Subgroups — C₃₁×#62612 #21519371

Order 7936.

1670 conjugacy classes of subgroups.

The subgroup lattice has 1666 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×#3562	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3377	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3371	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3323	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3323	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3316	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3300	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3241	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3223	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3222	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3177	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3174	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3172	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#564	—	2	1	no	—
33	C₃₁×#563	—	2	1	no	—
34	C₃₁×#562	—	2	1	no	—
35	C₃₁×#560	—	2	1	no	—
36	C₃₁×#559	C₂²	1	1	yes	characteristic
37	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#556	C₂²	1	1	yes	characteristic
40	C₃₁×#554	C₂²	1	1	yes	characteristic
41	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#553	—	2	1	no	—
43	C₃₁×#552	—	2	1	no	—
44	C₃₁×#552	—	2	1	no	—
45	C₃₁×#552	C₂²	1	1	yes	characteristic
46	C₃₁×#552	C₂²	1	1	yes	characteristic
47	C₃₁×#552	C₂²	1	1	yes	characteristic
48	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#551	—	2	1	no	—
50	C₃₁×#550	C₂²	1	1	yes	characteristic
51	C₃₁×#548	C₂²	1	1	yes	characteristic
52	C₃₁×#548	C₂²	1	1	yes	characteristic
53	C₃₁×#547	C₂²	1	1	yes	characteristic
54	C₃₁×#546	C₂²	1	1	yes	characteristic
55	C₃₁×#546	C₂²	1	1	yes	characteristic
56	C₃₁×#544	—	2	1	no	—
57	C₃₁×#544	C₂²	1	1	yes	characteristic
58	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#541	—	2	1	no	—
60	C₃₁×#541	—	2	1	no	—
61	C₃₁×#541	C₂²	1	1	yes	characteristic
62	C₃₁×#541	C₂²	1	1	yes	characteristic
63	C₃₁×#541	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#540	—	2	1	no	—
65	C₃₁×#540	C₂²	1	1	yes	characteristic
66	C₃₁×#539	—	2	1	no	—
67	C₃₁×#539	—	2	1	no	—
68	C₃₁×#538	—	2	1	no	—
69	C₃₁×#538	—	2	1	no	—
70	C₃₁×#536	C₂²	1	1	yes	characteristic
71	C₃₁×#535	C₂²	1	1	yes	characteristic
72	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#532	C₂²	1	1	yes	characteristic
74	C₃₁×#529	C₂²	1	1	yes	characteristic
75	C₃₁×#529	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#497	C₂²	1	1	yes	characteristic
81	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#492	C₂²	1	1	yes	characteristic
83	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#490	C₂²	1	1	yes	characteristic
88	C₃₁×#490	C₂²	1	1	yes	characteristic
89	C₃₁×#490	C₂²	1	1	yes	characteristic
90	C₃₁×#489	C₂²	1	1	yes	characteristic
91	C₃₁×#489	C₂²	1	1	yes	characteristic
92	C₃₁×#489	C₂²	1	1	yes	characteristic
93	C₃₁×#488	C₂²	1	1	yes	characteristic
94	C₃₁×#488	C₂²	1	1	yes	characteristic
95	C₃₁×#488	C₂²	1	1	yes	characteristic
96	C₃₁×#488	C₂²	1	1	yes	characteristic
97	C₃₁×#488	C₂²	1	1	yes	characteristic
98	C₃₁×#488	C₂²	1	1	yes	characteristic
99	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#486	C₂²	1	1	yes	characteristic
104	C₃₁×#486	C₂²	1	1	yes	characteristic
105	C₃₁×#485	C₂²	1	1	yes	characteristic
106	C₃₁×#485	C₂²	1	1	yes	characteristic
107	C₃₁×#484	C₂²	1	1	yes	characteristic
108	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#483	C₂²	1	1	yes	characteristic
110	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#482	C₂²	1	1	yes	characteristic
112	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#481	C₂²	1	1	yes	characteristic
114	C₃₁×#481	C₂²	1	1	yes	characteristic
115	C₃₁×#480	C₂²	1	1	yes	characteristic
116	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#478	C₂²	1	1	yes	characteristic
122	C₃₁×#478	C₂²	1	1	yes	characteristic
123	C₃₁×#478	C₂²	1	1	yes	characteristic
124	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#474	C₂²	1	1	yes	characteristic
129	C₃₁×#470	C₂²	1	1	yes	characteristic
130	C₃₁×#470	C₂²	1	1	yes	characteristic
131	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#468	C₂²	1	1	yes	characteristic
134	C₃₁×#468	C₂²	1	1	yes	characteristic
135	C₃₁×#468	C₂²	1	1	yes	characteristic
136	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#467	C₂²	1	1	yes	characteristic
138	C₃₁×#467	C₂²	1	1	yes	characteristic
139	C₃₁×#465	C₂²	1	1	yes	characteristic
140	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
141	C₃₁×#464	C₂²	1	1	yes	characteristic
142	C₃₁×#464	C₂²	1	1	yes	characteristic
143	C₃₁×#464	C₂²	1	1	yes	characteristic
144	C₃₁×#464	C₂²	1	1	yes	characteristic
145	C₃₁×#464	C₂²	1	1	yes	characteristic
146	C₃₁×#464	C₂²	1	1	yes	characteristic
147	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
150	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
151	C₃₁×#460	C₂²	1	1	yes	characteristic
152	C₃₁×#460	C₂²	1	1	yes	characteristic
153	C₃₁×#452	C₂²	1	1	yes	characteristic
154	C₃₁×#452	C₂²	1	1	yes	characteristic
155	C₃₁×#452	C₂²	1	1	yes	characteristic
156	C₃₁×#452	C₂²	1	1	yes	characteristic
157	C₃₁×#452	C₂²	1	1	yes	characteristic
158	C₃₁×#452	C₂²	1	1	yes	characteristic
159	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
160	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
161	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
162	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
163	C₃₁×#450	C₂²	1	1	yes	characteristic
164	C₃₁×#450	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
166	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
167	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
168	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
169	C₃₁×#440	C₂²	1	1	yes	characteristic
170	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
171	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
172	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
173	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
174	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
179	C₃₁×#436	C₂²	1	1	yes	characteristic
180	C₃₁×#436	C₂²	1	1	yes	characteristic
181	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
182	C₃₁×#435	C₂²	1	1	yes	characteristic
183	C₃₁×#435	C₂²	1	1	yes	characteristic, complemented
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, complemented
187	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
188	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
189	C₃₁×#418	C₂²	1	1	yes	characteristic
190	C₃₁×#417	C₂²	1	1	yes	characteristic
191	C₃₁×#417	C₂²	1	1	yes	characteristic
192	C₃₁×#417	C₂²	1	1	yes	characteristic
193	C₃₁×#417	C₂²	1	1	yes	characteristic
194	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
195	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
196	C₃₁×#416	C₂²	1	1	yes	characteristic
197	C₃₁×#416	C₂²	1	1	yes	characteristic
198	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
199	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
200	C₃₁×#405	C₂²	1	1	yes	characteristic
201	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
