Subgroups — C₃₁×#35000 #21491759

Order 7936.

3754 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#534	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2854	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2847	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2618	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2617	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2543	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2534	C₂	1	4	yes	maximal, complemented
10	C₃₁×#2486	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2416	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2408	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2308	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
18	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#534	—	2	16	no	—
21	C₂×C₃₁×#123	C₂²	1	4	yes	—
22	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
23	C₂×C₃₁×#121	—	2	8	no	—
24	C₂×C₃₁×#121	C₂²	1	2	yes	—
25	C₂×C₃₁×#121	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
27	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
28	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
29	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
30	C₂×C₃₁×#120	C₂²	1	4	yes	—
31	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
32	C₂×C₄×D₄×C₃₁	—	2	8	no	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
44	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#398	C₂²	1	4	yes	complemented
46	C₃₁×#397	C₂²	1	4	yes	complemented
47	C₃₁×#396	C₂²	1	8	yes	complemented
48	C₃₁×#394	C₂²	1	8	yes	complemented
49	C₃₁×#394	C₂²	1	4	yes	complemented
50	C₃₁×#392	C₂²	1	4	yes	complemented
51	C₃₁×#390	C₂²	1	4	yes	complemented
52	C₃₁×#389	C₂²	1	4	yes	complemented
53	C₃₁×#388	C₂²	1	8	yes	complemented
54	C₃₁×#386	C₂²	1	4	yes	complemented
55	C₃₁×#386	C₂²	1	4	yes	complemented
56	C₃₁×#386	C₂²	1	8	yes	complemented
57	C₃₁×#386	C₂²	1	8	yes	complemented
58	C₃₁×#381	C₂²	1	4	yes	complemented
59	C₃₁×#380	C₂²	1	2	yes	complemented
60	C₃₁×#380	C₂²	1	4	yes	complemented
61	C₃₁×#380	C₂²	1	2	yes	complemented
62	C₃₁×#380	C₂²	1	2	yes	complemented
63	C₃₁×#380	C₂²	1	2	yes	complemented
64	C₃₁×#379	C₂²	1	4	yes	complemented
65	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
66	C₂⁵×C₃₁	C₂³	1	2	yes	—
67	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
68	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₃₁	—	2	4	no	—
70	C₂²×D₄×C₃₁	—	2	4	no	—
71	C₂²×D₄×C₃₁	—	2	8	no	—
72	C₂²×D₄×C₃₁	—	2	8	no	—
73	C₂²×D₄×C₃₁	—	2	8	no	—
74	C₂²×D₄×C₃₁	—	2	4	no	—
75	C₂²×D₄×C₃₁	—	4	4	no	—
76	C₂²×D₄×C₃₁	D₄	1	8	yes	complemented
77	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
78	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
79	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
80	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
82	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
83	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₃₁	—	2	4	no	—
85	C₂³×C₄×C₃₁	—	4	4	no	—
86	C₂³×C₄×C₃₁	—	4	4	no	—
87	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
88	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
89	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
98	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₃₁×#123	—	2	16	no	—
102	C₃₁×#123	—	2	16	no	—
103	C₃₁×#121	—	2	32	no	—
104	C₃₁×#121	—	2	8	no	—
105	C₃₁×#121	—	2	8	no	—
106	C₃₁×#121	—	2	8	no	—
