Subgroups — C₃₁×#60984 #21517743

Order 7936.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3455	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3261	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3260	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3258	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3257	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3244	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3243	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3225	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3225	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3197	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3196	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3191	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3190	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3178	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3178	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3175	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3173	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3126	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3119	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3111	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#556	—	2	1	no	—
33	C₃₁×#554	—	2	1	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	—	2	1	no	—
36	C₃₁×#552	—	2	1	no	—
37	C₃₁×#552	—	2	1	no	—
38	C₃₁×#551	—	2	1	no	—
39	C₃₁×#551	—	2	1	no	—
40	C₃₁×#544	C₂²	1	1	yes	characteristic
41	C₃₁×#542	C₂²	1	1	yes	characteristic
42	C₃₁×#542	C₂²	1	1	yes	characteristic
43	C₃₁×#542	C₂²	1	1	yes	characteristic
44	C₃₁×#542	C₂²	1	1	yes	characteristic
45	C₃₁×#542	C₂²	1	1	yes	characteristic
46	C₃₁×#542	C₂²	1	1	yes	characteristic
47	C₃₁×#541	C₂²	1	1	yes	characteristic
48	C₃₁×#541	C₂²	1	1	yes	characteristic
49	C₃₁×#541	C₂²	1	1	yes	characteristic
50	C₃₁×#541	C₂²	1	1	yes	characteristic
51	C₃₁×#540	C₂²	1	1	yes	characteristic
52	C₃₁×#540	C₂²	1	1	yes	characteristic
53	C₃₁×#539	—	2	1	no	—
54	C₃₁×#539	—	2	1	no	—
55	C₃₁×#538	—	2	1	no	—
56	C₃₁×#538	—	2	1	no	—
57	C₃₁×#536	C₂²	1	1	yes	characteristic
58	C₃₁×#533	C₂²	1	1	yes	characteristic
59	C₃₁×#533	C₂²	1	1	yes	characteristic
60	C₃₁×#533	C₂²	1	1	yes	characteristic
61	C₃₁×#532	C₂²	1	1	yes	characteristic
62	C₃₁×#529	—	2	1	no	—
63	C₃₁×#529	—	2	1	no	—
64	C₃₁×#529	—	2	1	no	—
65	C₃₁×#529	—	2	1	no	—
66	C₃₁×#529	C₂²	1	1	yes	characteristic
67	C₃₁×#529	C₂²	1	1	yes	characteristic
68	C₃₁×#525	C₂²	1	1	yes	characteristic
69	C₃₁×#525	C₂²	1	1	yes	characteristic
70	C₃₁×#525	C₂²	1	1	yes	characteristic
71	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
72	C₃₁×#520	C₂²	1	1	yes	characteristic
73	C₃₁×#519	C₂²	1	1	yes	characteristic
74	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
75	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
77	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#485	C₂²	1	1	yes	characteristic
94	C₃₁×#485	C₂²	1	1	yes	characteristic
95	C₃₁×#485	C₂²	1	1	yes	characteristic
96	C₃₁×#485	C₂²	1	1	yes	characteristic
97	C₃₁×#485	C₂²	1	1	yes	characteristic
98	C₃₁×#485	C₂²	1	1	yes	characteristic
99	C₃₁×#485	C₂²	1	1	yes	characteristic
100	C₃₁×#485	C₂²	1	1	yes	characteristic
101	C₃₁×#484	C₂²	1	1	yes	characteristic
102	C₃₁×#483	C₂²	1	1	yes	characteristic
103	C₃₁×#482	C₂²	1	1	yes	characteristic
104	C₃₁×#482	C₂²	1	1	yes	characteristic
105	C₃₁×#482	C₂²	1	1	yes	characteristic
106	C₃₁×#482	C₂²	1	1	yes	characteristic
107	C₃₁×#481	C₂²	1	1	yes	characteristic
108	C₃₁×#480	C₂²	1	1	yes	characteristic
109	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#470	C₂²	1	1	yes	characteristic
126	C₃₁×#470	C₂²	1	1	yes	characteristic
127	C₃₁×#470	C₂²	1	1	yes	characteristic
128	C₃₁×#469	C₂²	1	1	yes	characteristic
129	C₃₁×#468	C₂²	1	1	yes	characteristic
130	C₃₁×#468	C₂²	1	1	yes	characteristic
131	C₃₁×#468	C₂²	1	1	yes	characteristic
132	C₃₁×#468	C₂²	1	1	yes	characteristic
133	C₃₁×#467	C₂²	1	1	yes	characteristic
134	C₃₁×#467	C₂²	1	1	yes	characteristic
135	C₃₁×#467	C₂²	1	1	yes	characteristic
136	C₃₁×#466	C₂²	1	1	yes	characteristic
137	C₃₁×#465	C₂²	1	1	yes	characteristic
138	C₃₁×#465	C₂²	1	1	yes	characteristic
139	C₃₁×#465	C₂²	1	1	yes	characteristic
140	C₃₁×#465	C₂²	1	1	yes	characteristic
141	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
142	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
143	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
144	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
145	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
146	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
147	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
150	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
151	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
152	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
153	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
154	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
155	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
156	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
157	C₃₁×#452	C₂²	1	1	yes	characteristic
158	C₃₁×#452	C₂²	1	1	yes	characteristic
159	C₃₁×#452	C₂²	1	1	yes	characteristic
160	C₃₁×#452	C₂²	1	1	yes	characteristic
161	C₃₁×#452	C₂²	1	1	yes	characteristic
162	C₃₁×#452	C₂²	1	1	yes	characteristic
163	C₃₁×#452	C₂²	1	1	yes	characteristic
164	C₃₁×#452	C₂²	1	1	yes	characteristic
165	C₃₁×#451	C₂²	1	1	yes	characteristic
166	C₃₁×#451	C₂²	1	1	yes	characteristic
167	C₃₁×#449	C₂²	1	1	yes	characteristic
168	C₃₁×#449	C₂²	1	1	yes	characteristic
169	C₃₁×#449	C₂²	1	1	yes	characteristic
170	C₃₁×#449	C₂²	1	1	yes	characteristic
171	C₃₁×#448	C₂²	1	1	yes	characteristic
172	C₃₁×#448	C₂²	1	1	yes	characteristic
173	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
174	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
175	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
176	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
177	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
178	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
179	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
180	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
182	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
183	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
184	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
185	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
186	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
187	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
188	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
189	C₃₁×#433	C₂²	1	1	yes	characteristic
190	C₃₁×#433	C₂²	1	1	yes	characteristic
191	C₃₁×#433	C₂²	1	1	yes	characteristic
192	C₃₁×#433	C₂²	1	1	yes	characteristic
193	C₃₁×#432	C₂²	1	1	yes	characteristic
194	C₃₁×#432	C₂²	1	1	yes	characteristic
195	C₃₁×#431	C₂²	1	1	yes	characteristic
196	C₃₁×#431	C₂²	1	1	yes	characteristic
197	C₃₁×#424	C₂²	1	1	yes	characteristic
198	C₃₁×#424	C₂²	1	1	yes	characteristic
199	C₃₁×#407	C₂²	1	1	yes	characteristic
200	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
201	C₃₁×#405	C₂²	1	1	yes	characteristic
202	C₃₁×#405	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
206	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
226	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₃₁×C₄⋊Q₈	—	2	1	no	—
