Subgroups — C₃₁×#34490 #21491249

Order 7936.

1840 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2382	C₂	1	2	yes	maximal
3	C₃₁×#2381	C₂	1	2	yes	maximal
4	C₃₁×#2371	C₂	1	2	yes	maximal
5	C₃₁×#2370	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2370	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2369	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2356	C₂	1	2	yes	maximal
10	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2336	C₂	1	2	yes	maximal
14	C₃₁×#2336	C₂	1	2	yes	maximal
15	C₃₁×#2331	C₂	1	1	yes	maximal, characteristic
16	C₃₁×#2331	C₂	1	2	yes	maximal
17	C₃₁×#2330	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic
20	C₃₁×#2320	C₂	1	2	yes	maximal
21	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic
23	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic
24	C₃₁×#557	C₄	1	16	yes	complemented
25	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#125	C₂²	1	2	yes	—
29	C₂×C₃₁×#125	C₂²	1	2	yes	—
30	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#391	C₂²	1	1	yes	characteristic
37	C₃₁×#391	C₂²	1	2	yes	—
38	C₃₁×#391	C₂²	1	1	yes	characteristic
39	C₃₁×#391	C₂²	1	1	yes	characteristic
40	C₃₁×#391	C₂²	1	2	yes	—
41	C₃₁×#391	C₂²	1	1	yes	characteristic
42	C₃₁×#391	C₂²	1	2	yes	—
43	C₃₁×#391	C₂²	1	2	yes	—
44	C₃₁×#391	C₂²	1	2	yes	—
45	C₃₁×#391	C₂²	1	1	yes	characteristic
46	C₃₁×#391	C₂²	1	1	yes	characteristic
47	C₃₁×#389	C₂²	1	2	yes	—
48	C₃₁×#389	C₂²	1	1	yes	characteristic
49	C₃₁×#389	C₂²	1	1	yes	characteristic
50	C₃₁×#389	C₂²	1	1	yes	characteristic
51	C₃₁×#389	C₂²	1	1	yes	characteristic
52	C₃₁×#389	C₂²	1	2	yes	—
53	C₃₁×#389	C₂²	1	2	yes	—
54	C₃₁×#389	C₂²	1	1	yes	characteristic
55	C₃₁×#389	C₂²	1	2	yes	—
56	C₃₁×#389	C₂²	1	1	yes	characteristic
57	C₃₁×#389	C₂²	1	2	yes	—
58	C₃₁×#389	C₂²	1	1	yes	characteristic
59	C₃₁×#389	C₂²	1	1	yes	characteristic
60	C₃₁×#387	C₂²	1	1	yes	characteristic
61	C₃₁×#387	C₂²	1	2	yes	—
62	C₃₁×#387	C₂²	1	2	yes	—
63	C₃₁×#387	C₂²	1	2	yes	—
64	C₃₁×#387	C₂²	1	2	yes	—
65	C₃₁×#387	C₂²	1	2	yes	—
66	C₃₁×#387	C₂²	1	2	yes	—
67	C₃₁×#387	C₂²	1	2	yes	—
68	C₃₁×#387	C₂²	1	2	yes	—
69	C₃₁×#387	C₂²	1	2	yes	—
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	1	yes	characteristic
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	1	yes	characteristic
85	C₃₁×#387	C₂²	1	1	yes	characteristic
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	2	yes	—
88	C₃₁×#384	C₂²	1	1	yes	characteristic
89	C₃₁×#383	C₂²	1	2	yes	—
90	C₃₁×#383	C₂²	1	2	yes	—
91	C₃₁×#383	C₂²	1	2	yes	—
92	C₃₁×#383	C₂²	1	2	yes	—
93	C₃₁×#382	C₂²	1	2	yes	—
94	C₃₁×#382	C₂²	1	2	yes	—
95	C₃₁×#382	C₂²	1	2	yes	—
96	C₃₁×#382	C₂²	1	1	yes	characteristic
97	C₃₁×#382	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₃₁×#376	C₂²	1	1	yes	characteristic
119	C₃₁×#376	C₂²	1	1	yes	characteristic
120	C₃₁×#376	C₂²	1	2	yes	—
121	C₃₁×#376	C₂²	1	2	yes	—
122	C₃₁×#376	C₂²	1	2	yes	—
123	C₄³×C₃₁	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
126	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
128	C₃₁×C₄⋊Q₈	C₂×C₄	1	16	yes	—
129	C₃₁×#125	C₂×C₄	1	8	yes	—
130	C₃₁×#125	C₂×C₄	1	16	yes	—
131	C₃₁×#125	C₂×C₄	1	16	yes	—
132	C₃₁×#125	C₂×C₄	1	8	yes	—
133	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	—
134	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	—
135	C₄×Q₈×C₃₁	C₂×C₄	1	16	yes	—
136	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	—
137	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
183	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
184	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
185	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	1	yes	characteristic
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	1	yes	characteristic
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	1	yes	characteristic
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	1	yes	characteristic
201	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	1	yes	characteristic
