Subgroups — C₃₁×#61879 #21518638

Order 7936.

1656 conjugacy classes of subgroups.

The subgroup lattice has 1600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3388	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3384	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×#3373	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3371	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3244	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3243	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3241	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3124	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3119	C₂	1	1	yes	maximal, characteristic
29	C₃₁×#3111	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3111	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2987	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	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
37	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#557	C₂²	1	1	yes	characteristic
39	C₃₁×#557	C₂²	1	1	yes	characteristic
40	C₃₁×#557	C₂²	1	1	yes	characteristic
41	C₃₁×#557	C₂²	1	1	yes	characteristic
42	C₃₁×#556	C₂²	1	1	yes	characteristic
43	C₃₁×#556	C₂²	1	1	yes	characteristic
44	C₃₁×#554	—	2	1	no	—
45	C₃₁×#554	—	2	1	no	—
46	C₃₁×#554	C₂²	1	1	yes	characteristic
47	C₃₁×#554	C₂²	1	1	yes	characteristic
48	C₃₁×#554	C₂²	1	1	yes	characteristic
49	C₃₁×#554	C₂²	1	1	yes	characteristic
50	C₃₁×#552	—	2	1	no	—
51	C₃₁×#552	—	2	1	no	—
52	D₄×Q₈×C₃₁	—	2	1	no	—
53	D₄×Q₈×C₃₁	—	2	1	no	—
54	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
55	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
56	C₃₁×#544	—	2	1	no	—
57	C₃₁×#544	—	2	1	no	—
58	C₃₁×#544	C₂²	1	1	yes	characteristic
59	C₃₁×#544	C₂²	1	1	yes	characteristic
60	C₃₁×#542	—	2	1	no	—
61	C₃₁×#542	—	2	1	no	—
62	C₃₁×#542	C₂²	1	1	yes	characteristic
63	C₃₁×#542	C₂²	1	1	yes	characteristic
64	C₃₁×#541	C₂²	1	1	yes	characteristic
65	C₃₁×#540	C₂²	1	1	yes	characteristic
66	C₃₁×#539	—	2	1	no	—
67	C₃₁×#539	—	2	1	no	—
68	C₃₁×#533	—	2	1	no	—
69	C₃₁×#533	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
71	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
72	C₃₁×#529	C₂²	1	1	yes	characteristic
73	C₃₁×#529	C₂²	1	1	yes	characteristic
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#520	C₂²	1	1	yes	characteristic
76	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#501	C₂²	1	1	yes	characteristic
78	C₃₁×#501	C₂²	1	1	yes	characteristic
79	C₃₁×#501	C₂²	1	1	yes	characteristic
80	C₃₁×#501	C₂²	1	1	yes	characteristic
81	C₃₁×#501	C₂²	1	1	yes	characteristic
82	C₃₁×#501	C₂²	1	1	yes	characteristic
83	C₃₁×#501	C₂²	1	1	yes	characteristic
84	C₃₁×#501	C₂²	1	1	yes	characteristic
85	C₃₁×#500	C₂²	1	1	yes	characteristic
86	C₃₁×#499	C₂²	1	1	yes	characteristic
87	C₃₁×#499	C₂²	1	1	yes	characteristic
88	C₃₁×#498	C₂²	1	1	yes	characteristic
89	C₃₁×#491	C₂²	1	1	yes	characteristic
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
95	C₃₁×#489	C₂²	1	1	yes	characteristic
96	C₃₁×#489	C₂²	1	1	yes	characteristic
97	C₃₁×#488	C₂²	1	1	yes	characteristic
98	C₃₁×#488	C₂²	1	1	yes	characteristic
99	C₃₁×#487	C₂²	1	1	yes	characteristic
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×#484	C₂²	1	1	yes	characteristic
104	C₃₁×#484	C₂²	1	1	yes	characteristic
105	C₃₁×#483	C₂²	1	1	yes	characteristic
106	C₃₁×#483	C₂²	1	1	yes	characteristic
107	C₃₁×#482	C₂²	1	1	yes	characteristic
108	C₃₁×#482	C₂²	1	1	yes	characteristic
109	C₃₁×#481	C₂²	1	1	yes	characteristic
110	C₃₁×#481	C₂²	1	1	yes	characteristic
111	C₃₁×#480	C₂²	1	1	yes	characteristic
112	C₃₁×#480	C₂²	1	1	yes	characteristic
113	C₃₁×#479	C₂²	1	1	yes	characteristic
114	C₃₁×#479	C₂²	1	1	yes	characteristic
115	C₃₁×#479	C₂²	1	1	yes	characteristic
116	C₃₁×#479	C₂²	1	1	yes	characteristic
117	C₃₁×#479	C₂²	1	1	yes	characteristic
118	C₃₁×#479	C₂²	1	1	yes	characteristic
119	C₃₁×#479	C₂²	1	1	yes	characteristic
120	C₃₁×#479	C₂²	1	1	yes	characteristic
121	C₃₁×#478	C₂²	1	1	yes	characteristic
122	C₃₁×#478	C₂²	1	1	yes	characteristic
123	C₃₁×#478	C₂²	1	1	yes	characteristic
124	C₃₁×#478	C₂²	1	1	yes	characteristic
125	C₃₁×#478	C₂²	1	1	yes	characteristic
126	C₃₁×#478	C₂²	1	1	yes	characteristic
127	C₃₁×#478	C₂²	1	1	yes	characteristic
128	C₃₁×#478	C₂²	1	1	yes	characteristic
129	C₃₁×#477	C₂²	1	1	yes	characteristic
130	C₃₁×#477	C₂²	1	1	yes	characteristic
131	C₃₁×#477	C₂²	1	1	yes	characteristic
132	C₃₁×#477	C₂²	1	1	yes	characteristic
133	C₃₁×#477	C₂²	1	1	yes	characteristic
134	C₃₁×#476	C₂²	1	1	yes	characteristic
135	C₃₁×#476	C₂²	1	1	yes	characteristic
136	C₃₁×#476	C₂²	1	1	yes	characteristic
137	C₃₁×#476	C₂²	1	1	yes	characteristic
138	C₃₁×#476	C₂²	1	1	yes	characteristic
139	C₃₁×#475	C₂²	1	1	yes	characteristic
140	C₃₁×#475	C₂²	1	1	yes	characteristic
141	C₃₁×#475	C₂²	1	1	yes	characteristic
142	C₃₁×#475	C₂²	1	1	yes	characteristic
143	C₃₁×#475	C₂²	1	1	yes	characteristic
144	C₃₁×#474	C₂²	1	1	yes	characteristic
145	C₃₁×#474	C₂²	1	1	yes	characteristic
146	C₃₁×#474	C₂²	1	1	yes	characteristic
147	C₃₁×#474	C₂²	1	1	yes	characteristic
148	C₃₁×#474	C₂²	1	1	yes	characteristic
149	C₃₁×#464	C₂²	1	1	yes	characteristic
150	C₃₁×#464	C₂²	1	1	yes	characteristic
151	C₃₁×#464	C₂²	1	1	yes	characteristic
152	C₃₁×#464	C₂²	1	1	yes	characteristic
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
158	C₃₁×#461	C₂²	1	1	yes	characteristic
159	C₃₁×#460	C₂²	1	1	yes	characteristic
160	C₃₁×#459	C₂²	1	1	yes	characteristic
161	C₃₁×#452	C₂²	1	1	yes	characteristic
162	C₃₁×#452	C₂²	1	1	yes	characteristic
163	C₃₁×#449	C₂²	1	1	yes	characteristic
164	C₃₁×#449	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic
166	C₃₁×#446	C₂²	1	1	yes	characteristic
167	C₃₁×#446	C₂²	1	1	yes	characteristic
168	C₃₁×#446	C₂²	1	1	yes	characteristic
169	C₃₁×#446	C₂²	1	1	yes	characteristic
170	C₃₁×#446	C₂²	1	1	yes	characteristic
171	C₃₁×#446	C₂²	1	1	yes	characteristic
172	C₃₁×#446	C₂²	1	1	yes	characteristic
173	C₃₁×#442	C₂²	1	1	yes	characteristic
174	C₃₁×#442	C₂²	1	1	yes	characteristic
175	C₃₁×#442	C₂²	1	1	yes	characteristic
176	C₃₁×#442	C₂²	1	1	yes	characteristic
177	C₃₁×#441	C₂²	1	1	yes	characteristic
178	C₃₁×#441	C₂²	1	1	yes	characteristic
179	C₃₁×#441	C₂²	1	1	yes	characteristic
180	C₃₁×#441	C₂²	1	1	yes	characteristic
181	C₃₁×#440	C₂²	1	1	yes	characteristic
