Subgroups — C₃₁×#61919 #21518678

Order 7936.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3402	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3401	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3401	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3377	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3376	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3371	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3370	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3224	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3224	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3222	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3220	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3124	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3119	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#563	—	2	1	no	—
33	C₃₁×#563	—	2	1	no	—
34	C₃₁×#559	C₂²	1	1	yes	characteristic
35	C₃₁×#559	C₂²	1	1	yes	characteristic
36	C₃₁×#559	C₂²	1	1	yes	characteristic
37	C₃₁×#559	C₂²	1	1	yes	characteristic
38	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#556	C₂²	1	1	yes	characteristic
43	C₃₁×#556	C₂²	1	1	yes	characteristic
44	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#555	—	2	1	no	—
47	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#553	—	2	1	no	—
50	C₃₁×#553	—	2	1	no	—
51	C₃₁×#552	—	2	1	no	—
52	C₃₁×#552	—	2	1	no	—
53	C₃₁×#550	C₂²	1	1	yes	characteristic
54	C₃₁×#550	C₂²	1	1	yes	characteristic
55	C₃₁×#547	—	2	1	no	—
56	C₃₁×#542	—	2	1	no	—
57	C₃₁×#542	—	2	1	no	—
58	C₃₁×#542	C₂²	1	1	yes	characteristic
59	C₃₁×#542	C₂²	1	1	yes	characteristic
60	C₃₁×#541	C₂²	1	1	yes	characteristic
61	C₃₁×#540	C₂²	1	1	yes	characteristic
62	C₃₁×#539	—	2	1	no	—
63	C₃₁×#539	—	2	1	no	—
64	C₃₁×#538	—	2	1	no	—
65	C₃₁×#538	—	2	1	no	—
66	C₃₁×#535	C₂²	1	1	yes	characteristic
67	C₃₁×#535	C₂²	1	1	yes	characteristic
68	C₃₁×#533	C₂²	1	1	yes	characteristic
69	C₃₁×#532	C₂²	1	1	yes	characteristic
70	C₃₁×#529	C₂²	1	1	yes	characteristic
71	C₃₁×#529	C₂²	1	1	yes	characteristic
72	C₃₁×#525	—	2	1	no	—
73	C₃₁×#525	—	2	1	no	—
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#520	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#497	C₂²	1	1	yes	characteristic
78	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#496	C₂²	1	1	yes	characteristic
80	C₃₁×#496	C₂²	1	1	yes	characteristic
81	C₃₁×#496	C₂²	1	1	yes	characteristic
82	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#495	C₂²	1	1	yes	characteristic
84	C₃₁×#495	C₂²	1	1	yes	characteristic
85	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#493	C₂²	1	1	yes	characteristic
88	C₃₁×#492	C₂²	1	1	yes	characteristic
89	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#490	C₂²	1	1	yes	characteristic
91	C₃₁×#490	C₂²	1	1	yes	characteristic
92	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#489	C₂²	1	1	yes	characteristic
94	C₃₁×#489	C₂²	1	1	yes	characteristic
95	C₃₁×#488	C₂²	1	1	yes	characteristic
96	C₃₁×#488	C₂²	1	1	yes	characteristic
97	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#486	C₂²	1	1	yes	characteristic
100	C₃₁×#486	C₂²	1	1	yes	characteristic
101	C₃₁×#484	C₂²	1	1	yes	characteristic
102	C₃₁×#483	C₂²	1	1	yes	characteristic
103	C₃₁×#481	C₂²	1	1	yes	characteristic
104	C₃₁×#480	C₂²	1	1	yes	characteristic
105	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#478	C₂²	1	1	yes	characteristic
108	C₃₁×#478	C₂²	1	1	yes	characteristic
109	C₃₁×#478	C₂²	1	1	yes	characteristic
110	C₃₁×#478	C₂²	1	1	yes	characteristic
111	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#464	C₂²	1	1	yes	characteristic
118	C₃₁×#464	C₂²	1	1	yes	characteristic
119	C₃₁×#464	C₂²	1	1	yes	characteristic
120	C₃₁×#464	C₂²	1	1	yes	characteristic
121	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#463	C₂²	1	1	yes	characteristic
126	C₃₁×#463	C₂²	1	1	yes	characteristic
127	C₃₁×#463	C₂²	1	1	yes	characteristic
128	C₃₁×#463	C₂²	1	1	yes	characteristic
129	C₃₁×#463	C₂²	1	1	yes	characteristic
130	C₃₁×#463	C₂²	1	1	yes	characteristic
131	C₃₁×#463	C₂²	1	1	yes	characteristic
132	C₃₁×#463	C₂²	1	1	yes	characteristic
133	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
138	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
139	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
140	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
141	C₃₁×#460	C₂²	1	1	yes	characteristic
142	C₃₁×#460	C₂²	1	1	yes	characteristic
143	C₃₁×#460	C₂²	1	1	yes	characteristic
144	C₃₁×#460	C₂²	1	1	yes	characteristic
145	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
146	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
147	C₃₁×#459	C₂²	1	1	yes	characteristic
148	C₃₁×#459	C₂²	1	1	yes	characteristic
149	C₃₁×#459	C₂²	1	1	yes	characteristic
150	C₃₁×#459	C₂²	1	1	yes	characteristic
151	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
152	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
153	C₃₁×#452	C₂²	1	1	yes	characteristic
154	C₃₁×#452	C₂²	1	1	yes	characteristic
155	C₃₁×#452	C₂²	1	1	yes	characteristic
156	C₃₁×#452	C₂²	1	1	yes	characteristic
157	C₃₁×#450	C₂²	1	1	yes	characteristic
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×#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×#446	C₂²	1	1	yes	characteristic, complemented
168	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
169	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
170	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
171	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
172	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
173	C₃₁×#442	C₂²	1	1	yes	characteristic
174	C₃₁×#442	C₂²	1	1	yes	characteristic
175	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
176	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
177	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
178	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
179	C₃₁×#440	C₂²	1	1	yes	characteristic
180	C₃₁×#440	C₂²	1	1	yes	characteristic
181	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
182	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
183	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
184	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
185	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
