Subgroups — C₃₁×#61862 #21518621

Order 7936.

1614 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3388	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3377	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3377	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3376	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3376	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3244	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3243	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3125	C₂	1	1	yes	maximal, characteristic
26	C₃₁×#3124	C₂	1	1	yes	maximal, characteristic
27	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3111	C₂	1	1	yes	maximal, characteristic
30	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#563	—	2	1	no	—
33	C₃₁×#563	—	2	1	no	—
34	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#557	C₂²	1	1	yes	characteristic
36	C₃₁×#557	C₂²	1	1	yes	characteristic
37	C₃₁×#557	C₂²	1	1	yes	characteristic
38	C₃₁×#557	C₂²	1	1	yes	characteristic
39	C₃₁×#557	C₂²	1	1	yes	characteristic
40	C₃₁×#557	C₂²	1	1	yes	characteristic
41	C₃₁×#557	C₂²	1	1	yes	characteristic
42	C₃₁×#556	—	2	1	no	—
43	C₃₁×#556	C₂²	1	1	yes	characteristic
44	C₃₁×#556	C₂²	1	1	yes	characteristic
45	C₃₁×#556	C₂²	1	1	yes	characteristic
46	C₃₁×#554	—	2	1	no	—
47	C₃₁×#554	—	2	1	no	—
48	C₃₁×#554	—	2	1	no	—
49	C₃₁×#554	—	2	1	no	—
50	C₃₁×#554	C₂²	1	1	yes	characteristic
51	C₃₁×#554	C₂²	1	1	yes	characteristic
52	C₃₁×#554	C₂²	1	1	yes	characteristic
53	C₃₁×#554	C₂²	1	1	yes	characteristic
54	C₃₁×#554	C₂²	1	1	yes	characteristic
55	C₃₁×#552	—	2	1	no	—
56	C₃₁×#544	—	2	1	no	—
57	C₃₁×#544	—	2	1	no	—
58	C₃₁×#544	—	2	1	no	—
59	C₃₁×#544	C₂²	1	1	yes	characteristic
60	C₃₁×#544	C₂²	1	1	yes	characteristic
61	C₃₁×#542	C₂²	1	1	yes	characteristic
62	C₃₁×#542	C₂²	1	1	yes	characteristic
63	C₃₁×#541	—	2	1	no	—
64	C₃₁×#541	—	2	1	no	—
65	C₃₁×#541	—	2	1	no	—
66	C₃₁×#541	C₂²	1	1	yes	characteristic
67	C₃₁×#541	C₂²	1	1	yes	characteristic
68	C₃₁×#533	—	2	1	no	—
69	C₃₁×#533	C₂²	1	1	yes	characteristic
70	C₃₁×#533	C₂²	1	1	yes	characteristic
71	C₃₁×#529	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×#125	—	2	1	no	—
73	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#520	C₂²	1	1	yes	characteristic
76	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#501	C₂²	1	1	yes	characteristic
78	C₃₁×#501	C₂²	1	1	yes	characteristic
79	C₃₁×#501	C₂²	1	1	yes	characteristic
80	C₃₁×#501	C₂²	1	1	yes	characteristic
81	C₃₁×#501	C₂²	1	1	yes	characteristic
82	C₃₁×#501	C₂²	1	1	yes	characteristic
83	C₃₁×#500	C₂²	1	1	yes	characteristic
84	C₃₁×#499	C₂²	1	1	yes	characteristic
85	C₃₁×#499	C₂²	1	1	yes	characteristic
86	C₃₁×#499	C₂²	1	1	yes	characteristic
87	C₃₁×#499	C₂²	1	1	yes	characteristic
88	C₃₁×#498	C₂²	1	1	yes	characteristic
89	C₃₁×#491	C₂²	1	1	yes	characteristic
90	C₃₁×#491	C₂²	1	1	yes	characteristic
91	C₃₁×#491	C₂²	1	1	yes	characteristic
92	C₃₁×#491	C₂²	1	1	yes	characteristic
93	C₃₁×#489	C₂²	1	1	yes	characteristic
94	C₃₁×#489	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×#487	C₂²	1	1	yes	characteristic
100	C₃₁×#487	C₂²	1	1	yes	characteristic
101	C₃₁×#485	C₂²	1	1	yes	characteristic
102	C₃₁×#485	C₂²	1	1	yes	characteristic
103	C₃₁×#485	C₂²	1	1	yes	characteristic
104	C₃₁×#484	C₂²	1	1	yes	characteristic
105	C₃₁×#484	C₂²	1	1	yes	characteristic
106	C₃₁×#484	C₂²	1	1	yes	characteristic
107	C₃₁×#483	C₂²	1	1	yes	characteristic
108	C₃₁×#483	C₂²	1	1	yes	characteristic
109	C₃₁×#483	C₂²	1	1	yes	characteristic
110	C₃₁×#482	C₂²	1	1	yes	characteristic
111	C₃₁×#481	C₂²	1	1	yes	characteristic
112	C₃₁×#480	C₂²	1	1	yes	characteristic
113	C₃₁×#479	C₂²	1	1	yes	characteristic
114	C₃₁×#479	C₂²	1	1	yes	characteristic
115	C₃₁×#479	C₂²	1	1	yes	characteristic
116	C₃₁×#479	C₂²	1	1	yes	characteristic
117	C₃₁×#479	C₂²	1	1	yes	characteristic
118	C₃₁×#479	C₂²	1	1	yes	characteristic
119	C₃₁×#479	C₂²	1	1	yes	characteristic
120	C₃₁×#479	C₂²	1	1	yes	characteristic
121	C₃₁×#479	C₂²	1	1	yes	characteristic
122	C₃₁×#479	C₂²	1	1	yes	characteristic
123	C₃₁×#479	C₂²	1	1	yes	characteristic
124	C₃₁×#479	C₂²	1	1	yes	characteristic
125	C₃₁×#479	C₂²	1	1	yes	characteristic
126	C₃₁×#479	C₂²	1	1	yes	characteristic
127	C₃₁×#479	C₂²	1	1	yes	characteristic
128	C₃₁×#478	C₂²	1	1	yes	characteristic
129	C₃₁×#478	C₂²	1	1	yes	characteristic
130	C₃₁×#478	C₂²	1	1	yes	characteristic
131	C₃₁×#478	C₂²	1	1	yes	characteristic
132	C₃₁×#478	C₂²	1	1	yes	characteristic
133	C₃₁×#478	C₂²	1	1	yes	characteristic
134	C₃₁×#478	C₂²	1	1	yes	characteristic
135	C₃₁×#477	C₂²	1	1	yes	characteristic
136	C₃₁×#477	C₂²	1	1	yes	characteristic
137	C₃₁×#477	C₂²	1	1	yes	characteristic
138	C₃₁×#477	C₂²	1	1	yes	characteristic
139	C₃₁×#476	C₂²	1	1	yes	characteristic
140	C₃₁×#476	C₂²	1	1	yes	characteristic
141	C₃₁×#475	C₂²	1	1	yes	characteristic
142	C₃₁×#475	C₂²	1	1	yes	characteristic
143	C₃₁×#475	C₂²	1	1	yes	characteristic
144	C₃₁×#475	C₂²	1	1	yes	characteristic
145	C₃₁×#475	C₂²	1	1	yes	characteristic
146	C₃₁×#474	C₂²	1	1	yes	characteristic
147	C₃₁×#474	C₂²	1	1	yes	characteristic
148	C₃₁×#474	C₂²	1	1	yes	characteristic
149	C₃₁×#464	C₂²	1	1	yes	characteristic
150	C₃₁×#464	C₂²	1	1	yes	characteristic
151	C₃₁×#464	C₂²	1	1	yes	characteristic
152	C₃₁×#463	C₂²	1	1	yes	characteristic
153	C₃₁×#463	C₂²	1	1	yes	characteristic
154	C₃₁×#463	C₂²	1	1	yes	characteristic
155	C₃₁×#462	C₂²	1	1	yes	characteristic
156	C₃₁×#462	C₂²	1	1	yes	characteristic
157	C₃₁×#462	C₂²	1	1	yes	characteristic
158	C₃₁×#461	C₂²	1	1	yes	characteristic
159	C₃₁×#461	C₂²	1	1	yes	characteristic
160	C₃₁×#461	C₂²	1	1	yes	characteristic
161	C₃₁×#452	C₂²	1	1	yes	characteristic
162	C₃₁×#452	C₂²	1	1	yes	characteristic
163	C₃₁×#452	C₂²	1	1	yes	characteristic
164	C₃₁×#449	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic
166	C₃₁×#446	C₂²	1	1	yes	characteristic
167	C₃₁×#446	C₂²	1	1	yes	characteristic
168	C₃₁×#446	C₂²	1	1	yes	characteristic
169	C₃₁×#446	C₂²	1	1	yes	characteristic
170	C₃₁×#446	C₂²	1	1	yes	characteristic
171	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
172	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
173	C₃₁×#442	C₂²	1	1	yes	characteristic
174	C₃₁×#442	C₂²	1	1	yes	characteristic
175	C₃₁×#441	C₂²	1	1	yes	characteristic
176	C₃₁×#441	C₂²	1	1	yes	characteristic
177	C₃₁×#441	C₂²	1	1	yes	characteristic
178	C₃₁×#441	C₂²	1	1	yes	characteristic
179	C₃₁×#440	C₂²	1	1	yes	characteristic
180	C₃₁×#440	C₂²	1	1	yes	characteristic
181	C₃₁×#440	C₂²	1	1	yes	characteristic
182	C₃₁×#440	C₂²	1	1	yes	characteristic
183	C₃₁×#440	C₂²	1	1	yes	characteristic
184	C₃₁×#440	C₂²	1	1	yes	characteristic
185	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
186	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
187	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