182	C₃₁×#440	C₂²	1	1	yes	characteristic
183	C₃₁×#440	C₂²	1	1	yes	characteristic
184	C₃₁×#440	C₂²	1	1	yes	characteristic
185	C₃₁×#440	C₂²	1	1	yes	characteristic
186	C₃₁×#440	C₂²	1	1	yes	characteristic
187	C₃₁×#440	C₂²	1	1	yes	characteristic
188	C₃₁×#440	C₂²	1	1	yes	characteristic
189	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
190	C₄×Q₁₆×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
194	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
195	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
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×#432	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂²×Q₈×C₃₁	—	2	1	no	—
205	C₂²×Q₈×C₃₁	—	2	1	no	—
206	C₂²×Q₈×C₃₁	—	2	1	no	—
207	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₃₁×C₄⋊Q₈	—	2	1	no	—
216	C₃₁×C₄⋊Q₈	—	2	1	no	—
217	C₃₁×C₄⋊Q₈	—	2	1	no	—
218	C₃₁×C₄⋊Q₈	—	2	1	no	—
219	C₃₁×C₄⋊Q₈	—	2	1	no	—
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	—	2	1	no	—
224	C₃₁×C₄⋊Q₈	—	2	1	no	—
225	C₃₁×C₄⋊Q₈	—	2	1	no	—
226	C₃₁×C₄⋊Q₈	—	2	1	no	—
227	C₃₁×C₄⋊Q₈	—	2	1	no	—
228	C₃₁×C₄⋊Q₈	—	2	1	no	—
229	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
230	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
231	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
233	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
234	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
235	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
236	C₃₁×C₄⋊Q₈	C₂³	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×#127	C₂³	1	1	yes	characteristic
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	—	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×#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	—	2	1	no	—
260	C₃₁×#125	—	2	1	no	—
261	C₃₁×#125	—	2	1	no	—
262	C₃₁×#125	—	2	1	no	—
263	C₃₁×#125	—	2	1	no	—
264	C₃₁×#125	—	2	1	no	—
265	C₃₁×#125	D₄	1	1	yes	characteristic
266	C₃₁×#125	D₄	1	1	yes	characteristic
267	C₃₁×#125	C₂³	1	1	yes	characteristic
268	C₃₁×#125	C₂³	1	1	yes	characteristic
269	C₃₁×#125	C₂³	1	1	yes	characteristic
270	C₃₁×#125	C₂³	1	1	yes	characteristic
271	C₃₁×#125	C₂³	1	1	yes	characteristic
272	C₃₁×#125	C₂³	1	1	yes	characteristic
273	C₃₁×#125	C₂³	1	1	yes	characteristic
274	C₃₁×#125	C₂³	1	1	yes	characteristic
275	C₃₁×#124	—	2	1	no	—
276	C₃₁×#124	—	2	1	no	—
277	C₃₁×#124	—	2	1	no	—
278	C₃₁×#124	—	2	1	no	—
279	C₃₁×#124	C₂³	1	1	yes	characteristic
280	C₃₁×#124	C₂³	1	1	yes	characteristic
281	C₃₁×#124	C₂³	1	1	yes	characteristic
282	C₃₁×#124	C₂³	1	1	yes	characteristic
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×C₂²⋊Q₈	—	2	1	no	—
294	C₃₁×C₂²⋊Q₈	—	2	1	no	—
295	C₃₁×C₂²⋊Q₈	—	2	1	no	—
296	C₃₁×C₂²⋊Q₈	—	2	1	no	—
297	C₃₁×C₂²⋊Q₈	—	2	1	no	—
298	C₃₁×C₂²⋊Q₈	—	2	1	no	—
299	C₃₁×C₂²⋊Q₈	—	2	1	no	—
300	C₃₁×C₂²⋊Q₈	—	2	1	no	—
301	C₃₁×C₂²⋊Q₈	—	2	1	no	—
302	C₃₁×C₂²⋊Q₈	—	2	1	no	—
303	C₃₁×C₂²⋊Q₈	—	2	1	no	—
304	C₃₁×C₂²⋊Q₈	—	2	1	no	—
305	C₃₁×C₂²⋊Q₈	—	2	1	no	—
306	C₃₁×C₂²⋊Q₈	—	2	1	no	—
307	C₃₁×C₂²⋊Q₈	—	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	—	2	1	no	—
312	C₃₁×C₂²⋊Q₈	—	2	1	no	—
313	C₃₁×C₂²⋊Q₈	—	2	1	no	—
314	C₃₁×C₂²⋊Q₈	—	2	1	no	—
315	C₃₁×C₂²⋊Q₈	—	2	1	no	—
316	C₃₁×C₂²⋊Q₈	—	2	1	no	—
317	C₃₁×C₂²⋊Q₈	—	2	1	no	—
318	C₃₁×C₂²⋊Q₈	—	2	1	no	—
319	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
320	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
321	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
322	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
323	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
325	C₃₁×#121	—	2	1	no	—
326	C₃₁×#121	—	2	1	no	—
327	C₃₁×#121	C₂³	1	1	yes	characteristic
328	C₃₁×#121	C₂³	1	1	yes	characteristic
329	C₄×Q₈×C₃₁	—	2	1	no	—
330	C₄×Q₈×C₃₁	—	2	1	no	—
331	C₄×Q₈×C₃₁	—	2	1	no	—
332	C₄×Q₈×C₃₁	—	2	1	no	—
333	C₄×Q₈×C₃₁	—	2	1	no	—
334	C₄×Q₈×C₃₁	—	2	1	no	—
335	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
336	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
337	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
338	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
351	C₄×D₄×C₃₁	—	2	1	no	—
352	C₄×D₄×C₃₁	—	2	1	no	—
353	C₄×D₄×C₃₁	—	2	1	no	—
354	C₄×D₄×C₃₁	—	2	1	no	—
355	C₄×D₄×C₃₁	—	2	1	no	—
356	C₄×D₄×C₃₁	—	2	1	no	—
357	C₄×D₄×C₃₁	—	2	1	no	—
358	C₄×D₄×C₃₁	—	2	1	no	—
359	C₄×D₄×C₃₁	—	2	1	no	—
360	C₄×D₄×C₃₁	—	2	1	no	—
361	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
373	C₃₁×#117	—	2	1	no	—
374	C₃₁×#117	—	2	1	no	—
375	C₃₁×#117	—	2	1	no	—
376	C₃₁×#117	—	2	1	no	—
377	C₃₁×#117	—	2	1	no	—
378	C₃₁×#117	—	2	1	no	—
379	C₃₁×#117	—	2	1	no	—
380	C₃₁×#117	C₂³	1	1	yes	characteristic
381	C₃₁×#117	C₂³	1	1	yes	characteristic
382	C₃₁×#117	C₂³	1	1	yes	characteristic
383	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
391	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
392	C₂×C₄²×C₃₁	—	2	1	no	—
393	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
394	C₃₁×#107	C₂³	1	1	yes	characteristic
395	C₃₁×#107	C₂³	1	1	yes	characteristic
396	C₃₁×#107	C₂³	1	1	yes	characteristic
397	C₃₁×#107	C₂³	1	1	yes	characteristic
398	C₃₁×#107	C₂³	1	1	yes	characteristic
399	C₃₁×#107	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×#106	C₂³	1	1	yes	characteristic
407	C₃₁×#106	C₂³	1	1	yes	characteristic
408	C₃₁×#106	C₂³	1	1	yes	characteristic
409	C₃₁×#106	C₂³	1	1	yes	characteristic
410	C₃₁×#106	C₂³	1	1	yes	characteristic
411	C₃₁×#106	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×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×#102	C₂³	1	1	yes	characteristic
447	C₃₁×#102	C₂³	1	1	yes	characteristic
448	C₃₁×#102	C₂³	1	1	yes	characteristic
449	C₃₁×#102	C₂³	1	1	yes	characteristic
450	C₃₁×#102	C₂³	1	1	yes	characteristic
451	C₃₁×#102	C₂³	1	1	yes	characteristic
452	C₃₁×#102	C₂³	1	1	yes	characteristic
453	C₃₁×#102	C₂³	1	1	yes	characteristic
454	C₃₁×#102	C₂³	1	1	yes	characteristic
455	C₃₁×#102	C₂³	1	1	yes	characteristic
456	C₃₁×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₃₁×#97	C₂³	1	1	yes	characteristic
467	C₃₁×#97	C₂³	1	1	yes	characteristic
468	C₃₁×#97	C₂³	1	1	yes	characteristic
469	C₃₁×#97	C₂³	1	1	yes	characteristic
470	C₃₁×#97	C₂³	1	1	yes	characteristic
471	C₃₁×#97	C₂³	1	1	yes	characteristic
472	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	#41×C₃₁	—	2	2	no	—
479	#41×C₃₁	—	2	2	no	—
