Subgroups — C₃₁×#34867 #21491626

Order 7936.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2605	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2604	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2601	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2599	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2594	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2577	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2560	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2528	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2521	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2478	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2474	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2469	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2465	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2401	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2399	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2398	C₂	1	1	yes	maximal, characteristic
20	C₃₁×#2396	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#126	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic
25	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#2290	C₂	1	1	yes	maximal, characteristic
30	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#401	C₂²	1	1	yes	characteristic
48	C₃₁×#400	C₂²	1	1	yes	characteristic
49	C₃₁×#400	C₂²	1	1	yes	characteristic
50	C₃₁×#400	C₂²	1	1	yes	characteristic
51	C₃₁×#400	C₂²	1	1	yes	characteristic
52	C₃₁×#400	C₂²	1	1	yes	characteristic
53	C₃₁×#400	C₂²	1	1	yes	characteristic
54	C₃₁×#399	C₂²	1	1	yes	characteristic
55	C₃₁×#398	C₂²	1	1	yes	characteristic
56	C₃₁×#398	C₂²	1	1	yes	characteristic
57	C₃₁×#398	C₂²	1	1	yes	characteristic
58	C₃₁×#398	C₂²	1	1	yes	characteristic
59	C₃₁×#398	C₂²	1	1	yes	characteristic
60	C₃₁×#398	C₂²	1	1	yes	characteristic
61	C₃₁×#397	C₂²	1	1	yes	characteristic
62	C₃₁×#397	C₂²	1	1	yes	characteristic
63	C₃₁×#397	C₂²	1	1	yes	characteristic
64	C₃₁×#397	C₂²	1	1	yes	characteristic
65	C₃₁×#397	C₂²	1	1	yes	characteristic
66	C₃₁×#396	C₂²	1	1	yes	characteristic
67	C₃₁×#396	C₂²	1	1	yes	characteristic
68	C₃₁×#396	C₂²	1	1	yes	characteristic
69	C₃₁×#395	C₂²	1	1	yes	characteristic
70	C₃₁×#395	C₂²	1	1	yes	characteristic
71	C₃₁×#395	C₂²	1	1	yes	characteristic
72	C₃₁×#395	C₂²	1	1	yes	characteristic
73	C₃₁×#395	C₂²	1	1	yes	characteristic
74	C₃₁×#394	C₂²	1	1	yes	characteristic
75	C₃₁×#394	C₂²	1	1	yes	characteristic
76	C₃₁×#393	C₂²	1	1	yes	characteristic
77	C₃₁×#393	C₂²	1	1	yes	characteristic
78	C₃₁×#393	C₂²	1	1	yes	characteristic
79	C₃₁×#391	C₂²	1	1	yes	characteristic
80	C₃₁×#391	C₂²	1	1	yes	characteristic
81	C₃₁×#391	C₂²	1	1	yes	characteristic
82	C₃₁×#391	C₂²	1	1	yes	characteristic
83	C₃₁×#391	C₂²	1	1	yes	characteristic
84	C₃₁×#391	C₂²	1	1	yes	characteristic
85	C₃₁×#390	C₂²	1	1	yes	characteristic
86	C₃₁×#389	C₂²	1	1	yes	characteristic
87	C₃₁×#389	C₂²	1	1	yes	characteristic
88	C₃₁×#389	C₂²	1	1	yes	characteristic
89	C₃₁×#389	C₂²	1	1	yes	characteristic
90	C₃₁×#389	C₂²	1	1	yes	characteristic
91	C₃₁×#388	C₂²	1	1	yes	characteristic
92	C₃₁×#388	C₂²	1	1	yes	characteristic
93	C₃₁×#388	C₂²	1	1	yes	characteristic
94	C₃₁×#388	C₂²	1	1	yes	characteristic
95	C₃₁×#388	C₂²	1	1	yes	characteristic
96	C₃₁×#388	C₂²	1	1	yes	characteristic
97	C₃₁×#388	C₂²	1	1	yes	characteristic
98	C₃₁×#388	C₂²	1	1	yes	characteristic
99	C₃₁×#388	C₂²	1	1	yes	characteristic
100	C₃₁×#388	C₂²	1	1	yes	characteristic
101	C₃₁×#388	C₂²	1	1	yes	characteristic
102	C₃₁×#388	C₂²	1	1	yes	characteristic
103	C₃₁×#388	C₂²	1	1	yes	characteristic
104	C₃₁×#388	C₂²	1	1	yes	characteristic
105	C₃₁×#388	C₂²	1	1	yes	characteristic
106	C₃₁×#388	C₂²	1	1	yes	characteristic
107	C₃₁×#388	C₂²	1	1	yes	characteristic
108	C₃₁×#388	C₂²	1	1	yes	characteristic
109	C₃₁×#388	C₂²	1	1	yes	characteristic
110	C₃₁×#387	C₂²	1	1	yes	characteristic
111	C₃₁×#387	C₂²	1	1	yes	characteristic
112	C₃₁×#387	C₂²	1	1	yes	characteristic
113	C₃₁×#387	C₂²	1	1	yes	characteristic
114	C₃₁×#387	C₂²	1	1	yes	characteristic
115	C₃₁×#387	C₂²	1	1	yes	characteristic
116	C₃₁×#387	C₂²	1	1	yes	characteristic
117	C₃₁×#387	C₂²	1	1	yes	characteristic
118	C₃₁×#387	C₂²	1	1	yes	characteristic
119	C₃₁×#387	C₂²	1	1	yes	characteristic
120	C₃₁×#387	C₂²	1	1	yes	characteristic
121	C₃₁×#387	C₂²	1	1	yes	characteristic
122	C₃₁×#387	C₂²	1	1	yes	characteristic
123	C₃₁×#387	C₂²	1	1	yes	characteristic
124	C₃₁×#387	C₂²	1	1	yes	characteristic
125	C₃₁×#387	C₂²	1	1	yes	characteristic
126	C₃₁×#387	C₂²	1	1	yes	characteristic
127	C₃₁×#387	C₂²	1	1	yes	characteristic
128	C₃₁×#387	C₂²	1	1	yes	characteristic
129	C₃₁×#387	C₂²	1	1	yes	characteristic
130	C₃₁×#387	C₂²	1	1	yes	characteristic
131	C₃₁×#387	C₂²	1	1	yes	characteristic
132	C₃₁×#387	C₂²	1	1	yes	characteristic
133	C₃₁×#387	C₂²	1	1	yes	characteristic
134	C₃₁×#387	C₂²	1	1	yes	characteristic
135	C₃₁×#386	C₂²	1	1	yes	characteristic
136	C₃₁×#386	C₂²	1	1	yes	characteristic
137	C₃₁×#385	C₂²	1	1	yes	characteristic
138	C₃₁×#385	C₂²	1	1	yes	characteristic
139	C₃₁×#385	C₂²	1	1	yes	characteristic
