Subgroups — C₃₁×#62208 #21518967

Order 7936.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3565	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3388	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3352	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3350	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3347	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3337	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3337	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3322	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3311	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3297	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3263	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3243	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3118	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#563	—	2	1	no	—
33	C₃₁×#562	—	2	1	no	—
34	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#556	—	2	1	no	—
36	C₃₁×#556	C₂²	1	1	yes	characteristic
37	C₃₁×#556	C₂²	1	1	yes	characteristic
38	C₃₁×#556	C₂²	1	1	yes	characteristic
39	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#554	C₂²	1	1	yes	characteristic
41	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#553	—	2	1	no	—
43	C₃₁×#553	C₂²	1	1	yes	characteristic
44	C₃₁×#553	C₂²	1	1	yes	characteristic
45	C₃₁×#553	C₂²	1	1	yes	characteristic
46	C₃₁×#552	—	2	1	no	—
47	C₃₁×#552	—	2	1	no	—
48	C₃₁×#552	C₂²	1	1	yes	characteristic
49	C₃₁×#552	C₂²	1	1	yes	characteristic
50	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#551	—	2	1	no	—
52	C₃₁×#551	—	2	1	no	—
53	C₃₁×#547	C₂²	1	1	yes	characteristic
54	C₃₁×#546	C₂²	1	1	yes	characteristic
55	C₃₁×#546	C₂²	1	1	yes	characteristic
56	C₃₁×#544	C₂²	1	1	yes	characteristic
57	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#542	—	2	1	no	—
59	C₃₁×#542	—	2	1	no	—
60	C₃₁×#542	C₂²	1	1	yes	characteristic
61	C₃₁×#542	C₂²	1	1	yes	characteristic
62	C₃₁×#542	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#541	—	2	1	no	—
64	C₃₁×#541	C₂²	1	1	yes	characteristic
65	C₃₁×#539	—	2	1	no	—
66	C₃₁×#539	—	2	1	no	—
67	C₃₁×#538	—	2	1	no	—
68	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#529	—	2	1	no	—
70	C₃₁×#529	C₂²	1	1	yes	characteristic
71	C₃₁×#529	C₂²	1	1	yes	characteristic
72	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₃₁×#126	—	2	1	no	—
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#518	C₂²	1	1	yes	characteristic
76	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#489	C₂²	1	1	yes	characteristic
85	C₃₁×#488	C₂²	1	1	yes	characteristic
86	C₃₁×#488	C₂²	1	1	yes	characteristic
87	C₃₁×#488	C₂²	1	1	yes	characteristic
88	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#485	C₂²	1	1	yes	characteristic
90	C₃₁×#485	C₂²	1	1	yes	characteristic
91	C₃₁×#485	C₂²	1	1	yes	characteristic
92	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#484	C₂²	1	1	yes	characteristic
97	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#483	C₂²	1	1	yes	characteristic
100	C₃₁×#482	C₂²	1	1	yes	characteristic
101	C₃₁×#482	C₂²	1	1	yes	characteristic
102	C₃₁×#482	C₂²	1	1	yes	characteristic
103	C₃₁×#482	C₂²	1	1	yes	characteristic
104	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#480	C₂²	1	1	yes	characteristic
106	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#478	C₂²	1	1	yes	characteristic
115	C₃₁×#478	C₂²	1	1	yes	characteristic
116	C₃₁×#478	C₂²	1	1	yes	characteristic
117	C₃₁×#478	C₂²	1	1	yes	characteristic
118	C₃₁×#478	C₂²	1	1	yes	characteristic
119	C₃₁×#478	C₂²	1	1	yes	characteristic
120	C₃₁×#478	C₂²	1	1	yes	characteristic
121	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#476	C₂²	1	1	yes	characteristic
126	C₃₁×#476	C₂²	1	1	yes	characteristic
127	C₃₁×#476	C₂²	1	1	yes	characteristic
128	C₃₁×#476	C₂²	1	1	yes	characteristic
129	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#474	C₂²	1	1	yes	characteristic
135	C₃₁×#474	C₂²	1	1	yes	characteristic
136	C₃₁×#474	C₂²	1	1	yes	characteristic
137	C₃₁×#470	C₂²	1	1	yes	characteristic
138	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
139	C₃₁×#469	C₂²	1	1	yes	characteristic
140	C₃₁×#468	C₂²	1	1	yes	characteristic
141	C₃₁×#467	C₂²	1	1	yes	characteristic
142	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
143	C₃₁×#466	C₂²	1	1	yes	characteristic
144	C₃₁×#465	C₂²	1	1	yes	characteristic
145	C₃₁×#465	C₂²	1	1	yes	characteristic
146	C₃₁×#465	C₂²	1	1	yes	characteristic
147	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#464	C₂²	1	1	yes	characteristic
150	C₃₁×#464	C₂²	1	1	yes	characteristic
151	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
152	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
153	C₃₁×#463	C₂²	1	1	yes	characteristic
154	C₃₁×#463	C₂²	1	1	yes	characteristic
155	C₃₁×#463	C₂²	1	1	yes	characteristic
156	C₃₁×#463	C₂²	1	1	yes	characteristic
157	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
158	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
159	C₃₁×#452	C₂²	1	1	yes	characteristic
160	C₃₁×#452	C₂²	1	1	yes	characteristic
161	C₃₁×#450	C₂²	1	1	yes	characteristic
162	C₃₁×#449	C₂²	1	1	yes	characteristic
163	C₃₁×#449	C₂²	1	1	yes	characteristic
164	C₃₁×#447	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
166	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
167	C₃₁×#442	C₂²	1	1	yes	characteristic
168	C₃₁×#440	C₂²	1	1	yes	characteristic
169	C₃₁×#440	C₂²	1	1	yes	characteristic
170	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
171	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
172	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
173	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
174	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
179	C₃₁×#436	C₂²	1	1	yes	characteristic
180	C₃₁×#435	C₂²	1	1	yes	characteristic
181	C₃₁×#435	C₂²	1	1	yes	characteristic, complemented
182	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
183	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
184	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
185	C₃₁×#433	C₂²	1	1	yes	characteristic
186	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
187	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
188	C₃₁×#428	C₂²	1	1	yes	characteristic
189	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
190	C₃₁×#427	C₂²	1	1	yes	characteristic
191	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
192	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
193	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
194	C₃₁×#424	C₂²	1	1	yes	characteristic
195	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
197	C₃₁×#418	C₂²	1	1	yes	characteristic
198	C₃₁×#417	C₂²	1	1	yes	characteristic
199	C₃₁×#416	C₂²	1	1	yes	characteristic
200	C₃₁×#416	C₂²	1	1	yes	characteristic
201	C₃₁×#416	C₂²	1	1	yes	characteristic