186	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
187	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
188	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
189	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
190	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
191	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
192	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
193	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
194	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
195	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
196	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
197	C₃₁×#433	C₂²	1	1	yes	characteristic
198	C₃₁×#433	C₂²	1	1	yes	characteristic
199	C₃₁×#433	C₂²	1	1	yes	characteristic
200	C₃₁×#433	C₂²	1	1	yes	characteristic
201	C₃₁×#432	C₂²	1	1	yes	characteristic
202	C₃₁×#431	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×D₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₃₁	—	2	1	no	—
209	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₃₁×C₄⋊Q₈	—	2	1	no	—
234	C₃₁×C₄⋊Q₈	—	2	1	no	—
235	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
236	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
237	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
238	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
239	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
241	C₃₁×#127	C₂³	1	1	yes	characteristic
242	C₃₁×#127	C₂³	1	1	yes	characteristic
243	C₃₁×#127	C₂³	1	1	yes	characteristic
244	C₃₁×#127	C₂³	1	1	yes	characteristic
245	C₃₁×#127	C₂³	1	1	yes	characteristic
246	C₃₁×#127	C₂³	1	1	yes	characteristic
247	C₃₁×#126	—	2	1	no	—
248	C₃₁×#126	—	2	1	no	—
249	C₃₁×#126	—	2	1	no	—
250	C₃₁×#126	—	2	1	no	—
251	C₃₁×#126	—	2	1	no	—
252	C₃₁×#126	—	2	1	no	—
253	C₃₁×#126	—	2	1	no	—
254	C₃₁×#126	—	2	1	no	—
255	C₃₁×#126	—	2	1	no	—
256	C₃₁×#126	—	2	1	no	—
257	C₃₁×#126	—	2	1	no	—
258	C₃₁×#126	—	2	1	no	—
259	C₃₁×#126	—	2	1	no	—
260	C₃₁×#126	—	2	1	no	—
261	C₃₁×#125	—	2	1	no	—
262	C₃₁×#125	—	2	1	no	—
263	C₃₁×#125	—	2	1	no	—
264	C₃₁×#125	—	2	1	no	—
265	C₃₁×#125	—	2	1	no	—
266	C₃₁×#125	—	2	1	no	—
267	C₃₁×#125	D₄	1	1	yes	characteristic
268	C₃₁×#125	D₄	1	1	yes	characteristic
269	C₃₁×#125	C₂³	1	1	yes	characteristic
270	C₃₁×#125	C₂³	1	1	yes	characteristic
271	C₃₁×#125	C₂³	1	1	yes	characteristic
272	C₃₁×#125	C₂³	1	1	yes	characteristic
273	C₃₁×#124	—	2	1	no	—
274	C₃₁×#124	—	2	1	no	—
275	C₃₁×#124	—	2	1	no	—
276	C₃₁×#124	—	2	1	no	—
277	C₃₁×#124	—	2	1	no	—
278	C₃₁×#124	—	2	1	no	—
279	C₃₁×#124	—	2	1	no	—
280	C₃₁×#124	—	2	1	no	—
281	C₃₁×#124	C₂³	1	1	yes	characteristic
282	C₃₁×#124	C₂³	1	1	yes	characteristic
283	C₃₁×#124	C₂³	1	1	yes	characteristic
284	C₃₁×#124	C₂³	1	1	yes	characteristic
285	C₃₁×#124	C₂³	1	1	yes	characteristic
286	C₃₁×#124	C₂³	1	1	yes	characteristic
287	C₃₁×#124	C₂³	1	1	yes	characteristic
288	C₃₁×#124	C₂³	1	1	yes	characteristic
289	C₃₁×#124	C₂³	1	1	yes	characteristic
290	C₃₁×#124	C₂³	1	1	yes	characteristic
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×#123	—	2	1	no	—
294	C₃₁×#123	—	2	1	no	—
295	C₃₁×#123	—	2	1	no	—
296	C₃₁×#123	—	2	1	no	—
297	C₃₁×#123	—	2	1	no	—
298	C₃₁×#123	—	2	1	no	—
299	C₃₁×#123	—	2	1	no	—
300	C₃₁×#123	—	2	1	no	—
301	C₃₁×#123	—	2	1	no	—
302	C₃₁×#123	—	2	1	no	—
303	C₃₁×#123	—	2	1	no	—
304	C₃₁×#123	—	2	1	no	—
305	C₃₁×#123	—	2	1	no	—
306	C₃₁×#123	—	2	1	no	—
307	C₃₁×#123	—	2	1	no	—
308	C₃₁×#123	—	2	1	no	—
309	C₃₁×C₂²⋊Q₈	—	2	1	no	—
310	C₃₁×C₂²⋊Q₈	—	2	1	no	—
311	C₃₁×C₂²⋊Q₈	—	2	1	no	—
312	C₃₁×C₂²⋊Q₈	—	2	1	no	—
313	C₃₁×C₂²⋊Q₈	—	2	1	no	—
314	C₃₁×C₂²⋊Q₈	—	2	1	no	—
315	C₃₁×C₂²⋊Q₈	—	2	1	no	—
316	C₃₁×C₂²⋊Q₈	—	2	1	no	—
317	C₃₁×C₂²⋊Q₈	—	2	1	no	—
318	C₃₁×C₂²⋊Q₈	—	2	1	no	—
319	C₃₁×C₂²⋊Q₈	—	2	1	no	—
320	C₃₁×C₂²⋊Q₈	—	2	1	no	—
321	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
322	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
323	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
324	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
325	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
326	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
327	C₃₁×#121	—	2	1	no	—
328	C₃₁×#121	—	2	1	no	—
329	C₃₁×#121	—	2	1	no	—
330	C₃₁×#121	—	2	1	no	—
331	C₃₁×#121	—	2	1	no	—
332	C₃₁×#121	—	2	1	no	—
333	C₃₁×#121	—	2	1	no	—
334	C₃₁×#121	—	2	1	no	—
335	C₃₁×#121	—	2	1	no	—
336	C₃₁×#121	—	2	1	no	—
337	C₃₁×#121	—	2	1	no	—
338	C₃₁×#121	—	2	1	no	—
339	C₃₁×#121	—	2	1	no	—
340	C₃₁×#121	—	2	1	no	—
341	C₃₁×#121	C₂³	1	1	yes	characteristic
342	C₃₁×#121	C₂³	1	1	yes	characteristic
343	C₃₁×#120	—	2	1	no	—
344	C₃₁×#120	—	2	1	no	—
345	C₃₁×#120	—	2	1	no	—
346	C₃₁×#120	—	2	1	no	—
347	C₄×Q₈×C₃₁	—	2	1	no	—
348	C₄×Q₈×C₃₁	—	2	1	no	—
349	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
354	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
355	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
356	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
357	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
358	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
359	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
360	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
361	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₃₁	—	2	1	no	—
364	C₄×D₄×C₃₁	—	2	1	no	—
365	C₄×D₄×C₃₁	—	2	1	no	—
366	C₄×D₄×C₃₁	—	2	1	no	—
367	C₄×D₄×C₃₁	—	2	1	no	—
368	C₄×D₄×C₃₁	—	2	1	no	—
369	C₄×D₄×C₃₁	—	2	1	no	—
370	C₄×D₄×C₃₁	—	2	1	no	—
371	C₄×D₄×C₃₁	—	2	1	no	—
372	C₄×D₄×C₃₁	—	2	1	no	—
373	C₄×D₄×C₃₁	—	2	1	no	—
374	C₄×D₄×C₃₁	—	2	1	no	—
375	C₄×D₄×C₃₁	—	2	1	no	—
376	C₄×D₄×C₃₁	—	2	1	no	—
377	C₄×D₄×C₃₁	—	2	1	no	—
378	C₄×D₄×C₃₁	—	2	1	no	—
379	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
381	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
382	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
383	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
384	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
385	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
386	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
387	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
388	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
389	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
390	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