202	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
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×#127	—	2	1	no	—
238	C₃₁×#127	C₂³	1	1	yes	characteristic
239	C₃₁×#127	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
268	C₃₁×#125	—	2	1	no	—
269	C₃₁×#125	—	2	1	no	—
270	C₃₁×#125	—	2	1	no	—
271	C₃₁×#125	—	2	1	no	—
272	C₃₁×#125	—	2	1	no	—
273	C₃₁×#125	—	2	1	no	—
274	C₃₁×#125	—	2	1	no	—
275	C₃₁×#125	—	2	1	no	—
276	C₃₁×#125	D₄	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×#124	C₂³	1	1	yes	characteristic
291	C₃₁×#124	C₂³	1	1	yes	characteristic
292	C₃₁×#124	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
299	C₃₁×#123	—	2	1	no	—
300	C₃₁×#123	—	2	1	no	—
301	C₃₁×#123	—	2	1	no	—
302	C₃₁×#123	—	2	1	no	—
303	C₃₁×#123	—	2	1	no	—
304	C₃₁×#123	—	2	1	no	—
305	C₃₁×#123	—	2	1	no	—
306	C₃₁×#123	—	2	1	no	—
307	C₃₁×#123	—	2	1	no	—
308	C₃₁×#123	D₄	1	1	yes	characteristic
309	C₃₁×#123	D₄	1	1	yes	characteristic
310	C₃₁×C₂²⋊Q₈	—	2	1	no	—
311	C₃₁×C₂²⋊Q₈	—	2	1	no	—
312	C₃₁×C₂²⋊Q₈	—	2	1	no	—
313	C₃₁×C₂²⋊Q₈	—	2	1	no	—
314	C₃₁×C₂²⋊Q₈	—	2	1	no	—
315	C₃₁×C₂²⋊Q₈	—	2	1	no	—
316	C₃₁×C₂²⋊Q₈	—	2	1	no	—
317	C₃₁×C₂²⋊Q₈	—	2	1	no	—
318	C₃₁×C₂²⋊Q₈	—	2	1	no	—
319	C₃₁×C₂²⋊Q₈	—	2	1	no	—
320	C₃₁×C₂²⋊Q₈	—	2	1	no	—
321	C₃₁×C₂²⋊Q₈	—	2	1	no	—
322	C₃₁×C₂²⋊Q₈	—	2	1	no	—
323	C₃₁×C₂²⋊Q₈	—	2	1	no	—
324	C₃₁×C₂²⋊Q₈	D₄	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×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
329	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
330	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
331	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
332	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
333	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
334	C₃₁×#121	—	2	1	no	—
335	C₃₁×#121	—	2	1	no	—
336	C₃₁×#121	—	2	1	no	—
337	C₃₁×#121	—	2	1	no	—
338	C₃₁×#121	—	2	1	no	—
339	C₃₁×#121	—	2	1	no	—
340	C₃₁×#121	—	2	1	no	—
341	C₃₁×#121	—	2	1	no	—
342	C₃₁×#121	—	2	1	no	—
343	C₃₁×#121	—	2	1	no	—
344	C₃₁×#121	—	2	1	no	—
345	C₃₁×#121	—	2	1	no	—
346	C₃₁×#121	—	2	1	no	—
347	C₃₁×#121	D₄	1	1	yes	characteristic
348	C₃₁×#121	C₂³	1	1	yes	characteristic
349	C₃₁×#121	C₂³	1	1	yes	characteristic
350	C₃₁×#121	C₂³	1	1	yes	characteristic
351	C₃₁×#120	—	2	1	no	—
352	C₃₁×#120	—	2	1	no	—
353	C₃₁×#120	—	2	1	no	—
354	C₃₁×#120	—	2	1	no	—
355	C₄×Q₈×C₃₁	—	2	1	no	—
356	C₄×Q₈×C₃₁	—	2	1	no	—
357	C₄×Q₈×C₃₁	—	2	1	no	—
358	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
359	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
360	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
361	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
365	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₃₁	—	2	1	no	—
369	C₄×D₄×C₃₁	—	2	1	no	—
370	C₄×D₄×C₃₁	—	2	1	no	—
371	C₄×D₄×C₃₁	—	2	1	no	—
372	C₄×D₄×C₃₁	—	2	1	no	—
373	C₄×D₄×C₃₁	—	2	1	no	—
374	C₄×D₄×C₃₁	—	2	1	no	—
375	C₄×D₄×C₃₁	—	2	1	no	—
376	C₄×D₄×C₃₁	—	2	1	no	—
377	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
379	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
381	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
382	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
383	C₃₁×#117	—	2	1	no	—
384	C₃₁×#117	—	2	1	no	—
385	C₃₁×#117	—	2	1	no	—
386	C₃₁×#117	—	2	1	no	—
387	C₃₁×#117	—	2	1	no	—
388	C₃₁×#117	—	2	1	no	—
389	C₃₁×#117	—	2	1	no	—
390	C₃₁×#117	C₂³	1	1	yes	characteristic
391	C₃₁×#117	C₂³	1	1	yes	characteristic
392	C₃₁×#117	C₂³	1	1	yes	characteristic
393	C₃₁×#117	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
398	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
399	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
400	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
401	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
402	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
403	C₂×C₄²×C₃₁	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×#106	C₂³	1	1	yes	characteristic
411	C₃₁×#106	C₂³	1	1	yes	characteristic
412	C₃₁×#106	C₂³	1	1	yes	characteristic
413	C₃₁×#106	C₂³	1	1	yes	characteristic
414	C₃₁×#106	C₂³	1	1	yes	characteristic
415	C₃₁×#106	C₂³	1	1	yes	characteristic
416	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
417	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
418	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
419	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
420	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
421	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
422	C₃₁×#103	C₂³	1	1	yes	characteristic
423	C₃₁×#103	C₂³	1	1	yes	characteristic
424	C₃₁×#103	C₂³	1	1	yes	characteristic
425	C₃₁×#103	C₂³	1	1	yes	characteristic
426	C₃₁×#103	C₂³	1	1	yes	characteristic
427	C₃₁×#103	C₂³	1	1	yes	characteristic
428	C₃₁×#103	C₂³	1	1	yes	characteristic
429	C₃₁×#103	C₂³	1	1	yes	characteristic
430	C₃₁×#103	C₂³	1	1	yes	characteristic
431	C₃₁×#103	C₂³	1	1	yes	characteristic
432	C₃₁×#103	C₂³	1	1	yes	characteristic
433	C₃₁×#103	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#102	C₂³	1	1	yes	characteristic
445	C₃₁×#102	C₂³	1	1	yes	characteristic
446	C₃₁×#102	C₂³	1	1	yes	characteristic
447	C₃₁×#102	C₂³	1	1	yes	characteristic
448	C₃₁×#102	C₂³	1	1	yes	characteristic
449	C₃₁×#102	C₂³	1	1	yes	characteristic
450	C₃₁×#102	C₂³	1	1	yes	characteristic
451	C₃₁×#102	C₂³	1	1	yes	characteristic
452	C₃₁×#102	C₂³	1	1	yes	characteristic
453	C₃₁×#102	C₂³	1	1	yes	characteristic
454	C₃₁×#102	C₂³	1	1	yes	characteristic
455	C₃₁×#102	C₂³	1	1	yes	characteristic
456	C₃₁×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₃₁×#97	C₂³	1	1	yes	characteristic
469	C₃₁×#97	C₂³	1	1	yes	characteristic
470	C₃₁×#97	C₂³	1	1	yes	characteristic
471	C₃₁×#97	C₂³	1	1	yes	characteristic
472	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
473	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
474	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
475	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
476	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
478	C₂⁴×C₃₁	—	2	1	no	—
479	#41×C₃₁	—	4	1	no	—
480	#41×C₃₁	—	4	1	no	—
481	#41×C₃₁	—	4	1	no	—
482	#41×C₃₁	—	4	1	no	—
483	#41×C₃₁	—	4	1	no	—
484	#41×C₃₁	—	4	1	no	—
485	#41×C₃₁	—	4	1	no	—
486	#41×C₃₁	—	4	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	1	no	—
491	C₂×Q₈×C₃₁	—	4	1	no	—
492	C₂×Q₈×C₃₁	—	4	1	no	—
493	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
496	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
497	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
498	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₂×D₄×C₃₁	—	2	1	no	—
500	C₂×D₄×C₃₁	—	2	1	no	—
501	C₂×D₄×C₃₁	—	2	1	no	—
502	C₂×D₄×C₃₁	—	2	1	no	—
503	C₂×D₄×C₃₁	—	2	1	no	—
504	C₂×D₄×C₃₁	—	2	1	no	—
505	C₂×D₄×C₃₁	—	2	1	no	—
506	C₂×D₄×C₃₁	—	2	1	no	—
507	C₂×D₄×C₃₁	—	2	1	no	—
508	C₂×D₄×C₃₁	—	2	1	no	—
509	C₂×D₄×C₃₁	—	2	1	no	—
510	C₂×D₄×C₃₁	—	2	1	no	—
511	C₂×D₄×C₃₁	—	4	1	no	—
512	C₂×D₄×C₃₁	—	4	1	no	—
513	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
514	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
515	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
