Subgroups — C₃₁×#61763 #21518522

Order 7936.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3539	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3352	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3351	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3350	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3346	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3337	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3336	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3317	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3302	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×#3201	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3201	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3190	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3126	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2976	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#560	—	2	1	no	—
33	C₃₁×#560	—	2	1	no	—
34	C₃₁×#556	C₂²	1	1	yes	characteristic
35	C₃₁×#556	C₂²	1	1	yes	characteristic
36	C₃₁×#554	C₂²	1	1	yes	characteristic
37	C₃₁×#554	C₂²	1	1	yes	characteristic
38	C₃₁×#553	—	2	1	no	—
39	C₃₁×#553	—	2	1	no	—
40	C₃₁×#553	C₂²	1	1	yes	characteristic
41	C₃₁×#553	C₂²	1	1	yes	characteristic
42	C₃₁×#552	—	2	1	no	—
43	C₃₁×#552	—	2	1	no	—
44	C₃₁×#552	C₂²	1	1	yes	characteristic
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
49	C₃₁×#552	C₂²	1	1	yes	characteristic
50	C₃₁×#551	—	2	1	no	—
51	C₃₁×#551	—	2	1	no	—
52	C₃₁×#550	C₂²	1	1	yes	characteristic
53	C₃₁×#550	C₂²	1	1	yes	characteristic
54	C₃₁×#547	C₂²	1	1	yes	characteristic
55	C₃₁×#547	C₂²	1	1	yes	characteristic
56	C₃₁×#544	C₂²	1	1	yes	characteristic
57	C₃₁×#542	—	2	1	no	—
58	C₃₁×#541	—	2	1	no	—
59	C₃₁×#541	C₂²	1	1	yes	characteristic
60	C₃₁×#540	—	2	1	no	—
61	C₃₁×#540	—	2	1	no	—
62	C₃₁×#540	C₂²	1	1	yes	characteristic
63	C₃₁×#539	—	2	1	no	—
64	C₃₁×#539	—	2	1	no	—
65	C₃₁×#537	C₂²	1	1	yes	characteristic
66	C₃₁×#537	C₂²	1	1	yes	characteristic
67	C₃₁×#536	C₂²	1	1	yes	characteristic
68	C₃₁×#533	—	2	1	no	—
69	C₃₁×#529	—	2	1	no	—
70	C₃₁×#525	C₂²	1	1	yes	characteristic
71	C₃₁×#525	C₂²	1	1	yes	characteristic
72	C₃₁×#525	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#519	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
77	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#485	C₂²	1	1	yes	characteristic
86	C₃₁×#485	C₂²	1	1	yes	characteristic
87	C₃₁×#485	C₂²	1	1	yes	characteristic
88	C₃₁×#485	C₂²	1	1	yes	characteristic
89	C₃₁×#485	C₂²	1	1	yes	characteristic
90	C₃₁×#485	C₂²	1	1	yes	characteristic
91	C₃₁×#485	C₂²	1	1	yes	characteristic
92	C₃₁×#485	C₂²	1	1	yes	characteristic
93	C₃₁×#485	C₂²	1	1	yes	characteristic
94	C₃₁×#485	C₂²	1	1	yes	characteristic
95	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#484	C₂²	1	1	yes	characteristic
98	C₃₁×#484	C₂²	1	1	yes	characteristic
99	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#483	C₂²	1	1	yes	characteristic
103	C₃₁×#483	C₂²	1	1	yes	characteristic
104	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#482	C₂²	1	1	yes	characteristic
108	C₃₁×#482	C₂²	1	1	yes	characteristic
109	C₃₁×#482	C₂²	1	1	yes	characteristic
110	C₃₁×#482	C₂²	1	1	yes	characteristic
111	C₃₁×#482	C₂²	1	1	yes	characteristic
112	C₃₁×#482	C₂²	1	1	yes	characteristic
113	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#481	C₂²	1	1	yes	characteristic
116	C₃₁×#481	C₂²	1	1	yes	characteristic
117	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#480	C₂²	1	1	yes	characteristic
119	C₃₁×#480	C₂²	1	1	yes	characteristic
120	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#470	C₂²	1	1	yes	characteristic
134	C₃₁×#470	C₂²	1	1	yes	characteristic
135	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#468	C₂²	1	1	yes	characteristic
138	C₃₁×#468	C₂²	1	1	yes	characteristic
139	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
140	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
141	C₃₁×#467	C₂²	1	1	yes	characteristic
142	C₃₁×#467	C₂²	1	1	yes	characteristic
143	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
144	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
145	C₃₁×#465	C₂²	1	1	yes	characteristic
146	C₃₁×#465	C₂²	1	1	yes	characteristic
147	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
150	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
151	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
152	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
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, complemented
158	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
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
162	C₃₁×#451	C₂²	1	1	yes	characteristic
163	C₃₁×#448	C₂²	1	1	yes	characteristic
164	C₃₁×#448	C₂²	1	1	yes	characteristic
165	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
166	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
167	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
168	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
169	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
170	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
171	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
172	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
173	C₃₁×#436	C₂²	1	1	yes	characteristic
174	C₃₁×#436	C₂²	1	1	yes	characteristic
175	C₃₁×#435	C₂²	1	1	yes	characteristic
176	C₃₁×#435	C₂²	1	1	yes	characteristic
177	C₃₁×#435	C₂²	1	1	yes	characteristic
178	C₃₁×#435	C₂²	1	1	yes	characteristic
179	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
180	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
181	C₃₁×#433	C₂²	1	1	yes	characteristic
182	C₃₁×#433	C₂²	1	1	yes	characteristic
183	C₃₁×#428	C₂²	1	1	yes	characteristic
184	C₃₁×#428	C₂²	1	1	yes	characteristic
185	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
186	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
187	C₃₁×#427	C₂²	1	1	yes	characteristic
188	C₃₁×#427	C₂²	1	1	yes	characteristic
189	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
190	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
191	C₃₁×#417	C₂²	1	1	yes	characteristic
192	C₃₁×#417	C₂²	1	1	yes	characteristic
193	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
194	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
195	C₃₁×#416	C₂²	1	1	yes	characteristic
196	C₃₁×#416	C₂²	1	1	yes	characteristic
197	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
198	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
