—
278	C₂³×C₁₃₁	—	8	8	no	—
279	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
280	C₂³×C₁₃₁	C₂³×C₄	1	8	yes	—
281	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
282	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
283	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
284	Q₈×C₁₃₁	—	4	4	no	—
285	D₄×C₁₃₁	—	2	16	no	—
286	D₄×C₁₃₁	—	4	8	no	—
287	D₄×C₁₃₁	—	4	16	no	—
288	D₄×C₁₃₁	—	4	16	no	—
289	D₄×C₁₃₁	—	4	4	no	—
290	D₄×C₁₃₁	—	4	4	no	—
291	D₄×C₁₃₁	—	4	4	no	—
292	C₂×C₄×C₁₃₁	—	2	2	no	—
293	C₂×C₄×C₁₃₁	—	2	4	no	—
294	C₂×C₄×C₁₃₁	—	2	2	no	—
295	C₂×C₄×C₁₃₁	—	2	1	no	—
296	C₂×C₄×C₁₃₁	—	2	1	no	—
297	C₂×C₄×C₁₃₁	—	2	1	no	—
298	C₂×C₄×C₁₃₁	—	2	1	no	—
299	C₂×C₄×C₁₃₁	—	2	1	no	—
300	C₂×C₄×C₁₃₁	—	2	1	no	—
301	C₂×C₄×C₁₃₁	—	2	4	no	—
302	C₂×C₄×C₁₃₁	—	2	8	no	—
303	C₂×C₄×C₁₃₁	—	2	8	no	—
304	C₂×C₄×C₁₃₁	—	2	8	no	—
305	C₂×C₄×C₁₃₁	—	2	2	no	—
306	C₂×C₄×C₁₃₁	—	2	2	no	—
307	C₂×C₄×C₁₃₁	—	2	2	no	—
308	C₂×C₄×C₁₃₁	—	2	2	no	—
309	C₂×C₄×C₁₃₁	—	2	4	no	—
310	C₂×C₄×C₁₃₁	—	2	4	no	—
311	C₂×C₄×C₁₃₁	—	2	4	no	—
312	C₂×C₄×C₁₃₁	—	2	2	no	—
313	C₂×C₄×C₁₃₁	—	2	4	no	—
314	C₂×C₄×C₁₃₁	—	2	4	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	4	no	—
319	C₂×C₄×C₁₃₁	—	2	2	no	—
320	C₂×C₄×C₁₃₁	—	4	4	no	—
321	C₂×C₄×C₁₃₁	—	4	4	no	—
322	C₂×C₄×C₁₃₁	—	8	8	no	—
323	C₂×C₄×C₁₃₁	—	8	4	no	—
324	C₂×C₄×C₁₃₁	—	8	8	no	—
325	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₁₃₁	C₂³×C₄	1	8	yes	—
327	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
331	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
332	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
333	C₂²×C₁₃₁	—	2	2	no	—
334	C₂²×C₁₃₁	—	2	2	no	—
335	C₂²×C₁₃₁	—	2	2	no	—
336	C₂²×C₁₃₁	—	2	8	no	—
337	C₂²×C₁₃₁	—	2	4	no	—
338	C₂²×C₁₃₁	—	2	4	no	—
339	C₂²×C₁₃₁	—	2	8	no	—
340	C₂²×C₁₃₁	—	2	8	no	—
341	C₂²×C₁₃₁	—	2	4	no	—
342	C₂²×C₁₃₁	—	4	1	no	—
343	C₂²×C₁₃₁	—	4	1	no	—
344	C₂²×C₁₃₁	—	4	4	no	—
345	C₂²×C₁₃₁	—	4	1	no	—
346	C₂²×C₁₃₁	—	4	1	no	—
347	C₂²×C₁₃₁	—	4	1	no	—
348	C₂²×C₁₃₁	—	4	4	no	—
349	C₂²×C₁₃₁	—	4	1	no	—
350	C₂²×C₁₃₁	—	4	4	no	—
351	C₂²×C₁₃₁	—	4	2	no	—
352	C₂²×C₁₃₁	—	4	2	no	—
353	C₂²×C₁₃₁	—	4	4	no	—
354	C₂²×C₁₃₁	—	4	2	no	—
355	C₂²×C₁₃₁	—	8	16	no	—
356	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
357	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
360	C₂²×C₁₃₁	#585	1	2	yes	—
361	C₄×C₁₃₁	—	2	2	no	—
362	C₄×C₁₃₁	—	2	2	no	—
363	C₄×C₁₃₁	—	2	2	no	—
364	C₄×C₁₃₁	—	2	8	no	—
365	C₄×C₁₃₁	—	2	4	no	—
366	C₄×C₁₃₁	—	4	4	no	—
367	C₄×C₁₃₁	—	4	2	no	—
368	C₄×C₁₃₁	—	4	2	no	—
369	C₄×C₁₃₁	—	4	4	no	—
370	C₄×C₁₃₁	—	4	2	no	—
371	C₄×C₁₃₁	#518	1	4	yes	—
372	C₂×C₁₃₁	—	4	2	no	—
373	C₂×C₁₃₁	—	4	2	no	—
374	C₂×C₁₃₁	—	4	8	no	—
375	C₂×C₁₃₁	—	4	2	no	—
376	C₂×C₁₃₁	C₂×#518	1	1	yes	characteristic
377	C₂×C₁₃₁	C₄×H(5,𝔽₂)	1	2	yes	—
378	C₂×C₁₃₁	#3537	1	1	yes	characteristic
379	C₂×C₁₃₁	#3540	1	1	yes	characteristic
380	C₂×C₁₃₁	#3546	1	2	yes	—
381	#34411	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₁₃₁	#34411	1	1	yes	characteristic, direct product factor, Sylow
383	C₂×#535	C₂×C₁₃₁	1	1	yes	characteristic
384	#2380	C₂×C₁₃₁	1	2	yes	complemented
385	#2375	C₂×C₁₃₁	1	2	yes	complemented
386	#2366	C₂×C₁₃₁	1	2	yes	complemented
