Subgroups — C₃₁×#61925 #21518684

Order 7936.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	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×#3400	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3393	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×#3375	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3371	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3370	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3225	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3224	C₂	1	1	yes	maximal, characteristic
21	C₃₁×#3223	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3222	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3211	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3123	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3121	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3118	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3111	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3107	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	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#557	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	—	2	1	no	—
43	C₃₁×#556	C₂²	1	1	yes	characteristic
44	C₃₁×#556	C₂²	1	1	yes	characteristic
45	C₃₁×#556	C₂²	1	1	yes	characteristic
46	C₃₁×#556	C₂²	1	1	yes	characteristic
47	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#552	—	2	1	no	—
52	C₃₁×#551	—	2	1	no	—
53	C₃₁×#551	—	2	1	no	—
54	C₃₁×#551	—	2	1	no	—
55	C₃₁×#551	—	2	1	no	—
56	C₃₁×#544	—	2	1	no	—
57	C₃₁×#542	—	2	1	no	—
58	C₃₁×#542	—	2	1	no	—
59	C₃₁×#542	C₂²	1	1	yes	characteristic
60	C₃₁×#542	C₂²	1	1	yes	characteristic
61	C₃₁×#541	—	2	1	no	—
62	C₃₁×#541	—	2	1	no	—
63	C₃₁×#541	—	2	1	no	—
64	C₃₁×#541	C₂²	1	1	yes	characteristic
65	C₃₁×#541	C₂²	1	1	yes	characteristic
66	C₃₁×#536	C₂²	1	1	yes	characteristic
67	C₃₁×#535	C₂²	1	1	yes	characteristic
68	C₃₁×#533	C₂²	1	1	yes	characteristic
69	C₃₁×#533	C₂²	1	1	yes	characteristic
70	C₃₁×#529	—	2	1	no	—
71	C₃₁×#529	—	2	1	no	—
72	C₃₁×#529	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
74	C₃₁×#519	C₂²	1	1	yes	characteristic
75	C₃₁×#518	C₂²	1	1	yes	characteristic
76	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#497	C₂²	1	1	yes	characteristic
78	C₃₁×#497	C₂²	1	1	yes	characteristic
79	C₃₁×#497	C₂²	1	1	yes	characteristic
80	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#496	C₂²	1	1	yes	characteristic
83	C₃₁×#495	C₂²	1	1	yes	characteristic
84	C₃₁×#495	C₂²	1	1	yes	characteristic
85	C₃₁×#495	C₂²	1	1	yes	characteristic
86	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
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×#489	C₂²	1	1	yes	characteristic
92	C₃₁×#489	C₂²	1	1	yes	characteristic
93	C₃₁×#489	C₂²	1	1	yes	characteristic
94	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#488	C₂²	1	1	yes	characteristic
96	C₃₁×#488	C₂²	1	1	yes	characteristic
97	C₃₁×#488	C₂²	1	1	yes	characteristic
98	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#486	C₂²	1	1	yes	characteristic
101	C₃₁×#485	C₂²	1	1	yes	characteristic
102	C₃₁×#485	C₂²	1	1	yes	characteristic
103	C₃₁×#485	C₂²	1	1	yes	characteristic
104	C₃₁×#482	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×#479	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#478	C₂²	1	1	yes	characteristic
109	C₃₁×#478	C₂²	1	1	yes	characteristic
110	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#476	C₂²	1	1	yes	characteristic
113	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#474	C₂²	1	1	yes	characteristic
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
122	C₃₁×#464	C₂²	1	1	yes	characteristic
123	C₃₁×#464	C₂²	1	1	yes	characteristic
124	C₃₁×#464	C₂²	1	1	yes	characteristic
125	C₃₁×#464	C₂²	1	1	yes	characteristic
126	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#463	C₂²	1	1	yes	characteristic
133	C₃₁×#463	C₂²	1	1	yes	characteristic
134	C₃₁×#463	C₂²	1	1	yes	characteristic
135	C₃₁×#463	C₂²	1	1	yes	characteristic
136	C₃₁×#463	C₂²	1	1	yes	characteristic
137	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
138	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
139	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
140	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
141	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
142	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
143	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
144	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
145	C₃₁×#461	C₂²	1	1	yes	characteristic
146	C₃₁×#461	C₂²	1	1	yes	characteristic
147	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#460	C₂²	1	1	yes	characteristic
150	C₃₁×#460	C₂²	1	1	yes	characteristic
151	C₃₁×#460	C₂²	1	1	yes	characteristic
152	C₃₁×#459	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
156	C₃₁×#451	C₂²	1	1	yes	characteristic
157	C₃₁×#451	C₂²	1	1	yes	characteristic
158	C₃₁×#451	C₂²	1	1	yes	characteristic
159	C₃₁×#450	C₂²	1	1	yes	characteristic
160	C₃₁×#450	C₂²	1	1	yes	characteristic
161	C₃₁×#450	C₂²	1	1	yes	characteristic
162	C₃₁×#449	C₂²	1	1	yes	characteristic
163	C₃₁×#448	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, complemented
175	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
176	C₃₁×#441	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
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×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
188	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
189	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
190	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
191	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
192	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
193	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
194	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
195	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
196	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
204	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×Q₁₆×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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆×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	C₃₁×C₄⋊Q₈	—	2	1	no	—
231	C₃₁×C₄⋊Q₈	—	2	1	no	—
232	C₃₁×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
242	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
243	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
244	C₃₁×C₄⋊Q₈	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×#126	—	2	1	no	—
262	C₃₁×#126	—	2	1	no	—
263	C₃₁×#126	—	2	1	no	—
264	C₃₁×#126	—	2	1	no	—
265	C₃₁×#126	—	2	1	no	—
266	C₃₁×#126	—	2	1	no	—
267	C₃₁×#126	—	2	1	no	—
268	C₃₁×#125	—	2	1	no	—
