Subgroups — C₃₁×#62228 #21518987

Order 7936.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3351	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3349	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3348	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3345	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3344	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3323	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3319	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3314	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3306	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3262	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3256	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3243	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3118	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3111	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2995	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, complemented
35	C₃₁×#556	C₂²	1	1	yes	characteristic
36	C₃₁×#556	C₂²	1	1	yes	characteristic
37	C₃₁×#555	C₂²	1	1	yes	characteristic
38	C₃₁×#554	C₂²	1	1	yes	characteristic
39	C₃₁×#554	C₂²	1	1	yes	characteristic
40	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#553	—	2	1	no	—
42	C₃₁×#553	C₂²	1	1	yes	characteristic
43	C₃₁×#552	—	2	1	no	—
44	C₃₁×#552	—	2	1	no	—
45	C₃₁×#552	C₂²	1	1	yes	characteristic
46	C₃₁×#552	C₂²	1	1	yes	characteristic
47	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#551	—	2	1	no	—
49	C₃₁×#551	—	2	1	no	—
50	C₃₁×#547	—	2	1	no	—
51	C₃₁×#547	C₂²	1	1	yes	characteristic
52	C₃₁×#547	C₂²	1	1	yes	characteristic
53	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#546	C₂²	1	1	yes	characteristic
55	C₃₁×#546	C₂²	1	1	yes	characteristic
56	C₃₁×#544	—	2	1	no	—
57	C₃₁×#544	C₂²	1	1	yes	characteristic
58	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#542	—	2	1	no	—
60	C₃₁×#542	C₂²	1	1	yes	characteristic
61	C₃₁×#542	C₂²	1	1	yes	characteristic
62	C₃₁×#542	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#541	C₂²	1	1	yes	characteristic
64	C₃₁×#539	—	2	1	no	—
65	C₃₁×#538	—	2	1	no	—
66	C₃₁×#536	—	2	1	no	—
67	C₃₁×#536	—	2	1	no	—
68	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#529	—	2	1	no	—
70	C₃₁×#529	C₂²	1	1	yes	characteristic
71	C₃₁×#529	C₂²	1	1	yes	characteristic
72	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₃₁×#126	—	2	1	no	—
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#518	C₂²	1	1	yes	characteristic
76	C₄×#41×C₃₁	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×#501	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#489	C₂²	1	1	yes	characteristic
85	C₃₁×#489	C₂²	1	1	yes	characteristic
86	C₃₁×#489	C₂²	1	1	yes	characteristic
87	C₃₁×#488	C₂²	1	1	yes	characteristic
88	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
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, complemented
93	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#484	C₂²	1	1	yes	characteristic
95	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#483	C₂²	1	1	yes	characteristic
99	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#482	C₂²	1	1	yes	characteristic
101	C₃₁×#482	C₂²	1	1	yes	characteristic
102	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#481	C₂²	1	1	yes	characteristic
104	C₃₁×#481	C₂²	1	1	yes	characteristic
105	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#480	C₂²	1	1	yes	characteristic
107	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#478	C₂²	1	1	yes	characteristic
113	C₃₁×#478	C₂²	1	1	yes	characteristic
114	C₃₁×#478	C₂²	1	1	yes	characteristic
115	C₃₁×#478	C₂²	1	1	yes	characteristic
116	C₃₁×#478	C₂²	1	1	yes	characteristic
117	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#476	C₂²	1	1	yes	characteristic
123	C₃₁×#476	C₂²	1	1	yes	characteristic
124	C₃₁×#476	C₂²	1	1	yes	characteristic
125	C₃₁×#476	C₂²	1	1	yes	characteristic
126	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#474	C₂²	1	1	yes	characteristic
132	C₃₁×#474	C₂²	1	1	yes	characteristic
133	C₃₁×#474	C₂²	1	1	yes	characteristic
134	C₃₁×#474	C₂²	1	1	yes	characteristic
135	C₃₁×#474	C₂²	1	1	yes	characteristic
136	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#470	C₂²	1	1	yes	characteristic
138	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
139	C₃₁×#469	C₂²	1	1	yes	characteristic
140	C₃₁×#468	C₂²	1	1	yes	characteristic
141	C₃₁×#468	C₂²	1	1	yes	characteristic
142	C₃₁×#468	C₂²	1	1	yes	characteristic
143	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
144	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
145	C₃₁×#467	C₂²	1	1	yes	characteristic
146	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
147	C₃₁×#466	C₂²	1	1	yes	characteristic
148	C₃₁×#465	C₂²	1	1	yes	characteristic
149	C₃₁×#464	C₂²	1	1	yes	characteristic
150	C₃₁×#464	C₂²	1	1	yes	characteristic
151	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
152	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
153	C₃₁×#463	C₂²	1	1	yes	characteristic
154	C₃₁×#463	C₂²	1	1	yes	characteristic
155	C₃₁×#463	C₂²	1	1	yes	characteristic
156	C₃₁×#463	C₂²	1	1	yes	characteristic
157	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
158	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
159	C₃₁×#452	C₂²	1	1	yes	characteristic
160	C₃₁×#452	C₂²	1	1	yes	characteristic
161	C₃₁×#450	C₂²	1	1	yes	characteristic
162	C₃₁×#449	C₂²	1	1	yes	characteristic
163	C₃₁×#449	C₂²	1	1	yes	characteristic
164	C₃₁×#447	C₂²	1	1	yes	characteristic
165	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
166	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
167	C₃₁×#442	C₂²	1	1	yes	characteristic
168	C₃₁×#442	C₂²	1	1	yes	characteristic
169	C₃₁×#442	C₂²	1	1	yes	characteristic
170	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
171	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
172	C₃₁×#440	C₂²	1	1	yes	characteristic
173	C₃₁×#440	C₂²	1	1	yes	characteristic
174	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
179	C₃₁×#436	C₂²	1	1	yes	characteristic
180	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
181	C₃₁×#435	C₂²	1	1	yes	characteristic
182	C₃₁×#435	C₂²	1	1	yes	characteristic
183	C₃₁×#435	C₂²	1	1	yes	characteristic
184	C₃₁×#435	C₂²	1	1	yes	characteristic, complemented
185	C₃₁×#433	C₂²	1	1	yes	characteristic
186	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
187	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
188	C₃₁×#428	C₂²	1	1	yes	characteristic
189	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
190	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
191	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
192	C₃₁×#427	C₂²	1	1	yes	characteristic
193	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
194	C₃₁×#424	C₂²	1	1	yes	characteristic
195	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
196	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
197	C₃₁×#418	C₂²	1	1	yes	characteristic
198	C₃₁×#417	C₂²	1	1	yes	characteristic
199	C₃₁×#417	C₂²	1	1	yes	characteristic
200	C₃₁×#417	C₂²	1	1	yes	characteristic
201	C₃₁×#416	C₂²	1	1	yes	characteristic