188	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
189	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
190	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
191	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
192	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
193	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
194	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
195	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
196	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
197	C₃₁×#433	C₂²	1	1	yes	characteristic
198	C₃₁×#433	C₂²	1	1	yes	characteristic
199	C₃₁×#433	C₂²	1	1	yes	characteristic
200	C₃₁×#433	C₂²	1	1	yes	characteristic
201	C₃₁×#432	C₂²	1	1	yes	characteristic
202	C₃₁×#431	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₃₁×C₄⋊Q₈	—	2	1	no	—
213	C₃₁×C₄⋊Q₈	—	2	1	no	—
214	C₃₁×C₄⋊Q₈	—	2	1	no	—
215	C₃₁×C₄⋊Q₈	—	2	1	no	—
216	C₃₁×C₄⋊Q₈	—	2	1	no	—
217	C₃₁×C₄⋊Q₈	—	2	1	no	—
218	C₃₁×C₄⋊Q₈	—	2	1	no	—
219	C₃₁×C₄⋊Q₈	—	2	1	no	—
220	C₃₁×C₄⋊Q₈	—	2	1	no	—
221	C₃₁×C₄⋊Q₈	—	2	1	no	—
222	C₃₁×C₄⋊Q₈	—	2	1	no	—
223	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
224	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
225	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
229	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
230	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	C₃₁×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×#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	—	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	D₄	1	1	yes	characteristic
273	C₃₁×#125	D₄	1	1	yes	characteristic
274	C₃₁×#125	C₂³	1	1	yes	characteristic
275	C₃₁×#125	C₂³	1	1	yes	characteristic
276	C₃₁×#125	C₂³	1	1	yes	characteristic
277	C₃₁×#125	C₂³	1	1	yes	characteristic
278	C₃₁×#125	C₂³	1	1	yes	characteristic
279	C₃₁×#125	C₂³	1	1	yes	characteristic
280	C₃₁×#125	C₂³	1	1	yes	characteristic
281	C₃₁×#125	C₂³	1	1	yes	characteristic
282	C₃₁×#125	C₂³	1	1	yes	characteristic
283	C₃₁×#125	C₂³	1	1	yes	characteristic
284	C₃₁×#125	C₂³	1	1	yes	characteristic
285	C₃₁×#124	—	2	1	no	—
286	C₃₁×#124	—	2	1	no	—
287	C₃₁×#124	C₂³	1	1	yes	characteristic
288	C₃₁×#124	C₂³	1	1	yes	characteristic
289	C₃₁×#124	C₂³	1	1	yes	characteristic
290	C₃₁×#123	—	2	1	no	—
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×C₂²⋊Q₈	—	2	1	no	—
294	C₃₁×C₂²⋊Q₈	—	2	1	no	—
295	C₃₁×C₂²⋊Q₈	—	2	1	no	—
296	C₃₁×C₂²⋊Q₈	—	2	1	no	—
297	C₃₁×C₂²⋊Q₈	—	2	1	no	—
298	C₃₁×C₂²⋊Q₈	—	2	1	no	—
299	C₃₁×C₂²⋊Q₈	—	2	1	no	—
300	C₃₁×C₂²⋊Q₈	—	2	1	no	—
301	C₃₁×C₂²⋊Q₈	—	2	1	no	—
302	C₃₁×C₂²⋊Q₈	—	2	1	no	—
303	C₃₁×C₂²⋊Q₈	—	2	1	no	—
304	C₃₁×C₂²⋊Q₈	—	2	1	no	—
305	C₃₁×C₂²⋊Q₈	—	2	1	no	—
306	C₃₁×C₂²⋊Q₈	—	2	1	no	—
307	C₃₁×C₂²⋊Q₈	—	2	1	no	—
308	C₃₁×C₂²⋊Q₈	—	2	1	no	—
309	C₃₁×C₂²⋊Q₈	—	2	1	no	—
310	C₃₁×C₂²⋊Q₈	—	2	1	no	—
311	C₃₁×C₂²⋊Q₈	—	2	1	no	—
312	C₃₁×C₂²⋊Q₈	—	2	1	no	—
313	C₃₁×C₂²⋊Q₈	—	2	1	no	—
314	C₃₁×C₂²⋊Q₈	—	2	1	no	—
315	C₃₁×C₂²⋊Q₈	—	2	1	no	—
316	C₃₁×C₂²⋊Q₈	—	2	1	no	—
317	C₃₁×C₂²⋊Q₈	—	2	1	no	—
318	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
319	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
320	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
321	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
322	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
325	C₃₁×#121	C₂³	1	1	yes	characteristic
326	C₄×Q₈×C₃₁	—	2	1	no	—
327	C₄×Q₈×C₃₁	—	2	1	no	—
328	C₄×Q₈×C₃₁	—	2	1	no	—
329	C₄×Q₈×C₃₁	—	2	1	no	—
330	C₄×Q₈×C₃₁	—	2	1	no	—
331	C₄×Q₈×C₃₁	—	2	1	no	—
332	C₄×Q₈×C₃₁	—	2	1	no	—
333	C₄×Q₈×C₃₁	—	2	1	no	—
334	C₄×Q₈×C₃₁	—	2	1	no	—
335	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
336	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
337	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
338	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
339	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
340	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
341	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
342	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
347	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
354	C₄×D₄×C₃₁	—	2	1	no	—
355	C₄×D₄×C₃₁	—	2	1	no	—
356	C₄×D₄×C₃₁	—	2	1	no	—
357	C₄×D₄×C₃₁	—	2	1	no	—
358	C₄×D₄×C₃₁	—	2	1	no	—
359	C₄×D₄×C₃₁	—	2	1	no	—
360	C₄×D₄×C₃₁	—	2	1	no	—
361	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
370	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	C₂³	1	1	yes	characteristic
379	C₃₁×#117	C₂³	1	1	yes	characteristic
380	C₃₁×#117	C₂³	1	1	yes	characteristic
381	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
391	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
392	C₂×C₄²×C₃₁	—	2	1	no	—
393	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
394	C₃₁×#107	C₂³	1	1	yes	characteristic
395	C₃₁×#107	C₂³	1	1	yes	characteristic
396	C₃₁×#107	C₂³	1	1	yes	characteristic
397	C₃₁×#107	C₂³	1	1	yes	characteristic
398	C₃₁×#107	C₂³	1	1	yes	characteristic
399	C₃₁×#107	C₂³	1	1	yes	characteristic
400	C₃₁×#107	C₂³	1	1	yes	characteristic
401	C₃₁×#107	C₂³	1	1	yes	characteristic
402	C₃₁×#107	C₂³	1	1	yes	characteristic
403	C₃₁×#107	C₂³	1	1	yes	characteristic
404	C₃₁×#107	C₂³	1	1	yes	characteristic
405	C₃₁×#107	C₂³	1	1	yes	characteristic
406	C₃₁×#106	C₂³	1	1	yes	characteristic
407	C₃₁×#106	C₂³	1	1	yes	characteristic
408	C₃₁×#106	C₂³	1	1	yes	characteristic
409	C₃₁×#106	C₂³	1	1	yes	characteristic
410	C₃₁×#106	C₂³	1	1	yes	characteristic
411	C₃₁×#106	C₂³	1	1	yes	characteristic
412	C₃₁×#106	C₂³	1	1	yes	characteristic
413	C₃₁×#106	C₂³	1	1	yes	characteristic
414	C₃₁×#106	C₂³	1	1	yes	characteristic
415	C₃₁×#106	C₂³	1	1	yes	characteristic
416	C₃₁×#106	C₂³	1	1	yes	characteristic
417	C₃₁×#106	C₂³	1	1	yes	characteristic
418	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
419	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
420	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
421	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
422	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
423	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
424	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×#103	C₂³	1	1	yes	characteristic
431	C₃₁×#103	C₂³	1	1	yes	characteristic
432	C₃₁×#103	C₂³	1	1	yes	characteristic
433	C₃₁×#103	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#103	C₂³	1	1	yes	characteristic
451	C₃₁×#103	C₂³	1	1	yes	characteristic
452	C₃₁×#102	C₂³	1	1	yes	characteristic
453	C₃₁×#102	C₂³	1	1	yes	characteristic
454	C₃₁×#102	C₂³	1	1	yes	characteristic
455	C₃₁×#102	C₂³	1	1	yes	characteristic
456	C₃₁×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₃₁×#97	C₂³	1	1	yes	characteristic
467	C₃₁×#97	C₂³	1	1	yes	characteristic
468	C₃₁×#97	C₂³	1	1	yes	characteristic
469	C₃₁×#97	C₂³	1	1	yes	characteristic