206	C₃₁×#95	C₂³	1	1	yes	characteristic
207	C₃₁×#95	C₂³	1	1	yes	characteristic
208	C₃₁×#95	C₂³	1	1	yes	characteristic
209	C₃₁×#95	C₂³	1	1	yes	characteristic
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	1	yes	characteristic
212	C₃₁×#95	C₂³	1	1	yes	characteristic
213	C₃₁×#95	C₂³	1	1	yes	characteristic
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	1	yes	characteristic
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	4	1	no	—
237	C₂×Q₈×C₃₁	—	4	2	no	—
238	C₂×Q₈×C₃₁	—	4	2	no	—
239	C₂×Q₈×C₃₁	—	4	1	no	—
240	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
241	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
242	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	2	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	4	1	no	—
273	C₄⋊C₄×C₃₁	—	4	2	no	—
274	C₄⋊C₄×C₃₁	—	4	2	no	—
275	C₄⋊C₄×C₃₁	—	4	1	no	—
276	C₄⋊C₄×C₃₁	—	4	1	no	—
277	C₄⋊C₄×C₃₁	—	4	2	no	—
278	C₄⋊C₄×C₃₁	—	4	2	no	—
279	C₄⋊C₄×C₃₁	—	4	2	no	—
280	C₄⋊C₄×C₃₁	—	4	1	no	—
281	C₄⋊C₄×C₃₁	—	4	2	no	—
282	C₄⋊C₄×C₃₁	—	4	2	no	—
283	C₄⋊C₄×C₃₁	—	4	2	no	—
284	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
285	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
286	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
287	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
288	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
289	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
290	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
291	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
292	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
293	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
294	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
295	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
296	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
297	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
298	C₄²×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	—	2	2	no	—
304	C₄²×C₃₁	—	4	2	no	—
305	C₄²×C₃₁	—	4	1	no	—
306	C₄²×C₃₁	—	4	2	no	—
307	C₄²×C₃₁	—	4	1	no	—
308	C₄²×C₃₁	—	4	2	no	—
309	C₄²×C₃₁	—	4	2	no	—
310	C₄²×C₃₁	—	4	2	no	—
311	C₄²×C₃₁	—	4	2	no	—
312	C₄²×C₃₁	—	4	2	no	—
313	C₄²×C₃₁	—	4	2	no	—
314	C₄²×C₃₁	—	4	1	no	—
315	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
316	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
317	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
318	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
319	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
320	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
321	#34490	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
323	Q₈×C₃₁	—	2	8	no	—
324	Q₈×C₃₁	—	4	4	no	—
325	Q₈×C₃₁	—	4	8	no	—
326	C₂×C₄×C₃₁	—	2	1	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	1	no	—
329	C₂×C₄×C₃₁	—	2	1	no	—
330	C₂×C₄×C₃₁	—	2	1	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	1	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	1	no	—
346	C₂×C₄×C₃₁	—	2	1	no	—
347	C₂×C₄×C₃₁	—	2	1	no	—
348	C₂×C₄×C₃₁	—	2	1	no	—
349	C₂×C₄×C₃₁	—	2	1	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	1	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	1	no	—
354	C₂×C₄×C₃₁	—	2	1	no	—
355	C₂×C₄×C₃₁	—	2	1	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
382	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
384	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
385	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
387	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
388	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
389	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
390	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
391	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
392	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
393	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
