Subgroups — C₃₁×#62158 #21518917

Order 7936.

1684 conjugacy classes of subgroups.

The subgroup lattice has 1632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3516	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3349	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3346	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3343	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3339	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3320	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3316	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3313	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3308	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3301	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3262	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3243	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3121	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3117	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×#477	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#563	—	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×#556	—	2	1	no	—
37	C₃₁×#556	C₂²	1	1	yes	characteristic
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×#553	C₂²	1	1	yes	characteristic
46	C₃₁×#553	C₂²	1	1	yes	characteristic
47	C₃₁×#552	—	2	1	no	—
48	C₃₁×#552	C₂²	1	1	yes	characteristic
49	D₄×Q₈×C₃₁	—	2	1	no	—
50	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
51	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
52	C₃₁×#548	—	2	1	no	—
53	C₃₁×#548	C₂²	1	1	yes	characteristic
54	C₃₁×#548	C₂²	1	1	yes	characteristic
55	C₃₁×#547	C₂²	1	1	yes	characteristic
56	C₃₁×#544	C₂²	1	1	yes	characteristic
57	C₃₁×#544	C₂²	1	1	yes	characteristic
58	C₃₁×#542	—	2	1	no	—
59	C₃₁×#542	C₂²	1	1	yes	characteristic
60	C₃₁×#542	C₂²	1	1	yes	characteristic
61	C₃₁×#542	C₂²	1	1	yes	characteristic
62	C₃₁×#541	—	2	1	no	—
63	C₃₁×#541	—	2	1	no	—
64	C₃₁×#541	C₂²	1	1	yes	characteristic
65	C₃₁×#539	—	2	1	no	—
66	C₃₁×#539	—	2	1	no	—
67	C₃₁×#536	—	2	1	no	—
68	C₂×C₃₁×C₄⋊Q₈	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	C₃₁×#529	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×#501	C₂²	1	1	yes	characteristic
80	C₃₁×#501	C₂²	1	1	yes	characteristic
81	C₃₁×#500	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×#489	C₂²	1	1	yes	characteristic
86	C₃₁×#489	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×#484	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×#483	C₂²	1	1	yes	characteristic
100	C₃₁×#482	C₂²	1	1	yes	characteristic
101	C₃₁×#482	C₂²	1	1	yes	characteristic
102	C₃₁×#481	C₂²	1	1	yes	characteristic
103	C₃₁×#481	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×#478	C₂²	1	1	yes	characteristic
116	C₃₁×#478	C₂²	1	1	yes	characteristic
117	C₃₁×#478	C₂²	1	1	yes	characteristic
118	C₃₁×#478	C₂²	1	1	yes	characteristic
119	C₃₁×#477	C₂²	1	1	yes	characteristic
120	C₃₁×#477	C₂²	1	1	yes	characteristic
121	C₃₁×#477	C₂²	1	1	yes	characteristic
122	C₃₁×#477	C₂²	1	1	yes	characteristic
123	C₃₁×#477	C₂²	1	1	yes	characteristic
124	C₃₁×#477	C₂²	1	1	yes	characteristic
125	C₃₁×#477	C₂²	1	1	yes	characteristic
126	C₃₁×#477	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×#475	C₂²	1	1	yes	characteristic
131	C₃₁×#475	C₂²	1	1	yes	characteristic
132	C₃₁×#475	C₂²	1	1	yes	characteristic
133	C₃₁×#474	C₂²	1	1	yes	characteristic
134	C₃₁×#474	C₂²	1	1	yes	characteristic
135	C₃₁×#474	C₂²	1	1	yes	characteristic
136	C₃₁×#474	C₂²	1	1	yes	characteristic
137	C₃₁×#470	C₂²	1	1	yes	characteristic
138	C₃₁×#468	C₂²	1	1	yes	characteristic
139	C₃₁×#468	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×#466	C₂²	1	1	yes	characteristic
145	C₃₁×#466	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×#464	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×#452	C₂²	1	1	yes	characteristic
160	C₃₁×#451	C₂²	1	1	yes	characteristic
161	C₃₁×#451	C₂²	1	1	yes	characteristic
162	C₃₁×#449	C₂²	1	1	yes	characteristic
163	C₃₁×#448	C₂²	1	1	yes	characteristic
164	C₃₁×#448	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic
166	C₃₁×#446	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	C₃₁×#440	C₂²	1	1	yes	characteristic
172	C₃₁×#440	C₂²	1	1	yes	characteristic
173	C₃₁×#440	C₂²	1	1	yes	characteristic
174	C₃₁×#440	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×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
179	C₃₁×#435	C₂²	1	1	yes	characteristic
180	C₃₁×#435	C₂²	1	1	yes	characteristic
181	C₃₁×#435	C₂²	1	1	yes	characteristic
182	C₃₁×#435	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×#432	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×#107	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	—	2	1	no	—
204	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
205	C₂²×Q₈×C₃₁	—	2	1	no	—
206	C₂²×Q₈×C₃₁	—	2	1	no	—
207	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
230	C₃₁×C₄⋊Q₈	C₂³	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×#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	—	2	1	no	—
249	C₃₁×#126	—	2	1	no	—
250	C₃₁×#126	—	2	1	no	—
251	C₃₁×#126	—	2	1	no	—
252	C₃₁×#126	—	2	1	no	—
253	C₃₁×#126	D₄	1	1	yes	characteristic
254	C₃₁×#126	D₄	1	1	yes	characteristic
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	D₄	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×#124	—	2	1	no	—
274	C₃₁×#124	—	2	1	no	—
275	C₃₁×#124	—	2	1	no	—
276	C₃₁×#124	—	2	1	no	—
277	C₃₁×#124	—	2	1	no	—
278	C₃₁×#124	—	2	1	no	—
279	C₃₁×#124	D₄	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×#123	—	2	1	no	—
294	C₃₁×#123	D₄	1	1	yes	characteristic
295	C₃₁×#123	D₄	1	1	yes	characteristic
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	D₄	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×#121	—	2	1	no	—