470	C₃₁×#97	C₂³	1	1	yes	characteristic
471	C₃₁×#97	C₂³	1	1	yes	characteristic
472	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	#41×C₃₁	—	2	2	no	—
479	#41×C₃₁	—	2	2	no	—
480	C₂×Q₈×C₃₁	—	2	1	no	—
481	C₂×Q₈×C₃₁	—	2	1	no	—
482	C₂×Q₈×C₃₁	—	2	1	no	—
483	C₂×Q₈×C₃₁	—	2	1	no	—
484	C₂×Q₈×C₃₁	—	2	1	no	—
485	C₂×Q₈×C₃₁	—	2	1	no	—
486	C₂×Q₈×C₃₁	—	2	1	no	—
487	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
488	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
489	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
490	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
491	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
492	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
493	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₂×D₄×C₃₁	—	2	1	no	—
496	C₂×D₄×C₃₁	—	2	1	no	—
497	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
498	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₃₁	—	2	1	no	—
500	C₂²×C₄×C₃₁	—	2	1	no	—
501	C₂²×C₄×C₃₁	—	2	1	no	—
502	C₂²×C₄×C₃₁	—	2	1	no	—
503	C₂²×C₄×C₃₁	—	2	1	no	—
504	C₂²×C₄×C₃₁	—	2	1	no	—
505	C₂²×C₄×C₃₁	—	2	1	no	—
506	C₂²×C₄×C₃₁	—	2	1	no	—
507	C₂²×C₄×C₃₁	—	2	1	no	—
508	C₂²×C₄×C₃₁	—	2	1	no	—
509	C₂²×C₄×C₃₁	—	2	1	no	—
510	C₂²×C₄×C₃₁	—	2	1	no	—
511	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
512	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
513	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
514	Q₁₆×C₃₁	—	2	2	no	—
515	Q₁₆×C₃₁	—	2	2	no	—
516	Q₁₆×C₃₁	—	2	2	no	—
517	SD₁₆×C₃₁	—	2	2	no	—
518	SD₁₆×C₃₁	—	2	2	no	—
519	SD₁₆×C₃₁	—	2	2	no	—
520	SD₁₆×C₃₁	—	2	2	no	—
521	D₈×C₃₁	—	2	2	no	—
522	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
523	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
524	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
525	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
526	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
527	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
528	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
529	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
530	C₄⋊C₄×C₃₁	—	2	1	no	—
531	C₄⋊C₄×C₃₁	—	2	1	no	—
532	C₄⋊C₄×C₃₁	—	2	1	no	—
533	C₄⋊C₄×C₃₁	—	2	1	no	—
534	C₄⋊C₄×C₃₁	—	2	1	no	—
535	C₄⋊C₄×C₃₁	—	2	1	no	—
536	C₄⋊C₄×C₃₁	—	2	1	no	—
537	C₄⋊C₄×C₃₁	—	2	1	no	—
538	C₄⋊C₄×C₃₁	—	2	1	no	—
539	C₄⋊C₄×C₃₁	—	2	1	no	—
540	C₄⋊C₄×C₃₁	—	2	1	no	—
541	C₄⋊C₄×C₃₁	—	2	1	no	—
542	C₄⋊C₄×C₃₁	—	2	1	no	—
543	C₄⋊C₄×C₃₁	—	2	1	no	—
544	C₄⋊C₄×C₃₁	—	2	1	no	—
545	C₄⋊C₄×C₃₁	—	2	1	no	—
546	C₄⋊C₄×C₃₁	—	2	1	no	—
547	C₄⋊C₄×C₃₁	—	2	1	no	—
548	C₄⋊C₄×C₃₁	—	2	1	no	—
549	C₄⋊C₄×C₃₁	—	2	1	no	—
550	C₄⋊C₄×C₃₁	—	2	1	no	—
551	C₄⋊C₄×C₃₁	—	2	1	no	—
552	C₄⋊C₄×C₃₁	—	2	1	no	—
553	C₄⋊C₄×C₃₁	—	2	1	no	—
554	C₄⋊C₄×C₃₁	—	2	1	no	—
555	C₄⋊C₄×C₃₁	—	2	1	no	—
556	C₄⋊C₄×C₃₁	—	2	1	no	—
557	C₄⋊C₄×C₃₁	—	2	1	no	—
558	C₄⋊C₄×C₃₁	—	2	1	no	—
559	C₄⋊C₄×C₃₁	—	2	1	no	—
560	C₄⋊C₄×C₃₁	—	2	1	no	—
561	C₄⋊C₄×C₃₁	—	2	1	no	—
562	C₄⋊C₄×C₃₁	—	2	1	no	—
563	C₄⋊C₄×C₃₁	—	2	1	no	—
564	C₄⋊C₄×C₃₁	—	2	1	no	—
565	C₄⋊C₄×C₃₁	—	2	1	no	—
566	C₄⋊C₄×C₃₁	—	2	1	no	—
567	C₄⋊C₄×C₃₁	—	2	1	no	—
568	C₄⋊C₄×C₃₁	—	2	1	no	—
569	C₄⋊C₄×C₃₁	—	2	1	no	—
570	C₄⋊C₄×C₃₁	—	2	1	no	—
571	C₄⋊C₄×C₃₁	—	2	1	no	—
572	C₄⋊C₄×C₃₁	—	2	1	no	—
573	C₄⋊C₄×C₃₁	—	2	1	no	—
574	C₄⋊C₄×C₃₁	—	2	1	no	—
575	C₄⋊C₄×C₃₁	—	2	1	no	—
576	C₄⋊C₄×C₃₁	—	2	1	no	—
577	C₄⋊C₄×C₃₁	—	2	1	no	—
578	C₄⋊C₄×C₃₁	—	2	1	no	—
579	C₄⋊C₄×C₃₁	—	2	1	no	—
580	C₄⋊C₄×C₃₁	—	2	1	no	—
581	C₄⋊C₄×C₃₁	—	2	1	no	—
582	C₄⋊C₄×C₃₁	—	2	1	no	—
583	C₄⋊C₄×C₃₁	—	2	1	no	—
584	C₄⋊C₄×C₃₁	—	2	1	no	—
585	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
586	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
587	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
588	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
589	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
590	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
591	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
592	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
593	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
607	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
611	C₂²⋊C₄×C₃₁	—	2	1	no	—
612	C₂²⋊C₄×C₃₁	—	2	1	no	—
613	C₂²⋊C₄×C₃₁	—	2	1	no	—
614	C₂²⋊C₄×C₃₁	—	2	1	no	—
615	C₂²⋊C₄×C₃₁	—	2	1	no	—
616	C₂²⋊C₄×C₃₁	—	2	1	no	—
617	C₂²⋊C₄×C₃₁	—	2	1	no	—
618	C₂²⋊C₄×C₃₁	—	2	1	no	—
619	C₂²⋊C₄×C₃₁	—	2	1	no	—
620	C₂²⋊C₄×C₃₁	—	2	1	no	—
621	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
632	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
633	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
634	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
635	C₄²×C₃₁	—	2	1	no	—
636	C₄²×C₃₁	—	2	1	no	—
637	C₄²×C₃₁	—	2	1	no	—
638	C₄²×C₃₁	—	2	1	no	—
639	C₄²×C₃₁	—	2	1	no	—
640	C₄²×C₃₁	—	2	1	no	—
641	C₄²×C₃₁	—	2	1	no	—
642	C₄²×C₃₁	—	2	1	no	—
643	C₄²×C₃₁	—	2	1	no	—
644	C₄²×C₃₁	—	2	1	no	—
645	C₄²×C₃₁	—	2	1	no	—
646	C₄²×C₃₁	—	2	1	no	—
647	C₄²×C₃₁	—	2	1	no	—
648	C₄²×C₃₁	—	2	1	no	—
649	C₄²×C₃₁	—	2	1	no	—
650	C₄²×C₃₁	—	2	1	no	—
651	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
652	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
653	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
654	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
655	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
656	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
657	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
658	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
659	#61862	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
660	C₂³×C₃₁	—	2	1	no	—
661	C₂³×C₃₁	—	2	1	no	—
662	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
663	Q₈×C₃₁	—	2	1	no	—
664	Q₈×C₃₁	—	2	1	no	—
665	Q₈×C₃₁	—	2	1	no	—
666	Q₈×C₃₁	—	2	1	no	—
667	Q₈×C₃₁	—	2	1	no	—
668	Q₈×C₃₁	—	2	1	no	—
669	Q₈×C₃₁	—	2	1	no	—
670	Q₈×C₃₁	—	4	1	no	—
671	Q₈×C₃₁	—	4	1	no	—
672	Q₈×C₃₁	—	4	1	no	—
673	Q₈×C₃₁	—	4	1	no	—
674	Q₈×C₃₁	—	8	1	no	—
675	Q₈×C₃₁	—	8	1	no	—
676	Q₈×C₃₁	—	8	1	no	—
677	Q₈×C₃₁	—	8	1	no	—
678	Q₈×C₃₁	—	8	1	no	—
679	Q₈×C₃₁	—	8	1	no	—
680	Q₈×C₃₁	—	8	1	no	—
681	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
682	D₄×C₃₁	—	2	4	no	—
683	D₄×C₃₁	—	2	1	no	—
684	D₄×C₃₁	—	2	1	no	—
685	D₄×C₃₁	—	2	1	no	—
686	D₄×C₃₁	—	8	1	no	—
687	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
688	C₂×C₄×C₃₁	—	2	4	no	—
689	C₂×C₄×C₃₁	—	2	1	no	—
690	C₂×C₄×C₃₁	—	2	1	no	—
691	C₂×C₄×C₃₁	—	2	1	no	—
692	C₂×C₄×C₃₁	—	2	1	no	—
693	C₂×C₄×C₃₁	—	2	1	no	—
694	C₂×C₄×C₃₁	—	2	1	no	—
695	C₂×C₄×C₃₁	—	2	1	no	—
696	C₂×C₄×C₃₁	—	2	1	no	—
697	C₂×C₄×C₃₁	—	2	1	no	—
698	C₂×C₄×C₃₁	—	2	1	no	—
699	C₂×C₄×C₃₁	—	2	1	no	—
700	C₂×C₄×C₃₁	—	2	1	no	—
701	C₂×C₄×C₃₁	—	2	1	no	—
702	C₂×C₄×C₃₁	—	2	1	no	—
703	C₂×C₄×C₃₁	—	2	1	no	—
704	C₂×C₄×C₃₁	—	2	1	no	—
705	C₂×C₄×C₃₁	—	4	1	no	—