202	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×#41×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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
216	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₃₁×C₄⋊Q₈	—	2	1	no	—
221	C₃₁×C₄⋊Q₈	—	2	1	no	—
222	C₃₁×C₄⋊Q₈	—	2	1	no	—
223	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
224	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
225	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
229	C₃₁×#126	—	2	1	no	—
230	C₃₁×#126	—	2	1	no	—
231	C₃₁×#126	—	2	1	no	—
232	C₃₁×#126	—	2	1	no	—
233	C₃₁×#126	—	2	1	no	—
234	C₃₁×#126	—	2	1	no	—
235	C₃₁×#126	—	2	1	no	—
236	C₃₁×#126	—	2	1	no	—
237	C₃₁×#126	—	2	1	no	—
238	C₃₁×#126	—	2	1	no	—
239	C₃₁×#126	—	2	1	no	—
240	C₃₁×#126	—	2	1	no	—
241	C₃₁×#126	—	2	1	no	—
242	C₃₁×#126	—	2	1	no	—
243	C₃₁×#126	—	2	1	no	—
244	C₃₁×#126	—	2	1	no	—
245	C₃₁×#126	—	2	1	no	—
246	C₃₁×#126	—	2	1	no	—
247	C₃₁×#126	—	2	1	no	—
248	C₃₁×#126	D₄	1	1	yes	characteristic
249	C₃₁×#126	D₄	1	1	yes	characteristic
250	C₃₁×#125	—	2	1	no	—
251	C₃₁×#125	—	2	1	no	—
252	C₃₁×#125	—	2	1	no	—
253	C₃₁×#125	—	2	1	no	—
254	C₃₁×#125	—	2	1	no	—
255	C₃₁×#125	—	2	1	no	—
256	C₃₁×#125	—	2	1	no	—
257	C₃₁×#125	—	2	1	no	—
258	C₃₁×#125	—	2	1	no	—
259	C₃₁×#125	D₄	1	1	yes	characteristic
260	C₃₁×#125	C₂³	1	1	yes	characteristic
261	C₃₁×#125	C₂³	1	1	yes	characteristic
262	C₃₁×#125	C₂³	1	1	yes	characteristic
263	C₃₁×#125	C₂³	1	1	yes	characteristic
264	C₃₁×#125	C₂³	1	1	yes	characteristic
265	C₃₁×#125	C₂³	1	1	yes	characteristic
266	C₃₁×#125	C₂³	1	1	yes	characteristic
267	C₃₁×#124	—	2	1	no	—
268	C₃₁×#124	—	2	1	no	—
269	C₃₁×#124	—	2	1	no	—
270	C₃₁×#124	—	2	1	no	—
271	C₃₁×#124	—	2	1	no	—
272	C₃₁×#124	—	2	1	no	—
273	C₃₁×#124	—	2	1	no	—
274	C₃₁×#124	D₄	1	1	yes	characteristic
275	C₃₁×#124	C₂³	1	1	yes	characteristic
276	C₃₁×#124	C₂³	1	1	yes	characteristic
277	C₃₁×#124	C₂³	1	1	yes	characteristic
278	C₃₁×#123	—	2	1	no	—
279	C₃₁×#123	—	2	1	no	—
280	C₃₁×#123	—	2	1	no	—
281	C₃₁×#123	—	2	1	no	—
282	C₃₁×#123	—	2	1	no	—
283	C₃₁×#123	—	2	1	no	—
284	C₃₁×#123	—	2	1	no	—
285	C₃₁×#123	—	2	1	no	—
286	C₃₁×#123	—	2	1	no	—
287	C₃₁×#123	—	2	1	no	—
288	C₃₁×#123	—	2	1	no	—
289	C₃₁×#123	—	2	1	no	—
290	C₃₁×#123	—	2	1	no	—
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×#123	D₄	1	1	yes	characteristic
294	C₃₁×#123	D₄	1	1	yes	characteristic
295	C₃₁×C₂²⋊Q₈	—	2	1	no	—
296	C₃₁×C₂²⋊Q₈	—	2	1	no	—
297	C₃₁×C₂²⋊Q₈	—	2	1	no	—
298	C₃₁×C₂²⋊Q₈	—	2	1	no	—
299	C₃₁×C₂²⋊Q₈	—	2	1	no	—
300	C₃₁×C₂²⋊Q₈	—	2	1	no	—
301	C₃₁×C₂²⋊Q₈	—	2	1	no	—
302	C₃₁×C₂²⋊Q₈	—	2	1	no	—
303	C₃₁×C₂²⋊Q₈	—	2	1	no	—
304	C₃₁×C₂²⋊Q₈	—	2	1	no	—
305	C₃₁×C₂²⋊Q₈	—	2	1	no	—
306	C₃₁×C₂²⋊Q₈	—	2	1	no	—
307	C₃₁×C₂²⋊Q₈	—	2	1	no	—
308	C₃₁×C₂²⋊Q₈	—	2	1	no	—
309	C₃₁×C₂²⋊Q₈	—	2	1	no	—
310	C₃₁×C₂²⋊Q₈	—	2	1	no	—
311	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
312	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
313	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
319	C₃₁×#121	—	2	1	no	—
320	C₃₁×#121	—	2	1	no	—
321	C₃₁×#121	—	2	1	no	—
322	C₃₁×#121	—	2	1	no	—
323	C₃₁×#121	—	2	1	no	—
324	C₃₁×#121	—	2	1	no	—
325	C₃₁×#121	—	2	1	no	—
326	C₃₁×#121	D₄	1	1	yes	characteristic
327	C₃₁×#121	C₂³	1	1	yes	characteristic
328	C₃₁×#121	C₂³	1	1	yes	characteristic
329	C₃₁×#121	C₂³	1	1	yes	characteristic
330	C₃₁×#121	C₂³	1	1	yes	characteristic
331	C₃₁×#121	C₂³	1	1	yes	characteristic
332	C₃₁×#120	—	2	1	no	—
333	C₃₁×#120	—	2	1	no	—
334	C₄×Q₈×C₃₁	—	2	1	no	—
335	C₄×Q₈×C₃₁	—	2	1	no	—
336	C₄×Q₈×C₃₁	—	2	1	no	—
337	C₄×Q₈×C₃₁	—	2	1	no	—
338	C₄×Q₈×C₃₁	—	2	1	no	—
339	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
340	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
341	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
342	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
347	C₄×D₄×C₃₁	—	2	1	no	—
348	C₄×D₄×C₃₁	—	2	1	no	—
349	C₄×D₄×C₃₁	—	2	1	no	—
350	C₄×D₄×C₃₁	—	2	1	no	—
351	C₄×D₄×C₃₁	—	2	1	no	—
352	C₄×D₄×C₃₁	—	2	1	no	—
353	C₄×D₄×C₃₁	—	2	1	no	—
354	C₄×D₄×C₃₁	—	2	1	no	—
355	C₄×D₄×C₃₁	—	2	1	no	—
356	C₄×D₄×C₃₁	—	2	1	no	—
357	C₄×D₄×C₃₁	—	2	1	no	—
358	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
359	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
360	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
361	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
370	C₃₁×#117	—	2	1	no	—
371	C₃₁×#117	—	2	1	no	—
372	C₃₁×#117	—	2	1	no	—
373	C₃₁×#117	—	2	1	no	—
374	C₃₁×#117	—	2	1	no	—
375	C₃₁×#117	—	2	1	no	—
376	C₃₁×#117	—	2	1	no	—
377	C₃₁×#117	—	2	1	no	—
378	C₃₁×#117	—	2	1	no	—
379	C₃₁×#117	C₂³	1	1	yes	characteristic
380	C₃₁×#117	C₂³	1	1	yes	characteristic
381	C₃₁×#117	C₂³	1	1	yes	characteristic
382	C₃₁×#117	C₂³	1	1	yes	characteristic
383	C₃₁×#117	C₂³	1	1	yes	characteristic
384	C₃₁×#117	C₂³	1	1	yes	characteristic
385	C₃₁×#117	C₂³	1	1	yes	characteristic
386	C₃₁×#117	C₂³	1	1	yes	characteristic
387	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
394	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
395	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
396	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
397	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
398	C₂×C₄²×C₃₁	—	2	1	no	—
399	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
400	C₃₁×#107	C₂³	1	1	yes	characteristic
401	C₃₁×#107	C₂³	1	1	yes	characteristic
402	C₃₁×#107	C₂³	1	1	yes	characteristic
403	C₃₁×#107	C₂³	1	1	yes	characteristic
404	C₃₁×#107	C₂³	1	1	yes	characteristic
405	C₃₁×#107	C₂³	1	1	yes	characteristic
406	C₃₁×#107	C₂³	1	1	yes	characteristic
407	C₃₁×#107	C₂³	1	1	yes	characteristic
408	C₃₁×#107	C₂³	1	1	yes	characteristic
409	C₃₁×#107	C₂³	1	1	yes	characteristic
410	C₃₁×#107	C₂³	1	1	yes	characteristic
411	C₃₁×#107	C₂³	1	1	yes	characteristic
412	C₃₁×#106	C₂³	1	1	yes	characteristic
413	C₃₁×#106	C₂³	1	1	yes	characteristic
414	C₃₁×#106	C₂³	1	1	yes	characteristic
415	C₃₁×#106	C₂³	1	1	yes	characteristic
416	C₃₁×#106	C₂³	1	1	yes	characteristic
417	C₃₁×#106	C₂³	1	1	yes	characteristic
418	C₃₁×#106	C₂³	1	1	yes	characteristic
419	C₃₁×#106	C₂³	1	1	yes	characteristic
420	C₃₁×#106	C₂³	1	1	yes	characteristic
421	C₃₁×#106	C₂³	1	1	yes	characteristic
422	C₃₁×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	C₂³	1	1	yes	characteristic
424	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#102	C₂³	1	1	yes	characteristic
451	C₃₁×#102	C₂³	1	1	yes	characteristic
452	C₃₁×#102	C₂³	1	1	yes	characteristic
453	C₃₁×#102	C₂³	1	1	yes	characteristic
454	C₃₁×#102	C₂³	1	1	yes	characteristic
455	C₃₁×#102	C₂³	1	1	yes	characteristic
456	C₃₁×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×#102	C₂³	1	1	yes	characteristic
463	C₃₁×#102	C₂³	1	1	yes	characteristic
464	C₃₁×#102	C₂³	1	1	yes	characteristic
465	C₃₁×#102	C₂³	1	1	yes	characteristic
466	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	C₃₁×#97	C₂³	1	1	yes	characteristic