480	C₂×Q₈×C₃₁	—	2	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	—	2	1	no	—
486	C₂×Q₈×C₃₁	—	2	1	no	—
487	C₂×Q₈×C₃₁	—	2	1	no	—
488	C₂×Q₈×C₃₁	—	2	1	no	—
489	C₂×Q₈×C₃₁	—	2	1	no	—
490	C₂×Q₈×C₃₁	—	8	2	no	—
491	C₂×Q₈×C₃₁	—	8	2	no	—
492	C₂×Q₈×C₃₁	—	8	2	no	—
493	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
497	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
498	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
500	C₂×D₄×C₃₁	—	2	1	no	—
501	C₂×D₄×C₃₁	—	2	1	no	—
502	C₂×D₄×C₃₁	—	2	1	no	—
503	C₂×D₄×C₃₁	—	2	1	no	—
504	C₂×D₄×C₃₁	—	2	1	no	—
505	C₂×D₄×C₃₁	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	—	2	1	no	—
523	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
524	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
525	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
526	Q₁₆×C₃₁	—	2	2	no	—
527	Q₁₆×C₃₁	—	2	2	no	—
528	SD₁₆×C₃₁	—	2	2	no	—
529	SD₁₆×C₃₁	—	2	2	no	—
530	SD₁₆×C₃₁	—	2	2	no	—
531	SD₁₆×C₃₁	—	2	2	no	—
532	D₈×C₃₁	—	2	2	no	—
533	D₈×C₃₁	—	2	2	no	—
534	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
535	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
536	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
537	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
538	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
539	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
540	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
541	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
542	C₄⋊C₄×C₃₁	—	2	1	no	—
543	C₄⋊C₄×C₃₁	—	2	1	no	—
544	C₄⋊C₄×C₃₁	—	2	1	no	—
545	C₄⋊C₄×C₃₁	—	2	1	no	—
546	C₄⋊C₄×C₃₁	—	2	1	no	—
547	C₄⋊C₄×C₃₁	—	2	1	no	—
548	C₄⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
607	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
612	C₂²⋊C₄×C₃₁	—	2	1	no	—
613	C₂²⋊C₄×C₃₁	—	2	1	no	—
614	C₂²⋊C₄×C₃₁	—	2	1	no	—
615	C₂²⋊C₄×C₃₁	—	2	1	no	—
616	C₂²⋊C₄×C₃₁	—	2	1	no	—
617	C₂²⋊C₄×C₃₁	—	2	1	no	—
618	C₂²⋊C₄×C₃₁	—	2	1	no	—
619	C₂²⋊C₄×C₃₁	—	2	1	no	—
620	C₂²⋊C₄×C₃₁	—	2	1	no	—
621	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
638	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
639	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
640	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
641	C₄²×C₃₁	—	2	1	no	—
642	C₄²×C₃₁	—	2	1	no	—
643	C₄²×C₃₁	—	2	1	no	—
644	C₄²×C₃₁	—	2	1	no	—
645	C₄²×C₃₁	—	2	1	no	—
646	C₄²×C₃₁	—	2	1	no	—
647	C₄²×C₃₁	—	2	1	no	—
648	C₄²×C₃₁	—	2	1	no	—
649	C₄²×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
655	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
656	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
657	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
658	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
659	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
660	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
661	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
662	#61879	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
663	C₂³×C₃₁	—	2	1	no	—
664	C₂³×C₃₁	—	2	1	no	—
665	C₂³×C₃₁	—	2	1	no	—
666	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
667	Q₈×C₃₁	—	2	1	no	—
668	Q₈×C₃₁	—	2	1	no	—
669	Q₈×C₃₁	—	2	1	no	—
670	Q₈×C₃₁	—	2	1	no	—
671	Q₈×C₃₁	—	2	1	no	—
672	Q₈×C₃₁	—	4	1	no	—
673	Q₈×C₃₁	—	4	1	no	—
674	Q₈×C₃₁	—	4	1	no	—
675	Q₈×C₃₁	—	4	1	no	—
676	Q₈×C₃₁	—	4	2	no	—
677	Q₈×C₃₁	—	4	2	no	—
678	Q₈×C₃₁	—	8	1	no	—
679	Q₈×C₃₁	—	8	1	no	—
680	Q₈×C₃₁	—	8	1	no	—
681	Q₈×C₃₁	—	8	1	no	—
682	Q₈×C₃₁	—	8	1	no	—
683	Q₈×C₃₁	—	8	1	no	—
684	Q₈×C₃₁	—	8	1	no	—
685	Q₈×C₃₁	—	8	1	no	—
686	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
687	D₄×C₃₁	—	2	4	no	—
688	D₄×C₃₁	—	2	1	no	—
689	D₄×C₃₁	—	2	1	no	—
690	D₄×C₃₁	—	2	1	no	—
691	D₄×C₃₁	—	2	1	no	—
692	D₄×C₃₁	—	2	1	no	—
693	D₄×C₃₁	—	8	1	no	—
694	D₄×C₃₁	—	8	1	no	—
695	D₄×C₃₁	—	8	1	no	—
696	D₄×C₃₁	—	8	1	no	—
697	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
698	C₂×C₄×C₃₁	—	2	4	no	—
699	C₂×C₄×C₃₁	—	2	1	no	—
700	C₂×C₄×C₃₁	—	2	1	no	—
701	C₂×C₄×C₃₁	—	2	1	no	—
702	C₂×C₄×C₃₁	—	2	1	no	—
703	C₂×C₄×C₃₁	—	2	1	no	—
704	C₂×C₄×C₃₁	—	2	1	no	—
705	C₂×C₄×C₃₁	—	2	1	no	—
706	C₂×C₄×C₃₁	—	2	1	no	—
707	C₂×C₄×C₃₁	—	2	1	no	—
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	—	4	1	no	—
715	C₂×C₄×C₃₁	—	4	1	no	—
716	C₂×C₄×C₃₁	—	4	2	no	—
717	C₂×C₄×C₃₁	—	4	2	no	—
718	C₂×C₄×C₃₁	—	8	1	no	—
719	C₂×C₄×C₃₁	—	8	1	no	—
720	C₂×C₄×C₃₁	—	8	1	no	—
721	C₂×C₄×C₃₁	—	8	1	no	—
722	C₂×C₄×C₃₁	—	8	1	no	—
723	C₂×C₄×C₃₁	—	8	1	no	—
724	C₂×C₄×C₃₁	—	8	1	no	—
725	C₂×C₄×C₃₁	—	8	1	no	—
726	C₂×C₄×C₃₁	—	8	1	no	—
727	C₂×C₄×C₃₁	—	8	1	no	—
728	C₂×C₄×C₃₁	—	8	1	no	—
729	C₂×C₄×C₃₁	—	8	1	no	—
730	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
731	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
732	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
733	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
734	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
735	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
736	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
737	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
738	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
739	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
740	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
741	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
742	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
743	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
744	C₈×C₃₁	—	2	1	no	—
745	C₈×C₃₁	—	2	1	no	—
746	C₈×C₃₁	—	2	1	no	—
747	C₈×C₃₁	—	2	1	no	—
748	C₈×C₃₁	—	2	1	no	—
749	C₈×C₃₁	—	2	1	no	—
750	C₈×C₃₁	—	2	1	no	—
751	C₈×C₃₁	—	2	1	no	—
752	#3557	C₂×C₃₁	1	1	yes	characteristic, complemented
753	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
754	#3390	C₂×C₃₁	1	1	yes	characteristic, complemented
755	#3389	C₂×C₃₁	1	1	yes	characteristic, complemented
756	#3388	C₂×C₃₁	1	1	yes	characteristic, complemented
757	#3388	C₂×C₃₁	1	1	yes	characteristic, complemented
758	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
759	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
760	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
761	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
762	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
763	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