140	C₃₁×#385	C₂²	1	1	yes	characteristic
141	C₃₁×#383	C₂²	1	1	yes	characteristic
142	C₃₁×#383	C₂²	1	1	yes	characteristic
143	C₃₁×#383	C₂²	1	1	yes	characteristic
144	C₃₁×#382	C₂²	1	1	yes	characteristic
145	C₃₁×#380	C₂²	1	1	yes	characteristic
146	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
147	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
148	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
156	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
157	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
158	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
159	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
166	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
167	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
168	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
169	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
170	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
171	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
178	C₃₁×#376	C₂²	1	1	yes	characteristic
179	C₃₁×#376	C₂²	1	1	yes	characteristic
180	C₃₁×#376	C₂²	1	1	yes	characteristic
181	C₃₁×#376	C₂²	1	1	yes	characteristic
182	C₃₁×#376	C₂²	1	1	yes	characteristic
183	C₄³×C₃₁	C₂²	1	1	yes	characteristic
184	C₄³×C₃₁	C₂²	1	1	yes	characteristic
185	C₄³×C₃₁	C₂²	1	1	yes	characteristic
186	C₄³×C₃₁	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₃₁×#126	—	2	4	no	—
196	C₃₁×#126	—	2	4	no	—
197	C₃₁×#126	—	2	4	no	—
198	C₃₁×#124	—	2	4	no	—
199	C₃₁×C₂²⋊Q₈	—	2	4	no	—
200	C₄×Q₈×C₃₁	—	2	4	no	—
201	C₄×Q₈×C₃₁	—	2	4	no	—
202	C₄×Q₈×C₃₁	—	2	4	no	—
203	C₄×Q₈×C₃₁	—	2	4	no	—
204	C₄×Q₈×C₃₁	—	2	4	no	—
205	C₄×D₄×C₃₁	—	2	4	no	—
206	C₃₁×#117	—	2	4	no	—
207	C₃₁×#117	—	2	4	no	—
208	C₃₁×#117	—	2	4	no	—
209	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₃₁	—	2	4	no	—
270	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
272	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
278	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
281	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
282	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
288	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
301	C₃₁×#95	C₂³	1	1	yes	characteristic
302	C₃₁×#95	C₂³	1	1	yes	characteristic
303	C₃₁×#95	C₂³	1	1	yes	characteristic
304	C₃₁×#95	C₂³	1	1	yes	characteristic
305	C₃₁×#95	C₂³	1	1	yes	characteristic
306	C₃₁×#95	C₂³	1	1	yes	characteristic
307	C₃₁×#95	C₂³	1	1	yes	characteristic
308	C₃₁×#95	C₂³	1	1	yes	characteristic
309	C₃₁×#95	C₂³	1	1	yes	characteristic
310	C₃₁×#95	C₂³	1	1	yes	characteristic
311	C₃₁×#95	C₂³	1	1	yes	characteristic
312	C₃₁×#95	C₂³	1	1	yes	characteristic
313	C₃₁×#95	C₂³	1	1	yes	characteristic
314	C₃₁×#95	C₂³	1	1	yes	characteristic
315	C₃₁×#95	C₂³	1	1	yes	characteristic
316	C₃₁×#95	C₂³	1	1	yes	characteristic
317	C₃₁×#95	C₂³	1	1	yes	characteristic
318	C₃₁×#95	C₂³	1	1	yes	characteristic
319	C₃₁×#95	C₂³	1	1	yes	characteristic
320	C₃₁×#95	C₂³	1	1	yes	characteristic
321	C₃₁×#95	C₂³	1	1	yes	characteristic
322	C₃₁×#95	C₂³	1	1	yes	characteristic
323	C₃₁×#95	C₂³	1	1	yes	characteristic
324	C₃₁×#95	C₂³	1	1	yes	characteristic
325	C₃₁×#95	C₂³	1	1	yes	characteristic
326	C₃₁×#95	C₂³	1	1	yes	characteristic
327	C₃₁×#95	C₂³	1	1	yes	characteristic
328	C₃₁×#95	C₂³	1	1	yes	characteristic
329	C₃₁×#95	C₂³	1	1	yes	characteristic
330	C₃₁×#95	C₂³	1	1	yes	characteristic
331	C₃₁×#95	C₂³	1	1	yes	characteristic
332	C₃₁×#95	C₂³	1	1	yes	characteristic
333	C₃₁×#95	C₂³	1	1	yes	characteristic
334	C₃₁×#95	C₂³	1	1	yes	characteristic
335	C₃₁×#95	C₂³	1	1	yes	characteristic
336	C₃₁×#95	C₂³	1	1	yes	characteristic
337	C₃₁×#95	C₂³	1	1	yes	characteristic
338	C₃₁×#95	C₂³	1	1	yes	characteristic
339	C₃₁×#95	C₂³	1	1	yes	characteristic
340	C₃₁×#95	C₂³	1	1	yes	characteristic
341	C₃₁×#95	C₂³	1	1	yes	characteristic
342	C₃₁×#95	C₂³	1	1	yes	characteristic
343	C₃₁×#95	C₂³	1	1	yes	characteristic
344	C₃₁×#95	C₂³	1	1	yes	characteristic
345	C₃₁×#95	C₂³	1	1	yes	characteristic
346	C₃₁×#95	C₂³	1	1	yes	characteristic
347	C₃₁×#95	C₂³	1	1	yes	characteristic
348	C₃₁×#95	C₂³	1	1	yes	characteristic
349	C₃₁×#95	C₂³	1	1	yes	characteristic
350	C₃₁×#95	C₂³	1	1	yes	characteristic
351	C₃₁×#95	C₂³	1	1	yes	characteristic
352	C₃₁×#95	C₂³	1	1	yes	characteristic
353	C₃₁×#95	C₂³	1	1	yes	characteristic
354	C₃₁×#95	C₂³	1	1	yes	characteristic
355	C₃₁×#95	C₂³	1	1	yes	characteristic
356	C₃₁×#95	C₂³	1	1	yes	characteristic
357	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂×Q₈×C₃₁	—	2	2	no	—
360	C₂×Q₈×C₃₁	—	2	2	no	—
361	C₂×Q₈×C₃₁	—	2	2	no	—
362	C₂×Q₈×C₃₁	—	2	2	no	—
363	C₂×Q₈×C₃₁	—	2	2	no	—
364	C₂×Q₈×C₃₁	—	2	2	no	—
365	C₂×Q₈×C₃₁	—	2	2	no	—
366	C₂×Q₈×C₃₁	—	4	1	no	—
367	C₂×Q₈×C₃₁	—	4	1	no	—
368	C₂×D₄×C₃₁	—	2	2	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	4	1	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	2	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	2	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	2	2	no	—
378	C₂²×C₄×C₃₁	—	2	2	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	2	no	—
382	C₂²×C₄×C₃₁	—	4	1	no	—