516	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
517	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
518	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
527	C₂²×C₄×C₃₁	—	2	1	no	—
528	C₂²×C₄×C₃₁	—	2	1	no	—
529	C₂²×C₄×C₃₁	—	2	1	no	—
530	C₂²×C₄×C₃₁	—	2	1	no	—
531	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
532	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
533	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
534	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
535	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
536	Q₁₆×C₃₁	—	4	1	no	—
537	Q₁₆×C₃₁	—	4	1	no	—
538	Q₁₆×C₃₁	—	4	1	no	—
539	Q₁₆×C₃₁	—	4	1	no	—
540	Q₁₆×C₃₁	—	4	1	no	—
541	Q₁₆×C₃₁	—	4	1	no	—
542	SD₁₆×C₃₁	—	4	1	no	—
543	SD₁₆×C₃₁	—	4	1	no	—
544	SD₁₆×C₃₁	—	4	1	no	—
545	SD₁₆×C₃₁	—	4	1	no	—
546	SD₁₆×C₃₁	—	4	1	no	—
547	SD₁₆×C₃₁	—	4	1	no	—
548	M₁₆×C₃₁	—	4	1	no	—
549	M₁₆×C₃₁	—	4	1	no	—
550	M₁₆×C₃₁	—	4	1	no	—
551	M₁₆×C₃₁	—	4	1	no	—
552	C₂×C₈×C₃₁	—	4	1	no	—
553	C₂×C₈×C₃₁	—	4	1	no	—
554	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
555	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
556	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
557	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
558	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
559	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
560	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
561	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
597	C₄⋊C₄×C₃₁	—	2	1	no	—
598	C₄⋊C₄×C₃₁	—	2	1	no	—
599	C₄⋊C₄×C₃₁	—	2	1	no	—
600	C₄⋊C₄×C₃₁	—	2	1	no	—
601	C₄⋊C₄×C₃₁	—	2	1	no	—
602	C₄⋊C₄×C₃₁	—	2	1	no	—
603	C₄⋊C₄×C₃₁	—	2	1	no	—
604	C₄⋊C₄×C₃₁	—	2	1	no	—
605	C₄⋊C₄×C₃₁	—	2	1	no	—
606	C₄⋊C₄×C₃₁	—	2	1	no	—
607	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
615	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
616	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
617	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
618	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
619	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
620	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
621	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
622	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
623	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
624	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	—	2	1	no	—
638	C₂²⋊C₄×C₃₁	—	2	1	no	—
639	C₂²⋊C₄×C₃₁	—	2	1	no	—
640	C₂²⋊C₄×C₃₁	—	2	1	no	—
641	C₂²⋊C₄×C₃₁	—	2	1	no	—
642	C₂²⋊C₄×C₃₁	—	2	1	no	—
643	C₂²⋊C₄×C₃₁	—	2	1	no	—
644	C₂²⋊C₄×C₃₁	—	2	1	no	—
645	C₂²⋊C₄×C₃₁	—	2	1	no	—
646	C₂²⋊C₄×C₃₁	—	2	1	no	—
647	C₂²⋊C₄×C₃₁	—	2	1	no	—
648	C₂²⋊C₄×C₃₁	—	2	1	no	—
649	C₂²⋊C₄×C₃₁	—	2	1	no	—
650	C₂²⋊C₄×C₃₁	—	2	1	no	—
651	C₂²⋊C₄×C₃₁	—	2	1	no	—
652	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
658	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
659	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
660	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
661	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
662	C₄²×C₃₁	—	2	1	no	—
663	C₄²×C₃₁	—	2	1	no	—
664	C₄²×C₃₁	—	2	1	no	—
665	C₄²×C₃₁	—	2	1	no	—
666	C₄²×C₃₁	—	2	1	no	—
667	C₄²×C₃₁	—	2	1	no	—
668	C₄²×C₃₁	—	2	1	no	—
669	C₄²×C₃₁	—	2	1	no	—
670	C₄²×C₃₁	—	2	1	no	—
671	C₄²×C₃₁	—	2	1	no	—
672	C₄²×C₃₁	—	2	1	no	—
673	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
674	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
675	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
676	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
677	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
678	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
679	#62612	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
680	C₂³×C₃₁	—	2	1	no	—
681	C₂³×C₃₁	—	2	1	no	—
682	C₂³×C₃₁	—	2	1	no	—
683	C₂³×C₃₁	—	8	1	no	—
684	C₂³×C₃₁	—	8	1	no	—
685	C₂³×C₃₁	—	8	1	no	—
686	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
687	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
688	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
689	Q₈×C₃₁	—	2	1	no	—
690	Q₈×C₃₁	—	2	1	no	—
691	Q₈×C₃₁	—	2	1	no	—
692	Q₈×C₃₁	—	2	1	no	—
693	Q₈×C₃₁	—	2	1	no	—
694	Q₈×C₃₁	—	2	1	no	—
695	Q₈×C₃₁	—	2	1	no	—
696	Q₈×C₃₁	—	2	1	no	—
697	Q₈×C₃₁	—	2	1	no	—
698	Q₈×C₃₁	—	2	1	no	—
699	Q₈×C₃₁	—	4	1	no	—
700	Q₈×C₃₁	—	8	1	no	—
701	Q₈×C₃₁	—	8	1	no	—
702	Q₈×C₃₁	—	8	1	no	—
703	Q₈×C₃₁	—	8	1	no	—
704	D₄×C₃₁	—	2	1	no	—
705	D₄×C₃₁	—	2	1	no	—
706	D₄×C₃₁	—	2	1	no	—
707	D₄×C₃₁	—	2	1	no	—
708	D₄×C₃₁	—	2	1	no	—
709	D₄×C₃₁	—	2	1	no	—
710	D₄×C₃₁	—	4	1	no	—
711	D₄×C₃₁	—	4	1	no	—
712	D₄×C₃₁	—	4	1	no	—
713	D₄×C₃₁	—	8	1	no	—
714	D₄×C₃₁	—	8	1	no	—
715	D₄×C₃₁	—	8	1	no	—
716	D₄×C₃₁	—	8	1	no	—
717	D₄×C₃₁	—	8	1	no	—
718	D₄×C₃₁	—	8	1	no	—
719	D₄×C₃₁	—	8	1	no	—
720	D₄×C₃₁	—	8	1	no	—
721	D₄×C₃₁	—	8	1	no	—
722	D₄×C₃₁	—	8	1	no	—
723	D₄×C₃₁	—	8	1	no	—
724	D₄×C₃₁	—	8	1	no	—
725	C₂×C₄×C₃₁	—	2	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	2	1	no	—
728	C₂×C₄×C₃₁	—	2	1	no	—
729	C₂×C₄×C₃₁	—	2	1	no	—
730	C₂×C₄×C₃₁	—	2	1	no	—
731	C₂×C₄×C₃₁	—	2	1	no	—
732	C₂×C₄×C₃₁	—	2	1	no	—
733	C₂×C₄×C₃₁	—	2	1	no	—
734	C₂×C₄×C₃₁	—	2	1	no	—
735	C₂×C₄×C₃₁	—	2	1	no	—
736	C₂×C₄×C₃₁	—	2	1	no	—
737	C₂×C₄×C₃₁	—	2	1	no	—
738	C₂×C₄×C₃₁	—	2	1	no	—
739	C₂×C₄×C₃₁	—	2	1	no	—
740	C₂×C₄×C₃₁	—	2	1	no	—
741	C₂×C₄×C₃₁	—	2	1	no	—
742	C₂×C₄×C₃₁	—	2	1	no	—
743	C₂×C₄×C₃₁	—	2	1	no	—
744	C₂×C₄×C₃₁	—	4	1	no	—
745	C₂×C₄×C₃₁	—	4	1	no	—
746	C₂×C₄×C₃₁	—	4	2	no	—
747	C₂×C₄×C₃₁	—	8	1	no	—
748	C₂×C₄×C₃₁	—	8	1	no	—
749	C₂×C₄×C₃₁	—	8	1	no	—
750	C₂×C₄×C₃₁	—	8	1	no	—
751	C₂×C₄×C₃₁	—	8	1	no	—
752	C₂×C₄×C₃₁	—	8	1	no	—
753	C₂×C₄×C₃₁	—	8	1	no	—
754	C₂×C₄×C₃₁	—	8	1	no	—
755	C₂×C₄×C₃₁	—	8	1	no	—
756	C₂×C₄×C₃₁	—	8	1	no	—
757	C₂×C₄×C₃₁	—	8	1	no	—
758	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
759	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
760	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
763	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
764	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
765	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
766	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
770	C₈×C₃₁	—	2	1	no	—
771	C₈×C₃₁	—	2	1	no	—
772	C₈×C₃₁	—	2	1	no	—
773	C₈×C₃₁	—	2	1	no	—
774	C₈×C₃₁	—	2	1	no	—
775	C₈×C₃₁	—	2	1	no	—
776	C₈×C₃₁	—	2	1	no	—
777	C₈×C₃₁	—	2	1	no	—
778	#3563	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3562	C₂×C₃₁	1	1	yes	characteristic
780	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3323	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3323	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3317	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3316	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3314	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3300	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3296	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3241	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3223	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3222	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3177	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3174	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3172	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3142	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#2969	C₂×C₃₁	1	1	yes	characteristic, complemented