764	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
765	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
766	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
767	#3370	C₂×C₃₁	1	1	yes	characteristic, complemented
768	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
769	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
770	#3244	C₂×C₃₁	1	1	yes	characteristic, complemented
771	#3243	C₂×C₃₁	1	1	yes	characteristic, complemented
772	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
773	#3241	C₂×C₃₁	1	1	yes	characteristic, complemented
774	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
775	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
776	#3125	C₂×C₃₁	1	1	yes	characteristic, complemented
777	#3124	C₂×C₃₁	1	1	yes	characteristic, complemented
778	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3119	C₂×C₃₁	1	1	yes	characteristic
780	#3111	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3111	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
783	C₂²×C₃₁	—	2	1	no	—
784	C₂²×C₃₁	—	2	1	no	—
785	C₂²×C₃₁	—	2	1	no	—
786	C₂²×C₃₁	—	2	2	no	—
787	C₂²×C₃₁	—	4	1	no	—
788	C₂²×C₃₁	—	4	1	no	—
789	C₂²×C₃₁	—	4	1	no	—
790	C₂²×C₃₁	—	4	1	no	—
791	C₂²×C₃₁	—	4	1	no	—
792	C₂²×C₃₁	—	4	1	no	—
793	C₂²×C₃₁	—	4	1	no	—
794	C₂²×C₃₁	—	4	1	no	—
795	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
796	C₄×C₃₁	—	2	1	no	—
797	C₄×C₃₁	—	2	1	no	—
798	C₄×C₃₁	—	2	1	no	—
799	C₄×C₃₁	—	2	1	no	—
800	C₄×C₃₁	—	2	1	no	—
801	C₄×C₃₁	—	2	1	no	—
802	C₄×C₃₁	—	2	1	no	—
803	C₄×C₃₁	—	2	1	no	—
804	C₄×C₃₁	—	2	1	no	—
805	C₄×C₃₁	—	2	1	no	—
806	C₄×C₃₁	—	2	1	no	—
807	C₄×C₃₁	—	2	1	no	—
808	C₄×C₃₁	—	2	1	no	—
809	C₄×C₃₁	—	2	2	no	—
810	C₄×C₃₁	—	4	1	no	—
811	C₄×C₃₁	—	4	1	no	—
812	C₄×C₃₁	—	4	1	no	—
813	C₄×C₃₁	—	4	1	no	—
814	C₄×C₃₁	—	4	1	no	—
815	C₄×C₃₁	—	4	1	no	—
816	C₄×C₃₁	—	4	1	no	—
817	C₄×C₃₁	—	4	1	no	—
818	C₄×C₃₁	—	4	1	no	—
819	C₄×C₃₁	—	4	1	no	—
820	C₄×C₃₁	—	4	1	no	—
821	C₄×C₃₁	—	4	1	no	—
822	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
823	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
824	#563	—	2	1	no	—
825	#563	—	2	1	no	—
826	#559	C₂²×C₃₁	1	1	yes	characteristic
827	#559	C₂²×C₃₁	1	1	yes	characteristic
828	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
829	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
830	#557	C₂²×C₃₁	1	1	yes	characteristic
831	#557	C₂²×C₃₁	1	1	yes	characteristic
832	#557	C₂²×C₃₁	1	1	yes	characteristic
833	#557	C₂²×C₃₁	1	1	yes	characteristic
834	#556	C₂²×C₃₁	1	1	yes	characteristic
835	#556	C₂²×C₃₁	1	1	yes	characteristic
836	#554	—	2	1	no	—
837	#554	—	2	1	no	—
838	#554	C₂²×C₃₁	1	1	yes	characteristic
839	#554	C₂²×C₃₁	1	1	yes	characteristic
840	#554	C₂²×C₃₁	1	1	yes	characteristic
841	#554	C₂²×C₃₁	1	1	yes	characteristic
842	#552	—	2	1	no	—
843	#552	—	2	1	no	—
844	D₄×Q₈	—	2	1	no	—
845	D₄×Q₈	—	2	1	no	—
846	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
847	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
848	#544	—	2	1	no	—
849	#544	—	2	1	no	—
850	#544	C₂²×C₃₁	1	1	yes	characteristic
851	#544	C₂²×C₃₁	1	1	yes	characteristic
852	#542	—	2	1	no	—
853	#542	—	2	1	no	—
854	#542	C₂²×C₃₁	1	1	yes	characteristic
855	#542	C₂²×C₃₁	1	1	yes	characteristic
856	#541	C₂²×C₃₁	1	1	yes	characteristic
857	#540	C₂²×C₃₁	1	1	yes	characteristic
858	#539	—	2	1	no	—
859	#539	—	2	1	no	—
860	#533	—	2	1	no	—
861	#533	C₂²×C₃₁	1	1	yes	characteristic
862	C₂×C₄⋊Q₈	—	2	1	no	—
863	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
864	#529	C₂²×C₃₁	1	1	yes	characteristic
865	#529	C₂²×C₃₁	1	1	yes	characteristic
866	#520	C₂²×C₃₁	1	1	yes	characteristic
867	#520	C₂²×C₃₁	1	1	yes	characteristic
868	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
869	#501	C₂²×C₃₁	1	1	yes	characteristic
870	#501	C₂²×C₃₁	1	1	yes	characteristic
871	#501	C₂²×C₃₁	1	1	yes	characteristic
872	#501	C₂²×C₃₁	1	1	yes	characteristic
873	#501	C₂²×C₃₁	1	1	yes	characteristic
874	#501	C₂²×C₃₁	1	1	yes	characteristic
875	#501	C₂²×C₃₁	1	1	yes	characteristic
876	#501	C₂²×C₃₁	1	1	yes	characteristic
877	#500	C₂²×C₃₁	1	1	yes	characteristic
878	#499	C₂²×C₃₁	1	1	yes	characteristic
879	#499	C₂²×C₃₁	1	1	yes	characteristic
880	#498	C₂²×C₃₁	1	1	yes	characteristic
881	#491	C₂²×C₃₁	1	1	yes	characteristic
882	#490	C₂²×C₃₁	1	1	yes	characteristic
883	#489	C₂²×C₃₁	1	1	yes	characteristic
884	#489	C₂²×C₃₁	1	1	yes	characteristic
885	#489	C₂²×C₃₁	1	1	yes	characteristic
886	#489	C₂²×C₃₁	1	1	yes	characteristic
887	#489	C₂²×C₃₁	1	1	yes	characteristic
888	#489	C₂²×C₃₁	1	1	yes	characteristic
889	#488	C₂²×C₃₁	1	1	yes	characteristic
890	#488	C₂²×C₃₁	1	1	yes	characteristic
891	#487	C₂²×C₃₁	1	1	yes	characteristic
892	#486	C₂²×C₃₁	1	1	yes	characteristic
893	#485	C₂²×C₃₁	1	1	yes	characteristic
894	#485	C₂²×C₃₁	1	1	yes	characteristic
895	#484	C₂²×C₃₁	1	1	yes	characteristic
896	#484	C₂²×C₃₁	1	1	yes	characteristic
897	#483	C₂²×C₃₁	1	1	yes	characteristic
898	#483	C₂²×C₃₁	1	1	yes	characteristic
899	#482	C₂²×C₃₁	1	1	yes	characteristic
900	#482	C₂²×C₃₁	1	1	yes	characteristic
901	#481	C₂²×C₃₁	1	1	yes	characteristic
902	#481	C₂²×C₃₁	1	1	yes	characteristic
903	#480	C₂²×C₃₁	1	1	yes	characteristic
904	#480	C₂²×C₃₁	1	1	yes	characteristic
905	#479	C₂²×C₃₁	1	1	yes	characteristic
906	#479	C₂²×C₃₁	1	1	yes	characteristic
907	#479	C₂²×C₃₁	1	1	yes	characteristic
908	#479	C₂²×C₃₁	1	1	yes	characteristic
909	#479	C₂²×C₃₁	1	1	yes	characteristic
910	#479	C₂²×C₃₁	1	1	yes	characteristic
911	#479	C₂²×C₃₁	1	1	yes	characteristic
912	#479	C₂²×C₃₁	1	1	yes	characteristic
913	#478	C₂²×C₃₁	1	1	yes	characteristic
914	#478	C₂²×C₃₁	1	1	yes	characteristic
915	#478	C₂²×C₃₁	1	1	yes	characteristic
916	#478	C₂²×C₃₁	1	1	yes	characteristic
917	#478	C₂²×C₃₁	1	1	yes	characteristic
918	#478	C₂²×C₃₁	1	1	yes	characteristic
919	#478	C₂²×C₃₁	1	1	yes	characteristic
920	#478	C₂²×C₃₁	1	1	yes	characteristic
921	#477	C₂²×C₃₁	1	1	yes	characteristic
922	#477	C₂²×C₃₁	1	1	yes	characteristic
923	#477	C₂²×C₃₁	1	1	yes	characteristic
924	#477	C₂²×C₃₁	1	1	yes	characteristic
925	#477	C₂²×C₃₁	1	1	yes	characteristic
926	#476	C₂²×C₃₁	1	1	yes	characteristic
927	#476	C₂²×C₃₁	1	1	yes	characteristic
928	#476	C₂²×C₃₁	1	1	yes	characteristic
929	#476	C₂²×C₃₁	1	1	yes	characteristic
930	#476	C₂²×C₃₁	1	1	yes	characteristic