391	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
392	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
393	C₃₁×#117	—	2	1	no	—
394	C₃₁×#117	—	2	1	no	—
395	C₃₁×#117	—	2	1	no	—
396	C₃₁×#117	—	2	1	no	—
397	C₃₁×#117	—	2	1	no	—
398	C₃₁×#117	—	2	1	no	—
399	C₃₁×#117	—	2	1	no	—
400	C₃₁×#117	—	2	1	no	—
401	C₃₁×#117	C₂³	1	1	yes	characteristic
402	C₃₁×#117	C₂³	1	1	yes	characteristic
403	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
408	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂×C₄²×C₃₁	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
419	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
420	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
421	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
422	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
423	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
424	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×#103	C₂³	1	1	yes	characteristic
431	C₃₁×#103	C₂³	1	1	yes	characteristic
432	C₃₁×#103	C₂³	1	1	yes	characteristic
433	C₃₁×#103	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#102	C₂³	1	1	yes	characteristic
443	C₃₁×#102	C₂³	1	1	yes	characteristic
444	C₃₁×#102	C₂³	1	1	yes	characteristic
445	C₃₁×#102	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×#97	C₂³	1	1	yes	characteristic
467	C₃₁×#97	C₂³	1	1	yes	characteristic
468	C₃₁×#97	C₂³	1	1	yes	characteristic
469	C₃₁×#97	C₂³	1	1	yes	characteristic
470	C₃₁×#97	C₂³	1	1	yes	characteristic
471	C₃₁×#97	C₂³	1	1	yes	characteristic
472	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
473	C₄×C₈×C₃₁	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	—	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	C₂×D₄	1	1	yes	characteristic
488	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
489	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
490	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
491	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
492	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
493	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₂×D₄×C₃₁	—	2	1	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	—	2	1	no	—
510	C₂×D₄×C₃₁	—	2	1	no	—
511	C₂×D₄×C₃₁	—	2	1	no	—
512	C₂×D₄×C₃₁	—	4	1	no	—
513	C₂×D₄×C₃₁	—	4	1	no	—
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	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
518	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
519	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
535	C₂²×C₄×C₃₁	—	2	1	no	—
536	C₂²×C₄×C₃₁	—	2	1	no	—
537	C₂²×C₄×C₃₁	—	8	2	no	—
538	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
539	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
540	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
541	Q₁₆×C₃₁	—	4	1	no	—
542	Q₁₆×C₃₁	—	4	1	no	—
543	Q₁₆×C₃₁	—	4	1	no	—
544	Q₁₆×C₃₁	—	4	1	no	—
545	SD₁₆×C₃₁	—	4	1	no	—
546	SD₁₆×C₃₁	—	4	1	no	—
547	SD₁₆×C₃₁	—	4	1	no	—
548	SD₁₆×C₃₁	—	4	1	no	—
549	SD₁₆×C₃₁	—	4	1	no	—
550	SD₁₆×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	SD₁₆×C₃₁	—	4	1	no	—
556	SD₁₆×C₃₁	—	4	1	no	—
557	D₈×C₃₁	—	4	1	no	—
558	D₈×C₃₁	—	4	1	no	—
559	D₈×C₃₁	—	4	1	no	—
560	D₈×C₃₁	—	4	1	no	—
561	D₈×C₃₁	—	4	1	no	—
562	D₈×C₃₁	—	4	1	no	—
563	D₈×C₃₁	—	4	1	no	—
564	D₈×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	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
615	C₄⋊C₄×C₃₁	C₂×D₄	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	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
657	C₂²⋊C₄×C₃₁	—	2	1	no	—
658	C₂²⋊C₄×C₃₁	—	2	1	no	—
659	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
675	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
676	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
677	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
678	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
679	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
680	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
681	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
682	#61919	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
683	C₂³×C₃₁	—	2	1	no	—
684	C₂³×C₃₁	—	2	1	no	—
685	C₂³×C₃₁	—	2	1	no	—
686	C₂³×C₃₁	—	2	1	no	—
687	C₂³×C₃₁	—	2	1	no	—
688	C₂³×C₃₁	—	2	1	no	—
689	C₂³×C₃₁	—	4	2	no	—
690	C₂³×C₃₁	—	8	1	no	—
691	C₂³×C₃₁	—	8	1	no	—
692	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
693	Q₈×C₃₁	—	2	1	no	—
694	Q₈×C₃₁	—	2	1	no	—
695	Q₈×C₃₁	—	2	1	no	—
696	Q₈×C₃₁	—	2	1	no	—
697	Q₈×C₃₁	—	2	1	no	—
698	Q₈×C₃₁	—	2	1	no	—
699	Q₈×C₃₁	—	2	1	no	—
700	Q₈×C₃₁	—	2	1	no	—
701	Q₈×C₃₁	—	4	1	no	—
702	Q₈×C₃₁	—	4	1	no	—
703	Q₈×C₃₁	—	4	1	no	—
704	Q₈×C₃₁	—	4	1	no	—
705	Q₈×C₃₁	—	8	1	no	—
706	Q₈×C₃₁	—	8	1	no	—
707	D₄×C₃₁	—	2	1	no	—
708	D₄×C₃₁	—	2	1	no	—
709	D₄×C₃₁	—	2	1	no	—
710	D₄×C₃₁	—	2	1	no	—
711	D₄×C₃₁	—	2	1	no	—
712	D₄×C₃₁	—	2	1	no	—
713	D₄×C₃₁	—	2	1	no	—
714	D₄×C₃₁	—	2	1	no	—
715	D₄×C₃₁	—	2	1	no	—
716	D₄×C₃₁	—	2	1	no	—
717	D₄×C₃₁	—	2	1	no	—
718	D₄×C₃₁	—	2	1	no	—
719	D₄×C₃₁	—	4	2	no	—
720	D₄×C₃₁	—	4	2	no	—
721	D₄×C₃₁	—	4	2	no	—
722	D₄×C₃₁	—	4	2	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	D₄×C₃₁	—	8	1	no	—
731	D₄×C₃₁	—	8	1	no	—
732	D₄×C₃₁	—	8	1	no	—
733	D₄×C₃₁	—	8	1	no	—
734	D₄×C₃₁	—	8	1	no	—
735	D₄×C₃₁	—	8	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	—	4	1	no	—
749	C₂×C₄×C₃₁	—	4	1	no	—
750	C₂×C₄×C₃₁	—	4	2	no	—
751	C₂×C₄×C₃₁	—	4	2	no	—
752	C₂×C₄×C₃₁	—	4	2	no	—
753	C₂×C₄×C₃₁	—	4	2	no	—
754	C₂×C₄×C₃₁	—	8	1	no	—
755	C₂×C₄×C₃₁	—	8	1	no	—
756	C₂×C₄×C₃₁	—	8	1	no	—
757	C₂×C₄×C₃₁	—	8	1	no	—
758	C₂×C₄×C₃₁	—	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	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
770	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	#3557	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3403	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3402	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3401	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3401	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3370	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3224	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#3224	C₂×C₃₁	1	1	yes	characteristic, complemented
809	#3222	C₂×C₃₁	1	1	yes	characteristic, complemented