809	C₂²×C₃₁	—	2	1	no	—
810	C₂²×C₃₁	—	2	1	no	—
811	C₂²×C₃₁	—	2	1	no	—
812	C₂²×C₃₁	—	2	1	no	—
813	C₂²×C₃₁	—	2	1	no	—
814	C₂²×C₃₁	—	2	1	no	—
815	C₂²×C₃₁	—	2	1	no	—
816	C₂²×C₃₁	—	2	1	no	—
817	C₂²×C₃₁	—	2	1	no	—
818	C₂²×C₃₁	—	4	1	no	—
819	C₂²×C₃₁	—	4	1	no	—
820	C₂²×C₃₁	—	4	1	no	—
821	C₂²×C₃₁	—	4	1	no	—
822	C₂²×C₃₁	—	4	1	no	—
823	C₂²×C₃₁	—	4	1	no	—
824	C₂²×C₃₁	—	4	1	no	—
825	C₂²×C₃₁	—	4	1	no	—
826	C₂²×C₃₁	—	4	1	no	—
827	C₂²×C₃₁	—	16	2	no	—
828	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
829	C₄×C₃₁	—	2	1	no	—
830	C₄×C₃₁	—	2	1	no	—
831	C₄×C₃₁	—	2	1	no	—
832	C₄×C₃₁	—	2	1	no	—
833	C₄×C₃₁	—	2	1	no	—
834	C₄×C₃₁	—	2	1	no	—
835	C₄×C₃₁	—	2	1	no	—
836	C₄×C₃₁	—	2	1	no	—
837	C₄×C₃₁	—	2	1	no	—
838	C₄×C₃₁	—	2	1	no	—
839	C₄×C₃₁	—	2	1	no	—
840	C₄×C₃₁	—	4	1	no	—
841	C₄×C₃₁	—	4	1	no	—
842	C₄×C₃₁	—	4	1	no	—
843	C₄×C₃₁	—	4	1	no	—
844	C₄×C₃₁	—	4	1	no	—
845	C₄×C₃₁	—	4	1	no	—
846	C₄×C₃₁	—	4	1	no	—
847	C₄×C₃₁	—	4	1	no	—
848	C₄×C₃₁	—	4	1	no	—
849	C₄×C₃₁	—	4	1	no	—
850	C₄×C₃₁	—	4	1	no	—
851	C₄×C₃₁	—	4	1	no	—
852	C₄×C₃₁	—	4	1	no	—
853	C₄×C₃₁	#585	1	1	yes	characteristic
854	C₄×C₃₁	#585	1	1	yes	characteristic
855	#564	—	2	1	no	—
856	#563	—	2	1	no	—
857	#562	—	2	1	no	—
858	#560	—	2	1	no	—
859	#559	C₂²×C₃₁	1	1	yes	characteristic
860	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
861	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
862	#556	C₂²×C₃₁	1	1	yes	characteristic
863	#554	C₂²×C₃₁	1	1	yes	characteristic
864	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
865	#553	—	2	1	no	—
866	#552	—	2	1	no	—
867	#552	—	2	1	no	—
868	#552	C₂²×C₃₁	1	1	yes	characteristic
869	#552	C₂²×C₃₁	1	1	yes	characteristic
870	#552	C₂²×C₃₁	1	1	yes	characteristic
871	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
872	#551	—	2	1	no	—
873	#550	C₂²×C₃₁	1	1	yes	characteristic
874	#548	C₂²×C₃₁	1	1	yes	characteristic
875	#548	C₂²×C₃₁	1	1	yes	characteristic
876	#547	C₂²×C₃₁	1	1	yes	characteristic
877	#546	C₂²×C₃₁	1	1	yes	characteristic
878	#546	C₂²×C₃₁	1	1	yes	characteristic
879	#544	—	2	1	no	—
880	#544	C₂²×C₃₁	1	1	yes	characteristic
881	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
882	#541	—	2	1	no	—
883	#541	—	2	1	no	—
884	#541	C₂²×C₃₁	1	1	yes	characteristic
885	#541	C₂²×C₃₁	1	1	yes	characteristic
886	#541	C₂²×C₃₁	1	1	yes	characteristic, complemented
887	#540	—	2	1	no	—
888	#540	C₂²×C₃₁	1	1	yes	characteristic
889	#539	—	2	1	no	—
890	#539	—	2	1	no	—
891	#538	—	2	1	no	—
892	#538	—	2	1	no	—
893	#536	C₂²×C₃₁	1	1	yes	characteristic
894	#535	C₂²×C₃₁	1	1	yes	characteristic
895	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
896	#532	C₂²×C₃₁	1	1	yes	characteristic
897	#529	C₂²×C₃₁	1	1	yes	characteristic
898	#529	C₂²×C₃₁	1	1	yes	characteristic
899	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
900	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
901	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
902	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
903	#497	C₂²×C₃₁	1	1	yes	characteristic
904	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
905	#492	C₂²×C₃₁	1	1	yes	characteristic
906	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
907	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
908	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
909	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
910	#490	C₂²×C₃₁	1	1	yes	characteristic
911	#490	C₂²×C₃₁	1	1	yes	characteristic
912	#490	C₂²×C₃₁	1	1	yes	characteristic
913	#489	C₂²×C₃₁	1	1	yes	characteristic
914	#489	C₂²×C₃₁	1	1	yes	characteristic
915	#489	C₂²×C₃₁	1	1	yes	characteristic
916	#488	C₂²×C₃₁	1	1	yes	characteristic
917	#488	C₂²×C₃₁	1	1	yes	characteristic
918	#488	C₂²×C₃₁	1	1	yes	characteristic
919	#488	C₂²×C₃₁	1	1	yes	characteristic
920	#488	C₂²×C₃₁	1	1	yes	characteristic
921	#488	C₂²×C₃₁	1	1	yes	characteristic
922	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
923	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
924	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
925	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
926	#486	C₂²×C₃₁	1	1	yes	characteristic
927	#486	C₂²×C₃₁	1	1	yes	characteristic
928	#485	C₂²×C₃₁	1	1	yes	characteristic
929	#485	C₂²×C₃₁	1	1	yes	characteristic
930	#484	C₂²×C₃₁	1	1	yes	characteristic
931	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
932	#483	C₂²×C₃₁	1	1	yes	characteristic
933	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
934	#482	C₂²×C₃₁	1	1	yes	characteristic
935	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
936	#481	C₂²×C₃₁	1	1	yes	characteristic
937	#481	C₂²×C₃₁	1	1	yes	characteristic
938	#480	C₂²×C₃₁	1	1	yes	characteristic
939	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
940	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
941	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
942	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
943	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
944	#478	C₂²×C₃₁	1	1	yes	characteristic
945	#478	C₂²×C₃₁	1	1	yes	characteristic
946	#478	C₂²×C₃₁	1	1	yes	characteristic
947	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
948	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
949	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
950	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
951	#474	C₂²×C₃₁	1	1	yes	characteristic
952	#470	C₂²×C₃₁	1	1	yes	characteristic
953	#470	C₂²×C₃₁	1	1	yes	characteristic
954	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
955	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
956	#468	C₂²×C₃₁	1	1	yes	characteristic
957	#468	C₂²×C₃₁	1	1	yes	characteristic
958	#468	C₂²×C₃₁	1	1	yes	characteristic
959	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
960	#467	C₂²×C₃₁	1	1	yes	characteristic
961	#467	C₂²×C₃₁	1	1	yes	characteristic
962	#465	C₂²×C₃₁	1	1	yes	characteristic
963	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
964	#464	C₂²×C₃₁	1	1	yes	characteristic
965	#464	C₂²×C₃₁	1	1	yes	characteristic
966	#464	C₂²×C₃₁	1	1	yes	characteristic
967	#464	C₂²×C₃₁	1	1	yes	characteristic
968	#464	C₂²×C₃₁	1	1	yes	characteristic
969	#464	C₂²×C₃₁	1	1	yes	characteristic
970	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
972	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
973	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
974	#460	C₂²×C₃₁	1	1	yes	characteristic
975	#460	C₂²×C₃₁	1	1	yes	characteristic
976	#452	C₂²×C₃₁	1	1	yes	characteristic
977	#452	C₂²×C₃₁	1	1	yes	characteristic
978	#452	C₂²×C₃₁	1	1	yes	characteristic
979	#452	C₂²×C₃₁	1	1	yes	characteristic
980	#452	C₂²×C₃₁	1	1	yes	characteristic
981	#452	C₂²×C₃₁	1	1	yes	characteristic
982	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
983	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
