Subgroups — C₃₁×#62214 #21518973

Order 7936.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3516	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3377	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×#3346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3344	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3337	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3336	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3316	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3312	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3300	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3300	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3261	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3248	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×#3232	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#564	—	2	1	no	—
33	C₃₁×#563	—	2	1	no	—
34	C₃₁×#557	C₂²	1	1	yes	characteristic
35	C₃₁×#557	C₂²	1	1	yes	characteristic
36	C₃₁×#557	C₂²	1	1	yes	characteristic
37	C₃₁×#556	—	2	1	no	—
38	C₃₁×#556	C₂²	1	1	yes	characteristic
39	C₃₁×#554	—	2	1	no	—
40	C₃₁×#554	C₂²	1	1	yes	characteristic
41	C₃₁×#554	C₂²	1	1	yes	characteristic
42	C₃₁×#554	C₂²	1	1	yes	characteristic
43	C₃₁×#553	—	2	1	no	—
44	C₃₁×#553	C₂²	1	1	yes	characteristic
45	C₃₁×#552	—	2	1	no	—
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
51	C₃₁×#552	C₂²	1	1	yes	characteristic
52	C₃₁×#552	C₂²	1	1	yes	characteristic
53	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
54	C₃₁×#548	C₂²	1	1	yes	characteristic
55	C₃₁×#548	C₂²	1	1	yes	characteristic
56	C₃₁×#544	—	2	1	no	—
57	C₃₁×#544	C₂²	1	1	yes	characteristic
58	C₃₁×#544	C₂²	1	1	yes	characteristic
59	C₃₁×#542	—	2	1	no	—
60	C₃₁×#542	C₂²	1	1	yes	characteristic
61	C₃₁×#541	—	2	1	no	—
62	C₃₁×#541	—	2	1	no	—
63	C₃₁×#541	—	2	1	no	—
64	C₃₁×#541	C₂²	1	1	yes	characteristic
65	C₃₁×#541	C₂²	1	1	yes	characteristic
66	C₃₁×#541	C₂²	1	1	yes	characteristic
67	C₃₁×#539	—	2	1	no	—
68	C₃₁×#533	C₂²	1	1	yes	characteristic
69	C₃₁×#529	—	2	1	no	—
70	C₃₁×#529	—	2	1	no	—
71	C₃₁×#529	C₂²	1	1	yes	characteristic
72	C₃₁×#529	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#519	C₂²	1	1	yes	characteristic
76	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#501	C₂²	1	1	yes	characteristic
78	C₃₁×#501	C₂²	1	1	yes	characteristic
79	C₃₁×#500	C₂²	1	1	yes	characteristic
80	C₃₁×#499	C₂²	1	1	yes	characteristic
81	C₃₁×#499	C₂²	1	1	yes	characteristic
82	C₃₁×#499	C₂²	1	1	yes	characteristic
83	C₃₁×#491	C₂²	1	1	yes	characteristic
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
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
93	C₃₁×#485	C₂²	1	1	yes	characteristic
94	C₃₁×#484	C₂²	1	1	yes	characteristic
95	C₃₁×#484	C₂²	1	1	yes	characteristic
96	C₃₁×#484	C₂²	1	1	yes	characteristic
97	C₃₁×#484	C₂²	1	1	yes	characteristic
98	C₃₁×#484	C₂²	1	1	yes	characteristic
99	C₃₁×#484	C₂²	1	1	yes	characteristic
100	C₃₁×#483	C₂²	1	1	yes	characteristic
101	C₃₁×#483	C₂²	1	1	yes	characteristic
102	C₃₁×#483	C₂²	1	1	yes	characteristic
103	C₃₁×#482	C₂²	1	1	yes	characteristic
104	C₃₁×#481	C₂²	1	1	yes	characteristic
105	C₃₁×#480	C₂²	1	1	yes	characteristic
106	C₃₁×#480	C₂²	1	1	yes	characteristic
107	C₃₁×#479	C₂²	1	1	yes	characteristic
108	C₃₁×#479	C₂²	1	1	yes	characteristic
109	C₃₁×#479	C₂²	1	1	yes	characteristic
110	C₃₁×#479	C₂²	1	1	yes	characteristic
111	C₃₁×#479	C₂²	1	1	yes	characteristic
112	C₃₁×#479	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×#479	C₂²	1	1	yes	characteristic
122	C₃₁×#479	C₂²	1	1	yes	characteristic
123	C₃₁×#479	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×#477	C₂²	1	1	yes	characteristic
128	C₃₁×#477	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×#475	C₂²	1	1	yes	characteristic
133	C₃₁×#475	C₂²	1	1	yes	characteristic
134	C₃₁×#475	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
139	C₃₁×#470	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
143	C₃₁×#467	C₂²	1	1	yes	characteristic
144	C₃₁×#467	C₂²	1	1	yes	characteristic
145	C₃₁×#467	C₂²	1	1	yes	characteristic
146	C₃₁×#465	C₂²	1	1	yes	characteristic
147	C₃₁×#465	C₂²	1	1	yes	characteristic
148	C₃₁×#465	C₂²	1	1	yes	characteristic
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×#462	C₂²	1	1	yes	characteristic
154	C₃₁×#462	C₂²	1	1	yes	characteristic
155	C₃₁×#462	C₂²	1	1	yes	characteristic
156	C₃₁×#462	C₂²	1	1	yes	characteristic
157	C₃₁×#462	C₂²	1	1	yes	characteristic
158	C₃₁×#461	C₂²	1	1	yes	characteristic
159	C₃₁×#452	C₂²	1	1	yes	characteristic
160	C₃₁×#452	C₂²	1	1	yes	characteristic
161	C₃₁×#451	C₂²	1	1	yes	characteristic
162	C₃₁×#451	C₂²	1	1	yes	characteristic
163	C₃₁×#451	C₂²	1	1	yes	characteristic
