Subgroups — C₃₁×#62171 #21518930

Order 7936.

1708 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×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3350	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3348	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3347	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3343	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3319	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3319	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3307	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3306	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3260	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3244	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3122	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3119	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#562	—	2	1	no	—
33	C₃₁×#562	—	2	1	no	—
34	C₃₁×#556	C₂²	1	1	yes	characteristic
35	C₃₁×#556	C₂²	1	1	yes	characteristic
36	C₃₁×#555	C₂²	1	1	yes	characteristic
37	C₃₁×#555	C₂²	1	1	yes	characteristic
38	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#554	C₂²	1	1	yes	characteristic
40	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#553	—	2	1	no	—
42	C₃₁×#553	C₂²	1	1	yes	characteristic
43	C₃₁×#553	C₂²	1	1	yes	characteristic
44	C₃₁×#553	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#552	—	2	1	no	—
46	C₃₁×#552	—	2	1	no	—
47	C₃₁×#552	C₂²	1	1	yes	characteristic
48	C₃₁×#551	—	2	1	no	—
49	C₃₁×#551	—	2	1	no	—
50	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#548	—	2	1	no	—
52	C₃₁×#547	C₂²	1	1	yes	characteristic
53	C₃₁×#547	C₂²	1	1	yes	characteristic
54	C₃₁×#546	C₂²	1	1	yes	characteristic
55	C₃₁×#546	C₂²	1	1	yes	characteristic
56	C₃₁×#544	C₂²	1	1	yes	characteristic
57	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#542	—	2	1	no	—
59	C₃₁×#542	—	2	1	no	—
60	C₃₁×#542	C₂²	1	1	yes	characteristic
61	C₃₁×#541	C₂²	1	1	yes	characteristic
62	C₃₁×#540	C₂²	1	1	yes	characteristic
63	C₃₁×#540	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#539	—	2	1	no	—
65	C₃₁×#538	—	2	1	no	—
66	C₃₁×#537	—	2	1	no	—
67	C₃₁×#536	—	2	1	no	—
68	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#529	—	2	1	no	—
71	C₃₁×#529	C₂²	1	1	yes	characteristic
72	C₃₁×#529	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#126	—	2	1	no	—
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#518	C₂²	1	1	yes	characteristic
76	C₄×#41×C₃₁	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×#501	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#489	C₂²	1	1	yes	characteristic
85	C₃₁×#489	C₂²	1	1	yes	characteristic
86	C₃₁×#489	C₂²	1	1	yes	characteristic
87	C₃₁×#488	C₂²	1	1	yes	characteristic
88	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#485	C₂²	1	1	yes	characteristic
90	C₃₁×#485	C₂²	1	1	yes	characteristic
91	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#484	C₂²	1	1	yes	characteristic
95	C₃₁×#483	C₂²	1	1	yes	characteristic
96	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#482	C₂²	1	1	yes	characteristic
98	C₃₁×#482	C₂²	1	1	yes	characteristic
99	C₃₁×#482	C₂²	1	1	yes	characteristic
100	C₃₁×#482	C₂²	1	1	yes	characteristic
101	C₃₁×#482	C₂²	1	1	yes	characteristic
102	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#481	C₂²	1	1	yes	characteristic
105	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
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×#478	C₂²	1	1	yes	characteristic
113	C₃₁×#478	C₂²	1	1	yes	characteristic
114	C₃₁×#478	C₂²	1	1	yes	characteristic
115	C₃₁×#478	C₂²	1	1	yes	characteristic
116	C₃₁×#478	C₂²	1	1	yes	characteristic
117	C₃₁×#478	C₂²	1	1	yes	characteristic
118	C₃₁×#478	C₂²	1	1	yes	characteristic
119	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#476	C₂²	1	1	yes	characteristic
127	C₃₁×#476	C₂²	1	1	yes	characteristic
128	C₃₁×#476	C₂²	1	1	yes	characteristic
129	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#474	C₂²	1	1	yes	characteristic
133	C₃₁×#474	C₂²	1	1	yes	characteristic
134	C₃₁×#474	C₂²	1	1	yes	characteristic
135	C₃₁×#474	C₂²	1	1	yes	characteristic
136	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#469	C₂²	1	1	yes	characteristic
138	C₃₁×#468	C₂²	1	1	yes	characteristic
139	C₃₁×#468	C₂²	1	1	yes	characteristic
140	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
141	C₃₁×#466	C₂²	1	1	yes	characteristic
142	C₃₁×#466	C₂²	1	1	yes	characteristic
143	C₃₁×#466	C₂²	1	1	yes	characteristic
144	C₃₁×#465	C₂²	1	1	yes	characteristic
145	C₃₁×#465	C₂²	1	1	yes	characteristic
146	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
147	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#463	C₂²	1	1	yes	characteristic
150	C₃₁×#463	C₂²	1	1	yes	characteristic
151	C₃₁×#463	C₂²	1	1	yes	characteristic
152	C₃₁×#463	C₂²	1	1	yes	characteristic
153	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
154	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
155	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
156	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
157	C₃₁×#459	C₂²	1	1	yes	characteristic
158	C₃₁×#459	C₂²	1	1	yes	characteristic
159	C₃₁×#449	C₂²	1	1	yes	characteristic
160	C₃₁×#449	C₂²	1	1	yes	characteristic
161	C₃₁×#449	C₂²	1	1	yes	characteristic
162	C₃₁×#449	C₂²	1	1	yes	characteristic
163	C₃₁×#447	C₂²	1	1	yes	characteristic
164	C₃₁×#447	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
166	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
167	C₃₁×#442	C₂²	1	1	yes	characteristic
168	C₃₁×#442	C₂²	1	1	yes	characteristic
169	C₃₁×#442	C₂²	1	1	yes	characteristic