931	#475	C₂²×C₃₁	1	1	yes	characteristic
932	#475	C₂²×C₃₁	1	1	yes	characteristic
933	#475	C₂²×C₃₁	1	1	yes	characteristic
934	#475	C₂²×C₃₁	1	1	yes	characteristic
935	#475	C₂²×C₃₁	1	1	yes	characteristic
936	#474	C₂²×C₃₁	1	1	yes	characteristic
937	#474	C₂²×C₃₁	1	1	yes	characteristic
938	#474	C₂²×C₃₁	1	1	yes	characteristic
939	#474	C₂²×C₃₁	1	1	yes	characteristic
940	#474	C₂²×C₃₁	1	1	yes	characteristic
941	#464	C₂²×C₃₁	1	1	yes	characteristic
942	#464	C₂²×C₃₁	1	1	yes	characteristic
943	#464	C₂²×C₃₁	1	1	yes	characteristic
944	#464	C₂²×C₃₁	1	1	yes	characteristic
945	#463	C₂²×C₃₁	1	1	yes	characteristic
946	#463	C₂²×C₃₁	1	1	yes	characteristic
947	#463	C₂²×C₃₁	1	1	yes	characteristic
948	#463	C₂²×C₃₁	1	1	yes	characteristic
949	#462	C₂²×C₃₁	1	1	yes	characteristic
950	#461	C₂²×C₃₁	1	1	yes	characteristic
951	#460	C₂²×C₃₁	1	1	yes	characteristic
952	#459	C₂²×C₃₁	1	1	yes	characteristic
953	#452	C₂²×C₃₁	1	1	yes	characteristic
954	#452	C₂²×C₃₁	1	1	yes	characteristic
955	#449	C₂²×C₃₁	1	1	yes	characteristic
956	#449	C₂²×C₃₁	1	1	yes	characteristic
957	#446	C₂²×C₃₁	1	1	yes	characteristic
958	#446	C₂²×C₃₁	1	1	yes	characteristic
959	#446	C₂²×C₃₁	1	1	yes	characteristic
960	#446	C₂²×C₃₁	1	1	yes	characteristic
961	#446	C₂²×C₃₁	1	1	yes	characteristic
962	#446	C₂²×C₃₁	1	1	yes	characteristic
963	#446	C₂²×C₃₁	1	1	yes	characteristic
964	#446	C₂²×C₃₁	1	1	yes	characteristic
965	#442	C₂²×C₃₁	1	1	yes	characteristic
966	#442	C₂²×C₃₁	1	1	yes	characteristic
967	#442	C₂²×C₃₁	1	1	yes	characteristic
968	#442	C₂²×C₃₁	1	1	yes	characteristic
969	#441	C₂²×C₃₁	1	1	yes	characteristic
970	#441	C₂²×C₃₁	1	1	yes	characteristic
971	#441	C₂²×C₃₁	1	1	yes	characteristic
972	#441	C₂²×C₃₁	1	1	yes	characteristic
973	#440	C₂²×C₃₁	1	1	yes	characteristic
974	#440	C₂²×C₃₁	1	1	yes	characteristic
975	#440	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
979	#440	C₂²×C₃₁	1	1	yes	characteristic
980	#440	C₂²×C₃₁	1	1	yes	characteristic
981	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
982	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
983	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
984	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
985	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
986	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
987	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
988	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
989	#433	C₂²×C₃₁	1	1	yes	characteristic
990	#433	C₂²×C₃₁	1	1	yes	characteristic
991	#433	C₂²×C₃₁	1	1	yes	characteristic
992	#433	C₂²×C₃₁	1	1	yes	characteristic
993	#432	C₂²×C₃₁	1	1	yes	characteristic
994	#432	C₂²×C₃₁	1	1	yes	characteristic
995	C₂×C₃₁	—	4	1	no	—
996	C₂×C₃₁	—	4	2	no	—
997	C₂×C₃₁	—	8	1	no	—
998	C₂×C₃₁	—	8	1	no	—
999	C₂×C₃₁	#3486	1	1	yes	characteristic
1000	C₂×C₃₁	#3585	1	1	yes	characteristic
1001	C₂×C₃₁	#3586	1	1	yes	characteristic
1002	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1003	C₂²×Q₈	—	2	1	no	—
1004	C₂²×Q₈	—	2	1	no	—
1005	C₂²×Q₈	—	2	1	no	—
1006	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1007	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1008	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1009	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1010	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1011	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1012	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1013	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1014	C₄⋊Q₈	—	2	1	no	—
1015	C₄⋊Q₈	—	2	1	no	—
1016	C₄⋊Q₈	—	2	1	no	—
1017	C₄⋊Q₈	—	2	1	no	—
1018	C₄⋊Q₈	—	2	1	no	—
1019	C₄⋊Q₈	—	2	1	no	—
1020	C₄⋊Q₈	—	2	1	no	—
1021	C₄⋊Q₈	—	2	1	no	—
1022	C₄⋊Q₈	—	2	1	no	—
1023	C₄⋊Q₈	—	2	1	no	—
1024	C₄⋊Q₈	—	2	1	no	—
1025	C₄⋊Q₈	—	2	1	no	—
1026	C₄⋊Q₈	—	2	1	no	—
1027	C₄⋊Q₈	—	2	1	no	—
1028	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1029	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1030	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1031	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1032	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1033	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1034	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1035	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1036	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1037	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1038	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1039	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1040	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1041	#127	C₂³×C₃₁	1	1	yes	characteristic
1042	#126	—	2	1	no	—
1043	#126	—	2	1	no	—
1044	#126	—	2	1	no	—
1045	#126	—	2	1	no	—
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	#125	—	2	1	no	—
1053	#125	—	2	1	no	—
1054	#125	—	2	1	no	—
1055	#125	—	2	1	no	—
1056	#125	—	2	1	no	—
1057	#125	—	2	1	no	—
1058	#125	—	2	1	no	—
1059	#125	—	2	1	no	—
1060	#125	—	2	1	no	—
1061	#125	—	2	1	no	—
1062	#125	—	2	1	no	—
1063	#125	—	2	1	no	—
1064	#125	D₄×C₃₁	1	1	yes	characteristic
1065	#125	D₄×C₃₁	1	1	yes	characteristic
1066	#125	C₂³×C₃₁	1	1	yes	characteristic
1067	#125	C₂³×C₃₁	1	1	yes	characteristic
1068	#125	C₂³×C₃₁	1	1	yes	characteristic
1069	#125	C₂³×C₃₁	1	1	yes	characteristic
1070	#125	C₂³×C₃₁	1	1	yes	characteristic
1071	#125	C₂³×C₃₁	1	1	yes	characteristic
1072	#125	C₂³×C₃₁	1	1	yes	characteristic
1073	#125	C₂³×C₃₁	1	1	yes	characteristic
1074	#124	—	2	1	no	—
1075	#124	—	2	1	no	—
1076	#124	—	2	1	no	—
1077	#124	—	2	1	no	—
1078	#124	C₂³×C₃₁	1	1	yes	characteristic
1079	#124	C₂³×C₃₁	1	1	yes	characteristic
1080	#124	C₂³×C₃₁	1	1	yes	characteristic
1081	#124	C₂³×C₃₁	1	1	yes	characteristic
1082	#123	—	2	1	no	—
1083	#123	—	2	1	no	—
1084	#123	—	2	1	no	—
1085	#123	—	2	1	no	—
1086	#123	—	2	1	no	—
1087	#123	—	2	1	no	—
1088	#123	—	2	1	no	—
1089	#123	—	2	1	no	—
1090	#123	—	2	1	no	—
1091	#123	—	2	1	no	—
1092	C₂²⋊Q₈	—	2	1	no	—
1093	C₂²⋊Q₈	—	2	1	no	—
1094	C₂²⋊Q₈	—	2	1	no	—
1095	C₂²⋊Q₈	—	2	1	no	—
1096	C₂²⋊Q₈	—	2	1	no	—
1097	C₂²⋊Q₈	—	2	1	no	—
1098	C₂²⋊Q₈	—	2	1	no	—
1099	C₂²⋊Q₈	—	2	1	no	—
1100	C₂²⋊Q₈	—	2	1	no	—
1101	C₂²⋊Q₈	—	2	1	no	—
1102	C₂²⋊Q₈	—	2	1	no	—
1103	C₂²⋊Q₈	—	2	1	no	—
1104	C₂²⋊Q₈	—	2	1	no	—
1105	C₂²⋊Q₈	—	2	1	no	—
1106	C₂²⋊Q₈	—	2	1	no	—
1107	C₂²⋊Q₈	—	2	1	no	—
1108	C₂²⋊Q₈	—	2	1	no	—