473	C₃₁×#97	C₂³	1	1	yes	characteristic
474	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	—	2	2	no	—
480	#41×C₃₁	—	2	2	no	—
481	#41×C₃₁	—	4	1	no	—
482	#41×C₃₁	—	4	1	no	—
483	C₂×Q₈×C₃₁	—	2	1	no	—
484	C₂×Q₈×C₃₁	—	2	1	no	—
485	C₂×Q₈×C₃₁	—	2	1	no	—
486	C₂×Q₈×C₃₁	—	2	1	no	—
487	C₂×Q₈×C₃₁	—	2	1	no	—
488	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
489	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
490	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
491	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
492	C₂×D₄×C₃₁	—	2	2	no	—
493	C₂×D₄×C₃₁	—	2	1	no	—
494	C₂×D₄×C₃₁	—	2	1	no	—
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	—	4	1	no	—
502	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
503	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
504	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
505	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
506	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
507	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₃₁	—	2	1	no	—
509	C₂²×C₄×C₃₁	—	2	1	no	—
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	—	2	1	no	—
522	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
523	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
524	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
526	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
527	Q₁₆×C₃₁	—	4	1	no	—
528	Q₁₆×C₃₁	—	4	1	no	—
529	SD₁₆×C₃₁	—	2	2	no	—
530	SD₁₆×C₃₁	—	4	1	no	—
531	SD₁₆×C₃₁	—	4	1	no	—
532	SD₁₆×C₃₁	—	4	1	no	—
533	D₈×C₃₁	—	2	2	no	—
534	D₈×C₃₁	—	4	1	no	—
535	M₁₆×C₃₁	—	4	1	no	—
536	M₁₆×C₃₁	—	4	1	no	—
537	C₂×C₈×C₃₁	—	4	1	no	—
538	C₂×C₈×C₃₁	—	4	1	no	—
539	C₂×C₈×C₃₁	—	4	1	no	—
540	C₂×C₈×C₃₁	—	4	1	no	—
541	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
542	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
543	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
544	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
545	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
546	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
547	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
548	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
549	C₄⋊C₄×C₃₁	—	2	1	no	—
550	C₄⋊C₄×C₃₁	—	2	1	no	—
551	C₄⋊C₄×C₃₁	—	2	1	no	—
552	C₄⋊C₄×C₃₁	—	2	1	no	—
553	C₄⋊C₄×C₃₁	—	2	1	no	—
554	C₄⋊C₄×C₃₁	—	2	1	no	—
555	C₄⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
588	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
589	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
590	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
591	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
592	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
593	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
598	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
600	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
607	C₂²⋊C₄×C₃₁	—	2	1	no	—
608	C₂²⋊C₄×C₃₁	—	2	1	no	—
609	C₂²⋊C₄×C₃₁	—	2	1	no	—
610	C₂²⋊C₄×C₃₁	—	2	1	no	—
611	C₂²⋊C₄×C₃₁	—	2	1	no	—
612	C₂²⋊C₄×C₃₁	—	2	1	no	—
613	C₂²⋊C₄×C₃₁	—	2	1	no	—
614	C₂²⋊C₄×C₃₁	—	2	1	no	—
615	C₂²⋊C₄×C₃₁	—	2	1	no	—
616	C₂²⋊C₄×C₃₁	—	2	1	no	—
617	C₂²⋊C₄×C₃₁	—	2	1	no	—
618	C₂²⋊C₄×C₃₁	—	2	1	no	—
619	C₂²⋊C₄×C₃₁	—	2	1	no	—
620	C₂²⋊C₄×C₃₁	—	2	1	no	—
621	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	—	2	1	no	—
638	C₂²⋊C₄×C₃₁	—	2	1	no	—
639	C₂²⋊C₄×C₃₁	—	2	1	no	—
640	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
641	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
642	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
643	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
644	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
645	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
646	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
647	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
648	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
649	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
650	C₄²×C₃₁	—	2	1	no	—
651	C₄²×C₃₁	—	2	1	no	—
652	C₄²×C₃₁	—	2	1	no	—
653	C₄²×C₃₁	—	2	1	no	—
654	C₄²×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
664	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
665	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
666	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
667	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
668	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
669	#62208	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
670	C₂³×C₃₁	—	2	1	no	—
671	C₂³×C₃₁	—	2	1	no	—
672	C₂³×C₃₁	—	2	1	no	—
673	C₂³×C₃₁	—	4	2	no	—
674	C₂³×C₃₁	—	8	1	no	—
675	C₂³×C₃₁	—	8	1	no	—
676	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
677	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
678	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
679	Q₈×C₃₁	—	2	1	no	—
680	Q₈×C₃₁	—	2	1	no	—
681	Q₈×C₃₁	—	2	1	no	—
682	Q₈×C₃₁	—	2	1	no	—
683	Q₈×C₃₁	—	2	1	no	—
684	Q₈×C₃₁	—	2	1	no	—
685	Q₈×C₃₁	—	4	1	no	—
686	Q₈×C₃₁	—	8	1	no	—
687	Q₈×C₃₁	—	8	1	no	—
688	Q₈×C₃₁	—	8	1	no	—
689	Q₈×C₃₁	—	8	1	no	—
690	Q₈×C₃₁	—	8	1	no	—
691	D₄×C₃₁	—	2	1	no	—
692	D₄×C₃₁	—	2	1	no	—
693	D₄×C₃₁	—	2	1	no	—
694	D₄×C₃₁	—	2	1	no	—
695	D₄×C₃₁	—	2	1	no	—
696	D₄×C₃₁	—	4	1	no	—
697	D₄×C₃₁	—	4	1	no	—
698	D₄×C₃₁	—	4	1	no	—
699	D₄×C₃₁	—	4	2	no	—
700	D₄×C₃₁	—	4	2	no	—
701	D₄×C₃₁	—	4	2	no	—
702	D₄×C₃₁	—	8	1	no	—
703	D₄×C₃₁	—	8	1	no	—
704	D₄×C₃₁	—	8	1	no	—
705	D₄×C₃₁	—	8	1	no	—
706	D₄×C₃₁	—	8	1	no	—
707	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
708	C₂×C₄×C₃₁	—	2	1	no	—
709	C₂×C₄×C₃₁	—	2	1	no	—
710	C₂×C₄×C₃₁	—	2	1	no	—
711	C₂×C₄×C₃₁	—	2	1	no	—
712	C₂×C₄×C₃₁	—	2	1	no	—
713	C₂×C₄×C₃₁	—	2	1	no	—
714	C₂×C₄×C₃₁	—	2	1	no	—
715	C₂×C₄×C₃₁	—	2	1	no	—
716	C₂×C₄×C₃₁	—	2	1	no	—
717	C₂×C₄×C₃₁	—	2	1	no	—
718	C₂×C₄×C₃₁	—	2	1	no	—
719	C₂×C₄×C₃₁	—	2	1	no	—
720	C₂×C₄×C₃₁	—	2	1	no	—
721	C₂×C₄×C₃₁	—	2	1	no	—
722	C₂×C₄×C₃₁	—	2	1	no	—
723	C₂×C₄×C₃₁	—	2	1	no	—
724	C₂×C₄×C₃₁	—	2	1	no	—
725	C₂×C₄×C₃₁	—	2	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	4	1	no	—
728	C₂×C₄×C₃₁	—	4	1	no	—
729	C₂×C₄×C₃₁	—	4	2	no	—
730	C₂×C₄×C₃₁	—	4	2	no	—
731	C₂×C₄×C₃₁	—	8	1	no	—
732	C₂×C₄×C₃₁	—	8	1	no	—
733	C₂×C₄×C₃₁	—	8	1	no	—
734	C₂×C₄×C₃₁	—	8	1	no	—
735	C₂×C₄×C₃₁	—	8	1	no	—
736	C₂×C₄×C₃₁	—	8	1	no	—
737	C₂×C₄×C₃₁	—	8	1	no	—
738	C₂×C₄×C₃₁	—	8	1	no	—
739	C₂×C₄×C₃₁	—	8	1	no	—
740	C₂×C₄×C₃₁	—	8	1	no	—
741	C₂×C₄×C₃₁	—	8	1	no	—
742	C₂×C₄×C₃₁	—	8	1	no	—
743	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
748	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
749	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
755	C₈×C₃₁	—	2	1	no	—
756	C₈×C₃₁	—	2	1	no	—
757	C₈×C₃₁	—	2	1	no	—
758	C₈×C₃₁	—	2	1	no	—
759	C₈×C₃₁	—	2	1	no	—
760	C₈×C₃₁	—	2	1	no	—
761	C₈×C₃₁	—	2	1	no	—
762	C₈×C₃₁	—	2	1	no	—