170	C₃₁×#442	C₂²	1	1	yes	characteristic
171	C₃₁×#442	C₂²	1	1	yes	characteristic
172	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
173	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
174	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
179	C₃₁×#435	C₂²	1	1	yes	characteristic
180	C₃₁×#435	C₂²	1	1	yes	characteristic
181	C₃₁×#435	C₂²	1	1	yes	characteristic
182	C₃₁×#435	C₂²	1	1	yes	characteristic, complemented
183	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
184	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
185	C₃₁×#433	C₂²	1	1	yes	characteristic
186	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
187	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
188	C₃₁×#428	C₂²	1	1	yes	characteristic
189	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
190	C₃₁×#427	C₂²	1	1	yes	characteristic
191	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
192	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
193	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
194	C₃₁×#424	C₂²	1	1	yes	characteristic
195	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
197	C₃₁×#418	C₂²	1	1	yes	characteristic
198	C₃₁×#417	C₂²	1	1	yes	characteristic
199	C₃₁×#416	C₂²	1	1	yes	characteristic
200	C₃₁×#416	C₂²	1	1	yes	characteristic
201	C₃₁×#416	C₂²	1	1	yes	characteristic
202	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	—	2	1	no	—
204	C₂×#41×C₃₁	—	2	1	no	—
205	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₃₁	—	2	1	no	—
208	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₃₁×C₄⋊Q₈	—	2	1	no	—
224	C₃₁×C₄⋊Q₈	—	2	1	no	—
225	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#127	C₂³	1	1	yes	characteristic
233	C₃₁×#126	—	2	1	no	—
234	C₃₁×#126	—	2	1	no	—
235	C₃₁×#126	—	2	1	no	—
236	C₃₁×#126	—	2	1	no	—
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	D₄	1	1	yes	characteristic
246	C₃₁×#126	D₄	1	1	yes	characteristic
247	C₃₁×#125	—	2	1	no	—
248	C₃₁×#125	—	2	1	no	—
249	C₃₁×#125	—	2	1	no	—
250	C₃₁×#125	—	2	1	no	—
251	C₃₁×#125	—	2	1	no	—
252	C₃₁×#125	D₄	1	1	yes	characteristic
253	C₃₁×#125	C₂³	1	1	yes	characteristic
254	C₃₁×#125	C₂³	1	1	yes	characteristic
255	C₃₁×#125	C₂³	1	1	yes	characteristic
256	C₃₁×#125	C₂³	1	1	yes	characteristic
257	C₃₁×#125	C₂³	1	1	yes	characteristic
258	C₃₁×#125	C₂³	1	1	yes	characteristic
259	C₃₁×#124	—	2	1	no	—
260	C₃₁×#124	—	2	1	no	—
261	C₃₁×#124	—	2	1	no	—
262	C₃₁×#124	—	2	1	no	—
263	C₃₁×#124	—	2	1	no	—
264	C₃₁×#124	—	2	1	no	—
265	C₃₁×#124	—	2	1	no	—
266	C₃₁×#124	—	2	1	no	—
267	C₃₁×#124	—	2	1	no	—
268	C₃₁×#124	D₄	1	1	yes	characteristic
269	C₃₁×#124	C₂³	1	1	yes	characteristic
270	C₃₁×#124	C₂³	1	1	yes	characteristic
271	C₃₁×#123	—	2	1	no	—
272	C₃₁×#123	—	2	1	no	—
273	C₃₁×#123	—	2	1	no	—
274	C₃₁×#123	—	2	1	no	—
275	C₃₁×#123	—	2	1	no	—
276	C₃₁×#123	—	2	1	no	—
277	C₃₁×#123	—	2	1	no	—
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	D₄	1	1	yes	characteristic
288	C₃₁×#123	D₄	1	1	yes	characteristic
289	C₃₁×C₂²⋊Q₈	—	2	1	no	—
290	C₃₁×C₂²⋊Q₈	—	2	1	no	—
291	C₃₁×C₂²⋊Q₈	—	2	1	no	—
292	C₃₁×C₂²⋊Q₈	—	2	1	no	—
293	C₃₁×C₂²⋊Q₈	—	2	1	no	—
294	C₃₁×C₂²⋊Q₈	—	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	D₄	1	1	yes	characteristic
308	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
311	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
312	C₃₁×#121	—	2	1	no	—
313	C₃₁×#121	—	2	1	no	—
314	C₃₁×#121	—	2	1	no	—
315	C₃₁×#121	—	2	1	no	—
316	C₃₁×#121	—	2	1	no	—
317	C₃₁×#121	—	2	1	no	—
318	C₃₁×#121	—	2	1	no	—
319	C₃₁×#121	—	2	1	no	—
320	C₃₁×#121	—	2	1	no	—
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	D₄	1	1	yes	characteristic
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×#121	C₂³	1	1	yes	characteristic
334	C₃₁×#121	C₂³	1	1	yes	characteristic
335	C₃₁×#120	—	2	1	no	—
336	C₃₁×#120	—	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	C₂³	1	1	yes	characteristic
341	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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×D₄×C₃₁	—	2	1	no	—
346	C₄×D₄×C₃₁	—	2	1	no	—
347	C₄×D₄×C₃₁	—	2	1	no	—
348	C₄×D₄×C₃₁	—	2	1	no	—
349	C₄×D₄×C₃₁	—	2	1	no	—
350	C₄×D₄×C₃₁	—	2	1	no	—
351	C₄×D₄×C₃₁	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
357	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
358	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
359	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
360	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
361	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#117	—	2	1	no	—
372	C₃₁×#117	—	2	1	no	—
373	C₃₁×#117	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
380	C₃₁×#117	C₂³	1	1	yes	characteristic
381	C₃₁×#117	C₂³	1	1	yes	characteristic
382	C₃₁×#117	C₂³	1	1	yes	characteristic
383	C₃₁×#117	C₂³	1	1	yes	characteristic
384	C₃₁×#117	C₂³	1	1	yes	characteristic
385	C₃₁×#117	C₂³	1	1	yes	characteristic
386	C₃₁×#117	C₂³	1	1	yes	characteristic
387	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
394	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
395	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
396	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
397	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
398	C₂×C₄²×C₃₁	—	2	1	no	—
399	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
400	C₃₁×#107	C₂³	1	1	yes	characteristic
401	C₃₁×#107	C₂³	1	1	yes	characteristic
402	C₃₁×#107	C₂³	1	1	yes	characteristic
403	C₃₁×#107	C₂³	1	1	yes	characteristic
404	C₃₁×#107	C₂³	1	1	yes	characteristic
405	C₃₁×#107	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×#106	C₂³	1	1	yes	characteristic
