Subgroups — C₃₁×#61790 #21518549

Order 7936.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3352	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3351	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3351	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3337	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3337	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3336	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3326	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3323	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3301	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3300	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3297	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3204	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3203	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3201	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3198	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#563	—	2	1	no	—
33	C₃₁×#560	—	2	1	no	—
34	C₃₁×#555	—	2	1	no	—
35	C₃₁×#553	—	2	1	no	—
36	C₃₁×#553	—	2	1	no	—
37	C₃₁×#553	—	2	1	no	—
38	C₃₁×#553	—	2	1	no	—
39	C₃₁×#553	C₂²	1	1	yes	characteristic
40	C₃₁×#553	C₂²	1	1	yes	characteristic
41	C₃₁×#553	C₂²	1	1	yes	characteristic
42	C₃₁×#553	C₂²	1	1	yes	characteristic
43	C₃₁×#553	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#553	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#552	C₂²	1	1	yes	characteristic
46	C₃₁×#552	C₂²	1	1	yes	characteristic
47	C₃₁×#552	C₂²	1	1	yes	characteristic
48	C₃₁×#552	C₂²	1	1	yes	characteristic
49	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#551	—	2	1	no	—
52	C₃₁×#548	C₂²	1	1	yes	characteristic
53	C₃₁×#548	C₂²	1	1	yes	characteristic
54	C₃₁×#546	C₂²	1	1	yes	characteristic
55	C₃₁×#546	C₂²	1	1	yes	characteristic
56	C₃₁×#541	—	2	1	no	—
57	C₃₁×#540	—	2	1	no	—
58	C₃₁×#540	—	2	1	no	—
59	C₃₁×#540	—	2	1	no	—
60	C₃₁×#538	—	2	1	no	—
61	C₃₁×#538	—	2	1	no	—
62	C₃₁×#537	C₂²	1	1	yes	characteristic
63	C₃₁×#537	C₂²	1	1	yes	characteristic
64	C₃₁×#537	C₂²	1	1	yes	characteristic
65	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#536	C₂²	1	1	yes	characteristic
67	C₃₁×#535	C₂²	1	1	yes	characteristic
68	C₃₁×#532	C₂²	1	1	yes	characteristic
69	C₃₁×#529	—	2	1	no	—
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×#125	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
76	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#488	C₂²	1	1	yes	characteristic
82	C₃₁×#488	C₂²	1	1	yes	characteristic
83	C₃₁×#488	C₂²	1	1	yes	characteristic
84	C₃₁×#488	C₂²	1	1	yes	characteristic
85	C₃₁×#485	C₂²	1	1	yes	characteristic
86	C₃₁×#485	C₂²	1	1	yes	characteristic
87	C₃₁×#485	C₂²	1	1	yes	characteristic
88	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#484	C₂²	1	1	yes	characteristic
94	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#483	C₂²	1	1	yes	characteristic
99	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
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×#482	C₂²	1	1	yes	characteristic
108	C₃₁×#482	C₂²	1	1	yes	characteristic
109	C₃₁×#482	C₂²	1	1	yes	characteristic
110	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#481	C₂²	1	1	yes	characteristic
112	C₃₁×#481	C₂²	1	1	yes	characteristic
113	C₃₁×#481	C₂²	1	1	yes	characteristic
114	C₃₁×#481	C₂²	1	1	yes	characteristic
115	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#480	C₂²	1	1	yes	characteristic
117	C₃₁×#480	C₂²	1	1	yes	characteristic
118	C₃₁×#480	C₂²	1	1	yes	characteristic
119	C₃₁×#480	C₂²	1	1	yes	characteristic
120	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#478	C₂²	1	1	yes	characteristic
128	C₃₁×#478	C₂²	1	1	yes	characteristic
129	C₃₁×#478	C₂²	1	1	yes	characteristic
130	C₃₁×#478	C₂²	1	1	yes	characteristic
131	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#470	C₂²	1	1	yes	characteristic
134	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#469	C₂²	1	1	yes	characteristic
136	C₃₁×#469	C₂²	1	1	yes	characteristic
137	C₃₁×#468	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×#467	C₂²	1	1	yes	characteristic
142	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
143	C₃₁×#466	C₂²	1	1	yes	characteristic
144	C₃₁×#466	C₂²	1	1	yes	characteristic
145	C₃₁×#465	C₂²	1	1	yes	characteristic
146	C₃₁×#465	C₂²	1	1	yes	characteristic
147	C₃₁×#465	C₂²	1	1	yes	characteristic
148	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#464	C₂²	1	1	yes	characteristic
150	C₃₁×#464	C₂²	1	1	yes	characteristic
151	C₃₁×#463	C₂²	1	1	yes	characteristic
152	C₃₁×#463	C₂²	1	1	yes	characteristic
153	C₃₁×#452	C₂²	1	1	yes	characteristic
154	C₃₁×#452	C₂²	1	1	yes	characteristic
155	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
156	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
157	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
158	C₃₁×#450	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×#448	C₂²	1	1	yes	characteristic, complemented
164	C₃₁×#447	C₂²	1	1	yes	characteristic
165	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
166	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
167	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
168	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
169	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
170	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
171	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
172	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
173	C₃₁×#436	C₂²	1	1	yes	characteristic
174	C₃₁×#436	C₂²	1	1	yes	characteristic
175	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
176	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
177	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
178	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
179	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
180	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
181	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
182	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
183	C₃₁×#428	C₂²	1	1	yes	characteristic
184	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
185	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
186	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
187	C₃₁×#427	C₂²	1	1	yes	characteristic
188	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
189	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
190	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
191	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
192	C₃₁×#418	C₂²	1	1	yes	characteristic
193	C₃₁×#417	C₂²	1	1	yes	characteristic
194	C₃₁×#417	C₂²	1	1	yes	characteristic
195	C₃₁×#416	C₂²	1	1	yes	characteristic
196	C₃₁×#416	C₂²	1	1	yes	characteristic