984	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
985	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
986	#450	C₂²×C₃₁	1	1	yes	characteristic
987	#450	C₂²×C₃₁	1	1	yes	characteristic
988	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
989	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
990	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
991	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
992	#440	C₂²×C₃₁	1	1	yes	characteristic
993	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
994	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
995	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
996	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
997	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
998	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
999	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1000	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1001	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	#436	C₂²×C₃₁	1	1	yes	characteristic
1003	#436	C₂²×C₃₁	1	1	yes	characteristic
1004	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	#435	C₂²×C₃₁	1	1	yes	characteristic
1006	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
1007	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1008	#433	C₂²×C₃₁	1	1	yes	characteristic
1009	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
1010	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
1011	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
1012	#418	C₂²×C₃₁	1	1	yes	characteristic
1013	#417	C₂²×C₃₁	1	1	yes	characteristic
1014	#417	C₂²×C₃₁	1	1	yes	characteristic
1015	#417	C₂²×C₃₁	1	1	yes	characteristic
1016	#417	C₂²×C₃₁	1	1	yes	characteristic
1017	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
1018	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
1019	#416	C₂²×C₃₁	1	1	yes	characteristic
1020	#416	C₂²×C₃₁	1	1	yes	characteristic
1021	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
1022	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
1023	#405	C₂²×C₃₁	1	1	yes	characteristic
1024	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
1025	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1026	C₂×C₃₁	—	4	1	no	—
1027	C₂×C₃₁	—	4	1	no	—
1028	C₂×C₃₁	—	4	1	no	—
1029	C₂×C₃₁	—	8	1	no	—
1030	C₂×C₃₁	—	8	1	no	—
1031	C₂×C₃₁	—	8	1	no	—
1032	C₂×C₃₁	#3500	1	1	yes	characteristic
1033	C₂×C₃₁	#3584	1	1	yes	characteristic
1034	C₂×C₃₁	#3586	1	1	yes	characteristic
1035	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1036	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1037	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1038	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1039	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1040	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1041	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1042	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1043	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1044	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1045	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1046	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1047	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1048	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1049	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1055	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1059	C₄⋊Q₈	—	2	1	no	—
1060	C₄⋊Q₈	—	2	1	no	—
1061	C₄⋊Q₈	—	2	1	no	—
1062	C₄⋊Q₈	—	2	1	no	—
1063	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1064	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1065	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1066	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1067	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1068	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1069	#127	—	2	1	no	—
1070	#127	C₂³×C₃₁	1	1	yes	characteristic
1071	#127	C₂³×C₃₁	1	1	yes	characteristic
1072	#126	—	2	1	no	—
1073	#126	—	2	1	no	—
1074	#126	—	2	1	no	—
1075	#126	—	2	1	no	—
1076	#126	—	2	1	no	—
1077	#126	—	2	1	no	—
1078	#126	—	2	1	no	—
1079	#126	—	2	1	no	—
1080	#126	—	2	1	no	—
1081	#126	—	2	1	no	—
1082	#126	—	2	1	no	—
1083	#126	—	2	1	no	—
1084	#126	—	2	1	no	—
1085	#126	D₄×C₃₁	1	1	yes	characteristic
1086	#126	D₄×C₃₁	1	1	yes	characteristic
1087	#125	—	2	1	no	—
1088	#125	—	2	1	no	—
1089	#125	—	2	1	no	—
1090	#125	—	2	1	no	—
1091	#125	—	2	1	no	—
1092	#125	—	2	1	no	—
1093	#125	—	2	1	no	—
1094	#125	—	2	1	no	—
1095	#125	—	2	1	no	—
1096	#125	—	2	1	no	—
1097	#125	—	2	1	no	—
1098	#125	—	2	1	no	—
1099	#125	—	2	1	no	—
1100	#125	—	2	1	no	—
1101	#125	—	2	1	no	—
1102	#125	—	2	1	no	—
1103	#125	—	2	1	no	—
1104	#125	—	2	1	no	—
1105	#125	—	2	1	no	—
1106	#125	—	2	1	no	—
1107	#125	—	2	1	no	—
1108	#125	D₄×C₃₁	1	1	yes	characteristic
1109	#125	C₂³×C₃₁	1	1	yes	characteristic
1110	#125	C₂³×C₃₁	1	1	yes	characteristic
1111	#125	C₂³×C₃₁	1	1	yes	characteristic
1112	#125	C₂³×C₃₁	1	1	yes	characteristic
1113	#125	C₂³×C₃₁	1	1	yes	characteristic
1114	#125	C₂³×C₃₁	1	1	yes	characteristic
1115	#125	C₂³×C₃₁	1	1	yes	characteristic
1116	#124	—	2	1	no	—
1117	#124	—	2	1	no	—
1118	#124	—	2	1	no	—
1119	#124	D₄×C₃₁	1	1	yes	characteristic
1120	#124	C₂³×C₃₁	1	1	yes	characteristic
1121	#124	C₂³×C₃₁	1	1	yes	characteristic
1122	#124	C₂³×C₃₁	1	1	yes	characteristic
1123	#124	C₂³×C₃₁	1	1	yes	characteristic
1124	#124	C₂³×C₃₁	1	1	yes	characteristic
1125	#123	—	2	1	no	—
1126	#123	—	2	1	no	—
1127	#123	—	2	1	no	—
1128	#123	—	2	1	no	—
1129	#123	—	2	1	no	—
1130	#123	—	2	1	no	—
1131	#123	—	2	1	no	—
1132	#123	—	2	1	no	—
1133	#123	—	2	1	no	—
1134	#123	—	2	1	no	—
1135	#123	—	2	1	no	—
1136	#123	—	2	1	no	—
1137	#123	—	2	1	no	—
1138	#123	—	2	1	no	—
1139	#123	—	2	1	no	—
1140	#123	D₄×C₃₁	1	1	yes	characteristic
1141	#123	D₄×C₃₁	1	1	yes	characteristic
1142	C₂²⋊Q₈	—	2	1	no	—
1143	C₂²⋊Q₈	—	2	1	no	—
1144	C₂²⋊Q₈	—	2	1	no	—
1145	C₂²⋊Q₈	—	2	1	no	—
1146	C₂²⋊Q₈	—	2	1	no	—
1147	C₂²⋊Q₈	—	2	1	no	—
1148	C₂²⋊Q₈	—	2	1	no	—
1149	C₂²⋊Q₈	—	2	1	no	—
1150	C₂²⋊Q₈	—	2	1	no	—
1151	C₂²⋊Q₈	—	2	1	no	—
1152	C₂²⋊Q₈	—	2	1	no	—
1153	C₂²⋊Q₈	—	2	1	no	—
1154	C₂²⋊Q₈	—	2	1	no	—
1155	C₂²⋊Q₈	—	2	1	no	—
1156	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1157	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1158	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1159	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1160	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1161	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1162	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1163	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1164	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1165	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1166	#121	—	2	1	no	—
1167	#121	—	2	1	no	—
1168	#121	—	2	1	no	—
1169	#121	—	2	1	no	—
1170	#121	—	2	1	no	—
1171	#121	—	2	1	no	—
1172	#121	—	2	1	no	—
1173	#121	—	2	1	no	—
1174	#121	—	2	1	no	—
1175	#121	—	2	1	no	—
1176	#121	—	2	1	no	—
1177	#121	—	2	1	no	—
1178	#121	—	2	1	no	—
1179	#121	D₄×C₃₁	1	1	yes	characteristic