107	C₃₁×#121	—	2	8	no	—
108	C₃₁×#121	—	4	8	no	—
109	C₃₁×#120	—	2	16	no	—
110	C₃₁×#120	—	2	16	no	—
111	C₄×D₄×C₃₁	—	2	8	no	—
112	C₄×D₄×C₃₁	—	2	8	no	—
113	C₄×D₄×C₃₁	—	2	8	no	—
114	C₄×D₄×C₃₁	—	2	8	no	—
115	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
116	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
117	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
127	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
141	C₂×C₄²×C₃₁	—	2	4	no	—
142	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
144	C₃₁×#95	C₂³	1	8	yes	—
145	C₃₁×#95	C₂³	1	4	yes	—
146	C₃₁×#95	C₂³	1	8	yes	—
147	C₃₁×#95	C₂³	1	4	yes	—
148	C₂⁴×C₃₁	—	2	2	no	—
149	C₂⁴×C₃₁	—	2	2	no	—
150	C₂⁴×C₃₁	—	2	4	no	—
151	C₂⁴×C₃₁	—	2	4	no	—
152	C₂⁴×C₃₁	—	2	4	no	—
153	C₂⁴×C₃₁	—	4	2	no	—
154	C₂⁴×C₃₁	—	4	2	no	—
155	C₂⁴×C₃₁	—	4	2	no	—
156	C₂⁴×C₃₁	—	4	2	no	—
157	C₂⁴×C₃₁	—	4	4	no	—
158	C₂⁴×C₃₁	—	4	4	no	—
159	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
160	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
161	C₂⁴×C₃₁	C₂×D₄	1	4	yes	complemented
162	C₂⁴×C₃₁	#41	1	4	yes	—
163	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
164	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
165	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
166	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
168	C₂×D₄×C₃₁	—	2	32	no	—
169	C₂×D₄×C₃₁	—	2	4	no	—
170	C₂×D₄×C₃₁	—	2	4	no	—
171	C₂×D₄×C₃₁	—	2	4	no	—
172	C₂×D₄×C₃₁	—	2	4	no	—
173	C₂×D₄×C₃₁	—	2	8	no	—
174	C₂×D₄×C₃₁	—	2	8	no	—
175	C₂×D₄×C₃₁	—	2	8	no	—
176	C₂×D₄×C₃₁	—	2	8	no	—
177	C₂×D₄×C₃₁	—	2	8	no	—
178	C₂×D₄×C₃₁	—	2	8	no	—
179	C₂×D₄×C₃₁	—	2	16	no	—
180	C₂×D₄×C₃₁	—	2	4	no	—
181	C₂×D₄×C₃₁	—	2	4	no	—
182	C₂×D₄×C₃₁	—	2	8	no	—
183	C₂×D₄×C₃₁	—	4	4	no	—
184	C₂×D₄×C₃₁	—	4	16	no	—
185	C₂×D₄×C₃₁	—	4	8	no	—
186	C₂×D₄×C₃₁	—	4	8	no	—
187	C₂×D₄×C₃₁	—	4	32	no	—
188	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
189	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	complemented
190	C₂²×C₄×C₃₁	—	2	2	no	—
191	C₂²×C₄×C₃₁	—	2	2	no	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
193	C₂²×C₄×C₃₁	—	2	4	no	—
194	C₂²×C₄×C₃₁	—	2	4	no	—
195	C₂²×C₄×C₃₁	—	2	2	no	—
196	C₂²×C₄×C₃₁	—	2	2	no	—
197	C₂²×C₄×C₃₁	—	2	4	no	—
198	C₂²×C₄×C₃₁	—	2	4	no	—
199	C₂²×C₄×C₃₁	—	2	4	no	—
200	C₂²×C₄×C₃₁	—	2	8	no	—
201	C₂²×C₄×C₃₁	—	2	4	no	—
202	C₂²×C₄×C₃₁	—	2	4	no	—
203	C₂²×C₄×C₃₁	—	2	8	no	—
204	C₂²×C₄×C₃₁	—	4	16	no	—
205	C₂²×C₄×C₃₁	—	4	2	no	—
206	C₂²×C₄×C₃₁	—	4	2	no	—
207	C₂²×C₄×C₃₁	—	4	2	no	—
208	C₂²×C₄×C₃₁	—	4	4	no	—
209	C₂²×C₄×C₃₁	—	4	2	no	—
210	C₂²×C₄×C₃₁	—	4	2	no	—
211	C₂²×C₄×C₃₁	—	4	4	no	—
212	C₂²×C₄×C₃₁	—	4	4	no	—
213	C₂²×C₄×C₃₁	—	4	16	no	—
214	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	complemented
221	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
223	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	—	2	4	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	2	16	no	—
235	C₄⋊C₄×C₃₁	—	2	8	no	—
236	C₄⋊C₄×C₃₁	—	4	4	no	—
237	C₂²⋊C₄×C₃₁	—	2	4	no	—
238	C₂²⋊C₄×C₃₁	—	2	4	no	—
239	C₂²⋊C₄×C₃₁	—	2	8	no	—
240	C₂²⋊C₄×C₃₁	—	2	8	no	—
241	C₂²⋊C₄×C₃₁	—	2	16	no	—
242	C₂²⋊C₄×C₃₁	—	2	4	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	8	no	—
245	C₂²⋊C₄×C₃₁	—	2	8	no	—
246	C₂²⋊C₄×C₃₁	—	2	16	no	—
247	C₂²⋊C₄×C₃₁	—	4	8	no	—
248	C₂²⋊C₄×C₃₁	—	4	8	no	—
249	C₄²×C₃₁	—	2	4	no	—
250	C₄²×C₃₁	—	2	4	no	—
251	#35000	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂³×C₃₁	—	2	2	no	—
