Subgroups — C₃₁×#62025 #21518784

Order 7936.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3524	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3371	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3321	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3320	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3309	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3300	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3271	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3271	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3270	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3269	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3263	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3225	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3221	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3121	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#562	—	2	1	no	—
39	C₃₁×#562	—	2	1	no	—
40	C₃₁×#559	—	2	1	no	—
41	C₃₁×#559	—	2	1	no	—
42	C₃₁×#559	C₂²	1	1	yes	characteristic
43	C₃₁×#559	C₂²	1	1	yes	characteristic
44	C₃₁×#557	C₂²	1	1	yes	characteristic
45	C₃₁×#557	C₂²	1	1	yes	characteristic
46	C₃₁×#555	—	2	1	no	—
47	C₃₁×#555	C₂²	1	1	yes	characteristic
48	C₃₁×#554	—	2	1	no	—
49	C₃₁×#553	—	2	1	no	—
50	C₃₁×#553	C₂²	1	1	yes	characteristic
51	C₃₁×#552	—	2	1	no	—
52	C₃₁×#552	C₂²	1	1	yes	characteristic
53	C₃₁×#550	C₂²	1	1	yes	characteristic
54	C₃₁×#550	C₂²	1	1	yes	characteristic
55	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
56	C₃₁×#548	C₂²	1	1	yes	characteristic
57	C₃₁×#548	C₂²	1	1	yes	characteristic
58	C₃₁×#548	C₂²	1	1	yes	characteristic
59	C₃₁×#548	C₂²	1	1	yes	characteristic
60	C₃₁×#547	C₂²	1	1	yes	characteristic
61	C₃₁×#547	C₂²	1	1	yes	characteristic
62	C₃₁×#542	—	2	1	no	—
63	C₃₁×#542	—	2	1	no	—
64	C₃₁×#542	C₂²	1	1	yes	characteristic
65	C₃₁×#542	C₂²	1	1	yes	characteristic
66	C₃₁×#542	C₂²	1	1	yes	characteristic
67	C₃₁×#540	—	2	1	no	—
68	C₃₁×#540	—	2	1	no	—
69	C₃₁×#540	C₂²	1	1	yes	characteristic
70	C₃₁×#539	—	2	1	no	—
71	C₃₁×#539	—	2	1	no	—
72	C₃₁×#536	C₂²	1	1	yes	characteristic
73	C₃₁×#536	C₂²	1	1	yes	characteristic
74	C₃₁×#533	C₂²	1	1	yes	characteristic
75	C₃₁×#532	C₂²	1	1	yes	characteristic
76	C₃₁×#529	—	2	1	no	—
77	C₃₁×#529	—	2	1	no	—
78	C₃₁×#529	C₂²	1	1	yes	characteristic
79	C₃₁×#529	C₂²	1	1	yes	characteristic
80	C₃₁×#520	C₂²	1	1	yes	characteristic
81	C₃₁×#519	C₂²	1	1	yes	characteristic
82	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
83	C₃₁×#497	C₂²	1	1	yes	characteristic
84	C₃₁×#497	C₂²	1	1	yes	characteristic
85	C₃₁×#496	C₂²	1	1	yes	characteristic
86	C₃₁×#496	C₂²	1	1	yes	characteristic
87	C₃₁×#495	C₂²	1	1	yes	characteristic
88	C₃₁×#492	C₂²	1	1	yes	characteristic
89	C₃₁×#491	C₂²	1	1	yes	characteristic
90	C₃₁×#491	C₂²	1	1	yes	characteristic
91	C₃₁×#490	C₂²	1	1	yes	characteristic
92	C₃₁×#489	C₂²	1	1	yes	characteristic
93	C₃₁×#488	C₂²	1	1	yes	characteristic
94	C₃₁×#487	C₂²	1	1	yes	characteristic
95	C₃₁×#485	C₂²	1	1	yes	characteristic
96	C₃₁×#485	C₂²	1	1	yes	characteristic
97	C₃₁×#485	C₂²	1	1	yes	characteristic
98	C₃₁×#484	C₂²	1	1	yes	characteristic
99	C₃₁×#482	C₂²	1	1	yes	characteristic
100	C₃₁×#480	C₂²	1	1	yes	characteristic
101	C₃₁×#479	C₂²	1	1	yes	characteristic