763	#3565	C₂×C₃₁	1	1	yes	characteristic, complemented
764	#3521	C₂×C₃₁	1	1	yes	characteristic, complemented
765	#3388	C₂×C₃₁	1	1	yes	characteristic, complemented
766	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
767	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
768	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
769	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
770	#3350	C₂×C₃₁	1	1	yes	characteristic, complemented
771	#3347	C₂×C₃₁	1	1	yes	characteristic, complemented
772	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
773	#3337	C₂×C₃₁	1	1	yes	characteristic, complemented
774	#3337	C₂×C₃₁	1	1	yes	characteristic, complemented
775	#3322	C₂×C₃₁	1	1	yes	characteristic, complemented
776	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
777	#3311	C₂×C₃₁	1	1	yes	characteristic, complemented
778	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3297	C₂×C₃₁	1	1	yes	characteristic, complemented
780	#3296	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3263	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3258	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3250	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3243	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3124	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3118	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
794	C₂²×C₃₁	—	2	1	no	—
795	C₂²×C₃₁	—	2	1	no	—
796	C₂²×C₃₁	—	2	1	no	—
797	C₂²×C₃₁	—	2	1	no	—
798	C₂²×C₃₁	—	2	1	no	—
799	C₂²×C₃₁	—	2	1	no	—
800	C₂²×C₃₁	—	2	1	no	—
801	C₂²×C₃₁	—	2	1	no	—
802	C₂²×C₃₁	—	2	1	no	—
803	C₂²×C₃₁	—	2	2	no	—
804	C₂²×C₃₁	—	4	1	no	—
805	C₂²×C₃₁	—	4	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	—	16	2	no	—
813	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
814	C₄×C₃₁	—	2	1	no	—
815	C₄×C₃₁	—	2	1	no	—
816	C₄×C₃₁	—	2	1	no	—
817	C₄×C₃₁	—	2	1	no	—
818	C₄×C₃₁	—	2	1	no	—
819	C₄×C₃₁	—	2	1	no	—
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	—	4	1	no	—
826	C₄×C₃₁	—	4	1	no	—
827	C₄×C₃₁	—	4	1	no	—
828	C₄×C₃₁	—	4	1	no	—
829	C₄×C₃₁	—	4	1	no	—
830	C₄×C₃₁	—	4	1	no	—
831	C₄×C₃₁	—	4	1	no	—
832	C₄×C₃₁	—	4	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	C₂×2₋¹⁺⁴	1	1	yes	characteristic
839	C₄×C₃₁	#585	1	1	yes	characteristic
840	#563	—	2	1	no	—
841	#562	—	2	1	no	—
842	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
843	#556	—	2	1	no	—
844	#556	C₂²×C₃₁	1	1	yes	characteristic
845	#556	C₂²×C₃₁	1	1	yes	characteristic
846	#556	C₂²×C₃₁	1	1	yes	characteristic
847	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
848	#554	C₂²×C₃₁	1	1	yes	characteristic
849	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
850	#553	—	2	1	no	—
851	#553	C₂²×C₃₁	1	1	yes	characteristic
852	#553	C₂²×C₃₁	1	1	yes	characteristic
853	#553	C₂²×C₃₁	1	1	yes	characteristic
854	#552	—	2	1	no	—
855	#552	—	2	1	no	—
856	#552	C₂²×C₃₁	1	1	yes	characteristic
857	#552	C₂²×C₃₁	1	1	yes	characteristic
858	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
859	#551	—	2	1	no	—
860	#551	—	2	1	no	—
861	#547	C₂²×C₃₁	1	1	yes	characteristic
862	#546	C₂²×C₃₁	1	1	yes	characteristic
863	#546	C₂²×C₃₁	1	1	yes	characteristic
864	#544	C₂²×C₃₁	1	1	yes	characteristic
865	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
866	#542	—	2	1	no	—
867	#542	—	2	1	no	—
868	#542	C₂²×C₃₁	1	1	yes	characteristic
869	#542	C₂²×C₃₁	1	1	yes	characteristic
870	#542	C₂²×C₃₁	1	1	yes	characteristic, complemented
871	#541	—	2	1	no	—
872	#541	C₂²×C₃₁	1	1	yes	characteristic
873	#539	—	2	1	no	—
874	#539	—	2	1	no	—
875	#538	—	2	1	no	—
876	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
877	#529	—	2	1	no	—
878	#529	C₂²×C₃₁	1	1	yes	characteristic
879	#529	C₂²×C₃₁	1	1	yes	characteristic
880	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
881	C₂×#126	—	2	1	no	—
882	#520	C₂²×C₃₁	1	1	yes	characteristic
883	#518	C₂²×C₃₁	1	1	yes	characteristic
884	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
885	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
886	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
887	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
888	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
889	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
890	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
891	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
892	#489	C₂²×C₃₁	1	1	yes	characteristic
893	#488	C₂²×C₃₁	1	1	yes	characteristic
894	#488	C₂²×C₃₁	1	1	yes	characteristic
895	#488	C₂²×C₃₁	1	1	yes	characteristic
896	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
897	#485	C₂²×C₃₁	1	1	yes	characteristic
898	#485	C₂²×C₃₁	1	1	yes	characteristic
899	#485	C₂²×C₃₁	1	1	yes	characteristic
900	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
901	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
902	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
903	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
904	#484	C₂²×C₃₁	1	1	yes	characteristic
905	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
906	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
907	#483	C₂²×C₃₁	1	1	yes	characteristic
908	#482	C₂²×C₃₁	1	1	yes	characteristic
909	#482	C₂²×C₃₁	1	1	yes	characteristic
910	#482	C₂²×C₃₁	1	1	yes	characteristic
911	#482	C₂²×C₃₁	1	1	yes	characteristic
912	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
913	#480	C₂²×C₃₁	1	1	yes	characteristic
914	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
916	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
917	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
918	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
919	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
920	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
921	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
922	#478	C₂²×C₃₁	1	1	yes	characteristic
923	#478	C₂²×C₃₁	1	1	yes	characteristic
924	#478	C₂²×C₃₁	1	1	yes	characteristic
925	#478	C₂²×C₃₁	1	1	yes	characteristic
926	#478	C₂²×C₃₁	1	1	yes	characteristic
927	#478	C₂²×C₃₁	1	1	yes	characteristic
928	#478	C₂²×C₃₁	1	1	yes	characteristic
929	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
930	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
931	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
932	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
933	#476	C₂²×C₃₁	1	1	yes	characteristic
934	#476	C₂²×C₃₁	1	1	yes	characteristic
935	#476	C₂²×C₃₁	1	1	yes	characteristic
936	#476	C₂²×C₃₁	1	1	yes	characteristic
937	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
938	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
939	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
940	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
941	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
942	#474	C₂²×C₃₁	1	1	yes	characteristic