327	C₃₁×#121	—	2	1	no	—
328	C₃₁×#121	—	2	1	no	—
329	C₃₁×#121	—	2	1	no	—
330	C₃₁×#121	—	2	1	no	—
331	C₃₁×#121	D₄	1	1	yes	characteristic
332	C₃₁×#121	C₂³	1	1	yes	characteristic
333	C₃₁×#121	C₂³	1	1	yes	characteristic
334	C₃₁×#121	C₂³	1	1	yes	characteristic
335	C₃₁×#121	C₂³	1	1	yes	characteristic
336	C₃₁×#121	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
343	C₄×Q₈×C₃₁	—	2	1	no	—
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×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	—	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	—	2	1	no	—
368	C₄×D₄×C₃₁	—	2	1	no	—
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	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
374	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
376	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
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	C₃₁×#117	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	1	yes	characteristic
415	C₃₁×#107	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×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×#102	C₂³	1	1	yes	characteristic
463	C₃₁×#102	C₂³	1	1	yes	characteristic
464	C₃₁×#102	C₂³	1	1	yes	characteristic
465	C₃₁×#102	C₂³	1	1	yes	characteristic
466	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	C₃₁×#97	C₂³	1	1	yes	characteristic
473	C₃₁×#97	C₂³	1	1	yes	characteristic
474	C₃₁×#97	C₂³	1	1	yes	characteristic
475	C₃₁×#97	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	#41×C₃₁	—	8	2	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	—	2	2	no	—
491	C₂×Q₈×C₃₁	—	2	2	no	—
492	C₂×Q₈×C₃₁	—	4	1	no	—
493	C₂×Q₈×C₃₁	—	4	1	no	—
494	C₂×Q₈×C₃₁	—	8	2	no	—
495	C₂×Q₈×C₃₁	—	8	2	no	—
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×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
501	C₂×D₄×C₃₁	—	2	1	no	—
502	C₂×D₄×C₃₁	—	2	1	no	—
503	C₂×D₄×C₃₁	—	2	1	no	—
504	C₂×D₄×C₃₁	—	2	1	no	—
505	C₂×D₄×C₃₁	—	2	1	no	—
506	C₂×D₄×C₃₁	—	2	1	no	—
507	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
508	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
509	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
510	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
511	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
524	C₂²×C₄×C₃₁	—	2	1	no	—
525	C₂²×C₄×C₃₁	—	2	1	no	—
526	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
527	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
528	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
529	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
530	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
531	Q₁₆×C₃₁	—	2	2	no	—
532	Q₁₆×C₃₁	—	4	1	no	—
533	Q₁₆×C₃₁	—	4	1	no	—
534	SD₁₆×C₃₁	—	2	2	no	—
535	SD₁₆×C₃₁	—	4	1	no	—
536	SD₁₆×C₃₁	—	4	1	no	—
537	SD₁₆×C₃₁	—	4	1	no	—
538	D₈×C₃₁	—	4	1	no	—
539	M₁₆×C₃₁	—	4	1	no	—
540	M₁₆×C₃₁	—	4	1	no	—
541	C₂×C₈×C₃₁	—	4	1	no	—
542	C₂×C₈×C₃₁	—	4	1	no	—
543	C₂×C₈×C₃₁	—	4	1	no	—
544	C₂×C₈×C₃₁	—	4	1	no	—
545	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
546	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
547	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
548	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
549	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
550	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
551	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
552	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
553	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	—	2	1	no	—
596	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	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	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
616	C₂²⋊C₄×C₃₁	—	2	1	no	—
617	C₂²⋊C₄×C₃₁	—	2	1	no	—
618	C₂²⋊C₄×C₃₁	—	2	1	no	—
619	C₂²⋊C₄×C₃₁	—	2	1	no	—
620	C₂²⋊C₄×C₃₁	—	2	1	no	—
621	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	—	2	1	no	—
638	C₂²⋊C₄×C₃₁	—	2	1	no	—
639	C₂²⋊C₄×C₃₁	—	2	1	no	—
640	C₂²⋊C₄×C₃₁	—	2	1	no	—
641	C₂²⋊C₄×C₃₁	—	2	1	no	—
642	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
643	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
644	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
645	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
646	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
647	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
648	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
649	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
650	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
664	C₄²×C₃₁	—	2	1	no	—
665	C₄²×C₃₁	—	2	1	no	—
666	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
667	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
668	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
669	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
670	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
671	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
672	#62158	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
673	C₂³×C₃₁	—	2	1	no	—
674	C₂³×C₃₁	—	2	1	no	—
675	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
676	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
677	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
684	Q₈×C₃₁	—	2	1	no	—
685	Q₈×C₃₁	—	4	1	no	—
686	Q₈×C₃₁	—	4	2	no	—
687	Q₈×C₃₁	—	4	2	no	—
688	Q₈×C₃₁	—	4	2	no	—
689	Q₈×C₃₁	—	4	2	no	—
690	Q₈×C₃₁	—	8	1	no	—
691	Q₈×C₃₁	—	8	1	no	—
692	Q₈×C₃₁	—	8	1	no	—
693	Q₈×C₃₁	—	8	1	no	—
694	Q₈×C₃₁	—	8	1	no	—
695	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
696	D₄×C₃₁	—	2	2	no	—
697	D₄×C₃₁	—	2	2	no	—
698	D₄×C₃₁	—	2	1	no	—
699	D₄×C₃₁	—	2	1	no	—
700	D₄×C₃₁	—	2	1	no	—
701	D₄×C₃₁	—	2	1	no	—
702	D₄×C₃₁	—	4	1	no	—