199	C₃₁×#408	C₂²	1	1	yes	characteristic
200	C₃₁×#408	C₂²	1	1	yes	characteristic
201	C₃₁×#407	C₂²	1	1	yes	characteristic
202	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
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	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₂³×C₄×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×SD₁₆×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×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×C₄⋊Q₈	—	2	1	no	—
227	C₃₁×C₄⋊Q₈	—	2	1	no	—
228	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
229	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
230	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×#127	—	2	1	no	—
232	C₃₁×#127	—	2	1	no	—
233	C₃₁×#127	C₂³	1	1	yes	characteristic
234	C₃₁×#126	—	2	1	no	—
235	C₃₁×#126	—	2	1	no	—
236	C₃₁×#126	—	2	1	no	—
237	C₃₁×#126	—	2	1	no	—
238	C₃₁×#126	—	2	1	no	—
239	C₃₁×#126	—	2	1	no	—
240	C₃₁×#126	—	2	1	no	—
241	C₃₁×#126	—	2	1	no	—
242	C₃₁×#126	—	2	1	no	—
243	C₃₁×#126	—	2	1	no	—
244	C₃₁×#126	—	2	1	no	—
245	C₃₁×#126	—	2	1	no	—
246	C₃₁×#126	—	2	1	no	—
247	C₃₁×#126	—	2	1	no	—
248	C₃₁×#125	—	2	1	no	—
249	C₃₁×#125	—	2	1	no	—
250	C₃₁×#125	—	2	1	no	—
251	C₃₁×#125	—	2	1	no	—
252	C₃₁×#125	—	2	1	no	—
253	C₃₁×#125	—	2	1	no	—
254	C₃₁×#125	—	2	1	no	—
255	C₃₁×#125	—	2	1	no	—
256	C₃₁×#125	—	2	1	no	—
257	C₃₁×#125	—	2	1	no	—
258	C₃₁×#125	—	2	1	no	—
259	C₃₁×#125	C₂³	1	1	yes	characteristic
260	C₃₁×#125	C₂³	1	1	yes	characteristic
261	C₃₁×#125	C₂³	1	1	yes	characteristic
262	C₃₁×#125	C₂³	1	1	yes	characteristic
263	C₃₁×#124	—	2	1	no	—
264	C₃₁×#124	—	2	1	no	—
265	C₃₁×#124	—	2	1	no	—
266	C₃₁×#123	—	2	1	no	—
267	C₃₁×#123	—	2	1	no	—
268	C₃₁×#123	—	2	1	no	—
269	C₃₁×#123	—	2	1	no	—
270	C₃₁×#123	—	2	1	no	—
271	C₃₁×#123	—	2	1	no	—
272	C₃₁×#123	—	2	1	no	—
273	C₃₁×#123	—	2	1	no	—
274	C₃₁×#123	—	2	1	no	—
275	C₃₁×#123	—	2	1	no	—
276	C₃₁×#123	—	2	1	no	—
277	C₃₁×#123	—	2	1	no	—
278	C₃₁×#123	—	2	1	no	—
279	C₃₁×#123	—	2	1	no	—
280	C₃₁×#123	—	2	1	no	—
281	C₃₁×#123	—	2	1	no	—
282	C₃₁×#123	—	2	1	no	—
283	C₃₁×#123	—	2	1	no	—
284	C₃₁×#123	D₄	1	1	yes	characteristic
285	C₃₁×#123	D₄	1	1	yes	characteristic
286	C₃₁×C₂²⋊Q₈	—	2	1	no	—
287	C₃₁×C₂²⋊Q₈	—	2	1	no	—
288	C₃₁×C₂²⋊Q₈	—	2	1	no	—
289	C₃₁×C₂²⋊Q₈	—	2	1	no	—
290	C₃₁×C₂²⋊Q₈	—	2	1	no	—
291	C₃₁×C₂²⋊Q₈	—	2	1	no	—
292	C₃₁×C₂²⋊Q₈	—	2	1	no	—
293	C₃₁×C₂²⋊Q₈	—	2	1	no	—
294	C₃₁×C₂²⋊Q₈	—	2	1	no	—
295	C₃₁×C₂²⋊Q₈	—	2	1	no	—
296	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
297	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
298	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
299	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
300	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
301	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
302	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
304	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
307	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
308	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
311	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
312	C₃₁×#121	—	2	1	no	—
313	C₃₁×#121	—	2	1	no	—
314	C₃₁×#121	—	2	1	no	—
315	C₃₁×#121	—	2	1	no	—
316	C₃₁×#121	—	2	1	no	—
317	C₃₁×#121	—	2	1	no	—
318	C₃₁×#121	—	2	1	no	—
319	C₃₁×#121	—	2	1	no	—
320	C₃₁×#121	—	2	1	no	—
321	C₃₁×#121	—	2	1	no	—
322	C₃₁×#121	—	2	1	no	—
323	C₃₁×#121	—	2	1	no	—
324	C₃₁×#121	—	2	1	no	—
325	C₃₁×#121	—	2	1	no	—
326	C₃₁×#121	—	2	1	no	—
327	C₃₁×#121	—	2	1	no	—
328	C₃₁×#121	D₄	1	1	yes	characteristic
329	C₃₁×#121	D₄	1	1	yes	characteristic
330	C₃₁×#121	C₂³	1	1	yes	characteristic
331	C₃₁×#121	C₂³	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×#120	—	2	1	no	—
337	C₃₁×#120	—	2	1	no	—
338	C₃₁×#120	D₄	1	1	yes	characteristic
339	C₃₁×#120	D₄	1	1	yes	characteristic
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	—	2	1	no	—
345	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
347	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
351	C₄×D₄×C₃₁	—	2	1	no	—
352	C₄×D₄×C₃₁	—	2	1	no	—
353	C₄×D₄×C₃₁	—	2	1	no	—
354	C₄×D₄×C₃₁	—	2	1	no	—
355	C₄×D₄×C₃₁	—	2	1	no	—
356	C₄×D₄×C₃₁	—	2	1	no	—
357	C₄×D₄×C₃₁	—	2	1	no	—
358	C₄×D₄×C₃₁	—	2	1	no	—
359	C₄×D₄×C₃₁	—	2	1	no	—
360	C₄×D₄×C₃₁	—	2	1	no	—
361	C₄×D₄×C₃₁	—	2	1	no	—
362	C₄×D₄×C₃₁	—	2	1	no	—
363	C₄×D₄×C₃₁	—	2	1	no	—
364	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
370	C₃₁×#117	—	2	1	no	—
371	C₃₁×#117	—	2	1	no	—
372	C₃₁×#117	—	2	1	no	—
373	C₃₁×#117	—	2	1	no	—
374	C₃₁×#117	—	2	1	no	—
375	C₃₁×#117	—	2	1	no	—
376	C₃₁×#117	—	2	1	no	—
377	C₃₁×#117	—	2	1	no	—
378	C₃₁×#117	—	2	1	no	—
379	C₃₁×#117	—	2	1	no	—
380	C₃₁×#117	C₂³	1	1	yes	characteristic
381	C₃₁×#117	C₂³	1	1	yes	characteristic
382	C₃₁×#117	C₂³	1	1	yes	characteristic
383	C₃₁×#117	C₂³	1	1	yes	characteristic
384	C₃₁×#117	C₂³	1	1	yes	characteristic
385	C₃₁×#117	C₂³	1	1	yes	characteristic
386	C₃₁×#117	C₂³	1	1	yes	characteristic
387	C₃₁×#117	C₂³	1	1	yes	characteristic
388	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×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
399	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
400	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
401	C₂×C₄²×C₃₁	—	2	1	no	—
402	C₃₁×#107	C₂³	1	1	yes	characteristic
403	C₃₁×#107	C₂³	1	1	yes	characteristic
404	C₃₁×#107	C₂³	1	1	yes	characteristic
405	C₃₁×#107	C₂³	1	1	yes	characteristic
406	C₃₁×#107	C₂³	1	1	yes	characteristic
407	C₃₁×#107	C₂³	1	1	yes	characteristic
408	C₃₁×#107	C₂³	1	1	yes	characteristic
409	C₃₁×#107	C₂³	1	1	yes	characteristic
410	C₃₁×#107	C₂³	1	1	yes	characteristic
411	C₃₁×#107	C₂³	1	1	yes	characteristic
412	C₃₁×#107	C₂³	1	1	yes	characteristic
413	C₃₁×#107	C₂³	1	1	yes	characteristic
414	C₃₁×#106	C₂³	1	1	yes	characteristic
415	C₃₁×#106	C₂³	1	1	yes	characteristic
416	C₃₁×#106	C₂³	1	1	yes	characteristic
417	C₃₁×#106	C₂³	1	1	yes	characteristic
418	C₃₁×#106	C₂³	1	1	yes	characteristic
419	C₃₁×#106	C₂³	1	1	yes	characteristic
420	C₃₁×#106	C₂³	1	1	yes	characteristic
421	C₃₁×#106	C₂³	1	1	yes	characteristic
422	C₃₁×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	C₂³	1	1	yes	characteristic
424	C₃₁×#106	C₂³	1	1	yes	characteristic
425	C₃₁×#106	C₂³	1	1	yes	characteristic
426	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×#103	C₂³	1	1	yes	characteristic
431	C₃₁×#103	C₂³	1	1	yes	characteristic
432	C₃₁×#103	C₂³	1	1	yes	characteristic
433	C₃₁×#103	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#102	C₂³	1	1	yes	characteristic
451	C₃₁×#102	C₂³	1	1	yes	characteristic
452	C₃₁×#102	C₂³	1	1	yes	characteristic