706	C₂×C₄×C₃₁	—	4	1	no	—
707	C₂×C₄×C₃₁	—	4	2	no	—
708	C₂×C₄×C₃₁	—	8	1	no	—
709	C₂×C₄×C₃₁	—	8	1	no	—
710	C₂×C₄×C₃₁	—	8	1	no	—
711	C₂×C₄×C₃₁	—	8	1	no	—
712	C₂×C₄×C₃₁	—	8	1	no	—
713	C₂×C₄×C₃₁	—	8	1	no	—
714	C₂×C₄×C₃₁	—	8	1	no	—
715	C₂×C₄×C₃₁	—	8	1	no	—
716	C₂×C₄×C₃₁	—	8	1	no	—
717	C₂×C₄×C₃₁	—	8	1	no	—
718	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
719	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
720	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
721	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
722	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
723	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
724	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
725	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
726	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
727	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
728	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
729	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
730	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
731	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
732	C₈×C₃₁	—	2	1	no	—
733	C₈×C₃₁	—	2	1	no	—
734	C₈×C₃₁	—	2	1	no	—
735	C₈×C₃₁	—	2	1	no	—
736	C₈×C₃₁	—	2	1	no	—
737	C₈×C₃₁	—	2	1	no	—
738	C₈×C₃₁	—	2	1	no	—
739	C₈×C₃₁	—	2	1	no	—
740	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
741	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
742	#3390	C₂×C₃₁	1	1	yes	characteristic, complemented
743	#3389	C₂×C₃₁	1	1	yes	characteristic, complemented
744	#3388	C₂×C₃₁	1	1	yes	characteristic, complemented
745	#3388	C₂×C₃₁	1	1	yes	characteristic, complemented
746	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
747	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
748	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
749	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
750	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
751	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
752	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
753	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
754	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
755	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
756	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
757	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
758	#3244	C₂×C₃₁	1	1	yes	characteristic, complemented
759	#3243	C₂×C₃₁	1	1	yes	characteristic, complemented
760	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
761	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
762	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
763	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
764	#3125	C₂×C₃₁	1	1	yes	characteristic
765	#3124	C₂×C₃₁	1	1	yes	characteristic
766	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
767	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
768	#3111	C₂×C₃₁	1	1	yes	characteristic
769	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
770	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
771	C₂²×C₃₁	—	2	1	no	—
772	C₂²×C₃₁	—	2	1	no	—
773	C₂²×C₃₁	—	2	1	no	—
774	C₂²×C₃₁	—	2	2	no	—
775	C₂²×C₃₁	—	4	1	no	—
776	C₂²×C₃₁	—	4	1	no	—
777	C₂²×C₃₁	—	4	1	no	—
778	C₂²×C₃₁	—	4	1	no	—
779	C₂²×C₃₁	—	4	1	no	—
780	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
781	C₄×C₃₁	—	2	1	no	—
782	C₄×C₃₁	—	2	1	no	—
783	C₄×C₃₁	—	2	1	no	—
784	C₄×C₃₁	—	2	1	no	—
785	C₄×C₃₁	—	2	1	no	—
786	C₄×C₃₁	—	2	1	no	—
787	C₄×C₃₁	—	2	1	no	—
788	C₄×C₃₁	—	2	1	no	—
789	C₄×C₃₁	—	2	1	no	—
790	C₄×C₃₁	—	2	1	no	—
791	C₄×C₃₁	—	2	1	no	—
792	C₄×C₃₁	—	2	1	no	—
793	C₄×C₃₁	—	2	1	no	—
794	C₄×C₃₁	—	2	2	no	—
795	C₄×C₃₁	—	4	1	no	—
796	C₄×C₃₁	—	4	1	no	—
797	C₄×C₃₁	—	4	1	no	—
798	C₄×C₃₁	—	4	1	no	—
799	C₄×C₃₁	—	4	1	no	—
800	C₄×C₃₁	—	4	1	no	—
801	C₄×C₃₁	—	4	1	no	—
802	C₄×C₃₁	—	4	1	no	—
803	C₄×C₃₁	—	4	1	no	—
804	C₄×C₃₁	—	4	1	no	—
805	C₄×C₃₁	—	4	1	no	—
806	C₄×C₃₁	—	4	1	no	—
807	C₄×C₃₁	—	4	1	no	—
808	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
809	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
810	#563	—	2	1	no	—
811	#563	—	2	1	no	—
812	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
813	#557	C₂²×C₃₁	1	1	yes	characteristic
814	#557	C₂²×C₃₁	1	1	yes	characteristic
815	#557	C₂²×C₃₁	1	1	yes	characteristic
816	#557	C₂²×C₃₁	1	1	yes	characteristic
817	#557	C₂²×C₃₁	1	1	yes	characteristic
818	#557	C₂²×C₃₁	1	1	yes	characteristic
819	#557	C₂²×C₃₁	1	1	yes	characteristic
820	#556	—	2	1	no	—
821	#556	C₂²×C₃₁	1	1	yes	characteristic
822	#556	C₂²×C₃₁	1	1	yes	characteristic
823	#556	C₂²×C₃₁	1	1	yes	characteristic
824	#554	—	2	1	no	—
825	#554	—	2	1	no	—
826	#554	—	2	1	no	—
827	#554	—	2	1	no	—
828	#554	C₂²×C₃₁	1	1	yes	characteristic
829	#554	C₂²×C₃₁	1	1	yes	characteristic
830	#554	C₂²×C₃₁	1	1	yes	characteristic
831	#554	C₂²×C₃₁	1	1	yes	characteristic
832	#554	C₂²×C₃₁	1	1	yes	characteristic
833	#552	—	2	1	no	—
834	#544	—	2	1	no	—
835	#544	—	2	1	no	—
836	#544	—	2	1	no	—
837	#544	C₂²×C₃₁	1	1	yes	characteristic
838	#544	C₂²×C₃₁	1	1	yes	characteristic
839	#542	C₂²×C₃₁	1	1	yes	characteristic
840	#542	C₂²×C₃₁	1	1	yes	characteristic
841	#541	—	2	1	no	—
842	#541	—	2	1	no	—
843	#541	—	2	1	no	—
844	#541	C₂²×C₃₁	1	1	yes	characteristic
845	#541	C₂²×C₃₁	1	1	yes	characteristic
846	#533	—	2	1	no	—
847	#533	C₂²×C₃₁	1	1	yes	characteristic
848	#533	C₂²×C₃₁	1	1	yes	characteristic
849	#529	C₂²×C₃₁	1	1	yes	characteristic
850	C₂×#125	—	2	1	no	—
851	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
852	#520	C₂²×C₃₁	1	1	yes	characteristic
853	#520	C₂²×C₃₁	1	1	yes	characteristic
854	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
855	#501	C₂²×C₃₁	1	1	yes	characteristic
856	#501	C₂²×C₃₁	1	1	yes	characteristic
857	#501	C₂²×C₃₁	1	1	yes	characteristic
858	#501	C₂²×C₃₁	1	1	yes	characteristic
859	#501	C₂²×C₃₁	1	1	yes	characteristic
860	#501	C₂²×C₃₁	1	1	yes	characteristic
861	#500	C₂²×C₃₁	1	1	yes	characteristic
862	#499	C₂²×C₃₁	1	1	yes	characteristic
863	#499	C₂²×C₃₁	1	1	yes	characteristic
864	#499	C₂²×C₃₁	1	1	yes	characteristic
865	#499	C₂²×C₃₁	1	1	yes	characteristic
866	#498	C₂²×C₃₁	1	1	yes	characteristic
867	#491	C₂²×C₃₁	1	1	yes	characteristic
868	#491	C₂²×C₃₁	1	1	yes	characteristic
869	#491	C₂²×C₃₁	1	1	yes	characteristic
870	#491	C₂²×C₃₁	1	1	yes	characteristic
871	#489	C₂²×C₃₁	1	1	yes	characteristic
872	#489	C₂²×C₃₁	1	1	yes	characteristic
873	#488	C₂²×C₃₁	1	1	yes	characteristic
874	#488	C₂²×C₃₁	1	1	yes	characteristic
875	#488	C₂²×C₃₁	1	1	yes	characteristic
876	#488	C₂²×C₃₁	1	1	yes	characteristic
877	#487	C₂²×C₃₁	1	1	yes	characteristic
878	#487	C₂²×C₃₁	1	1	yes	characteristic
879	#485	C₂²×C₃₁	1	1	yes	characteristic
880	#485	C₂²×C₃₁	1	1	yes	characteristic
881	#485	C₂²×C₃₁	1	1	yes	characteristic