197	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
198	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
199	C₃₁×#408	C₂²	1	1	yes	characteristic
200	C₃₁×#408	C₂²	1	1	yes	characteristic
201	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
202	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
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	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₂²×D₄×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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×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×D₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×C₄⋊Q₈	—	2	1	no	—
227	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
228	C₃₁×#127	—	2	1	no	—
229	C₃₁×#127	D₄	1	1	yes	characteristic
230	C₃₁×#126	—	2	1	no	—
231	C₃₁×#126	—	2	1	no	—
232	C₃₁×#126	—	2	1	no	—
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×#125	—	2	1	no	—
245	C₃₁×#125	—	2	1	no	—
246	C₃₁×#125	—	2	1	no	—
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	C₂³	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×#124	—	2	1	no	—
259	C₃₁×#124	—	2	1	no	—
260	C₃₁×#124	—	2	1	no	—
261	C₃₁×#124	—	2	1	no	—
262	C₃₁×#124	D₄	1	1	yes	characteristic
263	C₃₁×#124	D₄	1	1	yes	characteristic
264	C₃₁×#124	C₂³	1	1	yes	characteristic
265	C₃₁×#124	C₂³	1	1	yes	characteristic
266	C₃₁×#123	—	2	1	no	—
267	C₃₁×#123	—	2	1	no	—
268	C₃₁×#123	—	2	1	no	—
269	C₃₁×#123	—	2	1	no	—
270	C₃₁×#123	—	2	1	no	—
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×C₂²⋊Q₈	—	2	1	no	—
285	C₃₁×C₂²⋊Q₈	—	2	1	no	—
286	C₃₁×C₂²⋊Q₈	—	2	1	no	—
287	C₃₁×C₂²⋊Q₈	—	2	1	no	—
288	C₃₁×C₂²⋊Q₈	—	2	1	no	—
289	C₃₁×C₂²⋊Q₈	—	2	1	no	—
290	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
291	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
292	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
293	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
294	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
295	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
296	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
297	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
298	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
299	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
300	C₃₁×#121	—	2	1	no	—
301	C₃₁×#121	—	2	1	no	—
302	C₃₁×#121	—	2	1	no	—
303	C₃₁×#121	—	2	1	no	—
304	C₃₁×#121	—	2	1	no	—
305	C₃₁×#121	—	2	1	no	—
306	C₃₁×#121	—	2	1	no	—
307	C₃₁×#121	—	2	1	no	—
308	C₃₁×#121	—	2	1	no	—
309	C₃₁×#121	—	2	1	no	—
310	C₃₁×#121	—	2	1	no	—
311	C₃₁×#121	—	2	1	no	—
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	D₄	1	1	yes	characteristic
323	C₃₁×#121	D₄	1	1	yes	characteristic
324	C₃₁×#121	D₄	1	1	yes	characteristic
325	C₃₁×#121	D₄	1	1	yes	characteristic
326	C₃₁×#121	C₂³	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×#121	C₂³	1	1	yes	characteristic
336	C₃₁×#120	—	2	1	no	—
337	C₃₁×#120	—	2	1	no	—
338	C₃₁×#120	—	2	1	no	—
339	C₃₁×#120	—	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×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	—	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	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	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
380	C₃₁×#117	—	2	1	no	—
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	C₃₁×#117	C₂³	1	1	yes	characteristic
388	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
396	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
397	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
398	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
399	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
400	C₂×C₄²×C₃₁	—	2	1	no	—
401	C₂×C₄²×C₃₁	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×#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×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	C₂³	1	1	yes	characteristic
424	C₃₁×#106	C₂³	1	1	yes	characteristic
425	C₃₁×#106	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×#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×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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₃₁×C₂²⋊C₈	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	—	2	1	no	—
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	#41×C₃₁	—	4	1	no	—
486	#41×C₃₁	—	4	1	no	—
487	#41×C₃₁	—	4	1	no	—
488	#41×C₃₁	—	4	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	C₂×D₄	1	1	yes	characteristic
493	C₂×Q₈×C₃₁	C₂×D₄	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	—	2	1	no	—
509	C₂×D₄×C₃₁	—	2	1	no	—
510	C₂×D₄×C₃₁	—	2	1	no	—
511	C₂×D₄×C₃₁	—	4	1	no	—
512	C₂×D₄×C₃₁	—	4	1	no	—
513	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
514	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
515	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
516	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
517	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
518	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
519	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
520	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
521	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
522	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
523	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
524	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
525	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
535	C₂²×C₄×C₃₁	—	2	1	no	—
536	C₂²×C₄×C₃₁	—	2	1	no	—
537	C₂²×C₄×C₃₁	—	2	1	no	—
538	C₂²×C₄×C₃₁	—	2	1	no	—
539	C₂²×C₄×C₃₁	—	2	1	no	—
540	C₂²×C₄×C₃₁	—	2	1	no	—
541	C₂²×C₄×C₃₁	—	2	1	no	—
542	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
543	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
544	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
545	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
547	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
548	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
549	Q₁₆×C₃₁	—	4	1	no	—
550	Q₁₆×C₃₁	—	4	1	no	—
551	SD₁₆×C₃₁	—	4	1	no	—
552	SD₁₆×C₃₁	—	4	1	no	—
553	SD₁₆×C₃₁	—	4	1	no	—
554	SD₁₆×C₃₁	—	4	1	no	—
555	D₈×C₃₁	—	4	1	no	—
556	D₈×C₃₁	—	4	1	no	—
557	M₁₆×C₃₁	—	4	1	no	—
558	M₁₆×C₃₁	—	4	1	no	—
559	M₁₆×C₃₁	—	4	1	no	—
560	M₁₆×C₃₁	—	4	1	no	—
561	C₂×C₈×C₃₁	—	4	1	no	—
562	C₂×C₈×C₃₁	—	4	1	no	—
563	C₂×C₈×C₃₁	—	4	1	no	—
564	C₂×C₈×C₃₁	—	4	1	no	—
565	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
566	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
567	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
568	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
569	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
570	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