269	C₃₁×#125	—	2	1	no	—
270	C₃₁×#125	—	2	1	no	—
271	C₃₁×#125	—	2	1	no	—
272	C₃₁×#125	—	2	1	no	—
273	C₃₁×#125	—	2	1	no	—
274	C₃₁×#125	—	2	1	no	—
275	C₃₁×#125	—	2	1	no	—
276	C₃₁×#125	—	2	1	no	—
277	C₃₁×#125	—	2	1	no	—
278	C₃₁×#125	—	2	1	no	—
279	C₃₁×#125	—	2	1	no	—
280	C₃₁×#125	D₄	1	1	yes	characteristic
281	C₃₁×#125	D₄	1	1	yes	characteristic
282	C₃₁×#125	C₂³	1	1	yes	characteristic
283	C₃₁×#125	C₂³	1	1	yes	characteristic
284	C₃₁×#125	C₂³	1	1	yes	characteristic
285	C₃₁×#124	—	2	1	no	—
286	C₃₁×#124	—	2	1	no	—
287	C₃₁×#124	—	2	1	no	—
288	C₃₁×#124	—	2	1	no	—
289	C₃₁×#124	—	2	1	no	—
290	C₃₁×#124	—	2	1	no	—
291	C₃₁×#124	—	2	1	no	—
292	C₃₁×#124	—	2	1	no	—
293	C₃₁×#124	C₂³	1	1	yes	characteristic
294	C₃₁×#124	C₂³	1	1	yes	characteristic
295	C₃₁×#124	C₂³	1	1	yes	characteristic
296	C₃₁×#124	C₂³	1	1	yes	characteristic
297	C₃₁×#124	C₂³	1	1	yes	characteristic
298	C₃₁×#124	C₂³	1	1	yes	characteristic
299	C₃₁×#124	C₂³	1	1	yes	characteristic
300	C₃₁×#124	C₂³	1	1	yes	characteristic
301	C₃₁×#124	C₂³	1	1	yes	characteristic
302	C₃₁×#124	C₂³	1	1	yes	characteristic
303	C₃₁×#124	C₂³	1	1	yes	characteristic
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×#123	—	2	1	no	—
310	C₃₁×#123	—	2	1	no	—
311	C₃₁×#123	—	2	1	no	—
312	C₃₁×#123	—	2	1	no	—
313	C₃₁×#123	—	2	1	no	—
314	C₃₁×#123	—	2	1	no	—
315	C₃₁×#123	—	2	1	no	—
316	C₃₁×#123	—	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	—	2	1	no	—
322	C₃₁×C₂²⋊Q₈	—	2	1	no	—
323	C₃₁×C₂²⋊Q₈	—	2	1	no	—
324	C₃₁×C₂²⋊Q₈	—	2	1	no	—
325	C₃₁×C₂²⋊Q₈	—	2	1	no	—
326	C₃₁×C₂²⋊Q₈	—	2	1	no	—
327	C₃₁×C₂²⋊Q₈	—	2	1	no	—
328	C₃₁×C₂²⋊Q₈	—	2	1	no	—
329	C₃₁×C₂²⋊Q₈	—	2	1	no	—
330	C₃₁×C₂²⋊Q₈	—	2	1	no	—
331	C₃₁×C₂²⋊Q₈	—	2	1	no	—
332	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
333	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
334	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
335	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
336	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
337	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
338	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
339	C₃₁×#121	—	2	1	no	—
340	C₃₁×#121	—	2	1	no	—
341	C₃₁×#121	C₂³	1	1	yes	characteristic
342	C₃₁×#120	—	2	1	no	—
343	C₃₁×#120	—	2	1	no	—
344	C₄×Q₈×C₃₁	—	2	1	no	—
345	C₄×Q₈×C₃₁	—	2	1	no	—
346	C₄×Q₈×C₃₁	—	2	1	no	—
347	C₄×Q₈×C₃₁	—	2	1	no	—
348	C₄×Q₈×C₃₁	—	2	1	no	—
349	C₄×Q₈×C₃₁	—	2	1	no	—
350	C₄×Q₈×C₃₁	—	2	1	no	—
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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
365	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#117	—	2	1	no	—
389	C₃₁×#117	—	2	1	no	—
390	C₃₁×#117	—	2	1	no	—
391	C₃₁×#117	—	2	1	no	—
392	C₃₁×#117	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	—	2	1	no	—
405	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
406	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
407	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂×C₄²×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×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#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	C₂×Q₈×C₃₁	—	2	1	no	—
482	C₂×Q₈×C₃₁	—	2	1	no	—
483	C₂×Q₈×C₃₁	—	2	1	no	—
484	C₂×Q₈×C₃₁	—	2	1	no	—
485	C₂×Q₈×C₃₁	—	4	1	no	—
486	C₂×Q₈×C₃₁	—	4	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×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	—	4	1	no	—
505	C₂×D₄×C₃₁	—	4	1	no	—
506	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
507	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
508	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
509	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₃₁	—	2	1	no	—
511	C₂²×C₄×C₃₁	—	2	1	no	—
512	C₂²×C₄×C₃₁	—	2	1	no	—
513	C₂²×C₄×C₃₁	—	2	1	no	—
514	C₂²×C₄×C₃₁	—	2	1	no	—
515	C₂²×C₄×C₃₁	—	2	1	no	—
516	C₂²×C₄×C₃₁	—	2	1	no	—
517	C₂²×C₄×C₃₁	—	2	1	no	—
518	C₂²×C₄×C₃₁	—	2	1	no	—
519	C₂²×C₄×C₃₁	—	2	1	no	—
520	C₂²×C₄×C₃₁	—	2	1	no	—
521	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
522	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
523	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
524	Q₁₆×C₃₁	—	4	1	no	—
525	Q₁₆×C₃₁	—	4	1	no	—
526	Q₁₆×C₃₁	—	4	1	no	—
527	Q₁₆×C₃₁	—	4	1	no	—
528	Q₁₆×C₃₁	—	4	1	no	—
529	Q₁₆×C₃₁	—	4	1	no	—
530	Q₁₆×C₃₁	—	4	1	no	—
531	Q₁₆×C₃₁	—	4	1	no	—
532	Q₁₆×C₃₁	—	4	1	no	—
533	SD₁₆×C₃₁	—	4	1	no	—
534	SD₁₆×C₃₁	—	4	1	no	—
535	SD₁₆×C₃₁	—	4	1	no	—
536	SD₁₆×C₃₁	—	4	1	no	—
537	SD₁₆×C₃₁	—	4	1	no	—
538	SD₁₆×C₃₁	—	4	1	no	—
539	SD₁₆×C₃₁	—	4	1	no	—
540	SD₁₆×C₃₁	—	4	1	no	—
541	SD₁₆×C₃₁	—	4	1	no	—
542	SD₁₆×C₃₁	—	4	1	no	—
543	SD₁₆×C₃₁	—	4	1	no	—
544	SD₁₆×C₃₁	—	4	1	no	—
545	D₈×C₃₁	—	4	1	no	—
546	D₈×C₃₁	—	4	1	no	—
547	D₈×C₃₁	—	4	1	no	—
548	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
549	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
550	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
551	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
552	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
553	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
554	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
555	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
556	C₄⋊C₄×C₃₁	—	2	1	no	—
557	C₄⋊C₄×C₃₁	—	2	1	no	—
558	C₄⋊C₄×C₃₁	—	2	1	no	—
559	C₄⋊C₄×C₃₁	—	2	1	no	—
560	C₄⋊C₄×C₃₁	—	2	1	no	—
561	C₄⋊C₄×C₃₁	—	2	1	no	—
562	C₄⋊C₄×C₃₁	—	2	1	no	—
563	C₄⋊C₄×C₃₁	—	2	1	no	—
564	C₄⋊C₄×C₃₁	—	2	1	no	—
565	C₄⋊C₄×C₃₁	—	2	1	no	—
566	C₄⋊C₄×C₃₁	—	2	1	no	—
567	C₄⋊C₄×C₃₁	—	2	1	no	—
568	C₄⋊C₄×C₃₁	—	2	1	no	—
569	C₄⋊C₄×C₃₁	—	2	1	no	—
570	C₄⋊C₄×C₃₁	—	2	1	no	—
571	C₄⋊C₄×C₃₁	—	2	1	no	—
572	C₄⋊C₄×C₃₁	—	2	1	no	—
573	C₄⋊C₄×C₃₁	—	2	1	no	—
574	C₄⋊C₄×C₃₁	—	2	1	no	—
575	C₄⋊C₄×C₃₁	—	2	1	no	—
576	C₄⋊C₄×C₃₁	—	2	1	no	—
577	C₄⋊C₄×C₃₁	—	2	1	no	—
578	C₄⋊C₄×C₃₁	—	2	1	no	—
579	C₄⋊C₄×C₃₁	—	2	1	no	—
580	C₄⋊C₄×C₃₁	—	2	1	no	—
581	C₄⋊C₄×C₃₁	—	2	1	no	—
582	C₄⋊C₄×C₃₁	—	2	1	no	—
583	C₄⋊C₄×C₃₁	—	2	1	no	—
584	C₄⋊C₄×C₃₁	—	2	1	no	—
585	C₄⋊C₄×C₃₁	—	2	1	no	—
586	C₄⋊C₄×C₃₁	—	2	1	no	—
587	C₄⋊C₄×C₃₁	—	2	1	no	—
588	C₄⋊C₄×C₃₁	—	2	1	no	—
589	C₄⋊C₄×C₃₁	—	2	1	no	—
590	C₄⋊C₄×C₃₁	—	2	1	no	—
591	C₄⋊C₄×C₃₁	—	2	1	no	—
592	C₄⋊C₄×C₃₁	—	2	1	no	—
593	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
615	C₂²⋊C₄×C₃₁	—	2	1	no	—
616	C₂²⋊C₄×C₃₁	—	2	1	no	—
617	C₂²⋊C₄×C₃₁	—	2	1	no	—
618	C₂²⋊C₄×C₃₁	—	2	1	no	—
619	C₂²⋊C₄×C₃₁	—	2	1	no	—
620	C₂²⋊C₄×C₃₁	—	2	1	no	—
621	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	—	2	1	no	—
638	C₂²⋊C₄×C₃₁	—	2	1	no	—
639	C₂²⋊C₄×C₃₁	—	2	1	no	—
640	C₂²⋊C₄×C₃₁	—	2	1	no	—
641	C₂²⋊C₄×C₃₁	—	2	1	no	—
642	C₂²⋊C₄×C₃₁	—	2	1	no	—
643	C₂²⋊C₄×C₃₁	—	2	1	no	—
644	C₂²⋊C₄×C₃₁	—	2	1	no	—
645	C₂²⋊C₄×C₃₁	—	2	1	no	—
646	C₂²⋊C₄×C₃₁	—	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	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