453	C₃₁×#102	C₂³	1	1	yes	characteristic
454	C₃₁×#102	C₂³	1	1	yes	characteristic
455	C₃₁×#102	C₂³	1	1	yes	characteristic
456	C₃₁×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×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×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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₃₁×C₂²⋊C₈	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	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
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	#41×C₃₁	—	4	1	no	—
488	#41×C₃₁	—	4	1	no	—
489	C₂×Q₈×C₃₁	—	2	1	no	—
490	C₂×Q₈×C₃₁	—	2	1	no	—
491	C₂×Q₈×C₃₁	—	2	1	no	—
492	C₂×Q₈×C₃₁	—	4	1	no	—
493	C₂×Q₈×C₃₁	—	4	1	no	—
494	C₂×Q₈×C₃₁	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
512	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
517	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
518	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
519	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
532	C₂²×C₄×C₃₁	—	2	1	no	—
533	C₂²×C₄×C₃₁	—	2	1	no	—
534	C₂²×C₄×C₃₁	—	4	1	no	—
535	C₂²×C₄×C₃₁	—	4	1	no	—
536	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
537	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
538	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
539	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
540	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
541	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
542	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
543	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
544	Q₁₆×C₃₁	—	4	1	no	—
545	Q₁₆×C₃₁	—	4	1	no	—
546	Q₁₆×C₃₁	—	4	1	no	—
547	Q₁₆×C₃₁	—	4	1	no	—
548	SD₁₆×C₃₁	—	4	1	no	—
549	SD₁₆×C₃₁	—	4	1	no	—
550	SD₁₆×C₃₁	—	4	1	no	—
551	SD₁₆×C₃₁	—	4	1	no	—
552	M₁₆×C₃₁	—	4	1	no	—
553	M₁₆×C₃₁	—	4	1	no	—
554	M₁₆×C₃₁	—	4	1	no	—
555	M₁₆×C₃₁	—	4	1	no	—
556	C₂×C₈×C₃₁	—	4	1	no	—
557	C₂×C₈×C₃₁	—	4	1	no	—
558	C₂×C₈×C₃₁	—	4	1	no	—
559	C₂×C₈×C₃₁	—	4	1	no	—
560	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
561	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
562	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
563	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
564	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
565	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
566	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
567	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄×C₃₁	C₂⁴	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	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	—	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	—	2	1	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
674	C₄²×C₃₁	—	2	1	no	—
675	C₄²×C₃₁	—	2	1	no	—
676	C₄²×C₃₁	—	2	1	no	—
677	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
678	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
679	#61763	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	—	4	1	no	—
683	C₂³×C₃₁	—	4	1	no	—
684	C₂³×C₃₁	—	4	1	no	—
685	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	—	4	1	no	—
699	Q₈×C₃₁	—	4	2	no	—
700	Q₈×C₃₁	—	8	1	no	—
701	Q₈×C₃₁	—	8	1	no	—
702	D₄×C₃₁	—	2	1	no	—
703	D₄×C₃₁	—	2	1	no	—
704	D₄×C₃₁	—	2	1	no	—
705	D₄×C₃₁	—	2	1	no	—
706	D₄×C₃₁	—	4	1	no	—
707	D₄×C₃₁	—	4	1	no	—
708	D₄×C₃₁	—	4	1	no	—
709	D₄×C₃₁	—	4	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	—	2	1	no	—
745	C₂×C₄×C₃₁	—	2	1	no	—
746	C₂×C₄×C₃₁	—	2	1	no	—
747	C₂×C₄×C₃₁	—	2	1	no	—
748	C₂×C₄×C₃₁	—	2	1	no	—
749	C₂×C₄×C₃₁	—	4	1	no	—
750	C₂×C₄×C₃₁	—	4	1	no	—
751	C₂×C₄×C₃₁	—	4	1	no	—
752	C₂×C₄×C₃₁	—	4	2	no	—
753	C₂×C₄×C₃₁	—	4	2	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	—	8	1	no	—
759	C₂×C₄×C₃₁	—	8	1	no	—
760	C₂×C₄×C₃₁	—	8	1	no	—
761	C₂×C₄×C₃₁	—	8	1	no	—
762	C₂×C₄×C₃₁	—	8	1	no	—
763	C₂×C₄×C₃₁	—	8	1	no	—
764	C₂×C₄×C₃₁	—	8	1	no	—
765	C₂×C₄×C₃₁	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
770	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
771	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
772	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
773	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
774	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
775	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
776	C₈×C₃₁	—	2	1	no	—
777	C₈×C₃₁	—	2	1	no	—
778	C₈×C₃₁	—	2	1	no	—
779	C₈×C₃₁	—	2	1	no	—
780	C₈×C₃₁	—	2	1	no	—
781	C₈×C₃₁	—	2	1	no	—
782	C₈×C₃₁	—	2	1	no	—
783	C₈×C₃₁	—	2	1	no	—
784	#3539	C₂×C₃₁	1	1	yes	characteristic
785	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3351	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3350	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3349	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3346	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3344	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3337	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3336	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3317	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3317	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3241	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3201	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3201	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3196	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
809	#3126	C₂×C₃₁	1	1	yes	characteristic, complemented
810	#3099	C₂×C₃₁	1	1	yes	characteristic, complemented
811	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
812	#3093	C₂×C₃₁	1	1	yes	characteristic, complemented
813	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
814	#2976	C₂×C₃₁	1	1	yes	characteristic, complemented
815	C₂²×C₃₁	—	2	1	no	—
816	C₂²×C₃₁	—	2	1	no	—
817	C₂²×C₃₁	—	2	1	no	—
818	C₂²×C₃₁	—	2	1	no	—
819	C₂²×C₃₁	—	2	1	no	—
820	C₂²×C₃₁	—	2	1	no	—
821	C₂²×C₃₁	—	2	1	no	—
822	C₂²×C₃₁	—	2	1	no	—
823	C₂²×C₃₁	—	2	1	no	—
824	C₂²×C₃₁	—	2	1	no	—
825	C₂²×C₃₁	—	2	1	no	—
826	C₂²×C₃₁	—	2	1	no	—
827	C₂²×C₃₁	—	2	1	no	—
828	C₂²×C₃₁	—	2	1	no	—
829	C₂²×C₃₁	—	2	1	no	—
830	C₂²×C₃₁	—	4	1	no	—
831	C₂²×C₃₁	—	4	1	no	—
832	C₂²×C₃₁	—	4	1	no	—
833	C₂²×C₃₁	—	4	1	no	—
834	C₂²×C₃₁	—	4	1	no	—
835	C₂²×C₃₁	—	4	1	no	—
836	C₂²×C₃₁	—	8	2	no	—
837	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
838	C₄×C₃₁	—	2	1	no	—
839	C₄×C₃₁	—	2	1	no	—
840	C₄×C₃₁	—	2	1	no	—
841	C₄×C₃₁	—	2	1	no	—
842	C₄×C₃₁	—	2	1	no	—
843	C₄×C₃₁	—	2	1	no	—
844	C₄×C₃₁	—	2	1	no	—
845	C₄×C₃₁	—	2	1	no	—
846	C₄×C₃₁	—	2	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	—	4	1	no	—