387	#2363	C₂×C₁₃₁	1	2	yes	complemented
388	#2361	C₂×C₁₃₁	1	2	yes	complemented
389	#2358	C₂×C₁₃₁	1	2	yes	complemented
390	#2347	C₂×C₁₃₁	1	2	yes	complemented
391	D₄×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
392	#2337	C₂×C₁₃₁	1	4	yes	complemented
393	#2324	C₂×C₁₃₁	1	2	yes	complemented
394	#2321	C₂×C₁₃₁	1	4	yes	complemented
395	#2311	C₂×C₁₃₁	1	1	yes	characteristic, complemented
396	C₄×#121	C₂×C₁₃₁	1	2	yes	complemented
397	#2297	C₂×C₁₃₁	1	1	yes	characteristic, complemented
398	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic
399	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
400	#535	C₄×C₁₃₁	1	16	yes	complemented
401	C₂×#127	C₂²×C₁₃₁	1	2	yes	—
402	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
403	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
404	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
405	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
406	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	complemented
410	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	complemented
411	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
412	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
413	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
414	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
415	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
416	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
417	#391	C₂²×C₁₃₁	1	2	yes	complemented
418	#391	C₂²×C₁₃₁	1	2	yes	complemented
419	#390	C₂²×C₁₃₁	1	2	yes	—
420	#390	C₂²×C₁₃₁	1	2	yes	—
421	#390	C₂²×C₁₃₁	1	2	yes	—
422	#390	C₂²×C₁₃₁	1	2	yes	—
423	#390	C₂²×C₁₃₁	1	4	yes	complemented
424	#390	C₂²×C₁₃₁	1	4	yes	complemented
425	#389	C₂²×C₁₃₁	1	2	yes	complemented
426	#389	C₂²×C₁₃₁	1	2	yes	complemented
427	#388	C₂²×C₁₃₁	1	4	yes	—
428	#388	C₂²×C₁₃₁	1	4	yes	—
429	#388	C₂²×C₁₃₁	1	4	yes	complemented
430	#388	C₂²×C₁₃₁	1	4	yes	complemented
431	#388	C₂²×C₁₃₁	1	4	yes	complemented
432	#388	C₂²×C₁₃₁	1	4	yes	complemented
433	#386	C₂²×C₁₃₁	1	2	yes	—
434	#386	C₂²×C₁₃₁	1	4	yes	—
435	#386	C₂²×C₁₃₁	1	4	yes	—
436	#386	C₂²×C₁₃₁	1	1	yes	characteristic
437	#386	C₂²×C₁₃₁	1	1	yes	characteristic
438	#386	C₂²×C₁₃₁	1	2	yes	complemented
439	#386	C₂²×C₁₃₁	1	4	yes	complemented
440	#386	C₂²×C₁₃₁	1	4	yes	complemented
441	#386	C₂²×C₁₃₁	1	4	yes	complemented
442	#386	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
443	#386	C₂²×C₁₃₁	1	4	yes	complemented
444	#386	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
445	#385	C₂²×C₁₃₁	1	4	yes	complemented
446	#385	C₂²×C₁₃₁	1	4	yes	complemented
447	#383	C₂²×C₁₃₁	1	4	yes	complemented
448	#380	C₂²×C₁₃₁	1	2	yes	—
449	#380	C₂²×C₁₃₁	1	2	yes	complemented
450	#379	C₂²×C₁₃₁	1	4	yes	—
451	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
452	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
453	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
454	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
456	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
457	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
458	C₂⁵	C₂³×C₁₃₁	1	2	yes	—
459	C₂×#41	—	4	2	no	—
460	C₂×#41	—	4	2	no	—