229	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
230	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
233	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
234	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
235	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
236	C₃₁×#127	C₂³	1	1	yes	characteristic
237	C₃₁×#126	—	2	1	no	—
238	C₃₁×#126	—	2	1	no	—
239	C₃₁×#126	—	2	1	no	—
240	C₃₁×#126	—	2	1	no	—
241	C₃₁×#126	—	2	1	no	—
242	C₃₁×#126	—	2	1	no	—
243	C₃₁×#126	—	2	1	no	—
244	C₃₁×#126	—	2	1	no	—
245	C₃₁×#126	—	2	1	no	—
246	C₃₁×#126	—	2	1	no	—
247	C₃₁×#126	—	2	1	no	—
248	C₃₁×#126	—	2	1	no	—
249	C₃₁×#126	—	2	1	no	—
250	C₃₁×#126	—	2	1	no	—
251	C₃₁×#126	—	2	1	no	—
252	C₃₁×#126	—	2	1	no	—
253	C₃₁×#125	—	2	1	no	—
254	C₃₁×#125	—	2	1	no	—
255	C₃₁×#125	—	2	1	no	—
256	C₃₁×#125	—	2	1	no	—
257	C₃₁×#125	—	2	1	no	—
258	C₃₁×#125	—	2	1	no	—
259	C₃₁×#125	—	2	1	no	—
260	C₃₁×#125	—	2	1	no	—
261	C₃₁×#125	—	2	1	no	—
262	C₃₁×#125	—	2	1	no	—
263	C₃₁×#125	—	2	1	no	—
264	C₃₁×#125	C₂³	1	1	yes	characteristic
265	C₃₁×#125	C₂³	1	1	yes	characteristic
266	C₃₁×#125	C₂³	1	1	yes	characteristic
267	C₃₁×#125	C₂³	1	1	yes	characteristic
268	C₃₁×#124	—	2	1	no	—
269	C₃₁×#124	—	2	1	no	—
270	C₃₁×#124	—	2	1	no	—
271	C₃₁×#124	—	2	1	no	—
272	C₃₁×#124	—	2	1	no	—
273	C₃₁×#124	—	2	1	no	—
274	C₃₁×#124	C₂³	1	1	yes	characteristic
275	C₃₁×#124	C₂³	1	1	yes	characteristic
276	C₃₁×#124	C₂³	1	1	yes	characteristic
277	C₃₁×#124	C₂³	1	1	yes	characteristic
278	C₃₁×#123	—	2	1	no	—
279	C₃₁×#123	—	2	1	no	—
280	C₃₁×#123	—	2	1	no	—
281	C₃₁×#123	—	2	1	no	—
282	C₃₁×#123	—	2	1	no	—
283	C₃₁×#123	—	2	1	no	—
284	C₃₁×#123	—	2	1	no	—
285	C₃₁×#123	—	2	1	no	—
286	C₃₁×#123	—	2	1	no	—
287	C₃₁×#123	—	2	1	no	—
288	C₃₁×#123	—	2	1	no	—
289	C₃₁×#123	—	2	1	no	—
290	C₃₁×#123	—	2	1	no	—
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×#123	—	2	1	no	—
294	C₃₁×#123	—	2	1	no	—
295	C₃₁×C₂²⋊Q₈	—	2	1	no	—
296	C₃₁×C₂²⋊Q₈	—	2	1	no	—
297	C₃₁×C₂²⋊Q₈	—	2	1	no	—
298	C₃₁×C₂²⋊Q₈	—	2	1	no	—
299	C₃₁×C₂²⋊Q₈	—	2	1	no	—
300	C₃₁×C₂²⋊Q₈	—	2	1	no	—
301	C₃₁×C₂²⋊Q₈	—	2	1	no	—
302	C₃₁×C₂²⋊Q₈	—	2	1	no	—
303	C₃₁×C₂²⋊Q₈	—	2	1	no	—
304	C₃₁×C₂²⋊Q₈	—	2	1	no	—
305	C₃₁×C₂²⋊Q₈	—	2	1	no	—
306	C₃₁×C₂²⋊Q₈	—	2	1	no	—
307	C₃₁×C₂²⋊Q₈	—	2	1	no	—
308	C₃₁×C₂²⋊Q₈	—	2	1	no	—
309	C₃₁×C₂²⋊Q₈	—	2	1	no	—
310	C₃₁×C₂²⋊Q₈	—	2	1	no	—
311	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
312	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
313	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
319	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
320	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
321	C₃₁×#121	—	2	1	no	—
322	C₃₁×#121	—	2	1	no	—
323	C₃₁×#121	—	2	1	no	—
324	C₃₁×#121	—	2	1	no	—
325	C₃₁×#121	—	2	1	no	—
326	C₃₁×#121	—	2	1	no	—
327	C₃₁×#121	C₂³	1	1	yes	characteristic
328	C₃₁×#121	C₂³	1	1	yes	characteristic
329	C₃₁×#121	C₂³	1	1	yes	characteristic
330	C₃₁×#121	C₂³	1	1	yes	characteristic
331	C₃₁×#121	C₂³	1	1	yes	characteristic
332	C₃₁×#121	C₂³	1	1	yes	characteristic
333	C₃₁×#120	—	2	1	no	—
334	C₃₁×#120	—	2	1	no	—
335	C₃₁×#120	—	2	1	no	—
336	C₄×Q₈×C₃₁	—	2	1	no	—
337	C₄×Q₈×C₃₁	—	2	1	no	—
338	C₄×Q₈×C₃₁	—	2	1	no	—
339	C₄×Q₈×C₃₁	—	2	1	no	—
340	C₄×Q₈×C₃₁	—	2	1	no	—
341	C₄×Q₈×C₃₁	—	2	1	no	—
342	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
347	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
352	C₄×D₄×C₃₁	—	2	1	no	—
353	C₄×D₄×C₃₁	—	2	1	no	—
354	C₄×D₄×C₃₁	—	2	1	no	—
355	C₄×D₄×C₃₁	—	2	1	no	—
356	C₄×D₄×C₃₁	—	2	1	no	—
357	C₄×D₄×C₃₁	—	2	1	no	—
358	C₄×D₄×C₃₁	—	2	1	no	—
359	C₄×D₄×C₃₁	—	2	1	no	—
360	C₄×D₄×C₃₁	—	2	1	no	—
361	C₄×D₄×C₃₁	—	2	1	no	—
362	C₄×D₄×C₃₁	—	2	1	no	—
363	C₄×D₄×C₃₁	—	2	1	no	—
364	C₄×D₄×C₃₁	—	2	1	no	—
365	C₄×D₄×C₃₁	—	2	1	no	—
366	C₄×D₄×C₃₁	—	2	1	no	—
367	C₄×D₄×C₃₁	—	2	1	no	—
368	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
374	C₃₁×#117	—	2	1	no	—
375	C₃₁×#117	—	2	1	no	—
376	C₃₁×#117	—	2	1	no	—
377	C₃₁×#117	—	2	1	no	—
378	C₃₁×#117	—	2	1	no	—
379	C₃₁×#117	—	2	1	no	—
380	C₃₁×#117	—	2	1	no	—
381	C₃₁×#117	—	2	1	no	—
382	C₃₁×#117	—	2	1	no	—
383	C₃₁×#117	D₄	1	1	yes	characteristic
384	C₃₁×#117	D₄	1	1	yes	characteristic
385	C₃₁×#117	D₄	1	1	yes	characteristic
386	C₃₁×#117	D₄	1	1	yes	characteristic
387	C₃₁×#117	C₂³	1	1	yes	characteristic
388	C₃₁×#117	C₂³	1	1	yes	characteristic
389	C₃₁×#117	C₂³	1	1	yes	characteristic
390	C₃₁×#117	C₂³	1	1	yes	characteristic
391	C₃₁×#117	C₂³	1	1	yes	characteristic
392	C₃₁×#117	C₂³	1	1	yes	characteristic
393	C₃₁×#117	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
397	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
398	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
399	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
400	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
401	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
402	C₂×C₄²×C₃₁	—	2	1	no	—
403	C₂×C₄²×C₃₁	—	2	1	no	—
404	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
405	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
406	C₃₁×#107	C₂³	1	1	yes	characteristic
407	C₃₁×#107	C₂³	1	1	yes	characteristic
408	C₃₁×#107	C₂³	1	1	yes	characteristic
409	C₃₁×#107	C₂³	1	1	yes	characteristic
410	C₃₁×#107	C₂³	1	1	yes	characteristic
411	C₃₁×#107	C₂³	1	1	yes	characteristic
412	C₃₁×#107	C₂³	1	1	yes	characteristic
413	C₃₁×#107	C₂³	1	1	yes	characteristic
414	C₃₁×#106	C₂³	1	1	yes	characteristic
415	C₃₁×#106	C₂³	1	1	yes	characteristic
416	C₃₁×#106	C₂³	1	1	yes	characteristic
417	C₃₁×#106	C₂³	1	1	yes	characteristic
418	C₃₁×#106	C₂³	1	1	yes	characteristic
419	C₃₁×#106	C₂³	1	1	yes	characteristic
420	C₃₁×#106	C₂³	1	1	yes	characteristic
421	C₃₁×#106	C₂³	1	1	yes	characteristic
422	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
423	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
424	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×#103	C₂³	1	1	yes	characteristic
431	C₃₁×#103	C₂³	1	1	yes	characteristic
432	C₃₁×#103	C₂³	1	1	yes	characteristic
433	C₃₁×#103	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#102	C₂³	1	1	yes	characteristic
451	C₃₁×#102	C₂³	1	1	yes	characteristic
452	C₃₁×#102	C₂³	1	1	yes	characteristic
453	C₃₁×#102	C₂³	1	1	yes	characteristic
454	C₃₁×#102	C₂³	1	1	yes	characteristic
455	C₃₁×#102	C₂³	1	1	yes	characteristic
456	C₃₁×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₃₁×#97	C₂³	1	1	yes	characteristic
471	C₃₁×#97	C₂³	1	1	yes	characteristic
472	C₃₁×#97	C₂³	1	1	yes	characteristic
473	C₃₁×#97	C₂³	1	1	yes	characteristic
474	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
475	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
476	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
478	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
479	#41×C₃₁	—	4	1	no	—
480	#41×C₃₁	—	4	1	no	—
481	#41×C₃₁	—	4	1	no	—
482	#41×C₃₁	—	4	1	no	—
483	#41×C₃₁	—	4	1	no	—
484	#41×C₃₁	—	4	1	no	—
485	C₂×Q₈×C₃₁	—	2	1	no	—
486	C₂×Q₈×C₃₁	—	2	1	no	—
487	C₂×Q₈×C₃₁	—	2	1	no	—
488	C₂×Q₈×C₃₁	—	2	1	no	—
489	C₂×Q₈×C₃₁	—	2	1	no	—
490	C₂×Q₈×C₃₁	—	4	1	no	—
491	C₂×Q₈×C₃₁	—	4	1	no	—
492	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
493	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
496	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
497	C₂×D₄×C₃₁	—	2	1	no	—
498	C₂×D₄×C₃₁	—	2	1	no	—
499	C₂×D₄×C₃₁	—	2	1	no	—
500	C₂×D₄×C₃₁	—	2	1	no	—
501	C₂×D₄×C₃₁	—	2	1	no	—
502	C₂×D₄×C₃₁	—	2	1	no	—
503	C₂×D₄×C₃₁	—	2	1	no	—
504	C₂×D₄×C₃₁	—	2	1	no	—
505	C₂×D₄×C₃₁	—	2	1	no	—