810	#3220	C₂×C₃₁	1	1	yes	characteristic, complemented
811	#3219	C₂×C₃₁	1	1	yes	characteristic, complemented
812	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
813	#3125	C₂×C₃₁	1	1	yes	characteristic, complemented
814	#3124	C₂×C₃₁	1	1	yes	characteristic, complemented
815	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
816	#3119	C₂×C₃₁	1	1	yes	characteristic, complemented
817	#3114	C₂×C₃₁	1	1	yes	characteristic, complemented
818	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
819	#2985	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	—	4	1	no	—
824	C₂²×C₃₁	—	4	1	no	—
825	C₂²×C₃₁	—	4	1	no	—
826	C₂²×C₃₁	—	4	1	no	—
827	C₂²×C₃₁	—	4	1	no	—
828	C₂²×C₃₁	—	4	1	no	—
829	C₂²×C₃₁	—	4	1	no	—
830	C₂²×C₃₁	—	4	1	no	—
831	C₂²×C₃₁	—	4	1	no	—
832	C₂²×C₃₁	—	4	1	no	—
833	C₂²×C₃₁	—	4	1	no	—
834	C₂²×C₃₁	—	4	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	—	8	4	no	—
842	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
843	C₄×C₃₁	—	2	1	no	—
844	C₄×C₃₁	—	2	1	no	—
845	C₄×C₃₁	—	2	1	no	—
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	—	2	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	#585	1	1	yes	characteristic
867	C₄×C₃₁	#585	1	1	yes	characteristic
868	#563	—	2	1	no	—
869	#563	—	2	1	no	—
870	#559	C₂²×C₃₁	1	1	yes	characteristic
871	#559	C₂²×C₃₁	1	1	yes	characteristic
872	#559	C₂²×C₃₁	1	1	yes	characteristic
873	#559	C₂²×C₃₁	1	1	yes	characteristic
874	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
875	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
876	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
877	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
878	#556	C₂²×C₃₁	1	1	yes	characteristic
879	#556	C₂²×C₃₁	1	1	yes	characteristic
880	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
881	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
882	#555	—	2	1	no	—
883	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
884	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
885	#553	—	2	1	no	—
886	#553	—	2	1	no	—
887	#552	—	2	1	no	—
888	#552	—	2	1	no	—
889	#550	C₂²×C₃₁	1	1	yes	characteristic
890	#550	C₂²×C₃₁	1	1	yes	characteristic
891	#547	—	2	1	no	—
892	#542	—	2	1	no	—
893	#542	—	2	1	no	—
894	#542	C₂²×C₃₁	1	1	yes	characteristic
895	#542	C₂²×C₃₁	1	1	yes	characteristic
896	#541	C₂²×C₃₁	1	1	yes	characteristic
897	#540	C₂²×C₃₁	1	1	yes	characteristic
898	#539	—	2	1	no	—
899	#539	—	2	1	no	—
900	#538	—	2	1	no	—
901	#538	—	2	1	no	—
902	#535	C₂²×C₃₁	1	1	yes	characteristic
903	#535	C₂²×C₃₁	1	1	yes	characteristic
904	#533	C₂²×C₃₁	1	1	yes	characteristic
905	#532	C₂²×C₃₁	1	1	yes	characteristic
906	#529	C₂²×C₃₁	1	1	yes	characteristic
907	#529	C₂²×C₃₁	1	1	yes	characteristic
908	#525	—	2	1	no	—
909	#525	—	2	1	no	—
910	#520	C₂²×C₃₁	1	1	yes	characteristic
911	#520	C₂²×C₃₁	1	1	yes	characteristic
912	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
913	#497	C₂²×C₃₁	1	1	yes	characteristic
914	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#496	C₂²×C₃₁	1	1	yes	characteristic
916	#496	C₂²×C₃₁	1	1	yes	characteristic
917	#496	C₂²×C₃₁	1	1	yes	characteristic
918	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
919	#495	C₂²×C₃₁	1	1	yes	characteristic
920	#495	C₂²×C₃₁	1	1	yes	characteristic
921	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
922	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
923	#493	C₂²×C₃₁	1	1	yes	characteristic
924	#492	C₂²×C₃₁	1	1	yes	characteristic
925	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
926	#490	C₂²×C₃₁	1	1	yes	characteristic
927	#490	C₂²×C₃₁	1	1	yes	characteristic
928	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
929	#489	C₂²×C₃₁	1	1	yes	characteristic
930	#489	C₂²×C₃₁	1	1	yes	characteristic
931	#488	C₂²×C₃₁	1	1	yes	characteristic
932	#488	C₂²×C₃₁	1	1	yes	characteristic
933	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
934	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
935	#486	C₂²×C₃₁	1	1	yes	characteristic
936	#486	C₂²×C₃₁	1	1	yes	characteristic
937	#484	C₂²×C₃₁	1	1	yes	characteristic
938	#483	C₂²×C₃₁	1	1	yes	characteristic
939	#481	C₂²×C₃₁	1	1	yes	characteristic
940	#480	C₂²×C₃₁	1	1	yes	characteristic
941	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
942	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
943	#478	C₂²×C₃₁	1	1	yes	characteristic
944	#478	C₂²×C₃₁	1	1	yes	characteristic
945	#478	C₂²×C₃₁	1	1	yes	characteristic
946	#478	C₂²×C₃₁	1	1	yes	characteristic
947	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
948	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
949	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
950	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
951	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
952	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
953	#464	C₂²×C₃₁	1	1	yes	characteristic
954	#464	C₂²×C₃₁	1	1	yes	characteristic
955	#464	C₂²×C₃₁	1	1	yes	characteristic
956	#464	C₂²×C₃₁	1	1	yes	characteristic
957	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
958	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
959	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
960	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
961	#463	C₂²×C₃₁	1	1	yes	characteristic
962	#463	C₂²×C₃₁	1	1	yes	characteristic
963	#463	C₂²×C₃₁	1	1	yes	characteristic
964	#463	C₂²×C₃₁	1	1	yes	characteristic
965	#463	C₂²×C₃₁	1	1	yes	characteristic
966	#463	C₂²×C₃₁	1	1	yes	characteristic
967	#463	C₂²×C₃₁	1	1	yes	characteristic
968	#463	C₂²×C₃₁	1	1	yes	characteristic
969	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
970	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
972	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
973	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
974	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
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
978	#460	C₂²×C₃₁	1	1	yes	characteristic
979	#460	C₂²×C₃₁	1	1	yes	characteristic
980	#460	C₂²×C₃₁	1	1	yes	characteristic
981	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
982	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
983	#459	C₂²×C₃₁	1	1	yes	characteristic
984	#459	C₂²×C₃₁	1	1	yes	characteristic
985	#459	C₂²×C₃₁	1	1	yes	characteristic