394	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
395	C₂×#557	C₂×C₃₁	1	1	yes	characteristic
396	#2382	C₂×C₃₁	1	2	yes	—
397	#2381	C₂×C₃₁	1	2	yes	—
398	#2371	C₂×C₃₁	1	2	yes	—
399	#2370	C₂×C₃₁	1	1	yes	characteristic
400	#2370	C₂×C₃₁	1	1	yes	characteristic
401	#2369	C₂×C₃₁	1	1	yes	characteristic
402	#2356	C₂×C₃₁	1	1	yes	characteristic
403	#2356	C₂×C₃₁	1	2	yes	—
404	#2356	C₂×C₃₁	1	1	yes	characteristic
405	#2355	C₂×C₃₁	1	1	yes	characteristic
406	#2355	C₂×C₃₁	1	1	yes	characteristic
407	#2336	C₂×C₃₁	1	2	yes	—
408	#2336	C₂×C₃₁	1	2	yes	—
409	#2331	C₂×C₃₁	1	1	yes	characteristic
410	#2331	C₂×C₃₁	1	2	yes	—
411	#2330	C₂×C₃₁	1	1	yes	characteristic
412	#2320	C₂×C₃₁	1	1	yes	characteristic
413	#2320	C₂×C₃₁	1	1	yes	characteristic
414	#2320	C₂×C₃₁	1	2	yes	—
415	C₄×#125	C₂×C₃₁	1	1	yes	characteristic
416	#2295	C₂×C₃₁	1	1	yes	characteristic
417	#2295	C₂×C₃₁	1	1	yes	characteristic
418	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
419	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
420	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
421	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂²×C₃₁	#585	1	1	yes	characteristic
423	C₂²×C₃₁	#585	1	1	yes	characteristic
424	C₂²×C₃₁	#585	1	1	yes	characteristic
425	C₄×C₃₁	—	2	4	no	—
426	C₄×C₃₁	—	2	2	no	—
427	C₄×C₃₁	—	2	4	no	—
428	C₄×C₃₁	—	2	4	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	2	no	—
431	C₄×C₃₁	—	2	2	no	—
432	C₄×C₃₁	—	2	4	no	—
433	C₄×C₃₁	—	2	2	no	—
434	C₄×C₃₁	—	2	2	no	—
435	C₄×C₃₁	—	2	2	no	—
436	C₄×C₃₁	—	4	1	no	—
437	C₄×C₃₁	—	4	2	no	—
438	C₄×C₃₁	—	4	1	no	—
439	C₄×C₃₁	—	4	2	no	—
440	C₄×C₃₁	—	4	2	no	—
441	C₄×C₃₁	—	4	1	no	—
442	C₄×C₃₁	—	4	1	no	—
443	C₄×C₃₁	—	4	1	no	—
444	C₄×C₃₁	—	4	1	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	2	no	—
447	C₄×C₃₁	#519	1	4	yes	—
448	#557	C₄×C₃₁	1	16	yes	complemented
449	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
451	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×#125	C₂²×C₃₁	1	2	yes	—
454	C₂×#125	C₂²×C₃₁	1	2	yes	—
455	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
457	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
460	#391	C₂²×C₃₁	1	1	yes	characteristic
461	#391	C₂²×C₃₁	1	2	yes	—
462	#391	C₂²×C₃₁	1	1	yes	characteristic
463	#391	C₂²×C₃₁	1	1	yes	characteristic
464	#391	C₂²×C₃₁	1	2	yes	—
465	#391	C₂²×C₃₁	1	1	yes	characteristic
466	#391	C₂²×C₃₁	1	2	yes	—
467	#391	C₂²×C₃₁	1	2	yes	—
468	#391	C₂²×C₃₁	1	2	yes	—
469	#391	C₂²×C₃₁	1	1	yes	characteristic
470	#391	C₂²×C₃₁	1	1	yes	characteristic
471	#389	C₂²×C₃₁	1	1	yes	characteristic
472	#389	C₂²×C₃₁	1	1	yes	characteristic
473	#389	C₂²×C₃₁	1	2	yes	—
474	#389	C₂²×C₃₁	1	1	yes	characteristic
475	#389	C₂²×C₃₁	1	1	yes	characteristic
476	#389	C₂²×C₃₁	1	2	yes	—
477	#389	C₂²×C₃₁	1	2	yes	—
478	#389	C₂²×C₃₁	1	1	yes	characteristic
479	#389	C₂²×C₃₁	1	2	yes	—
480	#389	C₂²×C₃₁	1	1	yes	characteristic
481	#389	C₂²×C₃₁	1	2	yes	—
482	#389	C₂²×C₃₁	1	1	yes	characteristic
483	#389	C₂²×C₃₁	1	1	yes	characteristic
484	#387	C₂²×C₃₁	1	2	yes	—
485	#387	C₂²×C₃₁	1	2	yes	—
486	#387	C₂²×C₃₁	1	1	yes	characteristic
487	#387	C₂²×C₃₁	1	2	yes	—
488	#387	C₂²×C₃₁	1	2	yes	—
489	#387	C₂²×C₃₁	1	2	yes	—
490	#387	C₂²×C₃₁	1	2	yes	—
491	#387	C₂²×C₃₁	1	2	yes	—
492	#387	C₂²×C₃₁	1	2	yes	—
493	#387	C₂²×C₃₁	1	2	yes	—
494	#387	C₂²×C₃₁	1	2	yes	—
495	#387	C₂²×C₃₁	1	2	yes	—
496	#387	C₂²×C₃₁	1	2	yes	—
497	#387	C₂²×C₃₁	1	2	yes	—
498	#387	C₂²×C₃₁	1	2	yes	—
499	#387	C₂²×C₃₁	1	2	yes	—
500	#387	C₂²×C₃₁	1	1	yes	characteristic
501	#387	C₂²×C₃₁	1	2	yes	—
502	#387	C₂²×C₃₁	1	2	yes	—
503	#387	C₂²×C₃₁	1	2	yes	—
504	#387	C₂²×C₃₁	1	2	yes	—
505	#387	C₂²×C₃₁	1	2	yes	—
506	#387	C₂²×C₃₁	1	2	yes	—
507	#387	C₂²×C₃₁	1	2	yes	—
508	#387	C₂²×C₃₁	1	2	yes	—
509	#387	C₂²×C₃₁	1	1	yes	characteristic
510	#387	C₂²×C₃₁	1	1	yes	characteristic
511	#387	C₂²×C₃₁	1	2	yes	—
512	#384	C₂²×C₃₁	1	1	yes	characteristic
513	#383	C₂²×C₃₁	1	2	yes	—
514	#383	C₂²×C₃₁	1	2	yes	—