655	C₄²×C₃₁	—	2	1	no	—
656	C₄²×C₃₁	—	2	1	no	—
657	C₄²×C₃₁	—	2	1	no	—
658	C₄²×C₃₁	—	2	1	no	—
659	C₄²×C₃₁	—	2	1	no	—
660	C₄²×C₃₁	—	2	1	no	—
661	C₄²×C₃₁	—	2	1	no	—
662	C₄²×C₃₁	—	2	1	no	—
663	C₄²×C₃₁	—	2	1	no	—
664	C₄²×C₃₁	—	2	1	no	—
665	C₄²×C₃₁	—	2	1	no	—
666	C₄²×C₃₁	—	2	1	no	—
667	C₄²×C₃₁	—	2	1	no	—
668	C₄²×C₃₁	—	2	1	no	—
669	C₄²×C₃₁	—	2	1	no	—
670	C₄²×C₃₁	—	2	1	no	—
671	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
672	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
673	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
674	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
675	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
676	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
677	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
678	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
679	#61925	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	—	2	1	no	—
684	C₂³×C₃₁	—	4	2	no	—
685	C₂³×C₃₁	—	8	1	no	—
686	C₂³×C₃₁	—	8	1	no	—
687	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
688	Q₈×C₃₁	—	2	1	no	—
689	Q₈×C₃₁	—	2	1	no	—
690	Q₈×C₃₁	—	2	1	no	—
691	Q₈×C₃₁	—	2	1	no	—
692	Q₈×C₃₁	—	2	1	no	—
693	Q₈×C₃₁	—	2	1	no	—
694	Q₈×C₃₁	—	2	1	no	—
695	Q₈×C₃₁	—	2	1	no	—
696	Q₈×C₃₁	—	2	1	no	—
697	Q₈×C₃₁	—	2	1	no	—
698	Q₈×C₃₁	—	2	1	no	—
699	Q₈×C₃₁	—	2	1	no	—
700	Q₈×C₃₁	—	4	1	no	—
701	Q₈×C₃₁	—	4	1	no	—
702	Q₈×C₃₁	—	4	1	no	—
703	Q₈×C₃₁	—	4	1	no	—
704	Q₈×C₃₁	—	4	2	no	—
705	Q₈×C₃₁	—	8	1	no	—
706	Q₈×C₃₁	—	8	1	no	—
707	Q₈×C₃₁	—	8	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	—	4	2	no	—
717	D₄×C₃₁	—	4	2	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	C₂×C₄×C₃₁	—	2	1	no	—
724	C₂×C₄×C₃₁	—	2	1	no	—
725	C₂×C₄×C₃₁	—	2	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	2	1	no	—
728	C₂×C₄×C₃₁	—	2	1	no	—
729	C₂×C₄×C₃₁	—	2	1	no	—
730	C₂×C₄×C₃₁	—	2	1	no	—
731	C₂×C₄×C₃₁	—	2	1	no	—
732	C₂×C₄×C₃₁	—	2	1	no	—
733	C₂×C₄×C₃₁	—	2	1	no	—
734	C₂×C₄×C₃₁	—	2	1	no	—
735	C₂×C₄×C₃₁	—	2	1	no	—
736	C₂×C₄×C₃₁	—	2	1	no	—
737	C₂×C₄×C₃₁	—	4	1	no	—
738	C₂×C₄×C₃₁	—	4	1	no	—
739	C₂×C₄×C₃₁	—	4	2	no	—
740	C₂×C₄×C₃₁	—	4	2	no	—
741	C₂×C₄×C₃₁	—	4	2	no	—
742	C₂×C₄×C₃₁	—	8	1	no	—
743	C₂×C₄×C₃₁	—	8	1	no	—
744	C₂×C₄×C₃₁	—	8	1	no	—
745	C₂×C₄×C₃₁	—	8	1	no	—
746	C₂×C₄×C₃₁	—	8	1	no	—
747	C₂×C₄×C₃₁	—	8	1	no	—
748	C₂×C₄×C₃₁	—	8	1	no	—
749	C₂×C₄×C₃₁	—	8	1	no	—
750	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
751	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
752	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
753	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
754	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
755	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
756	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
757	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
758	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
759	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
760	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
763	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
764	C₈×C₃₁	—	2	1	no	—
765	C₈×C₃₁	—	2	1	no	—
766	C₈×C₃₁	—	2	1	no	—
767	C₈×C₃₁	—	2	1	no	—
768	C₈×C₃₁	—	2	1	no	—
769	C₈×C₃₁	—	2	1	no	—
770	C₈×C₃₁	—	2	1	no	—
771	C₈×C₃₁	—	2	1	no	—
772	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
773	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
774	#3402	C₂×C₃₁	1	1	yes	characteristic, complemented
775	#3402	C₂×C₃₁	1	1	yes	characteristic, complemented
776	#3401	C₂×C₃₁	1	1	yes	characteristic, complemented
777	#3401	C₂×C₃₁	1	1	yes	characteristic, complemented
778	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
780	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3370	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3225	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3224	C₂×C₃₁	1	1	yes	characteristic
792	#3223	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3222	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3211	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3123	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3121	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3118	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3111	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
803	C₂²×C₃₁	—	2	1	no	—
804	C₂²×C₃₁	—	2	1	no	—
805	C₂²×C₃₁	—	2	1	no	—
806	C₂²×C₃₁	—	4	1	no	—
807	C₂²×C₃₁	—	4	1	no	—
808	C₂²×C₃₁	—	4	1	no	—
809	C₂²×C₃₁	—	4	1	no	—
810	C₂²×C₃₁	—	4	1	no	—
811	C₂²×C₃₁	—	4	1	no	—
812	C₂²×C₃₁	—	4	1	no	—
813	C₂²×C₃₁	—	4	1	no	—
814	C₂²×C₃₁	—	4	1	no	—
815	C₂²×C₃₁	—	4	1	no	—
816	C₂²×C₃₁	—	4	1	no	—
817	C₂²×C₃₁	—	4	1	no	—
818	C₂²×C₃₁	—	16	2	no	—
819	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
820	C₄×C₃₁	—	2	1	no	—
821	C₄×C₃₁	—	2	1	no	—
822	C₄×C₃₁	—	2	1	no	—
823	C₄×C₃₁	—	2	1	no	—
824	C₄×C₃₁	—	2	1	no	—
825	C₄×C₃₁	—	2	1	no	—
826	C₄×C₃₁	—	2	1	no	—
827	C₄×C₃₁	—	2	1	no	—
828	C₄×C₃₁	—	2	1	no	—
829	C₄×C₃₁	—	2	1	no	—
830	C₄×C₃₁	—	2	1	no	—
831	C₄×C₃₁	—	2	1	no	—
832	C₄×C₃₁	—	2	1	no	—
833	C₄×C₃₁	—	4	1	no	—
834	C₄×C₃₁	—	4	1	no	—
835	C₄×C₃₁	—	4	1	no	—
836	C₄×C₃₁	—	4	1	no	—
837	C₄×C₃₁	—	4	1	no	—
838	C₄×C₃₁	—	4	1	no	—
839	C₄×C₃₁	—	4	1	no	—
840	C₄×C₃₁	—	4	1	no	—
841	C₄×C₃₁	—	4	1	no	—
842	C₄×C₃₁	—	4	1	no	—
843	C₄×C₃₁	—	4	1	no	—
844	C₄×C₃₁	—	4	1	no	—
845	C₄×C₃₁	#585	1	1	yes	characteristic
846	C₄×C₃₁	#585	1	1	yes	characteristic
847	#563	—	2	1	no	—
848	#563	—	2	1	no	—
849	#559	C₂²×C₃₁	1	1	yes	characteristic
850	#559	C₂²×C₃₁	1	1	yes	characteristic
851	#559	C₂²×C₃₁	1	1	yes	characteristic
852	#559	C₂²×C₃₁	1	1	yes	characteristic
853	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
854	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
855	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
856	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
857	#556	—	2	1	no	—
858	#556	C₂²×C₃₁	1	1	yes	characteristic
859	#556	C₂²×C₃₁	1	1	yes	characteristic
860	#556	C₂²×C₃₁	1	1	yes	characteristic
861	#556	C₂²×C₃₁	1	1	yes	characteristic
862	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
863	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
864	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
865	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
866	#552	—	2	1	no	—
867	#551	—	2	1	no	—
868	#551	—	2	1	no	—
869	#551	—	2	1	no	—
870	#551	—	2	1	no	—
871	#544	—	2	1	no	—
872	#542	—	2	1	no	—
873	#542	—	2	1	no	—
874	#542	C₂²×C₃₁	1	1	yes	characteristic
875	#542	C₂²×C₃₁	1	1	yes	characteristic
876	#541	—	2	1	no	—
877	#541	—	2	1	no	—
878	#541	—	2	1	no	—
879	#541	C₂²×C₃₁	1	1	yes	characteristic
880	#541	C₂²×C₃₁	1	1	yes	characteristic