986	#459	C₂²×C₃₁	1	1	yes	characteristic
987	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
988	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
989	#452	C₂²×C₃₁	1	1	yes	characteristic
990	#452	C₂²×C₃₁	1	1	yes	characteristic
991	#452	C₂²×C₃₁	1	1	yes	characteristic
992	#452	C₂²×C₃₁	1	1	yes	characteristic
993	#450	C₂²×C₃₁	1	1	yes	characteristic
994	#450	C₂²×C₃₁	1	1	yes	characteristic
995	#449	C₂²×C₃₁	1	1	yes	characteristic
996	#449	C₂²×C₃₁	1	1	yes	characteristic
997	#449	C₂²×C₃₁	1	1	yes	characteristic
998	#449	C₂²×C₃₁	1	1	yes	characteristic
999	#447	C₂²×C₃₁	1	1	yes	characteristic
1000	#447	C₂²×C₃₁	1	1	yes	characteristic
1001	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1003	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1004	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1006	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
1007	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1008	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1009	#442	C₂²×C₃₁	1	1	yes	characteristic
1010	#442	C₂²×C₃₁	1	1	yes	characteristic
1011	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
1012	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
1013	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
1014	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
1015	#440	C₂²×C₃₁	1	1	yes	characteristic
1016	#440	C₂²×C₃₁	1	1	yes	characteristic
1017	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1018	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1019	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1020	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1021	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1022	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1023	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1024	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1025	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1026	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1027	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1028	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1029	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1030	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1031	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1032	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1033	#433	C₂²×C₃₁	1	1	yes	characteristic
1034	#433	C₂²×C₃₁	1	1	yes	characteristic
1035	#433	C₂²×C₃₁	1	1	yes	characteristic
1036	#433	C₂²×C₃₁	1	1	yes	characteristic
1037	#432	C₂²×C₃₁	1	1	yes	characteristic
1038	#431	C₂²×C₃₁	1	1	yes	characteristic
1039	C₂×C₃₁	—	4	1	no	—
1040	C₂×C₃₁	—	8	1	no	—
1041	C₂×C₃₁	—	8	1	no	—
1042	C₂×C₃₁	—	8	1	no	—
1043	C₂×C₃₁	—	8	1	no	—
1044	C₂×C₃₁	—	8	1	no	—
1045	C₂×C₃₁	—	8	1	no	—
1046	C₂×C₃₁	#3487	1	1	yes	characteristic
1047	C₂×C₃₁	#3584	1	1	yes	characteristic
1048	C₂×C₃₁	#3585	1	1	yes	characteristic
1049	C₂×#41	—	2	1	no	—
1050	C₂×#41	—	2	1	no	—
1051	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂³×C₄	—	2	1	no	—
1055	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1059	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1060	C₂×SD₁₆	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×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1066	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1067	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1068	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1069	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1070	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1071	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1072	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1073	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1074	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1075	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1076	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1077	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1078	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1079	C₄⋊Q₈	—	2	1	no	—
1080	C₄⋊Q₈	—	2	1	no	—
1081	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1082	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1083	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1084	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1085	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1086	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1087	#127	C₂³×C₃₁	1	1	yes	characteristic
1088	#127	C₂³×C₃₁	1	1	yes	characteristic
1089	#127	C₂³×C₃₁	1	1	yes	characteristic
1090	#127	C₂³×C₃₁	1	1	yes	characteristic
1091	#127	C₂³×C₃₁	1	1	yes	characteristic
1092	#127	C₂³×C₃₁	1	1	yes	characteristic
1093	#126	—	2	1	no	—
1094	#126	—	2	1	no	—
1095	#126	—	2	1	no	—
1096	#126	—	2	1	no	—
1097	#126	—	2	1	no	—
1098	#126	—	2	1	no	—
1099	#126	—	2	1	no	—
1100	#126	—	2	1	no	—
1101	#126	—	2	1	no	—
1102	#126	—	2	1	no	—
1103	#126	—	2	1	no	—
1104	#126	—	2	1	no	—
1105	#126	—	2	1	no	—
1106	#126	—	2	1	no	—
1107	#125	—	2	1	no	—
1108	#125	—	2	1	no	—
1109	#125	—	2	1	no	—
1110	#125	—	2	1	no	—
1111	#125	—	2	1	no	—
1112	#125	—	2	1	no	—
1113	#125	D₄×C₃₁	1	1	yes	characteristic
1114	#125	D₄×C₃₁	1	1	yes	characteristic
1115	#125	C₂³×C₃₁	1	1	yes	characteristic
1116	#125	C₂³×C₃₁	1	1	yes	characteristic
1117	#125	C₂³×C₃₁	1	1	yes	characteristic
1118	#125	C₂³×C₃₁	1	1	yes	characteristic
1119	#124	—	2	1	no	—
1120	#124	—	2	1	no	—
1121	#124	—	2	1	no	—
1122	#124	—	2	1	no	—
1123	#124	—	2	1	no	—
1124	#124	—	2	1	no	—
1125	#124	—	2	1	no	—
1126	#124	—	2	1	no	—
1127	#124	C₂³×C₃₁	1	1	yes	characteristic
1128	#124	C₂³×C₃₁	1	1	yes	characteristic
1129	#124	C₂³×C₃₁	1	1	yes	characteristic
1130	#124	C₂³×C₃₁	1	1	yes	characteristic
1131	#124	C₂³×C₃₁	1	1	yes	characteristic
1132	#124	C₂³×C₃₁	1	1	yes	characteristic
1133	#124	C₂³×C₃₁	1	1	yes	characteristic
1134	#124	C₂³×C₃₁	1	1	yes	characteristic
1135	#124	C₂³×C₃₁	1	1	yes	characteristic
1136	#124	C₂³×C₃₁	1	1	yes	characteristic
1137	#123	—	2	1	no	—
1138	#123	—	2	1	no	—
1139	#123	—	2	1	no	—
1140	#123	—	2	1	no	—
1141	#123	—	2	1	no	—
1142	#123	—	2	1	no	—
1143	#123	—	2	1	no	—
1144	#123	—	2	1	no	—
1145	#123	—	2	1	no	—
1146	#123	—	2	1	no	—
1147	#123	—	2	1	no	—
1148	#123	—	2	1	no	—
1149	#123	—	2	1	no	—
1150	#123	—	2	1	no	—
1151	#123	—	2	1	no	—