1109	C₂²⋊Q₈	—	2	1	no	—
1110	C₂²⋊Q₈	—	2	1	no	—
1111	C₂²⋊Q₈	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
1119	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1120	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1121	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1122	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1123	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1124	#121	—	2	1	no	—
1125	#121	—	2	1	no	—
1126	#121	C₂³×C₃₁	1	1	yes	characteristic
1127	#121	C₂³×C₃₁	1	1	yes	characteristic
1128	C₄×Q₈	—	2	1	no	—
1129	C₄×Q₈	—	2	1	no	—
1130	C₄×Q₈	—	2	1	no	—
1131	C₄×Q₈	—	2	1	no	—
1132	C₄×Q₈	—	2	1	no	—
1133	C₄×Q₈	—	2	1	no	—
1134	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1135	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1136	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1137	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1138	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1139	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1140	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1141	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1142	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1143	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1144	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1145	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1146	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1147	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1148	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1149	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1150	C₄×D₄	—	2	1	no	—
1151	C₄×D₄	—	2	1	no	—
1152	C₄×D₄	—	2	1	no	—
1153	C₄×D₄	—	2	1	no	—
1154	C₄×D₄	—	2	1	no	—
1155	C₄×D₄	—	2	1	no	—
1156	C₄×D₄	—	2	1	no	—
1157	C₄×D₄	—	2	1	no	—
1158	C₄×D₄	—	2	1	no	—
1159	C₄×D₄	—	2	1	no	—
1160	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1161	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1162	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1163	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1164	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1165	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1166	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1167	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1168	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1169	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1170	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1171	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1172	#117	—	2	1	no	—
1173	#117	—	2	1	no	—
1174	#117	—	2	1	no	—
1175	#117	—	2	1	no	—
1176	#117	—	2	1	no	—
1177	#117	—	2	1	no	—
1178	#117	—	2	1	no	—
1179	#117	C₂³×C₃₁	1	1	yes	characteristic
1180	#117	C₂³×C₃₁	1	1	yes	characteristic
1181	#117	C₂³×C₃₁	1	1	yes	characteristic
1182	C₂×C₄⋊C₄	—	2	1	no	—
1183	C₂×C₄⋊C₄	—	2	1	no	—
1184	C₂×C₄⋊C₄	—	2	1	no	—
1185	C₂×C₄⋊C₄	—	2	1	no	—
1186	C₂×C₄⋊C₄	—	2	1	no	—
1187	C₂×C₄⋊C₄	—	2	1	no	—
1188	C₂×C₄⋊C₄	—	2	1	no	—
1189	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1190	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1191	C₂×C₄²	—	2	1	no	—
1192	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1193	#107	C₂³×C₃₁	1	1	yes	characteristic
1194	#107	C₂³×C₃₁	1	1	yes	characteristic
1195	#107	C₂³×C₃₁	1	1	yes	characteristic
1196	#107	C₂³×C₃₁	1	1	yes	characteristic
1197	#107	C₂³×C₃₁	1	1	yes	characteristic
1198	#107	C₂³×C₃₁	1	1	yes	characteristic
1199	#107	C₂³×C₃₁	1	1	yes	characteristic
1200	#107	C₂³×C₃₁	1	1	yes	characteristic
1201	#107	C₂³×C₃₁	1	1	yes	characteristic
1202	#107	C₂³×C₃₁	1	1	yes	characteristic
1203	#107	C₂³×C₃₁	1	1	yes	characteristic
1204	#107	C₂³×C₃₁	1	1	yes	characteristic
1205	#106	C₂³×C₃₁	1	1	yes	characteristic
1206	#106	C₂³×C₃₁	1	1	yes	characteristic
1207	#106	C₂³×C₃₁	1	1	yes	characteristic
1208	#106	C₂³×C₃₁	1	1	yes	characteristic
1209	#106	C₂³×C₃₁	1	1	yes	characteristic
1210	#106	C₂³×C₃₁	1	1	yes	characteristic
1211	#106	C₂³×C₃₁	1	1	yes	characteristic
1212	#106	C₂³×C₃₁	1	1	yes	characteristic
1213	#106	C₂³×C₃₁	1	1	yes	characteristic
1214	#106	C₂³×C₃₁	1	1	yes	characteristic
1215	#106	C₂³×C₃₁	1	1	yes	characteristic
1216	#106	C₂³×C₃₁	1	1	yes	characteristic
1217	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1218	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1219	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1220	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1221	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1222	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1223	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1224	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1225	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1226	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1227	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1228	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1229	#103	C₂³×C₃₁	1	1	yes	characteristic
1230	#103	C₂³×C₃₁	1	1	yes	characteristic
1231	#103	C₂³×C₃₁	1	1	yes	characteristic
1232	#103	C₂³×C₃₁	1	1	yes	characteristic
1233	#103	C₂³×C₃₁	1	1	yes	characteristic
1234	#103	C₂³×C₃₁	1	1	yes	characteristic
1235	#103	C₂³×C₃₁	1	1	yes	characteristic
1236	#103	C₂³×C₃₁	1	1	yes	characteristic
1237	#103	C₂³×C₃₁	1	1	yes	characteristic
1238	#103	C₂³×C₃₁	1	1	yes	characteristic
1239	#103	C₂³×C₃₁	1	1	yes	characteristic
1240	#103	C₂³×C₃₁	1	1	yes	characteristic
1241	#103	C₂³×C₃₁	1	1	yes	characteristic
1242	#103	C₂³×C₃₁	1	1	yes	characteristic
1243	#103	C₂³×C₃₁	1	1	yes	characteristic
1244	#103	C₂³×C₃₁	1	1	yes	characteristic
1245	#102	C₂³×C₃₁	1	1	yes	characteristic
1246	#102	C₂³×C₃₁	1	1	yes	characteristic
1247	#102	C₂³×C₃₁	1	1	yes	characteristic
1248	#102	C₂³×C₃₁	1	1	yes	characteristic
1249	#102	C₂³×C₃₁	1	1	yes	characteristic
1250	#102	C₂³×C₃₁	1	1	yes	characteristic
1251	#102	C₂³×C₃₁	1	1	yes	characteristic
1252	#102	C₂³×C₃₁	1	1	yes	characteristic
1253	#102	C₂³×C₃₁	1	1	yes	characteristic
1254	#102	C₂³×C₃₁	1	1	yes	characteristic
1255	#102	C₂³×C₃₁	1	1	yes	characteristic
1256	#102	C₂³×C₃₁	1	1	yes	characteristic
1257	#102	C₂³×C₃₁	1	1	yes	characteristic
1258	#102	C₂³×C₃₁	1	1	yes	characteristic
1259	#102	C₂³×C₃₁	1	1	yes	characteristic
1260	#102	C₂³×C₃₁	1	1	yes	characteristic