881	#536	C₂²×C₃₁	1	1	yes	characteristic
882	#535	C₂²×C₃₁	1	1	yes	characteristic
883	#533	C₂²×C₃₁	1	1	yes	characteristic
884	#533	C₂²×C₃₁	1	1	yes	characteristic
885	#529	—	2	1	no	—
886	#529	—	2	1	no	—
887	#529	C₂²×C₃₁	1	1	yes	characteristic
888	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
889	#519	C₂²×C₃₁	1	1	yes	characteristic
890	#518	C₂²×C₃₁	1	1	yes	characteristic
891	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
892	#497	C₂²×C₃₁	1	1	yes	characteristic
893	#497	C₂²×C₃₁	1	1	yes	characteristic
894	#497	C₂²×C₃₁	1	1	yes	characteristic
895	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
896	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
897	#496	C₂²×C₃₁	1	1	yes	characteristic
898	#495	C₂²×C₃₁	1	1	yes	characteristic
899	#495	C₂²×C₃₁	1	1	yes	characteristic
900	#495	C₂²×C₃₁	1	1	yes	characteristic
901	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
902	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
903	#492	C₂²×C₃₁	1	1	yes	characteristic
904	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
905	#490	C₂²×C₃₁	1	1	yes	characteristic
906	#489	C₂²×C₃₁	1	1	yes	characteristic
907	#489	C₂²×C₃₁	1	1	yes	characteristic
908	#489	C₂²×C₃₁	1	1	yes	characteristic
909	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
910	#488	C₂²×C₃₁	1	1	yes	characteristic
911	#488	C₂²×C₃₁	1	1	yes	characteristic
912	#488	C₂²×C₃₁	1	1	yes	characteristic
913	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
914	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#486	C₂²×C₃₁	1	1	yes	characteristic
916	#485	C₂²×C₃₁	1	1	yes	characteristic
917	#485	C₂²×C₃₁	1	1	yes	characteristic
918	#485	C₂²×C₃₁	1	1	yes	characteristic
919	#482	C₂²×C₃₁	1	1	yes	characteristic
920	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
921	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
922	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
923	#478	C₂²×C₃₁	1	1	yes	characteristic
924	#478	C₂²×C₃₁	1	1	yes	characteristic
925	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
926	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
927	#476	C₂²×C₃₁	1	1	yes	characteristic
928	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
929	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
930	#474	C₂²×C₃₁	1	1	yes	characteristic
931	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
932	#464	C₂²×C₃₁	1	1	yes	characteristic
933	#464	C₂²×C₃₁	1	1	yes	characteristic
934	#464	C₂²×C₃₁	1	1	yes	characteristic
935	#464	C₂²×C₃₁	1	1	yes	characteristic
936	#464	C₂²×C₃₁	1	1	yes	characteristic
937	#464	C₂²×C₃₁	1	1	yes	characteristic
938	#464	C₂²×C₃₁	1	1	yes	characteristic
939	#464	C₂²×C₃₁	1	1	yes	characteristic
940	#464	C₂²×C₃₁	1	1	yes	characteristic
941	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
942	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
943	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
944	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
945	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
946	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
947	#463	C₂²×C₃₁	1	1	yes	characteristic
948	#463	C₂²×C₃₁	1	1	yes	characteristic
949	#463	C₂²×C₃₁	1	1	yes	characteristic
950	#463	C₂²×C₃₁	1	1	yes	characteristic
951	#463	C₂²×C₃₁	1	1	yes	characteristic
952	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
953	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
954	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
955	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
956	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
957	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
958	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
959	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
960	#461	C₂²×C₃₁	1	1	yes	characteristic
961	#461	C₂²×C₃₁	1	1	yes	characteristic
962	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
963	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
964	#460	C₂²×C₃₁	1	1	yes	characteristic
965	#460	C₂²×C₃₁	1	1	yes	characteristic
966	#460	C₂²×C₃₁	1	1	yes	characteristic
967	#459	C₂²×C₃₁	1	1	yes	characteristic
968	#452	C₂²×C₃₁	1	1	yes	characteristic
969	#452	C₂²×C₃₁	1	1	yes	characteristic
970	#452	C₂²×C₃₁	1	1	yes	characteristic
971	#451	C₂²×C₃₁	1	1	yes	characteristic
972	#451	C₂²×C₃₁	1	1	yes	characteristic
973	#451	C₂²×C₃₁	1	1	yes	characteristic
974	#450	C₂²×C₃₁	1	1	yes	characteristic
975	#450	C₂²×C₃₁	1	1	yes	characteristic
976	#450	C₂²×C₃₁	1	1	yes	characteristic
977	#449	C₂²×C₃₁	1	1	yes	characteristic
978	#448	C₂²×C₃₁	1	1	yes	characteristic
979	#447	C₂²×C₃₁	1	1	yes	characteristic
980	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
981	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
982	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
983	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
984	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
985	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
986	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
987	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
988	#442	C₂²×C₃₁	1	1	yes	characteristic
989	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
990	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
991	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
992	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
993	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
994	#440	C₂²×C₃₁	1	1	yes	characteristic
995	#440	C₂²×C₃₁	1	1	yes	characteristic
996	#440	C₂²×C₃₁	1	1	yes	characteristic
997	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
998	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
999	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1000	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1001	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
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
1008	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1009	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1010	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1011	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1012	#433	C₂²×C₃₁	1	1	yes	characteristic
1013	#433	C₂²×C₃₁	1	1	yes	characteristic
1014	#433	C₂²×C₃₁	1	1	yes	characteristic
1015	#433	C₂²×C₃₁	1	1	yes	characteristic
1016	#432	C₂²×C₃₁	1	1	yes	characteristic
1017	#431	C₂²×C₃₁	1	1	yes	characteristic
1018	C₂×C₃₁	—	4	1	no	—
1019	C₂×C₃₁	—	8	1	no	—
1020	C₂×C₃₁	—	8	1	no	—
1021	C₂×C₃₁	—	8	1	no	—
1022	C₂×C₃₁	—	8	1	no	—
1023	C₂×C₃₁	#3487	1	1	yes	characteristic
1024	C₂×C₃₁	#3584	1	1	yes	characteristic
1025	C₂×C₃₁	#3586	1	1	yes	characteristic