102	C₃₁×#479	C₂²	1	1	yes	characteristic
103	C₃₁×#479	C₂²	1	1	yes	characteristic
104	C₃₁×#478	C₂²	1	1	yes	characteristic
105	C₃₁×#477	C₂²	1	1	yes	characteristic
106	C₃₁×#476	C₂²	1	1	yes	characteristic
107	C₃₁×#476	C₂²	1	1	yes	characteristic
108	C₃₁×#475	C₂²	1	1	yes	characteristic
109	C₃₁×#475	C₂²	1	1	yes	characteristic
110	C₃₁×#474	C₂²	1	1	yes	characteristic
111	C₃₁×#470	C₂²	1	1	yes	characteristic
112	C₃₁×#469	C₂²	1	1	yes	characteristic
113	C₃₁×#469	C₂²	1	1	yes	characteristic
114	C₃₁×#468	C₂²	1	1	yes	characteristic
115	C₃₁×#467	C₂²	1	1	yes	characteristic
116	C₃₁×#467	C₂²	1	1	yes	characteristic
117	C₃₁×#466	C₂²	1	1	yes	characteristic
118	C₃₁×#465	C₂²	1	1	yes	characteristic
119	C₃₁×#465	C₂²	1	1	yes	characteristic
120	C₃₁×#465	C₂²	1	1	yes	characteristic
121	C₃₁×#465	C₂²	1	1	yes	characteristic
122	C₃₁×#465	C₂²	1	1	yes	characteristic
123	C₃₁×#464	C₂²	1	1	yes	characteristic
124	C₃₁×#464	C₂²	1	1	yes	characteristic
125	C₃₁×#464	C₂²	1	1	yes	characteristic
126	C₃₁×#464	C₂²	1	1	yes	characteristic
127	C₃₁×#464	C₂²	1	1	yes	characteristic
128	C₃₁×#464	C₂²	1	1	yes	characteristic
129	C₃₁×#464	C₂²	1	1	yes	characteristic
130	C₃₁×#464	C₂²	1	1	yes	characteristic
131	C₃₁×#464	C₂²	1	1	yes	characteristic
132	C₃₁×#464	C₂²	1	1	yes	characteristic
133	C₃₁×#463	C₂²	1	1	yes	characteristic
134	C₃₁×#463	C₂²	1	1	yes	characteristic
135	C₃₁×#463	C₂²	1	1	yes	characteristic
136	C₃₁×#463	C₂²	1	1	yes	characteristic
137	C₃₁×#463	C₂²	1	1	yes	characteristic
138	C₃₁×#463	C₂²	1	1	yes	characteristic
139	C₃₁×#462	C₂²	1	1	yes	characteristic
140	C₃₁×#462	C₂²	1	1	yes	characteristic
141	C₃₁×#462	C₂²	1	1	yes	characteristic
142	C₃₁×#462	C₂²	1	1	yes	characteristic
143	C₃₁×#462	C₂²	1	1	yes	characteristic
144	C₃₁×#462	C₂²	1	1	yes	characteristic
145	C₃₁×#461	C₂²	1	1	yes	characteristic
146	C₃₁×#461	C₂²	1	1	yes	characteristic
147	C₃₁×#461	C₂²	1	1	yes	characteristic
148	C₃₁×#461	C₂²	1	1	yes	characteristic
149	C₃₁×#460	C₂²	1	1	yes	characteristic
150	C₃₁×#460	C₂²	1	1	yes	characteristic
151	C₃₁×#459	C₂²	1	1	yes	characteristic
152	C₃₁×#459	C₂²	1	1	yes	characteristic
153	C₃₁×#452	C₂²	1	1	yes	characteristic
154	C₃₁×#452	C₂²	1	1	yes	characteristic
155	C₃₁×#452	C₂²	1	1	yes	characteristic
156	C₃₁×#452	C₂²	1	1	yes	characteristic
157	C₃₁×#452	C₂²	1	1	yes	characteristic
158	C₃₁×#452	C₂²	1	1	yes	characteristic
159	C₃₁×#451	C₂²	1	1	yes	characteristic
160	C₃₁×#451	C₂²	1	1	yes	characteristic
161	C₃₁×#449	C₂²	1	1	yes	characteristic
162	C₃₁×#449	C₂²	1	1	yes	characteristic
163	C₃₁×#449	C₂²	1	1	yes	characteristic
164	C₃₁×#449	C₂²	1	1	yes	characteristic
165	C₃₁×#449	C₂²	1	1	yes	characteristic
166	C₃₁×#449	C₂²	1	1	yes	characteristic
167	C₃₁×#448	C₂²	1	1	yes	characteristic
168	C₃₁×#448	C₂²	1	1	yes	characteristic
169	C₃₁×#448	C₂²	1	1	yes	characteristic
170	C₃₁×#448	C₂²	1	1	yes	characteristic
171	C₃₁×#446	C₂²	1	1	yes	characteristic
172	C₃₁×#446	C₂²	1	1	yes	characteristic
173	C₃₁×#441	C₂²	1	1	yes	characteristic
174	C₃₁×#441	C₂²	1	1	yes	characteristic
175	C₃₁×#441	C₂²	1	1	yes	characteristic
176	C₃₁×#440	C₂²	1	1	yes	characteristic
177	C₃₁×#440	C₂²	1	1	yes	characteristic
178	C₃₁×#440	C₂²	1	1	yes	characteristic
179	C₃₁×#440	C₂²	1	1	yes	characteristic
180	C₃₁×#440	C₂²	1	1	yes	characteristic
181	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