506	C₂×D₄×C₃₁	—	2	1	no	—
507	C₂×D₄×C₃₁	—	2	1	no	—
508	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
509	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
510	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
511	C₂²×C₄×C₃₁	—	2	1	no	—
512	C₂²×C₄×C₃₁	—	2	1	no	—
513	C₂²×C₄×C₃₁	—	2	1	no	—
514	C₂²×C₄×C₃₁	—	2	1	no	—
515	C₂²×C₄×C₃₁	—	2	1	no	—
516	C₂²×C₄×C₃₁	—	2	1	no	—
517	C₂²×C₄×C₃₁	—	2	1	no	—
518	C₂²×C₄×C₃₁	—	2	1	no	—
519	C₂²×C₄×C₃₁	—	2	1	no	—
520	C₂²×C₄×C₃₁	—	2	1	no	—
521	C₂²×C₄×C₃₁	—	2	1	no	—
522	C₂²×C₄×C₃₁	—	4	1	no	—
523	C₂²×C₄×C₃₁	—	4	1	no	—
524	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
525	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
526	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
527	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
528	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
529	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
530	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
531	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
532	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
533	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
534	Q₁₆×C₃₁	—	4	1	no	—
535	Q₁₆×C₃₁	—	4	1	no	—
536	Q₁₆×C₃₁	—	4	1	no	—
537	Q₁₆×C₃₁	—	4	1	no	—
538	Q₁₆×C₃₁	—	4	1	no	—
539	Q₁₆×C₃₁	—	4	1	no	—
540	SD₁₆×C₃₁	—	4	1	no	—
541	SD₁₆×C₃₁	—	4	1	no	—
542	SD₁₆×C₃₁	—	4	1	no	—
543	SD₁₆×C₃₁	—	4	1	no	—
544	SD₁₆×C₃₁	—	4	1	no	—
545	SD₁₆×C₃₁	—	4	1	no	—
546	SD₁₆×C₃₁	—	4	1	no	—
547	SD₁₆×C₃₁	—	4	1	no	—
548	D₈×C₃₁	—	4	1	no	—
549	D₈×C₃₁	—	4	1	no	—
550	M₁₆×C₃₁	—	4	1	no	—
551	M₁₆×C₃₁	—	4	1	no	—
552	C₂×C₈×C₃₁	—	4	1	no	—
553	C₂×C₈×C₃₁	—	4	1	no	—
554	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
555	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
556	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
557	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
558	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
559	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
560	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
561	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
562	C₄⋊C₄×C₃₁	—	2	1	no	—
563	C₄⋊C₄×C₃₁	—	2	1	no	—
564	C₄⋊C₄×C₃₁	—	2	1	no	—
565	C₄⋊C₄×C₃₁	—	2	1	no	—
566	C₄⋊C₄×C₃₁	—	2	1	no	—
567	C₄⋊C₄×C₃₁	—	2	1	no	—
568	C₄⋊C₄×C₃₁	—	2	1	no	—
569	C₄⋊C₄×C₃₁	—	2	1	no	—
570	C₄⋊C₄×C₃₁	—	2	1	no	—
571	C₄⋊C₄×C₃₁	—	2	1	no	—
572	C₄⋊C₄×C₃₁	—	2	1	no	—
573	C₄⋊C₄×C₃₁	—	2	1	no	—
574	C₄⋊C₄×C₃₁	—	2	1	no	—
575	C₄⋊C₄×C₃₁	—	2	1	no	—
576	C₄⋊C₄×C₃₁	—	2	1	no	—
577	C₄⋊C₄×C₃₁	—	2	1	no	—
578	C₄⋊C₄×C₃₁	—	2	1	no	—
579	C₄⋊C₄×C₃₁	—	2	1	no	—
580	C₄⋊C₄×C₃₁	—	2	1	no	—
581	C₄⋊C₄×C₃₁	—	2	1	no	—
582	C₄⋊C₄×C₃₁	—	2	1	no	—
583	C₄⋊C₄×C₃₁	—	2	1	no	—
584	C₄⋊C₄×C₃₁	—	2	1	no	—
585	C₄⋊C₄×C₃₁	—	2	1	no	—
586	C₄⋊C₄×C₃₁	—	2	1	no	—
587	C₄⋊C₄×C₃₁	—	2	1	no	—
588	C₄⋊C₄×C₃₁	—	2	1	no	—
589	C₄⋊C₄×C₃₁	—	2	1	no	—
590	C₄⋊C₄×C₃₁	—	2	1	no	—
591	C₄⋊C₄×C₃₁	—	2	1	no	—
592	C₄⋊C₄×C₃₁	—	2	1	no	—
593	C₄⋊C₄×C₃₁	—	2	1	no	—
594	C₄⋊C₄×C₃₁	—	2	1	no	—
595	C₄⋊C₄×C₃₁	—	2	1	no	—
596	C₄⋊C₄×C₃₁	—	2	1	no	—
597	C₄⋊C₄×C₃₁	—	2	1	no	—
598	C₄⋊C₄×C₃₁	—	2	1	no	—
599	C₄⋊C₄×C₃₁	—	2	1	no	—
600	C₄⋊C₄×C₃₁	—	2	1	no	—
601	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
617	C₂²⋊C₄×C₃₁	—	2	1	no	—
618	C₂²⋊C₄×C₃₁	—	2	1	no	—
619	C₂²⋊C₄×C₃₁	—	2	1	no	—
620	C₂²⋊C₄×C₃₁	—	2	1	no	—
621	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	—	2	1	no	—
638	C₂²⋊C₄×C₃₁	—	2	1	no	—
639	C₂²⋊C₄×C₃₁	—	2	1	no	—
640	C₂²⋊C₄×C₃₁	—	2	1	no	—
641	C₂²⋊C₄×C₃₁	—	2	1	no	—
642	C₂²⋊C₄×C₃₁	—	2	1	no	—
643	C₂²⋊C₄×C₃₁	—	2	1	no	—
644	C₂²⋊C₄×C₃₁	—	2	1	no	—
645	C₂²⋊C₄×C₃₁	—	2	1	no	—
646	C₂²⋊C₄×C₃₁	—	2	1	no	—
647	C₂²⋊C₄×C₃₁	—	2	1	no	—
648	C₂²⋊C₄×C₃₁	—	2	1	no	—
649	C₂²⋊C₄×C₃₁	—	2	1	no	—
650	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
658	C₄²×C₃₁	—	2	1	no	—
659	C₄²×C₃₁	—	2	1	no	—
660	C₄²×C₃₁	—	2	1	no	—
661	C₄²×C₃₁	—	2	1	no	—
662	C₄²×C₃₁	—	2	1	no	—
663	C₄²×C₃₁	—	2	1	no	—
664	C₄²×C₃₁	—	2	1	no	—
665	C₄²×C₃₁	—	2	1	no	—
666	C₄²×C₃₁	—	2	1	no	—
667	C₄²×C₃₁	—	2	1	no	—
668	C₄²×C₃₁	—	2	1	no	—
669	C₄²×C₃₁	—	2	1	no	—
670	C₄²×C₃₁	—	2	1	no	—
671	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
672	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
673	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
674	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
675	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
676	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
677	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
678	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
679	#60984	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
680	C₂³×C₃₁	—	2	1	no	—
681	C₂³×C₃₁	—	2	1	no	—
682	C₂³×C₃₁	—	2	1	no	—
683	C₂³×C₃₁	—	4	1	no	—
684	C₂³×C₃₁	—	4	1	no	—
685	C₂³×C₃₁	—	4	1	no	—
686	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
687	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
688	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
689	Q₈×C₃₁	—	2	1	no	—
690	Q₈×C₃₁	—	2	1	no	—
691	Q₈×C₃₁	—	2	1	no	—
692	Q₈×C₃₁	—	2	1	no	—
693	Q₈×C₃₁	—	2	1	no	—
694	Q₈×C₃₁	—	2	1	no	—
695	Q₈×C₃₁	—	2	1	no	—
696	Q₈×C₃₁	—	2	1	no	—
697	Q₈×C₃₁	—	2	1	no	—
698	Q₈×C₃₁	—	2	1	no	—
699	Q₈×C₃₁	—	4	2	no	—
700	Q₈×C₃₁	—	8	1	no	—
701	Q₈×C₃₁	—	8	1	no	—
702	Q₈×C₃₁	—	8	1	no	—
703	Q₈×C₃₁	—	8	1	no	—
704	D₄×C₃₁	—	2	1	no	—
705	D₄×C₃₁	—	2	1	no	—
706	D₄×C₃₁	—	2	1	no	—
707	D₄×C₃₁	—	2	1	no	—
708	D₄×C₃₁	—	2	1	no	—
709	D₄×C₃₁	—	2	1	no	—
710	D₄×C₃₁	—	4	2	no	—
711	D₄×C₃₁	—	4	2	no	—
712	D₄×C₃₁	—	4	2	no	—
713	D₄×C₃₁	—	4	2	no	—
714	D₄×C₃₁	—	8	1	no	—
715	D₄×C₃₁	—	8	1	no	—
716	D₄×C₃₁	—	8	1	no	—
717	D₄×C₃₁	—	8	1	no	—
718	D₄×C₃₁	—	8	1	no	—
719	D₄×C₃₁	—	8	1	no	—
720	D₄×C₃₁	—	8	1	no	—
721	C₂×C₄×C₃₁	—	2	1	no	—
722	C₂×C₄×C₃₁	—	2	1	no	—
723	C₂×C₄×C₃₁	—	2	1	no	—
724	C₂×C₄×C₃₁	—	2	1	no	—
725	C₂×C₄×C₃₁	—	2	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	2	1	no	—
728	C₂×C₄×C₃₁	—	2	1	no	—
729	C₂×C₄×C₃₁	—	2	1	no	—
730	C₂×C₄×C₃₁	—	2	1	no	—
731	C₂×C₄×C₃₁	—	2	1	no	—
732	C₂×C₄×C₃₁	—	2	1	no	—
733	C₂×C₄×C₃₁	—	2	1	no	—
734	C₂×C₄×C₃₁	—	2	1	no	—
735	C₂×C₄×C₃₁	—	2	1	no	—
736	C₂×C₄×C₃₁	—	2	1	no	—
737	C₂×C₄×C₃₁	—	2	1	no	—
738	C₂×C₄×C₃₁	—	2	1	no	—
739	C₂×C₄×C₃₁	—	2	1	no	—
740	C₂×C₄×C₃₁	—	4	1	no	—
741	C₂×C₄×C₃₁	—	4	1	no	—
742	C₂×C₄×C₃₁	—	4	1	no	—
743	C₂×C₄×C₃₁	—	4	1	no	—
744	C₂×C₄×C₃₁	—	4	1	no	—
745	C₂×C₄×C₃₁	—	4	1	no	—
746	C₂×C₄×C₃₁	—	4	1	no	—
747	C₂×C₄×C₃₁	—	4	2	no	—
748	C₂×C₄×C₃₁	—	4	2	no	—
749	C₂×C₄×C₃₁	—	4	2	no	—
750	C₂×C₄×C₃₁	—	4	2	no	—
751	C₂×C₄×C₃₁	—	8	1	no	—
752	C₂×C₄×C₃₁	—	8	1	no	—
753	C₂×C₄×C₃₁	—	8	1	no	—
754	C₂×C₄×C₃₁	—	8	1	no	—
755	C₂×C₄×C₃₁	—	8	1	no	—
756	C₂×C₄×C₃₁	—	8	1	no	—
757	C₂×C₄×C₃₁	—	8	1	no	—
758	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
759	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
760	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
763	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
764	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
765	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
766	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
770	C₈×C₃₁	—	2	1	no	—
771	C₈×C₃₁	—	2	1	no	—
772	C₈×C₃₁	—	2	1	no	—
773	C₈×C₃₁	—	2	1	no	—
774	C₈×C₃₁	—	2	1	no	—
775	C₈×C₃₁	—	2	1	no	—
776	C₈×C₃₁	—	2	1	no	—
777	C₈×C₃₁	—	2	1	no	—
778	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3455	C₂×C₃₁	1	1	yes	characteristic, complemented