1026	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1027	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1028	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1029	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1030	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1031	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1032	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1033	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1034	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1035	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1036	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1037	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1038	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1039	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1040	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1041	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1042	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1043	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1044	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1045	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1046	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1047	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1048	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1049	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1053	C₄⋊Q₈	—	2	1	no	—
1054	C₄⋊Q₈	—	2	1	no	—
1055	C₄⋊Q₈	—	2	1	no	—
1056	C₄⋊Q₈	—	2	1	no	—
1057	C₄⋊Q₈	—	2	1	no	—
1058	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1059	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1060	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1061	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1062	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1063	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1064	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1065	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1066	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1067	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1068	#127	C₂³×C₃₁	1	1	yes	characteristic
1069	#127	C₂³×C₃₁	1	1	yes	characteristic
1070	#126	—	2	1	no	—
1071	#126	—	2	1	no	—
1072	#126	—	2	1	no	—
1073	#126	—	2	1	no	—
1074	#126	—	2	1	no	—
1075	#126	—	2	1	no	—
1076	#126	—	2	1	no	—
1077	#126	—	2	1	no	—
1078	#126	—	2	1	no	—
1079	#126	—	2	1	no	—
1080	#126	—	2	1	no	—
1081	#126	—	2	1	no	—
1082	#126	—	2	1	no	—
1083	#126	—	2	1	no	—
1084	#126	—	2	1	no	—
1085	#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	#125	—	2	1	no	—
1092	#125	—	2	1	no	—
1093	#125	—	2	1	no	—
1094	#125	—	2	1	no	—
1095	#125	—	2	1	no	—
1096	#125	—	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	—	2	1	no	—
1102	#125	—	2	1	no	—
1103	#125	D₄×C₃₁	1	1	yes	characteristic
1104	#125	D₄×C₃₁	1	1	yes	characteristic
1105	#125	C₂³×C₃₁	1	1	yes	characteristic
1106	#125	C₂³×C₃₁	1	1	yes	characteristic
1107	#125	C₂³×C₃₁	1	1	yes	characteristic
1108	#124	—	2	1	no	—
1109	#124	—	2	1	no	—
1110	#124	—	2	1	no	—
1111	#124	—	2	1	no	—
1112	#124	—	2	1	no	—
1113	#124	—	2	1	no	—
1114	#124	—	2	1	no	—
1115	#124	—	2	1	no	—
1116	#124	C₂³×C₃₁	1	1	yes	characteristic
1117	#124	C₂³×C₃₁	1	1	yes	characteristic
1118	#124	C₂³×C₃₁	1	1	yes	characteristic
1119	#124	C₂³×C₃₁	1	1	yes	characteristic
1120	#124	C₂³×C₃₁	1	1	yes	characteristic
1121	#124	C₂³×C₃₁	1	1	yes	characteristic
1122	#124	C₂³×C₃₁	1	1	yes	characteristic
1123	#124	C₂³×C₃₁	1	1	yes	characteristic
1124	#124	C₂³×C₃₁	1	1	yes	characteristic
1125	#124	C₂³×C₃₁	1	1	yes	characteristic
1126	#124	C₂³×C₃₁	1	1	yes	characteristic
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	#123	—	2	1	no	—
1134	#123	—	2	1	no	—
1135	#123	—	2	1	no	—
1136	#123	—	2	1	no	—
1137	#123	—	2	1	no	—
1138	#123	—	2	1	no	—
1139	#123	—	2	1	no	—
1140	C₂²⋊Q₈	—	2	1	no	—
1141	C₂²⋊Q₈	—	2	1	no	—
1142	C₂²⋊Q₈	—	2	1	no	—
1143	C₂²⋊Q₈	—	2	1	no	—
1144	C₂²⋊Q₈	—	2	1	no	—
1145	C₂²⋊Q₈	—	2	1	no	—
1146	C₂²⋊Q₈	—	2	1	no	—
1147	C₂²⋊Q₈	—	2	1	no	—
1148	C₂²⋊Q₈	—	2	1	no	—
1149	C₂²⋊Q₈	—	2	1	no	—
1150	C₂²⋊Q₈	—	2	1	no	—
1151	C₂²⋊Q₈	—	2	1	no	—
1152	C₂²⋊Q₈	—	2	1	no	—
1153	C₂²⋊Q₈	—	2	1	no	—
1154	C₂²⋊Q₈	—	2	1	no	—
1155	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1156	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1157	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1158	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1159	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1160	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1161	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1162	#121	—	2	1	no	—
1163	#121	—	2	1	no	—
1164	#121	C₂³×C₃₁	1	1	yes	characteristic
1165	#120	—	2	1	no	—
1166	#120	—	2	1	no	—
1167	C₄×Q₈	—	2	1	no	—
1168	C₄×Q₈	—	2	1	no	—
1169	C₄×Q₈	—	2	1	no	—
1170	C₄×Q₈	—	2	1	no	—
1171	C₄×Q₈	—	2	1	no	—
1172	C₄×Q₈	—	2	1	no	—
1173	C₄×Q₈	—	2	1	no	—
1174	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1175	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1176	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1177	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1178	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1179	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1180	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1181	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1182	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1183	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1184	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1185	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1186	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1187	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1188	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1189	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1190	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1191	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1192	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1193	C₄×D₄	—	2	1	no	—
1194	C₄×D₄	—	2	1	no	—
1195	C₄×D₄	—	2	1	no	—
1196	C₄×D₄	—	2	1	no	—
1197	C₄×D₄	—	2	1	no	—
1198	C₄×D₄	—	2	1	no	—
1199	C₄×D₄	—	2	1	no	—
1200	C₄×D₄	—	2	1	no	—
1201	C₄×D₄	—	2	1	no	—
1202	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1203	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1204	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1205	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1206	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1207	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1208	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1209	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1210	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1211	#117	—	2	1	no	—