1152	#123	—	2	1	no	—
1153	#123	—	2	1	no	—
1154	#123	—	2	1	no	—
1155	C₂²⋊Q₈	—	2	1	no	—
1156	C₂²⋊Q₈	—	2	1	no	—
1157	C₂²⋊Q₈	—	2	1	no	—
1158	C₂²⋊Q₈	—	2	1	no	—
1159	C₂²⋊Q₈	—	2	1	no	—
1160	C₂²⋊Q₈	—	2	1	no	—
1161	C₂²⋊Q₈	—	2	1	no	—
1162	C₂²⋊Q₈	—	2	1	no	—
1163	C₂²⋊Q₈	—	2	1	no	—
1164	C₂²⋊Q₈	—	2	1	no	—
1165	C₂²⋊Q₈	—	2	1	no	—
1166	C₂²⋊Q₈	—	2	1	no	—
1167	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1168	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1169	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1170	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1171	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1172	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1173	#121	—	2	1	no	—
1174	#121	—	2	1	no	—
1175	#121	—	2	1	no	—
1176	#121	—	2	1	no	—
1177	#121	—	2	1	no	—
1178	#121	—	2	1	no	—
1179	#121	—	2	1	no	—
1180	#121	—	2	1	no	—
1181	#121	—	2	1	no	—
1182	#121	—	2	1	no	—
1183	#121	—	2	1	no	—
1184	#121	—	2	1	no	—
1185	#121	—	2	1	no	—
1186	#121	—	2	1	no	—
1187	#121	C₂³×C₃₁	1	1	yes	characteristic
1188	#121	C₂³×C₃₁	1	1	yes	characteristic
1189	#120	—	2	1	no	—
1190	#120	—	2	1	no	—
1191	#120	—	2	1	no	—
1192	#120	—	2	1	no	—
1193	C₄×Q₈	—	2	1	no	—
1194	C₄×Q₈	—	2	1	no	—
1195	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1196	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1197	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1198	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1199	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1200	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1201	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1202	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1203	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1204	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1205	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1206	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1207	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1208	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1214	C₄×D₄	—	2	1	no	—
1215	C₄×D₄	—	2	1	no	—
1216	C₄×D₄	—	2	1	no	—
1217	C₄×D₄	—	2	1	no	—
1218	C₄×D₄	—	2	1	no	—
1219	C₄×D₄	—	2	1	no	—
1220	C₄×D₄	—	2	1	no	—
1221	C₄×D₄	—	2	1	no	—
1222	C₄×D₄	—	2	1	no	—
1223	C₄×D₄	—	2	1	no	—
1224	C₄×D₄	—	2	1	no	—
1225	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1226	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1227	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1228	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1229	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1230	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1231	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1232	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1233	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1234	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1235	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1236	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1237	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1238	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1239	#117	—	2	1	no	—
1240	#117	—	2	1	no	—
1241	#117	—	2	1	no	—
1242	#117	—	2	1	no	—
1243	#117	—	2	1	no	—
1244	#117	—	2	1	no	—
1245	#117	—	2	1	no	—
1246	#117	—	2	1	no	—
1247	#117	C₂³×C₃₁	1	1	yes	characteristic
1248	#117	C₂³×C₃₁	1	1	yes	characteristic
1249	C₂×C₄⋊C₄	—	2	1	no	—
1250	C₂×C₄⋊C₄	—	2	1	no	—
1251	C₂×C₄⋊C₄	—	2	1	no	—
1252	C₂×C₄⋊C₄	—	2	1	no	—
1253	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1254	C₂×C₂²⋊C₄	—	2	1	no	—
1255	C₂×C₄²	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	#106	C₂³×C₃₁	1	1	yes	characteristic
1261	#106	C₂³×C₃₁	1	1	yes	characteristic
1262	#106	C₂³×C₃₁	1	1	yes	characteristic
1263	#106	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1267	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1268	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1269	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1270	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1271	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1272	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1273	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1274	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1275	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1276	#103	C₂³×C₃₁	1	1	yes	characteristic
1277	#103	C₂³×C₃₁	1	1	yes	characteristic
1278	#103	C₂³×C₃₁	1	1	yes	characteristic
1279	#103	C₂³×C₃₁	1	1	yes	characteristic
1280	#103	C₂³×C₃₁	1	1	yes	characteristic
1281	#103	C₂³×C₃₁	1	1	yes	characteristic
1282	#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	#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	#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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1309	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1310	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1311	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1312	#97	C₂³×C₃₁	1	1	yes	characteristic
1313	#97	C₂³×C₃₁	1	1	yes	characteristic
1314	#97	C₂³×C₃₁	1	1	yes	characteristic
1315	#97	C₂³×C₃₁	1	1	yes	characteristic
1316	#97	C₂³×C₃₁	1	1	yes	characteristic
1317	#97	C₂³×C₃₁	1	1	yes	characteristic
1318	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1319	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1320	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1321	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1322	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1323	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1324	C₃₁	#61919	1	1	yes	characteristic, direct product factor, Sylow
1325	C₂⁴	—	2	1	no	—
1326	#41	—	4	1	no	—
1327	#41	—	4	1	no	—
1328	#41	—	4	1	no	—
1329	#41	—	4	1	no	—
1330	#41	—	8	2	no	—
1331	#41	—	8	2	no	—
1332	C₂×Q₈	—	2	1	no	—
1333	C₂×Q₈	—	2	1	no	—
1334	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1335	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1336	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1337	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1338	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1339	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1340	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1341	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1342	C₂×D₄	—	2	1	no	—