253	C₂³×C₃₁	—	2	2	no	—
254	C₂³×C₃₁	—	2	2	no	—
255	C₂³×C₃₁	—	2	2	no	—
256	C₂³×C₃₁	—	2	2	no	—
257	C₂³×C₃₁	—	2	2	no	—
258	C₂³×C₃₁	—	2	8	no	—
259	C₂³×C₃₁	—	2	2	no	—
260	C₂³×C₃₁	—	2	2	no	—
261	C₂³×C₃₁	—	2	4	no	—
262	C₂³×C₃₁	—	2	4	no	—
263	C₂³×C₃₁	—	2	4	no	—
264	C₂³×C₃₁	—	2	4	no	—
265	C₂³×C₃₁	—	2	4	no	—
266	C₂³×C₃₁	—	2	8	no	—
267	C₂³×C₃₁	—	2	8	no	—
268	C₂³×C₃₁	—	4	4	no	—
269	C₂³×C₃₁	—	4	4	no	—
270	C₂³×C₃₁	—	4	8	no	—
271	C₂³×C₃₁	—	4	8	no	—
272	C₂³×C₃₁	—	4	8	no	—
273	C₂³×C₃₁	—	4	4	no	—
274	C₂³×C₃₁	—	4	4	no	—
275	C₂³×C₃₁	—	4	8	no	—
276	C₂³×C₃₁	—	4	8	no	—
277	C₂³×C₃₁	—	4	8	no	—
278	C₂³×C₃₁	—	4	8	no	—
279	C₂³×C₃₁	—	8	8	no	—
280	C₂³×C₃₁	—	8	8	no	—
281	C₂³×C₃₁	#121	1	16	yes	complemented
282	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
283	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
284	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
285	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
286	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
287	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
288	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
289	C₂³×C₃₁	C₂×#41	1	2	yes	—
290	C₂³×C₃₁	C₂×#41	1	2	yes	—
291	C₂³×C₃₁	C₂×#41	1	2	yes	—
292	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
293	D₄×C₃₁	—	2	16	no	—
294	D₄×C₃₁	—	2	16	no	—
295	D₄×C₃₁	—	4	8	no	—
296	D₄×C₃₁	—	4	16	no	—
297	D₄×C₃₁	—	4	16	no	—
298	D₄×C₃₁	—	4	8	no	—
299	D₄×C₃₁	—	8	16	no	—
300	C₂×C₄×C₃₁	—	2	8	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	8	no	—
307	C₂×C₄×C₃₁	—	2	8	no	—
308	C₂×C₄×C₃₁	—	2	8	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	8	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	4	no	—
313	C₂×C₄×C₃₁	—	2	4	no	—
314	C₂×C₄×C₃₁	—	2	4	no	—
315	C₂×C₄×C₃₁	—	2	4	no	—
316	C₂×C₄×C₃₁	—	2	8	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	8	no	—
319	C₂×C₄×C₃₁	—	4	4	no	—
320	C₂×C₄×C₃₁	—	4	4	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	—	4	8	no	—
323	C₂×C₄×C₃₁	—	4	4	no	—
324	C₂×C₄×C₃₁	—	4	4	no	—
325	C₂×C₄×C₃₁	—	4	8	no	—
326	C₂×C₄×C₃₁	—	4	8	no	—
327	C₂×C₄×C₃₁	—	8	8	no	—
328	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
334	C₂×#534	C₂×C₃₁	1	2	yes	complemented
335	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
336	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#2854	C₂×C₃₁	1	2	yes	complemented
338	#2847	C₂×C₃₁	1	2	yes	complemented
339	#2618	C₂×C₃₁	1	2	yes	complemented
340	#2617	C₂×C₃₁	1	2	yes	complemented
341	#2543	C₂×C₃₁	1	4	yes	complemented
342	#2534	C₂×C₃₁	1	4	yes	complemented
343	#2486	C₂×C₃₁	1	2	yes	complemented
344	#2416	C₂×C₃₁	1	4	yes	complemented
345	#2408	C₂×C₃₁	1	2	yes	complemented
346	#2308	C₂×C₃₁	1	2	yes	complemented
347	C₂×#380	C₂×C₃₁	1	1	yes	characteristic, complemented
348	C₂²×C₃₁	—	2	2	no	—
349	C₂²×C₃₁	—	2	2	no	—
350	C₂²×C₃₁	—	2	2	no	—
351	C₂²×C₃₁	—	2	2	no	—
352	C₂²×C₃₁	—	2	2	no	—
353	C₂²×C₃₁	—	2	2	no	—
354	C₂²×C₃₁	—	2	4	no	—
355	C₂²×C₃₁	—	2	4	no	—
356	C₂²×C₃₁	—	2	4	no	—
357	C₂²×C₃₁	—	2	4	no	—
358	C₂²×C₃₁	—	2	4	no	—
359	C₂²×C₃₁	—	2	4	no	—
360	C₂²×C₃₁	—	2	4	no	—
361	C₂²×C₃₁	—	2	8	no	—
362	C₂²×C₃₁	—	4	16	no	—
363	C₂²×C₃₁	—	4	16	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	4	no	—
367	C₂²×C₃₁	—	4	4	no	—
368	C₂²×C₃₁	—	4	4	no	—
369	C₂²×C₃₁	—	4	4	no	—
370	C₂²×C₃₁	—	4	8	no	—
371	C₂²×C₃₁	—	4	8	no	—
372	C₂²×C₃₁	—	8	16	no	—
373	C₂²×C₃₁	C₂×#121	1	4	yes	—
374	C₂²×C₃₁	C₂×#121	1	4	yes	—