780	#3261	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3260	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3258	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3257	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3244	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3243	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3240	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3225	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3225	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3197	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3196	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3191	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3178	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3178	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3175	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3173	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3126	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3119	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3111	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
809	C₂²×C₃₁	—	2	1	no	—
810	C₂²×C₃₁	—	2	1	no	—
811	C₂²×C₃₁	—	2	1	no	—
812	C₂²×C₃₁	—	2	1	no	—
813	C₂²×C₃₁	—	2	1	no	—
814	C₂²×C₃₁	—	2	1	no	—
815	C₂²×C₃₁	—	2	1	no	—
816	C₂²×C₃₁	—	2	1	no	—
817	C₂²×C₃₁	—	2	1	no	—
818	C₂²×C₃₁	—	4	1	no	—
819	C₂²×C₃₁	—	4	1	no	—
820	C₂²×C₃₁	—	4	1	no	—
821	C₂²×C₃₁	—	4	1	no	—
822	C₂²×C₃₁	—	4	1	no	—
823	C₂²×C₃₁	—	4	1	no	—
824	C₂²×C₃₁	—	4	1	no	—
825	C₂²×C₃₁	—	4	1	no	—
826	C₂²×C₃₁	—	4	1	no	—
827	C₂²×C₃₁	—	8	2	no	—
828	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
829	C₄×C₃₁	—	2	1	no	—
830	C₄×C₃₁	—	2	1	no	—
831	C₄×C₃₁	—	2	1	no	—
832	C₄×C₃₁	—	2	1	no	—
833	C₄×C₃₁	—	2	1	no	—
834	C₄×C₃₁	—	2	1	no	—
835	C₄×C₃₁	—	2	1	no	—
836	C₄×C₃₁	—	2	1	no	—
837	C₄×C₃₁	—	2	1	no	—
838	C₄×C₃₁	—	2	1	no	—
839	C₄×C₃₁	—	2	1	no	—
840	C₄×C₃₁	—	4	1	no	—
841	C₄×C₃₁	—	4	1	no	—
842	C₄×C₃₁	—	4	1	no	—
843	C₄×C₃₁	—	4	1	no	—
844	C₄×C₃₁	—	4	1	no	—
845	C₄×C₃₁	—	4	1	no	—
846	C₄×C₃₁	—	4	1	no	—
847	C₄×C₃₁	—	4	1	no	—
848	C₄×C₃₁	—	4	1	no	—
849	C₄×C₃₁	—	4	1	no	—
850	C₄×C₃₁	—	4	1	no	—
851	C₄×C₃₁	—	4	1	no	—
852	C₄×C₃₁	—	4	1	no	—
853	C₄×C₃₁	#585	1	1	yes	characteristic
854	C₄×C₃₁	#585	1	1	yes	characteristic
855	#556	—	2	1	no	—
856	#554	—	2	1	no	—
857	#552	—	2	1	no	—
858	#552	—	2	1	no	—
859	#552	—	2	1	no	—
860	#552	—	2	1	no	—
861	#551	—	2	1	no	—
862	#551	—	2	1	no	—
863	#544	C₂²×C₃₁	1	1	yes	characteristic
864	#542	C₂²×C₃₁	1	1	yes	characteristic
865	#542	C₂²×C₃₁	1	1	yes	characteristic
866	#542	C₂²×C₃₁	1	1	yes	characteristic
867	#542	C₂²×C₃₁	1	1	yes	characteristic
868	#542	C₂²×C₃₁	1	1	yes	characteristic
869	#542	C₂²×C₃₁	1	1	yes	characteristic
870	#541	C₂²×C₃₁	1	1	yes	characteristic
871	#541	C₂²×C₃₁	1	1	yes	characteristic
872	#541	C₂²×C₃₁	1	1	yes	characteristic
873	#541	C₂²×C₃₁	1	1	yes	characteristic
874	#540	C₂²×C₃₁	1	1	yes	characteristic
875	#540	C₂²×C₃₁	1	1	yes	characteristic
876	#539	—	2	1	no	—
877	#539	—	2	1	no	—
878	#538	—	2	1	no	—
879	#538	—	2	1	no	—
880	#536	C₂²×C₃₁	1	1	yes	characteristic
881	#533	C₂²×C₃₁	1	1	yes	characteristic
882	#533	C₂²×C₃₁	1	1	yes	characteristic
883	#533	C₂²×C₃₁	1	1	yes	characteristic
884	#532	C₂²×C₃₁	1	1	yes	characteristic
885	#529	—	2	1	no	—
886	#529	—	2	1	no	—
887	#529	—	2	1	no	—
888	#529	—	2	1	no	—
889	#529	C₂²×C₃₁	1	1	yes	characteristic
890	#529	C₂²×C₃₁	1	1	yes	characteristic
891	#525	C₂²×C₃₁	1	1	yes	characteristic
892	#525	C₂²×C₃₁	1	1	yes	characteristic
893	#525	C₂²×C₃₁	1	1	yes	characteristic
894	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
895	#520	C₂²×C₃₁	1	1	yes	characteristic
896	#519	C₂²×C₃₁	1	1	yes	characteristic
897	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
898	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
899	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
900	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
901	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
902	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
903	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
904	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
905	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
906	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
907	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
908	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
909	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
910	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
911	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
912	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
913	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
914	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
916	#485	C₂²×C₃₁	1	1	yes	characteristic
917	#485	C₂²×C₃₁	1	1	yes	characteristic
918	#485	C₂²×C₃₁	1	1	yes	characteristic
919	#485	C₂²×C₃₁	1	1	yes	characteristic
920	#485	C₂²×C₃₁	1	1	yes	characteristic
921	#485	C₂²×C₃₁	1	1	yes	characteristic
922	#485	C₂²×C₃₁	1	1	yes	characteristic
923	#485	C₂²×C₃₁	1	1	yes	characteristic
924	#484	C₂²×C₃₁	1	1	yes	characteristic
925	#483	C₂²×C₃₁	1	1	yes	characteristic
926	#482	C₂²×C₃₁	1	1	yes	characteristic
927	#482	C₂²×C₃₁	1	1	yes	characteristic
928	#482	C₂²×C₃₁	1	1	yes	characteristic
929	#482	C₂²×C₃₁	1	1	yes	characteristic
930	#481	C₂²×C₃₁	1	1	yes	characteristic
931	#480	C₂²×C₃₁	1	1	yes	characteristic
932	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
933	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
934	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
935	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
936	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
937	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
938	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
939	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
940	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
941	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
942	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
943	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
944	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
945	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
946	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
947	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
948	#470	C₂²×C₃₁	1	1	yes	characteristic
949	#470	C₂²×C₃₁	1	1	yes	characteristic
950	#470	C₂²×C₃₁	1	1	yes	characteristic
951	#469	C₂²×C₃₁	1	1	yes	characteristic
952	#468	C₂²×C₃₁	1	1	yes	characteristic
953	#468	C₂²×C₃₁	1	1	yes	characteristic
954	#468	C₂²×C₃₁	1	1	yes	characteristic
955	#468	C₂²×C₃₁	1	1	yes	characteristic
956	#467	C₂²×C₃₁	1	1	yes	characteristic
957	#467	C₂²×C₃₁	1	1	yes	characteristic
958	#467	C₂²×C₃₁	1	1	yes	characteristic
959	#466	C₂²×C₃₁	1	1	yes	characteristic
960	#465	C₂²×C₃₁	1	1	yes	characteristic
961	#465	C₂²×C₃₁	1	1	yes	characteristic
962	#465	C₂²×C₃₁	1	1	yes	characteristic
963	#465	C₂²×C₃₁	1	1	yes	characteristic
964	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
965	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
966	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
967	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
968	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
969	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
970	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
972	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
973	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