202	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	—	2	1	no	—
204	C₂×#41×C₃₁	—	2	1	no	—
205	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₃₁	—	2	1	no	—
208	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₃₁×C₄⋊Q₈	—	2	1	no	—
224	C₃₁×C₄⋊Q₈	—	2	1	no	—
225	C₃₁×C₄⋊Q₈	—	2	1	no	—
226	C₃₁×C₄⋊Q₈	—	2	1	no	—
227	C₃₁×C₄⋊Q₈	—	2	1	no	—
228	C₃₁×C₄⋊Q₈	—	2	1	no	—
229	C₃₁×C₄⋊Q₈	—	2	1	no	—
230	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
233	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
234	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
235	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
236	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
237	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
238	C₃₁×#126	—	2	1	no	—
239	C₃₁×#126	—	2	1	no	—
240	C₃₁×#126	—	2	1	no	—
241	C₃₁×#126	—	2	1	no	—
242	C₃₁×#126	—	2	1	no	—
243	C₃₁×#126	—	2	1	no	—
244	C₃₁×#126	—	2	1	no	—
245	C₃₁×#126	—	2	1	no	—
246	C₃₁×#126	—	2	1	no	—
247	C₃₁×#126	—	2	1	no	—
248	C₃₁×#126	—	2	1	no	—
249	C₃₁×#126	—	2	1	no	—
250	C₃₁×#126	—	2	1	no	—
251	C₃₁×#126	—	2	1	no	—
252	C₃₁×#126	—	2	1	no	—
253	C₃₁×#126	D₄	1	1	yes	characteristic
254	C₃₁×#126	D₄	1	1	yes	characteristic
255	C₃₁×#125	—	2	1	no	—
256	C₃₁×#125	—	2	1	no	—
257	C₃₁×#125	—	2	1	no	—
258	C₃₁×#125	—	2	1	no	—
259	C₃₁×#125	—	2	1	no	—
260	C₃₁×#125	—	2	1	no	—
261	C₃₁×#125	—	2	1	no	—
262	C₃₁×#125	—	2	1	no	—
263	C₃₁×#125	D₄	1	1	yes	characteristic
264	C₃₁×#125	C₂³	1	1	yes	characteristic
265	C₃₁×#125	C₂³	1	1	yes	characteristic
266	C₃₁×#125	C₂³	1	1	yes	characteristic
267	C₃₁×#125	C₂³	1	1	yes	characteristic
268	C₃₁×#125	C₂³	1	1	yes	characteristic
269	C₃₁×#124	—	2	1	no	—
270	C₃₁×#124	—	2	1	no	—
271	C₃₁×#124	—	2	1	no	—
272	C₃₁×#124	—	2	1	no	—
273	C₃₁×#124	—	2	1	no	—
274	C₃₁×#124	—	2	1	no	—
275	C₃₁×#124	D₄	1	1	yes	characteristic
276	C₃₁×#124	C₂³	1	1	yes	characteristic
277	C₃₁×#124	C₂³	1	1	yes	characteristic
278	C₃₁×#124	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
285	C₃₁×#123	—	2	1	no	—
286	C₃₁×#123	—	2	1	no	—
287	C₃₁×#123	—	2	1	no	—
288	C₃₁×#123	—	2	1	no	—
289	C₃₁×#123	—	2	1	no	—
290	C₃₁×#123	—	2	1	no	—
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×#123	—	2	1	no	—
294	C₃₁×#123	—	2	1	no	—
295	C₃₁×#123	—	2	1	no	—
296	C₃₁×#123	D₄	1	1	yes	characteristic
297	C₃₁×#123	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
317	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
319	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
320	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
321	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
322	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₃₁×#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	—	2	1	no	—
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×#120	—	2	1	no	—
336	C₃₁×#120	—	2	1	no	—
337	C₄×Q₈×C₃₁	—	2	1	no	—
338	C₄×Q₈×C₃₁	—	2	1	no	—
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×D₄×C₃₁	—	2	1	no	—
348	C₄×D₄×C₃₁	—	2	1	no	—
349	C₄×D₄×C₃₁	—	2	1	no	—
350	C₄×D₄×C₃₁	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
358	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
359	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
360	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#117	—	2	1	no	—
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	C₃₁×#117	C₂³	1	1	yes	characteristic
382	C₃₁×#117	C₂³	1	1	yes	characteristic
383	C₃₁×#117	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
390	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
391	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
394	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
395	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
396	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
397	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
398	C₂×C₄²×C₃₁	—	2	1	no	—
399	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
400	C₃₁×#107	C₂³	1	1	yes	characteristic
401	C₃₁×#107	C₂³	1	1	yes	characteristic
402	C₃₁×#107	C₂³	1	1	yes	characteristic
403	C₃₁×#107	C₂³	1	1	yes	characteristic
404	C₃₁×#107	C₂³	1	1	yes	characteristic
405	C₃₁×#107	C₂³	1	1	yes	characteristic
406	C₃₁×#107	C₂³	1	1	yes	characteristic
407	C₃₁×#107	C₂³	1	1	yes	characteristic
408	C₃₁×#107	C₂³	1	1	yes	characteristic
409	C₃₁×#107	C₂³	1	1	yes	characteristic
410	C₃₁×#107	C₂³	1	1	yes	characteristic
411	C₃₁×#107	C₂³	1	1	yes	characteristic
412	C₃₁×#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×#106	C₂³	1	1	yes	characteristic
419	C₃₁×#106	C₂³	1	1	yes	characteristic
420	C₃₁×#106	C₂³	1	1	yes	characteristic
421	C₃₁×#106	C₂³	1	1	yes	characteristic
422	C₃₁×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	C₂³	1	1	yes	characteristic
424	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#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×#102	C₂³	1	1	yes	characteristic
463	C₃₁×#102	C₂³	1	1	yes	characteristic
464	C₃₁×#102	C₂³	1	1	yes	characteristic
465	C₃₁×#102	C₂³	1	1	yes	characteristic
466	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	C₃₁×#97	C₂³	1	1	yes	characteristic
473	C₃₁×#97	C₂³	1	1	yes	characteristic
474	C₃₁×#97	C₂³	1	1	yes	characteristic
475	C₃₁×#97	C₂³	1	1	yes	characteristic
476	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
478	C₂⁴×C₃₁	—	2	1	no	—
479	#41×C₃₁	—	2	2	no	—
480	#41×C₃₁	—	2	2	no	—
481	#41×C₃₁	—	4	1	no	—
482	#41×C₃₁	—	4	1	no	—
483	#41×C₃₁	—	8	2	no	—
484	#41×C₃₁	—	8	2	no	—
485	C₂×Q₈×C₃₁	—	2	1	no	—
486	C₂×Q₈×C₃₁	—	2	1	no	—
487	C₂×Q₈×C₃₁	—	2	1	no	—
488	C₂×Q₈×C₃₁	—	2	1	no	—
489	C₂×Q₈×C₃₁	—	2	1	no	—
490	C₂×Q₈×C₃₁	—	2	1	no	—
491	C₂×Q₈×C₃₁	—	2	1	no	—
492	C₂×Q₈×C₃₁	—	8	2	no	—
493	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
496	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
497	C₂×D₄×C₃₁	—	2	2	no	—
498	C₂×D₄×C₃₁	—	2	1	no	—
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	—	4	1	no	—
507	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
508	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
509	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
510	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
511	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
512	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄×C₃₁	—	2	1	no	—
514	C₂²×C₄×C₃₁	—	2	1	no	—
515	C₂²×C₄×C₃₁	—	2	1	no	—
516	C₂²×C₄×C₃₁	—	2	1	no	—
517	C₂²×C₄×C₃₁	—	2	1	no	—
518	C₂²×C₄×C₃₁	—	2	1	no	—
519	C₂²×C₄×C₃₁	—	2	1	no	—
520	C₂²×C₄×C₃₁	—	2	1	no	—
521	C₂²×C₄×C₃₁	—	2	1	no	—
522	C₂²×C₄×C₃₁	—	2	1	no	—
523	C₂²×C₄×C₃₁	—	2	1	no	—
524	C₂²×C₄×C₃₁	—	2	1	no	—
525	C₂²×C₄×C₃₁	—	2	1	no	—
526	C₂²×C₄×C₃₁	—	2	1	no	—
527	C₂²×C₄×C₃₁	—	2	1	no	—
528	C₂²×C₄×C₃₁	—	2	1	no	—
529	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
530	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
531	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
532	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
533	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
534	Q₁₆×C₃₁	—	4	1	no	—
535	Q₁₆×C₃₁	—	4	1	no	—
536	SD₁₆×C₃₁	—	2	2	no	—
537	SD₁₆×C₃₁	—	4	1	no	—
538	SD₁₆×C₃₁	—	4	1	no	—
539	SD₁₆×C₃₁	—	4	1	no	—
540	D₈×C₃₁	—	2	2	no	—
541	D₈×C₃₁	—	4	1	no	—
542	M₁₆×C₃₁	—	4	1	no	—
543	M₁₆×C₃₁	—	4	1	no	—
544	M₁₆×C₃₁	—	4	1	no	—