882	#484	C₂²×C₃₁	1	1	yes	characteristic
883	#484	C₂²×C₃₁	1	1	yes	characteristic
884	#484	C₂²×C₃₁	1	1	yes	characteristic
885	#483	C₂²×C₃₁	1	1	yes	characteristic
886	#483	C₂²×C₃₁	1	1	yes	characteristic
887	#483	C₂²×C₃₁	1	1	yes	characteristic
888	#482	C₂²×C₃₁	1	1	yes	characteristic
889	#481	C₂²×C₃₁	1	1	yes	characteristic
890	#480	C₂²×C₃₁	1	1	yes	characteristic
891	#479	C₂²×C₃₁	1	1	yes	characteristic
892	#479	C₂²×C₃₁	1	1	yes	characteristic
893	#479	C₂²×C₃₁	1	1	yes	characteristic
894	#479	C₂²×C₃₁	1	1	yes	characteristic
895	#479	C₂²×C₃₁	1	1	yes	characteristic
896	#479	C₂²×C₃₁	1	1	yes	characteristic
897	#479	C₂²×C₃₁	1	1	yes	characteristic
898	#479	C₂²×C₃₁	1	1	yes	characteristic
899	#479	C₂²×C₃₁	1	1	yes	characteristic
900	#479	C₂²×C₃₁	1	1	yes	characteristic
901	#479	C₂²×C₃₁	1	1	yes	characteristic
902	#479	C₂²×C₃₁	1	1	yes	characteristic
903	#479	C₂²×C₃₁	1	1	yes	characteristic
904	#479	C₂²×C₃₁	1	1	yes	characteristic
905	#479	C₂²×C₃₁	1	1	yes	characteristic
906	#478	C₂²×C₃₁	1	1	yes	characteristic
907	#478	C₂²×C₃₁	1	1	yes	characteristic
908	#478	C₂²×C₃₁	1	1	yes	characteristic
909	#478	C₂²×C₃₁	1	1	yes	characteristic
910	#478	C₂²×C₃₁	1	1	yes	characteristic
911	#478	C₂²×C₃₁	1	1	yes	characteristic
912	#478	C₂²×C₃₁	1	1	yes	characteristic
913	#477	C₂²×C₃₁	1	1	yes	characteristic
914	#477	C₂²×C₃₁	1	1	yes	characteristic
915	#477	C₂²×C₃₁	1	1	yes	characteristic
916	#477	C₂²×C₃₁	1	1	yes	characteristic
917	#476	C₂²×C₃₁	1	1	yes	characteristic
918	#476	C₂²×C₃₁	1	1	yes	characteristic
919	#475	C₂²×C₃₁	1	1	yes	characteristic
920	#475	C₂²×C₃₁	1	1	yes	characteristic
921	#475	C₂²×C₃₁	1	1	yes	characteristic
922	#475	C₂²×C₃₁	1	1	yes	characteristic
923	#475	C₂²×C₃₁	1	1	yes	characteristic
924	#474	C₂²×C₃₁	1	1	yes	characteristic
925	#474	C₂²×C₃₁	1	1	yes	characteristic
926	#474	C₂²×C₃₁	1	1	yes	characteristic
927	#464	C₂²×C₃₁	1	1	yes	characteristic
928	#464	C₂²×C₃₁	1	1	yes	characteristic
929	#464	C₂²×C₃₁	1	1	yes	characteristic
930	#463	C₂²×C₃₁	1	1	yes	characteristic
931	#463	C₂²×C₃₁	1	1	yes	characteristic
932	#463	C₂²×C₃₁	1	1	yes	characteristic
933	#462	C₂²×C₃₁	1	1	yes	characteristic
934	#462	C₂²×C₃₁	1	1	yes	characteristic
935	#462	C₂²×C₃₁	1	1	yes	characteristic
936	#461	C₂²×C₃₁	1	1	yes	characteristic
937	#461	C₂²×C₃₁	1	1	yes	characteristic
938	#461	C₂²×C₃₁	1	1	yes	characteristic
939	#452	C₂²×C₃₁	1	1	yes	characteristic
940	#452	C₂²×C₃₁	1	1	yes	characteristic
941	#452	C₂²×C₃₁	1	1	yes	characteristic
942	#449	C₂²×C₃₁	1	1	yes	characteristic
943	#446	C₂²×C₃₁	1	1	yes	characteristic
944	#446	C₂²×C₃₁	1	1	yes	characteristic
945	#446	C₂²×C₃₁	1	1	yes	characteristic
946	#446	C₂²×C₃₁	1	1	yes	characteristic
947	#446	C₂²×C₃₁	1	1	yes	characteristic
948	#446	C₂²×C₃₁	1	1	yes	characteristic
949	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
950	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
951	#442	C₂²×C₃₁	1	1	yes	characteristic
952	#442	C₂²×C₃₁	1	1	yes	characteristic
953	#441	C₂²×C₃₁	1	1	yes	characteristic
954	#441	C₂²×C₃₁	1	1	yes	characteristic
955	#441	C₂²×C₃₁	1	1	yes	characteristic
956	#441	C₂²×C₃₁	1	1	yes	characteristic
957	#440	C₂²×C₃₁	1	1	yes	characteristic
958	#440	C₂²×C₃₁	1	1	yes	characteristic
959	#440	C₂²×C₃₁	1	1	yes	characteristic
960	#440	C₂²×C₃₁	1	1	yes	characteristic
961	#440	C₂²×C₃₁	1	1	yes	characteristic
962	#440	C₂²×C₃₁	1	1	yes	characteristic
963	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
964	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
965	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
966	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
967	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
968	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
969	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
970	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
971	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
972	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
973	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
974	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
975	#433	C₂²×C₃₁	1	1	yes	characteristic
976	#433	C₂²×C₃₁	1	1	yes	characteristic
977	#433	C₂²×C₃₁	1	1	yes	characteristic
978	#433	C₂²×C₃₁	1	1	yes	characteristic
979	#432	C₂²×C₃₁	1	1	yes	characteristic
980	#431	C₂²×C₃₁	1	1	yes	characteristic
981	C₂×C₃₁	—	4	1	no	—
982	C₂×C₃₁	—	4	2	no	—
983	C₂×C₃₁	—	8	1	no	—
984	C₂×C₃₁	#3486	1	1	yes	characteristic
985	C₂×C₃₁	#3584	1	1	yes	characteristic
986	C₂×C₃₁	#3586	1	1	yes	characteristic
987	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
988	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
989	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
990	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
991	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
992	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
993	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
994	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
995	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
996	C₄⋊Q₈	—	2	1	no	—
997	C₄⋊Q₈	—	2	1	no	—
998	C₄⋊Q₈	—	2	1	no	—
999	C₄⋊Q₈	—	2	1	no	—
1000	C₄⋊Q₈	—	2	1	no	—
1001	C₄⋊Q₈	—	2	1	no	—
1002	C₄⋊Q₈	—	2	1	no	—
1003	C₄⋊Q₈	—	2	1	no	—
1004	C₄⋊Q₈	—	2	1	no	—
1005	C₄⋊Q₈	—	2	1	no	—
1006	C₄⋊Q₈	—	2	1	no	—
1007	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1008	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1009	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1010	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1011	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1012	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1013	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1014	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1015	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1016	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1017	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1018	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1019	#126	—	2	1	no	—
1020	#126	—	2	1	no	—
1021	#126	—	2	1	no	—
1022	#126	—	2	1	no	—
1023	#126	—	2	1	no	—
1024	#126	—	2	1	no	—
1025	#126	—	2	1	no	—
1026	#126	—	2	1	no	—
1027	#126	—	2	1	no	—
1028	#126	—	2	1	no	—
1029	#126	—	2	1	no	—
1030	#126	—	2	1	no	—
1031	#126	—	2	1	no	—
1032	#125	—	2	1	no	—
1033	#125	—	2	1	no	—
1034	#125	—	2	1	no	—
1035	#125	—	2	1	no	—
1036	#125	—	2	1	no	—
1037	#125	—	2	1	no	—
1038	#125	—	2	1	no	—
1039	#125	—	2	1	no	—
1040	#125	—	2	1	no	—
1041	#125	—	2	1	no	—
1042	#125	—	2	1	no	—
1043	#125	—	2	1	no	—
1044	#125	—	2	1	no	—
1045	#125	—	2	1	no	—
1046	#125	—	2	1	no	—
1047	#125	—	2	1	no	—
1048	#125	—	2	1	no	—
1049	#125	—	2	1	no	—
1050	#125	—	2	1	no	—
1051	#125	—	2	1	no	—
1052	#125	—	2	1	no	—