461	C₂×#41	C₂×C₄×C₁₃₁	1	8	yes	complemented
462	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
463	C₂²×D₄	—	4	2	no	—
464	C₂²×D₄	—	4	2	no	—
465	C₂²×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
466	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
467	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
468	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
469	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
472	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
478	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
479	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
481	#127	C₂×C₄×C₁₃₁	1	16	yes	complemented
482	#124	C₂×C₄×C₁₃₁	1	16	yes	complemented
483	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
484	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
485	#120	C₂×C₄×C₁₃₁	1	16	yes	complemented
486	#120	C₂×C₄×C₁₃₁	1	16	yes	complemented
487	C₄×D₄	—	4	4	no	—
488	C₄×D₄	—	4	4	no	—
489	C₄×D₄	—	4	8	no	—
490	C₄×D₄	—	4	8	no	—
491	#117	—	4	2	no	—
492	#117	—	4	2	no	—
493	#117	C₂×C₄×C₁₃₁	1	8	yes	complemented
494	C₂×C₄⋊C₄	—	4	2	no	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
502	C₂×C₂²⋊C₄	—	4	8	no	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
521	C₂×C₄²	—	4	2	no	—
522	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
523	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
525	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
526	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
527	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
529	#95	C₂³×C₁₃₁	1	2	yes	—
530	#95	C₂³×C₁₃₁	1	2	yes	—
531	#95	C₂³×C₁₃₁	1	2	yes	—
532	#95	C₂³×C₁₃₁	1	4	yes	—
533	#95	C₂³×C₁₃₁	1	4	yes	—
534	#95	C₂³×C₁₃₁	1	4	yes	—
535	#95	C₂³×C₁₃₁	1	2	yes	—
536	#95	C₂³×C₁₃₁	1	4	yes	—
537	#95	C₂³×C₁₃₁	1	4	yes	—
538	#95	C₂³×C₁₃₁	1	4	yes	—
539	C₂⁴	—	4	4	no	—
540	C₂⁴	—	4	2	no	—
541	C₂⁴	—	4	2	no	—
542	C₂⁴	—	4	4	no	—
543	C₂⁴	C₂²×C₄×C₁₃₁	1	8	yes	—
544	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
545	C₂⁴	C₂⁴×C₁₃₁	1	4	yes	—
546	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
547	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
548	#41	—	4	16	no	—
549	C₂×Q₈	—	4	1	no	—
550	C₂×Q₈	—	4	1	no	—
551	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	4	16	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
568	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
569	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
570	C₂×D₄	C₂²×C₄×C₁₃₁	1	16	yes	—
571	C₂×D₄	C₂²×C₄×C₁₃₁	1	16	yes	—
572	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
573	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	4	1	no	—
583	C₂²×C₄	—	4	1	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
593	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
594	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	1	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
629	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
630	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	4	2	no	—
634	C₄²	—	4	2	no	—
635	C₄²	—	4	4	no	—
636	C₄²	—	4	4	no	—
637	C₄²	C₂²×C₄×C₁₃₁	1	8	yes	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	4	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	16	no	—