974	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
975	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
976	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
977	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
978	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
979	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
980	#452	C₂²×C₃₁	1	1	yes	characteristic
981	#452	C₂²×C₃₁	1	1	yes	characteristic
982	#452	C₂²×C₃₁	1	1	yes	characteristic
983	#452	C₂²×C₃₁	1	1	yes	characteristic
984	#452	C₂²×C₃₁	1	1	yes	characteristic
985	#452	C₂²×C₃₁	1	1	yes	characteristic
986	#452	C₂²×C₃₁	1	1	yes	characteristic
987	#452	C₂²×C₃₁	1	1	yes	characteristic
988	#451	C₂²×C₃₁	1	1	yes	characteristic
989	#451	C₂²×C₃₁	1	1	yes	characteristic
990	#449	C₂²×C₃₁	1	1	yes	characteristic
991	#449	C₂²×C₃₁	1	1	yes	characteristic
992	#449	C₂²×C₃₁	1	1	yes	characteristic
993	#449	C₂²×C₃₁	1	1	yes	characteristic
994	#448	C₂²×C₃₁	1	1	yes	characteristic
995	#448	C₂²×C₃₁	1	1	yes	characteristic
996	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
997	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
998	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
999	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
1000	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1001	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1003	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1004	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1006	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1007	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1008	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1009	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1010	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1011	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1012	#433	C₂²×C₃₁	1	1	yes	characteristic
1013	#433	C₂²×C₃₁	1	1	yes	characteristic
1014	#433	C₂²×C₃₁	1	1	yes	characteristic
1015	#433	C₂²×C₃₁	1	1	yes	characteristic
1016	#432	C₂²×C₃₁	1	1	yes	characteristic
1017	#432	C₂²×C₃₁	1	1	yes	characteristic
1018	#431	C₂²×C₃₁	1	1	yes	characteristic
1019	#431	C₂²×C₃₁	1	1	yes	characteristic
1020	#424	C₂²×C₃₁	1	1	yes	characteristic
1021	#424	C₂²×C₃₁	1	1	yes	characteristic
1022	#407	C₂²×C₃₁	1	1	yes	characteristic
1023	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
1024	#405	C₂²×C₃₁	1	1	yes	characteristic
1025	#405	C₂²×C₃₁	1	1	yes	characteristic
1026	C₂×C₃₁	—	4	1	no	—
1027	C₂×C₃₁	—	4	1	no	—
1028	C₂×C₃₁	—	4	1	no	—
1029	C₂×C₃₁	—	8	1	no	—
1030	C₂×C₃₁	—	8	1	no	—
1031	C₂×C₃₁	—	8	1	no	—
1032	C₂×C₃₁	#3449	1	1	yes	characteristic
1033	C₂×C₃₁	#3584	1	1	yes	characteristic
1034	C₂×C₃₁	#3586	1	1	yes	characteristic
1035	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1036	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1037	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1038	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1039	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
1040	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1041	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1042	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1043	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1044	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1045	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1046	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1047	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1048	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1049	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1055	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1059	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1060	C₄⋊Q₈	—	2	1	no	—
1061	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1062	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1063	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1064	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1065	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1066	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1067	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1068	#127	C₂³×C₃₁	1	1	yes	characteristic
1069	#126	—	2	1	no	—
1070	#126	—	2	1	no	—
1071	#126	—	2	1	no	—
1072	#126	—	2	1	no	—
1073	#126	—	2	1	no	—
1074	#126	—	2	1	no	—
1075	#126	—	2	1	no	—
1076	#126	—	2	1	no	—
1077	#126	—	2	1	no	—
1078	#126	—	2	1	no	—
1079	#126	—	2	1	no	—
1080	#126	—	2	1	no	—
1081	#126	—	2	1	no	—
1082	#126	—	2	1	no	—
1083	#126	—	2	1	no	—
1084	#126	—	2	1	no	—
1085	#125	—	2	1	no	—
1086	#125	—	2	1	no	—
1087	#125	—	2	1	no	—
1088	#125	—	2	1	no	—
1089	#125	—	2	1	no	—
1090	#125	—	2	1	no	—
1091	#125	—	2	1	no	—
1092	#125	—	2	1	no	—
1093	#125	—	2	1	no	—
1094	#125	—	2	1	no	—
1095	#125	—	2	1	no	—
1096	#125	C₂³×C₃₁	1	1	yes	characteristic
1097	#125	C₂³×C₃₁	1	1	yes	characteristic
1098	#125	C₂³×C₃₁	1	1	yes	characteristic
1099	#125	C₂³×C₃₁	1	1	yes	characteristic
1100	#124	—	2	1	no	—
1101	#124	—	2	1	no	—
1102	#124	—	2	1	no	—
1103	#124	—	2	1	no	—
1104	#124	—	2	1	no	—
1105	#124	—	2	1	no	—
1106	#124	C₂³×C₃₁	1	1	yes	characteristic
1107	#124	C₂³×C₃₁	1	1	yes	characteristic
1108	#124	C₂³×C₃₁	1	1	yes	characteristic
1109	#124	C₂³×C₃₁	1	1	yes	characteristic
1110	#123	—	2	1	no	—
1111	#123	—	2	1	no	—
1112	#123	—	2	1	no	—
1113	#123	—	2	1	no	—
1114	#123	—	2	1	no	—
1115	#123	—	2	1	no	—
1116	#123	—	2	1	no	—
1117	#123	—	2	1	no	—
1118	#123	—	2	1	no	—
1119	#123	—	2	1	no	—
1120	#123	—	2	1	no	—
1121	#123	—	2	1	no	—
1122	#123	—	2	1	no	—
1123	#123	—	2	1	no	—
1124	#123	—	2	1	no	—
1125	#123	—	2	1	no	—
1126	#123	—	2	1	no	—
1127	C₂²⋊Q₈	—	2	1	no	—
1128	C₂²⋊Q₈	—	2	1	no	—
1129	C₂²⋊Q₈	—	2	1	no	—
1130	C₂²⋊Q₈	—	2	1	no	—
1131	C₂²⋊Q₈	—	2	1	no	—
1132	C₂²⋊Q₈	—	2	1	no	—
1133	C₂²⋊Q₈	—	2	1	no	—
1134	C₂²⋊Q₈	—	2	1	no	—
1135	C₂²⋊Q₈	—	2	1	no	—
1136	C₂²⋊Q₈	—	2	1	no	—
1137	C₂²⋊Q₈	—	2	1	no	—
1138	C₂²⋊Q₈	—	2	1	no	—
1139	C₂²⋊Q₈	—	2	1	no	—
1140	C₂²⋊Q₈	—	2	1	no	—
1141	C₂²⋊Q₈	—	2	1	no	—
1142	C₂²⋊Q₈	—	2	1	no	—
1143	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1144	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1145	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1146	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1147	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1148	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1149	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1150	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1151	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1152	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1153	#121	—	2	1	no	—
1154	#121	—	2	1	no	—
1155	#121	—	2	1	no	—
1156	#121	—	2	1	no	—
1157	#121	—	2	1	no	—
1158	#121	—	2	1	no	—
1159	#121	C₂³×C₃₁	1	1	yes	characteristic
1160	#121	C₂³×C₃₁	1	1	yes	characteristic
1161	#121	C₂³×C₃₁	1	1	yes	characteristic
1162	#121	C₂³×C₃₁	1	1	yes	characteristic
1163	#121	C₂³×C₃₁	1	1	yes	characteristic
1164	#121	C₂³×C₃₁	1	1	yes	characteristic
1165	#120	—	2	1	no	—
1166	#120	—	2	1	no	—
1167	#120	—	2	1	no	—
1168	C₄×Q₈	—	2	1	no	—
1169	C₄×Q₈	—	2	1	no	—
1170	C₄×Q₈	—	2	1	no	—
1171	C₄×Q₈	—	2	1	no	—
1172	C₄×Q₈	—	2	1	no	—
1173	C₄×Q₈	—	2	1	no	—