703	D₄×C₃₁	—	4	2	no	—
704	D₄×C₃₁	—	4	2	no	—
705	D₄×C₃₁	—	4	2	no	—
706	D₄×C₃₁	—	8	1	no	—
707	D₄×C₃₁	—	8	1	no	—
708	D₄×C₃₁	—	8	1	no	—
709	C₂×C₄×C₃₁	—	2	2	no	—
710	C₂×C₄×C₃₁	—	2	1	no	—
711	C₂×C₄×C₃₁	—	2	1	no	—
712	C₂×C₄×C₃₁	—	2	1	no	—
713	C₂×C₄×C₃₁	—	2	1	no	—
714	C₂×C₄×C₃₁	—	2	1	no	—
715	C₂×C₄×C₃₁	—	2	1	no	—
716	C₂×C₄×C₃₁	—	2	1	no	—
717	C₂×C₄×C₃₁	—	2	1	no	—
718	C₂×C₄×C₃₁	—	2	1	no	—
719	C₂×C₄×C₃₁	—	2	1	no	—
720	C₂×C₄×C₃₁	—	2	1	no	—
721	C₂×C₄×C₃₁	—	2	1	no	—
722	C₂×C₄×C₃₁	—	2	1	no	—
723	C₂×C₄×C₃₁	—	2	1	no	—
724	C₂×C₄×C₃₁	—	2	1	no	—
725	C₂×C₄×C₃₁	—	2	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	2	1	no	—
728	C₂×C₄×C₃₁	—	2	1	no	—
729	C₂×C₄×C₃₁	—	2	1	no	—
730	C₂×C₄×C₃₁	—	4	1	no	—
731	C₂×C₄×C₃₁	—	4	2	no	—
732	C₂×C₄×C₃₁	—	4	2	no	—
733	C₂×C₄×C₃₁	—	4	2	no	—
734	C₂×C₄×C₃₁	—	4	2	no	—
735	C₂×C₄×C₃₁	—	8	1	no	—
736	C₂×C₄×C₃₁	—	8	1	no	—
737	C₂×C₄×C₃₁	—	8	1	no	—
738	C₂×C₄×C₃₁	—	8	1	no	—
739	C₂×C₄×C₃₁	—	8	1	no	—
740	C₂×C₄×C₃₁	—	8	1	no	—
741	C₂×C₄×C₃₁	—	8	1	no	—
742	C₂×C₄×C₃₁	—	8	1	no	—
743	C₂×C₄×C₃₁	—	8	1	no	—
744	C₂×C₄×C₃₁	—	8	1	no	—
745	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
748	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
749	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
750	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
751	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
752	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
753	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
754	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
755	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
756	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
757	C₈×C₃₁	—	2	1	no	—
758	C₈×C₃₁	—	2	1	no	—
759	C₈×C₃₁	—	2	1	no	—
760	C₈×C₃₁	—	2	1	no	—
761	C₈×C₃₁	—	2	1	no	—
762	C₈×C₃₁	—	2	1	no	—
763	C₈×C₃₁	—	2	1	no	—
764	C₈×C₃₁	—	2	1	no	—
765	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
766	#3516	C₂×C₃₁	1	1	yes	characteristic, complemented
767	#3390	C₂×C₃₁	1	1	yes	characteristic, complemented
768	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
769	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
770	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
771	#3349	C₂×C₃₁	1	1	yes	characteristic, complemented
772	#3346	C₂×C₃₁	1	1	yes	characteristic, complemented
773	#3346	C₂×C₃₁	1	1	yes	characteristic, complemented
774	#3343	C₂×C₃₁	1	1	yes	characteristic, complemented
775	#3339	C₂×C₃₁	1	1	yes	characteristic, complemented
776	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
777	#3320	C₂×C₃₁	1	1	yes	characteristic, complemented
778	#3316	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3313	C₂×C₃₁	1	1	yes	characteristic, complemented
780	#3308	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3301	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3262	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3258	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3250	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3243	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3124	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3121	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3117	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
794	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
796	C₂²×C₃₁	—	2	1	no	—
797	C₂²×C₃₁	—	2	1	no	—
798	C₂²×C₃₁	—	2	1	no	—
799	C₂²×C₃₁	—	2	1	no	—
800	C₂²×C₃₁	—	2	1	no	—
801	C₂²×C₃₁	—	2	1	no	—
802	C₂²×C₃₁	—	2	1	no	—
803	C₂²×C₃₁	—	2	1	no	—
804	C₂²×C₃₁	—	4	1	no	—
805	C₂²×C₃₁	—	4	1	no	—
806	C₂²×C₃₁	—	4	1	no	—
807	C₂²×C₃₁	—	4	1	no	—
808	C₂²×C₃₁	—	4	1	no	—
809	C₂²×C₃₁	—	4	1	no	—
810	C₂²×C₃₁	#578	1	2	yes	—
811	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
812	C₄×C₃₁	—	2	1	no	—
813	C₄×C₃₁	—	2	1	no	—
814	C₄×C₃₁	—	2	1	no	—
815	C₄×C₃₁	—	2	1	no	—
816	C₄×C₃₁	—	2	1	no	—
817	C₄×C₃₁	—	2	1	no	—
818	C₄×C₃₁	—	2	1	no	—
819	C₄×C₃₁	—	2	2	no	—
820	C₄×C₃₁	—	2	1	no	—
821	C₄×C₃₁	—	2	1	no	—
822	C₄×C₃₁	—	2	1	no	—
823	C₄×C₃₁	—	2	1	no	—
824	C₄×C₃₁	—	4	1	no	—
825	C₄×C₃₁	—	4	1	no	—
826	C₄×C₃₁	—	4	1	no	—
827	C₄×C₃₁	—	4	1	no	—
828	C₄×C₃₁	—	4	1	no	—
829	C₄×C₃₁	—	4	1	no	—
830	C₄×C₃₁	—	4	1	no	—
831	C₄×C₃₁	—	4	1	no	—
832	C₄×C₃₁	—	4	1	no	—
833	C₄×C₃₁	—	4	1	no	—
834	C₄×C₃₁	—	4	1	no	—
835	C₄×C₃₁	—	4	1	no	—
836	C₄×C₃₁	—	4	1	no	—
837	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
838	C₄×C₃₁	#585	1	1	yes	characteristic
839	#563	—	2	1	no	—
840	#563	—	2	1	no	—
841	#557	C₂²×C₃₁	1	1	yes	characteristic
842	#557	C₂²×C₃₁	1	1	yes	characteristic
843	#556	—	2	1	no	—
844	#556	C₂²×C₃₁	1	1	yes	characteristic
845	#556	C₂²×C₃₁	1	1	yes	characteristic
846	#554	—	2	1	no	—
847	#554	C₂²×C₃₁	1	1	yes	characteristic
848	#554	C₂²×C₃₁	1	1	yes	characteristic
849	#554	C₂²×C₃₁	1	1	yes	characteristic
850	#553	—	2	1	no	—
851	#553	C₂²×C₃₁	1	1	yes	characteristic
852	#553	C₂²×C₃₁	1	1	yes	characteristic
853	#553	C₂²×C₃₁	1	1	yes	characteristic
854	#552	—	2	1	no	—
855	#552	C₂²×C₃₁	1	1	yes	characteristic
856	D₄×Q₈	—	2	1	no	—
857	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
858	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
859	#548	—	2	1	no	—
860	#548	C₂²×C₃₁	1	1	yes	characteristic
861	#548	C₂²×C₃₁	1	1	yes	characteristic
862	#547	C₂²×C₃₁	1	1	yes	characteristic
863	#544	C₂²×C₃₁	1	1	yes	characteristic
864	#544	C₂²×C₃₁	1	1	yes	characteristic
865	#542	—	2	1	no	—
866	#542	C₂²×C₃₁	1	1	yes	characteristic
867	#542	C₂²×C₃₁	1	1	yes	characteristic
868	#542	C₂²×C₃₁	1	1	yes	characteristic
869	#541	—	2	1	no	—
870	#541	—	2	1	no	—
871	#541	C₂²×C₃₁	1	1	yes	characteristic
872	#539	—	2	1	no	—
873	#539	—	2	1	no	—
874	#536	—	2	1	no	—
875	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
876	#529	—	2	1	no	—
877	#529	—	2	1	no	—