383	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	—	2	2	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	2	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	—	2	2	no	—
424	C₄⋊C₄×C₃₁	—	2	2	no	—
425	C₄⋊C₄×C₃₁	—	2	2	no	—
426	C₄⋊C₄×C₃₁	—	2	2	no	—
427	C₄⋊C₄×C₃₁	—	2	2	no	—
428	C₄⋊C₄×C₃₁	—	2	2	no	—
429	C₄⋊C₄×C₃₁	—	2	2	no	—
430	C₄⋊C₄×C₃₁	—	2	2	no	—
431	C₄⋊C₄×C₃₁	—	2	2	no	—
432	C₄⋊C₄×C₃₁	—	2	2	no	—
433	C₄⋊C₄×C₃₁	—	2	2	no	—
434	C₄⋊C₄×C₃₁	—	2	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	no	—
436	C₄⋊C₄×C₃₁	—	2	2	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	2	no	—
439	C₄⋊C₄×C₃₁	—	2	2	no	—
440	C₄⋊C₄×C₃₁	—	2	2	no	—
441	C₄⋊C₄×C₃₁	—	2	2	no	—
442	C₄⋊C₄×C₃₁	—	2	2	no	—
443	C₄⋊C₄×C₃₁	—	4	1	no	—
444	C₄⋊C₄×C₃₁	—	4	1	no	—
445	C₄⋊C₄×C₃₁	—	4	1	no	—
446	C₄⋊C₄×C₃₁	—	4	1	no	—
447	C₄⋊C₄×C₃₁	#41	1	4	yes	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	—	2	2	no	—
452	C₂²⋊C₄×C₃₁	—	2	2	no	—
453	C₂²⋊C₄×C₃₁	—	2	2	no	—
454	C₂²⋊C₄×C₃₁	—	2	2	no	—
455	C₂²⋊C₄×C₃₁	—	2	2	no	—
456	C₂²⋊C₄×C₃₁	—	2	2	no	—
457	C₂²⋊C₄×C₃₁	—	2	2	no	—
458	C₂²⋊C₄×C₃₁	—	2	2	no	—
459	C₂²⋊C₄×C₃₁	—	2	2	no	—
460	C₂²⋊C₄×C₃₁	—	2	2	no	—
461	C₂²⋊C₄×C₃₁	—	2	2	no	—
462	C₂²⋊C₄×C₃₁	—	2	2	no	—
463	C₂²⋊C₄×C₃₁	—	2	2	no	—
464	C₂²⋊C₄×C₃₁	—	2	2	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	2	no	—
468	C₂²⋊C₄×C₃₁	—	4	1	no	—
469	C₂²⋊C₄×C₃₁	—	4	1	no	—
470	C₂²⋊C₄×C₃₁	—	4	1	no	—
471	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
472	C₄²×C₃₁	—	2	2	no	—
473	C₄²×C₃₁	—	2	2	no	—
474	C₄²×C₃₁	—	2	2	no	—
475	C₄²×C₃₁	—	2	2	no	—
476	C₄²×C₃₁	—	2	2	no	—
477	C₄²×C₃₁	—	2	2	no	—
478	C₄²×C₃₁	—	2	2	no	—
479	C₄²×C₃₁	—	2	2	no	—
480	C₄²×C₃₁	—	2	2	no	—
481	C₄²×C₃₁	—	2	2	no	—
482	C₄²×C₃₁	—	2	2	no	—
483	C₄²×C₃₁	—	2	2	no	—
484	C₄²×C₃₁	—	2	2	no	—
485	C₄²×C₃₁	—	2	2	no	—
486	C₄²×C₃₁	—	2	2	no	—
487	C₄²×C₃₁	—	2	2	no	—
488	C₄²×C₃₁	—	2	2	no	—
489	C₄²×C₃₁	—	2	2	no	—
490	C₄²×C₃₁	—	2	2	no	—
491	C₄²×C₃₁	—	2	2	no	—
492	C₄²×C₃₁	—	2	2	no	—
493	C₄²×C₃₁	—	2	2	no	—
494	C₄²×C₃₁	—	2	2	no	—
495	C₄²×C₃₁	—	2	2	no	—
496	C₄²×C₃₁	—	4	1	no	—
497	C₄²×C₃₁	—	4	1	no	—
498	C₄²×C₃₁	—	4	1	no	—
499	C₄²×C₃₁	—	4	1	no	—
500	C₄²×C₃₁	#41	1	4	yes	—
501	C₄²×C₃₁	#41	1	4	yes	—
502	C₄²×C₃₁	#41	1	4	yes	—
503	#34867	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
504	C₂³×C₃₁	—	2	1	no	—
505	C₂³×C₃₁	—	2	1	no	—
506	C₂³×C₃₁	—	2	1	no	—
507	C₂³×C₃₁	—	2	1	no	—
508	C₂³×C₃₁	—	2	1	no	—
509	C₂³×C₃₁	—	2	1	no	—
510	C₂³×C₃₁	—	2	1	no	—
511	C₂³×C₃₁	—	2	1	no	—
512	C₂³×C₃₁	—	2	1	no	—
513	C₂³×C₃₁	—	2	1	no	—
514	C₂³×C₃₁	—	2	1	no	—
515	C₂³×C₃₁	—	2	1	no	—
516	C₂³×C₃₁	—	2	1	no	—
517	C₂³×C₃₁	C₂×#41	1	2	yes	—
518	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
519	Q₈×C₃₁	—	2	8	no	—
520	Q₈×C₃₁	—	4	4	no	—
521	Q₈×C₃₁	—	4	4	no	—
522	D₄×C₃₁	—	4	4	no	—
523	C₂×C₄×C₃₁	—	2	8	no	—
524	C₂×C₄×C₃₁	—	2	1	no	—
525	C₂×C₄×C₃₁	—	2	1	no	—
526	C₂×C₄×C₃₁	—	2	1	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	1	no	—
529	C₂×C₄×C₃₁	—	2	1	no	—
530	C₂×C₄×C₃₁	—	2	1	no	—
531	C₂×C₄×C₃₁	—	2	1	no	—
532	C₂×C₄×C₃₁	—	2	1	no	—
533	C₂×C₄×C₃₁	—	2	1	no	—
534	C₂×C₄×C₃₁	—	2	1	no	—
535	C₂×C₄×C₃₁	—	2	1	no	—
536	C₂×C₄×C₃₁	—	2	1	no	—
537	C₂×C₄×C₃₁	—	2	1	no	—
538	C₂×C₄×C₃₁	—	2	1	no	—
539	C₂×C₄×C₃₁	—	2	1	no	—
540	C₂×C₄×C₃₁	—	2	1	no	—
541	C₂×C₄×C₃₁	—	2	1	no	—
542	C₂×C₄×C₃₁	—	2	1	no	—
543	C₂×C₄×C₃₁	—	2	1	no	—
544	C₂×C₄×C₃₁	—	2	1	no	—
545	C₂×C₄×C₃₁	—	2	1	no	—
546	C₂×C₄×C₃₁	—	2	1	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	2	1	no	—
550	C₂×C₄×C₃₁	—	2	1	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	1	no	—
554	C₂×C₄×C₃₁	—	2	1	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	1	no	—
560	C₂×C₄×C₃₁	—	2	1	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	1	no	—
566	C₂×C₄×C₃₁	—	2	1	no	—
567	C₂×C₄×C₃₁	—	2	1	no	—
568	C₂×C₄×C₃₁	—	2	1	no	—
569	C₂×C₄×C₃₁	—	2	1	no	—
570	C₂×C₄×C₃₁	—	2	1	no	—
571	C₂×C₄×C₃₁	—	2	1	no	—
572	C₂×C₄×C₃₁	—	2	1	no	—
573	C₂×C₄×C₃₁	—	2	1	no	—
574	C₂×C₄×C₃₁	—	2	1	no	—
575	C₂×C₄×C₃₁	—	2	1	no	—
576	C₂×C₄×C₃₁	—	2	1	no	—
577	C₂×C₄×C₃₁	—	2	1	no	—
578	C₂×C₄×C₃₁	—	2	1	no	—
579	C₂×C₄×C₃₁	—	2	1	no	—
580	C₂×C₄×C₃₁	—	2	1	no	—
581	C₂×C₄×C₃₁	—	2	1	no	—
582	C₂×C₄×C₃₁	—	2	1	no	—
583	C₂×C₄×C₃₁	—	2	1	no	—
584	C₂×C₄×C₃₁	—	2	1	no	—
585	C₂×C₄×C₃₁	—	2	1	no	—
586	C₂×C₄×C₃₁	—	2	1	no	—
587	C₂×C₄×C₃₁	—	2	1	no	—
588	C₂×C₄×C₃₁	—	2	1	no	—
589	C₂×C₄×C₃₁	—	2	1	no	—
590	C₂×C₄×C₃₁	—	2	1	no	—
591	C₂×C₄×C₃₁	—	2	1	no	—
592	C₂×C₄×C₃₁	—	2	1	no	—
593	C₂×C₄×C₃₁	—	2	1	no	—
594	C₂×C₄×C₃₁	—	2	1	no	—
595	C₂×C₄×C₃₁	—	2	1	no	—
596	C₂×C₄×C₃₁	—	4	4	no	—
597	C₂×C₄×C₃₁	—	4	4	no	—
598	C₂×C₄×C₃₁	—	4	4	no	—
599	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
600	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
601	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
602	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
603	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
604	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
605	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
606	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
607	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
608	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