1212	#117	—	2	1	no	—
1213	#117	—	2	1	no	—
1214	#117	—	2	1	no	—
1215	#117	—	2	1	no	—
1216	#117	—	2	1	no	—
1217	#117	—	2	1	no	—
1218	#117	—	2	1	no	—
1219	#117	—	2	1	no	—
1220	#117	—	2	1	no	—
1221	#117	—	2	1	no	—
1222	#117	—	2	1	no	—
1223	#117	C₂³×C₃₁	1	1	yes	characteristic
1224	#117	C₂³×C₃₁	1	1	yes	characteristic
1225	#117	C₂³×C₃₁	1	1	yes	characteristic
1226	C₂×C₄⋊C₄	—	2	1	no	—
1227	C₂×C₂²⋊C₄	—	2	1	no	—
1228	C₂×C₂²⋊C₄	—	2	1	no	—
1229	C₂×C₂²⋊C₄	—	2	1	no	—
1230	C₂×C₂²⋊C₄	—	2	1	no	—
1231	C₂×C₄²	—	2	1	no	—
1232	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1233	#107	C₂³×C₃₁	1	1	yes	characteristic
1234	#107	C₂³×C₃₁	1	1	yes	characteristic
1235	#107	C₂³×C₃₁	1	1	yes	characteristic
1236	#107	C₂³×C₃₁	1	1	yes	characteristic
1237	#106	C₂³×C₃₁	1	1	yes	characteristic
1238	#106	C₂³×C₃₁	1	1	yes	characteristic
1239	#106	C₂³×C₃₁	1	1	yes	characteristic
1240	#106	C₂³×C₃₁	1	1	yes	characteristic
1241	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1242	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1243	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1244	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1245	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1246	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1247	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1248	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1249	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1250	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1251	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1252	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1253	#103	C₂³×C₃₁	1	1	yes	characteristic
1254	#103	C₂³×C₃₁	1	1	yes	characteristic
1255	#103	C₂³×C₃₁	1	1	yes	characteristic
1256	#103	C₂³×C₃₁	1	1	yes	characteristic
1257	#103	C₂³×C₃₁	1	1	yes	characteristic
1258	#103	C₂³×C₃₁	1	1	yes	characteristic
1259	#103	C₂³×C₃₁	1	1	yes	characteristic
1260	#103	C₂³×C₃₁	1	1	yes	characteristic
1261	#103	C₂³×C₃₁	1	1	yes	characteristic
1262	#103	C₂³×C₃₁	1	1	yes	characteristic
1263	#103	C₂³×C₃₁	1	1	yes	characteristic
1264	#103	C₂³×C₃₁	1	1	yes	characteristic
1265	#103	C₂³×C₃₁	1	1	yes	characteristic
1266	#103	C₂³×C₃₁	1	1	yes	characteristic
1267	#103	C₂³×C₃₁	1	1	yes	characteristic
1268	#103	C₂³×C₃₁	1	1	yes	characteristic
1269	#103	C₂³×C₃₁	1	1	yes	characteristic
1270	#103	C₂³×C₃₁	1	1	yes	characteristic
1271	#102	C₂³×C₃₁	1	1	yes	characteristic
1272	#102	C₂³×C₃₁	1	1	yes	characteristic
1273	#102	C₂³×C₃₁	1	1	yes	characteristic
1274	#102	C₂³×C₃₁	1	1	yes	characteristic
1275	#102	C₂³×C₃₁	1	1	yes	characteristic
1276	#102	C₂³×C₃₁	1	1	yes	characteristic
1277	#102	C₂³×C₃₁	1	1	yes	characteristic
1278	#102	C₂³×C₃₁	1	1	yes	characteristic
1279	#102	C₂³×C₃₁	1	1	yes	characteristic
1280	#102	C₂³×C₃₁	1	1	yes	characteristic
1281	#102	C₂³×C₃₁	1	1	yes	characteristic
1282	#102	C₂³×C₃₁	1	1	yes	characteristic
1283	#102	C₂³×C₃₁	1	1	yes	characteristic
1284	#102	C₂³×C₃₁	1	1	yes	characteristic
1285	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1286	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1287	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1288	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1289	#97	C₂³×C₃₁	1	1	yes	characteristic
1290	#97	C₂³×C₃₁	1	1	yes	characteristic
1291	#97	C₂³×C₃₁	1	1	yes	characteristic
1292	#97	C₂³×C₃₁	1	1	yes	characteristic
1293	#97	C₂³×C₃₁	1	1	yes	characteristic
1294	#97	C₂³×C₃₁	1	1	yes	characteristic
1295	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1296	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1297	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1298	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1299	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1300	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1301	C₃₁	#61925	1	1	yes	characteristic, direct product factor, Sylow
1302	C₂⁴	—	2	1	no	—
1303	#41	—	4	1	no	—
1304	#41	—	4	1	no	—
1305	C₂×Q₈	—	2	1	no	—
1306	C₂×Q₈	—	2	1	no	—
1307	C₂×Q₈	—	2	1	no	—
1308	C₂×Q₈	—	2	1	no	—
1309	C₂×Q₈	—	4	1	no	—
1310	C₂×Q₈	—	4	1	no	—
1311	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1312	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1313	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1314	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1315	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1316	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1317	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1318	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1319	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1320	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1321	C₂×D₄	—	2	1	no	—
1322	C₂×D₄	—	2	1	no	—
1323	C₂×D₄	—	2	1	no	—
1324	C₂×D₄	—	2	1	no	—
1325	C₂×D₄	—	2	1	no	—
1326	C₂×D₄	—	2	1	no	—
1327	C₂×D₄	—	2	1	no	—
1328	C₂×D₄	—	4	1	no	—
1329	C₂×D₄	—	4	1	no	—
1330	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1331	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1332	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1333	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1334	C₂²×C₄	—	2	1	no	—
1335	C₂²×C₄	—	2	1	no	—
1336	C₂²×C₄	—	2	1	no	—
1337	C₂²×C₄	—	2	1	no	—
1338	C₂²×C₄	—	2	1	no	—
1339	C₂²×C₄	—	2	1	no	—
1340	C₂²×C₄	—	2	1	no	—
1341	C₂²×C₄	—	2	1	no	—
1342	C₂²×C₄	—	2	1	no	—
1343	C₂²×C₄	—	2	1	no	—
1344	C₂²×C₄	—	2	1	no	—
1345	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1346	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1347	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1348	Q₁₆	—	4	1	no	—
1349	Q₁₆	—	4	1	no	—
1350	Q₁₆	—	4	1	no	—
1351	Q₁₆	—	4	1	no	—
1352	Q₁₆	—	4	1	no	—
1353	Q₁₆	—	4	1	no	—
1354	Q₁₆	—	4	1	no	—
1355	Q₁₆	—	4	1	no	—
1356	Q₁₆	—	4	1	no	—
1357	SD₁₆	—	4	1	no	—
1358	SD₁₆	—	4	1	no	—
1359	SD₁₆	—	4	1	no	—
1360	SD₁₆	—	4	1	no	—
1361	SD₁₆	—	4	1	no	—
1362	SD₁₆	—	4	1	no	—
1363	SD₁₆	—	4	1	no	—
1364	SD₁₆	—	4	1	no	—
1365	SD₁₆	—	4	1	no	—
1366	SD₁₆	—	4	1	no	—
1367	SD₁₆	—	4	1	no	—
1368	SD₁₆	—	4	1	no	—
1369	D₈	—	4	1	no	—
1370	D₈	—	4	1	no	—
1371	D₈	—	4	1	no	—
1372	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1373	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1374	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1375	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1376	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1377	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1378	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1379	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1380	C₄⋊C₄	—	2	1	no	—
1381	C₄⋊C₄	—	2	1	no	—