164	C₃₁×#451	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic
166	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
167	C₃₁×#441	C₂²	1	1	yes	characteristic
168	C₃₁×#441	C₂²	1	1	yes	characteristic
169	C₃₁×#441	C₂²	1	1	yes	characteristic
170	C₃₁×#440	C₂²	1	1	yes	characteristic
171	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
172	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
173	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
174	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×SD₁₆×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
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
185	C₃₁×#433	C₂²	1	1	yes	characteristic
186	C₃₁×#433	C₂²	1	1	yes	characteristic
187	C₃₁×#431	C₂²	1	1	yes	characteristic
188	C₃₁×#428	C₂²	1	1	yes	characteristic
189	C₃₁×#428	C₂²	1	1	yes	characteristic
190	C₃₁×#427	C₂²	1	1	yes	characteristic
191	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
192	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
193	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
194	C₃₁×#424	C₂²	1	1	yes	characteristic
195	C₃₁×#424	C₂²	1	1	yes	characteristic
196	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
197	C₃₁×#419	C₂²	1	1	yes	characteristic
198	C₃₁×#417	C₂²	1	1	yes	characteristic
199	C₃₁×#416	C₂²	1	1	yes	characteristic
200	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
201	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
202	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
205	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×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	—	2	1	no	—
224	C₃₁×C₄⋊Q₈	—	2	1	no	—
225	C₃₁×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
230	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	—	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	—	2	1	no	—
266	C₃₁×#125	—	2	1	no	—
267	C₃₁×#125	—	2	1	no	—
268	C₃₁×#125	—	2	1	no	—
269	C₃₁×#125	—	2	1	no	—
270	C₃₁×#125	—	2	1	no	—
271	C₃₁×#125	—	2	1	no	—
272	C₃₁×#125	—	2	1	no	—
273	C₃₁×#125	—	2	1	no	—
274	C₃₁×#125	—	2	1	no	—
275	C₃₁×#125	D₄	1	1	yes	characteristic
276	C₃₁×#125	C₂³	1	1	yes	characteristic
277	C₃₁×#125	C₂³	1	1	yes	characteristic
278	C₃₁×#125	C₂³	1	1	yes	characteristic
279	C₃₁×#125	C₂³	1	1	yes	characteristic
280	C₃₁×#125	C₂³	1	1	yes	characteristic
281	C₃₁×#125	C₂³	1	1	yes	characteristic
282	C₃₁×#125	C₂³	1	1	yes	characteristic
283	C₃₁×#125	C₂³	1	1	yes	characteristic
284	C₃₁×#124	—	2	1	no	—
285	C₃₁×#124	—	2	1	no	—
286	C₃₁×#124	—	2	1	no	—
287	C₃₁×#124	D₄	1	1	yes	characteristic
288	C₃₁×#124	C₂³	1	1	yes	characteristic
289	C₃₁×#124	C₂³	1	1	yes	characteristic
290	C₃₁×#123	—	2	1	no	—
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×#123	—	2	1	no	—
294	C₃₁×#123	—	2	1	no	—
295	C₃₁×#123	—	2	1	no	—
296	C₃₁×#123	—	2	1	no	—
297	C₃₁×#123	—	2	1	no	—
298	C₃₁×#123	D₄	1	1	yes	characteristic
299	C₃₁×#123	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
318	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
319	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
320	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
321	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
322	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
325	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
326	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
327	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
328	C₃₁×#121	—	2	1	no	—
329	C₃₁×#121	—	2	1	no	—
330	C₃₁×#121	—	2	1	no	—
331	C₃₁×#121	D₄	1	1	yes	characteristic
332	C₃₁×#121	C₂³	1	1	yes	characteristic
333	C₃₁×#121	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
340	C₄×Q₈×C₃₁	—	2	1	no	—
341	C₄×Q₈×C₃₁	—	2	1	no	—
342	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
346	C₄×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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
354	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
355	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
356	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
357	C₄×D₄×C₃₁	—	2	1	no	—
358	C₄×D₄×C₃₁	—	2	1	no	—
359	C₄×D₄×C₃₁	—	2	1	no	—
360	C₄×D₄×C₃₁	—	2	1	no	—
361	C₄×D₄×C₃₁	—	2	1	no	—
362	C₄×D₄×C₃₁	—	2	1	no	—
363	C₄×D₄×C₃₁	—	2	1	no	—
364	C₄×D₄×C₃₁	—	2	1	no	—
365	C₄×D₄×C₃₁	—	2	1	no	—
366	C₄×D₄×C₃₁	—	2	1	no	—
367	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
372	C₃₁×#117	—	2	1	no	—
373	C₃₁×#117	—	2	1	no	—
374	C₃₁×#117	—	2	1	no	—
375	C₃₁×#117	—	2	1	no	—
376	C₃₁×#117	—	2	1	no	—
377	C₃₁×#117	—	2	1	no	—
378	C₃₁×#117	—	2	1	no	—
379	C₃₁×#117	—	2	1	no	—
380	C₃₁×#117	—	2	1	no	—
381	C₃₁×#117	—	2	1	no	—
382	C₃₁×#117	—	2	1	no	—
383	C₃₁×#117	C₂³	1	1	yes	characteristic
384	C₃₁×#117	C₂³	1	1	yes	characteristic