1343	C₂×D₄	—	2	1	no	—
1344	C₂×D₄	—	2	1	no	—
1345	C₂×D₄	—	2	1	no	—
1346	C₂×D₄	—	2	1	no	—
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	—	4	1	no	—
1360	C₂×D₄	—	4	1	no	—
1361	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1362	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1363	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1364	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1365	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1366	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1367	C₂²×C₄	—	2	1	no	—
1368	C₂²×C₄	—	2	1	no	—
1369	C₂²×C₄	—	2	1	no	—
1370	C₂²×C₄	—	2	1	no	—
1371	C₂²×C₄	—	2	1	no	—
1372	C₂²×C₄	—	2	1	no	—
1373	C₂²×C₄	—	2	1	no	—
1374	C₂²×C₄	—	2	1	no	—
1375	C₂²×C₄	—	2	1	no	—
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	—	8	2	no	—
1385	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1386	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1387	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1388	Q₁₆	—	4	1	no	—
1389	Q₁₆	—	4	1	no	—
1390	Q₁₆	—	4	1	no	—
1391	Q₁₆	—	4	1	no	—
1392	SD₁₆	—	4	1	no	—
1393	SD₁₆	—	4	1	no	—
1394	SD₁₆	—	4	1	no	—
1395	SD₁₆	—	4	1	no	—
1396	SD₁₆	—	4	1	no	—
1397	SD₁₆	—	4	1	no	—
1398	SD₁₆	—	4	1	no	—
1399	SD₁₆	—	4	1	no	—
1400	SD₁₆	—	4	1	no	—
1401	SD₁₆	—	4	1	no	—
1402	SD₁₆	—	4	1	no	—
1403	SD₁₆	—	4	1	no	—
1404	D₈	—	4	1	no	—
1405	D₈	—	4	1	no	—
1406	D₈	—	4	1	no	—
1407	D₈	—	4	1	no	—
1408	D₈	—	4	1	no	—
1409	D₈	—	4	1	no	—
1410	D₈	—	4	1	no	—
1411	D₈	—	4	1	no	—
1412	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1413	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1414	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
1421	C₄⋊C₄	—	2	1	no	—
1422	C₄⋊C₄	—	2	1	no	—
1423	C₄⋊C₄	—	2	1	no	—
1424	C₄⋊C₄	—	2	1	no	—
1425	C₄⋊C₄	—	2	1	no	—
1426	C₄⋊C₄	—	2	1	no	—
1427	C₄⋊C₄	—	2	1	no	—
1428	C₄⋊C₄	—	2	1	no	—
1429	C₄⋊C₄	—	2	1	no	—
1430	C₄⋊C₄	—	2	1	no	—
1431	C₄⋊C₄	—	2	1	no	—
1432	C₄⋊C₄	—	2	1	no	—
1433	C₄⋊C₄	—	2	1	no	—
1434	C₄⋊C₄	—	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	C₂×D₄×C₃₁	1	1	yes	characteristic
1448	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1449	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1450	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1451	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1452	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1453	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1454	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1455	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1456	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1462	C₄⋊C₄	C₂×D₄×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	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	—	2	1	no	—
1476	C₂²⋊C₄	—	2	1	no	—
1477	C₂²⋊C₄	—	2	1	no	—
1478	C₂²⋊C₄	—	2	1	no	—
1479	C₂²⋊C₄	—	2	1	no	—
1480	C₂²⋊C₄	—	2	1	no	—
1481	C₂²⋊C₄	—	2	1	no	—
1482	C₂²⋊C₄	—	2	1	no	—
1483	C₂²⋊C₄	—	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	—	2	1	no	—
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	C₄²	—	2	1	no	—
1512	C₄²	—	2	1	no	—
1513	C₄²	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1522	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1523	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1524	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1525	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1526	C₄²	C₂⁴×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	—	2	1	no	—
1533	C₂³	—	2	1	no	—
1534	C₂³	—	2	1	no	—
1535	C₂³	—	4	2	no	—
1536	C₂³	—	8	1	no	—
1537	C₂³	—	8	1	no	—
1538	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1539	Q₈	—	2	1	no	—
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	—	2	1	no	—
1547	Q₈	—	4	1	no	—
1548	Q₈	—	4	1	no	—
1549	Q₈	—	4	1	no	—
1550	Q₈	—	4	1	no	—
1551	Q₈	—	8	1	no	—
1552	Q₈	—	8	1	no	—
1553	D₄	—	2	1	no	—
1554	D₄	—	2	1	no	—
1555	D₄	—	2	1	no	—
1556	D₄	—	2	1	no	—
1557	D₄	—	2	1	no	—
1558	D₄	—	2	1	no	—
1559	D₄	—	2	1	no	—
1560	D₄	—	2	1	no	—
1561	D₄	—	2	1	no	—
1562	D₄	—	2	1	no	—
1563	D₄	—	2	1	no	—
1564	D₄	—	2	1	no	—
1565	D₄	—	4	2	no	—
1566	D₄	—	4	2	no	—
1567	D₄	—	4	2	no	—
1568	D₄	—	4	2	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	D₄	—	8	1	no	—
1580	D₄	—	8	1	no	—
1581	D₄	—	8	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	—	4	1	no	—
1595	C₂×C₄	—	4	1	no	—
1596	C₂×C₄	—	4	2	no	—
1597	C₂×C₄	—	4	2	no	—
1598	C₂×C₄	—	4	2	no	—
1599	C₂×C₄	—	4	2	no	—
1600	C₂×C₄	—	8	1	no	—
1601	C₂×C₄	—	8	1	no	—
1602	C₂×C₄	—	8	1	no	—
1603	C₂×C₄	—	8	1	no	—
1604	C₂×C₄	—	8	1	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	C₂²×D₄×C₃₁	1	1	yes	characteristic
1614	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1615	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1616	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1617	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1618	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1619	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁵×C₃₁	1	1	yes	characteristic
1627	C₈	—	2	1	no	—
1628	C₈	—	2	1	no	—
1629	C₈	—	2	1	no	—
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	C₂²	—	2	1	no	—
1636	C₂²	—	2	1	no	—
1637	C₂²	—	2	1	no	—
1638	C₂²	—	4	1	no	—
1639	C₂²	—	4	1	no	—
1640	C₂²	—	4	1	no	—
1641	C₂²	—	4	1	no	—
1642	C₂²	—	4	1	no	—
1643	C₂²	—	4	1	no	—
1644	C₂²	—	4	1	no	—
1645	C₂²	—	4	1	no	—
1646	C₂²	—	4	1	no	—
1647	C₂²	—	4	1	no	—
1648	C₂²	—	4	1	no	—
1649	C₂²	—	4	1	no	—
1650	C₂²	—	4	1	no	—
1651	C₂²	—	4	1	no	—
1652	C₂²	—	4	1	no	—
1653	C₂²	—	4	1	no	—
1654	C₂²	—	4	1	no	—
1655	C₂²	—	4	1	no	—
1656	C₂²	—	8	4	no	—
1657	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1658	C₄	—	2	1	no	—
1659	C₄	—	2	1	no	—
1660	C₄	—	2	1	no	—
1661	C₄	—	2	1	no	—
1662	C₄	—	2	1	no	—
1663	C₄	—	2	1	no	—
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	—	4	1	no	—
1672	C₄	—	4	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	C₃₁×#585	1	1	yes	characteristic
1682	C₄	C₃₁×#585	1	1	yes	characteristic
1683	C₂	—	4	1	no	—
1684	C₂	—	8	1	no	—
1685	C₂	—	8	1	no	—
1686	C₂	—	8	1	no	—
1687	C₂	—	8	1	no	—
1688	C₂	—	8	1	no	—
1689	C₂	—	8	1	no	—
1690	C₂	C₃₁×#3487	1	1	yes	characteristic
1691	C₂	C₃₁×#3584	1	1	yes	characteristic