571	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
572	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
602	C₄⋊C₄×C₃₁	—	2	1	no	—
603	C₄⋊C₄×C₃₁	—	2	1	no	—
604	C₄⋊C₄×C₃₁	—	2	1	no	—
605	C₄⋊C₄×C₃₁	—	2	1	no	—
606	C₄⋊C₄×C₃₁	—	2	1	no	—
607	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂×D₄	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	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
618	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
619	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
620	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
651	C₂²⋊C₄×C₃₁	—	2	1	no	—
652	C₂²⋊C₄×C₃₁	—	2	1	no	—
653	C₂²⋊C₄×C₃₁	—	2	1	no	—
654	C₂²⋊C₄×C₃₁	—	2	1	no	—
655	C₂²⋊C₄×C₃₁	—	2	1	no	—
656	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
658	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
659	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
660	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
661	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
662	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
663	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
672	C₄²×C₃₁	—	2	1	no	—
673	C₄²×C₃₁	—	2	1	no	—
674	C₄²×C₃₁	—	2	1	no	—
675	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
676	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
677	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
678	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
679	#61790	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	—	8	1	no	—
684	C₂³×C₃₁	—	8	1	no	—
685	C₂³×C₃₁	—	8	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	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
690	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	—	4	1	no	—
698	Q₈×C₃₁	—	4	1	no	—
699	Q₈×C₃₁	—	8	1	no	—
700	D₄×C₃₁	—	2	1	no	—
701	D₄×C₃₁	—	2	1	no	—
702	D₄×C₃₁	—	2	1	no	—
703	D₄×C₃₁	—	2	1	no	—
704	D₄×C₃₁	—	2	1	no	—
705	D₄×C₃₁	—	2	1	no	—
706	D₄×C₃₁	—	4	1	no	—
707	D₄×C₃₁	—	4	1	no	—
708	D₄×C₃₁	—	4	1	no	—
709	D₄×C₃₁	—	4	1	no	—
710	D₄×C₃₁	—	4	1	no	—
711	D₄×C₃₁	—	4	1	no	—
712	D₄×C₃₁	—	4	1	no	—
713	D₄×C₃₁	—	4	1	no	—
714	D₄×C₃₁	—	4	1	no	—
715	D₄×C₃₁	—	4	1	no	—
716	D₄×C₃₁	—	4	2	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	D₄×C₃₁	—	8	1	no	—
722	D₄×C₃₁	—	8	1	no	—
723	D₄×C₃₁	—	8	1	no	—
724	D₄×C₃₁	—	8	1	no	—
725	D₄×C₃₁	—	8	1	no	—
726	D₄×C₃₁	—	8	1	no	—
727	D₄×C₃₁	—	8	1	no	—
728	D₄×C₃₁	—	8	1	no	—
729	D₄×C₃₁	—	8	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	—	2	1	no	—
741	C₂×C₄×C₃₁	—	2	1	no	—
742	C₂×C₄×C₃₁	—	2	1	no	—
743	C₂×C₄×C₃₁	—	2	1	no	—
744	C₂×C₄×C₃₁	—	2	1	no	—
745	C₂×C₄×C₃₁	—	2	1	no	—
746	C₂×C₄×C₃₁	—	2	1	no	—
747	C₂×C₄×C₃₁	—	2	1	no	—
748	C₂×C₄×C₃₁	—	2	1	no	—
749	C₂×C₄×C₃₁	—	2	1	no	—
750	C₂×C₄×C₃₁	—	2	1	no	—
751	C₂×C₄×C₃₁	—	2	1	no	—
752	C₂×C₄×C₃₁	—	2	1	no	—
753	C₂×C₄×C₃₁	—	4	1	no	—
754	C₂×C₄×C₃₁	—	4	1	no	—
755	C₂×C₄×C₃₁	—	4	2	no	—
756	C₂×C₄×C₃₁	—	8	1	no	—
757	C₂×C₄×C₃₁	—	8	1	no	—
758	C₂×C₄×C₃₁	—	8	1	no	—
759	C₂×C₄×C₃₁	—	8	1	no	—
760	C₂×C₄×C₃₁	—	8	1	no	—
761	C₂×C₄×C₃₁	—	8	1	no	—
762	C₂×C₄×C₃₁	—	8	1	no	—
763	C₂×C₄×C₃₁	—	8	1	no	—
764	C₂×C₄×C₃₁	—	8	1	no	—
765	C₂×C₄×C₃₁	—	8	1	no	—
766	C₂×C₄×C₃₁	—	8	1	no	—
767	C₂×C₄×C₃₁	—	8	1	no	—
768	C₂×C₄×C₃₁	—	8	1	no	—
769	C₂×C₄×C₃₁	—	8	1	no	—
770	C₂×C₄×C₃₁	—	8	1	no	—
771	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
772	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
773	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
774	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
775	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
776	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
777	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
778	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
779	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
780	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
781	C₈×C₃₁	—	2	1	no	—
782	C₈×C₃₁	—	2	1	no	—
783	C₈×C₃₁	—	2	1	no	—
784	C₈×C₃₁	—	2	1	no	—
785	C₈×C₃₁	—	2	1	no	—
786	C₈×C₃₁	—	2	1	no	—
787	C₈×C₃₁	—	2	1	no	—
788	C₈×C₃₁	—	2	1	no	—
789	#3551	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3512	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3355	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3351	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3351	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3339	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3337	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3337	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3336	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3326	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3323	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3322	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3301	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3300	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3297	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3296	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
809	#3204	C₂×C₃₁	1	1	yes	characteristic, complemented
810	#3203	C₂×C₃₁	1	1	yes	characteristic, complemented
811	#3201	C₂×C₃₁	1	1	yes	characteristic, complemented
812	#3198	C₂×C₃₁	1	1	yes	characteristic, complemented
813	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
814	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
815	#3099	C₂×C₃₁	1	1	yes	characteristic, complemented
816	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
817	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
818	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
819	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
820	C₂²×C₃₁	—	2	1	no	—
821	C₂²×C₃₁	—	2	1	no	—
822	C₂²×C₃₁	—	2	1	no	—
823	C₂²×C₃₁	—	2	1	no	—
824	C₂²×C₃₁	—	2	1	no	—
825	C₂²×C₃₁	—	2	1	no	—
826	C₂²×C₃₁	—	2	1	no	—
827	C₂²×C₃₁	—	2	1	no	—
828	C₂²×C₃₁	—	2	1	no	—
829	C₂²×C₃₁	—	2	1	no	—
830	C₂²×C₃₁	—	2	1	no	—
831	C₂²×C₃₁	—	2	1	no	—
832	C₂²×C₃₁	—	2	1	no	—
833	C₂²×C₃₁	—	2	1	no	—
834	C₂²×C₃₁	—	2	1	no	—
835	C₂²×C₃₁	—	4	1	no	—
836	C₂²×C₃₁	—	4	1	no	—
837	C₂²×C₃₁	—	4	1	no	—
838	C₂²×C₃₁	—	4	1	no	—
839	C₂²×C₃₁	—	4	1	no	—
840	C₂²×C₃₁	—	4	1	no	—
841	C₂²×C₃₁	—	4	1	no	—
842	C₂²×C₃₁	—	4	1	no	—
843	C₂²×C₃₁	—	4	1	no	—
844	C₂²×C₃₁	—	16	2	no	—
845	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
846	C₄×C₃₁	—	2	1	no	—
847	C₄×C₃₁	—	2	1	no	—
848	C₄×C₃₁	—	2	1	no	—
849	C₄×C₃₁	—	2	1	no	—
850	C₄×C₃₁	—	2	1	no	—
851	C₄×C₃₁	—	2	1	no	—
852	C₄×C₃₁	—	2	1	no	—
853	C₄×C₃₁	—	2	1	no	—
854	C₄×C₃₁	—	2	1	no	—
855	C₄×C₃₁	—	4	1	no	—
856	C₄×C₃₁	—	4	1	no	—
857	C₄×C₃₁	—	4	1	no	—
858	C₄×C₃₁	—	4	1	no	—
859	C₄×C₃₁	—	4	1	no	—
860	C₄×C₃₁	—	4	1	no	—
861	C₄×C₃₁	—	4	1	no	—
862	C₄×C₃₁	—	4	1	no	—
863	C₄×C₃₁	—	4	1	no	—
864	C₄×C₃₁	—	4	1	no	—