854	C₄×C₃₁	—	4	1	no	—
855	C₄×C₃₁	—	4	1	no	—
856	C₄×C₃₁	—	4	1	no	—
857	C₄×C₃₁	—	4	1	no	—
858	C₄×C₃₁	—	4	1	no	—
859	C₄×C₃₁	—	4	1	no	—
860	C₄×C₃₁	—	4	1	no	—
861	C₄×C₃₁	#585	1	1	yes	characteristic
862	C₄×C₃₁	#585	1	1	yes	characteristic
863	#560	—	2	1	no	—
864	#560	—	2	1	no	—
865	#556	C₂²×C₃₁	1	1	yes	characteristic
866	#556	C₂²×C₃₁	1	1	yes	characteristic
867	#554	C₂²×C₃₁	1	1	yes	characteristic
868	#554	C₂²×C₃₁	1	1	yes	characteristic
869	#553	—	2	1	no	—
870	#553	—	2	1	no	—
871	#553	C₂²×C₃₁	1	1	yes	characteristic
872	#553	C₂²×C₃₁	1	1	yes	characteristic
873	#552	—	2	1	no	—
874	#552	—	2	1	no	—
875	#552	C₂²×C₃₁	1	1	yes	characteristic
876	#552	C₂²×C₃₁	1	1	yes	characteristic
877	#552	C₂²×C₃₁	1	1	yes	characteristic
878	#552	C₂²×C₃₁	1	1	yes	characteristic
879	#552	C₂²×C₃₁	1	1	yes	characteristic
880	#552	C₂²×C₃₁	1	1	yes	characteristic
881	#551	—	2	1	no	—
882	#551	—	2	1	no	—
883	#550	C₂²×C₃₁	1	1	yes	characteristic
884	#550	C₂²×C₃₁	1	1	yes	characteristic
885	#547	C₂²×C₃₁	1	1	yes	characteristic
886	#547	C₂²×C₃₁	1	1	yes	characteristic
887	#544	C₂²×C₃₁	1	1	yes	characteristic
888	#542	—	2	1	no	—
889	#541	—	2	1	no	—
890	#541	C₂²×C₃₁	1	1	yes	characteristic
891	#540	—	2	1	no	—
892	#540	—	2	1	no	—
893	#540	C₂²×C₃₁	1	1	yes	characteristic
894	#539	—	2	1	no	—
895	#539	—	2	1	no	—
896	#537	C₂²×C₃₁	1	1	yes	characteristic
897	#537	C₂²×C₃₁	1	1	yes	characteristic
898	#536	C₂²×C₃₁	1	1	yes	characteristic
899	#533	—	2	1	no	—
900	#529	—	2	1	no	—
901	#525	C₂²×C₃₁	1	1	yes	characteristic
902	#525	C₂²×C₃₁	1	1	yes	characteristic
903	#525	C₂²×C₃₁	1	1	yes	characteristic
904	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
905	#520	C₂²×C₃₁	1	1	yes	characteristic
906	#519	C₂²×C₃₁	1	1	yes	characteristic
907	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
908	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
909	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
910	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
911	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
912	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
913	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
914	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
916	#485	C₂²×C₃₁	1	1	yes	characteristic
917	#485	C₂²×C₃₁	1	1	yes	characteristic
918	#485	C₂²×C₃₁	1	1	yes	characteristic
919	#485	C₂²×C₃₁	1	1	yes	characteristic
920	#485	C₂²×C₃₁	1	1	yes	characteristic
921	#485	C₂²×C₃₁	1	1	yes	characteristic
922	#485	C₂²×C₃₁	1	1	yes	characteristic
923	#485	C₂²×C₃₁	1	1	yes	characteristic
924	#485	C₂²×C₃₁	1	1	yes	characteristic
925	#485	C₂²×C₃₁	1	1	yes	characteristic
926	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
927	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
928	#484	C₂²×C₃₁	1	1	yes	characteristic
929	#484	C₂²×C₃₁	1	1	yes	characteristic
930	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
931	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
932	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
933	#483	C₂²×C₃₁	1	1	yes	characteristic
934	#483	C₂²×C₃₁	1	1	yes	characteristic
935	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
936	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
937	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
938	#482	C₂²×C₃₁	1	1	yes	characteristic
939	#482	C₂²×C₃₁	1	1	yes	characteristic
940	#482	C₂²×C₃₁	1	1	yes	characteristic
941	#482	C₂²×C₃₁	1	1	yes	characteristic
942	#482	C₂²×C₃₁	1	1	yes	characteristic
943	#482	C₂²×C₃₁	1	1	yes	characteristic
944	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
945	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
946	#481	C₂²×C₃₁	1	1	yes	characteristic
947	#481	C₂²×C₃₁	1	1	yes	characteristic
948	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
949	#480	C₂²×C₃₁	1	1	yes	characteristic
950	#480	C₂²×C₃₁	1	1	yes	characteristic
951	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
952	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
953	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
954	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
955	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
956	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
957	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
958	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
959	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
960	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
961	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
962	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
963	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
964	#470	C₂²×C₃₁	1	1	yes	characteristic
965	#470	C₂²×C₃₁	1	1	yes	characteristic
966	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
967	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
968	#468	C₂²×C₃₁	1	1	yes	characteristic
969	#468	C₂²×C₃₁	1	1	yes	characteristic
970	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
972	#467	C₂²×C₃₁	1	1	yes	characteristic
973	#467	C₂²×C₃₁	1	1	yes	characteristic
974	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
975	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
976	#465	C₂²×C₃₁	1	1	yes	characteristic
977	#465	C₂²×C₃₁	1	1	yes	characteristic
978	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
979	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
980	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
981	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
982	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
983	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
984	#452	C₂²×C₃₁	1	1	yes	characteristic
985	#452	C₂²×C₃₁	1	1	yes	characteristic
986	#452	C₂²×C₃₁	1	1	yes	characteristic
987	#452	C₂²×C₃₁	1	1	yes	characteristic
988	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
989	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
990	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
991	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
992	#451	C₂²×C₃₁	1	1	yes	characteristic
993	#451	C₂²×C₃₁	1	1	yes	characteristic
994	#448	C₂²×C₃₁	1	1	yes	characteristic
995	#448	C₂²×C₃₁	1	1	yes	characteristic
996	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
997	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
998	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
999	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
1000	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1001	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1003	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