878	#529	C₂²×C₃₁	1	1	yes	characteristic
879	#529	C₂²×C₃₁	1	1	yes	characteristic
880	#529	C₂²×C₃₁	1	1	yes	characteristic
881	#520	C₂²×C₃₁	1	1	yes	characteristic
882	#519	C₂²×C₃₁	1	1	yes	characteristic
883	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
884	#501	C₂²×C₃₁	1	1	yes	characteristic
885	#501	C₂²×C₃₁	1	1	yes	characteristic
886	#501	C₂²×C₃₁	1	1	yes	characteristic
887	#501	C₂²×C₃₁	1	1	yes	characteristic
888	#500	C₂²×C₃₁	1	1	yes	characteristic
889	#499	C₂²×C₃₁	1	1	yes	characteristic
890	#491	C₂²×C₃₁	1	1	yes	characteristic
891	#489	C₂²×C₃₁	1	1	yes	characteristic
892	#489	C₂²×C₃₁	1	1	yes	characteristic
893	#489	C₂²×C₃₁	1	1	yes	characteristic
894	#488	C₂²×C₃₁	1	1	yes	characteristic
895	#487	C₂²×C₃₁	1	1	yes	characteristic
896	#485	C₂²×C₃₁	1	1	yes	characteristic
897	#485	C₂²×C₃₁	1	1	yes	characteristic
898	#485	C₂²×C₃₁	1	1	yes	characteristic
899	#485	C₂²×C₃₁	1	1	yes	characteristic
900	#484	C₂²×C₃₁	1	1	yes	characteristic
901	#484	C₂²×C₃₁	1	1	yes	characteristic
902	#484	C₂²×C₃₁	1	1	yes	characteristic
903	#484	C₂²×C₃₁	1	1	yes	characteristic
904	#484	C₂²×C₃₁	1	1	yes	characteristic
905	#484	C₂²×C₃₁	1	1	yes	characteristic
906	#483	C₂²×C₃₁	1	1	yes	characteristic
907	#482	C₂²×C₃₁	1	1	yes	characteristic
908	#482	C₂²×C₃₁	1	1	yes	characteristic
909	#481	C₂²×C₃₁	1	1	yes	characteristic
910	#481	C₂²×C₃₁	1	1	yes	characteristic
911	#481	C₂²×C₃₁	1	1	yes	characteristic
912	#480	C₂²×C₃₁	1	1	yes	characteristic
913	#480	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	#479	C₂²×C₃₁	1	1	yes	characteristic
918	#479	C₂²×C₃₁	1	1	yes	characteristic
919	#479	C₂²×C₃₁	1	1	yes	characteristic
920	#479	C₂²×C₃₁	1	1	yes	characteristic
921	#479	C₂²×C₃₁	1	1	yes	characteristic
922	#478	C₂²×C₃₁	1	1	yes	characteristic
923	#478	C₂²×C₃₁	1	1	yes	characteristic
924	#478	C₂²×C₃₁	1	1	yes	characteristic
925	#478	C₂²×C₃₁	1	1	yes	characteristic
926	#477	C₂²×C₃₁	1	1	yes	characteristic
927	#477	C₂²×C₃₁	1	1	yes	characteristic
928	#477	C₂²×C₃₁	1	1	yes	characteristic
929	#477	C₂²×C₃₁	1	1	yes	characteristic
930	#477	C₂²×C₃₁	1	1	yes	characteristic
931	#477	C₂²×C₃₁	1	1	yes	characteristic
932	#477	C₂²×C₃₁	1	1	yes	characteristic
933	#477	C₂²×C₃₁	1	1	yes	characteristic
934	#477	C₂²×C₃₁	1	1	yes	characteristic
935	#477	C₂²×C₃₁	1	1	yes	characteristic
936	#477	C₂²×C₃₁	1	1	yes	characteristic
937	#475	C₂²×C₃₁	1	1	yes	characteristic
938	#475	C₂²×C₃₁	1	1	yes	characteristic
939	#475	C₂²×C₃₁	1	1	yes	characteristic
940	#474	C₂²×C₃₁	1	1	yes	characteristic
941	#474	C₂²×C₃₁	1	1	yes	characteristic
942	#474	C₂²×C₃₁	1	1	yes	characteristic
943	#474	C₂²×C₃₁	1	1	yes	characteristic
944	#470	C₂²×C₃₁	1	1	yes	characteristic
945	#468	C₂²×C₃₁	1	1	yes	characteristic
946	#468	C₂²×C₃₁	1	1	yes	characteristic
947	#468	C₂²×C₃₁	1	1	yes	characteristic
948	#467	C₂²×C₃₁	1	1	yes	characteristic
949	#467	C₂²×C₃₁	1	1	yes	characteristic
950	#467	C₂²×C₃₁	1	1	yes	characteristic
951	#466	C₂²×C₃₁	1	1	yes	characteristic
952	#466	C₂²×C₃₁	1	1	yes	characteristic
953	#465	C₂²×C₃₁	1	1	yes	characteristic
954	#465	C₂²×C₃₁	1	1	yes	characteristic
955	#465	C₂²×C₃₁	1	1	yes	characteristic
956	#464	C₂²×C₃₁	1	1	yes	characteristic
957	#464	C₂²×C₃₁	1	1	yes	characteristic
958	#464	C₂²×C₃₁	1	1	yes	characteristic
959	#464	C₂²×C₃₁	1	1	yes	characteristic
960	#464	C₂²×C₃₁	1	1	yes	characteristic
961	#463	C₂²×C₃₁	1	1	yes	characteristic
962	#463	C₂²×C₃₁	1	1	yes	characteristic
963	#463	C₂²×C₃₁	1	1	yes	characteristic
964	#462	C₂²×C₃₁	1	1	yes	characteristic
965	#461	C₂²×C₃₁	1	1	yes	characteristic
966	#452	C₂²×C₃₁	1	1	yes	characteristic
967	#451	C₂²×C₃₁	1	1	yes	characteristic
968	#451	C₂²×C₃₁	1	1	yes	characteristic
969	#449	C₂²×C₃₁	1	1	yes	characteristic
970	#448	C₂²×C₃₁	1	1	yes	characteristic
971	#448	C₂²×C₃₁	1	1	yes	characteristic
972	#446	C₂²×C₃₁	1	1	yes	characteristic
973	#446	C₂²×C₃₁	1	1	yes	characteristic
974	#441	C₂²×C₃₁	1	1	yes	characteristic
975	#441	C₂²×C₃₁	1	1	yes	characteristic
976	#441	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	#440	C₂²×C₃₁	1	1	yes	characteristic
982	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
983	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
984	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
985	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
986	#435	C₂²×C₃₁	1	1	yes	characteristic
987	#435	C₂²×C₃₁	1	1	yes	characteristic
988	#435	C₂²×C₃₁	1	1	yes	characteristic
989	#435	C₂²×C₃₁	1	1	yes	characteristic
990	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
991	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
992	#433	C₂²×C₃₁	1	1	yes	characteristic
993	#433	C₂²×C₃₁	1	1	yes	characteristic
994	#432	C₂²×C₃₁	1	1	yes	characteristic
995	#428	C₂²×C₃₁	1	1	yes	characteristic
996	#428	C₂²×C₃₁	1	1	yes	characteristic
997	#427	C₂²×C₃₁	1	1	yes	characteristic
998	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
999	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
1000	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
1001	#424	C₂²×C₃₁	1	1	yes	characteristic
1002	#424	C₂²×C₃₁	1	1	yes	characteristic
1003	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
1004	#419	C₂²×C₃₁	1	1	yes	characteristic
1005	#417	C₂²×C₃₁	1	1	yes	characteristic
1006	#416	C₂²×C₃₁	1	1	yes	characteristic
1007	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1008	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1009	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1010	C₂×C₃₁	—	2	2	no	—
1011	C₂×C₃₁	—	4	1	no	—
1012	C₂×C₃₁	—	4	1	no	—
1013	C₂×C₃₁	—	8	1	no	—
1014	C₂×C₃₁	—	8	1	no	—
1015	C₂×C₃₁	#3489	1	1	yes	characteristic
1016	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
1017	C₂×C₃₁	#3585	1	1	yes	characteristic
1018	C₂×#41	—	2	1	no	—