865	C₄×C₃₁	—	4	1	no	—
866	C₄×C₃₁	—	4	1	no	—
867	C₄×C₃₁	—	4	1	no	—
868	C₄×C₃₁	#585	1	1	yes	characteristic
869	C₄×C₃₁	#585	1	1	yes	characteristic
870	#563	—	2	1	no	—
871	#560	—	2	1	no	—
872	#555	—	2	1	no	—
873	#553	—	2	1	no	—
874	#553	—	2	1	no	—
875	#553	—	2	1	no	—
876	#553	—	2	1	no	—
877	#553	C₂²×C₃₁	1	1	yes	characteristic
878	#553	C₂²×C₃₁	1	1	yes	characteristic
879	#553	C₂²×C₃₁	1	1	yes	characteristic
880	#553	C₂²×C₃₁	1	1	yes	characteristic
881	#553	C₂²×C₃₁	1	1	yes	characteristic, complemented
882	#553	C₂²×C₃₁	1	1	yes	characteristic, complemented
883	#552	C₂²×C₃₁	1	1	yes	characteristic
884	#552	C₂²×C₃₁	1	1	yes	characteristic
885	#552	C₂²×C₃₁	1	1	yes	characteristic
886	#552	C₂²×C₃₁	1	1	yes	characteristic
887	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
888	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
889	#551	—	2	1	no	—
890	#548	C₂²×C₃₁	1	1	yes	characteristic
891	#548	C₂²×C₃₁	1	1	yes	characteristic
892	#546	C₂²×C₃₁	1	1	yes	characteristic
893	#546	C₂²×C₃₁	1	1	yes	characteristic
894	#541	—	2	1	no	—
895	#540	—	2	1	no	—
896	#540	—	2	1	no	—
897	#540	—	2	1	no	—
898	#538	—	2	1	no	—
899	#538	—	2	1	no	—
900	#537	C₂²×C₃₁	1	1	yes	characteristic
901	#537	C₂²×C₃₁	1	1	yes	characteristic
902	#537	C₂²×C₃₁	1	1	yes	characteristic
903	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
904	#536	C₂²×C₃₁	1	1	yes	characteristic
905	#535	C₂²×C₃₁	1	1	yes	characteristic
906	#532	C₂²×C₃₁	1	1	yes	characteristic
907	#529	—	2	1	no	—
908	#529	—	2	1	no	—
909	#529	C₂²×C₃₁	1	1	yes	characteristic
910	#529	C₂²×C₃₁	1	1	yes	characteristic
911	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
912	#520	C₂²×C₃₁	1	1	yes	characteristic
913	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
914	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
916	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
917	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
918	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
919	#488	C₂²×C₃₁	1	1	yes	characteristic
920	#488	C₂²×C₃₁	1	1	yes	characteristic
921	#488	C₂²×C₃₁	1	1	yes	characteristic
922	#488	C₂²×C₃₁	1	1	yes	characteristic
923	#485	C₂²×C₃₁	1	1	yes	characteristic
924	#485	C₂²×C₃₁	1	1	yes	characteristic
925	#485	C₂²×C₃₁	1	1	yes	characteristic
926	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
927	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
928	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
929	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
930	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
931	#484	C₂²×C₃₁	1	1	yes	characteristic
932	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
933	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
934	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
935	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
936	#483	C₂²×C₃₁	1	1	yes	characteristic
937	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
938	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
939	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
940	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
941	#482	C₂²×C₃₁	1	1	yes	characteristic
942	#482	C₂²×C₃₁	1	1	yes	characteristic
943	#482	C₂²×C₃₁	1	1	yes	characteristic
944	#482	C₂²×C₃₁	1	1	yes	characteristic
945	#482	C₂²×C₃₁	1	1	yes	characteristic
946	#482	C₂²×C₃₁	1	1	yes	characteristic
947	#482	C₂²×C₃₁	1	1	yes	characteristic
948	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
949	#481	C₂²×C₃₁	1	1	yes	characteristic
950	#481	C₂²×C₃₁	1	1	yes	characteristic
951	#481	C₂²×C₃₁	1	1	yes	characteristic
952	#481	C₂²×C₃₁	1	1	yes	characteristic
953	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
954	#480	C₂²×C₃₁	1	1	yes	characteristic
955	#480	C₂²×C₃₁	1	1	yes	characteristic
956	#480	C₂²×C₃₁	1	1	yes	characteristic
957	#480	C₂²×C₃₁	1	1	yes	characteristic
958	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
959	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
960	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
961	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
962	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
963	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
964	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
965	#478	C₂²×C₃₁	1	1	yes	characteristic
966	#478	C₂²×C₃₁	1	1	yes	characteristic
967	#478	C₂²×C₃₁	1	1	yes	characteristic
968	#478	C₂²×C₃₁	1	1	yes	characteristic
969	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
970	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#470	C₂²×C₃₁	1	1	yes	characteristic
972	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
973	#469	C₂²×C₃₁	1	1	yes	characteristic
974	#469	C₂²×C₃₁	1	1	yes	characteristic
975	#468	C₂²×C₃₁	1	1	yes	characteristic
976	#468	C₂²×C₃₁	1	1	yes	characteristic
977	#468	C₂²×C₃₁	1	1	yes	characteristic
978	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
979	#467	C₂²×C₃₁	1	1	yes	characteristic
980	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
981	#466	C₂²×C₃₁	1	1	yes	characteristic
982	#466	C₂²×C₃₁	1	1	yes	characteristic
983	#465	C₂²×C₃₁	1	1	yes	characteristic
984	#465	C₂²×C₃₁	1	1	yes	characteristic
985	#465	C₂²×C₃₁	1	1	yes	characteristic
986	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
987	#464	C₂²×C₃₁	1	1	yes	characteristic
988	#464	C₂²×C₃₁	1	1	yes	characteristic
989	#463	C₂²×C₃₁	1	1	yes	characteristic
990	#463	C₂²×C₃₁	1	1	yes	characteristic
991	#452	C₂²×C₃₁	1	1	yes	characteristic
992	#452	C₂²×C₃₁	1	1	yes	characteristic
993	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
994	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
995	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
996	#450	C₂²×C₃₁	1	1	yes	characteristic
997	#449	C₂²×C₃₁	1	1	yes	characteristic
998	#449	C₂²×C₃₁	1	1	yes	characteristic
999	#449	C₂²×C₃₁	1	1	yes	characteristic
1000	#449	C₂²×C₃₁	1	1	yes	characteristic
1001	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	#447	C₂²×C₃₁	1	1	yes	characteristic
1003	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1004	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1006	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1007	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1008	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1009	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1010	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1011	#436	C₂²×C₃₁	1	1	yes	characteristic
1012	#436	C₂²×C₃₁	1	1	yes	characteristic
1013	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
1014	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
1015	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1016	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1017	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