385	C₃₁×#117	C₂³	1	1	yes	characteristic
386	C₃₁×#117	C₂³	1	1	yes	characteristic
387	C₃₁×#117	C₂³	1	1	yes	characteristic
388	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
396	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
397	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
398	C₂×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×#107	C₂³	1	1	yes	characteristic
413	C₃₁×#107	C₂³	1	1	yes	characteristic
414	C₃₁×#106	C₂³	1	1	yes	characteristic
415	C₃₁×#106	C₂³	1	1	yes	characteristic
416	C₃₁×#106	C₂³	1	1	yes	characteristic
417	C₃₁×#106	C₂³	1	1	yes	characteristic
418	C₃₁×#106	C₂³	1	1	yes	characteristic
419	C₃₁×#106	C₂³	1	1	yes	characteristic
420	C₃₁×#106	C₂³	1	1	yes	characteristic
421	C₃₁×#106	C₂³	1	1	yes	characteristic
422	C₃₁×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	C₂³	1	1	yes	characteristic
424	C₃₁×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×#103	C₂³	1	1	yes	characteristic
451	C₃₁×#103	C₂³	1	1	yes	characteristic
452	C₃₁×#103	C₂³	1	1	yes	characteristic
453	C₃₁×#103	C₂³	1	1	yes	characteristic
454	C₃₁×#103	C₂³	1	1	yes	characteristic
455	C₃₁×#103	C₂³	1	1	yes	characteristic
456	C₃₁×#103	C₂³	1	1	yes	characteristic
457	C₃₁×#103	C₂³	1	1	yes	characteristic
458	C₃₁×#103	C₂³	1	1	yes	characteristic
459	C₃₁×#103	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	#41×C₃₁	—	2	2	no	—
479	#41×C₃₁	—	4	1	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	2	no	—
487	C₂×Q₈×C₃₁	—	2	2	no	—
488	C₂×Q₈×C₃₁	—	4	1	no	—
489	C₂×Q₈×C₃₁	—	4	1	no	—
490	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
491	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
492	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
493	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
496	C₂×D₄×C₃₁	—	2	1	no	—
497	C₂×D₄×C₃₁	—	2	1	no	—
498	C₂×D₄×C₃₁	—	2	1	no	—
499	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
500	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
501	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
502	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₃₁	—	2	1	no	—
504	C₂²×C₄×C₃₁	—	2	1	no	—
505	C₂²×C₄×C₃₁	—	2	1	no	—
506	C₂²×C₄×C₃₁	—	2	1	no	—
507	C₂²×C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
515	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
516	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
519	Q₁₆×C₃₁	—	2	2	no	—
520	Q₁₆×C₃₁	—	2	2	no	—
521	Q₁₆×C₃₁	—	4	1	no	—
522	Q₁₆×C₃₁	—	4	1	no	—
523	Q₁₆×C₃₁	—	4	1	no	—
524	Q₁₆×C₃₁	—	4	1	no	—
525	SD₁₆×C₃₁	—	4	1	no	—
526	SD₁₆×C₃₁	—	4	1	no	—
527	M₁₆×C₃₁	—	4	1	no	—
528	M₁₆×C₃₁	—	4	1	no	—
529	C₂×C₈×C₃₁	—	4	1	no	—
530	C₂×C₈×C₃₁	—	4	1	no	—
531	C₂×C₈×C₃₁	—	4	1	no	—
532	C₂×C₈×C₃₁	—	4	1	no	—
533	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	—	2	1	no	—
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	—	2	1	no	—
587	C₄⋊C₄×C₃₁	—	2	1	no	—
588	C₄⋊C₄×C₃₁	—	2	1	no	—
589	C₄⋊C₄×C₃₁	—	2	1	no	—
590	C₄⋊C₄×C₃₁	—	2	1	no	—
591	C₄⋊C₄×C₃₁	—	2	1	no	—
592	C₄⋊C₄×C₃₁	—	2	1	no	—
593	C₄⋊C₄×C₃₁	—	2	1	no	—
594	C₄⋊C₄×C₃₁	—	2	1	no	—
595	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	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	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
615	C₂²⋊C₄×C₃₁	—	2	1	no	—
616	C₂²⋊C₄×C₃₁	—	2	1	no	—
617	C₂²⋊C₄×C₃₁	—	2	1	no	—
618	C₂²⋊C₄×C₃₁	—	2	1	no	—
619	C₂²⋊C₄×C₃₁	—	2	1	no	—
620	C₂²⋊C₄×C₃₁	—	2	1	no	—
621	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	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	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	—	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	#62214	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
670	C₂³×C₃₁	—	2	1	no	—
671	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
672	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
673	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
674	Q₈×C₃₁	—	2	1	no	—
675	Q₈×C₃₁	—	2	1	no	—
676	Q₈×C₃₁	—	2	1	no	—
677	Q₈×C₃₁	—	2	1	no	—
678	Q₈×C₃₁	—	2	1	no	—
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	—	4	1	no	—
684	Q₈×C₃₁	—	4	2	no	—
685	Q₈×C₃₁	—	4	2	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	2₋¹⁺⁴	1	2	yes	—
691	D₄×C₃₁	—	2	2	no	—
692	D₄×C₃₁	—	2	2	no	—
693	D₄×C₃₁	—	2	1	no	—
694	D₄×C₃₁	—	2	1	no	—
695	D₄×C₃₁	—	4	1	no	—
696	D₄×C₃₁	—	4	2	no	—
697	D₄×C₃₁	—	4	2	no	—
698	D₄×C₃₁	—	8	1	no	—
699	C₂×C₄×C₃₁	—	2	2	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	—	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	—	4	1	no	—
722	C₂×C₄×C₃₁	—	4	2	no	—
723	C₂×C₄×C₃₁	—	4	2	no	—
724	C₂×C₄×C₃₁	—	4	2	no	—
725	C₂×C₄×C₃₁	—	4	2	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	—	8	1	no	—
731	C₂×C₄×C₃₁	—	8	1	no	—
732	C₂×C₄×C₃₁	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