1261	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1262	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1263	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1264	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1265	#97	C₂³×C₃₁	1	1	yes	characteristic
1266	#97	C₂³×C₃₁	1	1	yes	characteristic
1267	#97	C₂³×C₃₁	1	1	yes	characteristic
1268	#97	C₂³×C₃₁	1	1	yes	characteristic
1269	#97	C₂³×C₃₁	1	1	yes	characteristic
1270	#97	C₂³×C₃₁	1	1	yes	characteristic
1271	#97	C₂³×C₃₁	1	1	yes	characteristic
1272	#97	C₂³×C₃₁	1	1	yes	characteristic
1273	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1274	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1275	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1276	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1277	C₃₁	#61879	1	1	yes	characteristic, direct product factor, Sylow
1278	#41	—	2	2	no	—
1279	#41	—	2	2	no	—
1280	C₂×Q₈	—	2	1	no	—
1281	C₂×Q₈	—	2	1	no	—
1282	C₂×Q₈	—	2	1	no	—
1283	C₂×Q₈	—	2	1	no	—
1284	C₂×Q₈	—	2	1	no	—
1285	C₂×Q₈	—	2	1	no	—
1286	C₂×Q₈	—	2	1	no	—
1287	C₂×Q₈	—	2	1	no	—
1288	C₂×Q₈	—	2	1	no	—
1289	C₂×Q₈	—	2	1	no	—
1290	C₂×Q₈	—	8	2	no	—
1291	C₂×Q₈	—	8	2	no	—
1292	C₂×Q₈	—	8	2	no	—
1293	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1294	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1295	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1296	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1297	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1298	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1299	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1300	C₂×D₄	—	2	1	no	—
1301	C₂×D₄	—	2	1	no	—
1302	C₂×D₄	—	2	1	no	—
1303	C₂×D₄	—	2	1	no	—
1304	C₂×D₄	—	2	1	no	—
1305	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1306	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1307	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1308	C₂²×C₄	—	2	1	no	—
1309	C₂²×C₄	—	2	1	no	—
1310	C₂²×C₄	—	2	1	no	—
1311	C₂²×C₄	—	2	1	no	—
1312	C₂²×C₄	—	2	1	no	—
1313	C₂²×C₄	—	2	1	no	—
1314	C₂²×C₄	—	2	1	no	—
1315	C₂²×C₄	—	2	1	no	—
1316	C₂²×C₄	—	2	1	no	—
1317	C₂²×C₄	—	2	1	no	—
1318	C₂²×C₄	—	2	1	no	—
1319	C₂²×C₄	—	2	1	no	—
1320	C₂²×C₄	—	2	1	no	—
1321	C₂²×C₄	—	2	1	no	—
1322	C₂²×C₄	—	2	1	no	—
1323	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1324	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1325	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1326	Q₁₆	—	2	2	no	—
1327	Q₁₆	—	2	2	no	—
1328	SD₁₆	—	2	2	no	—
1329	SD₁₆	—	2	2	no	—
1330	SD₁₆	—	2	2	no	—
1331	SD₁₆	—	2	2	no	—
1332	D₈	—	2	2	no	—
1333	D₈	—	2	2	no	—
1334	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1335	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1336	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1337	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1338	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1339	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1340	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1341	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1342	C₄⋊C₄	—	2	1	no	—
1343	C₄⋊C₄	—	2	1	no	—
1344	C₄⋊C₄	—	2	1	no	—
1345	C₄⋊C₄	—	2	1	no	—
1346	C₄⋊C₄	—	2	1	no	—
1347	C₄⋊C₄	—	2	1	no	—
1348	C₄⋊C₄	—	2	1	no	—
1349	C₄⋊C₄	—	2	1	no	—
1350	C₄⋊C₄	—	2	1	no	—
1351	C₄⋊C₄	—	2	1	no	—
1352	C₄⋊C₄	—	2	1	no	—
1353	C₄⋊C₄	—	2	1	no	—
1354	C₄⋊C₄	—	2	1	no	—
1355	C₄⋊C₄	—	2	1	no	—
1356	C₄⋊C₄	—	2	1	no	—
1357	C₄⋊C₄	—	2	1	no	—
1358	C₄⋊C₄	—	2	1	no	—
1359	C₄⋊C₄	—	2	1	no	—
1360	C₄⋊C₄	—	2	1	no	—
1361	C₄⋊C₄	—	2	1	no	—
1362	C₄⋊C₄	—	2	1	no	—
1363	C₄⋊C₄	—	2	1	no	—
1364	C₄⋊C₄	—	2	1	no	—
1365	C₄⋊C₄	—	2	1	no	—
1366	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1387	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1388	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1389	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1390	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1391	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1392	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1393	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1394	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1395	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1396	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1397	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1398	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1399	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1400	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1401	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1402	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1403	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1404	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1405	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1406	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1407	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1408	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1409	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1410	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1411	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1412	C₂²⋊C₄	—	2	1	no	—
1413	C₂²⋊C₄	—	2	1	no	—
1414	C₂²⋊C₄	—	2	1	no	—
1415	C₂²⋊C₄	—	2	1	no	—
1416	C₂²⋊C₄	—	2	1	no	—
1417	C₂²⋊C₄	—	2	1	no	—
1418	C₂²⋊C₄	—	2	1	no	—
1419	C₂²⋊C₄	—	2	1	no	—
1420	C₂²⋊C₄	—	2	1	no	—
1421	C₂²⋊C₄	—	2	1	no	—
1422	C₂²⋊C₄	—	2	1	no	—
1423	C₂²⋊C₄	—	2	1	no	—
1424	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1438	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1439	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1440	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1441	C₄²	—	2	1	no	—
1442	C₄²	—	2	1	no	—
1443	C₄²	—	2	1	no	—
1444	C₄²	—	2	1	no	—
1445	C₄²	—	2	1	no	—
1446	C₄²	—	2	1	no	—
1447	C₄²	—	2	1	no	—
1448	C₄²	—	2	1	no	—
1449	C₄²	—	2	1	no	—
1450	C₄²	—	2	1	no	—
1451	C₄²	—	2	1	no	—
1452	C₄²	—	2	1	no	—
1453	C₄²	—	2	1	no	—
1454	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1455	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1456	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1457	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1458	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1459	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1460	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1461	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1462	C₂³	—	2	1	no	—