545	M₁₆×C₃₁	—	4	1	no	—
546	C₂×C₈×C₃₁	—	4	1	no	—
547	C₂×C₈×C₃₁	—	4	1	no	—
548	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
549	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
550	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
551	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
552	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
553	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
554	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
555	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
556	C₄⋊C₄×C₃₁	—	2	1	no	—
557	C₄⋊C₄×C₃₁	—	2	1	no	—
558	C₄⋊C₄×C₃₁	—	2	1	no	—
559	C₄⋊C₄×C₃₁	—	2	1	no	—
560	C₄⋊C₄×C₃₁	—	2	1	no	—
561	C₄⋊C₄×C₃₁	—	2	1	no	—
562	C₄⋊C₄×C₃₁	—	2	1	no	—
563	C₄⋊C₄×C₃₁	—	2	1	no	—
564	C₄⋊C₄×C₃₁	—	2	1	no	—
565	C₄⋊C₄×C₃₁	—	2	1	no	—
566	C₄⋊C₄×C₃₁	—	2	1	no	—
567	C₄⋊C₄×C₃₁	—	2	1	no	—
568	C₄⋊C₄×C₃₁	—	2	1	no	—
569	C₄⋊C₄×C₃₁	—	2	1	no	—
570	C₄⋊C₄×C₃₁	—	2	1	no	—
571	C₄⋊C₄×C₃₁	—	2	1	no	—
572	C₄⋊C₄×C₃₁	—	2	1	no	—
573	C₄⋊C₄×C₃₁	—	2	1	no	—
574	C₄⋊C₄×C₃₁	—	2	1	no	—
575	C₄⋊C₄×C₃₁	—	2	1	no	—
576	C₄⋊C₄×C₃₁	—	2	1	no	—
577	C₄⋊C₄×C₃₁	—	2	1	no	—
578	C₄⋊C₄×C₃₁	—	2	1	no	—
579	C₄⋊C₄×C₃₁	—	2	1	no	—
580	C₄⋊C₄×C₃₁	—	2	1	no	—
581	C₄⋊C₄×C₃₁	—	2	1	no	—
582	C₄⋊C₄×C₃₁	—	2	1	no	—
583	C₄⋊C₄×C₃₁	—	2	1	no	—
584	C₄⋊C₄×C₃₁	—	2	1	no	—
585	C₄⋊C₄×C₃₁	—	2	1	no	—
586	C₄⋊C₄×C₃₁	—	2	1	no	—
587	C₄⋊C₄×C₃₁	—	2	1	no	—
588	C₄⋊C₄×C₃₁	—	2	1	no	—
589	C₄⋊C₄×C₃₁	—	2	1	no	—
590	C₄⋊C₄×C₃₁	—	2	1	no	—
591	C₄⋊C₄×C₃₁	—	2	1	no	—
592	C₄⋊C₄×C₃₁	—	2	1	no	—
593	C₄⋊C₄×C₃₁	—	2	1	no	—
594	C₄⋊C₄×C₃₁	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	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄×C₃₁	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	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
614	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	—	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	C₂×D₄	1	1	yes	characteristic
646	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
647	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
648	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
649	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
650	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
655	C₄²×C₃₁	—	2	1	no	—
656	C₄²×C₃₁	—	2	1	no	—
657	C₄²×C₃₁	—	2	1	no	—
658	C₄²×C₃₁	—	2	1	no	—
659	C₄²×C₃₁	—	2	1	no	—
660	C₄²×C₃₁	—	2	1	no	—
661	C₄²×C₃₁	—	2	1	no	—
662	C₄²×C₃₁	—	2	1	no	—
663	C₄²×C₃₁	—	2	1	no	—
664	C₄²×C₃₁	—	2	1	no	—
665	C₄²×C₃₁	—	2	1	no	—
666	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
667	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
668	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
669	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
670	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
671	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
672	#62228	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
673	C₂³×C₃₁	—	2	1	no	—
674	C₂³×C₃₁	—	2	1	no	—
675	C₂³×C₃₁	—	2	1	no	—
676	C₂³×C₃₁	—	4	2	no	—
677	C₂³×C₃₁	—	8	1	no	—
678	C₂³×C₃₁	—	8	1	no	—
679	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
680	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
681	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
682	Q₈×C₃₁	—	2	1	no	—
683	Q₈×C₃₁	—	2	1	no	—
684	Q₈×C₃₁	—	2	1	no	—
685	Q₈×C₃₁	—	2	1	no	—
686	Q₈×C₃₁	—	2	1	no	—
687	Q₈×C₃₁	—	2	1	no	—
688	Q₈×C₃₁	—	4	1	no	—
689	Q₈×C₃₁	—	8	1	no	—
690	Q₈×C₃₁	—	8	1	no	—
691	Q₈×C₃₁	—	8	1	no	—
692	Q₈×C₃₁	—	8	1	no	—
693	Q₈×C₃₁	—	8	1	no	—
694	Q₈×C₃₁	—	8	1	no	—
695	Q₈×C₃₁	—	8	1	no	—
696	D₄×C₃₁	—	2	1	no	—
697	D₄×C₃₁	—	2	1	no	—
698	D₄×C₃₁	—	2	1	no	—
699	D₄×C₃₁	—	2	1	no	—
700	D₄×C₃₁	—	2	1	no	—
701	D₄×C₃₁	—	4	1	no	—
702	D₄×C₃₁	—	4	1	no	—
703	D₄×C₃₁	—	4	1	no	—
704	D₄×C₃₁	—	4	2	no	—
705	D₄×C₃₁	—	4	2	no	—
706	D₄×C₃₁	—	4	2	no	—
707	D₄×C₃₁	—	4	2	no	—
708	D₄×C₃₁	—	8	1	no	—
709	D₄×C₃₁	—	8	1	no	—
710	D₄×C₃₁	—	8	1	no	—
711	D₄×C₃₁	—	8	1	no	—
712	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
713	C₂×C₄×C₃₁	—	2	1	no	—
714	C₂×C₄×C₃₁	—	2	1	no	—
715	C₂×C₄×C₃₁	—	2	1	no	—
716	C₂×C₄×C₃₁	—	2	1	no	—
717	C₂×C₄×C₃₁	—	2	1	no	—
718	C₂×C₄×C₃₁	—	2	1	no	—
719	C₂×C₄×C₃₁	—	2	1	no	—
720	C₂×C₄×C₃₁	—	2	1	no	—
721	C₂×C₄×C₃₁	—	2	1	no	—
722	C₂×C₄×C₃₁	—	2	1	no	—
723	C₂×C₄×C₃₁	—	2	1	no	—
724	C₂×C₄×C₃₁	—	2	1	no	—
725	C₂×C₄×C₃₁	—	2	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	2	1	no	—
728	C₂×C₄×C₃₁	—	2	1	no	—
729	C₂×C₄×C₃₁	—	2	1	no	—
730	C₂×C₄×C₃₁	—	2	1	no	—
731	C₂×C₄×C₃₁	—	2	1	no	—
732	C₂×C₄×C₃₁	—	4	1	no	—
733	C₂×C₄×C₃₁	—	4	1	no	—
734	C₂×C₄×C₃₁	—	4	2	no	—
735	C₂×C₄×C₃₁	—	4	2	no	—
736	C₂×C₄×C₃₁	—	4	2	no	—
737	C₂×C₄×C₃₁	—	4	2	no	—
738	C₂×C₄×C₃₁	—	4	2	no	—
739	C₂×C₄×C₃₁	—	8	1	no	—
740	C₂×C₄×C₃₁	—	8	1	no	—
741	C₂×C₄×C₃₁	—	8	1	no	—
742	C₂×C₄×C₃₁	—	8	1	no	—
743	C₂×C₄×C₃₁	—	8	1	no	—
744	C₂×C₄×C₃₁	—	8	1	no	—
745	C₂×C₄×C₃₁	—	8	1	no	—
746	C₂×C₄×C₃₁	—	8	1	no	—
747	C₂×C₄×C₃₁	—	8	1	no	—
748	C₂×C₄×C₃₁	—	8	1	no	—
749	C₂×C₄×C₃₁	—	8	1	no	—
750	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
751	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
752	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
753	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
754	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
755	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
756	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
757	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
758	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
759	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
760	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
762	C₈×C₃₁	—	2	1	no	—
763	C₈×C₃₁	—	2	1	no	—
764	C₈×C₃₁	—	2	1	no	—
765	C₈×C₃₁	—	2	1	no	—
766	C₈×C₃₁	—	2	1	no	—
767	C₈×C₃₁	—	2	1	no	—
768	C₈×C₃₁	—	2	1	no	—
769	C₈×C₃₁	—	2	1	no	—
770	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
771	#3521	C₂×C₃₁	1	1	yes	characteristic, complemented
772	#3389	C₂×C₃₁	1	1	yes	characteristic, complemented
773	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
774	#3376	C₂×C₃₁	1	1	yes	characteristic, complemented
775	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
776	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
777	#3351	C₂×C₃₁	1	1	yes	characteristic, complemented
778	#3349	C₂×C₃₁	1	1	yes	characteristic, complemented
779	#3348	C₂×C₃₁	1	1	yes	characteristic, complemented
780	#3345	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3344	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3323	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3319	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3314	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3306	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3262	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3258	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3256	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3243	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3125	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3118	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3111	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#2995	C₂×C₃₁	1	1	yes	characteristic, complemented
801	C₂²×C₃₁	—	2	1	no	—