413	C₃₁×#106	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×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₃₁×C₄⋊C₈	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×#102	C₂³	1	1	yes	characteristic
447	C₃₁×#102	C₂³	1	1	yes	characteristic
448	C₃₁×#102	C₂³	1	1	yes	characteristic
449	C₃₁×#102	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×#102	C₂³	1	1	yes	characteristic
463	C₃₁×#102	C₂³	1	1	yes	characteristic
464	C₃₁×#102	C₂³	1	1	yes	characteristic
465	C₃₁×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	C₃₁×#97	C₂³	1	1	yes	characteristic
473	C₃₁×#97	C₂³	1	1	yes	characteristic
474	C₃₁×#97	C₂³	1	1	yes	characteristic
475	C₃₁×#97	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	—	2	1	no	—
479	#41×C₃₁	—	2	2	no	—
480	#41×C₃₁	—	2	2	no	—
481	#41×C₃₁	—	4	1	no	—
482	#41×C₃₁	—	4	1	no	—
483	#41×C₃₁	—	8	2	no	—
484	#41×C₃₁	—	8	2	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	—	2	1	no	—
491	C₂×Q₈×C₃₁	—	8	2	no	—
492	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₂×D₄×C₃₁	—	2	2	no	—
496	C₂×D₄×C₃₁	—	2	1	no	—
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	—	2	1	no	—
509	C₂×D₄×C₃₁	—	4	1	no	—
510	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
511	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
512	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
513	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
514	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
515	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
516	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
523	C₂²×C₄×C₃₁	—	2	1	no	—
524	C₂²×C₄×C₃₁	—	2	1	no	—
525	C₂²×C₄×C₃₁	—	2	1	no	—
526	C₂²×C₄×C₃₁	—	2	1	no	—
527	C₂²×C₄×C₃₁	—	2	1	no	—
528	C₂²×C₄×C₃₁	—	2	1	no	—
529	C₂²×C₄×C₃₁	—	2	1	no	—
530	C₂²×C₄×C₃₁	—	2	1	no	—
531	C₂²×C₄×C₃₁	—	2	1	no	—
532	C₂²×C₄×C₃₁	—	2	1	no	—
533	C₂²×C₄×C₃₁	—	2	1	no	—
534	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
535	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
536	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
539	SD₁₆×C₃₁	—	4	1	no	—
540	SD₁₆×C₃₁	—	4	1	no	—
541	SD₁₆×C₃₁	—	4	1	no	—
542	SD₁₆×C₃₁	—	4	1	no	—
543	D₈×C₃₁	—	2	2	no	—
544	D₈×C₃₁	—	2	2	no	—
545	D₈×C₃₁	—	4	1	no	—
546	D₈×C₃₁	—	4	1	no	—
547	M₁₆×C₃₁	—	4	1	no	—
548	M₁₆×C₃₁	—	4	1	no	—
549	C₂×C₈×C₃₁	—	4	1	no	—
550	C₂×C₈×C₃₁	—	4	1	no	—
551	C₂×C₈×C₃₁	—	4	1	no	—
552	C₂×C₈×C₃₁	—	4	1	no	—
553	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
593	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
607	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂⁴	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	C₂²⋊C₄×C₃₁	—	2	1	no	—
613	C₂²⋊C₄×C₃₁	—	2	1	no	—
614	C₂²⋊C₄×C₃₁	—	2	1	no	—
615	C₂²⋊C₄×C₃₁	—	2	1	no	—
616	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
647	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
648	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
649	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₃₁	—	2	1	no	—
657	C₄²×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
667	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
668	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
669	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
670	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
671	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
672	#62171	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
673	C₂³×C₃₁	—	2	1	no	—
674	C₂³×C₃₁	—	2	1	no	—
675	C₂³×C₃₁	—	2	1	no	—
676	C₂³×C₃₁	—	2	1	no	—
677	C₂³×C₃₁	—	4	2	no	—
678	C₂³×C₃₁	—	8	1	no	—
679	C₂³×C₃₁	—	8	1	no	—
680	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
681	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
682	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
683	Q₈×C₃₁	—	2	1	no	—
684	Q₈×C₃₁	—	2	1	no	—
685	Q₈×C₃₁	—	2	1	no	—
686	Q₈×C₃₁	—	2	1	no	—
687	Q₈×C₃₁	—	4	1	no	—
688	Q₈×C₃₁	—	4	2	no	—
689	Q₈×C₃₁	—	8	1	no	—
690	Q₈×C₃₁	—	8	1	no	—
691	Q₈×C₃₁	—	8	1	no	—
692	Q₈×C₃₁	—	8	1	no	—
693	Q₈×C₃₁	—	8	1	no	—
694	D₄×C₃₁	—	2	1	no	—
695	D₄×C₃₁	—	2	1	no	—
696	D₄×C₃₁	—	2	1	no	—
697	D₄×C₃₁	—	2	1	no	—
698	D₄×C₃₁	—	2	1	no	—
699	D₄×C₃₁	—	2	1	no	—
700	D₄×C₃₁	—	2	1	no	—
701	D₄×C₃₁	—	4	1	no	—
702	D₄×C₃₁	—	4	1	no	—
703	D₄×C₃₁	—	4	1	no	—
704	D₄×C₃₁	—	4	2	no	—
705	D₄×C₃₁	—	4	2	no	—
706	D₄×C₃₁	—	4	2	no	—
707	D₄×C₃₁	—	8	1	no	—
708	D₄×C₃₁	—	8	1	no	—
709	D₄×C₃₁	—	8	1	no	—
710	D₄×C₃₁	—	8	1	no	—
711	D₄×C₃₁	—	8	1	no	—
712	D₄×C₃₁	—	8	1	no	—
713	D₄×C₃₁	—	8	1	no	—
714	D₄×C₃₁	—	8	1	no	—
715	D₄×C₃₁	—	8	1	no	—
716	D₄×C₃₁	—	8	1	no	—
717	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
718	C₂×C₄×C₃₁	—	2	1	no	—
719	C₂×C₄×C₃₁	—	2	1	no	—
720	C₂×C₄×C₃₁	—	2	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	—	4	1	no	—
737	C₂×C₄×C₃₁	—	4	1	no	—
738	C₂×C₄×C₃₁	—	4	2	no	—
739	C₂×C₄×C₃₁	—	4	2	no	—
740	C₂×C₄×C₃₁	—	4	2	no	—
741	C₂×C₄×C₃₁	—	4	2	no	—
742	C₂×C₄×C₃₁	—	8	1	no	—
743	C₂×C₄×C₃₁	—	8	1	no	—
744	C₂×C₄×C₃₁	—	8	1	no	—
745	C₂×C₄×C₃₁	—	8	1	no	—
746	C₂×C₄×C₃₁	—	8	1	no	—
747	C₂×C₄×C₃₁	—	8	1	no	—
748	C₂×C₄×C₃₁	—	8	1	no	—
749	C₂×C₄×C₃₁	—	8	1	no	—
750	C₂×C₄×C₃₁	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
756	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
757	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
767	C₈×C₃₁	—	2	1	no	—
768	C₈×C₃₁	—	2	1	no	—
769	C₈×C₃₁	—	2	1	no	—
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	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
776	#3521	C₂×C₃₁	1	1	yes	characteristic, complemented
777	#3389	C₂×C₃₁	1	1	yes	characteristic, complemented
778	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