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	C₈×C₃₁	—	2	1	no	—
753	#3563	C₂×C₃₁	1	1	yes	characteristic, complemented
754	#3516	C₂×C₃₁	1	1	yes	characteristic
755	#3390	C₂×C₃₁	1	1	yes	characteristic, complemented
756	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
757	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
758	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
759	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
760	#3346	C₂×C₃₁	1	1	yes	characteristic, complemented
761	#3344	C₂×C₃₁	1	1	yes	characteristic, complemented
762	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
763	#3337	C₂×C₃₁	1	1	yes	characteristic, complemented
764	#3336	C₂×C₃₁	1	1	yes	characteristic, complemented
765	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
766	#3316	C₂×C₃₁	1	1	yes	characteristic, complemented
767	#3312	C₂×C₃₁	1	1	yes	characteristic, complemented
768	#3300	C₂×C₃₁	1	1	yes	characteristic, complemented
769	#3300	C₂×C₃₁	1	1	yes	characteristic, complemented
770	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
771	#3261	C₂×C₃₁	1	1	yes	characteristic, complemented
772	#3258	C₂×C₃₁	1	1	yes	characteristic, complemented
773	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
774	#3243	C₂×C₃₁	1	1	yes	characteristic, complemented
775	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
776	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
777	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
778	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
780	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
782	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
784	C₂²×C₃₁	—	2	1	no	—
785	C₂²×C₃₁	—	2	1	no	—
786	C₂²×C₃₁	—	2	1	no	—
787	C₂²×C₃₁	—	2	1	no	—
788	C₂²×C₃₁	—	2	1	no	—
789	C₂²×C₃₁	—	2	1	no	—
790	C₂²×C₃₁	—	2	1	no	—
791	C₂²×C₃₁	—	2	1	no	—
792	C₂²×C₃₁	—	4	1	no	—
793	C₂²×C₃₁	—	4	1	no	—
794	C₂²×C₃₁	—	4	1	no	—
795	C₂²×C₃₁	#578	1	2	yes	—
796	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	2	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	—	4	1	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	—	4	1	no	—
823	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
824	C₄×C₃₁	#585	1	1	yes	characteristic
825	#564	—	2	1	no	—
826	#563	—	2	1	no	—
827	#557	C₂²×C₃₁	1	1	yes	characteristic
828	#557	C₂²×C₃₁	1	1	yes	characteristic
829	#557	C₂²×C₃₁	1	1	yes	characteristic
830	#556	—	2	1	no	—
831	#556	C₂²×C₃₁	1	1	yes	characteristic
832	#554	—	2	1	no	—
833	#554	C₂²×C₃₁	1	1	yes	characteristic
834	#554	C₂²×C₃₁	1	1	yes	characteristic
835	#554	C₂²×C₃₁	1	1	yes	characteristic
836	#553	—	2	1	no	—
837	#553	C₂²×C₃₁	1	1	yes	characteristic
838	#552	—	2	1	no	—
839	#552	—	2	1	no	—
840	#552	—	2	1	no	—
841	#552	C₂²×C₃₁	1	1	yes	characteristic
842	#552	C₂²×C₃₁	1	1	yes	characteristic
843	#552	C₂²×C₃₁	1	1	yes	characteristic
844	#552	C₂²×C₃₁	1	1	yes	characteristic
845	#552	C₂²×C₃₁	1	1	yes	characteristic
846	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
847	#548	C₂²×C₃₁	1	1	yes	characteristic
848	#548	C₂²×C₃₁	1	1	yes	characteristic
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	C₂²×C₃₁	1	1	yes	characteristic
854	#541	—	2	1	no	—
855	#541	—	2	1	no	—
856	#541	—	2	1	no	—
857	#541	C₂²×C₃₁	1	1	yes	characteristic
858	#541	C₂²×C₃₁	1	1	yes	characteristic
859	#541	C₂²×C₃₁	1	1	yes	characteristic
860	#539	—	2	1	no	—
861	#533	C₂²×C₃₁	1	1	yes	characteristic
862	#529	—	2	1	no	—
863	#529	—	2	1	no	—
864	#529	C₂²×C₃₁	1	1	yes	characteristic
865	#529	C₂²×C₃₁	1	1	yes	characteristic
866	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
867	#520	C₂²×C₃₁	1	1	yes	characteristic
868	#519	C₂²×C₃₁	1	1	yes	characteristic
869	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
870	#501	C₂²×C₃₁	1	1	yes	characteristic
871	#501	C₂²×C₃₁	1	1	yes	characteristic
872	#500	C₂²×C₃₁	1	1	yes	characteristic
873	#499	C₂²×C₃₁	1	1	yes	characteristic
874	#499	C₂²×C₃₁	1	1	yes	characteristic
875	#499	C₂²×C₃₁	1	1	yes	characteristic
876	#491	C₂²×C₃₁	1	1	yes	characteristic
877	#489	C₂²×C₃₁	1	1	yes	characteristic
878	#488	C₂²×C₃₁	1	1	yes	characteristic
879	#488	C₂²×C₃₁	1	1	yes	characteristic
880	#488	C₂²×C₃₁	1	1	yes	characteristic
881	#487	C₂²×C₃₁	1	1	yes	characteristic
882	#485	C₂²×C₃₁	1	1	yes	characteristic
883	#485	C₂²×C₃₁	1	1	yes	characteristic
884	#485	C₂²×C₃₁	1	1	yes	characteristic
885	#485	C₂²×C₃₁	1	1	yes	characteristic
886	#485	C₂²×C₃₁	1	1	yes	characteristic
887	#484	C₂²×C₃₁	1	1	yes	characteristic
888	#484	C₂²×C₃₁	1	1	yes	characteristic
889	#484	C₂²×C₃₁	1	1	yes	characteristic
890	#484	C₂²×C₃₁	1	1	yes	characteristic
891	#484	C₂²×C₃₁	1	1	yes	characteristic
892	#484	C₂²×C₃₁	1	1	yes	characteristic
893	#483	C₂²×C₃₁	1	1	yes	characteristic