1174	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1175	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1176	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1177	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1178	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1179	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1180	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1181	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1182	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1183	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1184	C₄×D₄	—	2	1	no	—
1185	C₄×D₄	—	2	1	no	—
1186	C₄×D₄	—	2	1	no	—
1187	C₄×D₄	—	2	1	no	—
1188	C₄×D₄	—	2	1	no	—
1189	C₄×D₄	—	2	1	no	—
1190	C₄×D₄	—	2	1	no	—
1191	C₄×D₄	—	2	1	no	—
1192	C₄×D₄	—	2	1	no	—
1193	C₄×D₄	—	2	1	no	—
1194	C₄×D₄	—	2	1	no	—
1195	C₄×D₄	—	2	1	no	—
1196	C₄×D₄	—	2	1	no	—
1197	C₄×D₄	—	2	1	no	—
1198	C₄×D₄	—	2	1	no	—
1199	C₄×D₄	—	2	1	no	—
1200	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1201	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1202	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1203	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1204	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1205	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1206	#117	—	2	1	no	—
1207	#117	—	2	1	no	—
1208	#117	—	2	1	no	—
1209	#117	—	2	1	no	—
1210	#117	—	2	1	no	—
1211	#117	—	2	1	no	—
1212	#117	—	2	1	no	—
1213	#117	—	2	1	no	—
1214	#117	—	2	1	no	—
1215	#117	D₄×C₃₁	1	1	yes	characteristic
1216	#117	D₄×C₃₁	1	1	yes	characteristic
1217	#117	D₄×C₃₁	1	1	yes	characteristic
1218	#117	D₄×C₃₁	1	1	yes	characteristic
1219	#117	C₂³×C₃₁	1	1	yes	characteristic
1220	#117	C₂³×C₃₁	1	1	yes	characteristic
1221	#117	C₂³×C₃₁	1	1	yes	characteristic
1222	#117	C₂³×C₃₁	1	1	yes	characteristic
1223	#117	C₂³×C₃₁	1	1	yes	characteristic
1224	#117	C₂³×C₃₁	1	1	yes	characteristic
1225	#117	C₂³×C₃₁	1	1	yes	characteristic
1226	C₂×C₄⋊C₄	—	2	1	no	—
1227	C₂×C₄⋊C₄	—	2	1	no	—
1228	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
1229	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
1230	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1231	C₂×C₂²⋊C₄	—	2	1	no	—
1232	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
1233	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
1234	C₂×C₄²	—	2	1	no	—
1235	C₂×C₄²	—	2	1	no	—
1236	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1237	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1238	#107	C₂³×C₃₁	1	1	yes	characteristic
1239	#107	C₂³×C₃₁	1	1	yes	characteristic
1240	#107	C₂³×C₃₁	1	1	yes	characteristic
1241	#107	C₂³×C₃₁	1	1	yes	characteristic
1242	#107	C₂³×C₃₁	1	1	yes	characteristic
1243	#107	C₂³×C₃₁	1	1	yes	characteristic
1244	#107	C₂³×C₃₁	1	1	yes	characteristic
1245	#107	C₂³×C₃₁	1	1	yes	characteristic
1246	#106	C₂³×C₃₁	1	1	yes	characteristic
1247	#106	C₂³×C₃₁	1	1	yes	characteristic
1248	#106	C₂³×C₃₁	1	1	yes	characteristic
1249	#106	C₂³×C₃₁	1	1	yes	characteristic
1250	#106	C₂³×C₃₁	1	1	yes	characteristic
1251	#106	C₂³×C₃₁	1	1	yes	characteristic
1252	#106	C₂³×C₃₁	1	1	yes	characteristic
1253	#106	C₂³×C₃₁	1	1	yes	characteristic
1254	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1255	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1256	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1257	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1258	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1259	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1260	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1261	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1262	#103	C₂³×C₃₁	1	1	yes	characteristic
1263	#103	C₂³×C₃₁	1	1	yes	characteristic
1264	#103	C₂³×C₃₁	1	1	yes	characteristic
1265	#103	C₂³×C₃₁	1	1	yes	characteristic
1266	#103	C₂³×C₃₁	1	1	yes	characteristic
1267	#103	C₂³×C₃₁	1	1	yes	characteristic
1268	#103	C₂³×C₃₁	1	1	yes	characteristic
1269	#103	C₂³×C₃₁	1	1	yes	characteristic
1270	#103	C₂³×C₃₁	1	1	yes	characteristic
1271	#103	C₂³×C₃₁	1	1	yes	characteristic
1272	#103	C₂³×C₃₁	1	1	yes	characteristic
1273	#103	C₂³×C₃₁	1	1	yes	characteristic
1274	#103	C₂³×C₃₁	1	1	yes	characteristic
1275	#103	C₂³×C₃₁	1	1	yes	characteristic
1276	#103	C₂³×C₃₁	1	1	yes	characteristic
1277	#103	C₂³×C₃₁	1	1	yes	characteristic
1278	#103	C₂³×C₃₁	1	1	yes	characteristic
1279	#103	C₂³×C₃₁	1	1	yes	characteristic
1280	#103	C₂³×C₃₁	1	1	yes	characteristic
1281	#103	C₂³×C₃₁	1	1	yes	characteristic
1282	#102	C₂³×C₃₁	1	1	yes	characteristic
1283	#102	C₂³×C₃₁	1	1	yes	characteristic
1284	#102	C₂³×C₃₁	1	1	yes	characteristic
1285	#102	C₂³×C₃₁	1	1	yes	characteristic
1286	#102	C₂³×C₃₁	1	1	yes	characteristic
1287	#102	C₂³×C₃₁	1	1	yes	characteristic
1288	#102	C₂³×C₃₁	1	1	yes	characteristic
1289	#102	C₂³×C₃₁	1	1	yes	characteristic
1290	#102	C₂³×C₃₁	1	1	yes	characteristic
1291	#102	C₂³×C₃₁	1	1	yes	characteristic
1292	#102	C₂³×C₃₁	1	1	yes	characteristic
1293	#102	C₂³×C₃₁	1	1	yes	characteristic
1294	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1295	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1296	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1297	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1298	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1299	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1300	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1301	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1302	#97	C₂³×C₃₁	1	1	yes	characteristic
1303	#97	C₂³×C₃₁	1	1	yes	characteristic
1304	#97	C₂³×C₃₁	1	1	yes	characteristic
1305	#97	C₂³×C₃₁	1	1	yes	characteristic
1306	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1307	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1308	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1309	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1310	C₃₁	#60984	1	1	yes	characteristic, direct product factor, Sylow
1311	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
1312	#41	—	4	1	no	—
1313	#41	—	4	1	no	—
1314	#41	—	4	1	no	—
1315	#41	—	4	1	no	—
1316	#41	—	4	1	no	—
1317	#41	—	4	1	no	—
1318	C₂×Q₈	—	2	1	no	—
1319	C₂×Q₈	—	2	1	no	—
1320	C₂×Q₈	—	2	1	no	—
1321	C₂×Q₈	—	2	1	no	—
1322	C₂×Q₈	—	2	1	no	—
1323	C₂×Q₈	—	4	1	no	—
1324	C₂×Q₈	—	4	1	no	—
1325	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1326	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1327	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1328	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1329	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1330	C₂×D₄	—	2	1	no	—
1331	C₂×D₄	—	2	1	no	—
1332	C₂×D₄	—	2	1	no	—
1333	C₂×D₄	—	2	1	no	—
1334	C₂×D₄	—	2	1	no	—
1335	C₂×D₄	—	2	1	no	—
1336	C₂×D₄	—	2	1	no	—
1337	C₂×D₄	—	2	1	no	—
1338	C₂×D₄	—	2	1	no	—
1339	C₂×D₄	—	2	1	no	—
1340	C₂×D₄	—	2	1	no	—
1341	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1342	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1343	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1344	C₂²×C₄	—	2	1	no	—
1345	C₂²×C₄	—	2	1	no	—
1346	C₂²×C₄	—	2	1	no	—
1347	C₂²×C₄	—	2	1	no	—
1348	C₂²×C₄	—	2	1	no	—
1349	C₂²×C₄	—	2	1	no	—
1350	C₂²×C₄	—	2	1	no	—
1351	C₂²×C₄	—	2	1	no	—
1352	C₂²×C₄	—	2	1	no	—
1353	C₂²×C₄	—	2	1	no	—
1354	C₂²×C₄	—	2	1	no	—
1355	C₂²×C₄	—	4	1	no	—
1356	C₂²×C₄	—	4	1	no	—
1357	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1358	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1359	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1360	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1361	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1362	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1363	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1364	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1365	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1366	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1367	Q₁₆	—	4	1	no	—