375	C₂²×C₃₁	C₂×#121	1	4	yes	—
376	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
377	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
378	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
379	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
380	C₂²×C₃₁	#585	1	2	yes	—
381	C₄×C₃₁	—	2	4	no	—
382	C₄×C₃₁	—	2	2	no	—
383	C₄×C₃₁	—	2	2	no	—
384	C₄×C₃₁	—	2	2	no	—
385	C₄×C₃₁	—	4	4	no	—
386	C₄×C₃₁	—	4	2	no	—
387	C₄×C₃₁	—	4	2	no	—
388	C₄×C₃₁	—	4	8	no	—
389	C₄×C₃₁	#534	1	4	yes	complemented
390	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
391	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
392	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
394	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
395	#534	—	2	16	no	—
396	C₂×#123	C₂²×C₃₁	1	4	yes	—
397	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
398	C₂×#121	—	2	8	no	—
399	C₂×#121	C₂²×C₃₁	1	2	yes	—
400	C₂×#121	C₂²×C₃₁	1	2	yes	—
401	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
402	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
403	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
404	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
405	C₂×#120	C₂²×C₃₁	1	4	yes	—
406	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
407	C₂×C₄×D₄	—	2	8	no	—
408	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
411	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
412	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
413	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
414	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
415	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
417	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
418	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
419	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
420	#398	C₂²×C₃₁	1	4	yes	complemented
421	#397	C₂²×C₃₁	1	4	yes	complemented
422	#396	C₂²×C₃₁	1	8	yes	complemented
423	#394	C₂²×C₃₁	1	8	yes	complemented
424	#394	C₂²×C₃₁	1	4	yes	complemented
425	#392	C₂²×C₃₁	1	4	yes	complemented
426	#390	C₂²×C₃₁	1	4	yes	complemented
427	#389	C₂²×C₃₁	1	4	yes	complemented
428	#388	C₂²×C₃₁	1	8	yes	complemented
429	#386	C₂²×C₃₁	1	4	yes	complemented
430	#386	C₂²×C₃₁	1	4	yes	complemented
431	#386	C₂²×C₃₁	1	8	yes	complemented
432	#386	C₂²×C₃₁	1	8	yes	complemented
433	#381	C₂²×C₃₁	1	4	yes	complemented
434	#380	C₂²×C₃₁	1	2	yes	complemented
435	#380	C₂²×C₃₁	1	4	yes	complemented
436	#380	C₂²×C₃₁	1	2	yes	complemented
437	#380	C₂²×C₃₁	1	2	yes	complemented
438	#380	C₂²×C₃₁	1	2	yes	complemented
439	#379	C₂²×C₃₁	1	4	yes	complemented
440	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
441	C₂×C₃₁	—	2	4	no	—
442	C₂×C₃₁	—	2	4	no	—
443	C₂×C₃₁	—	2	4	no	—
444	C₂×C₃₁	—	4	4	no	—
445	C₂×C₃₁	—	8	4	no	—
446	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
447	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
448	C₂×C₃₁	#3449	1	1	yes	characteristic
449	C₂×C₃₁	#3496	1	2	yes	—
450	C₂×C₃₁	#3505	1	2	yes	—
451	C₂⁵	C₂³×C₃₁	1	2	yes	—
452	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
453	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
454	C₂²×D₄	—	2	4	no	—
455	C₂²×D₄	—	2	4	no	—
456	C₂²×D₄	—	2	8	no	—
457	C₂²×D₄	—	2	8	no	—
458	C₂²×D₄	—	2	8	no	—
459	C₂²×D₄	—	2	4	no	—
460	C₂²×D₄	—	4	4	no	—
461	C₂²×D₄	D₄×C₃₁	1	8	yes	complemented
462	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