1019	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1020	C₂²×Q₈	—	2	1	no	—
1021	C₂²×Q₈	—	2	1	no	—
1022	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1023	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1024	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1025	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1026	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1027	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1028	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1029	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1030	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1031	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1032	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1033	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1034	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1035	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1036	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1037	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1038	C₄⋊Q₈	—	2	1	no	—
1039	C₄⋊Q₈	—	2	1	no	—
1040	C₄⋊Q₈	—	2	1	no	—
1041	C₄⋊Q₈	—	2	1	no	—
1042	C₄⋊Q₈	—	2	1	no	—
1043	C₄⋊Q₈	—	2	1	no	—
1044	C₄⋊Q₈	—	2	1	no	—
1045	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1046	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1047	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1048	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1049	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1050	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1051	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1052	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1053	#126	—	2	1	no	—
1054	#126	—	2	1	no	—
1055	#126	—	2	1	no	—
1056	#126	—	2	1	no	—
1057	#126	—	2	1	no	—
1058	#126	—	2	1	no	—
1059	#126	—	2	1	no	—
1060	#126	—	2	1	no	—
1061	#126	—	2	1	no	—
1062	#126	—	2	1	no	—
1063	#126	—	2	1	no	—
1064	#126	—	2	1	no	—
1065	#126	—	2	1	no	—
1066	#126	—	2	1	no	—
1067	#126	—	2	1	no	—
1068	#126	D₄×C₃₁	1	1	yes	characteristic
1069	#126	D₄×C₃₁	1	1	yes	characteristic
1070	#125	—	2	1	no	—
1071	#125	—	2	1	no	—
1072	#125	—	2	1	no	—
1073	#125	—	2	1	no	—
1074	#125	—	2	1	no	—
1075	#125	—	2	1	no	—
1076	#125	—	2	1	no	—
1077	#125	—	2	1	no	—
1078	#125	—	2	1	no	—
1079	#125	—	2	1	no	—
1080	#125	—	2	1	no	—
1081	#125	—	2	1	no	—
1082	#125	D₄×C₃₁	1	1	yes	characteristic
1083	#125	C₂³×C₃₁	1	1	yes	characteristic
1084	#125	C₂³×C₃₁	1	1	yes	characteristic
1085	#125	C₂³×C₃₁	1	1	yes	characteristic
1086	#125	C₂³×C₃₁	1	1	yes	characteristic
1087	#125	C₂³×C₃₁	1	1	yes	characteristic
1088	#124	—	2	1	no	—
1089	#124	—	2	1	no	—
1090	#124	—	2	1	no	—
1091	#124	—	2	1	no	—
1092	#124	—	2	1	no	—
1093	#124	—	2	1	no	—
1094	#124	D₄×C₃₁	1	1	yes	characteristic
1095	#124	C₂³×C₃₁	1	1	yes	characteristic
1096	#124	C₂³×C₃₁	1	1	yes	characteristic
1097	#124	C₂³×C₃₁	1	1	yes	characteristic
1098	#123	—	2	1	no	—
1099	#123	—	2	1	no	—
1100	#123	—	2	1	no	—
1101	#123	—	2	1	no	—
1102	#123	—	2	1	no	—
1103	#123	—	2	1	no	—
1104	#123	—	2	1	no	—
1105	#123	—	2	1	no	—
1106	#123	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	—	2	1	no	—
1109	#123	D₄×C₃₁	1	1	yes	characteristic
1110	#123	D₄×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1119	C₂²⋊Q₈	—	2	1	no	—
1120	C₂²⋊Q₈	—	2	1	no	—
1121	C₂²⋊Q₈	—	2	1	no	—
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	—	2	1	no	—
1125	C₂²⋊Q₈	—	2	1	no	—
1126	C₂²⋊Q₈	—	2	1	no	—
1127	C₂²⋊Q₈	—	2	1	no	—
1128	C₂²⋊Q₈	—	2	1	no	—
1129	C₂²⋊Q₈	—	2	1	no	—
1130	C₂²⋊Q₈	—	2	1	no	—
1131	C₂²⋊Q₈	—	2	1	no	—
1132	C₂²⋊Q₈	—	2	1	no	—
1133	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1134	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1135	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1136	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1137	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1138	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1139	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1140	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1141	#121	—	2	1	no	—
1142	#121	—	2	1	no	—
1143	#121	—	2	1	no	—
1144	#121	—	2	1	no	—
1145	#121	—	2	1	no	—
1146	#121	D₄×C₃₁	1	1	yes	characteristic
1147	#121	C₂³×C₃₁	1	1	yes	characteristic
1148	#121	C₂³×C₃₁	1	1	yes	characteristic
1149	#121	C₂³×C₃₁	1	1	yes	characteristic
1150	#121	C₂³×C₃₁	1	1	yes	characteristic
1151	#121	C₂³×C₃₁	1	1	yes	characteristic
1152	C₄×Q₈	—	2	1	no	—
1153	C₄×Q₈	—	2	1	no	—
1154	C₄×Q₈	—	2	1	no	—
1155	C₄×Q₈	—	2	1	no	—
1156	C₄×Q₈	—	2	1	no	—
1157	C₄×Q₈	—	2	1	no	—
1158	C₄×Q₈	—	2	1	no	—
1159	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1160	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1161	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1162	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1163	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1164	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1165	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1166	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1167	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1168	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1169	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1170	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1171	C₄×D₄	—	2	1	no	—
1172	C₄×D₄	—	2	1	no	—
1173	C₄×D₄	—	2	1	no	—
1174	C₄×D₄	—	2	1	no	—
1175	C₄×D₄	—	2	1	no	—
1176	C₄×D₄	—	2	1	no	—
1177	C₄×D₄	—	2	1	no	—
1178	C₄×D₄	—	2	1	no	—
1179	C₄×D₄	—	2	1	no	—
1180	C₄×D₄	—	2	1	no	—
1181	C₄×D₄	—	2	1	no	—
1182	C₄×D₄	—	2	1	no	—
1183	C₄×D₄	—	2	1	no	—