780	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3350	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3348	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3347	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3343	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3339	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3319	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3319	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3307	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3306	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3297	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3260	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3257	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3244	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3240	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3122	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3119	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
806	C₂²×C₃₁	—	2	1	no	—
807	C₂²×C₃₁	—	2	1	no	—
808	C₂²×C₃₁	—	2	1	no	—
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	2	no	—
816	C₂²×C₃₁	—	4	1	no	—
817	C₂²×C₃₁	—	4	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	—	16	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	C₂×2₋¹⁺⁴	1	1	yes	characteristic
853	C₄×C₃₁	#585	1	1	yes	characteristic
854	#562	—	2	1	no	—
855	#562	—	2	1	no	—
856	#556	C₂²×C₃₁	1	1	yes	characteristic
857	#556	C₂²×C₃₁	1	1	yes	characteristic
858	#555	C₂²×C₃₁	1	1	yes	characteristic
859	#555	C₂²×C₃₁	1	1	yes	characteristic
860	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
861	#554	C₂²×C₃₁	1	1	yes	characteristic
862	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
863	#553	—	2	1	no	—
864	#553	C₂²×C₃₁	1	1	yes	characteristic
865	#553	C₂²×C₃₁	1	1	yes	characteristic
866	#553	C₂²×C₃₁	1	1	yes	characteristic, complemented
867	#552	—	2	1	no	—
868	#552	—	2	1	no	—
869	#552	C₂²×C₃₁	1	1	yes	characteristic
870	#551	—	2	1	no	—
871	#551	—	2	1	no	—
872	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
873	#548	—	2	1	no	—
874	#547	C₂²×C₃₁	1	1	yes	characteristic
875	#547	C₂²×C₃₁	1	1	yes	characteristic
876	#546	C₂²×C₃₁	1	1	yes	characteristic
877	#546	C₂²×C₃₁	1	1	yes	characteristic
878	#544	C₂²×C₃₁	1	1	yes	characteristic
879	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
880	#542	—	2	1	no	—
881	#542	—	2	1	no	—
882	#542	C₂²×C₃₁	1	1	yes	characteristic
883	#541	C₂²×C₃₁	1	1	yes	characteristic
884	#540	C₂²×C₃₁	1	1	yes	characteristic
885	#540	C₂²×C₃₁	1	1	yes	characteristic, complemented
886	#539	—	2	1	no	—
887	#538	—	2	1	no	—
888	#537	—	2	1	no	—
889	#536	—	2	1	no	—
890	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
891	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
892	#529	—	2	1	no	—
893	#529	C₂²×C₃₁	1	1	yes	characteristic
894	#529	C₂²×C₃₁	1	1	yes	characteristic
895	C₂×#126	—	2	1	no	—
896	#520	C₂²×C₃₁	1	1	yes	characteristic
897	#518	C₂²×C₃₁	1	1	yes	characteristic
898	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
899	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
900	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
901	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
902	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
903	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
904	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
905	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
906	#489	C₂²×C₃₁	1	1	yes	characteristic
907	#489	C₂²×C₃₁	1	1	yes	characteristic
908	#489	C₂²×C₃₁	1	1	yes	characteristic
909	#488	C₂²×C₃₁	1	1	yes	characteristic
910	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
911	#485	C₂²×C₃₁	1	1	yes	characteristic
912	#485	C₂²×C₃₁	1	1	yes	characteristic
913	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
914	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
916	#484	C₂²×C₃₁	1	1	yes	characteristic
917	#483	C₂²×C₃₁	1	1	yes	characteristic
918	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
919	#482	C₂²×C₃₁	1	1	yes	characteristic
920	#482	C₂²×C₃₁	1	1	yes	characteristic
921	#482	C₂²×C₃₁	1	1	yes	characteristic
922	#482	C₂²×C₃₁	1	1	yes	characteristic
923	#482	C₂²×C₃₁	1	1	yes	characteristic
924	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
925	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
926	#481	C₂²×C₃₁	1	1	yes	characteristic
927	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
928	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
929	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
930	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
931	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
932	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
933	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
934	#478	C₂²×C₃₁	1	1	yes	characteristic
935	#478	C₂²×C₃₁	1	1	yes	characteristic
936	#478	C₂²×C₃₁	1	1	yes	characteristic
937	#478	C₂²×C₃₁	1	1	yes	characteristic
938	#478	C₂²×C₃₁	1	1	yes	characteristic
939	#478	C₂²×C₃₁	1	1	yes	characteristic
940	#478	C₂²×C₃₁	1	1	yes	characteristic
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	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
945	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
946	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
947	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
948	#476	C₂²×C₃₁	1	1	yes	characteristic
949	#476	C₂²×C₃₁	1	1	yes	characteristic
950	#476	C₂²×C₃₁	1	1	yes	characteristic
951	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