802	C₂²×C₃₁	—	2	1	no	—
803	C₂²×C₃₁	—	2	1	no	—
804	C₂²×C₃₁	—	2	1	no	—
805	C₂²×C₃₁	—	2	1	no	—
806	C₂²×C₃₁	—	2	1	no	—
807	C₂²×C₃₁	—	2	1	no	—
808	C₂²×C₃₁	—	2	1	no	—
809	C₂²×C₃₁	—	2	1	no	—
810	C₂²×C₃₁	—	2	2	no	—
811	C₂²×C₃₁	—	4	1	no	—
812	C₂²×C₃₁	—	4	1	no	—
813	C₂²×C₃₁	—	4	1	no	—
814	C₂²×C₃₁	—	4	1	no	—
815	C₂²×C₃₁	—	4	1	no	—
816	C₂²×C₃₁	—	4	1	no	—
817	C₂²×C₃₁	—	4	1	no	—
818	C₂²×C₃₁	—	4	1	no	—
819	C₂²×C₃₁	—	16	2	no	—
820	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
821	C₄×C₃₁	—	2	1	no	—
822	C₄×C₃₁	—	2	1	no	—
823	C₄×C₃₁	—	2	1	no	—
824	C₄×C₃₁	—	2	1	no	—
825	C₄×C₃₁	—	2	1	no	—
826	C₄×C₃₁	—	2	1	no	—
827	C₄×C₃₁	—	2	1	no	—
828	C₄×C₃₁	—	2	1	no	—
829	C₄×C₃₁	—	2	1	no	—
830	C₄×C₃₁	—	2	1	no	—
831	C₄×C₃₁	—	2	1	no	—
832	C₄×C₃₁	—	4	1	no	—
833	C₄×C₃₁	—	4	1	no	—
834	C₄×C₃₁	—	4	1	no	—
835	C₄×C₃₁	—	4	1	no	—
836	C₄×C₃₁	—	4	1	no	—
837	C₄×C₃₁	—	4	1	no	—
838	C₄×C₃₁	—	4	1	no	—
839	C₄×C₃₁	—	4	1	no	—
840	C₄×C₃₁	—	4	1	no	—
841	C₄×C₃₁	—	4	1	no	—
842	C₄×C₃₁	—	4	1	no	—
843	C₄×C₃₁	—	4	1	no	—
844	C₄×C₃₁	—	4	1	no	—
845	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
846	C₄×C₃₁	#585	1	1	yes	characteristic
847	#563	—	2	1	no	—
848	#563	—	2	1	no	—
849	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
850	#556	C₂²×C₃₁	1	1	yes	characteristic
851	#556	C₂²×C₃₁	1	1	yes	characteristic
852	#555	C₂²×C₃₁	1	1	yes	characteristic
853	#554	C₂²×C₃₁	1	1	yes	characteristic
854	#554	C₂²×C₃₁	1	1	yes	characteristic
855	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
856	#553	—	2	1	no	—
857	#553	C₂²×C₃₁	1	1	yes	characteristic
858	#552	—	2	1	no	—
859	#552	—	2	1	no	—
860	#552	C₂²×C₃₁	1	1	yes	characteristic
861	#552	C₂²×C₃₁	1	1	yes	characteristic
862	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
863	#551	—	2	1	no	—
864	#551	—	2	1	no	—
865	#547	—	2	1	no	—
866	#547	C₂²×C₃₁	1	1	yes	characteristic
867	#547	C₂²×C₃₁	1	1	yes	characteristic
868	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
869	#546	C₂²×C₃₁	1	1	yes	characteristic
870	#546	C₂²×C₃₁	1	1	yes	characteristic
871	#544	—	2	1	no	—
872	#544	C₂²×C₃₁	1	1	yes	characteristic
873	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
874	#542	—	2	1	no	—
875	#542	C₂²×C₃₁	1	1	yes	characteristic
876	#542	C₂²×C₃₁	1	1	yes	characteristic
877	#542	C₂²×C₃₁	1	1	yes	characteristic, complemented
878	#541	C₂²×C₃₁	1	1	yes	characteristic
879	#539	—	2	1	no	—
880	#538	—	2	1	no	—
881	#536	—	2	1	no	—
882	#536	—	2	1	no	—
883	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
884	#529	—	2	1	no	—
885	#529	C₂²×C₃₁	1	1	yes	characteristic
886	#529	C₂²×C₃₁	1	1	yes	characteristic
887	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
888	C₂×#126	—	2	1	no	—
889	#520	C₂²×C₃₁	1	1	yes	characteristic
890	#518	C₂²×C₃₁	1	1	yes	characteristic
891	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
892	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
893	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
894	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
895	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
896	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
897	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
898	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
899	#489	C₂²×C₃₁	1	1	yes	characteristic
900	#489	C₂²×C₃₁	1	1	yes	characteristic
901	#489	C₂²×C₃₁	1	1	yes	characteristic
902	#488	C₂²×C₃₁	1	1	yes	characteristic
903	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
904	#485	C₂²×C₃₁	1	1	yes	characteristic
905	#485	C₂²×C₃₁	1	1	yes	characteristic
906	#485	C₂²×C₃₁	1	1	yes	characteristic
907	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
908	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
909	#484	C₂²×C₃₁	1	1	yes	characteristic
910	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
911	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
912	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
913	#483	C₂²×C₃₁	1	1	yes	characteristic
914	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#482	C₂²×C₃₁	1	1	yes	characteristic
916	#482	C₂²×C₃₁	1	1	yes	characteristic
917	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
918	#481	C₂²×C₃₁	1	1	yes	characteristic
919	#481	C₂²×C₃₁	1	1	yes	characteristic
920	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
921	#480	C₂²×C₃₁	1	1	yes	characteristic
922	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
923	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
924	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
925	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
926	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
927	#478	C₂²×C₃₁	1	1	yes	characteristic
928	#478	C₂²×C₃₁	1	1	yes	characteristic
929	#478	C₂²×C₃₁	1	1	yes	characteristic
930	#478	C₂²×C₃₁	1	1	yes	characteristic
931	#478	C₂²×C₃₁	1	1	yes	characteristic
932	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
933	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
934	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
935	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
936	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
937	#476	C₂²×C₃₁	1	1	yes	characteristic
938	#476	C₂²×C₃₁	1	1	yes	characteristic
939	#476	C₂²×C₃₁	1	1	yes	characteristic
940	#476	C₂²×C₃₁	1	1	yes	characteristic
941	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
942	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
943	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
944	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
945	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
946	#474	C₂²×C₃₁	1	1	yes	characteristic
947	#474	C₂²×C₃₁	1	1	yes	characteristic
948	#474	C₂²×C₃₁	1	1	yes	characteristic
949	#474	C₂²×C₃₁	1	1	yes	characteristic
950	#474	C₂²×C₃₁	1	1	yes	characteristic
951	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
952	#470	C₂²×C₃₁	1	1	yes	characteristic
953	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
954	#469	C₂²×C₃₁	1	1	yes	characteristic
955	#468	C₂²×C₃₁	1	1	yes	characteristic
956	#468	C₂²×C₃₁	1	1	yes	characteristic
957	#468	C₂²×C₃₁	1	1	yes	characteristic
958	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
959	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
960	#467	C₂²×C₃₁	1	1	yes	characteristic
961	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
962	#466	C₂²×C₃₁	1	1	yes	characteristic
963	#465	C₂²×C₃₁	1	1	yes	characteristic
964	#464	C₂²×C₃₁	1	1	yes	characteristic
965	#464	C₂²×C₃₁	1	1	yes	characteristic
966	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
967	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
968	#463	C₂²×C₃₁	1	1	yes	characteristic
969	#463	C₂²×C₃₁	1	1	yes	characteristic
970	#463	C₂²×C₃₁	1	1	yes	characteristic
971	#463	C₂²×C₃₁	1	1	yes	characteristic
972	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
973	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
974	#452	C₂²×C₃₁	1	1	yes	characteristic
975	#452	C₂²×C₃₁	1	1	yes	characteristic
976	#450	C₂²×C₃₁	1	1	yes	characteristic
977	#449	C₂²×C₃₁	1	1	yes	characteristic
978	#449	C₂²×C₃₁	1	1	yes	characteristic
979	#447	C₂²×C₃₁	1	1	yes	characteristic