658	C₂³	—	8	4	no	—
659	C₂³	—	8	4	no	—
660	C₂³	—	8	8	no	—
661	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
662	C₂³	C₂³×C₄×C₁₃₁	1	8	yes	—
663	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
664	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
665	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
666	Q₈	—	4	4	no	—
667	D₄	—	2	16	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	16	no	—
673	D₄	—	4	16	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	8	no	—
685	C₂×C₄	—	2	8	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	8	8	no	—
705	C₂×C₄	—	8	4	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
708	C₂×C₄	C₂³×C₄×C₁₃₁	1	8	yes	—
709	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
710	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
711	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
712	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
713	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
714	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	8	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	8	no	—
722	C₂²	—	2	8	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	16	no	—
738	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
739	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
740	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
741	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
742	C₂²	#585×C₁₃₁	1	2	yes	—
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	8	no	—
748	C₄	—	4	4	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	#518×C₁₃₁	1	4	yes	—
754	C₂	—	4	2	no	—
755	C₂	—	4	8	no	—
756	C₂	—	4	2	no	—
757	C₂	—	4	2	no	—
758	C₂	C₂×#518×C₁₃₁	1	1	yes	characteristic
759	C₂	C₄×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
760	C₂	#3537×C₁₃₁	1	1	yes	characteristic
761	C₂	#3540×C₁₃₁	1	1	yes	characteristic
762	C₂	#3546×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂×#535×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. #2375×C₁₃₁	C₂	semidirect
4. #2366×C₁₃₁	C₂	semidirect
5. #2363×C₁₃₁	C₂	semidirect
6. #2361×C₁₃₁	C₂	semidirect
7. #2358×C₁₃₁	C₂	semidirect
8. #2347×C₁₃₁	C₂	semidirect
9. D₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
10. #2337×C₁₃₁	C₂	semidirect
11. #2324×C₁₃₁	C₂	semidirect
12. #2321×C₁₃₁	C₂	semidirect
13. #2311×C₁₃₁	C₂	semidirect
14. C₄×#121×C₁₃₁	C₂	semidirect
15. #2297×C₁₃₁	C₂	semidirect
18. #535×C₁₃₁	C₄	semidirect
27. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
30. C₂×#117×C₁₃₁	C₂²	semidirect
31. C₂×#117×C₁₃₁	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
34. C₂²×C₄²×C₁₃₁	C₂²	semidirect
35. #391×C₁₃₁	C₂²	semidirect
36. #391×C₁₃₁	C₂²	semidirect
41. #390×C₁₃₁	C₂²	semidirect
42. #390×C₁₃₁	C₂²	semidirect
43. #389×C₁₃₁	C₂²	semidirect
44. #389×C₁₃₁	C₂²	semidirect
47. #388×C₁₃₁	C₂²	semidirect
48. #388×C₁₃₁	C₂²	semidirect
49. #388×C₁₃₁	C₂²	semidirect
50. #388×C₁₃₁	C₂²	semidirect
56. #386×C₁₃₁	C₂²	semidirect
57. #386×C₁₃₁	C₂²	semidirect
58. #386×C₁₃₁	C₂²	semidirect
59. #386×C₁₃₁	C₂²	semidirect
60. #386×C₁₃₁	C₂²	semidirect