952	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
953	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
954	#474	C₂²×C₃₁	1	1	yes	characteristic
955	#474	C₂²×C₃₁	1	1	yes	characteristic
956	#474	C₂²×C₃₁	1	1	yes	characteristic
957	#474	C₂²×C₃₁	1	1	yes	characteristic
958	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
959	#469	C₂²×C₃₁	1	1	yes	characteristic
960	#468	C₂²×C₃₁	1	1	yes	characteristic
961	#468	C₂²×C₃₁	1	1	yes	characteristic
962	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
963	#466	C₂²×C₃₁	1	1	yes	characteristic
964	#466	C₂²×C₃₁	1	1	yes	characteristic
965	#466	C₂²×C₃₁	1	1	yes	characteristic
966	#465	C₂²×C₃₁	1	1	yes	characteristic
967	#465	C₂²×C₃₁	1	1	yes	characteristic
968	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
969	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
970	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#463	C₂²×C₃₁	1	1	yes	characteristic
972	#463	C₂²×C₃₁	1	1	yes	characteristic
973	#463	C₂²×C₃₁	1	1	yes	characteristic
974	#463	C₂²×C₃₁	1	1	yes	characteristic
975	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
976	#461	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
980	#459	C₂²×C₃₁	1	1	yes	characteristic
981	#449	C₂²×C₃₁	1	1	yes	characteristic
982	#449	C₂²×C₃₁	1	1	yes	characteristic
983	#449	C₂²×C₃₁	1	1	yes	characteristic
984	#449	C₂²×C₃₁	1	1	yes	characteristic
985	#447	C₂²×C₃₁	1	1	yes	characteristic
986	#447	C₂²×C₃₁	1	1	yes	characteristic
987	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
988	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
989	#442	C₂²×C₃₁	1	1	yes	characteristic
990	#442	C₂²×C₃₁	1	1	yes	characteristic
991	#442	C₂²×C₃₁	1	1	yes	characteristic
992	#442	C₂²×C₃₁	1	1	yes	characteristic
993	#442	C₂²×C₃₁	1	1	yes	characteristic
994	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
995	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
996	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
997	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
998	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
999	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1000	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1001	#435	C₂²×C₃₁	1	1	yes	characteristic
1002	#435	C₂²×C₃₁	1	1	yes	characteristic
1003	#435	C₂²×C₃₁	1	1	yes	characteristic
1004	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1006	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
1007	#433	C₂²×C₃₁	1	1	yes	characteristic
1008	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
1009	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
1010	#428	C₂²×C₃₁	1	1	yes	characteristic
1011	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1012	#427	C₂²×C₃₁	1	1	yes	characteristic
1013	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
1014	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
1015	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
1016	#424	C₂²×C₃₁	1	1	yes	characteristic
1017	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
1018	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1019	#418	C₂²×C₃₁	1	1	yes	characteristic
1020	#417	C₂²×C₃₁	1	1	yes	characteristic
1021	#416	C₂²×C₃₁	1	1	yes	characteristic
1022	#416	C₂²×C₃₁	1	1	yes	characteristic
1023	#416	C₂²×C₃₁	1	1	yes	characteristic
1024	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
1025	C₂×C₃₁	—	4	1	no	—
1026	C₂×C₃₁	—	4	1	no	—
1027	C₂×C₃₁	—	4	1	no	—
1028	C₂×C₃₁	—	4	2	no	—
1029	C₂×C₃₁	—	8	1	no	—
1030	C₂×C₃₁	—	8	1	no	—
1031	C₂×C₃₁	—	8	1	no	—
1032	C₂×C₃₁	#3489	1	1	yes	characteristic
1033	C₂×C₃₁	#3584	1	1	yes	characteristic
1034	C₂×C₃₁	#3585	1	1	yes	characteristic
1035	C₂×#41	—	2	1	no	—
1036	C₂×#41	—	2	1	no	—
1037	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1038	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1039	C₂²×Q₈	—	2	1	no	—
1040	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1041	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1042	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1043	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1044	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1045	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1046	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1047	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1048	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1049	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1055	C₄⋊Q₈	—	2	1	no	—
1056	C₄⋊Q₈	—	2	1	no	—
1057	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1058	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1059	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1060	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	#127	C₂³×C₃₁	1	1	yes	characteristic
1065	#126	—	2	1	no	—
1066	#126	—	2	1	no	—
1067	#126	—	2	1	no	—
1068	#126	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
1078	#126	D₄×C₃₁	1	1	yes	characteristic
1079	#125	—	2	1	no	—
1080	#125	—	2	1	no	—
1081	#125	—	2	1	no	—
1082	#125	—	2	1	no	—
1083	#125	—	2	1	no	—
1084	#125	D₄×C₃₁	1	1	yes	characteristic
1085	#125	C₂³×C₃₁	1	1	yes	characteristic
1086	#125	C₂³×C₃₁	1	1	yes	characteristic
1087	#125	C₂³×C₃₁	1	1	yes	characteristic
1088	#125	C₂³×C₃₁	1	1	yes	characteristic
1089	#125	C₂³×C₃₁	1	1	yes	characteristic
1090	#125	C₂³×C₃₁	1	1	yes	characteristic
1091	#124	—	2	1	no	—
1092	#124	—	2	1	no	—
1093	#124	—	2	1	no	—
1094	#124	—	2	1	no	—
1095	#124	—	2	1	no	—
1096	#124	—	2	1	no	—
1097	#124	—	2	1	no	—
1098	#124	—	2	1	no	—
1099	#124	—	2	1	no	—
1100	#124	D₄×C₃₁	1	1	yes	characteristic