1053	#125	—	2	1	no	—
1054	#125	—	2	1	no	—
1055	#125	—	2	1	no	—
1056	#125	D₄×C₃₁	1	1	yes	characteristic
1057	#125	D₄×C₃₁	1	1	yes	characteristic
1058	#125	C₂³×C₃₁	1	1	yes	characteristic
1059	#125	C₂³×C₃₁	1	1	yes	characteristic
1060	#125	C₂³×C₃₁	1	1	yes	characteristic
1061	#125	C₂³×C₃₁	1	1	yes	characteristic
1062	#125	C₂³×C₃₁	1	1	yes	characteristic
1063	#125	C₂³×C₃₁	1	1	yes	characteristic
1064	#125	C₂³×C₃₁	1	1	yes	characteristic
1065	#125	C₂³×C₃₁	1	1	yes	characteristic
1066	#125	C₂³×C₃₁	1	1	yes	characteristic
1067	#125	C₂³×C₃₁	1	1	yes	characteristic
1068	#125	C₂³×C₃₁	1	1	yes	characteristic
1069	#124	—	2	1	no	—
1070	#124	—	2	1	no	—
1071	#124	C₂³×C₃₁	1	1	yes	characteristic
1072	#124	C₂³×C₃₁	1	1	yes	characteristic
1073	#124	C₂³×C₃₁	1	1	yes	characteristic
1074	#123	—	2	1	no	—
1075	#123	—	2	1	no	—
1076	#123	—	2	1	no	—
1077	C₂²⋊Q₈	—	2	1	no	—
1078	C₂²⋊Q₈	—	2	1	no	—
1079	C₂²⋊Q₈	—	2	1	no	—
1080	C₂²⋊Q₈	—	2	1	no	—
1081	C₂²⋊Q₈	—	2	1	no	—
1082	C₂²⋊Q₈	—	2	1	no	—
1083	C₂²⋊Q₈	—	2	1	no	—
1084	C₂²⋊Q₈	—	2	1	no	—
1085	C₂²⋊Q₈	—	2	1	no	—
1086	C₂²⋊Q₈	—	2	1	no	—
1087	C₂²⋊Q₈	—	2	1	no	—
1088	C₂²⋊Q₈	—	2	1	no	—
1089	C₂²⋊Q₈	—	2	1	no	—
1090	C₂²⋊Q₈	—	2	1	no	—
1091	C₂²⋊Q₈	—	2	1	no	—
1092	C₂²⋊Q₈	—	2	1	no	—
1093	C₂²⋊Q₈	—	2	1	no	—
1094	C₂²⋊Q₈	—	2	1	no	—
1095	C₂²⋊Q₈	—	2	1	no	—
1096	C₂²⋊Q₈	—	2	1	no	—
1097	C₂²⋊Q₈	—	2	1	no	—
1098	C₂²⋊Q₈	—	2	1	no	—
1099	C₂²⋊Q₈	—	2	1	no	—
1100	C₂²⋊Q₈	—	2	1	no	—
1101	C₂²⋊Q₈	—	2	1	no	—
1102	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1103	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1104	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1105	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1106	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1107	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1108	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1109	#121	C₂³×C₃₁	1	1	yes	characteristic
1110	C₄×Q₈	—	2	1	no	—
1111	C₄×Q₈	—	2	1	no	—
1112	C₄×Q₈	—	2	1	no	—
1113	C₄×Q₈	—	2	1	no	—
1114	C₄×Q₈	—	2	1	no	—
1115	C₄×Q₈	—	2	1	no	—
1116	C₄×Q₈	—	2	1	no	—
1117	C₄×Q₈	—	2	1	no	—
1118	C₄×Q₈	—	2	1	no	—
1119	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1120	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1121	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1122	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1123	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1124	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1125	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1126	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1127	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1128	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1129	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1130	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1131	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1132	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1133	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1134	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1135	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1136	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1137	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1138	C₄×D₄	—	2	1	no	—
1139	C₄×D₄	—	2	1	no	—
1140	C₄×D₄	—	2	1	no	—
1141	C₄×D₄	—	2	1	no	—
1142	C₄×D₄	—	2	1	no	—
1143	C₄×D₄	—	2	1	no	—
1144	C₄×D₄	—	2	1	no	—
1145	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1146	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1147	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1148	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1149	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1150	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1151	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1152	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1153	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1154	#117	—	2	1	no	—
1155	#117	—	2	1	no	—
1156	#117	—	2	1	no	—
1157	#117	—	2	1	no	—
1158	#117	—	2	1	no	—
1159	#117	—	2	1	no	—
1160	#117	—	2	1	no	—
1161	#117	—	2	1	no	—
1162	#117	C₂³×C₃₁	1	1	yes	characteristic
1163	#117	C₂³×C₃₁	1	1	yes	characteristic
1164	#117	C₂³×C₃₁	1	1	yes	characteristic
1165	C₂×C₄⋊C₄	—	2	1	no	—
1166	C₂×C₄⋊C₄	—	2	1	no	—
1167	C₂×C₄⋊C₄	—	2	1	no	—
1168	C₂×C₄⋊C₄	—	2	1	no	—
1169	C₂×C₄⋊C₄	—	2	1	no	—
1170	C₂×C₄⋊C₄	—	2	1	no	—
1171	C₂×C₄⋊C₄	—	2	1	no	—
1172	C₂×C₄⋊C₄	—	2	1	no	—
1173	C₂×C₄⋊C₄	—	2	1	no	—
1174	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1175	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1176	C₂×C₄²	—	2	1	no	—
1177	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1178	#107	C₂³×C₃₁	1	1	yes	characteristic
1179	#107	C₂³×C₃₁	1	1	yes	characteristic
1180	#107	C₂³×C₃₁	1	1	yes	characteristic
1181	#107	C₂³×C₃₁	1	1	yes	characteristic
1182	#107	C₂³×C₃₁	1	1	yes	characteristic
1183	#107	C₂³×C₃₁	1	1	yes	characteristic
1184	#107	C₂³×C₃₁	1	1	yes	characteristic
1185	#107	C₂³×C₃₁	1	1	yes	characteristic
1186	#107	C₂³×C₃₁	1	1	yes	characteristic
1187	#107	C₂³×C₃₁	1	1	yes	characteristic
1188	#107	C₂³×C₃₁	1	1	yes	characteristic
1189	#107	C₂³×C₃₁	1	1	yes	characteristic
1190	#106	C₂³×C₃₁	1	1	yes	characteristic
1191	#106	C₂³×C₃₁	1	1	yes	characteristic
1192	#106	C₂³×C₃₁	1	1	yes	characteristic
1193	#106	C₂³×C₃₁	1	1	yes	characteristic
1194	#106	C₂³×C₃₁	1	1	yes	characteristic
1195	#106	C₂³×C₃₁	1	1	yes	characteristic
1196	#106	C₂³×C₃₁	1	1	yes	characteristic
1197	#106	C₂³×C₃₁	1	1	yes	characteristic
1198	#106	C₂³×C₃₁	1	1	yes	characteristic
1199	#106	C₂³×C₃₁	1	1	yes	characteristic
1200	#106	C₂³×C₃₁	1	1	yes	characteristic
1201	#106	C₂³×C₃₁	1	1	yes	characteristic
1202	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1203	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1204	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1205	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1206	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1207	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1208	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1209	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1210	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1211	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1212	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1213	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1214	#103	C₂³×C₃₁	1	1	yes	characteristic
1215	#103	C₂³×C₃₁	1	1	yes	characteristic
1216	#103	C₂³×C₃₁	1	1	yes	characteristic
1217	#103	C₂³×C₃₁	1	1	yes	characteristic
1218	#103	C₂³×C₃₁	1	1	yes	characteristic
1219	#103	C₂³×C₃₁	1	1	yes	characteristic
1220	#103	C₂³×C₃₁	1	1	yes	characteristic
1221	#103	C₂³×C₃₁	1	1	yes	characteristic
1222	#103	C₂³×C₃₁	1	1	yes	characteristic