609	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
610	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
611	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
612	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
613	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
614	#2605	C₂×C₃₁	1	1	yes	characteristic, complemented
615	#2604	C₂×C₃₁	1	1	yes	characteristic, complemented
616	#2601	C₂×C₃₁	1	1	yes	characteristic
617	#2599	C₂×C₃₁	1	1	yes	characteristic, complemented
618	#2594	C₂×C₃₁	1	1	yes	characteristic, complemented
619	#2588	C₂×C₃₁	1	1	yes	characteristic, complemented
620	#2577	C₂×C₃₁	1	1	yes	characteristic, complemented
621	#2560	C₂×C₃₁	1	1	yes	characteristic
622	#2532	C₂×C₃₁	1	1	yes	characteristic, complemented
623	#2528	C₂×C₃₁	1	1	yes	characteristic, complemented
624	#2524	C₂×C₃₁	1	1	yes	characteristic, complemented
625	#2521	C₂×C₃₁	1	1	yes	characteristic
626	#2478	C₂×C₃₁	1	1	yes	characteristic, complemented
627	#2474	C₂×C₃₁	1	1	yes	characteristic
628	#2469	C₂×C₃₁	1	1	yes	characteristic, complemented
629	#2465	C₂×C₃₁	1	1	yes	characteristic, complemented
630	#2401	C₂×C₃₁	1	1	yes	characteristic, complemented
631	#2399	C₂×C₃₁	1	1	yes	characteristic, complemented
632	#2398	C₂×C₃₁	1	1	yes	characteristic
633	#2396	C₂×C₃₁	1	1	yes	characteristic, complemented
634	C₄×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
635	C₄×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
636	C₄×#126	C₂×C₃₁	1	1	yes	characteristic, complemented
637	C₄×#124	C₂×C₃₁	1	1	yes	characteristic
638	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
639	#2298	C₂×C₃₁	1	1	yes	characteristic, complemented
640	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
641	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
642	#2290	C₂×C₃₁	1	1	yes	characteristic
643	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
644	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
645	C₂²×C₃₁	—	2	2	no	—
646	C₂²×C₃₁	—	2	2	no	—
647	C₂²×C₃₁	—	2	2	no	—
648	C₂²×C₃₁	—	4	1	no	—
649	C₂²×C₃₁	—	4	1	no	—
650	C₂²×C₃₁	—	4	1	no	—
651	C₂²×C₃₁	—	4	1	no	—
652	C₂²×C₃₁	—	4	1	no	—
653	C₂²×C₃₁	—	4	1	no	—
654	C₂²×C₃₁	—	4	1	no	—
655	C₂²×C₃₁	—	4	1	no	—
656	C₂²×C₃₁	—	4	1	no	—
657	C₂²×C₃₁	—	4	1	no	—
658	C₂²×C₃₁	—	4	1	no	—
659	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
660	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
661	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
662	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
663	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
664	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
665	C₂²×C₃₁	#585	1	1	yes	characteristic
666	C₄×C₃₁	—	2	2	no	—
667	C₄×C₃₁	—	2	2	no	—
668	C₄×C₃₁	—	2	2	no	—
669	C₄×C₃₁	—	2	2	no	—
670	C₄×C₃₁	—	2	2	no	—
671	C₄×C₃₁	—	2	2	no	—
672	C₄×C₃₁	—	2	2	no	—
673	C₄×C₃₁	—	2	2	no	—
674	C₄×C₃₁	—	2	2	no	—
675	C₄×C₃₁	—	2	2	no	—
676	C₄×C₃₁	—	2	2	no	—
677	C₄×C₃₁	—	2	2	no	—
678	C₄×C₃₁	—	4	1	no	—
679	C₄×C₃₁	—	4	1	no	—
680	C₄×C₃₁	—	4	1	no	—
681	C₄×C₃₁	—	4	1	no	—
682	C₄×C₃₁	—	4	1	no	—
683	C₄×C₃₁	—	4	1	no	—
684	C₄×C₃₁	—	4	1	no	—
685	C₄×C₃₁	—	4	1	no	—
686	C₄×C₃₁	—	4	1	no	—
687	C₄×C₃₁	—	4	1	no	—
688	C₄×C₃₁	—	4	1	no	—
689	C₄×C₃₁	—	4	1	no	—
690	C₄×C₃₁	—	4	1	no	—
691	C₄×C₃₁	—	4	1	no	—
692	C₄×C₃₁	—	4	1	no	—
693	C₄×C₃₁	—	4	1	no	—
694	C₄×C₃₁	#556	1	4	yes	—
695	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
697	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
698	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
699	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
700	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
701	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
702	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
703	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
704	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
705	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
706	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
707	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
708	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
709	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
710	#401	C₂²×C₃₁	1	1	yes	characteristic
711	#400	C₂²×C₃₁	1	1	yes	characteristic
712	#400	C₂²×C₃₁	1	1	yes	characteristic
713	#400	C₂²×C₃₁	1	1	yes	characteristic
714	#400	C₂²×C₃₁	1	1	yes	characteristic
715	#400	C₂²×C₃₁	1	1	yes	characteristic
716	#400	C₂²×C₃₁	1	1	yes	characteristic
717	#399	C₂²×C₃₁	1	1	yes	characteristic
718	#398	C₂²×C₃₁	1	1	yes	characteristic
719	#398	C₂²×C₃₁	1	1	yes	characteristic
720	#398	C₂²×C₃₁	1	1	yes	characteristic
721	#398	C₂²×C₃₁	1	1	yes	characteristic
722	#398	C₂²×C₃₁	1	1	yes	characteristic
723	#398	C₂²×C₃₁	1	1	yes	characteristic
724	#397	C₂²×C₃₁	1	1	yes	characteristic
725	#397	C₂²×C₃₁	1	1	yes	characteristic
726	#397	C₂²×C₃₁	1	1	yes	characteristic
727	#397	C₂²×C₃₁	1	1	yes	characteristic
728	#397	C₂²×C₃₁	1	1	yes	characteristic
729	#396	C₂²×C₃₁	1	1	yes	characteristic
730	#396	C₂²×C₃₁	1	1	yes	characteristic
731	#396	C₂²×C₃₁	1	1	yes	characteristic