463	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
464	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
465	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
466	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
467	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
468	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
469	C₂³×C₄	—	2	4	no	—
470	C₂³×C₄	—	4	4	no	—
471	C₂³×C₄	—	4	4	no	—
472	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
473	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
474	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
475	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
481	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
483	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
486	#123	—	2	16	no	—
487	#123	—	2	16	no	—
488	#121	—	2	32	no	—
489	#121	—	2	8	no	—
490	#121	—	2	8	no	—
491	#121	—	2	8	no	—
492	#121	—	2	8	no	—
493	#121	—	4	8	no	—
494	#120	—	2	16	no	—
495	#120	—	2	16	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	8	no	—
499	C₄×D₄	—	2	8	no	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	—	2	4	no	—
502	C₂×C₄⋊C₄	—	4	4	no	—
503	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	8	no	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	8	no	—
514	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
526	C₂×C₄²	—	2	4	no	—
527	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
528	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
529	#95	C₂³×C₃₁	1	4	yes	—
530	#95	C₂³×C₃₁	1	4	yes	—
531	#95	C₂³×C₃₁	1	8	yes	—
532	#95	C₂³×C₃₁	1	8	yes	—
533	C₃₁	#35000	1	1	yes	characteristic, direct product factor, Sylow
534	C₂⁴	—	2	2	no	—
535	C₂⁴	—	2	2	no	—
536	C₂⁴	—	2	4	no	—
537	C₂⁴	—	2	4	no	—
538	C₂⁴	—	2	4	no	—
539	C₂⁴	—	4	2	no	—
540	C₂⁴	—	4	2	no	—
541	C₂⁴	—	4	2	no	—
542	C₂⁴	—	4	2	no	—
543	C₂⁴	—	4	4	no	—
544	C₂⁴	—	4	4	no	—
545	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
546	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
547	C₂⁴	C₂×D₄×C₃₁	1	4	yes	complemented
548	C₂⁴	#41×C₃₁	1	4	yes	—
549	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
550	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
551	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
552	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
553	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
554	C₂×D₄	—	2	32	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	8	no	—
561	C₂×D₄	—	2	8	no	—
562	C₂×D₄	—	2	8	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	16	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	16	no	—
571	C₂×D₄	—	4	8	no	—
572	C₂×D₄	—	4	8	no	—
573	C₂×D₄	—	4	32	no	—
574	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
575	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	complemented
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	8	no	—
590	C₂²×C₄	—	4	16	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	—	4	4	no	—
599	C₂²×C₄	—	4	16	no	—
600	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
601	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
602	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
603	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
604	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
605	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