1004	#436	C₂²×C₃₁	1	1	yes	characteristic
1005	#436	C₂²×C₃₁	1	1	yes	characteristic
1006	#435	C₂²×C₃₁	1	1	yes	characteristic
1007	#435	C₂²×C₃₁	1	1	yes	characteristic
1008	#435	C₂²×C₃₁	1	1	yes	characteristic
1009	#435	C₂²×C₃₁	1	1	yes	characteristic
1010	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1011	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1012	#433	C₂²×C₃₁	1	1	yes	characteristic
1013	#433	C₂²×C₃₁	1	1	yes	characteristic
1014	#428	C₂²×C₃₁	1	1	yes	characteristic
1015	#428	C₂²×C₃₁	1	1	yes	characteristic
1016	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1017	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1018	#427	C₂²×C₃₁	1	1	yes	characteristic
1019	#427	C₂²×C₃₁	1	1	yes	characteristic
1020	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
1021	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
1022	#417	C₂²×C₃₁	1	1	yes	characteristic
1023	#417	C₂²×C₃₁	1	1	yes	characteristic
1024	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
1025	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
1026	#416	C₂²×C₃₁	1	1	yes	characteristic
1027	#416	C₂²×C₃₁	1	1	yes	characteristic
1028	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
1029	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
1030	#408	C₂²×C₃₁	1	1	yes	characteristic
1031	#408	C₂²×C₃₁	1	1	yes	characteristic
1032	#407	C₂²×C₃₁	1	1	yes	characteristic
1033	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
1034	C₂×C₃₁	—	4	1	no	—
1035	C₂×C₃₁	—	4	1	no	—
1036	C₂×C₃₁	—	4	1	no	—
1037	C₂×C₃₁	—	4	1	no	—
1038	C₂×C₃₁	—	4	1	no	—
1039	C₂×C₃₁	—	8	1	no	—
1040	C₂×C₃₁	—	8	1	no	—
1041	C₂×C₃₁	#3485	1	1	yes	characteristic
1042	C₂×C₃₁	#3584	1	1	yes	characteristic
1043	C₂×C₃₁	#3586	1	1	yes	characteristic
1044	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1045	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1046	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1047	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1048	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1049	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1055	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1059	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1060	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1061	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1062	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1063	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1064	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1065	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1066	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1067	C₄⋊Q₈	—	2	1	no	—
1068	C₄⋊Q₈	—	2	1	no	—
1069	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1070	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1071	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1072	#127	—	2	1	no	—
1073	#127	—	2	1	no	—
1074	#127	C₂³×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1086	#126	—	2	1	no	—
1087	#126	—	2	1	no	—
1088	#126	—	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	C₂³×C₃₁	1	1	yes	characteristic
1101	#125	C₂³×C₃₁	1	1	yes	characteristic
1102	#125	C₂³×C₃₁	1	1	yes	characteristic
1103	#125	C₂³×C₃₁	1	1	yes	characteristic
1104	#124	—	2	1	no	—
1105	#124	—	2	1	no	—
1106	#124	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	—	2	1	no	—
1109	#123	—	2	1	no	—
1110	#123	—	2	1	no	—
1111	#123	—	2	1	no	—
1112	#123	—	2	1	no	—
1113	#123	—	2	1	no	—
1114	#123	—	2	1	no	—
1115	#123	—	2	1	no	—
1116	#123	—	2	1	no	—
1117	#123	—	2	1	no	—
1118	#123	—	2	1	no	—
1119	#123	—	2	1	no	—
1120	#123	—	2	1	no	—
1121	#123	—	2	1	no	—
1122	#123	—	2	1	no	—
1123	#123	—	2	1	no	—
1124	#123	—	2	1	no	—
1125	#123	D₄×C₃₁	1	1	yes	characteristic
1126	#123	D₄×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1134	C₂²⋊Q₈	—	2	1	no	—
1135	C₂²⋊Q₈	—	2	1	no	—
1136	C₂²⋊Q₈	—	2	1	no	—
1137	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1138	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1139	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1140	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1141	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1142	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1143	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1144	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1145	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1146	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1147	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1148	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1149	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1150	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1151	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1152	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1153	#121	—	2	1	no	—
1154	#121	—	2	1	no	—
1155	#121	—	2	1	no	—
1156	#121	—	2	1	no	—
1157	#121	—	2	1	no	—
1158	#121	—	2	1	no	—
1159	#121	—	2	1	no	—
1160	#121	—	2	1	no	—
1161	#121	—	2	1	no	—
1162	#121	—	2	1	no	—
1163	#121	—	2	1	no	—
1164	#121	—	2	1	no	—
1165	#121	—	2	1	no	—
1166	#121	—	2	1	no	—
1167	#121	—	2	1	no	—
1168	#121	—	2	1	no	—
1169	#121	D₄×C₃₁	1	1	yes	characteristic
1170	#121	D₄×C₃₁	1	1	yes	characteristic
1171	#121	C₂³×C₃₁	1	1	yes	characteristic
1172	#121	C₂³×C₃₁	1	1	yes	characteristic
1173	#121	C₂³×C₃₁	1	1	yes	characteristic
1174	#121	C₂³×C₃₁	1	1	yes	characteristic
1175	#121	C₂³×C₃₁	1	1	yes	characteristic
1176	#121	C₂³×C₃₁	1	1	yes	characteristic
1177	#120	—	2	1	no	—
1178	#120	—	2	1	no	—
1179	#120	D₄×C₃₁	1	1	yes	characteristic
1180	#120	D₄×C₃₁	1	1	yes	characteristic
1181	C₄×Q₈	—	2	1	no	—
1182	C₄×Q₈	—	2	1	no	—
1183	C₄×Q₈	—	2	1	no	—
1184	C₄×Q₈	—	2	1	no	—
1185	C₄×Q₈	—	2	1	no	—
1186	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1187	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1188	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1189	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1190	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1191	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1192	C₄×D₄	—	2	1	no	—
1193	C₄×D₄	—	2	1	no	—
1194	C₄×D₄	—	2	1	no	—
1195	C₄×D₄	—	2	1	no	—
1196	C₄×D₄	—	2	1	no	—
1197	C₄×D₄	—	2	1	no	—
1198	C₄×D₄	—	2	1	no	—
1199	C₄×D₄	—	2	1	no	—
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	C₂³×C₃₁	1	1	yes	characteristic