1368	Q₁₆	—	4	1	no	—
1369	Q₁₆	—	4	1	no	—
1370	Q₁₆	—	4	1	no	—
1371	Q₁₆	—	4	1	no	—
1372	Q₁₆	—	4	1	no	—
1373	SD₁₆	—	4	1	no	—
1374	SD₁₆	—	4	1	no	—
1375	SD₁₆	—	4	1	no	—
1376	SD₁₆	—	4	1	no	—
1377	SD₁₆	—	4	1	no	—
1378	SD₁₆	—	4	1	no	—
1379	SD₁₆	—	4	1	no	—
1380	SD₁₆	—	4	1	no	—
1381	D₈	—	4	1	no	—
1382	D₈	—	4	1	no	—
1383	M₁₆	—	4	1	no	—
1384	M₁₆	—	4	1	no	—
1385	C₂×C₈	—	4	1	no	—
1386	C₂×C₈	—	4	1	no	—
1387	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1388	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1389	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1390	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1391	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1392	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1393	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1394	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1395	C₄⋊C₄	—	2	1	no	—
1396	C₄⋊C₄	—	2	1	no	—
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	—	2	1	no	—
1400	C₄⋊C₄	—	2	1	no	—
1401	C₄⋊C₄	—	2	1	no	—
1402	C₄⋊C₄	—	2	1	no	—
1403	C₄⋊C₄	—	2	1	no	—
1404	C₄⋊C₄	—	2	1	no	—
1405	C₄⋊C₄	—	2	1	no	—
1406	C₄⋊C₄	—	2	1	no	—
1407	C₄⋊C₄	—	2	1	no	—
1408	C₄⋊C₄	—	2	1	no	—
1409	C₄⋊C₄	—	2	1	no	—
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	—	2	1	no	—
1413	C₄⋊C₄	—	2	1	no	—
1414	C₄⋊C₄	—	2	1	no	—
1415	C₄⋊C₄	—	2	1	no	—
1416	C₄⋊C₄	—	2	1	no	—
1417	C₄⋊C₄	—	2	1	no	—
1418	C₄⋊C₄	—	2	1	no	—
1419	C₄⋊C₄	—	2	1	no	—
1420	C₄⋊C₄	—	2	1	no	—
1421	C₄⋊C₄	—	2	1	no	—
1422	C₄⋊C₄	—	2	1	no	—
1423	C₄⋊C₄	—	2	1	no	—
1424	C₄⋊C₄	—	2	1	no	—
1425	C₄⋊C₄	—	2	1	no	—
1426	C₄⋊C₄	—	2	1	no	—
1427	C₄⋊C₄	—	2	1	no	—
1428	C₄⋊C₄	—	2	1	no	—
1429	C₄⋊C₄	—	2	1	no	—
1430	C₄⋊C₄	—	2	1	no	—
1431	C₄⋊C₄	—	2	1	no	—
1432	C₄⋊C₄	—	2	1	no	—
1433	C₄⋊C₄	—	2	1	no	—
1434	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1435	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1436	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1437	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1438	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1439	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1440	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1441	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1442	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1443	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1444	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1445	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1446	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1447	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1448	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1449	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1450	C₂²⋊C₄	—	2	1	no	—
1451	C₂²⋊C₄	—	2	1	no	—
1452	C₂²⋊C₄	—	2	1	no	—
1453	C₂²⋊C₄	—	2	1	no	—
1454	C₂²⋊C₄	—	2	1	no	—
1455	C₂²⋊C₄	—	2	1	no	—
1456	C₂²⋊C₄	—	2	1	no	—
1457	C₂²⋊C₄	—	2	1	no	—
1458	C₂²⋊C₄	—	2	1	no	—
1459	C₂²⋊C₄	—	2	1	no	—
1460	C₂²⋊C₄	—	2	1	no	—
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	—	2	1	no	—
1476	C₂²⋊C₄	—	2	1	no	—
1477	C₂²⋊C₄	—	2	1	no	—
1478	C₂²⋊C₄	—	2	1	no	—
1479	C₂²⋊C₄	—	2	1	no	—
1480	C₂²⋊C₄	—	2	1	no	—
1481	C₂²⋊C₄	—	2	1	no	—
1482	C₂²⋊C₄	—	2	1	no	—
1483	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1484	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1485	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1486	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1487	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1488	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1489	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1490	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1491	C₄²	—	2	1	no	—
1492	C₄²	—	2	1	no	—
1493	C₄²	—	2	1	no	—
1494	C₄²	—	2	1	no	—
1495	C₄²	—	2	1	no	—
1496	C₄²	—	2	1	no	—
1497	C₄²	—	2	1	no	—
1498	C₄²	—	2	1	no	—
1499	C₄²	—	2	1	no	—
1500	C₄²	—	2	1	no	—
1501	C₄²	—	2	1	no	—
1502	C₄²	—	2	1	no	—
1503	C₄²	—	2	1	no	—
1504	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1505	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1506	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1507	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1508	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1509	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1510	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1511	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1512	C₂³	—	2	1	no	—
1513	C₂³	—	2	1	no	—
1514	C₂³	—	2	1	no	—
1515	C₂³	—	4	1	no	—
1516	C₂³	—	4	1	no	—
1517	C₂³	—	4	1	no	—
1518	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1519	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1520	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1521	Q₈	—	2	1	no	—
1522	Q₈	—	2	1	no	—
1523	Q₈	—	2	1	no	—
1524	Q₈	—	2	1	no	—
1525	Q₈	—	2	1	no	—
1526	Q₈	—	2	1	no	—
1527	Q₈	—	2	1	no	—
1528	Q₈	—	2	1	no	—
1529	Q₈	—	2	1	no	—
1530	Q₈	—	2	1	no	—
1531	Q₈	—	4	2	no	—
1532	Q₈	—	8	1	no	—
1533	Q₈	—	8	1	no	—
1534	Q₈	—	8	1	no	—
1535	Q₈	—	8	1	no	—
1536	D₄	—	2	1	no	—
1537	D₄	—	2	1	no	—
1538	D₄	—	2	1	no	—
1539	D₄	—	2	1	no	—
1540	D₄	—	2	1	no	—
1541	D₄	—	2	1	no	—
1542	D₄	—	4	2	no	—
1543	D₄	—	4	2	no	—
1544	D₄	—	4	2	no	—
1545	D₄	—	4	2	no	—
1546	D₄	—	8	1	no	—
1547	D₄	—	8	1	no	—
1548	D₄	—	8	1	no	—
1549	D₄	—	8	1	no	—
1550	D₄	—	8	1	no	—
1551	D₄	—	8	1	no	—
1552	D₄	—	8	1	no	—
1553	C₂×C₄	—	2	1	no	—
1554	C₂×C₄	—	2	1	no	—
1555	C₂×C₄	—	2	1	no	—
1556	C₂×C₄	—	2	1	no	—
1557	C₂×C₄	—	2	1	no	—
1558	C₂×C₄	—	2	1	no	—
1559	C₂×C₄	—	2	1	no	—
1560	C₂×C₄	—	2	1	no	—
1561	C₂×C₄	—	2	1	no	—
1562	C₂×C₄	—	2	1	no	—
1563	C₂×C₄	—	2	1	no	—
1564	C₂×C₄	—	2	1	no	—
1565	C₂×C₄	—	2	1	no	—
1566	C₂×C₄	—	2	1	no	—
1567	C₂×C₄	—	2	1	no	—
1568	C₂×C₄	—	2	1	no	—
1569	C₂×C₄	—	2	1	no	—
1570	C₂×C₄	—	2	1	no	—
1571	C₂×C₄	—	2	1	no	—
1572	C₂×C₄	—	4	1	no	—
1573	C₂×C₄	—	4	1	no	—
1574	C₂×C₄	—	4	1	no	—
1575	C₂×C₄	—	4	1	no	—
1576	C₂×C₄	—	4	1	no	—
1577	C₂×C₄	—	4	1	no	—
1578	C₂×C₄	—	4	1	no	—
1579	C₂×C₄	—	4	2	no	—
1580	C₂×C₄	—	4	2	no	—
1581	C₂×C₄	—	4	2	no	—
1582	C₂×C₄	—	4	2	no	—
1583	C₂×C₄	—	8	1	no	—
1584	C₂×C₄	—	8	1	no	—
1585	C₂×C₄	—	8	1	no	—
1586	C₂×C₄	—	8	1	no	—
1587	C₂×C₄	—	8	1	no	—
1588	C₂×C₄	—	8	1	no	—
1589	C₂×C₄	—	8	1	no	—
1590	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1591	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1592	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1593	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1594	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1595	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1596	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1597	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1598	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1599	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1600	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1601	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1602	C₈	—	2	1	no	—
1603	C₈	—	2	1	no	—
1604	C₈	—	2	1	no	—
1605	C₈	—	2	1	no	—
1606	C₈	—	2	1	no	—
1607	C₈	—	2	1	no	—
1608	C₈	—	2	1	no	—
1609	C₈	—	2	1	no	—
1610	C₂²	—	2	1	no	—
1611	C₂²	—	2	1	no	—
1612	C₂²	—	2	1	no	—
1613	C₂²	—	2	1	no	—