894	#483	C₂²×C₃₁	1	1	yes	characteristic
895	#483	C₂²×C₃₁	1	1	yes	characteristic
896	#482	C₂²×C₃₁	1	1	yes	characteristic
897	#481	C₂²×C₃₁	1	1	yes	characteristic
898	#480	C₂²×C₃₁	1	1	yes	characteristic
899	#480	C₂²×C₃₁	1	1	yes	characteristic
900	#479	C₂²×C₃₁	1	1	yes	characteristic
901	#479	C₂²×C₃₁	1	1	yes	characteristic
902	#479	C₂²×C₃₁	1	1	yes	characteristic
903	#479	C₂²×C₃₁	1	1	yes	characteristic
904	#479	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	#479	C₂²×C₃₁	1	1	yes	characteristic
914	#479	C₂²×C₃₁	1	1	yes	characteristic
915	#479	C₂²×C₃₁	1	1	yes	characteristic
916	#479	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	#477	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	#475	C₂²×C₃₁	1	1	yes	characteristic
926	#475	C₂²×C₃₁	1	1	yes	characteristic
927	#475	C₂²×C₃₁	1	1	yes	characteristic
928	#474	C₂²×C₃₁	1	1	yes	characteristic
929	#474	C₂²×C₃₁	1	1	yes	characteristic
930	#470	C₂²×C₃₁	1	1	yes	characteristic
931	#470	C₂²×C₃₁	1	1	yes	characteristic
932	#470	C₂²×C₃₁	1	1	yes	characteristic
933	#468	C₂²×C₃₁	1	1	yes	characteristic
934	#467	C₂²×C₃₁	1	1	yes	characteristic
935	#467	C₂²×C₃₁	1	1	yes	characteristic
936	#467	C₂²×C₃₁	1	1	yes	characteristic
937	#467	C₂²×C₃₁	1	1	yes	characteristic
938	#467	C₂²×C₃₁	1	1	yes	characteristic
939	#465	C₂²×C₃₁	1	1	yes	characteristic
940	#465	C₂²×C₃₁	1	1	yes	characteristic
941	#465	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	#464	C₂²×C₃₁	1	1	yes	characteristic
946	#462	C₂²×C₃₁	1	1	yes	characteristic
947	#462	C₂²×C₃₁	1	1	yes	characteristic
948	#462	C₂²×C₃₁	1	1	yes	characteristic
949	#462	C₂²×C₃₁	1	1	yes	characteristic
950	#462	C₂²×C₃₁	1	1	yes	characteristic
951	#461	C₂²×C₃₁	1	1	yes	characteristic
952	#452	C₂²×C₃₁	1	1	yes	characteristic
953	#452	C₂²×C₃₁	1	1	yes	characteristic
954	#451	C₂²×C₃₁	1	1	yes	characteristic
955	#451	C₂²×C₃₁	1	1	yes	characteristic
956	#451	C₂²×C₃₁	1	1	yes	characteristic
957	#451	C₂²×C₃₁	1	1	yes	characteristic
958	#446	C₂²×C₃₁	1	1	yes	characteristic
959	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
960	#441	C₂²×C₃₁	1	1	yes	characteristic
961	#441	C₂²×C₃₁	1	1	yes	characteristic
962	#441	C₂²×C₃₁	1	1	yes	characteristic
963	#440	C₂²×C₃₁	1	1	yes	characteristic
964	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
965	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
966	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
967	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
968	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
969	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
970	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
971	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
972	#436	C₂²×C₃₁	1	1	yes	characteristic
973	#435	C₂²×C₃₁	1	1	yes	characteristic
974	#435	C₂²×C₃₁	1	1	yes	characteristic
975	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
976	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
977	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
978	#433	C₂²×C₃₁	1	1	yes	characteristic
979	#433	C₂²×C₃₁	1	1	yes	characteristic
980	#431	C₂²×C₃₁	1	1	yes	characteristic
981	#428	C₂²×C₃₁	1	1	yes	characteristic
982	#428	C₂²×C₃₁	1	1	yes	characteristic
983	#427	C₂²×C₃₁	1	1	yes	characteristic
984	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
985	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
986	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
987	#424	C₂²×C₃₁	1	1	yes	characteristic
988	#424	C₂²×C₃₁	1	1	yes	characteristic
989	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
990	#419	C₂²×C₃₁	1	1	yes	characteristic
991	#417	C₂²×C₃₁	1	1	yes	characteristic
992	#416	C₂²×C₃₁	1	1	yes	characteristic
993	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
994	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
995	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
996	C₂×C₃₁	—	2	2	no	—
997	C₂×C₃₁	—	4	1	no	—
998	C₂×C₃₁	—	4	1	no	—
999	C₂×C₃₁	—	8	1	no	—
1000	C₂×C₃₁	#3489	1	1	yes	characteristic
1001	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
1002	C₂×C₃₁	#3584	1	1	yes	characteristic
1003	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1004	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1005	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1006	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1007	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1008	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1009	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1010	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1011	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1012	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1013	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1014	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1015	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1016	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1017	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1018	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1019	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