732	#395	C₂²×C₃₁	1	1	yes	characteristic
733	#395	C₂²×C₃₁	1	1	yes	characteristic
734	#395	C₂²×C₃₁	1	1	yes	characteristic
735	#395	C₂²×C₃₁	1	1	yes	characteristic
736	#395	C₂²×C₃₁	1	1	yes	characteristic
737	#394	C₂²×C₃₁	1	1	yes	characteristic
738	#394	C₂²×C₃₁	1	1	yes	characteristic
739	#393	C₂²×C₃₁	1	1	yes	characteristic
740	#393	C₂²×C₃₁	1	1	yes	characteristic
741	#393	C₂²×C₃₁	1	1	yes	characteristic
742	#391	C₂²×C₃₁	1	1	yes	characteristic
743	#391	C₂²×C₃₁	1	1	yes	characteristic
744	#391	C₂²×C₃₁	1	1	yes	characteristic
745	#391	C₂²×C₃₁	1	1	yes	characteristic
746	#391	C₂²×C₃₁	1	1	yes	characteristic
747	#391	C₂²×C₃₁	1	1	yes	characteristic
748	#390	C₂²×C₃₁	1	1	yes	characteristic
749	#389	C₂²×C₃₁	1	1	yes	characteristic
750	#389	C₂²×C₃₁	1	1	yes	characteristic
751	#389	C₂²×C₃₁	1	1	yes	characteristic
752	#389	C₂²×C₃₁	1	1	yes	characteristic
753	#389	C₂²×C₃₁	1	1	yes	characteristic
754	#388	C₂²×C₃₁	1	1	yes	characteristic
755	#388	C₂²×C₃₁	1	1	yes	characteristic
756	#388	C₂²×C₃₁	1	1	yes	characteristic
757	#388	C₂²×C₃₁	1	1	yes	characteristic
758	#388	C₂²×C₃₁	1	1	yes	characteristic
759	#388	C₂²×C₃₁	1	1	yes	characteristic
760	#388	C₂²×C₃₁	1	1	yes	characteristic
761	#388	C₂²×C₃₁	1	1	yes	characteristic
762	#388	C₂²×C₃₁	1	1	yes	characteristic
763	#388	C₂²×C₃₁	1	1	yes	characteristic
764	#388	C₂²×C₃₁	1	1	yes	characteristic
765	#388	C₂²×C₃₁	1	1	yes	characteristic
766	#388	C₂²×C₃₁	1	1	yes	characteristic
767	#388	C₂²×C₃₁	1	1	yes	characteristic
768	#388	C₂²×C₃₁	1	1	yes	characteristic
769	#388	C₂²×C₃₁	1	1	yes	characteristic
770	#388	C₂²×C₃₁	1	1	yes	characteristic
771	#388	C₂²×C₃₁	1	1	yes	characteristic
772	#388	C₂²×C₃₁	1	1	yes	characteristic
773	#387	C₂²×C₃₁	1	1	yes	characteristic
774	#387	C₂²×C₃₁	1	1	yes	characteristic
775	#387	C₂²×C₃₁	1	1	yes	characteristic
776	#387	C₂²×C₃₁	1	1	yes	characteristic
777	#387	C₂²×C₃₁	1	1	yes	characteristic
778	#387	C₂²×C₃₁	1	1	yes	characteristic
779	#387	C₂²×C₃₁	1	1	yes	characteristic
780	#387	C₂²×C₃₁	1	1	yes	characteristic
781	#387	C₂²×C₃₁	1	1	yes	characteristic
782	#387	C₂²×C₃₁	1	1	yes	characteristic
783	#387	C₂²×C₃₁	1	1	yes	characteristic
784	#387	C₂²×C₃₁	1	1	yes	characteristic
785	#387	C₂²×C₃₁	1	1	yes	characteristic
786	#387	C₂²×C₃₁	1	1	yes	characteristic
787	#387	C₂²×C₃₁	1	1	yes	characteristic
788	#387	C₂²×C₃₁	1	1	yes	characteristic
789	#387	C₂²×C₃₁	1	1	yes	characteristic
790	#387	C₂²×C₃₁	1	1	yes	characteristic
791	#387	C₂²×C₃₁	1	1	yes	characteristic
792	#387	C₂²×C₃₁	1	1	yes	characteristic
793	#387	C₂²×C₃₁	1	1	yes	characteristic
794	#387	C₂²×C₃₁	1	1	yes	characteristic
795	#387	C₂²×C₃₁	1	1	yes	characteristic
796	#387	C₂²×C₃₁	1	1	yes	characteristic
797	#387	C₂²×C₃₁	1	1	yes	characteristic
798	#386	C₂²×C₃₁	1	1	yes	characteristic
799	#386	C₂²×C₃₁	1	1	yes	characteristic
800	#385	C₂²×C₃₁	1	1	yes	characteristic
801	#385	C₂²×C₃₁	1	1	yes	characteristic
802	#385	C₂²×C₃₁	1	1	yes	characteristic
803	#385	C₂²×C₃₁	1	1	yes	characteristic
804	#383	C₂²×C₃₁	1	1	yes	characteristic
805	#383	C₂²×C₃₁	1	1	yes	characteristic
806	#383	C₂²×C₃₁	1	1	yes	characteristic
807	#382	C₂²×C₃₁	1	1	yes	characteristic
808	#380	C₂²×C₃₁	1	1	yes	characteristic
809	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
810	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
811	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
812	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
813	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
814	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
815	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
816	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
817	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
818	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
819	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
820	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
821	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
822	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
823	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
824	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
825	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
826	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
827	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
828	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
829	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
830	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
831	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
832	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
833	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
834	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
835	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
836	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
837	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
838	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
839	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
840	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
841	#376	C₂²×C₃₁	1	1	yes	characteristic