1180	#121	C₂³×C₃₁	1	1	yes	characteristic
1181	#121	C₂³×C₃₁	1	1	yes	characteristic
1182	#121	C₂³×C₃₁	1	1	yes	characteristic
1183	#120	—	2	1	no	—
1184	#120	—	2	1	no	—
1185	#120	—	2	1	no	—
1186	#120	—	2	1	no	—
1187	C₄×Q₈	—	2	1	no	—
1188	C₄×Q₈	—	2	1	no	—
1189	C₄×Q₈	—	2	1	no	—
1190	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1191	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1192	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1193	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1194	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1195	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1196	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1197	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1198	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1199	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1200	C₄×D₄	—	2	1	no	—
1201	C₄×D₄	—	2	1	no	—
1202	C₄×D₄	—	2	1	no	—
1203	C₄×D₄	—	2	1	no	—
1204	C₄×D₄	—	2	1	no	—
1205	C₄×D₄	—	2	1	no	—
1206	C₄×D₄	—	2	1	no	—
1207	C₄×D₄	—	2	1	no	—
1208	C₄×D₄	—	2	1	no	—
1209	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1210	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1211	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1212	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1213	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1214	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1215	#117	—	2	1	no	—
1216	#117	—	2	1	no	—
1217	#117	—	2	1	no	—
1218	#117	—	2	1	no	—
1219	#117	—	2	1	no	—
1220	#117	—	2	1	no	—
1221	#117	—	2	1	no	—
1222	#117	C₂³×C₃₁	1	1	yes	characteristic
1223	#117	C₂³×C₃₁	1	1	yes	characteristic
1224	#117	C₂³×C₃₁	1	1	yes	characteristic
1225	#117	C₂³×C₃₁	1	1	yes	characteristic
1226	C₂×C₄⋊C₄	—	2	1	no	—
1227	C₂×C₄⋊C₄	—	2	1	no	—
1228	C₂×C₄⋊C₄	—	2	1	no	—
1229	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1230	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1231	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1232	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1233	C₂×C₂²⋊C₄	—	2	1	no	—
1234	C₂×C₂²⋊C₄	—	2	1	no	—
1235	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1236	#107	C₂³×C₃₁	1	1	yes	characteristic
1237	#107	C₂³×C₃₁	1	1	yes	characteristic
1238	#107	C₂³×C₃₁	1	1	yes	characteristic
1239	#107	C₂³×C₃₁	1	1	yes	characteristic
1240	#107	C₂³×C₃₁	1	1	yes	characteristic
1241	#107	C₂³×C₃₁	1	1	yes	characteristic
1242	#106	C₂³×C₃₁	1	1	yes	characteristic
1243	#106	C₂³×C₃₁	1	1	yes	characteristic
1244	#106	C₂³×C₃₁	1	1	yes	characteristic
1245	#106	C₂³×C₃₁	1	1	yes	characteristic
1246	#106	C₂³×C₃₁	1	1	yes	characteristic
1247	#106	C₂³×C₃₁	1	1	yes	characteristic
1248	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1249	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1250	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1251	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1252	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1253	C₄⋊C₈	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	#103	C₂³×C₃₁	1	1	yes	characteristic
1272	#103	C₂³×C₃₁	1	1	yes	characteristic
1273	#103	C₂³×C₃₁	1	1	yes	characteristic
1274	#103	C₂³×C₃₁	1	1	yes	characteristic
1275	#103	C₂³×C₃₁	1	1	yes	characteristic
1276	#102	C₂³×C₃₁	1	1	yes	characteristic
1277	#102	C₂³×C₃₁	1	1	yes	characteristic
1278	#102	C₂³×C₃₁	1	1	yes	characteristic
1279	#102	C₂³×C₃₁	1	1	yes	characteristic
1280	#102	C₂³×C₃₁	1	1	yes	characteristic
1281	#102	C₂³×C₃₁	1	1	yes	characteristic
1282	#102	C₂³×C₃₁	1	1	yes	characteristic
1283	#102	C₂³×C₃₁	1	1	yes	characteristic
1284	#102	C₂³×C₃₁	1	1	yes	characteristic
1285	#102	C₂³×C₃₁	1	1	yes	characteristic
1286	#102	C₂³×C₃₁	1	1	yes	characteristic
1287	#102	C₂³×C₃₁	1	1	yes	characteristic
1288	#102	C₂³×C₃₁	1	1	yes	characteristic
1289	#102	C₂³×C₃₁	1	1	yes	characteristic
1290	#102	C₂³×C₃₁	1	1	yes	characteristic
1291	#102	C₂³×C₃₁	1	1	yes	characteristic
1292	#102	C₂³×C₃₁	1	1	yes	characteristic
1293	#102	C₂³×C₃₁	1	1	yes	characteristic
1294	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1295	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1296	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1297	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1298	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1299	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1300	#97	C₂³×C₃₁	1	1	yes	characteristic
1301	#97	C₂³×C₃₁	1	1	yes	characteristic
1302	#97	C₂³×C₃₁	1	1	yes	characteristic
1303	#97	C₂³×C₃₁	1	1	yes	characteristic
1304	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1305	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1306	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1307	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1308	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1309	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1310	C₃₁	#62612	1	1	yes	characteristic, direct product factor, Sylow
1311	C₂⁴	—	2	1	no	—
1312	#41	—	4	1	no	—
1313	#41	—	4	1	no	—
1314	#41	—	4	1	no	—
1315	#41	—	4	1	no	—
1316	#41	—	4	1	no	—
1317	#41	—	4	1	no	—
1318	#41	—	4	1	no	—
1319	#41	—	4	1	no	—
1320	C₂×Q₈	—	2	1	no	—
1321	C₂×Q₈	—	2	1	no	—
1322	C₂×Q₈	—	2	1	no	—
1323	C₂×Q₈	—	2	1	no	—
1324	C₂×Q₈	—	4	1	no	—
1325	C₂×Q₈	—	4	1	no	—
1326	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1327	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1328	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1329	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1330	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1331	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1332	C₂×D₄	—	2	1	no	—
1333	C₂×D₄	—	2	1	no	—
1334	C₂×D₄	—	2	1	no	—
1335	C₂×D₄	—	2	1	no	—
1336	C₂×D₄	—	2	1	no	—
1337	C₂×D₄	—	2	1	no	—
1338	C₂×D₄	—	2	1	no	—
1339	C₂×D₄	—	2	1	no	—
1340	C₂×D₄	—	2	1	no	—
1341	C₂×D₄	—	2	1	no	—
1342	C₂×D₄	—	2	1	no	—
1343	C₂×D₄	—	2	1	no	—
1344	C₂×D₄	—	4	1	no	—
1345	C₂×D₄	—	4	1	no	—
1346	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1347	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1348	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1349	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1350	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1351	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1352	C₂²×C₄	—	2	1	no	—
1353	C₂²×C₄	—	2	1	no	—
1354	C₂²×C₄	—	2	1	no	—
1355	C₂²×C₄	—	2	1	no	—
1356	C₂²×C₄	—	2	1	no	—
1357	C₂²×C₄	—	2	1	no	—
1358	C₂²×C₄	—	2	1	no	—
1359	C₂²×C₄	—	2	1	no	—
1360	C₂²×C₄	—	2	1	no	—
1361	C₂²×C₄	—	2	1	no	—
1362	C₂²×C₄	—	2	1	no	—
1363	C₂²×C₄	—	2	1	no	—
1364	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1365	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1366	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1367	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1368	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1369	Q₁₆	—	4	1	no	—
1370	Q₁₆	—	4	1	no	—
1371	Q₁₆	—	4	1	no	—
1372	Q₁₆	—	4	1	no	—
1373	Q₁₆	—	4	1	no	—
1374	Q₁₆	—	4	1	no	—
1375	SD₁₆	—	4	1	no	—
1376	SD₁₆	—	4	1	no	—
1377	SD₁₆	—	4	1	no	—
1378	SD₁₆	—	4	1	no	—
1379	SD₁₆	—	4	1	no	—