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	C₂³×C₃₁	1	1	yes	characteristic
1027	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1028	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1029	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1030	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1031	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1032	#126	—	2	1	no	—
1033	#126	—	2	1	no	—
1034	#126	—	2	1	no	—
1035	#126	—	2	1	no	—
1036	#126	—	2	1	no	—
1037	#126	—	2	1	no	—
1038	#126	—	2	1	no	—
1039	#126	—	2	1	no	—
1040	#126	—	2	1	no	—
1041	#126	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
1049	#126	D₄×C₃₁	1	1	yes	characteristic
1050	#125	—	2	1	no	—
1051	#125	—	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	—	2	1	no	—
1065	#125	—	2	1	no	—
1066	#125	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
1076	#125	C₂³×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	D₄×C₃₁	1	1	yes	characteristic
1088	#124	C₂³×C₃₁	1	1	yes	characteristic
1089	#124	C₂³×C₃₁	1	1	yes	characteristic
1090	#123	—	2	1	no	—
1091	#123	—	2	1	no	—
1092	#123	—	2	1	no	—
1093	#123	—	2	1	no	—
1094	#123	—	2	1	no	—
1095	#123	—	2	1	no	—
1096	#123	—	2	1	no	—
1097	#123	—	2	1	no	—
1098	#123	D₄×C₃₁	1	1	yes	characteristic
1099	#123	D₄×C₃₁	1	1	yes	characteristic
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	D₄×C₃₁	1	1	yes	characteristic
1118	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1119	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1120	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1121	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1122	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1123	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1124	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1125	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1126	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1127	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1128	#121	—	2	1	no	—
1129	#121	—	2	1	no	—
1130	#121	—	2	1	no	—
1131	#121	D₄×C₃₁	1	1	yes	characteristic
1132	#121	C₂³×C₃₁	1	1	yes	characteristic
1133	#121	C₂³×C₃₁	1	1	yes	characteristic
1134	C₄×Q₈	—	2	1	no	—
1135	C₄×Q₈	—	2	1	no	—
1136	C₄×Q₈	—	2	1	no	—
1137	C₄×Q₈	—	2	1	no	—
1138	C₄×Q₈	—	2	1	no	—
1139	C₄×Q₈	—	2	1	no	—
1140	C₄×Q₈	—	2	1	no	—
1141	C₄×Q₈	—	2	1	no	—
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×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1151	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1152	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1153	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1154	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1155	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1156	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1157	C₄×D₄	—	2	1	no	—
1158	C₄×D₄	—	2	1	no	—
1159	C₄×D₄	—	2	1	no	—
1160	C₄×D₄	—	2	1	no	—
1161	C₄×D₄	—	2	1	no	—
1162	C₄×D₄	—	2	1	no	—
1163	C₄×D₄	—	2	1	no	—
1164	C₄×D₄	—	2	1	no	—
1165	C₄×D₄	—	2	1	no	—
1166	C₄×D₄	—	2	1	no	—
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	—	2	1	no	—
1180	#117	—	2	1	no	—
1181	#117	—	2	1	no	—
1182	#117	—	2	1	no	—
1183	#117	C₂³×C₃₁	1	1	yes	characteristic
1184	#117	C₂³×C₃₁	1	1	yes	characteristic
1185	#117	C₂³×C₃₁	1	1	yes	characteristic
1186	#117	C₂³×C₃₁	1	1	yes	characteristic
1187	#117	C₂³×C₃₁	1	1	yes	characteristic
1188	C₂×C₄⋊C₄	—	2	1	no	—
1189	C₂×C₄⋊C₄	—	2	1	no	—
1190	C₂×C₄⋊C₄	—	2	1	no	—
1191	C₂×C₄⋊C₄	—	2	1	no	—
1192	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1193	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1194	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1195	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1196	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1197	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1198	C₂×C₄²	—	2	1	no	—
1199	C₂×C₄²	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	#107	C₂³×C₃₁	1	1	yes	characteristic
1206	#107	C₂³×C₃₁	1	1	yes	characteristic
1207	#107	C₂³×C₃₁	1	1	yes	characteristic
1208	#107	C₂³×C₃₁	1	1	yes	characteristic
1209	#107	C₂³×C₃₁	1	1	yes	characteristic
1210	#107	C₂³×C₃₁	1	1	yes	characteristic
1211	#107	C₂³×C₃₁	1	1	yes	characteristic
1212	#107	C₂³×C₃₁	1	1	yes	characteristic