842	#376	C₂²×C₃₁	1	1	yes	characteristic
843	#376	C₂²×C₃₁	1	1	yes	characteristic
844	#376	C₂²×C₃₁	1	1	yes	characteristic
845	#376	C₂²×C₃₁	1	1	yes	characteristic
846	C₄³	C₂²×C₃₁	1	1	yes	characteristic
847	C₄³	C₂²×C₃₁	1	1	yes	characteristic
848	C₄³	C₂²×C₃₁	1	1	yes	characteristic
849	C₄³	C₂²×C₃₁	1	1	yes	characteristic
850	C₂×C₃₁	—	4	2	no	—
851	C₂×C₃₁	—	8	1	no	—
852	C₂×C₃₁	#3444	1	1	yes	characteristic
853	C₂×C₃₁	#3444	1	1	yes	characteristic
854	C₂×C₃₁	#3461	1	1	yes	characteristic
855	C₂×C₃₁	C₂×#556	1	1	yes	characteristic
856	C₂×C₃₁	#3475	1	1	yes	characteristic
857	C₂×C₃₁	#3475	1	1	yes	characteristic
858	C₂×C₃₁	#3482	1	1	yes	characteristic
859	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
863	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
864	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
865	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
866	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
867	#126	—	2	4	no	—
868	#126	—	2	4	no	—
869	#126	—	2	4	no	—
870	#124	—	2	4	no	—
871	C₂²⋊Q₈	—	2	4	no	—
872	C₄×Q₈	—	2	4	no	—
873	C₄×Q₈	—	2	4	no	—
874	C₄×Q₈	—	2	4	no	—
875	C₄×Q₈	—	2	4	no	—
876	C₄×Q₈	—	2	4	no	—
877	C₄×D₄	—	2	4	no	—
878	#117	—	2	4	no	—
879	#117	—	2	4	no	—
880	#117	—	2	4	no	—
881	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
898	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
900	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
913	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
918	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
919	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
920	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
921	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
922	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
923	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
927	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
928	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
929	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
930	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
931	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
932	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
933	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
934	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
935	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
936	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
937	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
938	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
939	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
941	C₂×C₄²	—	2	4	no	—
942	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
944	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
945	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
946	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
947	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
948	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
949	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
950	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
951	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
952	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
953	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
954	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
955	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
956	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
957	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
958	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
959	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
960	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
961	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
962	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
963	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
964	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
965	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
966	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
967	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
968	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
969	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
970	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
971	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
972	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
973	#95	C₂³×C₃₁	1	1	yes	characteristic
974	#95	C₂³×C₃₁	1	1	yes	characteristic
975	#95	C₂³×C₃₁	1	1	yes	characteristic
976	#95	C₂³×C₃₁	1	1	yes	characteristic
977	#95	C₂³×C₃₁	1	1	yes	characteristic
978	#95	C₂³×C₃₁	1	1	yes	characteristic
979	#95	C₂³×C₃₁	1	1	yes	characteristic
980	#95	C₂³×C₃₁	1	1	yes	characteristic
981	#95	C₂³×C₃₁	1	1	yes	characteristic
982	#95	C₂³×C₃₁	1	1	yes	characteristic
983	#95	C₂³×C₃₁	1	1	yes	characteristic
984	#95	C₂³×C₃₁	1	1	yes	characteristic
985	#95	C₂³×C₃₁	1	1	yes	characteristic
986	#95	C₂³×C₃₁	1	1	yes	characteristic
987	#95	C₂³×C₃₁	1	1	yes	characteristic
988	#95	C₂³×C₃₁	1	1	yes	characteristic