1018	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
1019	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
1020	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
1021	#428	C₂²×C₃₁	1	1	yes	characteristic
1022	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1023	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1024	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1025	#427	C₂²×C₃₁	1	1	yes	characteristic
1026	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
1027	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
1028	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
1029	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
1030	#418	C₂²×C₃₁	1	1	yes	characteristic
1031	#417	C₂²×C₃₁	1	1	yes	characteristic
1032	#417	C₂²×C₃₁	1	1	yes	characteristic
1033	#416	C₂²×C₃₁	1	1	yes	characteristic
1034	#416	C₂²×C₃₁	1	1	yes	characteristic
1035	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
1036	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
1037	#408	C₂²×C₃₁	1	1	yes	characteristic
1038	#408	C₂²×C₃₁	1	1	yes	characteristic
1039	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
1040	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
1041	C₂×C₃₁	—	4	1	no	—
1042	C₂×C₃₁	—	4	1	no	—
1043	C₂×C₃₁	—	4	1	no	—
1044	C₂×C₃₁	—	4	1	no	—
1045	C₂×C₃₁	—	4	1	no	—
1046	C₂×C₃₁	—	8	1	no	—
1047	C₂×C₃₁	—	8	1	no	—
1048	C₂×C₃₁	—	8	1	no	—
1049	C₂×C₃₁	#3485	1	1	yes	characteristic
1050	C₂×C₃₁	#3584	1	1	yes	characteristic
1051	C₂×C₃₁	#3584	1	1	yes	characteristic
1052	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1055	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1059	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1060	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1061	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1062	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1063	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1064	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1065	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1066	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1067	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1068	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1069	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1070	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1071	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1072	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1073	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1074	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1075	C₄⋊Q₈	—	2	1	no	—
1076	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1077	#127	—	2	1	no	—
1078	#127	D₄×C₃₁	1	1	yes	characteristic
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	#126	—	2	1	no	—
1086	#126	—	2	1	no	—
1087	#126	—	2	1	no	—
1088	#126	—	2	1	no	—
1089	#126	—	2	1	no	—
1090	#126	—	2	1	no	—
1091	#126	—	2	1	no	—
1092	#126	—	2	1	no	—
1093	#125	—	2	1	no	—
1094	#125	—	2	1	no	—
1095	#125	—	2	1	no	—
1096	#125	—	2	1	no	—
1097	#125	—	2	1	no	—
1098	#125	—	2	1	no	—
1099	#125	—	2	1	no	—
1100	#125	—	2	1	no	—
1101	#125	C₂³×C₃₁	1	1	yes	characteristic
1102	#125	C₂³×C₃₁	1	1	yes	characteristic
1103	#125	C₂³×C₃₁	1	1	yes	characteristic
1104	#125	C₂³×C₃₁	1	1	yes	characteristic
1105	#125	C₂³×C₃₁	1	1	yes	characteristic
1106	#125	C₂³×C₃₁	1	1	yes	characteristic
1107	#124	—	2	1	no	—
1108	#124	—	2	1	no	—
1109	#124	—	2	1	no	—
1110	#124	—	2	1	no	—
1111	#124	D₄×C₃₁	1	1	yes	characteristic
1112	#124	D₄×C₃₁	1	1	yes	characteristic
1113	#124	C₂³×C₃₁	1	1	yes	characteristic
1114	#124	C₂³×C₃₁	1	1	yes	characteristic
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	#123	—	2	1	no	—
1128	#123	—	2	1	no	—
1129	#123	—	2	1	no	—
1130	#123	—	2	1	no	—
1131	#123	—	2	1	no	—
1132	#123	—	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	C₂³×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	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	#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	—	2	1	no	—
1159	#121	—	2	1	no	—
1160	#121	—	2	1	no	—
1161	#121	—	2	1	no	—
1162	#121	—	2	1	no	—
1163	#121	—	2	1	no	—
1164	#121	—	2	1	no	—
1165	#121	—	2	1	no	—
1166	#121	—	2	1	no	—
1167	#121	—	2	1	no	—
1168	#121	—	2	1	no	—
1169	#121	—	2	1	no	—
1170	#121	—	2	1	no	—
1171	#121	D₄×C₃₁	1	1	yes	characteristic
1172	#121	D₄×C₃₁	1	1	yes	characteristic
1173	#121	D₄×C₃₁	1	1	yes	characteristic
1174	#121	D₄×C₃₁	1	1	yes	characteristic
1175	#121	C₂³×C₃₁	1	1	yes	characteristic
1176	#121	C₂³×C₃₁	1	1	yes	characteristic
1177	#121	C₂³×C₃₁	1	1	yes	characteristic
1178	#121	C₂³×C₃₁	1	1	yes	characteristic
1179	#121	C₂³×C₃₁	1	1	yes	characteristic
1180	#121	C₂³×C₃₁	1	1	yes	characteristic
1181	#121	C₂³×C₃₁	1	1	yes	characteristic
1182	#121	C₂³×C₃₁	1	1	yes	characteristic
1183	#121	C₂³×C₃₁	1	1	yes	characteristic
1184	#121	C₂³×C₃₁	1	1	yes	characteristic
1185	#120	—	2	1	no	—
1186	#120	—	2	1	no	—
1187	#120	—	2	1	no	—
1188	#120	—	2	1	no	—
1189	C₄×Q₈	—	2	1	no	—
1190	C₄×Q₈	—	2	1	no	—
1191	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1192	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1193	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1194	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1201	C₄×D₄	—	2	1	no	—
1202	C₄×D₄	—	2	1	no	—
1203	C₄×D₄	—	2	1	no	—
1204	C₄×D₄	—	2	1	no	—
1205	C₄×D₄	—	2	1	no	—
1206	C₄×D₄	—	2	1	no	—
1207	C₄×D₄	—	2	1	no	—
1208	C₄×D₄	—	2	1	no	—
1209	C₄×D₄	—	2	1	no	—
1210	C₄×D₄	—	2	1	no	—
1211	C₄×D₄	—	2	1	no	—
1212	C₄×D₄	—	2	1	no	—
1213	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1214	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1215	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1216	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1217	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1218	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1219	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1220	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1221	#117	—	2	1	no	—
1222	#117	—	2	1	no	—
1223	#117	—	2	1	no	—
1224	#117	—	2	1	no	—
1225	#117	—	2	1	no	—
1226	#117	—	2	1	no	—
1227	#117	—	2	1	no	—
1228	#117	—	2	1	no	—
1229	#117	—	2	1	no	—
1230	#117	C₂³×C₃₁	1	1	yes	characteristic
1231	#117	C₂³×C₃₁	1	1	yes	characteristic
1232	#117	C₂³×C₃₁	1	1	yes	characteristic
1233	#117	C₂³×C₃₁	1	1	yes	characteristic
1234	#117	C₂³×C₃₁	1	1	yes	characteristic
1235	#117	C₂³×C₃₁	1	1	yes	characteristic
1236	#117	C₂³×C₃₁	1	1	yes	characteristic
1237	C₂×C₄⋊C₄	—	2	1	no	—
1238	C₂×C₄⋊C₄	—	2	1	no	—