1184	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1185	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1186	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1187	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1188	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1189	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1190	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1191	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1192	#117	—	2	1	no	—
1193	#117	—	2	1	no	—
1194	#117	—	2	1	no	—
1195	#117	—	2	1	no	—
1196	#117	—	2	1	no	—
1197	#117	—	2	1	no	—
1198	#117	—	2	1	no	—
1199	#117	C₂³×C₃₁	1	1	yes	characteristic
1200	#117	C₂³×C₃₁	1	1	yes	characteristic
1201	#117	C₂³×C₃₁	1	1	yes	characteristic
1202	#117	C₂³×C₃₁	1	1	yes	characteristic
1203	#117	C₂³×C₃₁	1	1	yes	characteristic
1204	C₂×C₄⋊C₄	—	2	1	no	—
1205	C₂×C₄⋊C₄	—	2	1	no	—
1206	C₂×C₄⋊C₄	—	2	1	no	—
1207	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1208	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1209	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1210	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1211	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1212	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1213	C₂×C₄²	—	2	1	no	—
1214	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1215	#107	C₂³×C₃₁	1	1	yes	characteristic
1216	#107	C₂³×C₃₁	1	1	yes	characteristic
1217	#107	C₂³×C₃₁	1	1	yes	characteristic
1218	#107	C₂³×C₃₁	1	1	yes	characteristic
1219	#107	C₂³×C₃₁	1	1	yes	characteristic
1220	#107	C₂³×C₃₁	1	1	yes	characteristic
1221	#107	C₂³×C₃₁	1	1	yes	characteristic
1222	#107	C₂³×C₃₁	1	1	yes	characteristic
1223	#107	C₂³×C₃₁	1	1	yes	characteristic
1224	#107	C₂³×C₃₁	1	1	yes	characteristic
1225	#107	C₂³×C₃₁	1	1	yes	characteristic
1226	#107	C₂³×C₃₁	1	1	yes	characteristic
1227	#107	C₂³×C₃₁	1	1	yes	characteristic
1228	#107	C₂³×C₃₁	1	1	yes	characteristic
1229	#107	C₂³×C₃₁	1	1	yes	characteristic
1230	#107	C₂³×C₃₁	1	1	yes	characteristic
1231	#106	C₂³×C₃₁	1	1	yes	characteristic
1232	#106	C₂³×C₃₁	1	1	yes	characteristic
1233	#106	C₂³×C₃₁	1	1	yes	characteristic
1234	#106	C₂³×C₃₁	1	1	yes	characteristic
1235	#106	C₂³×C₃₁	1	1	yes	characteristic
1236	#106	C₂³×C₃₁	1	1	yes	characteristic
1237	#106	C₂³×C₃₁	1	1	yes	characteristic
1238	#106	C₂³×C₃₁	1	1	yes	characteristic
1239	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1240	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1241	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1242	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1243	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1244	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1245	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1246	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1247	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1248	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1249	#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	#103	C₂³×C₃₁	1	1	yes	characteristic
1261	#103	C₂³×C₃₁	1	1	yes	characteristic
1262	#103	C₂³×C₃₁	1	1	yes	characteristic
1263	#103	C₂³×C₃₁	1	1	yes	characteristic
1264	#103	C₂³×C₃₁	1	1	yes	characteristic
1265	#103	C₂³×C₃₁	1	1	yes	characteristic
1266	#103	C₂³×C₃₁	1	1	yes	characteristic
1267	#103	C₂³×C₃₁	1	1	yes	characteristic
1268	#103	C₂³×C₃₁	1	1	yes	characteristic
1269	#103	C₂³×C₃₁	1	1	yes	characteristic
1270	#103	C₂³×C₃₁	1	1	yes	characteristic
1271	#102	C₂³×C₃₁	1	1	yes	characteristic
1272	#102	C₂³×C₃₁	1	1	yes	characteristic
1273	#102	C₂³×C₃₁	1	1	yes	characteristic
1274	#102	C₂³×C₃₁	1	1	yes	characteristic
1275	#102	C₂³×C₃₁	1	1	yes	characteristic
1276	#102	C₂³×C₃₁	1	1	yes	characteristic
1277	#102	C₂³×C₃₁	1	1	yes	characteristic
1278	#102	C₂³×C₃₁	1	1	yes	characteristic
1279	#102	C₂³×C₃₁	1	1	yes	characteristic
1280	#102	C₂³×C₃₁	1	1	yes	characteristic
1281	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1282	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1283	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1284	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1285	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1286	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1287	#97	C₂³×C₃₁	1	1	yes	characteristic
1288	#97	C₂³×C₃₁	1	1	yes	characteristic
1289	#97	C₂³×C₃₁	1	1	yes	characteristic
1290	#97	C₂³×C₃₁	1	1	yes	characteristic
1291	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1292	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1293	C₃₁	#62158	1	1	yes	characteristic, direct product factor, Sylow
1294	#41	—	2	2	no	—
1295	#41	—	4	1	no	—
1296	#41	—	8	2	no	—
1297	C₂×Q₈	—	2	1	no	—
1298	C₂×Q₈	—	2	1	no	—
1299	C₂×Q₈	—	2	1	no	—
1300	C₂×Q₈	—	2	1	no	—
1301	C₂×Q₈	—	2	1	no	—
1302	C₂×Q₈	—	2	1	no	—
1303	C₂×Q₈	—	2	1	no	—
1304	C₂×Q₈	—	2	1	no	—
1305	C₂×Q₈	—	2	1	no	—
1306	C₂×Q₈	—	2	2	no	—
1307	C₂×Q₈	—	2	2	no	—
1308	C₂×Q₈	—	4	1	no	—
1309	C₂×Q₈	—	4	1	no	—
1310	C₂×Q₈	—	8	2	no	—
1311	C₂×Q₈	—	8	2	no	—
1312	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1313	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1314	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1315	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1316	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1317	C₂×D₄	—	2	1	no	—
1318	C₂×D₄	—	2	1	no	—
1319	C₂×D₄	—	2	1	no	—
1320	C₂×D₄	—	2	1	no	—
1321	C₂×D₄	—	2	1	no	—
1322	C₂×D₄	—	2	1	no	—
1323	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1324	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1325	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1326	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1327	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1328	C₂²×C₄	—	2	1	no	—
1329	C₂²×C₄	—	2	1	no	—
1330	C₂²×C₄	—	2	1	no	—
1331	C₂²×C₄	—	2	1	no	—
1332	C₂²×C₄	—	2	1	no	—