515	#383	C₂²×C₃₁	1	2	yes	—
516	#383	C₂²×C₃₁	1	2	yes	—
517	#382	C₂²×C₃₁	1	1	yes	characteristic
518	#382	C₂²×C₃₁	1	2	yes	—
519	#382	C₂²×C₃₁	1	2	yes	—
520	#382	C₂²×C₃₁	1	2	yes	—
521	#382	C₂²×C₃₁	1	1	yes	characteristic
522	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
524	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
527	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
529	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
532	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
534	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
536	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
537	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
538	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
541	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
542	#376	C₂²×C₃₁	1	1	yes	characteristic
543	#376	C₂²×C₃₁	1	1	yes	characteristic
544	#376	C₂²×C₃₁	1	2	yes	—
545	#376	C₂²×C₃₁	1	2	yes	—
546	#376	C₂²×C₃₁	1	2	yes	—
547	C₄³	C₂²×C₃₁	1	1	yes	characteristic
548	C₂×C₃₁	C₂×#519	1	1	yes	characteristic
549	C₂×C₃₁	#3428	1	1	yes	characteristic
550	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂×C₃₁	#3555	1	1	yes	characteristic
552	C₂×C₃₁	#3557	1	1	yes	characteristic
553	C₂×C₃₁	#3563	1	1	yes	characteristic
554	C₂×C₃₁	#3565	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
557	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
558	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
559	C₄⋊Q₈	C₂×C₄×C₃₁	1	16	yes	—
560	#125	C₂×C₄×C₃₁	1	8	yes	—
561	#125	C₂×C₄×C₃₁	1	8	yes	—
562	#125	C₂×C₄×C₃₁	1	16	yes	—
563	#125	C₂×C₄×C₃₁	1	16	yes	—
564	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	—
565	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	—
566	C₄×Q₈	C₂×C₄×C₃₁	1	16	yes	—
567	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	—
568	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	—
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
611	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
612	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
614	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
616	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
617	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
618	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
622	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
624	#95	C₂³×C₃₁	1	1	yes	characteristic
625	#95	C₂³×C₃₁	1	2	yes	—
626	#95	C₂³×C₃₁	1	1	yes	characteristic
627	#95	C₂³×C₃₁	1	2	yes	—
628	#95	C₂³×C₃₁	1	2	yes	—
629	#95	C₂³×C₃₁	1	1	yes	characteristic
630	#95	C₂³×C₃₁	1	2	yes	—
631	#95	C₂³×C₃₁	1	1	yes	characteristic
632	#95	C₂³×C₃₁	1	2	yes	—
633	#95	C₂³×C₃₁	1	2	yes	—
634	#95	C₂³×C₃₁	1	2	yes	—
635	#95	C₂³×C₃₁	1	2	yes	—
636	#95	C₂³×C₃₁	1	1	yes	characteristic
637	#95	C₂³×C₃₁	1	1	yes	characteristic
638	#95	C₂³×C₃₁	1	1	yes	characteristic
639	#95	C₂³×C₃₁	1	1	yes	characteristic
640	#95	C₂³×C₃₁	1	1	yes	characteristic
641	#95	C₂³×C₃₁	1	2	yes	—
642	#95	C₂³×C₃₁	1	1	yes	characteristic
643	#95	C₂³×C₃₁	1	1	yes	characteristic
644	#95	C₂³×C₃₁	1	1	yes	characteristic
645	#95	C₂³×C₃₁	1	2	yes	—
646	#95	C₂³×C₃₁	1	2	yes	—
647	#95	C₂³×C₃₁	1	2	yes	—
648	#95	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	2	yes	—
650	#95	C₂³×C₃₁	1	2	yes	—
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	2	yes	—
653	#95	C₂³×C₃₁	1	2	yes	—
654	#95	C₂³×C₃₁	1	1	yes	characteristic
655	#95	C₂³×C₃₁	1	2	yes	—
656	#95	C₂³×C₃₁	1	2	yes	—
657	#95	C₂³×C₃₁	1	2	yes	—
658	#95	C₂³×C₃₁	1	2	yes	—
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	2	yes	—
661	#95	C₂³×C₃₁	1	2	yes	—
662	#95	C₂³×C₃₁	1	2	yes	—
663	#95	C₂³×C₃₁	1	1	yes	characteristic
664	#95	C₂³×C₃₁	1	2	yes	—
665	C₃₁	#34490	1	1	yes	characteristic, direct product factor, Sylow
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	1	no	—
672	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