1239	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1240	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1241	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1242	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1243	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1244	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1245	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1246	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1247	C₂×C₂²⋊C₄	—	2	1	no	—
1248	C₂×C₂²⋊C₄	—	2	1	no	—
1249	C₂×C₄²	—	2	1	no	—
1250	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1251	#107	C₂³×C₃₁	1	1	yes	characteristic
1252	#107	C₂³×C₃₁	1	1	yes	characteristic
1253	#107	C₂³×C₃₁	1	1	yes	characteristic
1254	#107	C₂³×C₃₁	1	1	yes	characteristic
1255	#107	C₂³×C₃₁	1	1	yes	characteristic
1256	#107	C₂³×C₃₁	1	1	yes	characteristic
1257	#107	C₂³×C₃₁	1	1	yes	characteristic
1258	#107	C₂³×C₃₁	1	1	yes	characteristic
1259	#107	C₂³×C₃₁	1	1	yes	characteristic
1260	#107	C₂³×C₃₁	1	1	yes	characteristic
1261	#107	C₂³×C₃₁	1	1	yes	characteristic
1262	#107	C₂³×C₃₁	1	1	yes	characteristic
1263	#106	C₂³×C₃₁	1	1	yes	characteristic
1264	#106	C₂³×C₃₁	1	1	yes	characteristic
1265	#106	C₂³×C₃₁	1	1	yes	characteristic
1266	#106	C₂³×C₃₁	1	1	yes	characteristic
1267	#106	C₂³×C₃₁	1	1	yes	characteristic
1268	#106	C₂³×C₃₁	1	1	yes	characteristic
1269	#106	C₂³×C₃₁	1	1	yes	characteristic
1270	#106	C₂³×C₃₁	1	1	yes	characteristic
1271	#106	C₂³×C₃₁	1	1	yes	characteristic
1272	#106	C₂³×C₃₁	1	1	yes	characteristic
1273	#106	C₂³×C₃₁	1	1	yes	characteristic
1274	#106	C₂³×C₃₁	1	1	yes	characteristic
1275	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1276	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1277	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1278	C₄⋊C₈	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	#103	C₂³×C₃₁	1	1	yes	characteristic
1283	#103	C₂³×C₃₁	1	1	yes	characteristic
1284	#103	C₂³×C₃₁	1	1	yes	characteristic
1285	#103	C₂³×C₃₁	1	1	yes	characteristic
1286	#103	C₂³×C₃₁	1	1	yes	characteristic
1287	#103	C₂³×C₃₁	1	1	yes	characteristic
1288	#103	C₂³×C₃₁	1	1	yes	characteristic
1289	#103	C₂³×C₃₁	1	1	yes	characteristic
1290	#103	C₂³×C₃₁	1	1	yes	characteristic
1291	#103	C₂³×C₃₁	1	1	yes	characteristic
1292	#103	C₂³×C₃₁	1	1	yes	characteristic
1293	#103	C₂³×C₃₁	1	1	yes	characteristic
1294	#103	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	#102	C₂³×C₃₁	1	1	yes	characteristic
1299	#102	C₂³×C₃₁	1	1	yes	characteristic
1300	#102	C₂³×C₃₁	1	1	yes	characteristic
1301	#102	C₂³×C₃₁	1	1	yes	characteristic
1302	#102	C₂³×C₃₁	1	1	yes	characteristic
1303	#102	C₂³×C₃₁	1	1	yes	characteristic
1304	#102	C₂³×C₃₁	1	1	yes	characteristic
1305	#102	C₂³×C₃₁	1	1	yes	characteristic
1306	#102	C₂³×C₃₁	1	1	yes	characteristic
1307	#102	C₂³×C₃₁	1	1	yes	characteristic
1308	#102	C₂³×C₃₁	1	1	yes	characteristic
1309	#102	C₂³×C₃₁	1	1	yes	characteristic
1310	#102	C₂³×C₃₁	1	1	yes	characteristic
1311	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1312	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1313	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1314	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1315	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1316	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1317	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1318	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1319	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1320	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1321	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1322	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1323	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1324	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1325	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1326	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1327	C₃₁	#61790	1	1	yes	characteristic, direct product factor, Sylow
1328	C₂⁴	—	2	1	no	—
1329	#41	—	4	1	no	—
1330	#41	—	4	1	no	—
1331	#41	—	4	1	no	—
1332	#41	—	4	1	no	—
1333	#41	—	4	1	no	—
1334	#41	—	4	1	no	—
1335	#41	—	4	1	no	—
1336	#41	—	4	1	no	—
1337	#41	—	4	1	no	—
1338	#41	—	4	1	no	—
1339	C₂×Q₈	—	2	1	no	—
1340	C₂×Q₈	—	4	1	no	—
1341	C₂×Q₈	—	4	1	no	—
1342	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1343	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1344	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1345	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1346	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1347	C₂×D₄	—	2	1	no	—
1348	C₂×D₄	—	2	1	no	—
1349	C₂×D₄	—	2	1	no	—
1350	C₂×D₄	—	2	1	no	—
1351	C₂×D₄	—	2	1	no	—
1352	C₂×D₄	—	2	1	no	—
1353	C₂×D₄	—	2	1	no	—
1354	C₂×D₄	—	2	1	no	—
1355	C₂×D₄	—	2	1	no	—
1356	C₂×D₄	—	2	1	no	—
1357	C₂×D₄	—	2	1	no	—
1358	C₂×D₄	—	2	1	no	—
1359	C₂×D₄	—	2	1	no	—
1360	C₂×D₄	—	2	1	no	—
1361	C₂×D₄	—	4	1	no	—
1362	C₂×D₄	—	4	1	no	—
1363	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1364	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1365	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1366	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1367	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1368	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1369	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1370	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1371	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1372	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1373	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1374	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1375	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1376	C₂²×C₄	—	2	1	no	—
1377	C₂²×C₄	—	2	1	no	—
1378	C₂²×C₄	—	2	1	no	—
1379	C₂²×C₄	—	2	1	no	—
1380	C₂²×C₄	—	2	1	no	—
1381	C₂²×C₄	—	2	1	no	—
1382	C₂²×C₄	—	2	1	no	—
1383	C₂²×C₄	—	2	1	no	—
1384	C₂²×C₄	—	2	1	no	—
1385	C₂²×C₄	—	2	1	no	—
1386	C₂²×C₄	—	2	1	no	—
1387	C₂²×C₄	—	2	1	no	—
1388	C₂²×C₄	—	2	1	no	—
1389	C₂²×C₄	—	2	1	no	—
1390	C₂²×C₄	—	2	1	no	—
1391	C₂²×C₄	—	2	1	no	—
1392	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1393	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1394	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1395	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1396	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1397	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1398	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1399	Q₁₆	—	4	1	no	—
1400	Q₁₆	—	4	1	no	—
1401	SD₁₆	—	4	1	no	—
1402	SD₁₆	—	4	1	no	—
1403	SD₁₆	—	4	1	no	—
1404	SD₁₆	—	4	1	no	—
1405	D₈	—	4	1	no	—
1406	D₈	—	4	1	no	—
1407	M₁₆	—	4	1	no	—
1408	M₁₆	—	4	1	no	—
1409	M₁₆	—	4	1	no	—
1410	M₁₆	—	4	1	no	—
1411	C₂×C₈	—	4	1	no	—
1412	C₂×C₈	—	4	1	no	—
1413	C₂×C₈	—	4	1	no	—