1380	SD₁₆	—	4	1	no	—
1381	M₁₆	—	4	1	no	—
1382	M₁₆	—	4	1	no	—
1383	M₁₆	—	4	1	no	—
1384	M₁₆	—	4	1	no	—
1385	C₂×C₈	—	4	1	no	—
1386	C₂×C₈	—	4	1	no	—
1387	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1388	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1389	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1390	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1391	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1392	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1393	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1394	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1395	C₄⋊C₄	—	2	1	no	—
1396	C₄⋊C₄	—	2	1	no	—
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	—	2	1	no	—
1400	C₄⋊C₄	—	2	1	no	—
1401	C₄⋊C₄	—	2	1	no	—
1402	C₄⋊C₄	—	2	1	no	—
1403	C₄⋊C₄	—	2	1	no	—
1404	C₄⋊C₄	—	2	1	no	—
1405	C₄⋊C₄	—	2	1	no	—
1406	C₄⋊C₄	—	2	1	no	—
1407	C₄⋊C₄	—	2	1	no	—
1408	C₄⋊C₄	—	2	1	no	—
1409	C₄⋊C₄	—	2	1	no	—
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	—	2	1	no	—
1413	C₄⋊C₄	—	2	1	no	—
1414	C₄⋊C₄	—	2	1	no	—
1415	C₄⋊C₄	—	2	1	no	—
1416	C₄⋊C₄	—	2	1	no	—
1417	C₄⋊C₄	—	2	1	no	—
1418	C₄⋊C₄	—	2	1	no	—
1419	C₄⋊C₄	—	2	1	no	—
1420	C₄⋊C₄	—	2	1	no	—
1421	C₄⋊C₄	—	2	1	no	—
1422	C₄⋊C₄	—	2	1	no	—
1423	C₄⋊C₄	—	2	1	no	—
1424	C₄⋊C₄	—	2	1	no	—
1425	C₄⋊C₄	—	2	1	no	—
1426	C₄⋊C₄	—	2	1	no	—
1427	C₄⋊C₄	—	2	1	no	—
1428	C₄⋊C₄	—	2	1	no	—
1429	C₄⋊C₄	—	2	1	no	—
1430	C₄⋊C₄	—	2	1	no	—
1431	C₄⋊C₄	—	2	1	no	—
1432	C₄⋊C₄	—	2	1	no	—
1433	C₄⋊C₄	—	2	1	no	—
1434	C₄⋊C₄	—	2	1	no	—
1435	C₄⋊C₄	—	2	1	no	—
1436	C₄⋊C₄	—	2	1	no	—
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1441	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1442	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1443	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1444	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1445	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1446	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1447	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1448	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1449	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1450	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1451	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1452	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1453	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1454	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1455	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1456	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1457	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1458	C₂²⋊C₄	—	2	1	no	—
1459	C₂²⋊C₄	—	2	1	no	—
1460	C₂²⋊C₄	—	2	1	no	—
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	—	2	1	no	—
1476	C₂²⋊C₄	—	2	1	no	—
1477	C₂²⋊C₄	—	2	1	no	—
1478	C₂²⋊C₄	—	2	1	no	—
1479	C₂²⋊C₄	—	2	1	no	—
1480	C₂²⋊C₄	—	2	1	no	—
1481	C₂²⋊C₄	—	2	1	no	—
1482	C₂²⋊C₄	—	2	1	no	—
1483	C₂²⋊C₄	—	2	1	no	—
1484	C₂²⋊C₄	—	2	1	no	—
1485	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1486	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1487	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1488	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1489	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1490	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1491	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1492	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1493	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1494	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1495	C₄²	—	2	1	no	—
1496	C₄²	—	2	1	no	—
1497	C₄²	—	2	1	no	—
1498	C₄²	—	2	1	no	—
1499	C₄²	—	2	1	no	—
1500	C₄²	—	2	1	no	—
1501	C₄²	—	2	1	no	—
1502	C₄²	—	2	1	no	—
1503	C₄²	—	2	1	no	—
1504	C₄²	—	2	1	no	—
1505	C₄²	—	2	1	no	—
1506	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1507	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1508	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1509	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1510	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1511	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1512	C₂³	—	2	1	no	—
1513	C₂³	—	2	1	no	—
1514	C₂³	—	2	1	no	—
1515	C₂³	—	8	1	no	—
1516	C₂³	—	8	1	no	—
1517	C₂³	—	8	1	no	—
1518	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1519	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1520	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1521	Q₈	—	2	1	no	—
1522	Q₈	—	2	1	no	—
1523	Q₈	—	2	1	no	—
1524	Q₈	—	2	1	no	—
1525	Q₈	—	2	1	no	—
1526	Q₈	—	2	1	no	—
1527	Q₈	—	2	1	no	—
1528	Q₈	—	2	1	no	—
1529	Q₈	—	2	1	no	—
1530	Q₈	—	2	1	no	—
1531	Q₈	—	4	1	no	—
1532	Q₈	—	8	1	no	—
1533	Q₈	—	8	1	no	—
1534	Q₈	—	8	1	no	—
1535	Q₈	—	8	1	no	—
1536	D₄	—	2	1	no	—
1537	D₄	—	2	1	no	—
1538	D₄	—	2	1	no	—
1539	D₄	—	2	1	no	—
1540	D₄	—	2	1	no	—
1541	D₄	—	2	1	no	—
1542	D₄	—	4	1	no	—
1543	D₄	—	4	1	no	—
1544	D₄	—	4	1	no	—
1545	D₄	—	8	1	no	—
1546	D₄	—	8	1	no	—
1547	D₄	—	8	1	no	—
1548	D₄	—	8	1	no	—
1549	D₄	—	8	1	no	—
1550	D₄	—	8	1	no	—
1551	D₄	—	8	1	no	—
1552	D₄	—	8	1	no	—
1553	D₄	—	8	1	no	—
1554	D₄	—	8	1	no	—
1555	D₄	—	8	1	no	—
1556	D₄	—	8	1	no	—
1557	C₂×C₄	—	2	1	no	—
1558	C₂×C₄	—	2	1	no	—
1559	C₂×C₄	—	2	1	no	—
1560	C₂×C₄	—	2	1	no	—
1561	C₂×C₄	—	2	1	no	—
1562	C₂×C₄	—	2	1	no	—
1563	C₂×C₄	—	2	1	no	—
1564	C₂×C₄	—	2	1	no	—
1565	C₂×C₄	—	2	1	no	—
1566	C₂×C₄	—	2	1	no	—
1567	C₂×C₄	—	2	1	no	—
1568	C₂×C₄	—	2	1	no	—
1569	C₂×C₄	—	2	1	no	—
1570	C₂×C₄	—	2	1	no	—
1571	C₂×C₄	—	2	1	no	—
1572	C₂×C₄	—	2	1	no	—
1573	C₂×C₄	—	2	1	no	—
1574	C₂×C₄	—	2	1	no	—
1575	C₂×C₄	—	2	1	no	—
1576	C₂×C₄	—	4	1	no	—
1577	C₂×C₄	—	4	1	no	—
1578	C₂×C₄	—	4	2	no	—
1579	C₂×C₄	—	8	1	no	—
1580	C₂×C₄	—	8	1	no	—
1581	C₂×C₄	—	8	1	no	—
1582	C₂×C₄	—	8	1	no	—
1583	C₂×C₄	—	8	1	no	—
1584	C₂×C₄	—	8	1	no	—
1585	C₂×C₄	—	8	1	no	—
1586	C₂×C₄	—	8	1	no	—
1587	C₂×C₄	—	8	1	no	—
1588	C₂×C₄	—	8	1	no	—
1589	C₂×C₄	—	8	1	no	—
1590	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1591	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1592	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1593	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1594	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1595	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1596	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1597	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1598	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1599	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1600	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1601	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1602	C₈	—	2	1	no	—
1603	C₈	—	2	1	no	—
1604	C₈	—	2	1	no	—
1605	C₈	—	2	1	no	—
1606	C₈	—	2	1	no	—
1607	C₈	—	2	1	no	—
1608	C₈	—	2	1	no	—
1609	C₈	—	2	1	no	—
1610	C₂²	—	2	1	no	—
1611	C₂²	—	2	1	no	—
1612	C₂²	—	2	1	no	—
1613	C₂²	—	2	1	no	—
1614	C₂²	—	2	1	no	—
1615	C₂²	—	2	1	no	—
1616	C₂²	—	2	1	no	—
1617	C₂²	—	2	1	no	—
1618	C₂²	—	2	1	no	—
1619	C₂²	—	4	1	no	—
1620	C₂²	—	4	1	no	—
1621	C₂²	—	4	1	no	—
1622	C₂²	—	4	1	no	—
1623	C₂²	—	4	1	no	—
1624	C₂²	—	4	1	no	—
1625	C₂²	—	4	1	no	—
1626	C₂²	—	4	1	no	—