61. #386×C₁₃₁	C₂²	semidirect
62. #386×C₁₃₁	C₂²	semidirect
63. #385×C₁₃₁	C₂²	semidirect
64. #385×C₁₃₁	C₂²	semidirect
65. #383×C₁₃₁	C₂²	semidirect
67. #380×C₁₃₁	C₂²	semidirect
69. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
70. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
71. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
79. C₂×#41×C₁₃₁	C₂×C₄	semidirect
83. C₂²×D₄×C₁₃₁	C₂×C₄	semidirect
99. #127×C₁₃₁	C₂×C₄	semidirect
100. #124×C₁₃₁	C₂×C₄	semidirect
101. #121×C₁₃₁	C₂×C₄	semidirect
102. #121×C₁₃₁	C₂×C₄	semidirect
103. #120×C₁₃₁	C₂×C₄	semidirect
104. #120×C₁₃₁	C₂×C₄	semidirect
111. #117×C₁₃₁	C₂×C₄	semidirect
381. #34411	C₁₃₁	direct (N × H)
382. C₁₃₁	#34411	direct (N × H)
384. #2380	C₂×C₁₃₁	semidirect
385. #2375	C₂×C₁₃₁	semidirect
386. #2366	C₂×C₁₃₁	semidirect
387. #2363	C₂×C₁₃₁	semidirect
388. #2361	C₂×C₁₃₁	semidirect
389. #2358	C₂×C₁₃₁	semidirect
390. #2347	C₂×C₁₃₁	semidirect
391. D₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
392. #2337	C₂×C₁₃₁	semidirect
393. #2324	C₂×C₁₃₁	semidirect
394. #2321	C₂×C₁₃₁	semidirect
395. #2311	C₂×C₁₃₁	semidirect
396. C₄×#121	C₂×C₁₃₁	semidirect
397. #2297	C₂×C₁₃₁	semidirect
400. #535	C₄×C₁₃₁	semidirect
409. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
410. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
412. C₂×#117	C₂²×C₁₃₁	semidirect
413. C₂×#117	C₂²×C₁₃₁	semidirect
414. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
416. C₂²×C₄²	C₂²×C₁₃₁	semidirect
417. #391	C₂²×C₁₃₁	semidirect
418. #391	C₂²×C₁₃₁	semidirect
423. #390	C₂²×C₁₃₁	semidirect
424. #390	C₂²×C₁₃₁	semidirect
425. #389	C₂²×C₁₃₁	semidirect
426. #389	C₂²×C₁₃₁	semidirect
429. #388	C₂²×C₁₃₁	semidirect
430. #388	C₂²×C₁₃₁	semidirect
431. #388	C₂²×C₁₃₁	semidirect
432. #388	C₂²×C₁₃₁	semidirect
438. #386	C₂²×C₁₃₁	semidirect
439. #386	C₂²×C₁₃₁	semidirect
440. #386	C₂²×C₁₃₁	semidirect
441. #386	C₂²×C₁₃₁	semidirect
442. #386	C₂²×C₁₃₁	semidirect
443. #386	C₂²×C₁₃₁	semidirect
444. #386	C₂²×C₁₃₁	semidirect
445. #385	C₂²×C₁₃₁	semidirect
446. #385	C₂²×C₁₃₁	semidirect
447. #383	C₂²×C₁₃₁	semidirect
449. #380	C₂²×C₁₃₁	semidirect
451. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
452. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
453. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
455. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
456. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
457. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
461. C₂×#41	C₂×C₄×C₁₃₁	semidirect
465. C₂²×D₄	C₂×C₄×C₁₃₁	semidirect
481. #127	C₂×C₄×C₁₃₁	semidirect
482. #124	C₂×C₄×C₁₃₁	semidirect
483. #121	C₂×C₄×C₁₃₁	semidirect
484. #121	C₂×C₄×C₁₃₁	semidirect
485. #120	C₂×C₄×C₁₃₁	semidirect
486. #120	C₂×C₄×C₁₃₁	semidirect
493. #117	C₂×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×#535×C₁₃₁	2
#2380×C₁₃₁	2
#2375×C₁₃₁	2
#2366×C₁₃₁	2
#2363×C₁₃₁	2
#2361×C₁₃₁	2
#2358×C₁₃₁	2
#2347×C₁₃₁	2
D₄×C₂²⋊C₄×C₁₃₁	2
#2337×C₁₃₁	2
#2324×C₁₃₁	2
#2321×C₁₃₁	2
#2311×C₁₃₁	2
C₄×#121×C₁₃₁	2
#2297×C₁₃₁	2
#34411	131

Subgroups — C131×#34411 #45720295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34411 #45720295