673	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
674	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
675	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	1	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	1	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
717	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
718	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
719	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
720	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
721	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
722	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
723	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
724	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
725	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
726	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
727	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
728	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
729	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	4	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	4	2	no	—
737	C₄²	—	4	1	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	1	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	2	no	—
746	C₄²	—	4	1	no	—
747	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
748	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
749	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
750	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
751	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
752	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
753	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
754	Q₈	—	2	8	no	—
755	Q₈	—	4	4	no	—
756	Q₈	—	4	8	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
813	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
814	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
815	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
816	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
817	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
818	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
819	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
820	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
821	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
822	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
823	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
824	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
825	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
826	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
827	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
828	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
829	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
830	C₂²	C₃₁×#585	1	1	yes	characteristic
831	C₂²	C₃₁×#585	1	1	yes	characteristic
832	C₂²	C₃₁×#585	1	1	yes	characteristic
833	C₄	—	2	4	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	4	no	—
837	C₄	—	2	4	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	4	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	C₃₁×#519	1	4	yes	—
856	C₂	C₂×C₃₁×#519	1	1	yes	characteristic
857	C₂	C₃₁×#3428	1	1	yes	characteristic
858	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂	C₃₁×#3555	1	1	yes	characteristic
860	C₂	C₃₁×#3557	1	1	yes	characteristic
861	C₂	C₃₁×#3563	1	1	yes	characteristic
862	C₂	C₃₁×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
24. C₃₁×#557	C₄	semidirect
321. #34490	C₃₁	direct (N × H)
448. #557	C₄×C₃₁	semidirect
665. C₃₁	#34490	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#557	2
C₃₁×#2382	2
C₃₁×#2381	2
C₃₁×#2371	2
C₃₁×#2370	2
C₃₁×#2369	2
C₃₁×#2356	2
C₃₁×#2355	2
C₃₁×#2336	2
C₃₁×#2331	2
C₃₁×#2330	2
C₃₁×#2320	2
C₄×C₃₁×#125	2
C₃₁×#2295	2
#34490	31

Subgroups — C31×#34490 #21491249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34490 #21491249