980	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
981	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
982	#442	C₂²×C₃₁	1	1	yes	characteristic
983	#442	C₂²×C₃₁	1	1	yes	characteristic
984	#442	C₂²×C₃₁	1	1	yes	characteristic
985	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
986	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
987	#440	C₂²×C₃₁	1	1	yes	characteristic
988	#440	C₂²×C₃₁	1	1	yes	characteristic
989	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
990	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
991	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
992	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
993	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
994	#436	C₂²×C₃₁	1	1	yes	characteristic
995	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
996	#435	C₂²×C₃₁	1	1	yes	characteristic
997	#435	C₂²×C₃₁	1	1	yes	characteristic
998	#435	C₂²×C₃₁	1	1	yes	characteristic
999	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
1000	#433	C₂²×C₃₁	1	1	yes	characteristic
1001	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
1002	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
1003	#428	C₂²×C₃₁	1	1	yes	characteristic
1004	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1005	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1006	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1007	#427	C₂²×C₃₁	1	1	yes	characteristic
1008	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
1009	#424	C₂²×C₃₁	1	1	yes	characteristic
1010	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
1011	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
1012	#418	C₂²×C₃₁	1	1	yes	characteristic
1013	#417	C₂²×C₃₁	1	1	yes	characteristic
1014	#417	C₂²×C₃₁	1	1	yes	characteristic
1015	#417	C₂²×C₃₁	1	1	yes	characteristic
1016	#416	C₂²×C₃₁	1	1	yes	characteristic
1017	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
1018	C₂×C₃₁	—	4	1	no	—
1019	C₂×C₃₁	—	4	1	no	—
1020	C₂×C₃₁	—	4	1	no	—
1021	C₂×C₃₁	—	4	2	no	—
1022	C₂×C₃₁	—	8	1	no	—
1023	C₂×C₃₁	—	8	1	no	—
1024	C₂×C₃₁	#3489	1	1	yes	characteristic
1025	C₂×C₃₁	#3585	1	1	yes	characteristic
1026	C₂×C₃₁	#3586	1	1	yes	characteristic
1027	C₂×#41	—	2	1	no	—
1028	C₂×#41	—	2	1	no	—
1029	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1030	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1031	C₂²×Q₈	—	2	1	no	—
1032	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
1033	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1034	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1035	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1036	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1037	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1038	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1039	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1040	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1041	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1042	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1043	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1044	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1045	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1046	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1047	C₄⋊Q₈	—	2	1	no	—
1048	C₄⋊Q₈	—	2	1	no	—
1049	C₄⋊Q₈	—	2	1	no	—
1050	C₄⋊Q₈	—	2	1	no	—
1051	C₄⋊Q₈	—	2	1	no	—
1052	C₄⋊Q₈	—	2	1	no	—
1053	C₄⋊Q₈	—	2	1	no	—
1054	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1055	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1056	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1057	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1058	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1059	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1060	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1061	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1062	#126	—	2	1	no	—
1063	#126	—	2	1	no	—
1064	#126	—	2	1	no	—
1065	#126	—	2	1	no	—
1066	#126	—	2	1	no	—
1067	#126	—	2	1	no	—
1068	#126	—	2	1	no	—
1069	#126	—	2	1	no	—
1070	#126	—	2	1	no	—
1071	#126	—	2	1	no	—
1072	#126	—	2	1	no	—
1073	#126	—	2	1	no	—
1074	#126	—	2	1	no	—
1075	#126	—	2	1	no	—
1076	#126	—	2	1	no	—
1077	#126	D₄×C₃₁	1	1	yes	characteristic
1078	#126	D₄×C₃₁	1	1	yes	characteristic
1079	#125	—	2	1	no	—
1080	#125	—	2	1	no	—
1081	#125	—	2	1	no	—
1082	#125	—	2	1	no	—
1083	#125	—	2	1	no	—
1084	#125	—	2	1	no	—
1085	#125	—	2	1	no	—
1086	#125	—	2	1	no	—
1087	#125	D₄×C₃₁	1	1	yes	characteristic
1088	#125	C₂³×C₃₁	1	1	yes	characteristic
1089	#125	C₂³×C₃₁	1	1	yes	characteristic
1090	#125	C₂³×C₃₁	1	1	yes	characteristic
1091	#125	C₂³×C₃₁	1	1	yes	characteristic
1092	#125	C₂³×C₃₁	1	1	yes	characteristic
1093	#124	—	2	1	no	—
1094	#124	—	2	1	no	—
1095	#124	—	2	1	no	—
1096	#124	—	2	1	no	—
1097	#124	—	2	1	no	—
1098	#124	—	2	1	no	—
1099	#124	D₄×C₃₁	1	1	yes	characteristic
1100	#124	C₂³×C₃₁	1	1	yes	characteristic
1101	#124	C₂³×C₃₁	1	1	yes	characteristic
1102	#124	C₂³×C₃₁	1	1	yes	characteristic
1103	#123	—	2	1	no	—
1104	#123	—	2	1	no	—
1105	#123	—	2	1	no	—
1106	#123	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	—	2	1	no	—
1109	#123	—	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	D₄×C₃₁	1	1	yes	characteristic
1121	#123	D₄×C₃₁	1	1	yes	characteristic
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	—	2	1	no	—
1125	C₂²⋊Q₈	—	2	1	no	—
1126	C₂²⋊Q₈	—	2	1	no	—
1127	C₂²⋊Q₈	—	2	1	no	—
1128	C₂²⋊Q₈	—	2	1	no	—
1129	C₂²⋊Q₈	—	2	1	no	—
1130	C₂²⋊Q₈	—	2	1	no	—
1131	C₂²⋊Q₈	—	2	1	no	—
1132	C₂²⋊Q₈	—	2	1	no	—
1133	C₂²⋊Q₈	—	2	1	no	—
1134	C₂²⋊Q₈	—	2	1	no	—
1135	C₂²⋊Q₈	—	2	1	no	—
1136	C₂²⋊Q₈	—	2	1	no	—
1137	C₂²⋊Q₈	—	2	1	no	—
1138	C₂²⋊Q₈	—	2	1	no	—
1139	C₂²⋊Q₈	—	2	1	no	—
1140	C₂²⋊Q₈	D₄×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	#121	—	2	1	no	—
1149	#121	—	2	1	no	—
1150	#121	—	2	1	no	—
1151	#121	—	2	1	no	—
1152	#121	—	2	1	no	—
1153	#121	D₄×C₃₁	1	1	yes	characteristic
1154	#121	C₂³×C₃₁	1	1	yes	characteristic
1155	#121	C₂³×C₃₁	1	1	yes	characteristic
1156	#121	C₂³×C₃₁	1	1	yes	characteristic
1157	#121	C₂³×C₃₁	1	1	yes	characteristic
1158	#121	C₂³×C₃₁	1	1	yes	characteristic
1159	#120	—	2	1	no	—
1160	#120	—	2	1	no	—
1161	C₄×Q₈	—	2	1	no	—
1162	C₄×Q₈	—	2	1	no	—
1163	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1164	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1165	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1166	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1167	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1168	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1169	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1170	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1171	C₄×D₄	—	2	1	no	—
1172	C₄×D₄	—	2	1	no	—
1173	C₄×D₄	—	2	1	no	—
1174	C₄×D₄	—	2	1	no	—
1175	C₄×D₄	—	2	1	no	—
1176	C₄×D₄	—	2	1	no	—
1177	C₄×D₄	—	2	1	no	—
1178	C₄×D₄	—	2	1	no	—
1179	C₄×D₄	—	2	1	no	—
1180	C₄×D₄	—	2	1	no	—