1101	#124	C₂³×C₃₁	1	1	yes	characteristic
1102	#124	C₂³×C₃₁	1	1	yes	characteristic
1103	#123	—	2	1	no	—
1104	#123	—	2	1	no	—
1105	#123	—	2	1	no	—
1106	#123	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	—	2	1	no	—
1109	#123	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
1120	#123	D₄×C₃₁	1	1	yes	characteristic
1121	C₂²⋊Q₈	—	2	1	no	—
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	—	2	1	no	—
1125	C₂²⋊Q₈	—	2	1	no	—
1126	C₂²⋊Q₈	—	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	D₄×C₃₁	1	1	yes	characteristic
1140	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1141	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1142	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1143	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1144	#121	—	2	1	no	—
1145	#121	—	2	1	no	—
1146	#121	—	2	1	no	—
1147	#121	—	2	1	no	—
1148	#121	—	2	1	no	—
1149	#121	—	2	1	no	—
1150	#121	—	2	1	no	—
1151	#121	—	2	1	no	—
1152	#121	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
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	#121	C₂³×C₃₁	1	1	yes	characteristic
1166	#121	C₂³×C₃₁	1	1	yes	characteristic
1167	#120	—	2	1	no	—
1168	#120	—	2	1	no	—
1169	C₄×Q₈	—	2	1	no	—
1170	C₄×Q₈	—	2	1	no	—
1171	C₄×Q₈	—	2	1	no	—
1172	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1173	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
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×D₄	—	2	1	no	—
1178	C₄×D₄	—	2	1	no	—
1179	C₄×D₄	—	2	1	no	—
1180	C₄×D₄	—	2	1	no	—
1181	C₄×D₄	—	2	1	no	—
1182	C₄×D₄	—	2	1	no	—
1183	C₄×D₄	—	2	1	no	—
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	C₂³×C₃₁	1	1	yes	characteristic
1189	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1190	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1191	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1192	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1193	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1194	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1195	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1196	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1197	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1198	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1199	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
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	#117	—	2	1	no	—
1204	#117	—	2	1	no	—
1205	#117	—	2	1	no	—
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	C₂³×C₃₁	1	1	yes	characteristic
1212	#117	C₂³×C₃₁	1	1	yes	characteristic
1213	#117	C₂³×C₃₁	1	1	yes	characteristic
1214	#117	C₂³×C₃₁	1	1	yes	characteristic
1215	#117	C₂³×C₃₁	1	1	yes	characteristic
1216	#117	C₂³×C₃₁	1	1	yes	characteristic
1217	#117	C₂³×C₃₁	1	1	yes	characteristic
1218	#117	C₂³×C₃₁	1	1	yes	characteristic
1219	C₂×C₄⋊C₄	—	2	1	no	—
1220	C₂×C₄⋊C₄	—	2	1	no	—
1221	C₂×C₄⋊C₄	—	2	1	no	—
1222	C₂×C₄⋊C₄	—	2	1	no	—
1223	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1224	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1225	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1226	C₂×C₂²⋊C₄	—	2	1	no	—
1227	C₂×C₂²⋊C₄	—	2	1	no	—
1228	C₂×C₂²⋊C₄	—	2	1	no	—
1229	C₂×C₂²⋊C₄	—	2	1	no	—
1230	C₂×C₄²	—	2	1	no	—
1231	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1232	#107	C₂³×C₃₁	1	1	yes	characteristic
1233	#107	C₂³×C₃₁	1	1	yes	characteristic
1234	#107	C₂³×C₃₁	1	1	yes	characteristic
1235	#107	C₂³×C₃₁	1	1	yes	characteristic
1236	#107	C₂³×C₃₁	1	1	yes	characteristic
1237	#107	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	#106	C₂³×C₃₁	1	1	yes	characteristic
1245	#106	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	#106	C₂³×C₃₁	1	1	yes	characteristic
1255	#106	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1263	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1264	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1265	C₄⋊C₈	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	#102	C₂³×C₃₁	1	1	yes	characteristic
1279	#102	C₂³×C₃₁	1	1	yes	characteristic
1280	#102	C₂³×C₃₁	1	1	yes	characteristic
1281	#102	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	#102	C₂³×C₃₁	1	1	yes	characteristic
1295	#102	C₂³×C₃₁	1	1	yes	characteristic
1296	#102	C₂³×C₃₁	1	1	yes	characteristic
1297	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1303	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1304	#97	C₂³×C₃₁	1	1	yes	characteristic
1305	#97	C₂³×C₃₁	1	1	yes	characteristic
1306	#97	C₂³×C₃₁	1	1	yes	characteristic
1307	#97	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	#62171	1	1	yes	characteristic, direct product factor, Sylow
1311	C₂⁴	—	2	1	no	—
1312	#41	—	2	2	no	—
1313	#41	—	2	2	no	—
1314	#41	—	4	1	no	—
1315	#41	—	4	1	no	—
1316	#41	—	8	2	no	—
1317	#41	—	8	2	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	—	2	1	no	—
1324	C₂×Q₈	—	8	2	no	—
1325	C₂×Q₈	C₂×D₄×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×D₄	—	2	2	no	—
1329	C₂×D₄	—	2	1	no	—
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	—	2	1	no	—
1342	C₂×D₄	—	4	1	no	—
1343	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1344	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1345	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1346	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1347	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1348	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1349	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1356	C₂²×C₄	—	2	1	no	—
1357	C₂²×C₄	—	2	1	no	—
1358	C₂²×C₄	—	2	1	no	—
1359	C₂²×C₄	—	2	1	no	—
1360	C₂²×C₄	—	2	1	no	—