1223	#103	C₂³×C₃₁	1	1	yes	characteristic
1224	#103	C₂³×C₃₁	1	1	yes	characteristic
1225	#103	C₂³×C₃₁	1	1	yes	characteristic
1226	#103	C₂³×C₃₁	1	1	yes	characteristic
1227	#103	C₂³×C₃₁	1	1	yes	characteristic
1228	#103	C₂³×C₃₁	1	1	yes	characteristic
1229	#103	C₂³×C₃₁	1	1	yes	characteristic
1230	#103	C₂³×C₃₁	1	1	yes	characteristic
1231	#103	C₂³×C₃₁	1	1	yes	characteristic
1232	#103	C₂³×C₃₁	1	1	yes	characteristic
1233	#103	C₂³×C₃₁	1	1	yes	characteristic
1234	#103	C₂³×C₃₁	1	1	yes	characteristic
1235	#103	C₂³×C₃₁	1	1	yes	characteristic
1236	#102	C₂³×C₃₁	1	1	yes	characteristic
1237	#102	C₂³×C₃₁	1	1	yes	characteristic
1238	#102	C₂³×C₃₁	1	1	yes	characteristic
1239	#102	C₂³×C₃₁	1	1	yes	characteristic
1240	#102	C₂³×C₃₁	1	1	yes	characteristic
1241	#102	C₂³×C₃₁	1	1	yes	characteristic
1242	#102	C₂³×C₃₁	1	1	yes	characteristic
1243	#102	C₂³×C₃₁	1	1	yes	characteristic
1244	#102	C₂³×C₃₁	1	1	yes	characteristic
1245	#102	C₂³×C₃₁	1	1	yes	characteristic
1246	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1247	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1248	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1249	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1250	#97	C₂³×C₃₁	1	1	yes	characteristic
1251	#97	C₂³×C₃₁	1	1	yes	characteristic
1252	#97	C₂³×C₃₁	1	1	yes	characteristic
1253	#97	C₂³×C₃₁	1	1	yes	characteristic
1254	#97	C₂³×C₃₁	1	1	yes	characteristic
1255	#97	C₂³×C₃₁	1	1	yes	characteristic
1256	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1257	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1258	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1259	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1260	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1261	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1262	C₃₁	#61862	1	1	yes	characteristic, direct product factor, Sylow
1263	#41	—	2	2	no	—
1264	#41	—	2	2	no	—
1265	C₂×Q₈	—	2	1	no	—
1266	C₂×Q₈	—	2	1	no	—
1267	C₂×Q₈	—	2	1	no	—
1268	C₂×Q₈	—	2	1	no	—
1269	C₂×Q₈	—	2	1	no	—
1270	C₂×Q₈	—	2	1	no	—
1271	C₂×Q₈	—	2	1	no	—
1272	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1273	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1274	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1275	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1276	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1277	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1278	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1279	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1280	C₂×D₄	—	2	1	no	—
1281	C₂×D₄	—	2	1	no	—
1282	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1283	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1284	C₂²×C₄	—	2	1	no	—
1285	C₂²×C₄	—	2	1	no	—
1286	C₂²×C₄	—	2	1	no	—
1287	C₂²×C₄	—	2	1	no	—
1288	C₂²×C₄	—	2	1	no	—
1289	C₂²×C₄	—	2	1	no	—
1290	C₂²×C₄	—	2	1	no	—
1291	C₂²×C₄	—	2	1	no	—
1292	C₂²×C₄	—	2	1	no	—
1293	C₂²×C₄	—	2	1	no	—
1294	C₂²×C₄	—	2	1	no	—
1295	C₂²×C₄	—	2	1	no	—
1296	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1297	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1298	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1299	Q₁₆	—	2	2	no	—
1300	Q₁₆	—	2	2	no	—
1301	Q₁₆	—	2	2	no	—
1302	SD₁₆	—	2	2	no	—
1303	SD₁₆	—	2	2	no	—
1304	SD₁₆	—	2	2	no	—
1305	SD₁₆	—	2	2	no	—
1306	D₈	—	2	2	no	—
1307	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1308	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1309	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1310	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1311	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1312	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1313	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1314	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1315	C₄⋊C₄	—	2	1	no	—
1316	C₄⋊C₄	—	2	1	no	—
1317	C₄⋊C₄	—	2	1	no	—
1318	C₄⋊C₄	—	2	1	no	—
1319	C₄⋊C₄	—	2	1	no	—
1320	C₄⋊C₄	—	2	1	no	—
1321	C₄⋊C₄	—	2	1	no	—
1322	C₄⋊C₄	—	2	1	no	—
1323	C₄⋊C₄	—	2	1	no	—
1324	C₄⋊C₄	—	2	1	no	—
1325	C₄⋊C₄	—	2	1	no	—
1326	C₄⋊C₄	—	2	1	no	—
1327	C₄⋊C₄	—	2	1	no	—
1328	C₄⋊C₄	—	2	1	no	—
1329	C₄⋊C₄	—	2	1	no	—
1330	C₄⋊C₄	—	2	1	no	—
1331	C₄⋊C₄	—	2	1	no	—
1332	C₄⋊C₄	—	2	1	no	—
1333	C₄⋊C₄	—	2	1	no	—
1334	C₄⋊C₄	—	2	1	no	—
1335	C₄⋊C₄	—	2	1	no	—
1336	C₄⋊C₄	—	2	1	no	—
1337	C₄⋊C₄	—	2	1	no	—
1338	C₄⋊C₄	—	2	1	no	—
1339	C₄⋊C₄	—	2	1	no	—
1340	C₄⋊C₄	—	2	1	no	—
1341	C₄⋊C₄	—	2	1	no	—
1342	C₄⋊C₄	—	2	1	no	—
1343	C₄⋊C₄	—	2	1	no	—
1344	C₄⋊C₄	—	2	1	no	—
1345	C₄⋊C₄	—	2	1	no	—
1346	C₄⋊C₄	—	2	1	no	—
1347	C₄⋊C₄	—	2	1	no	—
1348	C₄⋊C₄	—	2	1	no	—
1349	C₄⋊C₄	—	2	1	no	—
1350	C₄⋊C₄	—	2	1	no	—
1351	C₄⋊C₄	—	2	1	no	—
1352	C₄⋊C₄	—	2	1	no	—
1353	C₄⋊C₄	—	2	1	no	—
1354	C₄⋊C₄	—	2	1	no	—
1355	C₄⋊C₄	—	2	1	no	—
1356	C₄⋊C₄	—	2	1	no	—
1357	C₄⋊C₄	—	2	1	no	—
1358	C₄⋊C₄	—	2	1	no	—
1359	C₄⋊C₄	—	2	1	no	—
1360	C₄⋊C₄	—	2	1	no	—
1361	C₄⋊C₄	—	2	1	no	—
1362	C₄⋊C₄	—	2	1	no	—
1363	C₄⋊C₄	—	2	1	no	—
1364	C₄⋊C₄	—	2	1	no	—
1365	C₄⋊C₄	—	2	1	no	—
1366	C₄⋊C₄	—	2	1	no	—
1367	C₄⋊C₄	—	2	1	no	—
1368	C₄⋊C₄	—	2	1	no	—
1369	C₄⋊C₄	—	2	1	no	—
1370	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1371	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1372	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1373	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1374	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1375	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1376	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1377	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1378	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1379	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1380	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1381	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1382	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1383	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1384	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1385	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1386	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1387	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1388	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1389	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1390	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1391	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1392	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1393	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1394	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1395	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1396	C₂²⋊C₄	—	2	1	no	—
1397	C₂²⋊C₄	—	2	1	no	—
1398	C₂²⋊C₄	—	2	1	no	—
1399	C₂²⋊C₄	—	2	1	no	—
1400	C₂²⋊C₄	—	2	1	no	—
1401	C₂²⋊C₄	—	2	1	no	—
1402	C₂²⋊C₄	—	2	1	no	—