989	#95	C₂³×C₃₁	1	1	yes	characteristic
990	#95	C₂³×C₃₁	1	1	yes	characteristic
991	#95	C₂³×C₃₁	1	1	yes	characteristic
992	#95	C₂³×C₃₁	1	1	yes	characteristic
993	#95	C₂³×C₃₁	1	1	yes	characteristic
994	#95	C₂³×C₃₁	1	1	yes	characteristic
995	#95	C₂³×C₃₁	1	1	yes	characteristic
996	#95	C₂³×C₃₁	1	1	yes	characteristic
997	#95	C₂³×C₃₁	1	1	yes	characteristic
998	#95	C₂³×C₃₁	1	1	yes	characteristic
999	#95	C₂³×C₃₁	1	1	yes	characteristic
1000	#95	C₂³×C₃₁	1	1	yes	characteristic
1001	#95	C₂³×C₃₁	1	1	yes	characteristic
1002	#95	C₂³×C₃₁	1	1	yes	characteristic
1003	#95	C₂³×C₃₁	1	1	yes	characteristic
1004	#95	C₂³×C₃₁	1	1	yes	characteristic
1005	#95	C₂³×C₃₁	1	1	yes	characteristic
1006	#95	C₂³×C₃₁	1	1	yes	characteristic
1007	#95	C₂³×C₃₁	1	1	yes	characteristic
1008	#95	C₂³×C₃₁	1	1	yes	characteristic
1009	#95	C₂³×C₃₁	1	1	yes	characteristic
1010	#95	C₂³×C₃₁	1	1	yes	characteristic
1011	#95	C₂³×C₃₁	1	1	yes	characteristic
1012	#95	C₂³×C₃₁	1	1	yes	characteristic
1013	#95	C₂³×C₃₁	1	1	yes	characteristic
1014	#95	C₂³×C₃₁	1	1	yes	characteristic
1015	#95	C₂³×C₃₁	1	1	yes	characteristic
1016	#95	C₂³×C₃₁	1	1	yes	characteristic
1017	#95	C₂³×C₃₁	1	1	yes	characteristic
1018	#95	C₂³×C₃₁	1	1	yes	characteristic
1019	#95	C₂³×C₃₁	1	1	yes	characteristic
1020	#95	C₂³×C₃₁	1	1	yes	characteristic
1021	#95	C₂³×C₃₁	1	1	yes	characteristic
1022	#95	C₂³×C₃₁	1	1	yes	characteristic
1023	#95	C₂³×C₃₁	1	1	yes	characteristic
1024	#95	C₂³×C₃₁	1	1	yes	characteristic
1025	#95	C₂³×C₃₁	1	1	yes	characteristic
1026	#95	C₂³×C₃₁	1	1	yes	characteristic
1027	#95	C₂³×C₃₁	1	1	yes	characteristic
1028	#95	C₂³×C₃₁	1	1	yes	characteristic
1029	C₃₁	#34867	1	1	yes	characteristic, direct product factor, Sylow
1030	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₂×Q₈	—	2	2	no	—
1033	C₂×Q₈	—	2	2	no	—
1034	C₂×Q₈	—	2	2	no	—
1035	C₂×Q₈	—	2	2	no	—
1036	C₂×Q₈	—	2	2	no	—
1037	C₂×Q₈	—	2	2	no	—
1038	C₂×Q₈	—	2	2	no	—
1039	C₂×Q₈	—	4	1	no	—
1040	C₂×Q₈	—	4	1	no	—
1041	C₂×D₄	—	2	2	no	—
1042	C₂×D₄	—	2	2	no	—
1043	C₂×D₄	—	4	1	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	2	no	—
1048	C₂²×C₄	—	2	2	no	—
1049	C₂²×C₄	—	2	2	no	—
1050	C₂²×C₄	—	2	2	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	2	2	no	—
1054	C₂²×C₄	—	2	2	no	—
1055	C₂²×C₄	—	4	1	no	—
1056	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1057	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1058	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1067	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1068	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1069	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1070	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1071	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1072	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1073	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1074	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1075	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1076	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1077	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1078	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1079	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1080	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1081	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1082	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1083	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1084	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	2	2	no	—
1095	C₄⋊C₄	—	2	2	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	2	no	—
1100	C₄⋊C₄	—	2	2	no	—
1101	C₄⋊C₄	—	2	2	no	—
1102	C₄⋊C₄	—	2	2	no	—
1103	C₄⋊C₄	—	2	2	no	—
1104	C₄⋊C₄	—	2	2	no	—
1105	C₄⋊C₄	—	2	2	no	—
1106	C₄⋊C₄	—	2	2	no	—
1107	C₄⋊C₄	—	2	2	no	—
1108	C₄⋊C₄	—	2	2	no	—
1109	C₄⋊C₄	—	2	2	no	—
1110	C₄⋊C₄	—	2	2	no	—
1111	C₄⋊C₄	—	2	2	no	—
1112	C₄⋊C₄	—	2	2	no	—
1113	C₄⋊C₄	—	2	2	no	—
1114	C₄⋊C₄	—	2	2	no	—
1115	C₄⋊C₄	—	2	2	no	—
1116	C₄⋊C₄	—	4	1	no	—
1117	C₄⋊C₄	—	4	1	no	—
1118	C₄⋊C₄	—	4	1	no	—
1119	C₄⋊C₄	—	4	1	no	—
1120	C₄⋊C₄	#41×C₃₁	1	4	yes	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	2	no	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	2	no	—
1140	C₂²⋊C₄	—	2	2	no	—
1141	C₂²⋊C₄	—	4	1	no	—
1142	C₂²⋊C₄	—	4	1	no	—
1143	C₂²⋊C₄	—	4	1	no	—
1144	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
1145	C₄²	—	2	2	no	—
1146	C₄²	—	2	2	no	—
1147	C₄²	—	2	2	no	—
1148	C₄²	—	2	2	no	—
1149	C₄²	—	2	2	no	—
1150	C₄²	—	2	2	no	—
1151	C₄²	—	2	2	no	—
1152	C₄²	—	2	2	no	—
1153	C₄²	—	2	2	no	—
1154	C₄²	—	2	2	no	—
1155	C₄²	—	2	2	no	—
1156	C₄²	—	2	2	no	—
1157	C₄²	—	2	2	no	—
1158	C₄²	—	2	2	no	—
1159	C₄²	—	2	2	no	—
1160	C₄²	—	2	2	no	—
1161	C₄²	—	2	2	no	—
1162	C₄²	—	2	2	no	—
1163	C₄²	—	2	2	no	—
1164	C₄²	—	2	2	no	—
1165	C₄²	—	2	2	no	—
1166	C₄²	—	2	2	no	—
1167	C₄²	—	2	2	no	—
1168	C₄²	—	2	2	no	—
1169	C₄²	—	4	1	no	—
1170	C₄²	—	4	1	no	—
1171	C₄²	—	4	1	no	—
1172	C₄²	—	4	1	no	—
1173	C₄²	#41×C₃₁	1	4	yes	—
1174	C₄²	#41×C₃₁	1	4	yes	—
1175	C₄²	#41×C₃₁	1	4	yes	—
1176	C₂³	—	2	1	no	—
1177	C₂³	—	2	1	no	—
1178	C₂³	—	2	1	no	—
1179	C₂³	—	2	1	no	—