1692	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3557	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3402	C₂	semidirect
5. C₃₁×#3401	C₂	semidirect
6. C₃₁×#3401	C₂	semidirect
7. C₃₁×#3399	C₂	semidirect
8. C₃₁×#3397	C₂	semidirect
9. C₃₁×#3396	C₂	semidirect
10. C₃₁×#3394	C₂	semidirect
11. C₃₁×#3377	C₂	semidirect
12. C₃₁×#3376	C₂	semidirect
13. C₃₁×#3371	C₂	semidirect
14. C₃₁×#3370	C₂	semidirect
15. C₃₁×#3368	C₂	semidirect
16. C₃₁×#3366	C₂	semidirect
17. C₃₁×#3365	C₂	semidirect
18. C₃₁×#3361	C₂	semidirect
19. C₃₁×#3224	C₂	semidirect
20. C₃₁×#3224	C₂	semidirect
21. C₃₁×#3222	C₂	semidirect
22. C₃₁×#3220	C₂	semidirect
23. C₃₁×#3219	C₂	semidirect
24. C₃₁×#3212	C₂	semidirect
25. C₃₁×#3125	C₂	semidirect
26. C₃₁×#3124	C₂	semidirect
27. C₃₁×#3120	C₂	semidirect
28. C₃₁×#3119	C₂	semidirect
29. C₃₁×#3114	C₂	semidirect
30. C₃₁×#3105	C₂	semidirect
31. C₃₁×#2985	C₂	semidirect
38. C₃₁×#559	C₂²	semidirect
39. C₃₁×#559	C₂²	semidirect
40. C₃₁×#557	C₂²	semidirect
41. C₃₁×#557	C₂²	semidirect
44. C₃₁×#556	C₂²	semidirect
45. C₃₁×#556	C₂²	semidirect
47. C₃₁×#554	C₂²	semidirect
48. C₃₁×#554	C₂²	semidirect
78. C₃₁×#497	C₂²	semidirect
82. C₃₁×#496	C₂²	semidirect
85. C₃₁×#495	C₂²	semidirect
86. C₃₁×#495	C₂²	semidirect
89. C₃₁×#491	C₂²	semidirect
92. C₃₁×#490	C₂²	semidirect
97. C₃₁×#488	C₂²	semidirect
98. C₃₁×#488	C₂²	semidirect
105. C₃₁×#479	C₂²	semidirect
106. C₃₁×#479	C₂²	semidirect
111. C₃₁×#478	C₂²	semidirect
112. C₃₁×#478	C₂²	semidirect
113. C₃₁×#477	C₂²	semidirect
114. C₃₁×#476	C₂²	semidirect
115. C₃₁×#475	C₂²	semidirect
116. C₃₁×#474	C₂²	semidirect
121. C₃₁×#464	C₂²	semidirect
122. C₃₁×#464	C₂²	semidirect
123. C₃₁×#464	C₂²	semidirect
124. C₃₁×#464	C₂²	semidirect
133. C₃₁×#463	C₂²	semidirect
134. C₃₁×#463	C₂²	semidirect
135. C₃₁×#463	C₂²	semidirect
136. C₃₁×#463	C₂²	semidirect
137. C₃₁×#462	C₂²	semidirect
138. C₃₁×#462	C₂²	semidirect
139. C₃₁×#461	C₂²	semidirect
140. C₃₁×#461	C₂²	semidirect
145. C₃₁×#460	C₂²	semidirect
146. C₃₁×#460	C₂²	semidirect
151. C₃₁×#459	C₂²	semidirect
152. C₃₁×#459	C₂²	semidirect
165. C₃₁×#446	C₂²	semidirect
166. C₃₁×#446	C₂²	semidirect
167. C₃₁×#446	C₂²	semidirect
168. C₃₁×#446	C₂²	semidirect
169. C₃₁×#446	C₂²	semidirect
170. C₃₁×#446	C₂²	semidirect
171. C₈×Q₈×C₃₁	C₂²	semidirect
172. C₈×Q₈×C₃₁	C₂²	semidirect
175. C₃₁×#442	C₂²	semidirect
176. C₃₁×#442	C₂²	semidirect
177. C₃₁×#441	C₂²	semidirect
178. C₃₁×#441	C₂²	semidirect
181. C₃₁×#440	C₂²	semidirect
182. C₃₁×#440	C₂²	semidirect
183. C₃₁×#440	C₂²	semidirect
184. C₃₁×#440	C₂²	semidirect
185. C₄×Q₁₆×C₃₁	C₂²	semidirect
186. C₄×Q₁₆×C₃₁	C₂²	semidirect
189. C₄×SD₁₆×C₃₁	C₂²	semidirect
190. C₄×SD₁₆×C₃₁	C₂²	semidirect
191. C₄×SD₁₆×C₃₁	C₂²	semidirect
192. C₄×SD₁₆×C₃₁	C₂²	semidirect
195. C₄×D₈×C₃₁	C₂²	semidirect
196. C₄×D₈×C₃₁	C₂²	semidirect
682. #61919	C₃₁	direct (N × H)
789. #3557	C₂×C₃₁	semidirect
790. #3506	C₂×C₃₁	semidirect
791. #3403	C₂×C₃₁	semidirect
792. #3402	C₂×C₃₁	semidirect
793. #3401	C₂×C₃₁	semidirect
794. #3401	C₂×C₃₁	semidirect
795. #3399	C₂×C₃₁	semidirect
796. #3397	C₂×C₃₁	semidirect
797. #3396	C₂×C₃₁	semidirect
798. #3394	C₂×C₃₁	semidirect
799. #3377	C₂×C₃₁	semidirect
800. #3376	C₂×C₃₁	semidirect
801. #3371	C₂×C₃₁	semidirect
802. #3370	C₂×C₃₁	semidirect
803. #3368	C₂×C₃₁	semidirect
804. #3366	C₂×C₃₁	semidirect
805. #3365	C₂×C₃₁	semidirect
806. #3361	C₂×C₃₁	semidirect
807. #3224	C₂×C₃₁	semidirect
808. #3224	C₂×C₃₁	semidirect
809. #3222	C₂×C₃₁	semidirect
810. #3220	C₂×C₃₁	semidirect
811. #3219	C₂×C₃₁	semidirect
812. #3212	C₂×C₃₁	semidirect
813. #3125	C₂×C₃₁	semidirect
814. #3124	C₂×C₃₁	semidirect
815. #3120	C₂×C₃₁	semidirect
816. #3119	C₂×C₃₁	semidirect
817. #3114	C₂×C₃₁	semidirect
818. #3105	C₂×C₃₁	semidirect
819. #2985	C₂×C₃₁	semidirect
874. #559	C₂²×C₃₁	semidirect
875. #559	C₂²×C₃₁	semidirect
876. #557	C₂²×C₃₁	semidirect
877. #557	C₂²×C₃₁	semidirect
880. #556	C₂²×C₃₁	semidirect
881. #556	C₂²×C₃₁	semidirect
883. #554	C₂²×C₃₁	semidirect
884. #554	C₂²×C₃₁	semidirect
914. #497	C₂²×C₃₁	semidirect
918. #496	C₂²×C₃₁	semidirect
921. #495	C₂²×C₃₁	semidirect
922. #495	C₂²×C₃₁	semidirect
925. #491	C₂²×C₃₁	semidirect
928. #490	C₂²×C₃₁	semidirect
933. #488	C₂²×C₃₁	semidirect
934. #488	C₂²×C₃₁	semidirect
941. #479	C₂²×C₃₁	semidirect
942. #479	C₂²×C₃₁	semidirect
947. #478	C₂²×C₃₁	semidirect
948. #478	C₂²×C₃₁	semidirect
949. #477	C₂²×C₃₁	semidirect
950. #476	C₂²×C₃₁	semidirect
951. #475	C₂²×C₃₁	semidirect
952. #474	C₂²×C₃₁	semidirect
957. #464	C₂²×C₃₁	semidirect
958. #464	C₂²×C₃₁	semidirect
959. #464	C₂²×C₃₁	semidirect
960. #464	C₂²×C₃₁	semidirect
969. #463	C₂²×C₃₁	semidirect
970. #463	C₂²×C₃₁	semidirect
971. #463	C₂²×C₃₁	semidirect
972. #463	C₂²×C₃₁	semidirect
973. #462	C₂²×C₃₁	semidirect
974. #462	C₂²×C₃₁	semidirect
975. #461	C₂²×C₃₁	semidirect
976. #461	C₂²×C₃₁	semidirect
981. #460	C₂²×C₃₁	semidirect
982. #460	C₂²×C₃₁	semidirect
987. #459	C₂²×C₃₁	semidirect
988. #459	C₂²×C₃₁	semidirect
1001. #446	C₂²×C₃₁	semidirect
1002. #446	C₂²×C₃₁	semidirect
1003. #446	C₂²×C₃₁	semidirect
1004. #446	C₂²×C₃₁	semidirect
1005. #446	C₂²×C₃₁	semidirect
1006. #446	C₂²×C₃₁	semidirect
1007. C₈×Q₈	C₂²×C₃₁	semidirect
1008. C₈×Q₈	C₂²×C₃₁	semidirect
1011. #442	C₂²×C₃₁	semidirect
1012. #442	C₂²×C₃₁	semidirect
1013. #441	C₂²×C₃₁	semidirect
1014. #441	C₂²×C₃₁	semidirect
1017. #440	C₂²×C₃₁	semidirect
1018. #440	C₂²×C₃₁	semidirect
1019. #440	C₂²×C₃₁	semidirect
1020. #440	C₂²×C₃₁	semidirect
1021. C₄×Q₁₆	C₂²×C₃₁	semidirect
1022. C₄×Q₁₆	C₂²×C₃₁	semidirect
1025. C₄×SD₁₆	C₂²×C₃₁	semidirect
1026. C₄×SD₁₆	C₂²×C₃₁	semidirect
1027. C₄×SD₁₆	C₂²×C₃₁	semidirect
1028. C₄×SD₁₆	C₂²×C₃₁	semidirect
1031. C₄×D₈	C₂²×C₃₁	semidirect
1032. C₄×D₈	C₂²×C₃₁	semidirect
1324. C₃₁	#61919	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×#3557	2
C₃₁×#3506	2
C₃₁×#3403	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3399	2
C₃₁×#3397	2
C₃₁×#3396	2
C₃₁×#3394	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3365	2
C₃₁×#3361	2
C₃₁×#3224	2
C₃₁×#3222	2
C₃₁×#3220	2
C₃₁×#3219	2
C₃₁×#3212	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3120	2
C₃₁×#3119	2
C₃₁×#3114	2
C₃₁×#3105	2
C₃₁×#2985	2
#61919	31

Subgroups — C31×#61919 #21518678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61919 #21518678