943	#474	C₂²×C₃₁	1	1	yes	characteristic
944	#474	C₂²×C₃₁	1	1	yes	characteristic
945	#470	C₂²×C₃₁	1	1	yes	characteristic
946	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
947	#469	C₂²×C₃₁	1	1	yes	characteristic
948	#468	C₂²×C₃₁	1	1	yes	characteristic
949	#467	C₂²×C₃₁	1	1	yes	characteristic
950	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
951	#466	C₂²×C₃₁	1	1	yes	characteristic
952	#465	C₂²×C₃₁	1	1	yes	characteristic
953	#465	C₂²×C₃₁	1	1	yes	characteristic
954	#465	C₂²×C₃₁	1	1	yes	characteristic
955	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
956	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
957	#464	C₂²×C₃₁	1	1	yes	characteristic
958	#464	C₂²×C₃₁	1	1	yes	characteristic
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	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
966	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
967	#452	C₂²×C₃₁	1	1	yes	characteristic
968	#452	C₂²×C₃₁	1	1	yes	characteristic
969	#450	C₂²×C₃₁	1	1	yes	characteristic
970	#449	C₂²×C₃₁	1	1	yes	characteristic
971	#449	C₂²×C₃₁	1	1	yes	characteristic
972	#447	C₂²×C₃₁	1	1	yes	characteristic
973	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
974	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
975	#442	C₂²×C₃₁	1	1	yes	characteristic
976	#440	C₂²×C₃₁	1	1	yes	characteristic
977	#440	C₂²×C₃₁	1	1	yes	characteristic
978	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
979	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
980	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
981	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
982	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
983	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
984	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
985	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
986	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
987	#436	C₂²×C₃₁	1	1	yes	characteristic
988	#435	C₂²×C₃₁	1	1	yes	characteristic
989	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
990	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
991	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
992	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
993	#433	C₂²×C₃₁	1	1	yes	characteristic
994	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
995	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
996	#428	C₂²×C₃₁	1	1	yes	characteristic
997	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
998	#427	C₂²×C₃₁	1	1	yes	characteristic
999	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
1000	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
1001	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	#424	C₂²×C₃₁	1	1	yes	characteristic
1003	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
1004	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	#418	C₂²×C₃₁	1	1	yes	characteristic
1006	#417	C₂²×C₃₁	1	1	yes	characteristic
1007	#416	C₂²×C₃₁	1	1	yes	characteristic
1008	#416	C₂²×C₃₁	1	1	yes	characteristic
1009	#416	C₂²×C₃₁	1	1	yes	characteristic
1010	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
1011	C₂×C₃₁	—	4	1	no	—
1012	C₂×C₃₁	—	4	1	no	—
1013	C₂×C₃₁	—	4	1	no	—
1014	C₂×C₃₁	—	4	2	no	—
1015	C₂×C₃₁	—	8	1	no	—
1016	C₂×C₃₁	—	8	1	no	—
1017	C₂×C₃₁	#3489	1	1	yes	characteristic
1018	C₂×C₃₁	#3584	1	1	yes	characteristic
1019	C₂×C₃₁	#3584	1	1	yes	characteristic
1020	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1021	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1022	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1023	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1024	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1025	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1026	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1027	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1028	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1029	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1030	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1031	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1032	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1033	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1034	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1035	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1036	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1037	C₄⋊Q₈	—	2	1	no	—
1038	C₄⋊Q₈	—	2	1	no	—
1039	C₄⋊Q₈	—	2	1	no	—
1040	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1041	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1042	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1043	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1044	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1045	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1046	#126	—	2	1	no	—
1047	#126	—	2	1	no	—
1048	#126	—	2	1	no	—
1049	#126	—	2	1	no	—
1050	#126	—	2	1	no	—
1051	#126	—	2	1	no	—
1052	#126	—	2	1	no	—
1053	#126	—	2	1	no	—
1054	#126	—	2	1	no	—
1055	#126	—	2	1	no	—
1056	#126	—	2	1	no	—
1057	#126	—	2	1	no	—
1058	#126	—	2	1	no	—
1059	#126	—	2	1	no	—
1060	#126	—	2	1	no	—
1061	#126	—	2	1	no	—
1062	#126	—	2	1	no	—
1063	#126	—	2	1	no	—
1064	#126	—	2	1	no	—
1065	#126	D₄×C₃₁	1	1	yes	characteristic
1066	#126	D₄×C₃₁	1	1	yes	characteristic
1067	#125	—	2	1	no	—
1068	#125	—	2	1	no	—
1069	#125	—	2	1	no	—
1070	#125	—	2	1	no	—
1071	#125	—	2	1	no	—
1072	#125	—	2	1	no	—
1073	#125	—	2	1	no	—
1074	#125	—	2	1	no	—
1075	#125	—	2	1	no	—
1076	#125	D₄×C₃₁	1	1	yes	characteristic
1077	#125	C₂³×C₃₁	1	1	yes	characteristic
1078	#125	C₂³×C₃₁	1	1	yes	characteristic
1079	#125	C₂³×C₃₁	1	1	yes	characteristic
1080	#125	C₂³×C₃₁	1	1	yes	characteristic
1081	#125	C₂³×C₃₁	1	1	yes	characteristic
1082	#125	C₂³×C₃₁	1	1	yes	characteristic
1083	#125	C₂³×C₃₁	1	1	yes	characteristic
1084	#124	—	2	1	no	—
1085	#124	—	2	1	no	—
1086	#124	—	2	1	no	—
1087	#124	—	2	1	no	—
1088	#124	—	2	1	no	—
1089	#124	—	2	1	no	—
1090	#124	—	2	1	no	—
1091	#124	D₄×C₃₁	1	1	yes	characteristic
1092	#124	C₂³×C₃₁	1	1	yes	characteristic
1093	#124	C₂³×C₃₁	1	1	yes	characteristic
1094	#124	C₂³×C₃₁	1	1	yes	characteristic
1095	#123	—	2	1	no	—
1096	#123	—	2	1	no	—
1097	#123	—	2	1	no	—
1098	#123	—	2	1	no	—
1099	#123	—	2	1	no	—
1100	#123	—	2	1	no	—
1101	#123	—	2	1	no	—
1102	#123	—	2	1	no	—
1103	#123	—	2	1	no	—
1104	#123	—	2	1	no	—
1105	#123	—	2	1	no	—
1106	#123	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	—	2	1	no	—
1109	#123	—	2	1	no	—
1110	#123	D₄×C₃₁	1	1	yes	characteristic
1111	#123	D₄×C₃₁	1	1	yes	characteristic
1112	C₂²⋊Q₈	—	2	1	no	—
1113	C₂²⋊Q₈	—	2	1	no	—
1114	C₂²⋊Q₈	—	2	1	no	—
1115	C₂²⋊Q₈	—	2	1	no	—
1116	C₂²⋊Q₈	—	2	1	no	—
1117	C₂²⋊Q₈	—	2	1	no	—
1118	C₂²⋊Q₈	—	2	1	no	—
1119	C₂²⋊Q₈	—	2	1	no	—
1120	C₂²⋊Q₈	—	2	1	no	—
1121	C₂²⋊Q₈	—	2	1	no	—