1333	C₂²×C₄	—	2	1	no	—
1334	C₂²×C₄	—	2	1	no	—
1335	C₂²×C₄	—	2	1	no	—
1336	C₂²×C₄	—	2	1	no	—
1337	C₂²×C₄	—	2	1	no	—
1338	C₂²×C₄	—	2	1	no	—
1339	C₂²×C₄	—	2	1	no	—
1340	C₂²×C₄	—	2	1	no	—
1341	C₂²×C₄	—	2	1	no	—
1342	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1343	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1344	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1345	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1346	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1347	Q₁₆	—	2	2	no	—
1348	Q₁₆	—	4	1	no	—
1349	Q₁₆	—	4	1	no	—
1350	SD₁₆	—	2	2	no	—
1351	SD₁₆	—	4	1	no	—
1352	SD₁₆	—	4	1	no	—
1353	SD₁₆	—	4	1	no	—
1354	D₈	—	4	1	no	—
1355	M₁₆	—	4	1	no	—
1356	M₁₆	—	4	1	no	—
1357	C₂×C₈	—	4	1	no	—
1358	C₂×C₈	—	4	1	no	—
1359	C₂×C₈	—	4	1	no	—
1360	C₂×C₈	—	4	1	no	—
1361	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1362	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1363	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1364	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1365	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1366	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1367	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1368	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1369	C₄⋊C₄	—	2	1	no	—
1370	C₄⋊C₄	—	2	1	no	—
1371	C₄⋊C₄	—	2	1	no	—
1372	C₄⋊C₄	—	2	1	no	—
1373	C₄⋊C₄	—	2	1	no	—
1374	C₄⋊C₄	—	2	1	no	—
1375	C₄⋊C₄	—	2	1	no	—
1376	C₄⋊C₄	—	2	1	no	—
1377	C₄⋊C₄	—	2	1	no	—
1378	C₄⋊C₄	—	2	1	no	—
1379	C₄⋊C₄	—	2	1	no	—
1380	C₄⋊C₄	—	2	1	no	—
1381	C₄⋊C₄	—	2	1	no	—
1382	C₄⋊C₄	—	2	1	no	—
1383	C₄⋊C₄	—	2	1	no	—
1384	C₄⋊C₄	—	2	1	no	—
1385	C₄⋊C₄	—	2	1	no	—
1386	C₄⋊C₄	—	2	1	no	—
1387	C₄⋊C₄	—	2	1	no	—
1388	C₄⋊C₄	—	2	1	no	—
1389	C₄⋊C₄	—	2	1	no	—
1390	C₄⋊C₄	—	2	1	no	—
1391	C₄⋊C₄	—	2	1	no	—
1392	C₄⋊C₄	—	2	1	no	—
1393	C₄⋊C₄	—	2	1	no	—
1394	C₄⋊C₄	—	2	1	no	—
1395	C₄⋊C₄	—	2	1	no	—
1396	C₄⋊C₄	—	2	1	no	—
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	—	2	1	no	—
1400	C₄⋊C₄	—	2	1	no	—
1401	C₄⋊C₄	—	2	1	no	—
1402	C₄⋊C₄	—	2	1	no	—
1403	C₄⋊C₄	—	2	1	no	—
1404	C₄⋊C₄	—	2	1	no	—
1405	C₄⋊C₄	—	2	1	no	—
1406	C₄⋊C₄	—	2	1	no	—
1407	C₄⋊C₄	—	2	1	no	—
1408	C₄⋊C₄	—	2	1	no	—
1409	C₄⋊C₄	—	2	1	no	—
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1413	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1414	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1415	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1416	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1417	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1418	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1419	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1420	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1421	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1422	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1423	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1424	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1425	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1426	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1427	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1428	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1429	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1430	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1431	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1432	C₂²⋊C₄	—	2	1	no	—
1433	C₂²⋊C₄	—	2	1	no	—
1434	C₂²⋊C₄	—	2	1	no	—
1435	C₂²⋊C₄	—	2	1	no	—
1436	C₂²⋊C₄	—	2	1	no	—
1437	C₂²⋊C₄	—	2	1	no	—
1438	C₂²⋊C₄	—	2	1	no	—
1439	C₂²⋊C₄	—	2	1	no	—
1440	C₂²⋊C₄	—	2	1	no	—
1441	C₂²⋊C₄	—	2	1	no	—
1442	C₂²⋊C₄	—	2	1	no	—
1443	C₂²⋊C₄	—	2	1	no	—
1444	C₂²⋊C₄	—	2	1	no	—
1445	C₂²⋊C₄	—	2	1	no	—
1446	C₂²⋊C₄	—	2	1	no	—
1447	C₂²⋊C₄	—	2	1	no	—
1448	C₂²⋊C₄	—	2	1	no	—
1449	C₂²⋊C₄	—	2	1	no	—
1450	C₂²⋊C₄	—	2	1	no	—
1451	C₂²⋊C₄	—	2	1	no	—
1452	C₂²⋊C₄	—	2	1	no	—
1453	C₂²⋊C₄	—	2	1	no	—
1454	C₂²⋊C₄	—	2	1	no	—
1455	C₂²⋊C₄	—	2	1	no	—
1456	C₂²⋊C₄	—	2	1	no	—
1457	C₂²⋊C₄	—	2	1	no	—
1458	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1459	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1460	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1461	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1462	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1463	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1464	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1465	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1466	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1467	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1468	C₄²	—	2	1	no	—
1469	C₄²	—	2	1	no	—
1470	C₄²	—	2	1	no	—
1471	C₄²	—	2	1	no	—
1472	C₄²	—	2	1	no	—
1473	C₄²	—	2	1	no	—
1474	C₄²	—	2	1	no	—
1475	C₄²	—	2	1	no	—
1476	C₄²	—	2	1	no	—
1477	C₄²	—	2	1	no	—
1478	C₄²	—	2	1	no	—
1479	C₄²	—	2	1	no	—
1480	C₄²	—	2	1	no	—
1481	C₄²	—	2	1	no	—
1482	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1483	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1484	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1485	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1486	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1487	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1488	C₂³	—	2	1	no	—
1489	C₂³	—	2	1	no	—
1490	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1491	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1492	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1493	Q₈	—	2	1	no	—
1494	Q₈	—	2	1	no	—
1495	Q₈	—	2	1	no	—
1496	Q₈	—	2	1	no	—
1497	Q₈	—	2	1	no	—
1498	Q₈	—	2	1	no	—
1499	Q₈	—	2	1	no	—
1500	Q₈	—	4	1	no	—
1501	Q₈	—	4	2	no	—
1502	Q₈	—	4	2	no	—
1503	Q₈	—	4	2	no	—
1504	Q₈	—	4	2	no	—
1505	Q₈	—	8	1	no	—