1614	C₂²	—	2	1	no	—
1615	C₂²	—	2	1	no	—
1616	C₂²	—	2	1	no	—
1617	C₂²	—	2	1	no	—
1618	C₂²	—	2	1	no	—
1619	C₂²	—	4	1	no	—
1620	C₂²	—	4	1	no	—
1621	C₂²	—	4	1	no	—
1622	C₂²	—	4	1	no	—
1623	C₂²	—	4	1	no	—
1624	C₂²	—	4	1	no	—
1625	C₂²	—	4	1	no	—
1626	C₂²	—	4	1	no	—
1627	C₂²	—	4	1	no	—
1628	C₂²	—	8	2	no	—
1629	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1630	C₄	—	2	1	no	—
1631	C₄	—	2	1	no	—
1632	C₄	—	2	1	no	—
1633	C₄	—	2	1	no	—
1634	C₄	—	2	1	no	—
1635	C₄	—	2	1	no	—
1636	C₄	—	2	1	no	—
1637	C₄	—	2	1	no	—
1638	C₄	—	2	1	no	—
1639	C₄	—	2	1	no	—
1640	C₄	—	2	1	no	—
1641	C₄	—	4	1	no	—
1642	C₄	—	4	1	no	—
1643	C₄	—	4	1	no	—
1644	C₄	—	4	1	no	—
1645	C₄	—	4	1	no	—
1646	C₄	—	4	1	no	—
1647	C₄	—	4	1	no	—
1648	C₄	—	4	1	no	—
1649	C₄	—	4	1	no	—
1650	C₄	—	4	1	no	—
1651	C₄	—	4	1	no	—
1652	C₄	—	4	1	no	—
1653	C₄	—	4	1	no	—
1654	C₄	C₃₁×#585	1	1	yes	characteristic
1655	C₄	C₃₁×#585	1	1	yes	characteristic
1656	C₂	—	4	1	no	—
1657	C₂	—	4	1	no	—
1658	C₂	—	4	1	no	—
1659	C₂	—	8	1	no	—
1660	C₂	—	8	1	no	—
1661	C₂	—	8	1	no	—
1662	C₂	C₃₁×#3449	1	1	yes	characteristic
1663	C₂	C₃₁×#3584	1	1	yes	characteristic
1664	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₃₁×#3455	C₂	semidirect
3. C₃₁×#3261	C₂	semidirect
4. C₃₁×#3260	C₂	semidirect
5. C₃₁×#3258	C₂	semidirect
6. C₃₁×#3257	C₂	semidirect
7. C₃₁×#3244	C₂	semidirect
8. C₃₁×#3243	C₂	semidirect
9. C₃₁×#3240	C₂	semidirect
10. C₃₁×#3231	C₂	semidirect
11. C₃₁×#3225	C₂	semidirect
12. C₃₁×#3225	C₂	semidirect
13. C₃₁×#3216	C₂	semidirect
14. C₃₁×#3212	C₂	semidirect
15. C₃₁×#3197	C₂	semidirect
16. C₃₁×#3196	C₂	semidirect
17. C₃₁×#3191	C₂	semidirect
18. C₃₁×#3190	C₂	semidirect
19. C₃₁×#3178	C₂	semidirect
20. C₃₁×#3178	C₂	semidirect
21. C₃₁×#3175	C₂	semidirect
22. C₃₁×#3173	C₂	semidirect
23. C₃₁×#3127	C₂	semidirect
24. C₃₁×#3126	C₂	semidirect
25. C₃₁×#3120	C₂	semidirect
26. C₃₁×#3119	C₂	semidirect
27. C₃₁×#3116	C₂	semidirect
28. C₃₁×#3111	C₂	semidirect
29. C₃₁×#3107	C₂	semidirect
30. C₃₁×#3102	C₂	semidirect
31. C₃₁×#2924	C₂	semidirect
77. C₃₁×#501	C₂²	semidirect
78. C₃₁×#501	C₂²	semidirect
79. C₃₁×#500	C₂²	semidirect
80. C₃₁×#498	C₂²	semidirect
81. C₃₁×#497	C₂²	semidirect
82. C₃₁×#497	C₂²	semidirect
83. C₃₁×#495	C₂²	semidirect
84. C₃₁×#495	C₂²	semidirect
85. C₃₁×#489	C₂²	semidirect
86. C₃₁×#489	C₂²	semidirect
87. C₃₁×#489	C₂²	semidirect
88. C₃₁×#489	C₂²	semidirect
89. C₃₁×#488	C₂²	semidirect
90. C₃₁×#488	C₂²	semidirect
91. C₃₁×#487	C₂²	semidirect
92. C₃₁×#487	C₂²	semidirect
109. C₃₁×#479	C₂²	semidirect
110. C₃₁×#479	C₂²	semidirect
111. C₃₁×#479	C₂²	semidirect
112. C₃₁×#479	C₂²	semidirect
113. C₃₁×#479	C₂²	semidirect
114. C₃₁×#479	C₂²	semidirect
115. C₃₁×#479	C₂²	semidirect
116. C₃₁×#479	C₂²	semidirect
117. C₃₁×#478	C₂²	semidirect
118. C₃₁×#478	C₂²	semidirect
119. C₃₁×#478	C₂²	semidirect
120. C₃₁×#478	C₂²	semidirect
121. C₃₁×#477	C₂²	semidirect
122. C₃₁×#476	C₂²	semidirect
123. C₃₁×#475	C₂²	semidirect
124. C₃₁×#474	C₂²	semidirect
141. C₃₁×#464	C₂²	semidirect
142. C₃₁×#464	C₂²	semidirect
143. C₃₁×#463	C₂²	semidirect
144. C₃₁×#463	C₂²	semidirect
145. C₃₁×#462	C₂²	semidirect
146. C₃₁×#462	C₂²	semidirect
147. C₃₁×#462	C₂²	semidirect
148. C₃₁×#462	C₂²	semidirect
149. C₃₁×#462	C₂²	semidirect
150. C₃₁×#461	C₂²	semidirect
151. C₃₁×#461	C₂²	semidirect
152. C₃₁×#461	C₂²	semidirect
153. C₃₁×#460	C₂²	semidirect
154. C₃₁×#460	C₂²	semidirect
155. C₃₁×#460	C₂²	semidirect
156. C₃₁×#459	C₂²	semidirect
173. C₃₁×#442	C₂²	semidirect
174. C₃₁×#441	C₂²	semidirect
175. C₃₁×#441	C₂²	semidirect
176. C₃₁×#441	C₂²	semidirect
177. C₃₁×#440	C₂²	semidirect
178. C₃₁×#440	C₂²	semidirect
179. C₃₁×#440	C₂²	semidirect
180. C₃₁×#440	C₂²	semidirect
181. C₄×Q₁₆×C₃₁	C₂²	semidirect
182. C₄×Q₁₆×C₃₁	C₂²	semidirect
183. C₄×Q₁₆×C₃₁	C₂²	semidirect
184. C₄×SD₁₆×C₃₁	C₂²	semidirect
185. C₄×SD₁₆×C₃₁	C₂²	semidirect
186. C₄×SD₁₆×C₃₁	C₂²	semidirect
187. C₄×SD₁₆×C₃₁	C₂²	semidirect
188. C₄×D₈×C₃₁	C₂²	semidirect
679. #60984	C₃₁	direct (N × H)
778. #3495	C₂×C₃₁	semidirect
779. #3455	C₂×C₃₁	semidirect
780. #3261	C₂×C₃₁	semidirect
781. #3260	C₂×C₃₁	semidirect
782. #3258	C₂×C₃₁	semidirect
783. #3257	C₂×C₃₁	semidirect
784. #3244	C₂×C₃₁	semidirect
785. #3243	C₂×C₃₁	semidirect
786. #3240	C₂×C₃₁	semidirect
787. #3231	C₂×C₃₁	semidirect
788. #3225	C₂×C₃₁	semidirect
789. #3225	C₂×C₃₁	semidirect
790. #3216	C₂×C₃₁	semidirect
791. #3212	C₂×C₃₁	semidirect
792. #3197	C₂×C₃₁	semidirect
793. #3196	C₂×C₃₁	semidirect
794. #3191	C₂×C₃₁	semidirect
795. #3190	C₂×C₃₁	semidirect
796. #3178	C₂×C₃₁	semidirect
797. #3178	C₂×C₃₁	semidirect
798. #3175	C₂×C₃₁	semidirect
799. #3173	C₂×C₃₁	semidirect
800. #3127	C₂×C₃₁	semidirect
801. #3126	C₂×C₃₁	semidirect
802. #3120	C₂×C₃₁	semidirect
803. #3119	C₂×C₃₁	semidirect
804. #3116	C₂×C₃₁	semidirect
805. #3111	C₂×C₃₁	semidirect
806. #3107	C₂×C₃₁	semidirect
807. #3102	C₂×C₃₁	semidirect
808. #2924	C₂×C₃₁	semidirect
900. #501	C₂²×C₃₁	semidirect
901. #501	C₂²×C₃₁	semidirect
902. #500	C₂²×C₃₁	semidirect
903. #498	C₂²×C₃₁	semidirect
904. #497	C₂²×C₃₁	semidirect
905. #497	C₂²×C₃₁	semidirect
906. #495	C₂²×C₃₁	semidirect
907. #495	C₂²×C₃₁	semidirect
908. #489	C₂²×C₃₁	semidirect
909. #489	C₂²×C₃₁	semidirect
910. #489	C₂²×C₃₁	semidirect
911. #489	C₂²×C₃₁	semidirect
912. #488	C₂²×C₃₁	semidirect
913. #488	C₂²×C₃₁	semidirect
914. #487	C₂²×C₃₁	semidirect
915. #487	C₂²×C₃₁	semidirect
932. #479	C₂²×C₃₁	semidirect
933. #479	C₂²×C₃₁	semidirect
934. #479	C₂²×C₃₁	semidirect
935. #479	C₂²×C₃₁	semidirect
936. #479	C₂²×C₃₁	semidirect
937. #479	C₂²×C₃₁	semidirect
938. #479	C₂²×C₃₁	semidirect
939. #479	C₂²×C₃₁	semidirect
940. #478	C₂²×C₃₁	semidirect
941. #478	C₂²×C₃₁	semidirect
942. #478	C₂²×C₃₁	semidirect
943. #478	C₂²×C₃₁	semidirect
944. #477	C₂²×C₃₁	semidirect
945. #476	C₂²×C₃₁	semidirect
946. #475	C₂²×C₃₁	semidirect
947. #474	C₂²×C₃₁	semidirect
964. #464	C₂²×C₃₁	semidirect
965. #464	C₂²×C₃₁	semidirect
966. #463	C₂²×C₃₁	semidirect
967. #463	C₂²×C₃₁	semidirect
968. #462	C₂²×C₃₁	semidirect
969. #462	C₂²×C₃₁	semidirect
970. #462	C₂²×C₃₁	semidirect
971. #462	C₂²×C₃₁	semidirect
972. #462	C₂²×C₃₁	semidirect
973. #461	C₂²×C₃₁	semidirect
974. #461	C₂²×C₃₁	semidirect
975. #461	C₂²×C₃₁	semidirect
976. #460	C₂²×C₃₁	semidirect
977. #460	C₂²×C₃₁	semidirect
978. #460	C₂²×C₃₁	semidirect
979. #459	C₂²×C₃₁	semidirect
996. #442	C₂²×C₃₁	semidirect
997. #441	C₂²×C₃₁	semidirect
998. #441	C₂²×C₃₁	semidirect
999. #441	C₂²×C₃₁	semidirect
1000. #440	C₂²×C₃₁	semidirect
1001. #440	C₂²×C₃₁	semidirect
1002. #440	C₂²×C₃₁	semidirect
1003. #440	C₂²×C₃₁	semidirect
1004. C₄×Q₁₆	C₂²×C₃₁	semidirect
1005. C₄×Q₁₆	C₂²×C₃₁	semidirect
1006. C₄×Q₁₆	C₂²×C₃₁	semidirect
1007. C₄×SD₁₆	C₂²×C₃₁	semidirect
1008. C₄×SD₁₆	C₂²×C₃₁	semidirect
1009. C₄×SD₁₆	C₂²×C₃₁	semidirect
1010. C₄×SD₁₆	C₂²×C₃₁	semidirect
1011. C₄×D₈	C₂²×C₃₁	semidirect
1310. C₃₁	#60984	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×#3495	2
C₃₁×#3455	2
C₃₁×#3261	2
C₃₁×#3260	2
C₃₁×#3258	2
C₃₁×#3257	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3240	2
C₃₁×#3231	2
C₃₁×#3225	2
C₃₁×#3216	2
C₃₁×#3212	2
C₃₁×#3197	2
C₃₁×#3196	2
C₃₁×#3191	2
C₃₁×#3190	2
C₃₁×#3178	2
C₃₁×#3175	2
C₃₁×#3173	2
C₃₁×#3127	2
C₃₁×#3126	2
C₃₁×#3120	2
C₃₁×#3119	2
C₃₁×#3116	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#3102	2
C₃₁×#2924	2
#60984	31

Subgroups — C31×#60984 #21517743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60984 #21517743