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	—	2	1	no	—
1125	C₂²⋊Q₈	—	2	1	no	—
1126	C₂²⋊Q₈	—	2	1	no	—
1127	C₂²⋊Q₈	—	2	1	no	—
1128	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1129	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1130	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1131	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1132	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1133	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1134	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1135	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1136	#121	—	2	1	no	—
1137	#121	—	2	1	no	—
1138	#121	—	2	1	no	—
1139	#121	—	2	1	no	—
1140	#121	—	2	1	no	—
1141	#121	—	2	1	no	—
1142	#121	—	2	1	no	—
1143	#121	D₄×C₃₁	1	1	yes	characteristic
1144	#121	C₂³×C₃₁	1	1	yes	characteristic
1145	#121	C₂³×C₃₁	1	1	yes	characteristic
1146	#121	C₂³×C₃₁	1	1	yes	characteristic
1147	#121	C₂³×C₃₁	1	1	yes	characteristic
1148	#121	C₂³×C₃₁	1	1	yes	characteristic
1149	#120	—	2	1	no	—
1150	#120	—	2	1	no	—
1151	C₄×Q₈	—	2	1	no	—
1152	C₄×Q₈	—	2	1	no	—
1153	C₄×Q₈	—	2	1	no	—
1154	C₄×Q₈	—	2	1	no	—
1155	C₄×Q₈	—	2	1	no	—
1156	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1157	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1158	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1159	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1160	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1161	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1162	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1163	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1164	C₄×D₄	—	2	1	no	—
1165	C₄×D₄	—	2	1	no	—
1166	C₄×D₄	—	2	1	no	—
1167	C₄×D₄	—	2	1	no	—
1168	C₄×D₄	—	2	1	no	—
1169	C₄×D₄	—	2	1	no	—
1170	C₄×D₄	—	2	1	no	—
1171	C₄×D₄	—	2	1	no	—
1172	C₄×D₄	—	2	1	no	—
1173	C₄×D₄	—	2	1	no	—
1174	C₄×D₄	—	2	1	no	—
1175	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1176	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1177	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1178	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1179	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1180	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1181	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1182	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1183	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1184	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1185	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1186	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1187	#117	—	2	1	no	—
1188	#117	—	2	1	no	—
1189	#117	—	2	1	no	—
1190	#117	—	2	1	no	—
1191	#117	—	2	1	no	—
1192	#117	—	2	1	no	—
1193	#117	—	2	1	no	—
1194	#117	—	2	1	no	—
1195	#117	—	2	1	no	—
1196	#117	C₂³×C₃₁	1	1	yes	characteristic
1197	#117	C₂³×C₃₁	1	1	yes	characteristic
1198	#117	C₂³×C₃₁	1	1	yes	characteristic
1199	#117	C₂³×C₃₁	1	1	yes	characteristic
1200	#117	C₂³×C₃₁	1	1	yes	characteristic
1201	#117	C₂³×C₃₁	1	1	yes	characteristic
1202	#117	C₂³×C₃₁	1	1	yes	characteristic
1203	#117	C₂³×C₃₁	1	1	yes	characteristic
1204	C₂×C₄⋊C₄	—	2	1	no	—
1205	C₂×C₄⋊C₄	—	2	1	no	—
1206	C₂×C₄⋊C₄	—	2	1	no	—
1207	C₂×C₄⋊C₄	—	2	1	no	—
1208	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1209	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1210	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1211	C₂×C₂²⋊C₄	—	2	1	no	—
1212	C₂×C₂²⋊C₄	—	2	1	no	—
1213	C₂×C₂²⋊C₄	—	2	1	no	—
1214	C₂×C₂²⋊C₄	—	2	1	no	—
1215	C₂×C₄²	—	2	1	no	—
1216	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1217	#107	C₂³×C₃₁	1	1	yes	characteristic
1218	#107	C₂³×C₃₁	1	1	yes	characteristic
1219	#107	C₂³×C₃₁	1	1	yes	characteristic
1220	#107	C₂³×C₃₁	1	1	yes	characteristic
1221	#107	C₂³×C₃₁	1	1	yes	characteristic
1222	#107	C₂³×C₃₁	1	1	yes	characteristic
1223	#107	C₂³×C₃₁	1	1	yes	characteristic
1224	#107	C₂³×C₃₁	1	1	yes	characteristic
1225	#107	C₂³×C₃₁	1	1	yes	characteristic
1226	#107	C₂³×C₃₁	1	1	yes	characteristic
1227	#107	C₂³×C₃₁	1	1	yes	characteristic
1228	#107	C₂³×C₃₁	1	1	yes	characteristic
1229	#106	C₂³×C₃₁	1	1	yes	characteristic
1230	#106	C₂³×C₃₁	1	1	yes	characteristic
1231	#106	C₂³×C₃₁	1	1	yes	characteristic
1232	#106	C₂³×C₃₁	1	1	yes	characteristic
1233	#106	C₂³×C₃₁	1	1	yes	characteristic
1234	#106	C₂³×C₃₁	1	1	yes	characteristic
1235	#106	C₂³×C₃₁	1	1	yes	characteristic
1236	#106	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	#103	C₂³×C₃₁	1	1	yes	characteristic
1252	#103	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	#102	C₂³×C₃₁	1	1	yes	characteristic
1268	#102	C₂³×C₃₁	1	1	yes	characteristic
1269	#102	C₂³×C₃₁	1	1	yes	characteristic
1270	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1284	C₂²⋊C₈	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	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1292	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1293	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1294	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1295	C₃₁	#62208	1	1	yes	characteristic, direct product factor, Sylow
1296	C₂⁴	—	2	1	no	—
1297	#41	—	2	2	no	—
1298	#41	—	2	2	no	—
1299	#41	—	4	1	no	—
1300	#41	—	4	1	no	—
1301	C₂×Q₈	—	2	1	no	—
1302	C₂×Q₈	—	2	1	no	—
1303	C₂×Q₈	—	2	1	no	—
1304	C₂×Q₈	—	2	1	no	—
1305	C₂×Q₈	—	2	1	no	—
1306	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1307	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1308	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1309	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1310	C₂×D₄	—	2	2	no	—
1311	C₂×D₄	—	2	1	no	—
1312	C₂×D₄	—	2	1	no	—
1313	C₂×D₄	—	2	1	no	—
1314	C₂×D₄	—	2	1	no	—
1315	C₂×D₄	—	2	1	no	—
1316	C₂×D₄	—	2	1	no	—
1317	C₂×D₄	—	2	1	no	—
1318	C₂×D₄	—	2	1	no	—
1319	C₂×D₄	—	4	1	no	—
1320	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1321	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1322	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1323	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1324	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1325	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1326	C₂²×C₄	—	2	1	no	—
1327	C₂²×C₄	—	2	1	no	—
1328	C₂²×C₄	—	2	1	no	—
1329	C₂²×C₄	—	2	1	no	—
1330	C₂²×C₄	—	2	1	no	—
1331	C₂²×C₄	—	2	1	no	—
1332	C₂²×C₄	—	2	1	no	—
1333	C₂²×C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1341	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1342	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1343	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1344	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1345	Q₁₆	—	4	1	no	—
1346	Q₁₆	—	4	1	no	—
1347	SD₁₆	—	2	2	no	—
1348	SD₁₆	—	4	1	no	—
1349	SD₁₆	—	4	1	no	—
1350	SD₁₆	—	4	1	no	—
1351	D₈	—	2	2	no	—
1352	D₈	—	4	1	no	—
1353	M₁₆	—	4	1	no	—
1354	M₁₆	—	4	1	no	—