1414	C₂×C₈	—	4	1	no	—
1415	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1416	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1417	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1418	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1419	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1420	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1421	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1422	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1435	C₄⋊C₄	—	2	1	no	—
1436	C₄⋊C₄	—	2	1	no	—
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	—	2	1	no	—
1448	C₄⋊C₄	—	2	1	no	—
1449	C₄⋊C₄	—	2	1	no	—
1450	C₄⋊C₄	—	2	1	no	—
1451	C₄⋊C₄	—	2	1	no	—
1452	C₄⋊C₄	—	2	1	no	—
1453	C₄⋊C₄	—	2	1	no	—
1454	C₄⋊C₄	—	2	1	no	—
1455	C₄⋊C₄	—	2	1	no	—
1456	C₄⋊C₄	—	2	1	no	—
1457	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1458	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1459	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1460	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1461	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1462	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1463	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1464	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1465	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1466	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1467	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1468	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1469	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1470	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1484	C₂²⋊C₄	—	2	1	no	—
1485	C₂²⋊C₄	—	2	1	no	—
1486	C₂²⋊C₄	—	2	1	no	—
1487	C₂²⋊C₄	—	2	1	no	—
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	—	2	1	no	—
1496	C₂²⋊C₄	—	2	1	no	—
1497	C₂²⋊C₄	—	2	1	no	—
1498	C₂²⋊C₄	—	2	1	no	—
1499	C₂²⋊C₄	—	2	1	no	—
1500	C₂²⋊C₄	—	2	1	no	—
1501	C₂²⋊C₄	—	2	1	no	—
1502	C₂²⋊C₄	—	2	1	no	—
1503	C₂²⋊C₄	—	2	1	no	—
1504	C₂²⋊C₄	—	2	1	no	—
1505	C₂²⋊C₄	—	2	1	no	—
1506	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1507	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1508	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1509	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1510	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1511	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1512	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1513	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1514	C₄²	—	2	1	no	—
1515	C₄²	—	2	1	no	—
1516	C₄²	—	2	1	no	—
1517	C₄²	—	2	1	no	—
1518	C₄²	—	2	1	no	—
1519	C₄²	—	2	1	no	—
1520	C₄²	—	2	1	no	—
1521	C₄²	—	2	1	no	—
1522	C₄²	—	2	1	no	—
1523	C₄²	—	2	1	no	—
1524	C₄²	—	2	1	no	—
1525	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1526	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1527	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1528	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1529	C₂³	—	2	1	no	—
1530	C₂³	—	2	1	no	—
1531	C₂³	—	2	1	no	—
1532	C₂³	—	8	1	no	—
1533	C₂³	—	8	1	no	—
1534	C₂³	—	8	1	no	—
1535	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1536	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1537	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1538	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1539	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1540	Q₈	—	2	1	no	—
1541	Q₈	—	2	1	no	—
1542	Q₈	—	2	1	no	—
1543	Q₈	—	2	1	no	—
1544	Q₈	—	2	1	no	—
1545	Q₈	—	2	1	no	—
1546	Q₈	—	4	1	no	—
1547	Q₈	—	4	1	no	—
1548	Q₈	—	8	1	no	—
1549	D₄	—	2	1	no	—
1550	D₄	—	2	1	no	—
1551	D₄	—	2	1	no	—
1552	D₄	—	2	1	no	—
1553	D₄	—	2	1	no	—
1554	D₄	—	2	1	no	—
1555	D₄	—	4	1	no	—
1556	D₄	—	4	1	no	—
1557	D₄	—	4	1	no	—
1558	D₄	—	4	1	no	—
1559	D₄	—	4	1	no	—
1560	D₄	—	4	1	no	—
1561	D₄	—	4	1	no	—
1562	D₄	—	4	1	no	—
1563	D₄	—	4	1	no	—
1564	D₄	—	4	1	no	—
1565	D₄	—	4	2	no	—
1566	D₄	—	8	1	no	—
1567	D₄	—	8	1	no	—
1568	D₄	—	8	1	no	—
1569	D₄	—	8	1	no	—
1570	D₄	—	8	1	no	—
1571	D₄	—	8	1	no	—
1572	D₄	—	8	1	no	—
1573	D₄	—	8	1	no	—
1574	D₄	—	8	1	no	—
1575	D₄	—	8	1	no	—
1576	D₄	—	8	1	no	—
1577	D₄	—	8	1	no	—
1578	D₄	—	8	1	no	—
1579	C₂×C₄	—	2	1	no	—
1580	C₂×C₄	—	2	1	no	—
1581	C₂×C₄	—	2	1	no	—
1582	C₂×C₄	—	2	1	no	—
1583	C₂×C₄	—	2	1	no	—
1584	C₂×C₄	—	2	1	no	—
1585	C₂×C₄	—	2	1	no	—
1586	C₂×C₄	—	2	1	no	—
1587	C₂×C₄	—	2	1	no	—
1588	C₂×C₄	—	2	1	no	—
1589	C₂×C₄	—	2	1	no	—
1590	C₂×C₄	—	2	1	no	—
1591	C₂×C₄	—	2	1	no	—
1592	C₂×C₄	—	2	1	no	—
1593	C₂×C₄	—	2	1	no	—
1594	C₂×C₄	—	2	1	no	—
1595	C₂×C₄	—	2	1	no	—
1596	C₂×C₄	—	2	1	no	—
1597	C₂×C₄	—	2	1	no	—
1598	C₂×C₄	—	2	1	no	—
1599	C₂×C₄	—	2	1	no	—
1600	C₂×C₄	—	2	1	no	—
1601	C₂×C₄	—	2	1	no	—
1602	C₂×C₄	—	4	1	no	—
1603	C₂×C₄	—	4	1	no	—
1604	C₂×C₄	—	4	2	no	—
1605	C₂×C₄	—	8	1	no	—
1606	C₂×C₄	—	8	1	no	—
1607	C₂×C₄	—	8	1	no	—
1608	C₂×C₄	—	8	1	no	—
1609	C₂×C₄	—	8	1	no	—
1610	C₂×C₄	—	8	1	no	—
1611	C₂×C₄	—	8	1	no	—
1612	C₂×C₄	—	8	1	no	—
1613	C₂×C₄	—	8	1	no	—
1614	C₂×C₄	—	8	1	no	—
1615	C₂×C₄	—	8	1	no	—
1616	C₂×C₄	—	8	1	no	—
1617	C₂×C₄	—	8	1	no	—
1618	C₂×C₄	—	8	1	no	—
1619	C₂×C₄	—	8	1	no	—
1620	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1621	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1622	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1623	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1624	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1625	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1626	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1627	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1628	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1629	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1630	C₈	—	2	1	no	—
1631	C₈	—	2	1	no	—
1632	C₈	—	2	1	no	—
1633	C₈	—	2	1	no	—
1634	C₈	—	2	1	no	—
1635	C₈	—	2	1	no	—
1636	C₈	—	2	1	no	—
1637	C₈	—	2	1	no	—
1638	C₂²	—	2	1	no	—
1639	C₂²	—	2	1	no	—
1640	C₂²	—	2	1	no	—
1641	C₂²	—	2	1	no	—
1642	C₂²	—	2	1	no	—
1643	C₂²	—	2	1	no	—
1644	C₂²	—	2	1	no	—
1645	C₂²	—	2	1	no	—
1646	C₂²	—	2	1	no	—
1647	C₂²	—	2	1	no	—
1648	C₂²	—	2	1	no	—
1649	C₂²	—	2	1	no	—
1650	C₂²	—	2	1	no	—
1651	C₂²	—	2	1	no	—
1652	C₂²	—	2	1	no	—
1653	C₂²	—	4	1	no	—
1654	C₂²	—	4	1	no	—
1655	C₂²	—	4	1	no	—
1656	C₂²	—	4	1	no	—
1657	C₂²	—	4	1	no	—
1658	C₂²	—	4	1	no	—
1659	C₂²	—	4	1	no	—
1660	C₂²	—	4	1	no	—
1661	C₂²	—	4	1	no	—
1662	C₂²	—	16	2	no	—
1663	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1664	C₄	—	2	1	no	—
1665	C₄	—	2	1	no	—
1666	C₄	—	2	1	no	—
1667	C₄	—	2	1	no	—
1668	C₄	—	2	1	no	—
1669	C₄	—	2	1	no	—
1670	C₄	—	2	1	no	—
1671	C₄	—	2	1	no	—
1672	C₄	—	2	1	no	—
1673	C₄	—	4	1	no	—
1674	C₄	—	4	1	no	—
1675	C₄	—	4	1	no	—
1676	C₄	—	4	1	no	—
1677	C₄	—	4	1	no	—
1678	C₄	—	4	1	no	—
1679	C₄	—	4	1	no	—