1181	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1182	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1183	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1184	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1185	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1186	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1187	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1188	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1189	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1190	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1191	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1192	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1193	#117	—	2	1	no	—
1194	#117	—	2	1	no	—
1195	#117	—	2	1	no	—
1196	#117	—	2	1	no	—
1197	#117	—	2	1	no	—
1198	#117	—	2	1	no	—
1199	#117	—	2	1	no	—
1200	#117	—	2	1	no	—
1201	#117	—	2	1	no	—
1202	#117	C₂³×C₃₁	1	1	yes	characteristic
1203	#117	C₂³×C₃₁	1	1	yes	characteristic
1204	#117	C₂³×C₃₁	1	1	yes	characteristic
1205	#117	C₂³×C₃₁	1	1	yes	characteristic
1206	#117	C₂³×C₃₁	1	1	yes	characteristic
1207	#117	C₂³×C₃₁	1	1	yes	characteristic
1208	C₂×C₄⋊C₄	—	2	1	no	—
1209	C₂×C₄⋊C₄	—	2	1	no	—
1210	C₂×C₄⋊C₄	—	2	1	no	—
1211	C₂×C₄⋊C₄	—	2	1	no	—
1212	C₂×C₄⋊C₄	—	2	1	no	—
1213	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1214	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1215	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1216	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1217	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1218	C₂×C₂²⋊C₄	—	2	1	no	—
1219	C₂×C₂²⋊C₄	—	2	1	no	—
1220	C₂×C₂²⋊C₄	—	2	1	no	—
1221	C₂×C₂²⋊C₄	—	2	1	no	—
1222	C₂×C₄²	—	2	1	no	—
1223	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1224	#107	C₂³×C₃₁	1	1	yes	characteristic
1225	#107	C₂³×C₃₁	1	1	yes	characteristic
1226	#107	C₂³×C₃₁	1	1	yes	characteristic
1227	#107	C₂³×C₃₁	1	1	yes	characteristic
1228	#107	C₂³×C₃₁	1	1	yes	characteristic
1229	#107	C₂³×C₃₁	1	1	yes	characteristic
1230	#107	C₂³×C₃₁	1	1	yes	characteristic
1231	#107	C₂³×C₃₁	1	1	yes	characteristic
1232	#107	C₂³×C₃₁	1	1	yes	characteristic
1233	#107	C₂³×C₃₁	1	1	yes	characteristic
1234	#107	C₂³×C₃₁	1	1	yes	characteristic
1235	#107	C₂³×C₃₁	1	1	yes	characteristic
1236	#106	C₂³×C₃₁	1	1	yes	characteristic
1237	#106	C₂³×C₃₁	1	1	yes	characteristic
1238	#106	C₂³×C₃₁	1	1	yes	characteristic
1239	#106	C₂³×C₃₁	1	1	yes	characteristic
1240	#106	C₂³×C₃₁	1	1	yes	characteristic
1241	#106	C₂³×C₃₁	1	1	yes	characteristic
1242	#106	C₂³×C₃₁	1	1	yes	characteristic
1243	#106	C₂³×C₃₁	1	1	yes	characteristic
1244	#106	C₂³×C₃₁	1	1	yes	characteristic
1245	#106	C₂³×C₃₁	1	1	yes	characteristic
1246	#106	C₂³×C₃₁	1	1	yes	characteristic
1247	#106	C₂³×C₃₁	1	1	yes	characteristic
1248	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1249	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1250	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1251	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1252	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1253	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1254	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1255	C₄⋊C₈	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	#103	C₂³×C₃₁	1	1	yes	characteristic
1259	#103	C₂³×C₃₁	1	1	yes	characteristic
1260	#103	C₂³×C₃₁	1	1	yes	characteristic
1261	#103	C₂³×C₃₁	1	1	yes	characteristic
1262	#103	C₂³×C₃₁	1	1	yes	characteristic
1263	#103	C₂³×C₃₁	1	1	yes	characteristic
1264	#103	C₂³×C₃₁	1	1	yes	characteristic
1265	#103	C₂³×C₃₁	1	1	yes	characteristic
1266	#103	C₂³×C₃₁	1	1	yes	characteristic
1267	#103	C₂³×C₃₁	1	1	yes	characteristic
1268	#103	C₂³×C₃₁	1	1	yes	characteristic
1269	#103	C₂³×C₃₁	1	1	yes	characteristic
1270	#103	C₂³×C₃₁	1	1	yes	characteristic
1271	#103	C₂³×C₃₁	1	1	yes	characteristic
1272	#103	C₂³×C₃₁	1	1	yes	characteristic
1273	#103	C₂³×C₃₁	1	1	yes	characteristic
1274	#102	C₂³×C₃₁	1	1	yes	characteristic
1275	#102	C₂³×C₃₁	1	1	yes	characteristic
1276	#102	C₂³×C₃₁	1	1	yes	characteristic
1277	#102	C₂³×C₃₁	1	1	yes	characteristic
1278	#102	C₂³×C₃₁	1	1	yes	characteristic
1279	#102	C₂³×C₃₁	1	1	yes	characteristic
1280	#102	C₂³×C₃₁	1	1	yes	characteristic
1281	#102	C₂³×C₃₁	1	1	yes	characteristic
1282	#102	C₂³×C₃₁	1	1	yes	characteristic
1283	#102	C₂³×C₃₁	1	1	yes	characteristic
1284	#102	C₂³×C₃₁	1	1	yes	characteristic
1285	#102	C₂³×C₃₁	1	1	yes	characteristic
1286	#102	C₂³×C₃₁	1	1	yes	characteristic
1287	#102	C₂³×C₃₁	1	1	yes	characteristic
1288	#102	C₂³×C₃₁	1	1	yes	characteristic
1289	#102	C₂³×C₃₁	1	1	yes	characteristic
1290	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1291	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1292	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1293	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1294	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1295	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1296	#97	C₂³×C₃₁	1	1	yes	characteristic
1297	#97	C₂³×C₃₁	1	1	yes	characteristic
1298	#97	C₂³×C₃₁	1	1	yes	characteristic
1299	#97	C₂³×C₃₁	1	1	yes	characteristic
1300	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1301	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1302	C₃₁	#62228	1	1	yes	characteristic, direct product factor, Sylow
1303	C₂⁴	—	2	1	no	—
1304	#41	—	2	2	no	—
1305	#41	—	2	2	no	—
1306	#41	—	4	1	no	—
1307	#41	—	4	1	no	—
1308	#41	—	8	2	no	—
1309	#41	—	8	2	no	—
1310	C₂×Q₈	—	2	1	no	—
1311	C₂×Q₈	—	2	1	no	—
1312	C₂×Q₈	—	2	1	no	—
1313	C₂×Q₈	—	2	1	no	—
1314	C₂×Q₈	—	2	1	no	—
1315	C₂×Q₈	—	2	1	no	—
1316	C₂×Q₈	—	2	1	no	—
1317	C₂×Q₈	—	8	2	no	—
1318	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1319	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1320	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1321	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1322	C₂×D₄	—	2	2	no	—
1323	C₂×D₄	—	2	1	no	—
1324	C₂×D₄	—	2	1	no	—
1325	C₂×D₄	—	2	1	no	—
1326	C₂×D₄	—	2	1	no	—
1327	C₂×D₄	—	2	1	no	—
1328	C₂×D₄	—	2	1	no	—
1329	C₂×D₄	—	2	1	no	—
1330	C₂×D₄	—	2	1	no	—
1331	C₂×D₄	—	4	1	no	—
1332	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1333	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1334	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1335	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1336	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1337	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1338	C₂²×C₄	—	2	1	no	—
1339	C₂²×C₄	—	2	1	no	—
1340	C₂²×C₄	—	2	1	no	—
1341	C₂²×C₄	—	2	1	no	—
1342	C₂²×C₄	—	2	1	no	—
1343	C₂²×C₄	—	2	1	no	—
1344	C₂²×C₄	—	2	1	no	—
1345	C₂²×C₄	—	2	1	no	—
1346	C₂²×C₄	—	2	1	no	—
1347	C₂²×C₄	—	2	1	no	—
1348	C₂²×C₄	—	2	1	no	—
1349	C₂²×C₄	—	2	1	no	—
1350	C₂²×C₄	—	2	1	no	—
1351	C₂²×C₄	—	2	1	no	—
1352	C₂²×C₄	—	2	1	no	—
1353	C₂²×C₄	—	2	1	no	—
1354	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1355	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1356	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1357	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1358	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1359	Q₁₆	—	4	1	no	—
1360	Q₁₆	—	4	1	no	—
1361	SD₁₆	—	2	2	no	—
1362	SD₁₆	—	4	1	no	—
1363	SD₁₆	—	4	1	no	—
1364	SD₁₆	—	4	1	no	—
1365	D₈	—	2	2	no	—
1366	D₈	—	4	1	no	—
1367	M₁₆	—	4	1	no	—
1368	M₁₆	—	4	1	no	—
1369	M₁₆	—	4	1	no	—
1370	M₁₆	—	4	1	no	—
1371	C₂×C₈	—	4	1	no	—