1213	#107	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	#106	C₂³×C₃₁	1	1	yes	characteristic
1218	#106	C₂³×C₃₁	1	1	yes	characteristic
1219	#106	C₂³×C₃₁	1	1	yes	characteristic
1220	#106	C₂³×C₃₁	1	1	yes	characteristic
1221	#106	C₂³×C₃₁	1	1	yes	characteristic
1222	#106	C₂³×C₃₁	1	1	yes	characteristic
1223	#106	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1230	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1231	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1232	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1233	C₄⋊C₈	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	#103	C₂³×C₃₁	1	1	yes	characteristic
1246	#103	C₂³×C₃₁	1	1	yes	characteristic
1247	#103	C₂³×C₃₁	1	1	yes	characteristic
1248	#103	C₂³×C₃₁	1	1	yes	characteristic
1249	#103	C₂³×C₃₁	1	1	yes	characteristic
1250	#103	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	#102	C₂³×C₃₁	1	1	yes	characteristic
1261	#102	C₂³×C₃₁	1	1	yes	characteristic
1262	#102	C₂³×C₃₁	1	1	yes	characteristic
1263	#102	C₂³×C₃₁	1	1	yes	characteristic
1264	#102	C₂³×C₃₁	1	1	yes	characteristic
1265	#102	C₂³×C₃₁	1	1	yes	characteristic
1266	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1267	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1268	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1269	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1270	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1271	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1272	#97	C₂³×C₃₁	1	1	yes	characteristic
1273	#97	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	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1278	C₃₁	#62214	1	1	yes	characteristic, direct product factor, Sylow
1279	#41	—	2	2	no	—
1280	#41	—	4	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	2	no	—
1288	C₂×Q₈	—	2	2	no	—
1289	C₂×Q₈	—	4	1	no	—
1290	C₂×Q₈	—	4	1	no	—
1291	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1292	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1293	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1294	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1295	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1296	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1297	C₂×D₄	—	2	1	no	—
1298	C₂×D₄	—	2	1	no	—
1299	C₂×D₄	—	2	1	no	—
1300	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1301	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1302	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1303	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1304	C₂²×C₄	—	2	1	no	—
1305	C₂²×C₄	—	2	1	no	—
1306	C₂²×C₄	—	2	1	no	—
1307	C₂²×C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1316	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1317	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1318	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1319	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1320	Q₁₆	—	2	2	no	—
1321	Q₁₆	—	2	2	no	—
1322	Q₁₆	—	4	1	no	—
1323	Q₁₆	—	4	1	no	—
1324	Q₁₆	—	4	1	no	—
1325	Q₁₆	—	4	1	no	—
1326	SD₁₆	—	4	1	no	—
1327	SD₁₆	—	4	1	no	—
1328	M₁₆	—	4	1	no	—
1329	M₁₆	—	4	1	no	—
1330	C₂×C₈	—	4	1	no	—
1331	C₂×C₈	—	4	1	no	—
1332	C₂×C₈	—	4	1	no	—
1333	C₂×C₈	—	4	1	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	—	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	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	C₂×D₄×C₃₁	1	1	yes	characteristic
1403	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1404	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1405	C₄⋊C₄	C₂×D₄×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	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1413	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1414	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1415	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1442	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1443	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1444	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1445	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1446	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1455	C₄²	—	2	1	no	—
1456	C₄²	—	2	1	no	—
1457	C₄²	—	2	1	no	—
1458	C₄²	—	2	1	no	—
1459	C₄²	—	2	1	no	—
1460	C₄²	—	2	1	no	—
1461	C₄²	—	2	1	no	—
1462	C₄²	—	2	1	no	—
1463	C₄²	—	2	1	no	—
1464	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1465	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1466	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1467	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1468	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1469	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1470	C₂³	—	2	1	no	—