1627	C₂²	—	4	1	no	—
1628	C₂²	—	16	2	no	—
1629	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1630	C₄	—	2	1	no	—
1631	C₄	—	2	1	no	—
1632	C₄	—	2	1	no	—
1633	C₄	—	2	1	no	—
1634	C₄	—	2	1	no	—
1635	C₄	—	2	1	no	—
1636	C₄	—	2	1	no	—
1637	C₄	—	2	1	no	—
1638	C₄	—	2	1	no	—
1639	C₄	—	2	1	no	—
1640	C₄	—	2	1	no	—
1641	C₄	—	4	1	no	—
1642	C₄	—	4	1	no	—
1643	C₄	—	4	1	no	—
1644	C₄	—	4	1	no	—
1645	C₄	—	4	1	no	—
1646	C₄	—	4	1	no	—
1647	C₄	—	4	1	no	—
1648	C₄	—	4	1	no	—
1649	C₄	—	4	1	no	—
1650	C₄	—	4	1	no	—
1651	C₄	—	4	1	no	—
1652	C₄	—	4	1	no	—
1653	C₄	—	4	1	no	—
1654	C₄	C₃₁×#585	1	1	yes	characteristic
1655	C₄	C₃₁×#585	1	1	yes	characteristic
1656	C₂	—	4	1	no	—
1657	C₂	—	4	1	no	—
1658	C₂	—	4	1	no	—
1659	C₂	—	8	1	no	—
1660	C₂	—	8	1	no	—
1661	C₂	—	8	1	no	—
1662	C₂	C₃₁×#3500	1	1	yes	characteristic
1663	C₂	C₃₁×#3584	1	1	yes	characteristic
1664	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3562	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×#3377	C₂	semidirect
4. C₃₁×#3371	C₂	semidirect
5. C₃₁×#3365	C₂	semidirect
6. C₃₁×#3364	C₂	semidirect
7. C₃₁×#3333	C₂	semidirect
8. C₃₁×#3331	C₂	semidirect
9. C₃₁×#3327	C₂	semidirect
10. C₃₁×#3327	C₂	semidirect
11. C₃₁×#3323	C₂	semidirect
12. C₃₁×#3323	C₂	semidirect
13. C₃₁×#3317	C₂	semidirect
14. C₃₁×#3316	C₂	semidirect
15. C₃₁×#3315	C₂	semidirect
16. C₃₁×#3314	C₂	semidirect
17. C₃₁×#3300	C₂	semidirect
18. C₃₁×#3296	C₂	semidirect
19. C₃₁×#3242	C₂	semidirect
20. C₃₁×#3241	C₂	semidirect
21. C₃₁×#3232	C₂	semidirect
22. C₃₁×#3223	C₂	semidirect
23. C₃₁×#3222	C₂	semidirect
24. C₃₁×#3210	C₂	semidirect
25. C₃₁×#3177	C₂	semidirect
26. C₃₁×#3174	C₂	semidirect
27. C₃₁×#3172	C₂	semidirect
28. C₃₁×#3142	C₂	semidirect
29. C₃₁×#3137	C₂	semidirect
30. C₃₁×#3136	C₂	semidirect
31. C₃₁×#2969	C₂	semidirect
37. C₃₁×#557	C₂²	semidirect
38. C₃₁×#557	C₂²	semidirect
41. C₃₁×#554	C₂²	semidirect
48. C₃₁×#552	C₂²	semidirect
58. C₃₁×#544	C₂²	semidirect
63. C₃₁×#541	C₂²	semidirect
72. C₃₁×#533	C₂²	semidirect
76. C₂×C₃₁×#125	C₂²	semidirect
77. C₃₁×#501	C₂²	semidirect
78. C₃₁×#499	C₂²	semidirect
79. C₃₁×#499	C₂²	semidirect
81. C₃₁×#494	C₂²	semidirect
83. C₃₁×#491	C₂²	semidirect
84. C₃₁×#491	C₂²	semidirect
85. C₃₁×#491	C₂²	semidirect
86. C₃₁×#491	C₂²	semidirect
99. C₃₁×#488	C₂²	semidirect
100. C₃₁×#488	C₂²	semidirect
101. C₃₁×#487	C₂²	semidirect
102. C₃₁×#487	C₂²	semidirect
108. C₃₁×#484	C₂²	semidirect
110. C₃₁×#483	C₂²	semidirect
112. C₃₁×#482	C₂²	semidirect
116. C₃₁×#480	C₂²	semidirect
117. C₃₁×#479	C₂²	semidirect
118. C₃₁×#479	C₂²	semidirect
119. C₃₁×#479	C₂²	semidirect
120. C₃₁×#479	C₂²	semidirect
124. C₃₁×#478	C₂²	semidirect
125. C₃₁×#477	C₂²	semidirect
126. C₃₁×#476	C₂²	semidirect
127. C₃₁×#475	C₂²	semidirect
131. C₃₁×#470	C₂²	semidirect
132. C₃₁×#470	C₂²	semidirect
136. C₃₁×#468	C₂²	semidirect
140. C₃₁×#465	C₂²	semidirect
147. C₃₁×#464	C₂²	semidirect
148. C₃₁×#464	C₂²	semidirect
149. C₃₁×#462	C₂²	semidirect
150. C₃₁×#462	C₂²	semidirect
159. C₃₁×#452	C₂²	semidirect
160. C₃₁×#452	C₂²	semidirect
161. C₃₁×#451	C₂²	semidirect
162. C₃₁×#451	C₂²	semidirect
165. C₃₁×#446	C₂²	semidirect
166. C₈×Q₈×C₃₁	C₂²	semidirect
167. C₃₁×#441	C₂²	semidirect
168. C₃₁×#441	C₂²	semidirect
170. C₃₁×#440	C₂²	semidirect
171. C₄×Q₁₆×C₃₁	C₂²	semidirect
172. C₄×Q₁₆×C₃₁	C₂²	semidirect
173. C₄×Q₁₆×C₃₁	C₂²	semidirect
174. C₄×Q₁₆×C₃₁	C₂²	semidirect
178. C₄×SD₁₆×C₃₁	C₂²	semidirect
181. C₃₁×#436	C₂²	semidirect
183. C₃₁×#435	C₂²	semidirect
186. C₃₁×#433	C₂²	semidirect
187. C₃₁×#431	C₂²	semidirect
188. C₃₁×#419	C₂²	semidirect
194. C₃₁×#417	C₂²	semidirect
195. C₃₁×#417	C₂²	semidirect
198. C₂×C₃₁×#103	C₂²	semidirect
201. C₃₁×#405	C₂²	semidirect
202. C₄×M₁₆×C₃₁	C₂²	semidirect
679. #62612	C₃₁	direct (N × H)
778. #3563	C₂×C₃₁	semidirect
780. #3377	C₂×C₃₁	semidirect
781. #3371	C₂×C₃₁	semidirect
782. #3365	C₂×C₃₁	semidirect
783. #3364	C₂×C₃₁	semidirect
784. #3333	C₂×C₃₁	semidirect
785. #3331	C₂×C₃₁	semidirect
786. #3327	C₂×C₃₁	semidirect
787. #3327	C₂×C₃₁	semidirect
788. #3323	C₂×C₃₁	semidirect
789. #3323	C₂×C₃₁	semidirect
790. #3317	C₂×C₃₁	semidirect
791. #3316	C₂×C₃₁	semidirect
792. #3315	C₂×C₃₁	semidirect
793. #3314	C₂×C₃₁	semidirect
794. #3300	C₂×C₃₁	semidirect
795. #3296	C₂×C₃₁	semidirect
796. #3242	C₂×C₃₁	semidirect
797. #3241	C₂×C₃₁	semidirect
798. #3232	C₂×C₃₁	semidirect
799. #3223	C₂×C₃₁	semidirect
800. #3222	C₂×C₃₁	semidirect
801. #3210	C₂×C₃₁	semidirect
802. #3177	C₂×C₃₁	semidirect
803. #3174	C₂×C₃₁	semidirect
804. #3172	C₂×C₃₁	semidirect
805. #3142	C₂×C₃₁	semidirect
806. #3137	C₂×C₃₁	semidirect
807. #3136	C₂×C₃₁	semidirect
808. #2969	C₂×C₃₁	semidirect
860. #557	C₂²×C₃₁	semidirect
861. #557	C₂²×C₃₁	semidirect
864. #554	C₂²×C₃₁	semidirect
871. #552	C₂²×C₃₁	semidirect
881. #544	C₂²×C₃₁	semidirect
886. #541	C₂²×C₃₁	semidirect
895. #533	C₂²×C₃₁	semidirect
899. C₂×#125	C₂²×C₃₁	semidirect
900. #501	C₂²×C₃₁	semidirect
901. #499	C₂²×C₃₁	semidirect
902. #499	C₂²×C₃₁	semidirect
904. #494	C₂²×C₃₁	semidirect
906. #491	C₂²×C₃₁	semidirect
907. #491	C₂²×C₃₁	semidirect
908. #491	C₂²×C₃₁	semidirect
909. #491	C₂²×C₃₁	semidirect
922. #488	C₂²×C₃₁	semidirect
923. #488	C₂²×C₃₁	semidirect
924. #487	C₂²×C₃₁	semidirect
925. #487	C₂²×C₃₁	semidirect
931. #484	C₂²×C₃₁	semidirect
933. #483	C₂²×C₃₁	semidirect
935. #482	C₂²×C₃₁	semidirect
939. #480	C₂²×C₃₁	semidirect
940. #479	C₂²×C₃₁	semidirect
941. #479	C₂²×C₃₁	semidirect
942. #479	C₂²×C₃₁	semidirect
943. #479	C₂²×C₃₁	semidirect
947. #478	C₂²×C₃₁	semidirect
948. #477	C₂²×C₃₁	semidirect
949. #476	C₂²×C₃₁	semidirect
950. #475	C₂²×C₃₁	semidirect
954. #470	C₂²×C₃₁	semidirect
955. #470	C₂²×C₃₁	semidirect
959. #468	C₂²×C₃₁	semidirect
963. #465	C₂²×C₃₁	semidirect
970. #464	C₂²×C₃₁	semidirect
971. #464	C₂²×C₃₁	semidirect
972. #462	C₂²×C₃₁	semidirect
973. #462	C₂²×C₃₁	semidirect
982. #452	C₂²×C₃₁	semidirect
983. #452	C₂²×C₃₁	semidirect
984. #451	C₂²×C₃₁	semidirect
985. #451	C₂²×C₃₁	semidirect
988. #446	C₂²×C₃₁	semidirect
989. C₈×Q₈	C₂²×C₃₁	semidirect
990. #441	C₂²×C₃₁	semidirect
991. #441	C₂²×C₃₁	semidirect
993. #440	C₂²×C₃₁	semidirect
994. C₄×Q₁₆	C₂²×C₃₁	semidirect
995. C₄×Q₁₆	C₂²×C₃₁	semidirect
996. C₄×Q₁₆	C₂²×C₃₁	semidirect
997. C₄×Q₁₆	C₂²×C₃₁	semidirect
1001. C₄×SD₁₆	C₂²×C₃₁	semidirect
1004. #436	C₂²×C₃₁	semidirect
1006. #435	C₂²×C₃₁	semidirect
1009. #433	C₂²×C₃₁	semidirect
1010. #431	C₂²×C₃₁	semidirect
1011. #419	C₂²×C₃₁	semidirect
1017. #417	C₂²×C₃₁	semidirect
1018. #417	C₂²×C₃₁	semidirect
1021. C₂×#103	C₂²×C₃₁	semidirect
1024. #405	C₂²×C₃₁	semidirect
1025. C₄×M₁₆	C₂²×C₃₁	semidirect
1310. C₃₁	#62612	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×#3562	2
C₃₁×#3377	2
C₃₁×#3371	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3333	2
C₃₁×#3331	2
C₃₁×#3327	2
C₃₁×#3323	2
C₃₁×#3317	2
C₃₁×#3316	2
C₃₁×#3315	2
C₃₁×#3314	2
C₃₁×#3300	2
C₃₁×#3296	2
C₃₁×#3242	2
C₃₁×#3241	2
C₃₁×#3232	2
C₃₁×#3223	2
C₃₁×#3222	2
C₃₁×#3210	2
C₃₁×#3177	2
C₃₁×#3174	2
C₃₁×#3172	2
C₃₁×#3142	2
C₃₁×#3137	2
C₃₁×#3136	2
C₃₁×#2969	2
#62612	31

Subgroups — C31×#62612 #21519371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62612 #21519371