1355	C₂×C₈	—	4	1	no	—
1356	C₂×C₈	—	4	1	no	—
1357	C₂×C₈	—	4	1	no	—
1358	C₂×C₈	—	4	1	no	—
1359	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1360	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1361	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1362	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1363	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1364	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1365	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1366	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1367	C₄⋊C₄	—	2	1	no	—
1368	C₄⋊C₄	—	2	1	no	—
1369	C₄⋊C₄	—	2	1	no	—
1370	C₄⋊C₄	—	2	1	no	—
1371	C₄⋊C₄	—	2	1	no	—
1372	C₄⋊C₄	—	2	1	no	—
1373	C₄⋊C₄	—	2	1	no	—
1374	C₄⋊C₄	—	2	1	no	—
1375	C₄⋊C₄	—	2	1	no	—
1376	C₄⋊C₄	—	2	1	no	—
1377	C₄⋊C₄	—	2	1	no	—
1378	C₄⋊C₄	—	2	1	no	—
1379	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1406	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1407	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1408	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1409	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1410	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1411	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1412	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1413	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1414	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1415	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1416	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1417	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1418	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1419	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1420	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1421	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1422	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1423	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1424	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1425	C₂²⋊C₄	—	2	1	no	—
1426	C₂²⋊C₄	—	2	1	no	—
1427	C₂²⋊C₄	—	2	1	no	—
1428	C₂²⋊C₄	—	2	1	no	—
1429	C₂²⋊C₄	—	2	1	no	—
1430	C₂²⋊C₄	—	2	1	no	—
1431	C₂²⋊C₄	—	2	1	no	—
1432	C₂²⋊C₄	—	2	1	no	—
1433	C₂²⋊C₄	—	2	1	no	—
1434	C₂²⋊C₄	—	2	1	no	—
1435	C₂²⋊C₄	—	2	1	no	—
1436	C₂²⋊C₄	—	2	1	no	—
1437	C₂²⋊C₄	—	2	1	no	—
1438	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1459	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1460	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1461	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1462	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1463	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1464	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1465	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1466	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1467	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1468	C₄²	—	2	1	no	—
1469	C₄²	—	2	1	no	—
1470	C₄²	—	2	1	no	—
1471	C₄²	—	2	1	no	—
1472	C₄²	—	2	1	no	—
1473	C₄²	—	2	1	no	—
1474	C₄²	—	2	1	no	—
1475	C₄²	—	2	1	no	—
1476	C₄²	—	2	1	no	—
1477	C₄²	—	2	1	no	—
1478	C₄²	—	2	1	no	—
1479	C₄²	—	2	1	no	—
1480	C₄²	—	2	1	no	—
1481	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1482	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1483	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1484	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1485	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1486	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1487	C₂³	—	2	1	no	—
1488	C₂³	—	2	1	no	—
1489	C₂³	—	2	1	no	—
1490	C₂³	—	4	2	no	—
1491	C₂³	—	8	1	no	—
1492	C₂³	—	8	1	no	—
1493	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1494	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1495	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1496	Q₈	—	2	1	no	—
1497	Q₈	—	2	1	no	—
1498	Q₈	—	2	1	no	—
1499	Q₈	—	2	1	no	—
1500	Q₈	—	2	1	no	—
1501	Q₈	—	2	1	no	—
1502	Q₈	—	4	1	no	—
1503	Q₈	—	8	1	no	—
1504	Q₈	—	8	1	no	—
1505	Q₈	—	8	1	no	—
1506	Q₈	—	8	1	no	—
1507	Q₈	—	8	1	no	—
1508	D₄	—	2	1	no	—
1509	D₄	—	2	1	no	—
1510	D₄	—	2	1	no	—
1511	D₄	—	2	1	no	—
1512	D₄	—	2	1	no	—
1513	D₄	—	4	1	no	—
1514	D₄	—	4	1	no	—
1515	D₄	—	4	1	no	—
1516	D₄	—	4	2	no	—
1517	D₄	—	4	2	no	—
1518	D₄	—	4	2	no	—
1519	D₄	—	8	1	no	—
1520	D₄	—	8	1	no	—
1521	D₄	—	8	1	no	—
1522	D₄	—	8	1	no	—
1523	D₄	—	8	1	no	—
1524	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1525	C₂×C₄	—	2	1	no	—
1526	C₂×C₄	—	2	1	no	—
1527	C₂×C₄	—	2	1	no	—
1528	C₂×C₄	—	2	1	no	—
1529	C₂×C₄	—	2	1	no	—
1530	C₂×C₄	—	2	1	no	—
1531	C₂×C₄	—	2	1	no	—
1532	C₂×C₄	—	2	1	no	—
1533	C₂×C₄	—	2	1	no	—
1534	C₂×C₄	—	2	1	no	—
1535	C₂×C₄	—	2	1	no	—
1536	C₂×C₄	—	2	1	no	—
1537	C₂×C₄	—	2	1	no	—
1538	C₂×C₄	—	2	1	no	—
1539	C₂×C₄	—	2	1	no	—
1540	C₂×C₄	—	2	1	no	—
1541	C₂×C₄	—	2	1	no	—
1542	C₂×C₄	—	2	1	no	—
1543	C₂×C₄	—	2	1	no	—
1544	C₂×C₄	—	4	1	no	—
1545	C₂×C₄	—	4	1	no	—
1546	C₂×C₄	—	4	2	no	—
1547	C₂×C₄	—	4	2	no	—
1548	C₂×C₄	—	8	1	no	—
1549	C₂×C₄	—	8	1	no	—
1550	C₂×C₄	—	8	1	no	—
1551	C₂×C₄	—	8	1	no	—
1552	C₂×C₄	—	8	1	no	—
1553	C₂×C₄	—	8	1	no	—
1554	C₂×C₄	—	8	1	no	—
1555	C₂×C₄	—	8	1	no	—
1556	C₂×C₄	—	8	1	no	—
1557	C₂×C₄	—	8	1	no	—
1558	C₂×C₄	—	8	1	no	—
1559	C₂×C₄	—	8	1	no	—
1560	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1561	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1562	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1563	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1564	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1565	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1566	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1567	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1568	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1569	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1570	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1571	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1572	C₈	—	2	1	no	—
1573	C₈	—	2	1	no	—
1574	C₈	—	2	1	no	—
1575	C₈	—	2	1	no	—
1576	C₈	—	2	1	no	—
1577	C₈	—	2	1	no	—
1578	C₈	—	2	1	no	—
1579	C₈	—	2	1	no	—
1580	C₂²	—	2	1	no	—
1581	C₂²	—	2	1	no	—
1582	C₂²	—	2	1	no	—
1583	C₂²	—	2	2	no	—
1584	C₂²	—	2	1	no	—
1585	C₂²	—	2	1	no	—
1586	C₂²	—	2	1	no	—
1587	C₂²	—	2	1	no	—
1588	C₂²	—	2	1	no	—
1589	C₂²	—	2	1	no	—
1590	C₂²	—	4	1	no	—
1591	C₂²	—	4	1	no	—
1592	C₂²	—	4	1	no	—
1593	C₂²	—	4	1	no	—
1594	C₂²	—	4	1	no	—
1595	C₂²	—	4	1	no	—
1596	C₂²	—	4	1	no	—
1597	C₂²	—	4	1	no	—
1598	C₂²	—	16	2	no	—
1599	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1600	C₄	—	2	1	no	—
1601	C₄	—	2	1	no	—
1602	C₄	—	2	1	no	—
1603	C₄	—	2	1	no	—
1604	C₄	—	2	1	no	—
1605	C₄	—	2	1	no	—
1606	C₄	—	2	1	no	—
1607	C₄	—	2	1	no	—
1608	C₄	—	2	1	no	—
1609	C₄	—	2	1	no	—
1610	C₄	—	2	1	no	—
1611	C₄	—	4	1	no	—
1612	C₄	—	4	1	no	—
1613	C₄	—	4	1	no	—