1372	C₂×C₈	—	4	1	no	—
1373	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1374	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1375	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1376	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1377	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1378	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1379	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1380	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1381	C₄⋊C₄	—	2	1	no	—
1382	C₄⋊C₄	—	2	1	no	—
1383	C₄⋊C₄	—	2	1	no	—
1384	C₄⋊C₄	—	2	1	no	—
1385	C₄⋊C₄	—	2	1	no	—
1386	C₄⋊C₄	—	2	1	no	—
1387	C₄⋊C₄	—	2	1	no	—
1388	C₄⋊C₄	—	2	1	no	—
1389	C₄⋊C₄	—	2	1	no	—
1390	C₄⋊C₄	—	2	1	no	—
1391	C₄⋊C₄	—	2	1	no	—
1392	C₄⋊C₄	—	2	1	no	—
1393	C₄⋊C₄	—	2	1	no	—
1394	C₄⋊C₄	—	2	1	no	—
1395	C₄⋊C₄	—	2	1	no	—
1396	C₄⋊C₄	—	2	1	no	—
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	—	2	1	no	—
1400	C₄⋊C₄	—	2	1	no	—
1401	C₄⋊C₄	—	2	1	no	—
1402	C₄⋊C₄	—	2	1	no	—
1403	C₄⋊C₄	—	2	1	no	—
1404	C₄⋊C₄	—	2	1	no	—
1405	C₄⋊C₄	—	2	1	no	—
1406	C₄⋊C₄	—	2	1	no	—
1407	C₄⋊C₄	—	2	1	no	—
1408	C₄⋊C₄	—	2	1	no	—
1409	C₄⋊C₄	—	2	1	no	—
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	—	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	C₂×D₄×C₃₁	1	1	yes	characteristic
1420	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1421	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1422	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1423	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1424	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1425	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1426	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1427	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1428	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1429	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1430	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1431	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1432	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1433	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1434	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1435	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1436	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1437	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1438	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1439	C₂²⋊C₄	—	2	1	no	—
1440	C₂²⋊C₄	—	2	1	no	—
1441	C₂²⋊C₄	—	2	1	no	—
1442	C₂²⋊C₄	—	2	1	no	—
1443	C₂²⋊C₄	—	2	1	no	—
1444	C₂²⋊C₄	—	2	1	no	—
1445	C₂²⋊C₄	—	2	1	no	—
1446	C₂²⋊C₄	—	2	1	no	—
1447	C₂²⋊C₄	—	2	1	no	—
1448	C₂²⋊C₄	—	2	1	no	—
1449	C₂²⋊C₄	—	2	1	no	—
1450	C₂²⋊C₄	—	2	1	no	—
1451	C₂²⋊C₄	—	2	1	no	—
1452	C₂²⋊C₄	—	2	1	no	—
1453	C₂²⋊C₄	—	2	1	no	—
1454	C₂²⋊C₄	—	2	1	no	—
1455	C₂²⋊C₄	—	2	1	no	—
1456	C₂²⋊C₄	—	2	1	no	—
1457	C₂²⋊C₄	—	2	1	no	—
1458	C₂²⋊C₄	—	2	1	no	—
1459	C₂²⋊C₄	—	2	1	no	—
1460	C₂²⋊C₄	—	2	1	no	—
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1471	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1472	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1473	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1474	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1475	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1476	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1477	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1478	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1479	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1480	C₄²	—	2	1	no	—
1481	C₄²	—	2	1	no	—
1482	C₄²	—	2	1	no	—
1483	C₄²	—	2	1	no	—
1484	C₄²	—	2	1	no	—
1485	C₄²	—	2	1	no	—
1486	C₄²	—	2	1	no	—
1487	C₄²	—	2	1	no	—
1488	C₄²	—	2	1	no	—
1489	C₄²	—	2	1	no	—
1490	C₄²	—	2	1	no	—
1491	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1492	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1493	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1494	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1495	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1496	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1497	C₂³	—	2	1	no	—
1498	C₂³	—	2	1	no	—
1499	C₂³	—	2	1	no	—
1500	C₂³	—	4	2	no	—
1501	C₂³	—	8	1	no	—
1502	C₂³	—	8	1	no	—
1503	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1504	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1505	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1506	Q₈	—	2	1	no	—
1507	Q₈	—	2	1	no	—
1508	Q₈	—	2	1	no	—
1509	Q₈	—	2	1	no	—
1510	Q₈	—	2	1	no	—
1511	Q₈	—	2	1	no	—
1512	Q₈	—	4	1	no	—
1513	Q₈	—	8	1	no	—
1514	Q₈	—	8	1	no	—
1515	Q₈	—	8	1	no	—
1516	Q₈	—	8	1	no	—
1517	Q₈	—	8	1	no	—
1518	Q₈	—	8	1	no	—
1519	Q₈	—	8	1	no	—
1520	D₄	—	2	1	no	—
1521	D₄	—	2	1	no	—
1522	D₄	—	2	1	no	—
1523	D₄	—	2	1	no	—
1524	D₄	—	2	1	no	—
1525	D₄	—	4	1	no	—
1526	D₄	—	4	1	no	—
1527	D₄	—	4	1	no	—
1528	D₄	—	4	2	no	—
1529	D₄	—	4	2	no	—
1530	D₄	—	4	2	no	—
1531	D₄	—	4	2	no	—
1532	D₄	—	8	1	no	—
1533	D₄	—	8	1	no	—
1534	D₄	—	8	1	no	—
1535	D₄	—	8	1	no	—
1536	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1537	C₂×C₄	—	2	1	no	—
1538	C₂×C₄	—	2	1	no	—
1539	C₂×C₄	—	2	1	no	—
1540	C₂×C₄	—	2	1	no	—
1541	C₂×C₄	—	2	1	no	—
1542	C₂×C₄	—	2	1	no	—
1543	C₂×C₄	—	2	1	no	—
1544	C₂×C₄	—	2	1	no	—
1545	C₂×C₄	—	2	1	no	—
1546	C₂×C₄	—	2	1	no	—
1547	C₂×C₄	—	2	1	no	—
1548	C₂×C₄	—	2	1	no	—
1549	C₂×C₄	—	2	1	no	—
1550	C₂×C₄	—	2	1	no	—
1551	C₂×C₄	—	2	1	no	—
1552	C₂×C₄	—	2	1	no	—
1553	C₂×C₄	—	2	1	no	—
1554	C₂×C₄	—	2	1	no	—
1555	C₂×C₄	—	2	1	no	—
1556	C₂×C₄	—	4	1	no	—
1557	C₂×C₄	—	4	1	no	—
1558	C₂×C₄	—	4	2	no	—
1559	C₂×C₄	—	4	2	no	—
1560	C₂×C₄	—	4	2	no	—
1561	C₂×C₄	—	4	2	no	—
1562	C₂×C₄	—	4	2	no	—
1563	C₂×C₄	—	8	1	no	—
1564	C₂×C₄	—	8	1	no	—
1565	C₂×C₄	—	8	1	no	—
1566	C₂×C₄	—	8	1	no	—
1567	C₂×C₄	—	8	1	no	—
1568	C₂×C₄	—	8	1	no	—
1569	C₂×C₄	—	8	1	no	—
1570	C₂×C₄	—	8	1	no	—
1571	C₂×C₄	—	8	1	no	—
1572	C₂×C₄	—	8	1	no	—
1573	C₂×C₄	—	8	1	no	—
1574	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1575	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1576	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1577	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1578	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1579	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1580	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1581	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1582	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1583	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1584	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1585	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1586	C₈	—	2	1	no	—
1587	C₈	—	2	1	no	—
1588	C₈	—	2	1	no	—
1589	C₈	—	2	1	no	—
1590	C₈	—	2	1	no	—
1591	C₈	—	2	1	no	—
1592	C₈	—	2	1	no	—
1593	C₈	—	2	1	no	—
1594	C₂²	—	2	1	no	—
1595	C₂²	—	2	1	no	—
1596	C₂²	—	2	1	no	—
1597	C₂²	—	2	2	no	—
1598	C₂²	—	2	1	no	—
1599	C₂²	—	2	1	no	—
1600	C₂²	—	2	1	no	—
1601	C₂²	—	2	1	no	—
1602	C₂²	—	2	1	no	—
1603	C₂²	—	2	1	no	—
1604	C₂²	—	4	1	no	—
1605	C₂²	—	4	1	no	—
1606	C₂²	—	4	1	no	—
1607	C₂²	—	4	1	no	—
1608	C₂²	—	4	1	no	—
1609	C₂²	—	4	1	no	—
1610	C₂²	—	4	1	no	—
1611	C₂²	—	4	1	no	—
1612	C₂²	—	16	2	no	—