1471	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1472	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1473	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1474	Q₈	—	2	1	no	—
1475	Q₈	—	2	1	no	—
1476	Q₈	—	2	1	no	—
1477	Q₈	—	2	1	no	—
1478	Q₈	—	2	1	no	—
1479	Q₈	—	2	1	no	—
1480	Q₈	—	2	1	no	—
1481	Q₈	—	2	1	no	—
1482	Q₈	—	2	1	no	—
1483	Q₈	—	4	1	no	—
1484	Q₈	—	4	2	no	—
1485	Q₈	—	4	2	no	—
1486	Q₈	—	8	1	no	—
1487	Q₈	—	8	1	no	—
1488	Q₈	—	8	1	no	—
1489	Q₈	—	8	1	no	—
1490	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1491	D₄	—	2	2	no	—
1492	D₄	—	2	2	no	—
1493	D₄	—	2	1	no	—
1494	D₄	—	2	1	no	—
1495	D₄	—	4	1	no	—
1496	D₄	—	4	2	no	—
1497	D₄	—	4	2	no	—
1498	D₄	—	8	1	no	—
1499	C₂×C₄	—	2	2	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	—	2	1	no	—
1514	C₂×C₄	—	2	1	no	—
1515	C₂×C₄	—	2	1	no	—
1516	C₂×C₄	—	2	1	no	—
1517	C₂×C₄	—	2	1	no	—
1518	C₂×C₄	—	2	1	no	—
1519	C₂×C₄	—	2	1	no	—
1520	C₂×C₄	—	2	1	no	—
1521	C₂×C₄	—	4	1	no	—
1522	C₂×C₄	—	4	2	no	—
1523	C₂×C₄	—	4	2	no	—
1524	C₂×C₄	—	4	2	no	—
1525	C₂×C₄	—	4	2	no	—
1526	C₂×C₄	—	8	1	no	—
1527	C₂×C₄	—	8	1	no	—
1528	C₂×C₄	—	8	1	no	—
1529	C₂×C₄	—	8	1	no	—
1530	C₂×C₄	—	8	1	no	—
1531	C₂×C₄	—	8	1	no	—
1532	C₂×C₄	—	8	1	no	—
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	C₂²×D₄×C₃₁	1	1	yes	characteristic
1543	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1544	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
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	C₈	—	2	1	no	—
1552	C₈	—	2	1	no	—
1553	C₂²	—	2	1	no	—
1554	C₂²	—	2	1	no	—
1555	C₂²	—	2	1	no	—
1556	C₂²	—	2	1	no	—
1557	C₂²	—	2	1	no	—
1558	C₂²	—	2	1	no	—
1559	C₂²	—	2	1	no	—
1560	C₂²	—	2	1	no	—
1561	C₂²	—	4	1	no	—
1562	C₂²	—	4	1	no	—
1563	C₂²	—	4	1	no	—
1564	C₂²	C₃₁×#578	1	2	yes	—
1565	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1566	C₄	—	2	1	no	—
1567	C₄	—	2	1	no	—
1568	C₄	—	2	1	no	—
1569	C₄	—	2	2	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	—	4	1	no	—
1591	C₄	—	4	1	no	—
1592	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1593	C₄	C₃₁×#585	1	1	yes	characteristic
1594	C₂	—	2	2	no	—
1595	C₂	—	4	1	no	—
1596	C₂	—	4	1	no	—
1597	C₂	—	8	1	no	—
1598	C₂	C₃₁×#3489	1	1	yes	characteristic
1599	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1600	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3516	C₂
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×#3563	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3383	C₂	semidirect
5. C₃₁×#3377	C₂	semidirect
6. C₃₁×#3364	C₂	semidirect
7. C₃₁×#3352	C₂	semidirect
8. C₃₁×#3346	C₂	semidirect
9. C₃₁×#3344	C₂	semidirect
10. C₃₁×#3338	C₂	semidirect
11. C₃₁×#3337	C₂	semidirect
12. C₃₁×#3336	C₂	semidirect
13. C₃₁×#3327	C₂	semidirect
14. C₃₁×#3316	C₂	semidirect
15. C₃₁×#3312	C₂	semidirect
16. C₃₁×#3300	C₂	semidirect
17. C₃₁×#3300	C₂	semidirect
18. C₃₁×#3299	C₂	semidirect
19. C₃₁×#3261	C₂	semidirect
20. C₃₁×#3258	C₂	semidirect
21. C₃₁×#3248	C₂	semidirect
22. C₃₁×#3243	C₂	semidirect
23. C₃₁×#3242	C₂	semidirect
24. C₃₁×#3232	C₂	semidirect
25. C₃₁×#3127	C₂	semidirect
26. C₃₁×#3120	C₂	semidirect
27. C₃₁×#3104	C₂	semidirect
28. C₃₁×#3083	C₂	semidirect
29. C₃₁×#3082	C₂	semidirect
30. C₂×C₃₁×#479	C₂	semidirect
31. C₃₁×#2994	C₂	semidirect
669. #62214	C₃₁	direct (N × H)
753. #3563	C₂×C₃₁	semidirect
755. #3390	C₂×C₃₁	semidirect
756. #3383	C₂×C₃₁	semidirect
757. #3377	C₂×C₃₁	semidirect
758. #3364	C₂×C₃₁	semidirect
759. #3352	C₂×C₃₁	semidirect
760. #3346	C₂×C₃₁	semidirect
761. #3344	C₂×C₃₁	semidirect
762. #3338	C₂×C₃₁	semidirect
763. #3337	C₂×C₃₁	semidirect
764. #3336	C₂×C₃₁	semidirect
765. #3327	C₂×C₃₁	semidirect
766. #3316	C₂×C₃₁	semidirect
767. #3312	C₂×C₃₁	semidirect
768. #3300	C₂×C₃₁	semidirect
769. #3300	C₂×C₃₁	semidirect
770. #3299	C₂×C₃₁	semidirect
771. #3261	C₂×C₃₁	semidirect
772. #3258	C₂×C₃₁	semidirect
773. #3248	C₂×C₃₁	semidirect
774. #3243	C₂×C₃₁	semidirect
775. #3242	C₂×C₃₁	semidirect
776. #3232	C₂×C₃₁	semidirect
777. #3127	C₂×C₃₁	semidirect
778. #3120	C₂×C₃₁	semidirect
779. #3104	C₂×C₃₁	semidirect
780. #3083	C₂×C₃₁	semidirect
781. #3082	C₂×C₃₁	semidirect
782. C₂×#479	C₂×C₃₁	semidirect
783. #2994	C₂×C₃₁	semidirect
1278. C₃₁	#62214	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×#3563	2
C₃₁×#3516	2
C₃₁×#3390	2
C₃₁×#3383	2
C₃₁×#3377	2
C₃₁×#3364	2
C₃₁×#3352	2
C₃₁×#3346	2
C₃₁×#3344	2
C₃₁×#3338	2
C₃₁×#3337	2
C₃₁×#3336	2
C₃₁×#3327	2
C₃₁×#3316	2
C₃₁×#3312	2
C₃₁×#3300	2
C₃₁×#3299	2
C₃₁×#3261	2
C₃₁×#3258	2
C₃₁×#3248	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3232	2
C₃₁×#3127	2
C₃₁×#3120	2
C₃₁×#3104	2
C₃₁×#3083	2
C₃₁×#3082	2
C₂×C₃₁×#479	2
C₃₁×#2994	2
#62214	31

Subgroups — C31×#62214 #21518973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62214 #21518973