1506	Q₈	—	8	1	no	—
1507	Q₈	—	8	1	no	—
1508	Q₈	—	8	1	no	—
1509	Q₈	—	8	1	no	—
1510	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1511	D₄	—	2	2	no	—
1512	D₄	—	2	2	no	—
1513	D₄	—	2	1	no	—
1514	D₄	—	2	1	no	—
1515	D₄	—	2	1	no	—
1516	D₄	—	2	1	no	—
1517	D₄	—	4	1	no	—
1518	D₄	—	4	2	no	—
1519	D₄	—	4	2	no	—
1520	D₄	—	4	2	no	—
1521	D₄	—	8	1	no	—
1522	D₄	—	8	1	no	—
1523	D₄	—	8	1	no	—
1524	C₂×C₄	—	2	2	no	—
1525	C₂×C₄	—	2	1	no	—
1526	C₂×C₄	—	2	1	no	—
1527	C₂×C₄	—	2	1	no	—
1528	C₂×C₄	—	2	1	no	—
1529	C₂×C₄	—	2	1	no	—
1530	C₂×C₄	—	2	1	no	—
1531	C₂×C₄	—	2	1	no	—
1532	C₂×C₄	—	2	1	no	—
1533	C₂×C₄	—	2	1	no	—
1534	C₂×C₄	—	2	1	no	—
1535	C₂×C₄	—	2	1	no	—
1536	C₂×C₄	—	2	1	no	—
1537	C₂×C₄	—	2	1	no	—
1538	C₂×C₄	—	2	1	no	—
1539	C₂×C₄	—	2	1	no	—
1540	C₂×C₄	—	2	1	no	—
1541	C₂×C₄	—	2	1	no	—
1542	C₂×C₄	—	2	1	no	—
1543	C₂×C₄	—	2	1	no	—
1544	C₂×C₄	—	2	1	no	—
1545	C₂×C₄	—	4	1	no	—
1546	C₂×C₄	—	4	2	no	—
1547	C₂×C₄	—	4	2	no	—
1548	C₂×C₄	—	4	2	no	—
1549	C₂×C₄	—	4	2	no	—
1550	C₂×C₄	—	8	1	no	—
1551	C₂×C₄	—	8	1	no	—
1552	C₂×C₄	—	8	1	no	—
1553	C₂×C₄	—	8	1	no	—
1554	C₂×C₄	—	8	1	no	—
1555	C₂×C₄	—	8	1	no	—
1556	C₂×C₄	—	8	1	no	—
1557	C₂×C₄	—	8	1	no	—
1558	C₂×C₄	—	8	1	no	—
1559	C₂×C₄	—	8	1	no	—
1560	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1561	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1562	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1563	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1564	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1565	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1566	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1567	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1568	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1569	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1570	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1571	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1572	C₈	—	2	1	no	—
1573	C₈	—	2	1	no	—
1574	C₈	—	2	1	no	—
1575	C₈	—	2	1	no	—
1576	C₈	—	2	1	no	—
1577	C₈	—	2	1	no	—
1578	C₈	—	2	1	no	—
1579	C₈	—	2	1	no	—
1580	C₂²	—	2	1	no	—
1581	C₂²	—	2	1	no	—
1582	C₂²	—	2	1	no	—
1583	C₂²	—	2	1	no	—
1584	C₂²	—	2	1	no	—
1585	C₂²	—	2	1	no	—
1586	C₂²	—	2	1	no	—
1587	C₂²	—	2	1	no	—
1588	C₂²	—	4	1	no	—
1589	C₂²	—	4	1	no	—
1590	C₂²	—	4	1	no	—
1591	C₂²	—	4	1	no	—
1592	C₂²	—	4	1	no	—
1593	C₂²	—	4	1	no	—
1594	C₂²	C₃₁×#578	1	2	yes	—
1595	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1596	C₄	—	2	1	no	—
1597	C₄	—	2	1	no	—
1598	C₄	—	2	1	no	—
1599	C₄	—	2	2	no	—
1600	C₄	—	2	1	no	—
1601	C₄	—	2	1	no	—
1602	C₄	—	2	1	no	—
1603	C₄	—	2	1	no	—
1604	C₄	—	2	1	no	—
1605	C₄	—	2	1	no	—
1606	C₄	—	2	1	no	—
1607	C₄	—	2	1	no	—
1608	C₄	—	4	1	no	—
1609	C₄	—	4	1	no	—
1610	C₄	—	4	1	no	—
1611	C₄	—	4	1	no	—
1612	C₄	—	4	1	no	—
1613	C₄	—	4	1	no	—
1614	C₄	—	4	1	no	—
1615	C₄	—	4	1	no	—
1616	C₄	—	4	1	no	—
1617	C₄	—	4	1	no	—
1618	C₄	—	4	1	no	—
1619	C₄	—	4	1	no	—
1620	C₄	—	4	1	no	—
1621	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1622	C₄	C₃₁×#585	1	1	yes	characteristic
1623	C₂	—	2	2	no	—
1624	C₂	—	4	1	no	—
1625	C₂	—	4	1	no	—
1626	C₂	—	8	1	no	—
1627	C₂	—	8	1	no	—
1628	C₂	C₃₁×#3489	1	1	yes	characteristic
1629	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1630	C₂	C₃₁×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3552	C₂	semidirect
2. C₃₁×#3516	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3386	C₂	semidirect
5. C₃₁×#3377	C₂	semidirect
6. C₃₁×#3367	C₂	semidirect
7. C₃₁×#3349	C₂	semidirect
8. C₃₁×#3346	C₂	semidirect
9. C₃₁×#3346	C₂	semidirect
10. C₃₁×#3343	C₂	semidirect
11. C₃₁×#3339	C₂	semidirect
12. C₃₁×#3338	C₂	semidirect
13. C₃₁×#3320	C₂	semidirect
14. C₃₁×#3316	C₂	semidirect
15. C₃₁×#3313	C₂	semidirect
16. C₃₁×#3308	C₂	semidirect
17. C₃₁×#3301	C₂	semidirect
18. C₃₁×#3299	C₂	semidirect
19. C₃₁×#3262	C₂	semidirect
20. C₃₁×#3258	C₂	semidirect
21. C₃₁×#3250	C₂	semidirect
22. C₃₁×#3243	C₂	semidirect
23. C₃₁×#3242	C₂	semidirect
24. C₃₁×#3239	C₂	semidirect
25. C₃₁×#3124	C₂	semidirect
26. C₃₁×#3121	C₂	semidirect
27. C₃₁×#3117	C₂	semidirect
28. C₃₁×#3083	C₂	semidirect
29. C₃₁×#3082	C₂	semidirect
30. C₂×C₃₁×#477	C₂	semidirect
31. C₃₁×#2992	C₂	semidirect
672. #62158	C₃₁	direct (N × H)
765. #3552	C₂×C₃₁	semidirect
766. #3516	C₂×C₃₁	semidirect
767. #3390	C₂×C₃₁	semidirect
768. #3386	C₂×C₃₁	semidirect
769. #3377	C₂×C₃₁	semidirect
770. #3367	C₂×C₃₁	semidirect
771. #3349	C₂×C₃₁	semidirect
772. #3346	C₂×C₃₁	semidirect
773. #3346	C₂×C₃₁	semidirect
774. #3343	C₂×C₃₁	semidirect
775. #3339	C₂×C₃₁	semidirect
776. #3338	C₂×C₃₁	semidirect
777. #3320	C₂×C₃₁	semidirect
778. #3316	C₂×C₃₁	semidirect
779. #3313	C₂×C₃₁	semidirect
780. #3308	C₂×C₃₁	semidirect
781. #3301	C₂×C₃₁	semidirect
782. #3299	C₂×C₃₁	semidirect
783. #3262	C₂×C₃₁	semidirect
784. #3258	C₂×C₃₁	semidirect
785. #3250	C₂×C₃₁	semidirect
786. #3243	C₂×C₃₁	semidirect
787. #3242	C₂×C₃₁	semidirect
788. #3239	C₂×C₃₁	semidirect
789. #3124	C₂×C₃₁	semidirect
790. #3121	C₂×C₃₁	semidirect
791. #3117	C₂×C₃₁	semidirect
792. #3083	C₂×C₃₁	semidirect
793. #3082	C₂×C₃₁	semidirect
794. C₂×#477	C₂×C₃₁	semidirect
795. #2992	C₂×C₃₁	semidirect
1293. C₃₁	#62158	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×#3552	2
C₃₁×#3516	2
C₃₁×#3390	2
C₃₁×#3386	2
C₃₁×#3377	2
C₃₁×#3367	2
C₃₁×#3349	2
C₃₁×#3346	2
C₃₁×#3343	2
C₃₁×#3339	2
C₃₁×#3338	2
C₃₁×#3320	2
C₃₁×#3316	2
C₃₁×#3313	2
C₃₁×#3308	2
C₃₁×#3301	2
C₃₁×#3299	2
C₃₁×#3262	2
C₃₁×#3258	2
C₃₁×#3250	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3239	2
C₃₁×#3124	2
C₃₁×#3121	2
C₃₁×#3117	2
C₃₁×#3083	2
C₃₁×#3082	2
C₂×C₃₁×#477	2
C₃₁×#2992	2
#62158	31

Subgroups — C31×#62158 #21518917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62158 #21518917