1463	C₂³	—	2	1	no	—
1464	C₂³	—	2	1	no	—
1465	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1466	Q₈	—	2	1	no	—
1467	Q₈	—	2	1	no	—
1468	Q₈	—	2	1	no	—
1469	Q₈	—	2	1	no	—
1470	Q₈	—	2	1	no	—
1471	Q₈	—	4	1	no	—
1472	Q₈	—	4	1	no	—
1473	Q₈	—	4	1	no	—
1474	Q₈	—	4	1	no	—
1475	Q₈	—	4	2	no	—
1476	Q₈	—	4	2	no	—
1477	Q₈	—	8	1	no	—
1478	Q₈	—	8	1	no	—
1479	Q₈	—	8	1	no	—
1480	Q₈	—	8	1	no	—
1481	Q₈	—	8	1	no	—
1482	Q₈	—	8	1	no	—
1483	Q₈	—	8	1	no	—
1484	Q₈	—	8	1	no	—
1485	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1486	D₄	—	2	4	no	—
1487	D₄	—	2	1	no	—
1488	D₄	—	2	1	no	—
1489	D₄	—	2	1	no	—
1490	D₄	—	2	1	no	—
1491	D₄	—	2	1	no	—
1492	D₄	—	8	1	no	—
1493	D₄	—	8	1	no	—
1494	D₄	—	8	1	no	—
1495	D₄	—	8	1	no	—
1496	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1497	C₂×C₄	—	2	4	no	—
1498	C₂×C₄	—	2	1	no	—
1499	C₂×C₄	—	2	1	no	—
1500	C₂×C₄	—	2	1	no	—
1501	C₂×C₄	—	2	1	no	—
1502	C₂×C₄	—	2	1	no	—
1503	C₂×C₄	—	2	1	no	—
1504	C₂×C₄	—	2	1	no	—
1505	C₂×C₄	—	2	1	no	—
1506	C₂×C₄	—	2	1	no	—
1507	C₂×C₄	—	2	1	no	—
1508	C₂×C₄	—	2	1	no	—
1509	C₂×C₄	—	2	1	no	—
1510	C₂×C₄	—	2	1	no	—
1511	C₂×C₄	—	2	1	no	—
1512	C₂×C₄	—	2	1	no	—
1513	C₂×C₄	—	4	1	no	—
1514	C₂×C₄	—	4	1	no	—
1515	C₂×C₄	—	4	2	no	—
1516	C₂×C₄	—	4	2	no	—
1517	C₂×C₄	—	8	1	no	—
1518	C₂×C₄	—	8	1	no	—
1519	C₂×C₄	—	8	1	no	—
1520	C₂×C₄	—	8	1	no	—
1521	C₂×C₄	—	8	1	no	—
1522	C₂×C₄	—	8	1	no	—
1523	C₂×C₄	—	8	1	no	—
1524	C₂×C₄	—	8	1	no	—
1525	C₂×C₄	—	8	1	no	—
1526	C₂×C₄	—	8	1	no	—
1527	C₂×C₄	—	8	1	no	—
1528	C₂×C₄	—	8	1	no	—
1529	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1530	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1531	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1532	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1533	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1534	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1535	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1536	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1537	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1538	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1539	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1540	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1541	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1542	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1543	C₈	—	2	1	no	—
1544	C₈	—	2	1	no	—
1545	C₈	—	2	1	no	—
1546	C₈	—	2	1	no	—
1547	C₈	—	2	1	no	—
1548	C₈	—	2	1	no	—
1549	C₈	—	2	1	no	—
1550	C₈	—	2	1	no	—
1551	C₂²	—	2	1	no	—
1552	C₂²	—	2	2	no	—
1553	C₂²	—	2	1	no	—
1554	C₂²	—	2	1	no	—
1555	C₂²	—	4	1	no	—
1556	C₂²	—	4	1	no	—
1557	C₂²	—	4	1	no	—
1558	C₂²	—	4	1	no	—
1559	C₂²	—	4	1	no	—
1560	C₂²	—	4	1	no	—
1561	C₂²	—	4	1	no	—
1562	C₂²	—	4	1	no	—
1563	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1564	C₄	—	2	1	no	—
1565	C₄	—	2	2	no	—
1566	C₄	—	2	1	no	—
1567	C₄	—	2	1	no	—
1568	C₄	—	2	1	no	—
1569	C₄	—	2	1	no	—
1570	C₄	—	2	1	no	—
1571	C₄	—	2	1	no	—
1572	C₄	—	2	1	no	—
1573	C₄	—	2	1	no	—
1574	C₄	—	2	1	no	—
1575	C₄	—	2	1	no	—
1576	C₄	—	2	1	no	—
1577	C₄	—	2	1	no	—
1578	C₄	—	4	1	no	—
1579	C₄	—	4	1	no	—
1580	C₄	—	4	1	no	—
1581	C₄	—	4	1	no	—
1582	C₄	—	4	1	no	—
1583	C₄	—	4	1	no	—
1584	C₄	—	4	1	no	—
1585	C₄	—	4	1	no	—
1586	C₄	—	4	1	no	—
1587	C₄	—	4	1	no	—
1588	C₄	—	4	1	no	—
1589	C₄	—	4	1	no	—
1590	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1591	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1592	C₂	—	4	1	no	—
1593	C₂	—	4	2	no	—
1594	C₂	—	8	1	no	—
1595	C₂	—	8	1	no	—
1596	C₂	C₃₁×#3486	1	1	yes	characteristic
1597	C₂	C₃₁×#3585	1	1	yes	characteristic
1598	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×#3119	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×#3557	C₂	semidirect
2. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3389	C₂	semidirect
5. C₃₁×#3388	C₂	semidirect
6. C₃₁×#3388	C₂	semidirect
7. C₃₁×#3387	C₂	semidirect
8. C₃₁×#3386	C₂	semidirect
9. C₃₁×#3385	C₂	semidirect
10. C₃₁×#3384	C₂	semidirect
11. C₃₁×#3377	C₂	semidirect
12. C₃₁×#3376	C₂	semidirect
13. C₃₁×#3375	C₂	semidirect
14. C₃₁×#3373	C₂	semidirect
15. C₃₁×#3371	C₂	semidirect
16. C₃₁×#3370	C₂	semidirect
17. C₃₁×#3369	C₂	semidirect
18. C₃₁×#3367	C₂	semidirect
19. C₃₁×#3244	C₂	semidirect
20. C₃₁×#3243	C₂	semidirect
21. C₃₁×#3242	C₂	semidirect
22. C₃₁×#3241	C₂	semidirect
23. C₃₁×#3239	C₂	semidirect
24. C₃₁×#3238	C₂	semidirect
25. C₃₁×#3125	C₂	semidirect
26. C₃₁×#3124	C₂	semidirect
27. C₃₁×#3120	C₂	semidirect
29. C₃₁×#3111	C₂	semidirect
30. C₃₁×#3111	C₂	semidirect
31. C₃₁×#2987	C₂	semidirect
662. #61879	C₃₁	direct (N × H)
752. #3557	C₂×C₃₁	semidirect
753. #3503	C₂×C₃₁	semidirect
754. #3390	C₂×C₃₁	semidirect
755. #3389	C₂×C₃₁	semidirect
756. #3388	C₂×C₃₁	semidirect
757. #3388	C₂×C₃₁	semidirect
758. #3387	C₂×C₃₁	semidirect
759. #3386	C₂×C₃₁	semidirect
760. #3385	C₂×C₃₁	semidirect
761. #3384	C₂×C₃₁	semidirect
762. #3377	C₂×C₃₁	semidirect
763. #3376	C₂×C₃₁	semidirect
764. #3375	C₂×C₃₁	semidirect
765. #3373	C₂×C₃₁	semidirect
766. #3371	C₂×C₃₁	semidirect
767. #3370	C₂×C₃₁	semidirect
768. #3369	C₂×C₃₁	semidirect
769. #3367	C₂×C₃₁	semidirect
770. #3244	C₂×C₃₁	semidirect
771. #3243	C₂×C₃₁	semidirect
772. #3242	C₂×C₃₁	semidirect
773. #3241	C₂×C₃₁	semidirect
774. #3239	C₂×C₃₁	semidirect
775. #3238	C₂×C₃₁	semidirect
776. #3125	C₂×C₃₁	semidirect
777. #3124	C₂×C₃₁	semidirect
778. #3120	C₂×C₃₁	semidirect
780. #3111	C₂×C₃₁	semidirect
781. #3111	C₂×C₃₁	semidirect
782. #2987	C₂×C₃₁	semidirect
1277. C₃₁	#61879	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3557	2
C₃₁×#3503	2
C₃₁×#3390	2
C₃₁×#3389	2
C₃₁×#3388	2
C₃₁×#3387	2
C₃₁×#3386	2
C₃₁×#3385	2
C₃₁×#3384	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3375	2
C₃₁×#3373	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3369	2
C₃₁×#3367	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3241	2
C₃₁×#3239	2
C₃₁×#3238	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3120	2
C₃₁×#3119	2
C₃₁×#3111	2
C₃₁×#2987	2
#61879	31

Subgroups — C31×#61879 #21518638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61879 #21518638