1361	C₂²×C₄	—	2	1	no	—
1362	C₂²×C₄	—	2	1	no	—
1363	C₂²×C₄	—	2	1	no	—
1364	C₂²×C₄	—	2	1	no	—
1365	C₂²×C₄	—	2	1	no	—
1366	C₂²×C₄	—	2	1	no	—
1367	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1368	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1369	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1370	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1371	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1372	SD₁₆	—	4	1	no	—
1373	SD₁₆	—	4	1	no	—
1374	SD₁₆	—	4	1	no	—
1375	SD₁₆	—	4	1	no	—
1376	D₈	—	2	2	no	—
1377	D₈	—	2	2	no	—
1378	D₈	—	4	1	no	—
1379	D₈	—	4	1	no	—
1380	M₁₆	—	4	1	no	—
1381	M₁₆	—	4	1	no	—
1382	C₂×C₈	—	4	1	no	—
1383	C₂×C₈	—	4	1	no	—
1384	C₂×C₈	—	4	1	no	—
1385	C₂×C₈	—	4	1	no	—
1386	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1426	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1427	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1428	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1429	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1430	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1431	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1432	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1433	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1434	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1435	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1436	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1437	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1438	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1439	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1440	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1441	C₄⋊C₄	C₂⁴×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	C₂²⋊C₄	—	2	1	no	—
1446	C₂²⋊C₄	—	2	1	no	—
1447	C₂²⋊C₄	—	2	1	no	—
1448	C₂²⋊C₄	—	2	1	no	—
1449	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1480	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1481	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1482	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₄²	—	2	1	no	—
1490	C₄²	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1500	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1501	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1502	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1503	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1504	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1505	C₂³	—	2	1	no	—
1506	C₂³	—	2	1	no	—
1507	C₂³	—	2	1	no	—
1508	C₂³	—	2	1	no	—
1509	C₂³	—	4	2	no	—
1510	C₂³	—	8	1	no	—
1511	C₂³	—	8	1	no	—
1512	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1513	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1514	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1515	Q₈	—	2	1	no	—
1516	Q₈	—	2	1	no	—
1517	Q₈	—	2	1	no	—
1518	Q₈	—	2	1	no	—
1519	Q₈	—	4	1	no	—
1520	Q₈	—	4	2	no	—
1521	Q₈	—	8	1	no	—
1522	Q₈	—	8	1	no	—
1523	Q₈	—	8	1	no	—
1524	Q₈	—	8	1	no	—
1525	Q₈	—	8	1	no	—
1526	D₄	—	2	1	no	—
1527	D₄	—	2	1	no	—
1528	D₄	—	2	1	no	—
1529	D₄	—	2	1	no	—
1530	D₄	—	2	1	no	—
1531	D₄	—	2	1	no	—
1532	D₄	—	2	1	no	—
1533	D₄	—	4	1	no	—
1534	D₄	—	4	1	no	—
1535	D₄	—	4	1	no	—
1536	D₄	—	4	2	no	—
1537	D₄	—	4	2	no	—
1538	D₄	—	4	2	no	—
1539	D₄	—	8	1	no	—
1540	D₄	—	8	1	no	—
1541	D₄	—	8	1	no	—
1542	D₄	—	8	1	no	—
1543	D₄	—	8	1	no	—
1544	D₄	—	8	1	no	—
1545	D₄	—	8	1	no	—
1546	D₄	—	8	1	no	—
1547	D₄	—	8	1	no	—
1548	D₄	—	8	1	no	—
1549	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1550	C₂×C₄	—	2	1	no	—
1551	C₂×C₄	—	2	1	no	—
1552	C₂×C₄	—	2	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	—	4	1	no	—
1569	C₂×C₄	—	4	1	no	—
1570	C₂×C₄	—	4	2	no	—
1571	C₂×C₄	—	4	2	no	—
1572	C₂×C₄	—	4	2	no	—
1573	C₂×C₄	—	4	2	no	—
1574	C₂×C₄	—	8	1	no	—
1575	C₂×C₄	—	8	1	no	—
1576	C₂×C₄	—	8	1	no	—
1577	C₂×C₄	—	8	1	no	—
1578	C₂×C₄	—	8	1	no	—
1579	C₂×C₄	—	8	1	no	—
1580	C₂×C₄	—	8	1	no	—
1581	C₂×C₄	—	8	1	no	—
1582	C₂×C₄	—	8	1	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	C₂²×D₄×C₃₁	1	1	yes	characteristic
1588	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1589	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁵×C₃₁	1	1	yes	characteristic
1599	C₈	—	2	1	no	—
1600	C₈	—	2	1	no	—
1601	C₈	—	2	1	no	—
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	C₂²	—	2	1	no	—
1608	C₂²	—	2	1	no	—
1609	C₂²	—	2	1	no	—
1610	C₂²	—	2	2	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	—	4	1	no	—
1618	C₂²	—	4	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	—	16	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	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1654	C₄	C₃₁×#585	1	1	yes	characteristic
1655	C₂	—	4	1	no	—
1656	C₂	—	4	1	no	—
1657	C₂	—	4	1	no	—
1658	C₂	—	4	2	no	—
1659	C₂	—	8	1	no	—
1660	C₂	—	8	1	no	—
1661	C₂	—	8	1	no	—
1662	C₂	C₃₁×#3489	1	1	yes	characteristic
1663	C₂	C₃₁×#3584	1	1	yes	characteristic
1664	C₂	C₃₁×#3585	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3547	C₂	semidirect
2. C₃₁×#3521	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3376	C₂	semidirect
6. C₃₁×#3367	C₂	semidirect
7. C₃₁×#3350	C₂	semidirect
8. C₃₁×#3348	C₂	semidirect
9. C₃₁×#3347	C₂	semidirect
10. C₃₁×#3343	C₂	semidirect
11. C₃₁×#3340	C₂	semidirect
12. C₃₁×#3339	C₂	semidirect
13. C₃₁×#3319	C₂	semidirect
14. C₃₁×#3319	C₂	semidirect
15. C₃₁×#3307	C₂	semidirect
16. C₃₁×#3306	C₂	semidirect
17. C₃₁×#3303	C₂	semidirect
18. C₃₁×#3297	C₂	semidirect
19. C₃₁×#3260	C₂	semidirect
20. C₃₁×#3257	C₂	semidirect
21. C₃₁×#3247	C₂	semidirect
22. C₃₁×#3244	C₂	semidirect
23. C₃₁×#3242	C₂	semidirect
24. C₃₁×#3240	C₂	semidirect