1614	C₄	—	4	1	no	—
1615	C₄	—	4	1	no	—
1616	C₄	—	4	1	no	—
1617	C₄	—	4	1	no	—
1618	C₄	—	4	1	no	—
1619	C₄	—	4	1	no	—
1620	C₄	—	4	1	no	—
1621	C₄	—	4	1	no	—
1622	C₄	—	4	1	no	—
1623	C₄	—	4	1	no	—
1624	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1625	C₄	C₃₁×#585	1	1	yes	characteristic
1626	C₂	—	4	1	no	—
1627	C₂	—	4	1	no	—
1628	C₂	—	4	1	no	—
1629	C₂	—	4	2	no	—
1630	C₂	—	8	1	no	—
1631	C₂	—	8	1	no	—
1632	C₂	C₃₁×#3489	1	1	yes	characteristic
1633	C₂	C₃₁×#3584	1	1	yes	characteristic
1634	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3565	C₂	semidirect
2. C₃₁×#3521	C₂	semidirect
3. C₃₁×#3388	C₂	semidirect
4. C₃₁×#3380	C₂	semidirect
5. C₃₁×#3376	C₂	semidirect
6. C₃₁×#3364	C₂	semidirect
7. C₃₁×#3352	C₂	semidirect
8. C₃₁×#3350	C₂	semidirect
9. C₃₁×#3347	C₂	semidirect
10. C₃₁×#3342	C₂	semidirect
11. C₃₁×#3337	C₂	semidirect
12. C₃₁×#3337	C₂	semidirect
13. C₃₁×#3322	C₂	semidirect
14. C₃₁×#3315	C₂	semidirect
15. C₃₁×#3311	C₂	semidirect
16. C₃₁×#3303	C₂	semidirect
17. C₃₁×#3297	C₂	semidirect
18. C₃₁×#3296	C₂	semidirect
19. C₃₁×#3263	C₂	semidirect
20. C₃₁×#3258	C₂	semidirect
21. C₃₁×#3250	C₂	semidirect
22. C₃₁×#3243	C₂	semidirect
23. C₃₁×#3242	C₂	semidirect
24. C₃₁×#3233	C₂	semidirect
25. C₃₁×#3124	C₂	semidirect
26. C₃₁×#3118	C₂	semidirect
27. C₃₁×#3102	C₂	semidirect
28. C₃₁×#3084	C₂	semidirect
29. C₃₁×#3081	C₂	semidirect
30. C₃₁×#3076	C₂	semidirect
31. C₃₁×#2994	C₂	semidirect
34. C₃₁×#557	C₂²	semidirect
39. C₃₁×#555	C₂²	semidirect
41. C₃₁×#554	C₂²	semidirect
50. C₃₁×#552	C₂²	semidirect
57. C₃₁×#544	C₂²	semidirect
62. C₃₁×#542	C₂²	semidirect
68. C₃₁×#533	C₂²	semidirect
72. C₃₁×#529	C₂²	semidirect
77. C₃₁×#501	C₂²	semidirect
78. C₃₁×#501	C₂²	semidirect
79. C₃₁×#500	C₂²	semidirect
80. C₃₁×#499	C₂²	semidirect
81. C₃₁×#499	C₂²	semidirect
82. C₃₁×#499	C₂²	semidirect
83. C₃₁×#491	C₂²	semidirect
88. C₃₁×#487	C₂²	semidirect
92. C₃₁×#485	C₂²	semidirect
93. C₃₁×#485	C₂²	semidirect
94. C₃₁×#485	C₂²	semidirect
95. C₃₁×#485	C₂²	semidirect
97. C₃₁×#484	C₂²	semidirect
98. C₃₁×#484	C₂²	semidirect
104. C₃₁×#482	C₂²	semidirect
106. C₃₁×#480	C₂²	semidirect
107. C₃₁×#479	C₂²	semidirect
108. C₃₁×#479	C₂²	semidirect
109. C₃₁×#479	C₂²	semidirect
110. C₃₁×#479	C₂²	semidirect
111. C₃₁×#479	C₂²	semidirect
112. C₃₁×#479	C₂²	semidirect
113. C₃₁×#479	C₂²	semidirect
121. C₃₁×#478	C₂²	semidirect
122. C₃₁×#478	C₂²	semidirect
123. C₃₁×#477	C₂²	semidirect
124. C₃₁×#477	C₂²	semidirect
129. C₃₁×#476	C₂²	semidirect
130. C₃₁×#475	C₂²	semidirect
131. C₃₁×#475	C₂²	semidirect
132. C₃₁×#475	C₂²	semidirect
133. C₃₁×#475	C₂²	semidirect
138. C₃₁×#470	C₂²	semidirect
142. C₃₁×#467	C₂²	semidirect
147. C₃₁×#465	C₂²	semidirect
148. C₃₁×#465	C₂²	semidirect
151. C₃₁×#464	C₂²	semidirect
152. C₃₁×#464	C₂²	semidirect
157. C₃₁×#462	C₂²	semidirect
158. C₃₁×#461	C₂²	semidirect
165. C₃₁×#446	C₂²	semidirect
166. C₈×Q₈×C₃₁	C₂²	semidirect
170. C₃₁×#440	C₂²	semidirect
171. C₄×Q₁₆×C₃₁	C₂²	semidirect
172. C₄×Q₁₆×C₃₁	C₂²	semidirect
175. C₄×SD₁₆×C₃₁	C₂²	semidirect
181. C₃₁×#435	C₂²	semidirect
184. C₈×D₄×C₃₁	C₂²	semidirect
186. C₃₁×#433	C₂²	semidirect
187. C₃₁×#431	C₂²	semidirect
189. C₃₁×#428	C₂²	semidirect
191. C₃₁×#427	C₂²	semidirect
192. C₃₁×#427	C₂²	semidirect
193. C₂×C₃₁×#106	C₂²	semidirect
195. C₃₁×#424	C₂²	semidirect
196. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
669. #62208	C₃₁	direct (N × H)
763. #3565	C₂×C₃₁	semidirect
764. #3521	C₂×C₃₁	semidirect
765. #3388	C₂×C₃₁	semidirect
766. #3380	C₂×C₃₁	semidirect
767. #3376	C₂×C₃₁	semidirect
768. #3364	C₂×C₃₁	semidirect
769. #3352	C₂×C₃₁	semidirect
770. #3350	C₂×C₃₁	semidirect
771. #3347	C₂×C₃₁	semidirect
772. #3342	C₂×C₃₁	semidirect
773. #3337	C₂×C₃₁	semidirect
774. #3337	C₂×C₃₁	semidirect
775. #3322	C₂×C₃₁	semidirect
776. #3315	C₂×C₃₁	semidirect
777. #3311	C₂×C₃₁	semidirect
778. #3303	C₂×C₃₁	semidirect
779. #3297	C₂×C₃₁	semidirect
780. #3296	C₂×C₃₁	semidirect
781. #3263	C₂×C₃₁	semidirect
782. #3258	C₂×C₃₁	semidirect
783. #3250	C₂×C₃₁	semidirect
784. #3243	C₂×C₃₁	semidirect
785. #3242	C₂×C₃₁	semidirect
786. #3233	C₂×C₃₁	semidirect
787. #3124	C₂×C₃₁	semidirect
788. #3118	C₂×C₃₁	semidirect
789. #3102	C₂×C₃₁	semidirect
790. #3084	C₂×C₃₁	semidirect
791. #3081	C₂×C₃₁	semidirect
792. #3076	C₂×C₃₁	semidirect
793. #2994	C₂×C₃₁	semidirect
842. #557	C₂²×C₃₁	semidirect
847. #555	C₂²×C₃₁	semidirect
849. #554	C₂²×C₃₁	semidirect
858. #552	C₂²×C₃₁	semidirect
865. #544	C₂²×C₃₁	semidirect
870. #542	C₂²×C₃₁	semidirect
876. #533	C₂²×C₃₁	semidirect
880. #529	C₂²×C₃₁	semidirect
885. #501	C₂²×C₃₁	semidirect
886. #501	C₂²×C₃₁	semidirect
887. #500	C₂²×C₃₁	semidirect
888. #499	C₂²×C₃₁	semidirect
889. #499	C₂²×C₃₁	semidirect
890. #499	C₂²×C₃₁	semidirect
891. #491	C₂²×C₃₁	semidirect
896. #487	C₂²×C₃₁	semidirect
900. #485	C₂²×C₃₁	semidirect
901. #485	C₂²×C₃₁	semidirect
902. #485	C₂²×C₃₁	semidirect
903. #485	C₂²×C₃₁	semidirect
905. #484	C₂²×C₃₁	semidirect
906. #484	C₂²×C₃₁	semidirect
912. #482	C₂²×C₃₁	semidirect
914. #480	C₂²×C₃₁	semidirect
915. #479	C₂²×C₃₁	semidirect
916. #479	C₂²×C₃₁	semidirect
917. #479	C₂²×C₃₁	semidirect
918. #479	C₂²×C₃₁	semidirect
919. #479	C₂²×C₃₁	semidirect
920. #479	C₂²×C₃₁	semidirect
921. #479	C₂²×C₃₁	semidirect
929. #478	C₂²×C₃₁	semidirect
930. #478	C₂²×C₃₁	semidirect
931. #477	C₂²×C₃₁	semidirect
932. #477	C₂²×C₃₁	semidirect
937. #476	C₂²×C₃₁	semidirect
938. #475	C₂²×C₃₁	semidirect
939. #475	C₂²×C₃₁	semidirect
940. #475	C₂²×C₃₁	semidirect
941. #475	C₂²×C₃₁	semidirect
946. #470	C₂²×C₃₁	semidirect
950. #467	C₂²×C₃₁	semidirect
955. #465	C₂²×C₃₁	semidirect
956. #465	C₂²×C₃₁	semidirect
959. #464	C₂²×C₃₁	semidirect
960. #464	C₂²×C₃₁	semidirect
965. #462	C₂²×C₃₁	semidirect
966. #461	C₂²×C₃₁	semidirect
973. #446	C₂²×C₃₁	semidirect
974. C₈×Q₈	C₂²×C₃₁	semidirect
978. #440	C₂²×C₃₁	semidirect
979. C₄×Q₁₆	C₂²×C₃₁	semidirect
980. C₄×Q₁₆	C₂²×C₃₁	semidirect
983. C₄×SD₁₆	C₂²×C₃₁	semidirect
989. #435	C₂²×C₃₁	semidirect
992. C₈×D₄	C₂²×C₃₁	semidirect
994. #433	C₂²×C₃₁	semidirect
995. #431	C₂²×C₃₁	semidirect
997. #428	C₂²×C₃₁	semidirect
999. #427	C₂²×C₃₁	semidirect
1000. #427	C₂²×C₃₁	semidirect
1001. C₂×#106	C₂²×C₃₁	semidirect
1003. #424	C₂²×C₃₁	semidirect
1004. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
1295. C₃₁	#62208	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×#3565	2
C₃₁×#3521	2
C₃₁×#3388	2
C₃₁×#3380	2
C₃₁×#3376	2
C₃₁×#3364	2
C₃₁×#3352	2
C₃₁×#3350	2
C₃₁×#3347	2
C₃₁×#3342	2
C₃₁×#3337	2
C₃₁×#3322	2
C₃₁×#3315	2
C₃₁×#3311	2
C₃₁×#3303	2
C₃₁×#3297	2
C₃₁×#3296	2
C₃₁×#3263	2
C₃₁×#3258	2
C₃₁×#3250	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3233	2
C₃₁×#3124	2
C₃₁×#3118	2
C₃₁×#3102	2
C₃₁×#3084	2
C₃₁×#3081	2
C₃₁×#3076	2
C₃₁×#2994	2
#62208	31

Subgroups — C31×#62208 #21518967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62208 #21518967