1382	C₄⋊C₄	—	2	1	no	—
1383	C₄⋊C₄	—	2	1	no	—
1384	C₄⋊C₄	—	2	1	no	—
1385	C₄⋊C₄	—	2	1	no	—
1386	C₄⋊C₄	—	2	1	no	—
1387	C₄⋊C₄	—	2	1	no	—
1388	C₄⋊C₄	—	2	1	no	—
1389	C₄⋊C₄	—	2	1	no	—
1390	C₄⋊C₄	—	2	1	no	—
1391	C₄⋊C₄	—	2	1	no	—
1392	C₄⋊C₄	—	2	1	no	—
1393	C₄⋊C₄	—	2	1	no	—
1394	C₄⋊C₄	—	2	1	no	—
1395	C₄⋊C₄	—	2	1	no	—
1396	C₄⋊C₄	—	2	1	no	—
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	—	2	1	no	—
1400	C₄⋊C₄	—	2	1	no	—
1401	C₄⋊C₄	—	2	1	no	—
1402	C₄⋊C₄	—	2	1	no	—
1403	C₄⋊C₄	—	2	1	no	—
1404	C₄⋊C₄	—	2	1	no	—
1405	C₄⋊C₄	—	2	1	no	—
1406	C₄⋊C₄	—	2	1	no	—
1407	C₄⋊C₄	—	2	1	no	—
1408	C₄⋊C₄	—	2	1	no	—
1409	C₄⋊C₄	—	2	1	no	—
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	—	2	1	no	—
1413	C₄⋊C₄	—	2	1	no	—
1414	C₄⋊C₄	—	2	1	no	—
1415	C₄⋊C₄	—	2	1	no	—
1416	C₄⋊C₄	—	2	1	no	—
1417	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1418	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1419	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1420	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1421	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1422	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1423	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1424	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1425	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1426	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1427	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1428	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1429	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1430	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1431	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1432	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1433	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1434	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1435	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1436	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1437	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1438	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1439	C₂²⋊C₄	—	2	1	no	—
1440	C₂²⋊C₄	—	2	1	no	—
1441	C₂²⋊C₄	—	2	1	no	—
1442	C₂²⋊C₄	—	2	1	no	—
1443	C₂²⋊C₄	—	2	1	no	—
1444	C₂²⋊C₄	—	2	1	no	—
1445	C₂²⋊C₄	—	2	1	no	—
1446	C₂²⋊C₄	—	2	1	no	—
1447	C₂²⋊C₄	—	2	1	no	—
1448	C₂²⋊C₄	—	2	1	no	—
1449	C₂²⋊C₄	—	2	1	no	—
1450	C₂²⋊C₄	—	2	1	no	—
1451	C₂²⋊C₄	—	2	1	no	—
1452	C₂²⋊C₄	—	2	1	no	—
1453	C₂²⋊C₄	—	2	1	no	—
1454	C₂²⋊C₄	—	2	1	no	—
1455	C₂²⋊C₄	—	2	1	no	—
1456	C₂²⋊C₄	—	2	1	no	—
1457	C₂²⋊C₄	—	2	1	no	—
1458	C₂²⋊C₄	—	2	1	no	—
1459	C₂²⋊C₄	—	2	1	no	—
1460	C₂²⋊C₄	—	2	1	no	—
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1476	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1477	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1478	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1479	C₄²	—	2	1	no	—
1480	C₄²	—	2	1	no	—
1481	C₄²	—	2	1	no	—
1482	C₄²	—	2	1	no	—
1483	C₄²	—	2	1	no	—
1484	C₄²	—	2	1	no	—
1485	C₄²	—	2	1	no	—
1486	C₄²	—	2	1	no	—
1487	C₄²	—	2	1	no	—
1488	C₄²	—	2	1	no	—
1489	C₄²	—	2	1	no	—
1490	C₄²	—	2	1	no	—
1491	C₄²	—	2	1	no	—
1492	C₄²	—	2	1	no	—
1493	C₄²	—	2	1	no	—
1494	C₄²	—	2	1	no	—
1495	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1496	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1497	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1498	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1499	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1500	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1501	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1502	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1503	C₂³	—	2	1	no	—
1504	C₂³	—	2	1	no	—
1505	C₂³	—	2	1	no	—
1506	C₂³	—	2	1	no	—
1507	C₂³	—	4	2	no	—
1508	C₂³	—	8	1	no	—
1509	C₂³	—	8	1	no	—
1510	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1511	Q₈	—	2	1	no	—
1512	Q₈	—	2	1	no	—
1513	Q₈	—	2	1	no	—
1514	Q₈	—	2	1	no	—
1515	Q₈	—	2	1	no	—
1516	Q₈	—	2	1	no	—
1517	Q₈	—	2	1	no	—
1518	Q₈	—	2	1	no	—
1519	Q₈	—	2	1	no	—
1520	Q₈	—	2	1	no	—
1521	Q₈	—	2	1	no	—
1522	Q₈	—	2	1	no	—
1523	Q₈	—	4	1	no	—
1524	Q₈	—	4	1	no	—
1525	Q₈	—	4	1	no	—
1526	Q₈	—	4	1	no	—
1527	Q₈	—	4	2	no	—
1528	Q₈	—	8	1	no	—
1529	Q₈	—	8	1	no	—
1530	Q₈	—	8	1	no	—
1531	D₄	—	2	1	no	—
1532	D₄	—	2	1	no	—
1533	D₄	—	2	1	no	—
1534	D₄	—	2	1	no	—
1535	D₄	—	2	1	no	—
1536	D₄	—	2	1	no	—
1537	D₄	—	2	1	no	—
1538	D₄	—	2	1	no	—
1539	D₄	—	4	2	no	—
1540	D₄	—	4	2	no	—
1541	D₄	—	8	1	no	—
1542	D₄	—	8	1	no	—
1543	D₄	—	8	1	no	—
1544	D₄	—	8	1	no	—
1545	D₄	—	8	1	no	—
1546	C₂×C₄	—	2	1	no	—
1547	C₂×C₄	—	2	1	no	—
1548	C₂×C₄	—	2	1	no	—
1549	C₂×C₄	—	2	1	no	—
1550	C₂×C₄	—	2	1	no	—
1551	C₂×C₄	—	2	1	no	—
1552	C₂×C₄	—	2	1	no	—
1553	C₂×C₄	—	2	1	no	—
1554	C₂×C₄	—	2	1	no	—
1555	C₂×C₄	—	2	1	no	—
1556	C₂×C₄	—	2	1	no	—
1557	C₂×C₄	—	2	1	no	—
1558	C₂×C₄	—	2	1	no	—
1559	C₂×C₄	—	2	1	no	—
1560	C₂×C₄	—	4	1	no	—
1561	C₂×C₄	—	4	1	no	—
1562	C₂×C₄	—	4	2	no	—
1563	C₂×C₄	—	4	2	no	—
1564	C₂×C₄	—	4	2	no	—
1565	C₂×C₄	—	8	1	no	—
1566	C₂×C₄	—	8	1	no	—
1567	C₂×C₄	—	8	1	no	—
1568	C₂×C₄	—	8	1	no	—
1569	C₂×C₄	—	8	1	no	—
1570	C₂×C₄	—	8	1	no	—
1571	C₂×C₄	—	8	1	no	—
1572	C₂×C₄	—	8	1	no	—
1573	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1574	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1575	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1576	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1577	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1578	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1579	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1580	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1581	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1582	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1583	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1584	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1585	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1586	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1587	C₈	—	2	1	no	—
1588	C₈	—	2	1	no	—
1589	C₈	—	2	1	no	—
1590	C₈	—	2	1	no	—
1591	C₈	—	2	1	no	—
1592	C₈	—	2	1	no	—
1593	C₈	—	2	1	no	—
1594	C₈	—	2	1	no	—
1595	C₂²	—	2	1	no	—
1596	C₂²	—	2	1	no	—
1597	C₂²	—	2	1	no	—
1598	C₂²	—	4	1	no	—
1599	C₂²	—	4	1	no	—
1600	C₂²	—	4	1	no	—
1601	C₂²	—	4	1	no	—
1602	C₂²	—	4	1	no	—
1603	C₂²	—	4	1	no	—
1604	C₂²	—	4	1	no	—
1605	C₂²	—	4	1	no	—
1606	C₂²	—	4	1	no	—
1607	C₂²	—	4	1	no	—
1608	C₂²	—	4	1	no	—
1609	C₂²	—	4	1	no	—
1610	C₂²	—	16	2	no	—
1611	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1612	C₄	—	2	1	no	—
1613	C₄	—	2	1	no	—
1614	C₄	—	2	1	no	—
1615	C₄	—	2	1	no	—
1616	C₄	—	2	1	no	—
1617	C₄	—	2	1	no	—
1618	C₄	—	2	1	no	—
1619	C₄	—	2	1	no	—