1180	C₂³	—	2	1	no	—
1181	C₂³	—	2	1	no	—
1182	C₂³	—	2	1	no	—
1183	C₂³	—	2	1	no	—
1184	C₂³	—	2	1	no	—
1185	C₂³	—	2	1	no	—
1186	C₂³	—	2	1	no	—
1187	C₂³	—	2	1	no	—
1188	C₂³	—	2	1	no	—
1189	C₂³	C₂×#41×C₃₁	1	2	yes	—
1190	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1191	Q₈	—	2	8	no	—
1192	Q₈	—	4	4	no	—
1193	Q₈	—	4	4	no	—
1194	D₄	—	4	4	no	—
1195	C₂×C₄	—	2	8	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	2	1	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	4	4	no	—
1269	C₂×C₄	—	4	4	no	—
1270	C₂×C₄	—	4	4	no	—
1271	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1272	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1273	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1274	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1275	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1276	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1277	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1278	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1279	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1280	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1281	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1282	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1283	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1284	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1285	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1286	C₂²	—	2	2	no	—
1287	C₂²	—	2	2	no	—
1288	C₂²	—	2	2	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	4	1	no	—
1292	C₂²	—	4	1	no	—
1293	C₂²	—	4	1	no	—
1294	C₂²	—	4	1	no	—
1295	C₂²	—	4	1	no	—
1296	C₂²	—	4	1	no	—
1297	C₂²	—	4	1	no	—
1298	C₂²	—	4	1	no	—
1299	C₂²	—	4	1	no	—
1300	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1301	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1302	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1303	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1304	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1305	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1306	C₂²	C₃₁×#585	1	1	yes	characteristic
1307	C₄	—	2	2	no	—
1308	C₄	—	2	2	no	—
1309	C₄	—	2	2	no	—
1310	C₄	—	2	2	no	—
1311	C₄	—	2	2	no	—
1312	C₄	—	2	2	no	—
1313	C₄	—	2	2	no	—
1314	C₄	—	2	2	no	—
1315	C₄	—	2	2	no	—
1316	C₄	—	2	2	no	—
1317	C₄	—	2	2	no	—
1318	C₄	—	2	2	no	—
1319	C₄	—	4	1	no	—
1320	C₄	—	4	1	no	—
1321	C₄	—	4	1	no	—
1322	C₄	—	4	1	no	—
1323	C₄	—	4	1	no	—
1324	C₄	—	4	1	no	—
1325	C₄	—	4	1	no	—
1326	C₄	—	4	1	no	—
1327	C₄	—	4	1	no	—
1328	C₄	—	4	1	no	—
1329	C₄	—	4	1	no	—
1330	C₄	—	4	1	no	—
1331	C₄	—	4	1	no	—
1332	C₄	—	4	1	no	—
1333	C₄	—	4	1	no	—
1334	C₄	—	4	1	no	—
1335	C₄	C₃₁×#556	1	4	yes	—
1336	C₂	—	4	2	no	—
1337	C₂	—	8	1	no	—
1338	C₂	C₃₁×#3444	1	1	yes	characteristic
1339	C₂	C₃₁×#3444	1	1	yes	characteristic
1340	C₂	C₃₁×#3461	1	1	yes	characteristic
1341	C₂	C₂×C₃₁×#556	1	1	yes	characteristic
1342	C₂	C₃₁×#3475	1	1	yes	characteristic
1343	C₂	C₃₁×#3475	1	1	yes	characteristic
1344	C₂	C₃₁×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2605	C₂	semidirect
2. C₃₁×#2604	C₂	semidirect
4. C₃₁×#2599	C₂	semidirect
5. C₃₁×#2594	C₂	semidirect
6. C₃₁×#2588	C₂	semidirect
7. C₃₁×#2577	C₂	semidirect
9. C₃₁×#2532	C₂	semidirect
10. C₃₁×#2528	C₂	semidirect
11. C₃₁×#2524	C₂	semidirect
13. C₃₁×#2478	C₂	semidirect
15. C₃₁×#2469	C₂	semidirect
16. C₃₁×#2465	C₂	semidirect
17. C₃₁×#2401	C₂	semidirect
18. C₃₁×#2399	C₂	semidirect
20. C₃₁×#2396	C₂	semidirect
21. C₄×C₃₁×#126	C₂	semidirect
22. C₄×C₃₁×#126	C₂	semidirect
23. C₄×C₃₁×#126	C₂	semidirect
25. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
26. C₃₁×#2298	C₂	semidirect
27. C₃₁×#2295	C₂	semidirect
28. C₃₁×#2295	C₂	semidirect
30. C₄²×Q₈×C₃₁	C₂	semidirect
31. C₄×C₃₁×#117	C₂	semidirect
503. #34867	C₃₁	direct (N × H)
614. #2605	C₂×C₃₁	semidirect
615. #2604	C₂×C₃₁	semidirect
617. #2599	C₂×C₃₁	semidirect
618. #2594	C₂×C₃₁	semidirect
619. #2588	C₂×C₃₁	semidirect
620. #2577	C₂×C₃₁	semidirect
622. #2532	C₂×C₃₁	semidirect
623. #2528	C₂×C₃₁	semidirect
624. #2524	C₂×C₃₁	semidirect
626. #2478	C₂×C₃₁	semidirect
628. #2469	C₂×C₃₁	semidirect
629. #2465	C₂×C₃₁	semidirect
630. #2401	C₂×C₃₁	semidirect
631. #2399	C₂×C₃₁	semidirect
633. #2396	C₂×C₃₁	semidirect
634. C₄×#126	C₂×C₃₁	semidirect
635. C₄×#126	C₂×C₃₁	semidirect
636. C₄×#126	C₂×C₃₁	semidirect
638. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
639. #2298	C₂×C₃₁	semidirect
640. #2295	C₂×C₃₁	semidirect
641. #2295	C₂×C₃₁	semidirect
643. C₄²×Q₈	C₂×C₃₁	semidirect
644. C₄×#117	C₂×C₃₁	semidirect
1029. C₃₁	#34867	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2605	2
C₃₁×#2604	2
C₃₁×#2601	2
C₃₁×#2599	2
C₃₁×#2594	2
C₃₁×#2588	2
C₃₁×#2577	2
C₃₁×#2560	2
C₃₁×#2532	2
C₃₁×#2528	2
C₃₁×#2524	2
C₃₁×#2521	2
C₃₁×#2478	2
C₃₁×#2474	2
C₃₁×#2469	2
C₃₁×#2465	2
C₃₁×#2401	2
C₃₁×#2399	2
C₃₁×#2398	2
C₃₁×#2396	2
C₄×C₃₁×#126	2
C₄×C₃₁×#124	2
C₄×C₃₁×C₂²⋊Q₈	2
C₃₁×#2298	2
C₃₁×#2295	2
C₃₁×#2290	2
C₄²×Q₈×C₃₁	2
C₄×C₃₁×#117	2
#34867	31

Subgroups — C31×#34867 #21491626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34867 #21491626