1613	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1614	C₄	—	2	1	no	—
1615	C₄	—	2	1	no	—
1616	C₄	—	2	1	no	—
1617	C₄	—	2	1	no	—
1618	C₄	—	2	1	no	—
1619	C₄	—	2	1	no	—
1620	C₄	—	2	1	no	—
1621	C₄	—	2	1	no	—
1622	C₄	—	2	1	no	—
1623	C₄	—	2	1	no	—
1624	C₄	—	2	1	no	—
1625	C₄	—	4	1	no	—
1626	C₄	—	4	1	no	—
1627	C₄	—	4	1	no	—
1628	C₄	—	4	1	no	—
1629	C₄	—	4	1	no	—
1630	C₄	—	4	1	no	—
1631	C₄	—	4	1	no	—
1632	C₄	—	4	1	no	—
1633	C₄	—	4	1	no	—
1634	C₄	—	4	1	no	—
1635	C₄	—	4	1	no	—
1636	C₄	—	4	1	no	—
1637	C₄	—	4	1	no	—
1638	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1639	C₄	C₃₁×#585	1	1	yes	characteristic
1640	C₂	—	4	1	no	—
1641	C₂	—	4	1	no	—
1642	C₂	—	4	1	no	—
1643	C₂	—	4	2	no	—
1644	C₂	—	8	1	no	—
1645	C₂	—	8	1	no	—
1646	C₂	C₃₁×#3489	1	1	yes	characteristic
1647	C₂	C₃₁×#3585	1	1	yes	characteristic
1648	C₂	C₃₁×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3544	C₂	semidirect
2. C₃₁×#3521	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3385	C₂	semidirect
5. C₃₁×#3376	C₂	semidirect
6. C₃₁×#3369	C₂	semidirect
7. C₃₁×#3353	C₂	semidirect
8. C₃₁×#3351	C₂	semidirect
9. C₃₁×#3349	C₂	semidirect
10. C₃₁×#3348	C₂	semidirect
11. C₃₁×#3345	C₂	semidirect
12. C₃₁×#3344	C₂	semidirect
13. C₃₁×#3330	C₂	semidirect
14. C₃₁×#3323	C₂	semidirect
15. C₃₁×#3319	C₂	semidirect
16. C₃₁×#3315	C₂	semidirect
17. C₃₁×#3314	C₂	semidirect
18. C₃₁×#3306	C₂	semidirect
19. C₃₁×#3262	C₂	semidirect
20. C₃₁×#3258	C₂	semidirect
21. C₃₁×#3256	C₂	semidirect
22. C₃₁×#3243	C₂	semidirect
23. C₃₁×#3242	C₂	semidirect
24. C₃₁×#3239	C₂	semidirect
25. C₃₁×#3125	C₂	semidirect
26. C₃₁×#3118	C₂	semidirect
27. C₃₁×#3111	C₂	semidirect
28. C₃₁×#3084	C₂	semidirect
29. C₃₁×#3081	C₂	semidirect
30. C₃₁×#3079	C₂	semidirect
31. C₃₁×#2995	C₂	semidirect
34. Q₈²×C₃₁	C₂²	semidirect
40. C₃₁×#554	C₂²	semidirect
47. C₃₁×#552	C₂²	semidirect
53. C₃₁×#547	C₂²	semidirect
58. C₃₁×#544	C₂²	semidirect
62. C₃₁×#542	C₂²	semidirect
68. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
72. C₃₁×#529	C₂²	semidirect
77. C₃₁×#501	C₂²	semidirect
78. C₃₁×#501	C₂²	semidirect
79. C₃₁×#501	C₂²	semidirect
80. C₃₁×#501	C₂²	semidirect
81. C₃₁×#500	C₂²	semidirect
82. C₃₁×#499	C₂²	semidirect
83. C₃₁×#491	C₂²	semidirect
88. C₃₁×#487	C₂²	semidirect
92. C₃₁×#485	C₂²	semidirect
93. C₃₁×#485	C₂²	semidirect
95. C₃₁×#484	C₂²	semidirect
96. C₃₁×#484	C₂²	semidirect
97. C₃₁×#484	C₂²	semidirect
99. C₃₁×#483	C₂²	semidirect
102. C₃₁×#482	C₂²	semidirect
105. C₃₁×#481	C₂²	semidirect
107. C₃₁×#479	C₂²	semidirect
108. C₃₁×#479	C₂²	semidirect
109. C₃₁×#479	C₂²	semidirect
110. C₃₁×#479	C₂²	semidirect
111. C₃₁×#479	C₂²	semidirect
117. C₃₁×#478	C₂²	semidirect
118. C₃₁×#478	C₂²	semidirect
119. C₃₁×#477	C₂²	semidirect
120. C₃₁×#477	C₂²	semidirect
121. C₃₁×#477	C₂²	semidirect
126. C₃₁×#475	C₂²	semidirect
127. C₃₁×#475	C₂²	semidirect
128. C₃₁×#475	C₂²	semidirect
129. C₃₁×#475	C₂²	semidirect
130. C₃₁×#475	C₂²	semidirect
136. C₃₁×#474	C₂²	semidirect
138. C₃₁×#470	C₂²	semidirect
143. C₃₁×#468	C₂²	semidirect
144. C₃₁×#468	C₂²	semidirect
146. C₃₁×#467	C₂²	semidirect
151. C₃₁×#464	C₂²	semidirect
152. C₃₁×#464	C₂²	semidirect
157. C₃₁×#462	C₂²	semidirect
158. C₃₁×#461	C₂²	semidirect
165. C₃₁×#446	C₂²	semidirect
166. C₃₁×#446	C₂²	semidirect
170. C₃₁×#441	C₂²	semidirect
171. C₃₁×#441	C₂²	semidirect
174. C₃₁×#440	C₂²	semidirect
177. C₄×SD₁₆×C₃₁	C₂²	semidirect
180. C₃₁×#436	C₂²	semidirect
184. C₃₁×#435	C₂²	semidirect
186. C₃₁×#433	C₂²	semidirect
187. C₃₁×#432	C₂²	semidirect
189. C₃₁×#428	C₂²	semidirect
190. C₃₁×#428	C₂²	semidirect
191. C₃₁×#428	C₂²	semidirect
193. C₂×C₃₁×#106	C₂²	semidirect
195. C₃₁×#424	C₂²	semidirect
196. C₃₁×#423	C₂²	semidirect
672. #62228	C₃₁	direct (N × H)
770. #3544	C₂×C₃₁	semidirect
771. #3521	C₂×C₃₁	semidirect
772. #3389	C₂×C₃₁	semidirect
773. #3385	C₂×C₃₁	semidirect
774. #3376	C₂×C₃₁	semidirect
775. #3369	C₂×C₃₁	semidirect
776. #3353	C₂×C₃₁	semidirect
777. #3351	C₂×C₃₁	semidirect
778. #3349	C₂×C₃₁	semidirect
779. #3348	C₂×C₃₁	semidirect
780. #3345	C₂×C₃₁	semidirect
781. #3344	C₂×C₃₁	semidirect
782. #3330	C₂×C₃₁	semidirect
783. #3323	C₂×C₃₁	semidirect
784. #3319	C₂×C₃₁	semidirect
785. #3315	C₂×C₃₁	semidirect
786. #3314	C₂×C₃₁	semidirect
787. #3306	C₂×C₃₁	semidirect
788. #3262	C₂×C₃₁	semidirect
789. #3258	C₂×C₃₁	semidirect
790. #3256	C₂×C₃₁	semidirect
791. #3243	C₂×C₃₁	semidirect
792. #3242	C₂×C₃₁	semidirect
793. #3239	C₂×C₃₁	semidirect
794. #3125	C₂×C₃₁	semidirect
795. #3118	C₂×C₃₁	semidirect
796. #3111	C₂×C₃₁	semidirect
797. #3084	C₂×C₃₁	semidirect
798. #3081	C₂×C₃₁	semidirect
799. #3079	C₂×C₃₁	semidirect
800. #2995	C₂×C₃₁	semidirect
849. Q₈²	C₂²×C₃₁	semidirect
855. #554	C₂²×C₃₁	semidirect
862. #552	C₂²×C₃₁	semidirect
868. #547	C₂²×C₃₁	semidirect
873. #544	C₂²×C₃₁	semidirect
877. #542	C₂²×C₃₁	semidirect
883. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
887. #529	C₂²×C₃₁	semidirect
892. #501	C₂²×C₃₁	semidirect
893. #501	C₂²×C₃₁	semidirect
894. #501	C₂²×C₃₁	semidirect
895. #501	C₂²×C₃₁	semidirect
896. #500	C₂²×C₃₁	semidirect
897. #499	C₂²×C₃₁	semidirect
898. #491	C₂²×C₃₁	semidirect
903. #487	C₂²×C₃₁	semidirect
907. #485	C₂²×C₃₁	semidirect
908. #485	C₂²×C₃₁	semidirect
910. #484	C₂²×C₃₁	semidirect
911. #484	C₂²×C₃₁	semidirect
912. #484	C₂²×C₃₁	semidirect
914. #483	C₂²×C₃₁	semidirect
917. #482	C₂²×C₃₁	semidirect
920. #481	C₂²×C₃₁	semidirect
922. #479	C₂²×C₃₁	semidirect
923. #479	C₂²×C₃₁	semidirect
924. #479	C₂²×C₃₁	semidirect
925. #479	C₂²×C₃₁	semidirect
926. #479	C₂²×C₃₁	semidirect
932. #478	C₂²×C₃₁	semidirect
933. #478	C₂²×C₃₁	semidirect
934. #477	C₂²×C₃₁	semidirect
935. #477	C₂²×C₃₁	semidirect
936. #477	C₂²×C₃₁	semidirect
941. #475	C₂²×C₃₁	semidirect
942. #475	C₂²×C₃₁	semidirect
943. #475	C₂²×C₃₁	semidirect
944. #475	C₂²×C₃₁	semidirect
945. #475	C₂²×C₃₁	semidirect
951. #474	C₂²×C₃₁	semidirect
953. #470	C₂²×C₃₁	semidirect
958. #468	C₂²×C₃₁	semidirect
959. #468	C₂²×C₃₁	semidirect
961. #467	C₂²×C₃₁	semidirect
966. #464	C₂²×C₃₁	semidirect
967. #464	C₂²×C₃₁	semidirect
972. #462	C₂²×C₃₁	semidirect
973. #461	C₂²×C₃₁	semidirect
980. #446	C₂²×C₃₁	semidirect
981. #446	C₂²×C₃₁	semidirect
985. #441	C₂²×C₃₁	semidirect
986. #441	C₂²×C₃₁	semidirect
989. #440	C₂²×C₃₁	semidirect
992. C₄×SD₁₆	C₂²×C₃₁	semidirect
995. #436	C₂²×C₃₁	semidirect
999. #435	C₂²×C₃₁	semidirect
1001. #433	C₂²×C₃₁	semidirect
1002. #432	C₂²×C₃₁	semidirect
1004. #428	C₂²×C₃₁	semidirect
1005. #428	C₂²×C₃₁	semidirect
1006. #428	C₂²×C₃₁	semidirect
1008. C₂×#106	C₂²×C₃₁	semidirect
1010. #424	C₂²×C₃₁	semidirect
1011. #423	C₂²×C₃₁	semidirect
1302. C₃₁	#62228	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×#3544	2
C₃₁×#3521	2
C₃₁×#3389	2
C₃₁×#3385	2
C₃₁×#3376	2
C₃₁×#3369	2
C₃₁×#3353	2
C₃₁×#3351	2
C₃₁×#3349	2
C₃₁×#3348	2
C₃₁×#3345	2
C₃₁×#3344	2
C₃₁×#3330	2
C₃₁×#3323	2
C₃₁×#3319	2
C₃₁×#3315	2
C₃₁×#3314	2
C₃₁×#3306	2
C₃₁×#3262	2
C₃₁×#3258	2
C₃₁×#3256	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3239	2
C₃₁×#3125	2
C₃₁×#3118	2
C₃₁×#3111	2
C₃₁×#3084	2
C₃₁×#3081	2
C₃₁×#3079	2
C₃₁×#2995	2
#62228	31

Subgroups — C31×#62228 #21518987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62228 #21518987