606	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	complemented
607	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
609	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	16	no	—
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	8	no	—
627	C₂²⋊C₄	—	2	16	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	16	no	—
633	C₂²⋊C₄	—	4	8	no	—
634	C₂²⋊C₄	—	4	8	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	8	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	8	no	—
652	C₂³	—	2	8	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	8	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	8	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	8	no	—
661	C₂³	—	4	8	no	—
662	C₂³	—	4	8	no	—
663	C₂³	—	4	8	no	—
664	C₂³	—	8	8	no	—
665	C₂³	—	8	8	no	—
666	C₂³	C₃₁×#121	1	16	yes	complemented
667	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
668	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
669	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
670	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
671	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
672	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
673	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
674	C₂³	C₂×#41×C₃₁	1	2	yes	—
675	C₂³	C₂×#41×C₃₁	1	2	yes	—
676	C₂³	C₂×#41×C₃₁	1	2	yes	—
677	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
678	D₄	—	2	16	no	—
679	D₄	—	2	16	no	—
680	D₄	—	4	8	no	—
681	D₄	—	4	16	no	—
682	D₄	—	4	16	no	—
683	D₄	—	4	8	no	—
684	D₄	—	8	16	no	—
685	C₂×C₄	—	2	8	no	—
686	C₂×C₄	—	2	2	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	8	no	—
692	C₂×C₄	—	2	8	no	—
693	C₂×C₄	—	2	8	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	8	8	no	—
713	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
716	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
718	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	4	16	no	—
734	C₂²	—	4	16	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	8	no	—
742	C₂²	—	4	8	no	—
743	C₂²	—	8	16	no	—
744	C₂²	C₂×C₃₁×#121	1	4	yes	—
745	C₂²	C₂×C₃₁×#121	1	4	yes	—
746	C₂²	C₂×C₃₁×#121	1	4	yes	—
747	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
748	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
750	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
751	C₂²	C₃₁×#585	1	2	yes	—
752	C₄	—	2	4	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	4	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	8	no	—
760	C₄	C₃₁×#534	1	4	yes	complemented
761	C₂	—	2	4	no	—
762	C₂	—	2	4	no	—
763	C₂	—	2	4	no	—
764	C₂	—	4	4	no	—
765	C₂	—	8	4	no	—
766	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic
767	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
768	C₂	C₃₁×#3449	1	1	yes	characteristic
769	C₂	C₃₁×#3496	1	2	yes	—
770	C₂	C₃₁×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#534	C₂	semidirect
2. C₂²×C₃₁×#121	C₂	semidirect
3. C₂²×C₄×D₄×C₃₁	C₂	semidirect
4. C₃₁×#2854	C₂	semidirect
5. C₃₁×#2847	C₂	semidirect
6. C₃₁×#2618	C₂	semidirect
7. C₃₁×#2617	C₂	semidirect
8. C₃₁×#2543	C₂	semidirect
9. C₃₁×#2534	C₂	semidirect
10. C₃₁×#2486	C₂	semidirect
11. C₃₁×#2416	C₂	semidirect
12. C₃₁×#2408	C₂	semidirect
13. C₃₁×#2308	C₂	semidirect
14. C₂×C₃₁×#380	C₂	semidirect
17. C₂³×D₄×C₃₁	C₂²	semidirect
19. C₂⁴×C₄×C₃₁	C₂²	semidirect
22. C₂×C₃₁×#123	C₂²	semidirect
26. C₂×C₃₁×#121	C₂²	semidirect
27. C₂×C₃₁×#121	C₂²	semidirect