1620	C₄	—	2	1	no	—
1621	C₄	—	2	1	no	—
1622	C₄	—	2	1	no	—
1623	C₄	—	2	1	no	—
1624	C₄	—	2	1	no	—
1625	C₄	—	4	1	no	—
1626	C₄	—	4	1	no	—
1627	C₄	—	4	1	no	—
1628	C₄	—	4	1	no	—
1629	C₄	—	4	1	no	—
1630	C₄	—	4	1	no	—
1631	C₄	—	4	1	no	—
1632	C₄	—	4	1	no	—
1633	C₄	—	4	1	no	—
1634	C₄	—	4	1	no	—
1635	C₄	—	4	1	no	—
1636	C₄	—	4	1	no	—
1637	C₄	C₃₁×#585	1	1	yes	characteristic
1638	C₄	C₃₁×#585	1	1	yes	characteristic
1639	C₂	—	4	1	no	—
1640	C₂	—	8	1	no	—
1641	C₂	—	8	1	no	—
1642	C₂	—	8	1	no	—
1643	C₂	—	8	1	no	—
1644	C₂	C₃₁×#3487	1	1	yes	characteristic
1645	C₂	C₃₁×#3584	1	1	yes	characteristic
1646	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3224	C₂
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×#3555	C₂	semidirect
2. C₃₁×#3510	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3402	C₂	semidirect
5. C₃₁×#3401	C₂	semidirect
6. C₃₁×#3401	C₂	semidirect
7. C₃₁×#3400	C₂	semidirect
8. C₃₁×#3398	C₂	semidirect
9. C₃₁×#3394	C₂	semidirect
10. C₃₁×#3393	C₂	semidirect
11. C₃₁×#3377	C₂	semidirect
12. C₃₁×#3376	C₂	semidirect
13. C₃₁×#3375	C₂	semidirect
14. C₃₁×#3371	C₂	semidirect
15. C₃₁×#3370	C₂	semidirect
16. C₃₁×#3369	C₂	semidirect
17. C₃₁×#3365	C₂	semidirect
18. C₃₁×#3364	C₂	semidirect
19. C₃₁×#3225	C₂	semidirect
21. C₃₁×#3223	C₂	semidirect
22. C₃₁×#3222	C₂	semidirect
23. C₃₁×#3215	C₂	semidirect
24. C₃₁×#3211	C₂	semidirect
25. C₃₁×#3127	C₂	semidirect
26. C₃₁×#3123	C₂	semidirect
27. C₃₁×#3121	C₂	semidirect
28. C₃₁×#3118	C₂	semidirect
29. C₃₁×#3111	C₂	semidirect
30. C₃₁×#3107	C₂	semidirect
31. C₃₁×#2985	C₂	semidirect
38. Q₈²×C₃₁	C₂²	semidirect
39. C₃₁×#557	C₂²	semidirect
40. C₃₁×#557	C₂²	semidirect
41. C₃₁×#557	C₂²	semidirect
47. C₃₁×#556	C₂²	semidirect
48. C₃₁×#556	C₂²	semidirect
49. C₃₁×#556	C₂²	semidirect
50. C₃₁×#554	C₂²	semidirect
80. C₃₁×#497	C₂²	semidirect
81. C₃₁×#497	C₂²	semidirect
86. C₃₁×#495	C₂²	semidirect
87. C₃₁×#494	C₂²	semidirect
89. C₃₁×#491	C₂²	semidirect
94. C₃₁×#489	C₂²	semidirect
98. C₃₁×#488	C₂²	semidirect
99. C₃₁×#487	C₂²	semidirect
105. C₃₁×#479	C₂²	semidirect
106. C₃₁×#479	C₂²	semidirect
107. C₃₁×#479	C₂²	semidirect
110. C₃₁×#478	C₂²	semidirect
111. C₃₁×#477	C₂²	semidirect
113. C₃₁×#475	C₂²	semidirect
114. C₃₁×#475	C₂²	semidirect
116. C₃₁×#474	C₂²	semidirect
126. C₃₁×#464	C₂²	semidirect
127. C₃₁×#464	C₂²	semidirect
128. C₃₁×#464	C₂²	semidirect
129. C₃₁×#464	C₂²	semidirect
130. C₃₁×#464	C₂²	semidirect
131. C₃₁×#464	C₂²	semidirect
137. C₃₁×#463	C₂²	semidirect
138. C₃₁×#463	C₂²	semidirect
139. C₃₁×#462	C₂²	semidirect
140. C₃₁×#462	C₂²	semidirect
141. C₃₁×#462	C₂²	semidirect
142. C₃₁×#462	C₂²	semidirect
143. C₃₁×#462	C₂²	semidirect
144. C₃₁×#462	C₂²	semidirect
147. C₃₁×#461	C₂²	semidirect
148. C₃₁×#461	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
174. C₃₁×#442	C₂²	semidirect
175. C₃₁×#441	C₂²	semidirect
176. C₃₁×#441	C₂²	semidirect
177. C₃₁×#441	C₂²	semidirect
178. C₃₁×#441	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
187. C₄×Q₁₆×C₃₁	C₂²	semidirect
188. C₄×Q₁₆×C₃₁	C₂²	semidirect
189. C₄×Q₁₆×C₃₁	C₂²	semidirect
193. C₄×SD₁₆×C₃₁	C₂²	semidirect
194. C₄×SD₁₆×C₃₁	C₂²	semidirect
195. C₄×SD₁₆×C₃₁	C₂²	semidirect
679. #61925	C₃₁	direct (N × H)
772. #3555	C₂×C₃₁	semidirect
773. #3510	C₂×C₃₁	semidirect
774. #3402	C₂×C₃₁	semidirect
775. #3402	C₂×C₃₁	semidirect
776. #3401	C₂×C₃₁	semidirect
777. #3401	C₂×C₃₁	semidirect
778. #3400	C₂×C₃₁	semidirect
779. #3398	C₂×C₃₁	semidirect
780. #3394	C₂×C₃₁	semidirect
781. #3393	C₂×C₃₁	semidirect
782. #3377	C₂×C₃₁	semidirect
783. #3376	C₂×C₃₁	semidirect
784. #3375	C₂×C₃₁	semidirect
785. #3371	C₂×C₃₁	semidirect
786. #3370	C₂×C₃₁	semidirect
787. #3369	C₂×C₃₁	semidirect
788. #3365	C₂×C₃₁	semidirect
789. #3364	C₂×C₃₁	semidirect
790. #3225	C₂×C₃₁	semidirect
792. #3223	C₂×C₃₁	semidirect
793. #3222	C₂×C₃₁	semidirect
794. #3215	C₂×C₃₁	semidirect
795. #3211	C₂×C₃₁	semidirect
796. #3127	C₂×C₃₁	semidirect
797. #3123	C₂×C₃₁	semidirect
798. #3121	C₂×C₃₁	semidirect
799. #3118	C₂×C₃₁	semidirect
800. #3111	C₂×C₃₁	semidirect
801. #3107	C₂×C₃₁	semidirect
802. #2985	C₂×C₃₁	semidirect
853. Q₈²	C₂²×C₃₁	semidirect
854. #557	C₂²×C₃₁	semidirect
855. #557	C₂²×C₃₁	semidirect
856. #557	C₂²×C₃₁	semidirect
862. #556	C₂²×C₃₁	semidirect
863. #556	C₂²×C₃₁	semidirect
864. #556	C₂²×C₃₁	semidirect
865. #554	C₂²×C₃₁	semidirect
895. #497	C₂²×C₃₁	semidirect
896. #497	C₂²×C₃₁	semidirect
901. #495	C₂²×C₃₁	semidirect
902. #494	C₂²×C₃₁	semidirect
904. #491	C₂²×C₃₁	semidirect
909. #489	C₂²×C₃₁	semidirect
913. #488	C₂²×C₃₁	semidirect
914. #487	C₂²×C₃₁	semidirect
920. #479	C₂²×C₃₁	semidirect
921. #479	C₂²×C₃₁	semidirect
922. #479	C₂²×C₃₁	semidirect
925. #478	C₂²×C₃₁	semidirect
926. #477	C₂²×C₃₁	semidirect
928. #475	C₂²×C₃₁	semidirect
929. #475	C₂²×C₃₁	semidirect
931. #474	C₂²×C₃₁	semidirect
941. #464	C₂²×C₃₁	semidirect
942. #464	C₂²×C₃₁	semidirect
943. #464	C₂²×C₃₁	semidirect
944. #464	C₂²×C₃₁	semidirect
945. #464	C₂²×C₃₁	semidirect
946. #464	C₂²×C₃₁	semidirect
952. #463	C₂²×C₃₁	semidirect
953. #463	C₂²×C₃₁	semidirect
954. #462	C₂²×C₃₁	semidirect
955. #462	C₂²×C₃₁	semidirect
956. #462	C₂²×C₃₁	semidirect
957. #462	C₂²×C₃₁	semidirect
958. #462	C₂²×C₃₁	semidirect
959. #462	C₂²×C₃₁	semidirect
962. #461	C₂²×C₃₁	semidirect
963. #461	C₂²×C₃₁	semidirect
980. #446	C₂²×C₃₁	semidirect
981. #446	C₂²×C₃₁	semidirect
982. #446	C₂²×C₃₁	semidirect
983. #446	C₂²×C₃₁	semidirect
984. #446	C₂²×C₃₁	semidirect
985. #446	C₂²×C₃₁	semidirect
986. C₈×Q₈	C₂²×C₃₁	semidirect
987. C₈×Q₈	C₂²×C₃₁	semidirect
989. #442	C₂²×C₃₁	semidirect
990. #441	C₂²×C₃₁	semidirect
991. #441	C₂²×C₃₁	semidirect
992. #441	C₂²×C₃₁	semidirect
993. #441	C₂²×C₃₁	semidirect
997. #440	C₂²×C₃₁	semidirect
998. #440	C₂²×C₃₁	semidirect
999. #440	C₂²×C₃₁	semidirect
1000. C₄×Q₁₆	C₂²×C₃₁	semidirect
1001. C₄×Q₁₆	C₂²×C₃₁	semidirect
1002. C₄×Q₁₆	C₂²×C₃₁	semidirect
1003. C₄×Q₁₆	C₂²×C₃₁	semidirect
1004. C₄×Q₁₆	C₂²×C₃₁	semidirect
1008. C₄×SD₁₆	C₂²×C₃₁	semidirect
1009. C₄×SD₁₆	C₂²×C₃₁	semidirect
1010. C₄×SD₁₆	C₂²×C₃₁	semidirect
1301. C₃₁	#61925	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×#3555	2
C₃₁×#3510	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3400	2
C₃₁×#3398	2
C₃₁×#3394	2
C₃₁×#3393	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3375	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3369	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3225	2
C₃₁×#3224	2
C₃₁×#3223	2
C₃₁×#3222	2
C₃₁×#3215	2
C₃₁×#3211	2
C₃₁×#3127	2
C₃₁×#3123	2
C₃₁×#3121	2
C₃₁×#3118	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#2985	2
#61925	31

Subgroups — C31×#61925 #21518684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61925 #21518684