1206	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1207	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1208	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1209	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1210	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1211	#117	—	2	1	no	—
1212	#117	—	2	1	no	—
1213	#117	—	2	1	no	—
1214	#117	—	2	1	no	—
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	C₂³×C₃₁	1	1	yes	characteristic
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	#117	C₂³×C₃₁	1	1	yes	characteristic
1227	#117	C₂³×C₃₁	1	1	yes	characteristic
1228	#117	C₂³×C₃₁	1	1	yes	characteristic
1229	#117	C₂³×C₃₁	1	1	yes	characteristic
1230	C₂×C₄⋊C₄	—	2	1	no	—
1231	C₂×C₄⋊C₄	—	2	1	no	—
1232	C₂×C₄⋊C₄	—	2	1	no	—
1233	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1234	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1235	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1236	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1237	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1238	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1239	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1240	C₂×C₂²⋊C₄	—	2	1	no	—
1241	C₂×C₂²⋊C₄	—	2	1	no	—
1242	C₂×C₄²	—	2	1	no	—
1243	#107	C₂³×C₃₁	1	1	yes	characteristic
1244	#107	C₂³×C₃₁	1	1	yes	characteristic
1245	#107	C₂³×C₃₁	1	1	yes	characteristic
1246	#107	C₂³×C₃₁	1	1	yes	characteristic
1247	#107	C₂³×C₃₁	1	1	yes	characteristic
1248	#107	C₂³×C₃₁	1	1	yes	characteristic
1249	#107	C₂³×C₃₁	1	1	yes	characteristic
1250	#107	C₂³×C₃₁	1	1	yes	characteristic
1251	#107	C₂³×C₃₁	1	1	yes	characteristic
1252	#107	C₂³×C₃₁	1	1	yes	characteristic
1253	#107	C₂³×C₃₁	1	1	yes	characteristic
1254	#107	C₂³×C₃₁	1	1	yes	characteristic
1255	#106	C₂³×C₃₁	1	1	yes	characteristic
1256	#106	C₂³×C₃₁	1	1	yes	characteristic
1257	#106	C₂³×C₃₁	1	1	yes	characteristic
1258	#106	C₂³×C₃₁	1	1	yes	characteristic
1259	#106	C₂³×C₃₁	1	1	yes	characteristic
1260	#106	C₂³×C₃₁	1	1	yes	characteristic
1261	#106	C₂³×C₃₁	1	1	yes	characteristic
1262	#106	C₂³×C₃₁	1	1	yes	characteristic
1263	#106	C₂³×C₃₁	1	1	yes	characteristic
1264	#106	C₂³×C₃₁	1	1	yes	characteristic
1265	#106	C₂³×C₃₁	1	1	yes	characteristic
1266	#106	C₂³×C₃₁	1	1	yes	characteristic
1267	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1268	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1269	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1270	C₄⋊C₈	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	#103	C₂³×C₃₁	1	1	yes	characteristic
1277	#103	C₂³×C₃₁	1	1	yes	characteristic
1278	#103	C₂³×C₃₁	1	1	yes	characteristic
1279	#103	C₂³×C₃₁	1	1	yes	characteristic
1280	#103	C₂³×C₃₁	1	1	yes	characteristic
1281	#103	C₂³×C₃₁	1	1	yes	characteristic
1282	#103	C₂³×C₃₁	1	1	yes	characteristic
1283	#103	C₂³×C₃₁	1	1	yes	characteristic
1284	#103	C₂³×C₃₁	1	1	yes	characteristic
1285	#103	C₂³×C₃₁	1	1	yes	characteristic
1286	#103	C₂³×C₃₁	1	1	yes	characteristic
1287	#103	C₂³×C₃₁	1	1	yes	characteristic
1288	#103	C₂³×C₃₁	1	1	yes	characteristic
1289	#103	C₂³×C₃₁	1	1	yes	characteristic
1290	#103	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	#102	C₂³×C₃₁	1	1	yes	characteristic
1295	#102	C₂³×C₃₁	1	1	yes	characteristic
1296	#102	C₂³×C₃₁	1	1	yes	characteristic
1297	#102	C₂³×C₃₁	1	1	yes	characteristic
1298	#102	C₂³×C₃₁	1	1	yes	characteristic
1299	#102	C₂³×C₃₁	1	1	yes	characteristic
1300	#102	C₂³×C₃₁	1	1	yes	characteristic
1301	#102	C₂³×C₃₁	1	1	yes	characteristic
1302	#102	C₂³×C₃₁	1	1	yes	characteristic
1303	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1304	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1305	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1306	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1307	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1308	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1309	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1310	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1311	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1312	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1313	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1314	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1315	#97	C₂³×C₃₁	1	1	yes	characteristic
1316	#97	C₂³×C₃₁	1	1	yes	characteristic
1317	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1318	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1319	C₃₁	#61763	1	1	yes	characteristic, direct product factor, Sylow
1320	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
1321	#41	—	4	1	no	—
1322	#41	—	4	1	no	—
1323	#41	—	4	1	no	—
1324	#41	—	4	1	no	—
1325	#41	—	4	1	no	—
1326	#41	—	4	1	no	—
1327	#41	—	4	1	no	—
1328	#41	—	4	1	no	—
1329	#41	—	4	1	no	—
1330	#41	—	4	1	no	—
1331	C₂×Q₈	—	2	1	no	—
1332	C₂×Q₈	—	2	1	no	—
1333	C₂×Q₈	—	2	1	no	—
1334	C₂×Q₈	—	4	1	no	—
1335	C₂×Q₈	—	4	1	no	—
1336	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1337	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1338	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1339	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1340	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1341	C₂×D₄	—	2	1	no	—
1342	C₂×D₄	—	2	1	no	—
1343	C₂×D₄	—	2	1	no	—
1344	C₂×D₄	—	2	1	no	—
1345	C₂×D₄	—	2	1	no	—
1346	C₂×D₄	—	2	1	no	—
1347	C₂×D₄	—	2	1	no	—
1348	C₂×D₄	—	2	1	no	—
1349	C₂×D₄	—	2	1	no	—
1350	C₂×D₄	—	2	1	no	—
1351	C₂×D₄	—	2	1	no	—
1352	C₂×D₄	—	2	1	no	—
1353	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1354	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1355	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1356	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1357	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1358	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1359	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1360	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1361	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1362	C₂²×C₄	—	2	1	no	—
1363	C₂²×C₄	—	2	1	no	—
1364	C₂²×C₄	—	2	1	no	—
1365	C₂²×C₄	—	2	1	no	—
1366	C₂²×C₄	—	2	1	no	—
1367	C₂²×C₄	—	2	1	no	—
1368	C₂²×C₄	—	2	1	no	—
1369	C₂²×C₄	—	2	1	no	—
1370	C₂²×C₄	—	2	1	no	—
1371	C₂²×C₄	—	2	1	no	—
1372	C₂²×C₄	—	2	1	no	—
1373	C₂²×C₄	—	2	1	no	—
1374	C₂²×C₄	—	2	1	no	—
1375	C₂²×C₄	—	2	1	no	—
1376	C₂²×C₄	—	4	1	no	—
1377	C₂²×C₄	—	4	1	no	—