28. C₂×C₃₁×#121	C₂²	semidirect
29. C₂×C₃₁×#121	C₂²	semidirect
31. C₂×C₃₁×#120	C₂²	semidirect
35. C₂×C₄×D₄×C₃₁	C₂²	semidirect
36. C₂×C₄×D₄×C₃₁	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
44. C₂²×C₄²×C₃₁	C₂²	semidirect
45. C₃₁×#398	C₂²	semidirect
46. C₃₁×#397	C₂²	semidirect
47. C₃₁×#396	C₂²	semidirect
48. C₃₁×#394	C₂²	semidirect
49. C₃₁×#394	C₂²	semidirect
50. C₃₁×#392	C₂²	semidirect
51. C₃₁×#390	C₂²	semidirect
52. C₃₁×#389	C₂²	semidirect
53. C₃₁×#388	C₂²	semidirect
54. C₃₁×#386	C₂²	semidirect
55. C₃₁×#386	C₂²	semidirect
56. C₃₁×#386	C₂²	semidirect
57. C₃₁×#386	C₂²	semidirect
58. C₃₁×#381	C₂²	semidirect
59. C₃₁×#380	C₂²	semidirect
60. C₃₁×#380	C₂²	semidirect
61. C₃₁×#380	C₂²	semidirect
62. C₃₁×#380	C₂²	semidirect
63. C₃₁×#380	C₂²	semidirect
64. C₃₁×#379	C₂²	semidirect
65. C₂×C₃₁×#95	C₂²	semidirect
76. C₂²×D₄×C₃₁	D₄	semidirect
87. C₂³×C₄×C₃₁	D₄	semidirect
161. C₂⁴×C₃₁	C₂×D₄	semidirect
189. C₂×D₄×C₃₁	C₂×D₄	semidirect
220. C₂²×C₄×C₃₁	C₂×D₄	semidirect
251. #35000	C₃₁	direct (N × H)
281. C₂³×C₃₁	#121	semidirect
334. C₂×#534	C₂×C₃₁	semidirect
335. C₂²×#121	C₂×C₃₁	semidirect
336. C₂²×C₄×D₄	C₂×C₃₁	semidirect
337. #2854	C₂×C₃₁	semidirect
338. #2847	C₂×C₃₁	semidirect
339. #2618	C₂×C₃₁	semidirect
340. #2617	C₂×C₃₁	semidirect
341. #2543	C₂×C₃₁	semidirect
342. #2534	C₂×C₃₁	semidirect
343. #2486	C₂×C₃₁	semidirect
344. #2416	C₂×C₃₁	semidirect
345. #2408	C₂×C₃₁	semidirect
346. #2308	C₂×C₃₁	semidirect
347. C₂×#380	C₂×C₃₁	semidirect
389. C₄×C₃₁	#534	semidirect
392. C₂³×D₄	C₂²×C₃₁	semidirect
394. C₂⁴×C₄	C₂²×C₃₁	semidirect
397. C₂×#123	C₂²×C₃₁	semidirect
401. C₂×#121	C₂²×C₃₁	semidirect
402. C₂×#121	C₂²×C₃₁	semidirect
403. C₂×#121	C₂²×C₃₁	semidirect
404. C₂×#121	C₂²×C₃₁	semidirect
406. C₂×#120	C₂²×C₃₁	semidirect
410. C₂×C₄×D₄	C₂²×C₃₁	semidirect
411. C₂×C₄×D₄	C₂²×C₃₁	semidirect
412. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
413. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
414. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
417. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
418. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
419. C₂²×C₄²	C₂²×C₃₁	semidirect
420. #398	C₂²×C₃₁	semidirect
421. #397	C₂²×C₃₁	semidirect
422. #396	C₂²×C₃₁	semidirect
423. #394	C₂²×C₃₁	semidirect
424. #394	C₂²×C₃₁	semidirect
425. #392	C₂²×C₃₁	semidirect
426. #390	C₂²×C₃₁	semidirect
427. #389	C₂²×C₃₁	semidirect
428. #388	C₂²×C₃₁	semidirect
429. #386	C₂²×C₃₁	semidirect
430. #386	C₂²×C₃₁	semidirect
431. #386	C₂²×C₃₁	semidirect
432. #386	C₂²×C₃₁	semidirect
433. #381	C₂²×C₃₁	semidirect
434. #380	C₂²×C₃₁	semidirect
435. #380	C₂²×C₃₁	semidirect
436. #380	C₂²×C₃₁	semidirect
437. #380	C₂²×C₃₁	semidirect
438. #380	C₂²×C₃₁	semidirect
439. #379	C₂²×C₃₁	semidirect
440. C₂×#95	C₂²×C₃₁	semidirect
461. C₂²×D₄	D₄×C₃₁	semidirect
472. C₂³×C₄	D₄×C₃₁	semidirect
533. C₃₁	#35000	direct (N × H)
547. C₂⁴	C₂×D₄×C₃₁	semidirect
575. C₂×D₄	C₂×D₄×C₃₁	semidirect
606. C₂²×C₄	C₂×D₄×C₃₁	semidirect
666. C₂³	C₃₁×#121	semidirect
760. C₄	C₃₁×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#534	2
C₂²×C₃₁×#121	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2854	2
C₃₁×#2847	2
C₃₁×#2618	2
C₃₁×#2617	2
C₃₁×#2543	2
C₃₁×#2534	2
C₃₁×#2486	2
C₃₁×#2416	2
C₃₁×#2408	2
C₃₁×#2308	2
C₂×C₃₁×#380	2
#35000	31

Subgroups — C31×#35000 #21491759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35000 #21491759