25. C₃₁×#3122	C₂	semidirect
26. C₃₁×#3119	C₂	semidirect
27. C₃₁×#3115	C₂	semidirect
28. C₃₁×#3083	C₂	semidirect
29. C₃₁×#3081	C₂	semidirect
30. C₃₁×#3076	C₂	semidirect
31. C₃₁×#2992	C₂	semidirect
38. C₃₁×#555	C₂²	semidirect
40. C₃₁×#554	C₂²	semidirect
44. C₃₁×#553	C₂²	semidirect
50. D₄×Q₈×C₃₁	C₂²	semidirect
57. C₃₁×#544	C₂²	semidirect
63. C₃₁×#540	C₂²	semidirect
68. C₃₁×#533	C₂²	semidirect
69. C₃₁×#532	C₂²	semidirect
77. C₃₁×#501	C₂²	semidirect
78. C₃₁×#501	C₂²	semidirect
79. C₃₁×#501	C₂²	semidirect
80. C₃₁×#501	C₂²	semidirect
81. C₃₁×#499	C₂²	semidirect
82. C₃₁×#498	C₂²	semidirect
83. C₃₁×#491	C₂²	semidirect
88. C₃₁×#487	C₂²	semidirect
91. C₃₁×#485	C₂²	semidirect
92. C₃₁×#485	C₂²	semidirect
93. C₃₁×#485	C₂²	semidirect
96. C₃₁×#483	C₂²	semidirect
102. C₃₁×#482	C₂²	semidirect
103. C₃₁×#482	C₂²	semidirect
105. C₃₁×#481	C₂²	semidirect
106. C₃₁×#480	C₂²	semidirect
107. C₃₁×#479	C₂²	semidirect
108. C₃₁×#479	C₂²	semidirect
109. C₃₁×#479	C₂²	semidirect
110. C₃₁×#479	C₂²	semidirect
111. C₃₁×#479	C₂²	semidirect
119. C₃₁×#478	C₂²	semidirect
120. C₃₁×#478	C₂²	semidirect
121. C₃₁×#478	C₂²	semidirect
122. C₃₁×#478	C₂²	semidirect
123. C₃₁×#477	C₂²	semidirect
124. C₃₁×#477	C₂²	semidirect
125. C₃₁×#477	C₂²	semidirect
129. C₃₁×#476	C₂²	semidirect
130. C₃₁×#475	C₂²	semidirect
131. C₃₁×#475	C₂²	semidirect
136. C₃₁×#474	C₂²	semidirect
140. C₃₁×#468	C₂²	semidirect
146. C₃₁×#465	C₂²	semidirect
147. C₃₁×#465	C₂²	semidirect
148. C₃₁×#465	C₂²	semidirect
153. C₃₁×#461	C₂²	semidirect
154. C₃₁×#461	C₂²	semidirect
155. C₃₁×#460	C₂²	semidirect
156. C₃₁×#460	C₂²	semidirect
165. C₃₁×#446	C₂²	semidirect
166. C₃₁×#446	C₂²	semidirect
172. C₃₁×#440	C₂²	semidirect
173. C₃₁×#440	C₂²	semidirect
174. C₃₁×#440	C₂²	semidirect
175. C₄×SD₁₆×C₃₁	C₂²	semidirect
182. C₃₁×#435	C₂²	semidirect
184. C₈×D₄×C₃₁	C₂²	semidirect
186. C₃₁×#433	C₂²	semidirect
187. C₃₁×#432	C₂²	semidirect
189. C₃₁×#428	C₂²	semidirect
191. C₃₁×#427	C₂²	semidirect
192. C₃₁×#427	C₂²	semidirect
193. C₂×C₃₁×#107	C₂²	semidirect
195. C₃₁×#424	C₂²	semidirect
196. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
672. #62171	C₃₁	direct (N × H)
775. #3547	C₂×C₃₁	semidirect
776. #3521	C₂×C₃₁	semidirect
777. #3389	C₂×C₃₁	semidirect
778. #3384	C₂×C₃₁	semidirect
779. #3376	C₂×C₃₁	semidirect
780. #3367	C₂×C₃₁	semidirect
781. #3350	C₂×C₃₁	semidirect
782. #3348	C₂×C₃₁	semidirect
783. #3347	C₂×C₃₁	semidirect
784. #3343	C₂×C₃₁	semidirect
785. #3340	C₂×C₃₁	semidirect
786. #3339	C₂×C₃₁	semidirect
787. #3319	C₂×C₃₁	semidirect
788. #3319	C₂×C₃₁	semidirect
789. #3307	C₂×C₃₁	semidirect
790. #3306	C₂×C₃₁	semidirect
791. #3303	C₂×C₃₁	semidirect
792. #3297	C₂×C₃₁	semidirect
793. #3260	C₂×C₃₁	semidirect
794. #3257	C₂×C₃₁	semidirect
795. #3247	C₂×C₃₁	semidirect
796. #3244	C₂×C₃₁	semidirect
797. #3242	C₂×C₃₁	semidirect
798. #3240	C₂×C₃₁	semidirect
799. #3122	C₂×C₃₁	semidirect
800. #3119	C₂×C₃₁	semidirect
801. #3115	C₂×C₃₁	semidirect
802. #3083	C₂×C₃₁	semidirect
803. #3081	C₂×C₃₁	semidirect
804. #3076	C₂×C₃₁	semidirect
805. #2992	C₂×C₃₁	semidirect
860. #555	C₂²×C₃₁	semidirect
862. #554	C₂²×C₃₁	semidirect
866. #553	C₂²×C₃₁	semidirect
872. D₄×Q₈	C₂²×C₃₁	semidirect
879. #544	C₂²×C₃₁	semidirect
885. #540	C₂²×C₃₁	semidirect
890. #533	C₂²×C₃₁	semidirect
891. #532	C₂²×C₃₁	semidirect
899. #501	C₂²×C₃₁	semidirect
900. #501	C₂²×C₃₁	semidirect
901. #501	C₂²×C₃₁	semidirect
902. #501	C₂²×C₃₁	semidirect
903. #499	C₂²×C₃₁	semidirect
904. #498	C₂²×C₃₁	semidirect
905. #491	C₂²×C₃₁	semidirect
910. #487	C₂²×C₃₁	semidirect
913. #485	C₂²×C₃₁	semidirect
914. #485	C₂²×C₃₁	semidirect
915. #485	C₂²×C₃₁	semidirect
918. #483	C₂²×C₃₁	semidirect
924. #482	C₂²×C₃₁	semidirect
925. #482	C₂²×C₃₁	semidirect
927. #481	C₂²×C₃₁	semidirect
928. #480	C₂²×C₃₁	semidirect
929. #479	C₂²×C₃₁	semidirect
930. #479	C₂²×C₃₁	semidirect
931. #479	C₂²×C₃₁	semidirect
932. #479	C₂²×C₃₁	semidirect
933. #479	C₂²×C₃₁	semidirect
941. #478	C₂²×C₃₁	semidirect
942. #478	C₂²×C₃₁	semidirect
943. #478	C₂²×C₃₁	semidirect
944. #478	C₂²×C₃₁	semidirect
945. #477	C₂²×C₃₁	semidirect
946. #477	C₂²×C₃₁	semidirect
947. #477	C₂²×C₃₁	semidirect
951. #476	C₂²×C₃₁	semidirect
952. #475	C₂²×C₃₁	semidirect
953. #475	C₂²×C₃₁	semidirect
958. #474	C₂²×C₃₁	semidirect
962. #468	C₂²×C₃₁	semidirect
968. #465	C₂²×C₃₁	semidirect
969. #465	C₂²×C₃₁	semidirect
970. #465	C₂²×C₃₁	semidirect
975. #461	C₂²×C₃₁	semidirect
976. #461	C₂²×C₃₁	semidirect
977. #460	C₂²×C₃₁	semidirect
978. #460	C₂²×C₃₁	semidirect
987. #446	C₂²×C₃₁	semidirect
988. #446	C₂²×C₃₁	semidirect
994. #440	C₂²×C₃₁	semidirect
995. #440	C₂²×C₃₁	semidirect
996. #440	C₂²×C₃₁	semidirect
997. C₄×SD₁₆	C₂²×C₃₁	semidirect
1004. #435	C₂²×C₃₁	semidirect
1006. C₈×D₄	C₂²×C₃₁	semidirect
1008. #433	C₂²×C₃₁	semidirect
1009. #432	C₂²×C₃₁	semidirect
1011. #428	C₂²×C₃₁	semidirect
1013. #427	C₂²×C₃₁	semidirect
1014. #427	C₂²×C₃₁	semidirect
1015. C₂×#107	C₂²×C₃₁	semidirect
1017. #424	C₂²×C₃₁	semidirect
1018. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
1310. C₃₁	#62171	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×#3547	2
C₃₁×#3521	2
C₃₁×#3389	2
C₃₁×#3384	2
C₃₁×#3376	2
C₃₁×#3367	2
C₃₁×#3350	2
C₃₁×#3348	2
C₃₁×#3347	2
C₃₁×#3343	2
C₃₁×#3340	2
C₃₁×#3339	2
C₃₁×#3319	2
C₃₁×#3307	2
C₃₁×#3306	2
C₃₁×#3303	2
C₃₁×#3297	2
C₃₁×#3260	2
C₃₁×#3257	2
C₃₁×#3247	2
C₃₁×#3244	2
C₃₁×#3242	2
C₃₁×#3240	2
C₃₁×#3122	2
C₃₁×#3119	2
C₃₁×#3115	2
C₃₁×#3083	2
C₃₁×#3081	2
C₃₁×#3076	2
C₃₁×#2992	2
#62171	31

Subgroups — C31×#62171 #21518930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62171 #21518930