1378	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1379	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1380	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1381	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1382	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1383	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1384	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1385	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1386	Q₁₆	—	4	1	no	—
1387	Q₁₆	—	4	1	no	—
1388	Q₁₆	—	4	1	no	—
1389	Q₁₆	—	4	1	no	—
1390	SD₁₆	—	4	1	no	—
1391	SD₁₆	—	4	1	no	—
1392	SD₁₆	—	4	1	no	—
1393	SD₁₆	—	4	1	no	—
1394	M₁₆	—	4	1	no	—
1395	M₁₆	—	4	1	no	—
1396	M₁₆	—	4	1	no	—
1397	M₁₆	—	4	1	no	—
1398	C₂×C₈	—	4	1	no	—
1399	C₂×C₈	—	4	1	no	—
1400	C₂×C₈	—	4	1	no	—
1401	C₂×C₈	—	4	1	no	—
1402	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1403	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1404	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1405	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1406	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1407	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1408	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1409	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	—	2	1	no	—
1448	C₄⋊C₄	—	2	1	no	—
1449	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1450	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1451	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1452	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1453	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1454	C₄⋊C₄	C₂×D₄×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	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1459	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1460	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1461	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1462	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1463	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1464	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1486	C₂²⋊C₄	—	2	1	no	—
1487	C₂²⋊C₄	—	2	1	no	—
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1496	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1497	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1498	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1499	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1500	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1501	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1502	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1503	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1504	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1505	C₄²	—	2	1	no	—
1506	C₄²	—	2	1	no	—
1507	C₄²	—	2	1	no	—
1508	C₄²	—	2	1	no	—
1509	C₄²	—	2	1	no	—
1510	C₄²	—	2	1	no	—
1511	C₄²	—	2	1	no	—
1512	C₄²	—	2	1	no	—
1513	C₄²	—	2	1	no	—
1514	C₄²	—	2	1	no	—
1515	C₄²	—	2	1	no	—
1516	C₄²	—	2	1	no	—
1517	C₄²	—	2	1	no	—
1518	C₄²	—	2	1	no	—
1519	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1520	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1521	C₂³	—	2	1	no	—
1522	C₂³	—	2	1	no	—
1523	C₂³	—	4	1	no	—
1524	C₂³	—	4	1	no	—
1525	C₂³	—	4	1	no	—
1526	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1527	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1528	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1529	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1530	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1531	Q₈	—	2	1	no	—
1532	Q₈	—	2	1	no	—
1533	Q₈	—	2	1	no	—
1534	Q₈	—	2	1	no	—
1535	Q₈	—	2	1	no	—
1536	Q₈	—	2	1	no	—
1537	Q₈	—	2	1	no	—
1538	Q₈	—	2	1	no	—
1539	Q₈	—	4	1	no	—
1540	Q₈	—	4	2	no	—
1541	Q₈	—	8	1	no	—
1542	Q₈	—	8	1	no	—
1543	D₄	—	2	1	no	—
1544	D₄	—	2	1	no	—
1545	D₄	—	2	1	no	—
1546	D₄	—	2	1	no	—
1547	D₄	—	4	1	no	—
1548	D₄	—	4	1	no	—
1549	D₄	—	4	1	no	—
1550	D₄	—	4	1	no	—
1551	D₄	—	4	1	no	—
1552	D₄	—	4	1	no	—
1553	D₄	—	4	1	no	—
1554	D₄	—	8	1	no	—
1555	D₄	—	8	1	no	—
1556	D₄	—	8	1	no	—
1557	D₄	—	8	1	no	—
1558	D₄	—	8	1	no	—
1559	D₄	—	8	1	no	—
1560	D₄	—	8	1	no	—
1561	D₄	—	8	1	no	—
1562	D₄	—	8	1	no	—
1563	D₄	—	8	1	no	—
1564	D₄	—	8	1	no	—
1565	D₄	—	8	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	—	2	1	no	—
1577	C₂×C₄	—	2	1	no	—
1578	C₂×C₄	—	2	1	no	—
1579	C₂×C₄	—	2	1	no	—
1580	C₂×C₄	—	2	1	no	—
1581	C₂×C₄	—	2	1	no	—
1582	C₂×C₄	—	2	1	no	—
1583	C₂×C₄	—	2	1	no	—
1584	C₂×C₄	—	2	1	no	—
1585	C₂×C₄	—	2	1	no	—
1586	C₂×C₄	—	2	1	no	—
1587	C₂×C₄	—	2	1	no	—
1588	C₂×C₄	—	2	1	no	—
1589	C₂×C₄	—	2	1	no	—
1590	C₂×C₄	—	4	1	no	—
1591	C₂×C₄	—	4	1	no	—
1592	C₂×C₄	—	4	1	no	—
1593	C₂×C₄	—	4	2	no	—
1594	C₂×C₄	—	4	2	no	—
1595	C₂×C₄	—	8	1	no	—
1596	C₂×C₄	—	8	1	no	—
1597	C₂×C₄	—	8	1	no	—
1598	C₂×C₄	—	8	1	no	—
1599	C₂×C₄	—	8	1	no	—
1600	C₂×C₄	—	8	1	no	—
1601	C₂×C₄	—	8	1	no	—
1602	C₂×C₄	—	8	1	no	—
1603	C₂×C₄	—	8	1	no	—
1604	C₂×C₄	—	8	1	no	—
1605	C₂×C₄	—	8	1	no	—
1606	C₂×C₄	—	8	1	no	—
1607	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1608	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1609	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1610	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1611	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1612	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1613	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1614	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1615	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1616	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1617	C₈	—	2	1	no	—
1618	C₈	—	2	1	no	—
1619	C₈	—	2	1	no	—
1620	C₈	—	2	1	no	—
1621	C₈	—	2	1	no	—
1622	C₈	—	2	1	no	—
1623	C₈	—	2	1	no	—
1624	C₈	—	2	1	no	—
1625	C₂²	—	2	1	no	—
1626	C₂²	—	2	1	no	—
1627	C₂²	—	2	1	no	—
1628	C₂²	—	2	1	no	—
1629	C₂²	—	2	1	no	—
1630	C₂²	—	2	1	no	—
1631	C₂²	—	2	1	no	—
1632	C₂²	—	2	1	no	—
1633	C₂²	—	2	1	no	—
1634	C₂²	—	2	1	no	—
1635	C₂²	—	2	1	no	—
1636	C₂²	—	2	1	no	—
1637	C₂²	—	2	1	no	—
1638	C₂²	—	2	1	no	—
1639	C₂²	—	2	1	no	—
1640	C₂²	—	4	1	no	—
1641	C₂²	—	4	1	no	—
1642	C₂²	—	4	1	no	—
1643	C₂²	—	4	1	no	—
1644	C₂²	—	4	1	no	—
1645	C₂²	—	4	1	no	—
1646	C₂²	—	8	2	no	—
1647	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1648	C₄	—	2	1	no	—
1649	C₄	—	2	1	no	—
1650	C₄	—	2	1	no	—
1651	C₄	—	2	1	no	—
1652	C₄	—	2	1	no	—
1653	C₄	—	2	1	no	—
1654	C₄	—	2	1	no	—
1655	C₄	—	2	1	no	—
1656	C₄	—	2	1	no	—
1657	C₄	—	4	1	no	—
1658	C₄	—	4	1	no	—
1659	C₄	—	4	1	no	—
1660	C₄	—	4	1	no	—
1661	C₄	—	4	1	no	—
1662	C₄	—	4	1	no	—
1663	C₄	—	4	1	no	—
1664	C₄	—	4	1	no	—
1665	C₄	—	4	1	no	—
1666	C₄	—	4	1	no	—
1667	C₄	—	4	1	no	—
1668	C₄	—	4	1	no	—
1669	C₄	—	4	1	no	—
1670	C₄	—	4	1	no	—
1671	C₄	C₃₁×#585	1	1	yes	characteristic