1403	C₂²⋊C₄	—	2	1	no	—
1404	C₂²⋊C₄	—	2	1	no	—
1405	C₂²⋊C₄	—	2	1	no	—
1406	C₂²⋊C₄	—	2	1	no	—
1407	C₂²⋊C₄	—	2	1	no	—
1408	C₂²⋊C₄	—	2	1	no	—
1409	C₂²⋊C₄	—	2	1	no	—
1410	C₂²⋊C₄	—	2	1	no	—
1411	C₂²⋊C₄	—	2	1	no	—
1412	C₂²⋊C₄	—	2	1	no	—
1413	C₂²⋊C₄	—	2	1	no	—
1414	C₂²⋊C₄	—	2	1	no	—
1415	C₂²⋊C₄	—	2	1	no	—
1416	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1417	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1418	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1419	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1420	C₄²	—	2	1	no	—
1421	C₄²	—	2	1	no	—
1422	C₄²	—	2	1	no	—
1423	C₄²	—	2	1	no	—
1424	C₄²	—	2	1	no	—
1425	C₄²	—	2	1	no	—
1426	C₄²	—	2	1	no	—
1427	C₄²	—	2	1	no	—
1428	C₄²	—	2	1	no	—
1429	C₄²	—	2	1	no	—
1430	C₄²	—	2	1	no	—
1431	C₄²	—	2	1	no	—
1432	C₄²	—	2	1	no	—
1433	C₄²	—	2	1	no	—
1434	C₄²	—	2	1	no	—
1435	C₄²	—	2	1	no	—
1436	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1437	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1438	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1439	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1440	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1441	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1442	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1443	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1444	C₂³	—	2	1	no	—
1445	C₂³	—	2	1	no	—
1446	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1447	Q₈	—	2	1	no	—
1448	Q₈	—	2	1	no	—
1449	Q₈	—	2	1	no	—
1450	Q₈	—	2	1	no	—
1451	Q₈	—	2	1	no	—
1452	Q₈	—	2	1	no	—
1453	Q₈	—	2	1	no	—
1454	Q₈	—	4	1	no	—
1455	Q₈	—	4	1	no	—
1456	Q₈	—	4	1	no	—
1457	Q₈	—	4	1	no	—
1458	Q₈	—	8	1	no	—
1459	Q₈	—	8	1	no	—
1460	Q₈	—	8	1	no	—
1461	Q₈	—	8	1	no	—
1462	Q₈	—	8	1	no	—
1463	Q₈	—	8	1	no	—
1464	Q₈	—	8	1	no	—
1465	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1466	D₄	—	2	4	no	—
1467	D₄	—	2	1	no	—
1468	D₄	—	2	1	no	—
1469	D₄	—	2	1	no	—
1470	D₄	—	8	1	no	—
1471	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1472	C₂×C₄	—	2	4	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	4	1	no	—
1490	C₂×C₄	—	4	1	no	—
1491	C₂×C₄	—	4	2	no	—
1492	C₂×C₄	—	8	1	no	—
1493	C₂×C₄	—	8	1	no	—
1494	C₂×C₄	—	8	1	no	—
1495	C₂×C₄	—	8	1	no	—
1496	C₂×C₄	—	8	1	no	—
1497	C₂×C₄	—	8	1	no	—
1498	C₂×C₄	—	8	1	no	—
1499	C₂×C₄	—	8	1	no	—
1500	C₂×C₄	—	8	1	no	—
1501	C₂×C₄	—	8	1	no	—
1502	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1503	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1504	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1505	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1506	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1507	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1508	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1509	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1510	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1511	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1512	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1513	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1514	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1515	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1516	C₈	—	2	1	no	—
1517	C₈	—	2	1	no	—
1518	C₈	—	2	1	no	—
1519	C₈	—	2	1	no	—
1520	C₈	—	2	1	no	—
1521	C₈	—	2	1	no	—
1522	C₈	—	2	1	no	—
1523	C₈	—	2	1	no	—
1524	C₂²	—	2	1	no	—
1525	C₂²	—	2	2	no	—
1526	C₂²	—	2	1	no	—
1527	C₂²	—	2	1	no	—
1528	C₂²	—	4	1	no	—
1529	C₂²	—	4	1	no	—
1530	C₂²	—	4	1	no	—
1531	C₂²	—	4	1	no	—
1532	C₂²	—	4	1	no	—
1533	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1534	C₄	—	2	1	no	—
1535	C₄	—	2	2	no	—
1536	C₄	—	2	1	no	—
1537	C₄	—	2	1	no	—
1538	C₄	—	2	1	no	—
1539	C₄	—	2	1	no	—
1540	C₄	—	2	1	no	—
1541	C₄	—	2	1	no	—
1542	C₄	—	2	1	no	—
1543	C₄	—	2	1	no	—
1544	C₄	—	2	1	no	—
1545	C₄	—	2	1	no	—
1546	C₄	—	2	1	no	—
1547	C₄	—	2	1	no	—
1548	C₄	—	4	1	no	—
1549	C₄	—	4	1	no	—
1550	C₄	—	4	1	no	—
1551	C₄	—	4	1	no	—
1552	C₄	—	4	1	no	—
1553	C₄	—	4	1	no	—
1554	C₄	—	4	1	no	—
1555	C₄	—	4	1	no	—
1556	C₄	—	4	1	no	—
1557	C₄	—	4	1	no	—
1558	C₄	—	4	1	no	—
1559	C₄	—	4	1	no	—
1560	C₄	—	4	1	no	—
1561	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1562	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1563	C₂	—	4	1	no	—
1564	C₂	—	4	2	no	—
1565	C₂	—	8	1	no	—
1566	C₂	C₃₁×#3486	1	1	yes	characteristic
1567	C₂	C₃₁×#3584	1	1	yes	characteristic
1568	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×#449	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3555	C₂	semidirect
2. C₃₁×#3504	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3389	C₂	semidirect
5. C₃₁×#3388	C₂	semidirect
6. C₃₁×#3388	C₂	semidirect
7. C₃₁×#3387	C₂	semidirect
8. C₃₁×#3385	C₂	semidirect
9. C₃₁×#3383	C₂	semidirect
10. C₃₁×#3381	C₂	semidirect
11. C₃₁×#3377	C₂	semidirect
12. C₃₁×#3377	C₂	semidirect
13. C₃₁×#3376	C₂	semidirect
14. C₃₁×#3376	C₂	semidirect
15. C₃₁×#3374	C₂	semidirect
16. C₃₁×#3372	C₂	semidirect
17. C₃₁×#3364	C₂	semidirect
18. C₃₁×#3360	C₂	semidirect
19. C₃₁×#3244	C₂	semidirect
20. C₃₁×#3243	C₂	semidirect
21. C₃₁×#3242	C₂	semidirect
22. C₃₁×#3242	C₂	semidirect
23. C₃₁×#3236	C₂	semidirect
24. C₃₁×#3232	C₂	semidirect
27. C₃₁×#3120	C₂	semidirect
28. C₃₁×#3120	C₂	semidirect
30. C₃₁×#3107	C₂	semidirect
31. C₃₁×#2985	C₂	semidirect
659. #61862	C₃₁	direct (N × H)
740. #3555	C₂×C₃₁	semidirect
741. #3504	C₂×C₃₁	semidirect
742. #3390	C₂×C₃₁	semidirect
743. #3389	C₂×C₃₁	semidirect
744. #3388	C₂×C₃₁	semidirect
745. #3388	C₂×C₃₁	semidirect
746. #3387	C₂×C₃₁	semidirect
747. #3385	C₂×C₃₁	semidirect
748. #3383	C₂×C₃₁	semidirect
749. #3381	C₂×C₃₁	semidirect
750. #3377	C₂×C₃₁	semidirect
751. #3377	C₂×C₃₁	semidirect
752. #3376	C₂×C₃₁	semidirect
753. #3376	C₂×C₃₁	semidirect
754. #3374	C₂×C₃₁	semidirect
755. #3372	C₂×C₃₁	semidirect
756. #3364	C₂×C₃₁	semidirect
757. #3360	C₂×C₃₁	semidirect
758. #3244	C₂×C₃₁	semidirect
759. #3243	C₂×C₃₁	semidirect
760. #3242	C₂×C₃₁	semidirect
761. #3242	C₂×C₃₁	semidirect
762. #3236	C₂×C₃₁	semidirect
763. #3232	C₂×C₃₁	semidirect
766. #3120	C₂×C₃₁	semidirect
767. #3120	C₂×C₃₁	semidirect
769. #3107	C₂×C₃₁	semidirect
770. #2985	C₂×C₃₁	semidirect
1262. C₃₁	#61862	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×#3555	2
C₃₁×#3504	2
C₃₁×#3390	2
C₃₁×#3389	2
C₃₁×#3388	2
C₃₁×#3387	2
C₃₁×#3385	2
C₃₁×#3383	2
C₃₁×#3381	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3374	2
C₃₁×#3372	2
C₃₁×#3364	2
C₃₁×#3360	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3236	2
C₃₁×#3232	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3120	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#2985	2
#61862	31

Subgroups — C31×#61862 #21518621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61862 #21518621