1680	C₄	—	4	1	no	—
1681	C₄	—	4	1	no	—
1682	C₄	—	4	1	no	—
1683	C₄	—	4	1	no	—
1684	C₄	—	4	1	no	—
1685	C₄	—	4	1	no	—
1686	C₄	C₃₁×#585	1	1	yes	characteristic
1687	C₄	C₃₁×#585	1	1	yes	characteristic
1688	C₂	—	4	1	no	—
1689	C₂	—	4	1	no	—
1690	C₂	—	4	1	no	—
1691	C₂	—	4	1	no	—
1692	C₂	—	4	1	no	—
1693	C₂	—	8	1	no	—
1694	C₂	—	8	1	no	—
1695	C₂	—	8	1	no	—
1696	C₂	C₃₁×#3485	1	1	yes	characteristic
1697	C₂	C₃₁×#3584	1	1	yes	characteristic
1698	C₂	C₃₁×#3584	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3551	C₂	semidirect
2. C₃₁×#3512	C₂	semidirect
3. C₃₁×#3355	C₂	semidirect
4. C₃₁×#3352	C₂	semidirect
5. C₃₁×#3351	C₂	semidirect
6. C₃₁×#3351	C₂	semidirect
7. C₃₁×#3339	C₂	semidirect
8. C₃₁×#3337	C₂	semidirect
9. C₃₁×#3337	C₂	semidirect
10. C₃₁×#3336	C₂	semidirect
11. C₃₁×#3327	C₂	semidirect
12. C₃₁×#3326	C₂	semidirect
13. C₃₁×#3323	C₂	semidirect
14. C₃₁×#3322	C₂	semidirect
15. C₃₁×#3301	C₂	semidirect
16. C₃₁×#3300	C₂	semidirect
17. C₃₁×#3297	C₂	semidirect
18. C₃₁×#3296	C₂	semidirect
19. C₃₁×#3232	C₂	semidirect
20. C₃₁×#3232	C₂	semidirect
21. C₃₁×#3204	C₂	semidirect
22. C₃₁×#3203	C₂	semidirect
23. C₃₁×#3201	C₂	semidirect
24. C₃₁×#3198	C₂	semidirect
25. C₃₁×#3102	C₂	semidirect
26. C₃₁×#3102	C₂	semidirect
27. C₃₁×#3099	C₂	semidirect
28. C₃₁×#3098	C₂	semidirect
29. C₃₁×#3097	C₂	semidirect
30. C₃₁×#3096	C₂	semidirect
31. C₃₁×#2979	C₂	semidirect
43. C₃₁×#553	C₂²	semidirect
44. C₃₁×#553	C₂²	semidirect
49. C₃₁×#552	C₂²	semidirect
50. C₃₁×#552	C₂²	semidirect
65. C₃₁×#537	C₂²	semidirect
73. C₂×C₃₁×#125	C₂²	semidirect
75. C₃₁×#520	C₂²	semidirect
76. C₄×#41×C₃₁	C₂²	semidirect
77. C₃₁×#499	C₂²	semidirect
78. C₃₁×#499	C₂²	semidirect
79. C₃₁×#499	C₂²	semidirect
80. C₃₁×#499	C₂²	semidirect
88. C₃₁×#485	C₂²	semidirect
89. C₃₁×#485	C₂²	semidirect
90. C₃₁×#485	C₂²	semidirect
91. C₃₁×#485	C₂²	semidirect
92. C₃₁×#485	C₂²	semidirect
94. C₃₁×#484	C₂²	semidirect
95. C₃₁×#484	C₂²	semidirect
96. C₃₁×#484	C₂²	semidirect
97. C₃₁×#484	C₂²	semidirect
99. C₃₁×#483	C₂²	semidirect
100. C₃₁×#483	C₂²	semidirect
101. C₃₁×#483	C₂²	semidirect
102. C₃₁×#483	C₂²	semidirect
110. C₃₁×#482	C₂²	semidirect
115. C₃₁×#481	C₂²	semidirect
120. C₃₁×#480	C₂²	semidirect
121. C₃₁×#479	C₂²	semidirect
122. C₃₁×#479	C₂²	semidirect
123. C₃₁×#479	C₂²	semidirect
124. C₃₁×#479	C₂²	semidirect
125. C₃₁×#479	C₂²	semidirect
126. C₃₁×#479	C₂²	semidirect
131. C₃₁×#478	C₂²	semidirect
132. C₃₁×#478	C₂²	semidirect
134. C₃₁×#470	C₂²	semidirect
140. C₃₁×#468	C₂²	semidirect
142. C₃₁×#467	C₂²	semidirect
148. C₃₁×#465	C₂²	semidirect
155. C₃₁×#452	C₂²	semidirect
156. C₃₁×#452	C₂²	semidirect
157. C₃₁×#451	C₂²	semidirect
163. C₃₁×#448	C₂²	semidirect
165. C₄×Q₁₆×C₃₁	C₂²	semidirect
166. C₄×Q₁₆×C₃₁	C₂²	semidirect
169. C₄×SD₁₆×C₃₁	C₂²	semidirect
170. C₄×SD₁₆×C₃₁	C₂²	semidirect
175. C₃₁×#436	C₂²	semidirect
176. C₃₁×#436	C₂²	semidirect
179. C₈×D₄×C₃₁	C₂²	semidirect
180. C₈×D₄×C₃₁	C₂²	semidirect
181. C₃₁×#431	C₂²	semidirect
182. C₃₁×#431	C₂²	semidirect
184. C₃₁×#428	C₂²	semidirect
185. C₃₁×#428	C₂²	semidirect
186. C₃₁×#428	C₂²	semidirect
188. C₃₁×#427	C₂²	semidirect
189. C₂×C₃₁×#107	C₂²	semidirect
190. C₂×C₃₁×#106	C₂²	semidirect
191. C₃₁×#419	C₂²	semidirect
197. C₂×C₃₁×#103	C₂²	semidirect
201. C₃₁×#408	C₂²	semidirect
202. C₃₁×#408	C₂²	semidirect
679. #61790	C₃₁	direct (N × H)
789. #3551	C₂×C₃₁	semidirect
790. #3512	C₂×C₃₁	semidirect
791. #3355	C₂×C₃₁	semidirect
792. #3352	C₂×C₃₁	semidirect
793. #3351	C₂×C₃₁	semidirect
794. #3351	C₂×C₃₁	semidirect
795. #3339	C₂×C₃₁	semidirect
796. #3337	C₂×C₃₁	semidirect
797. #3337	C₂×C₃₁	semidirect
798. #3336	C₂×C₃₁	semidirect
799. #3327	C₂×C₃₁	semidirect
800. #3326	C₂×C₃₁	semidirect
801. #3323	C₂×C₃₁	semidirect
802. #3322	C₂×C₃₁	semidirect
803. #3301	C₂×C₃₁	semidirect
804. #3300	C₂×C₃₁	semidirect
805. #3297	C₂×C₃₁	semidirect
806. #3296	C₂×C₃₁	semidirect
807. #3232	C₂×C₃₁	semidirect
808. #3232	C₂×C₃₁	semidirect
809. #3204	C₂×C₃₁	semidirect
810. #3203	C₂×C₃₁	semidirect
811. #3201	C₂×C₃₁	semidirect
812. #3198	C₂×C₃₁	semidirect
813. #3102	C₂×C₃₁	semidirect
814. #3102	C₂×C₃₁	semidirect
815. #3099	C₂×C₃₁	semidirect
816. #3098	C₂×C₃₁	semidirect
817. #3097	C₂×C₃₁	semidirect
818. #3096	C₂×C₃₁	semidirect
819. #2979	C₂×C₃₁	semidirect
881. #553	C₂²×C₃₁	semidirect
882. #553	C₂²×C₃₁	semidirect
887. #552	C₂²×C₃₁	semidirect
888. #552	C₂²×C₃₁	semidirect
903. #537	C₂²×C₃₁	semidirect
911. C₂×#125	C₂²×C₃₁	semidirect
913. #520	C₂²×C₃₁	semidirect
914. C₄×#41	C₂²×C₃₁	semidirect
915. #499	C₂²×C₃₁	semidirect
916. #499	C₂²×C₃₁	semidirect
917. #499	C₂²×C₃₁	semidirect
918. #499	C₂²×C₃₁	semidirect
926. #485	C₂²×C₃₁	semidirect
927. #485	C₂²×C₃₁	semidirect
928. #485	C₂²×C₃₁	semidirect
929. #485	C₂²×C₃₁	semidirect
930. #485	C₂²×C₃₁	semidirect
932. #484	C₂²×C₃₁	semidirect
933. #484	C₂²×C₃₁	semidirect
934. #484	C₂²×C₃₁	semidirect
935. #484	C₂²×C₃₁	semidirect
937. #483	C₂²×C₃₁	semidirect
938. #483	C₂²×C₃₁	semidirect
939. #483	C₂²×C₃₁	semidirect
940. #483	C₂²×C₃₁	semidirect
948. #482	C₂²×C₃₁	semidirect
953. #481	C₂²×C₃₁	semidirect
958. #480	C₂²×C₃₁	semidirect
959. #479	C₂²×C₃₁	semidirect
960. #479	C₂²×C₃₁	semidirect
961. #479	C₂²×C₃₁	semidirect
962. #479	C₂²×C₃₁	semidirect
963. #479	C₂²×C₃₁	semidirect
964. #479	C₂²×C₃₁	semidirect
969. #478	C₂²×C₃₁	semidirect
970. #478	C₂²×C₃₁	semidirect
972. #470	C₂²×C₃₁	semidirect
978. #468	C₂²×C₃₁	semidirect
980. #467	C₂²×C₃₁	semidirect
986. #465	C₂²×C₃₁	semidirect
993. #452	C₂²×C₃₁	semidirect
994. #452	C₂²×C₃₁	semidirect
995. #451	C₂²×C₃₁	semidirect
1001. #448	C₂²×C₃₁	semidirect
1003. C₄×Q₁₆	C₂²×C₃₁	semidirect
1004. C₄×Q₁₆	C₂²×C₃₁	semidirect
1007. C₄×SD₁₆	C₂²×C₃₁	semidirect
1008. C₄×SD₁₆	C₂²×C₃₁	semidirect
1013. #436	C₂²×C₃₁	semidirect
1014. #436	C₂²×C₃₁	semidirect
1017. C₈×D₄	C₂²×C₃₁	semidirect
1018. C₈×D₄	C₂²×C₃₁	semidirect
1019. #431	C₂²×C₃₁	semidirect
1020. #431	C₂²×C₃₁	semidirect
1022. #428	C₂²×C₃₁	semidirect
1023. #428	C₂²×C₃₁	semidirect
1024. #428	C₂²×C₃₁	semidirect
1026. #427	C₂²×C₃₁	semidirect
1027. C₂×#107	C₂²×C₃₁	semidirect
1028. C₂×#106	C₂²×C₃₁	semidirect
1029. #419	C₂²×C₃₁	semidirect
1035. C₂×#103	C₂²×C₃₁	semidirect
1039. #408	C₂²×C₃₁	semidirect
1040. #408	C₂²×C₃₁	semidirect
1327. C₃₁	#61790	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×#3551	2
C₃₁×#3512	2
C₃₁×#3355	2
C₃₁×#3352	2
C₃₁×#3351	2
C₃₁×#3339	2
C₃₁×#3337	2
C₃₁×#3336	2
C₃₁×#3327	2
C₃₁×#3326	2
C₃₁×#3323	2
C₃₁×#3322	2
C₃₁×#3301	2
C₃₁×#3300	2
C₃₁×#3297	2
C₃₁×#3296	2
C₃₁×#3232	2
C₃₁×#3204	2
C₃₁×#3203	2
C₃₁×#3201	2
C₃₁×#3198	2
C₃₁×#3102	2
C₃₁×#3099	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#3096	2
C₃₁×#2979	2
#61790	31

Subgroups — C31×#61790 #21518549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61790 #21518549