1672	C₄	C₃₁×#585	1	1	yes	characteristic
1673	C₂	—	4	1	no	—
1674	C₂	—	4	1	no	—
1675	C₂	—	4	1	no	—
1676	C₂	—	4	1	no	—
1677	C₂	—	4	1	no	—
1678	C₂	—	8	1	no	—
1679	C₂	—	8	1	no	—
1680	C₂	C₃₁×#3485	1	1	yes	characteristic
1681	C₂	C₃₁×#3584	1	1	yes	characteristic
1682	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×#3539	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3495	C₂	semidirect
3. C₃₁×#3352	C₂	semidirect
4. C₃₁×#3351	C₂	semidirect
5. C₃₁×#3350	C₂	semidirect
6. C₃₁×#3349	C₂	semidirect
7. C₃₁×#3346	C₂	semidirect
8. C₃₁×#3344	C₂	semidirect
9. C₃₁×#3337	C₂	semidirect
10. C₃₁×#3336	C₂	semidirect
11. C₃₁×#3333	C₂	semidirect
12. C₃₁×#3331	C₂	semidirect
13. C₃₁×#3317	C₂	semidirect
14. C₃₁×#3317	C₂	semidirect
15. C₃₁×#3315	C₂	semidirect
16. C₃₁×#3315	C₂	semidirect
17. C₃₁×#3304	C₂	semidirect
18. C₃₁×#3302	C₂	semidirect
19. C₃₁×#3242	C₂	semidirect
20. C₃₁×#3241	C₂	semidirect
21. C₃₁×#3201	C₂	semidirect
22. C₃₁×#3201	C₂	semidirect
23. C₃₁×#3196	C₂	semidirect
24. C₃₁×#3190	C₂	semidirect
25. C₃₁×#3127	C₂	semidirect
26. C₃₁×#3126	C₂	semidirect
27. C₃₁×#3099	C₂	semidirect
28. C₃₁×#3098	C₂	semidirect
29. C₃₁×#3093	C₂	semidirect
30. C₃₁×#3091	C₂	semidirect
31. C₃₁×#2976	C₂	semidirect
77. C₃₁×#501	C₂²	semidirect
78. C₃₁×#501	C₂²	semidirect
79. C₃₁×#499	C₂²	semidirect
80. C₃₁×#499	C₂²	semidirect
81. C₃₁×#491	C₂²	semidirect
82. C₃₁×#490	C₂²	semidirect
83. C₃₁×#487	C₂²	semidirect
84. C₃₁×#486	C₂²	semidirect
95. C₃₁×#485	C₂²	semidirect
96. C₃₁×#485	C₂²	semidirect
99. C₃₁×#484	C₂²	semidirect
100. C₃₁×#484	C₂²	semidirect
101. C₃₁×#484	C₂²	semidirect
104. C₃₁×#483	C₂²	semidirect
105. C₃₁×#483	C₂²	semidirect
106. C₃₁×#483	C₂²	semidirect
113. C₃₁×#482	C₂²	semidirect
114. C₃₁×#482	C₂²	semidirect
117. C₃₁×#481	C₂²	semidirect
120. C₃₁×#480	C₂²	semidirect
121. C₃₁×#479	C₂²	semidirect
122. C₃₁×#479	C₂²	semidirect
123. C₃₁×#479	C₂²	semidirect
124. C₃₁×#479	C₂²	semidirect
125. C₃₁×#479	C₂²	semidirect
126. C₃₁×#479	C₂²	semidirect
127. C₃₁×#478	C₂²	semidirect
128. C₃₁×#478	C₂²	semidirect
129. C₃₁×#477	C₂²	semidirect
130. C₃₁×#476	C₂²	semidirect
131. C₃₁×#475	C₂²	semidirect
132. C₃₁×#474	C₂²	semidirect
135. C₃₁×#470	C₂²	semidirect
136. C₃₁×#470	C₂²	semidirect
139. C₃₁×#468	C₂²	semidirect
140. C₃₁×#468	C₂²	semidirect
143. C₃₁×#467	C₂²	semidirect
144. C₃₁×#467	C₂²	semidirect
147. C₃₁×#465	C₂²	semidirect
148. C₃₁×#465	C₂²	semidirect
149. C₃₁×#462	C₂²	semidirect
150. C₃₁×#462	C₂²	semidirect
151. C₃₁×#460	C₂²	semidirect
152. C₃₁×#460	C₂²	semidirect
157. C₃₁×#452	C₂²	semidirect
158. C₃₁×#452	C₂²	semidirect
159. C₃₁×#452	C₂²	semidirect
160. C₃₁×#452	C₂²	semidirect
165. C₃₁×#441	C₂²	semidirect
166. C₃₁×#441	C₂²	semidirect
167. C₃₁×#440	C₂²	semidirect
168. C₃₁×#440	C₂²	semidirect
169. C₄×Q₁₆×C₃₁	C₂²	semidirect
170. C₄×Q₁₆×C₃₁	C₂²	semidirect
171. C₄×SD₁₆×C₃₁	C₂²	semidirect
172. C₄×SD₁₆×C₃₁	C₂²	semidirect
185. C₃₁×#428	C₂²	semidirect
186. C₃₁×#428	C₂²	semidirect
189. C₂×C₃₁×#107	C₂²	semidirect
190. C₂×C₃₁×#106	C₂²	semidirect
193. C₃₁×#417	C₂²	semidirect
194. C₃₁×#417	C₂²	semidirect
197. C₃₁×#416	C₂²	semidirect
198. C₃₁×#416	C₂²	semidirect
679. #61763	C₃₁	direct (N × H)
785. #3495	C₂×C₃₁	semidirect
786. #3352	C₂×C₃₁	semidirect
787. #3351	C₂×C₃₁	semidirect
788. #3350	C₂×C₃₁	semidirect
789. #3349	C₂×C₃₁	semidirect
790. #3346	C₂×C₃₁	semidirect
791. #3344	C₂×C₃₁	semidirect
792. #3337	C₂×C₃₁	semidirect
793. #3336	C₂×C₃₁	semidirect
794. #3333	C₂×C₃₁	semidirect
795. #3331	C₂×C₃₁	semidirect
796. #3317	C₂×C₃₁	semidirect
797. #3317	C₂×C₃₁	semidirect
798. #3315	C₂×C₃₁	semidirect
799. #3315	C₂×C₃₁	semidirect
800. #3304	C₂×C₃₁	semidirect
801. #3302	C₂×C₃₁	semidirect
802. #3242	C₂×C₃₁	semidirect
803. #3241	C₂×C₃₁	semidirect
804. #3201	C₂×C₃₁	semidirect
805. #3201	C₂×C₃₁	semidirect
806. #3196	C₂×C₃₁	semidirect
807. #3190	C₂×C₃₁	semidirect
808. #3127	C₂×C₃₁	semidirect
809. #3126	C₂×C₃₁	semidirect
810. #3099	C₂×C₃₁	semidirect
811. #3098	C₂×C₃₁	semidirect
812. #3093	C₂×C₃₁	semidirect
813. #3091	C₂×C₃₁	semidirect
814. #2976	C₂×C₃₁	semidirect
908. #501	C₂²×C₃₁	semidirect
909. #501	C₂²×C₃₁	semidirect
910. #499	C₂²×C₃₁	semidirect
911. #499	C₂²×C₃₁	semidirect
912. #491	C₂²×C₃₁	semidirect
913. #490	C₂²×C₃₁	semidirect
914. #487	C₂²×C₃₁	semidirect
915. #486	C₂²×C₃₁	semidirect
926. #485	C₂²×C₃₁	semidirect
927. #485	C₂²×C₃₁	semidirect
930. #484	C₂²×C₃₁	semidirect
931. #484	C₂²×C₃₁	semidirect
932. #484	C₂²×C₃₁	semidirect
935. #483	C₂²×C₃₁	semidirect
936. #483	C₂²×C₃₁	semidirect
937. #483	C₂²×C₃₁	semidirect
944. #482	C₂²×C₃₁	semidirect
945. #482	C₂²×C₃₁	semidirect
948. #481	C₂²×C₃₁	semidirect
951. #480	C₂²×C₃₁	semidirect
952. #479	C₂²×C₃₁	semidirect
953. #479	C₂²×C₃₁	semidirect
954. #479	C₂²×C₃₁	semidirect
955. #479	C₂²×C₃₁	semidirect
956. #479	C₂²×C₃₁	semidirect
957. #479	C₂²×C₃₁	semidirect
958. #478	C₂²×C₃₁	semidirect
959. #478	C₂²×C₃₁	semidirect
960. #477	C₂²×C₃₁	semidirect
961. #476	C₂²×C₃₁	semidirect
962. #475	C₂²×C₃₁	semidirect
963. #474	C₂²×C₃₁	semidirect
966. #470	C₂²×C₃₁	semidirect
967. #470	C₂²×C₃₁	semidirect
970. #468	C₂²×C₃₁	semidirect
971. #468	C₂²×C₃₁	semidirect
974. #467	C₂²×C₃₁	semidirect
975. #467	C₂²×C₃₁	semidirect
978. #465	C₂²×C₃₁	semidirect
979. #465	C₂²×C₃₁	semidirect
980. #462	C₂²×C₃₁	semidirect
981. #462	C₂²×C₃₁	semidirect
982. #460	C₂²×C₃₁	semidirect
983. #460	C₂²×C₃₁	semidirect
988. #452	C₂²×C₃₁	semidirect
989. #452	C₂²×C₃₁	semidirect
990. #452	C₂²×C₃₁	semidirect
991. #452	C₂²×C₃₁	semidirect
996. #441	C₂²×C₃₁	semidirect
997. #441	C₂²×C₃₁	semidirect
998. #440	C₂²×C₃₁	semidirect
999. #440	C₂²×C₃₁	semidirect
1000. C₄×Q₁₆	C₂²×C₃₁	semidirect
1001. C₄×Q₁₆	C₂²×C₃₁	semidirect
1002. C₄×SD₁₆	C₂²×C₃₁	semidirect
1003. C₄×SD₁₆	C₂²×C₃₁	semidirect
1016. #428	C₂²×C₃₁	semidirect
1017. #428	C₂²×C₃₁	semidirect
1020. C₂×#107	C₂²×C₃₁	semidirect
1021. C₂×#106	C₂²×C₃₁	semidirect
1024. #417	C₂²×C₃₁	semidirect
1025. #417	C₂²×C₃₁	semidirect
1028. #416	C₂²×C₃₁	semidirect
1029. #416	C₂²×C₃₁	semidirect
1319. C₃₁	#61763	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×#3539	2
C₃₁×#3495	2
C₃₁×#3352	2
C₃₁×#3351	2
C₃₁×#3350	2
C₃₁×#3349	2
C₃₁×#3346	2
C₃₁×#3344	2
C₃₁×#3337	2
C₃₁×#3336	2
C₃₁×#3333	2
C₃₁×#3331	2
C₃₁×#3317	2
C₃₁×#3315	2
C₃₁×#3304	2
C₃₁×#3302	2
C₃₁×#3242	2
C₃₁×#3241	2
C₃₁×#3201	2
C₃₁×#3196	2
C₃₁×#3190	2
C₃₁×#3127	2
C₃₁×#3126	2
C₃₁×#3099	2
C₃₁×#3098	2
C₃₁×#3093	2
C₃₁×#3091	2
C₃₁×#2976	2
#61763	31

Subgroups — C31×#61763 #21518522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61763 #21518522