182	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
183	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
184	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
185	C₃₁×#435	C₂²	1	1	yes	characteristic
186	C₃₁×#435	C₂²	1	1	yes	characteristic
187	C₃₁×#435	C₂²	1	1	yes	characteristic
188	C₃₁×#435	C₂²	1	1	yes	characteristic
189	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
190	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
191	C₃₁×#433	C₂²	1	1	yes	characteristic
192	C₃₁×#433	C₂²	1	1	yes	characteristic
193	C₃₁×#432	C₂²	1	1	yes	characteristic
194	C₃₁×#424	C₂²	1	1	yes	characteristic
195	C₃₁×#424	C₂²	1	1	yes	characteristic
196	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
197	C₃₁×#419	C₂²	1	1	yes	characteristic
198	C₃₁×#417	C₂²	1	1	yes	characteristic
199	C₃₁×#416	C₂²	1	1	yes	characteristic
200	C₃₁×#416	C₂²	1	1	yes	characteristic
201	C₃₁×#416	C₂²	1	1	yes	characteristic
202	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
209	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₃₁×#137	—	4	2	no	—
213	C₃₁×#137	—	4	2	no	—
214	C₃₁×#135	—	4	2	no	—
215	C₃₁×#135	—	4	2	no	—
216	C₃₁×#135	—	4	2	no	—
217	C₂×Q₁₆×C₃₁	—	4	2	no	—
218	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
243	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
244	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
245	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
246	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
247	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
248	C₃₁×C₄⋊Q₈	—	2	1	no	—
249	C₃₁×C₄⋊Q₈	—	2	1	no	—
250	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
251	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
252	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
253	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
254	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
256	C₃₁×#127	—	2	1	no	—
257	C₃₁×#127	—	2	1	no	—
258	C₃₁×#127	C₂³	1	1	yes	characteristic
259	C₃₁×#127	C₂³	1	1	yes	characteristic
260	C₃₁×#126	—	2	1	no	—
261	C₃₁×#126	—	2	1	no	—
262	C₃₁×#126	—	2	1	no	—
263	C₃₁×#126	—	2	1	no	—
264	C₃₁×#126	—	2	1	no	—
265	C₃₁×#126	—	2	1	no	—
266	C₃₁×#126	D₄	1	1	yes	characteristic
267	C₃₁×#126	D₄	1	1	yes	characteristic
268	C₃₁×#125	—	2	1	no	—
269	C₃₁×#125	—	2	1	no	—
270	C₃₁×#125	—	2	1	no	—
271	C₃₁×#125	—	2	1	no	—
272	C₃₁×#125	—	2	1	no	—
273	C₃₁×#125	—	2	1	no	—
274	C₃₁×#125	—	2	1	no	—
275	C₃₁×#125	D₄	1	1	yes	characteristic
276	C₃₁×#125	C₂³	1	1	yes	characteristic
277	C₃₁×#125	C₂³	1	1	yes	characteristic
278	C₃₁×#124	—	2	1	no	—
279	C₃₁×#124	—	2	1	no	—
280	C₃₁×#124	—	2	1	no	—
281	C₃₁×#124	—	2	1	no	—
282	C₃₁×#124	—	2	1	no	—
283	C₃₁×#124	—	2	1	no	—
284	C₃₁×#124	—	2	1	no	—
285	C₃₁×#124	—	2	1	no	—
286	C₃₁×#124	—	2	1	no	—
287	C₃₁×#124	—	2	1	no	—
288	C₃₁×#124	—	2	1	no	—
289	C₃₁×#124	D₄	1	1	yes	characteristic
290	C₃₁×#124	C₂³	1	1	yes	characteristic
291	C₃₁×#124	C₂³	1	1	yes	characteristic
292	C₃₁×#124	C₂³	1	1	yes	characteristic
293	C₃₁×#124	C₂³	1	1	yes	characteristic
294	C₃₁×#124	C₂³	1	1	yes	characteristic
295	C₃₁×#124	C₂³	1	1	yes	characteristic
296	C₃₁×#123	—	2	1	no	—
297	C₃₁×#123	—	2	1	no	—
298	C₃₁×#123	—	2	1	no	—
299	C₃₁×#123	—	2	1	no	—
300	C₃₁×#123	—	2	1	no	—
301	C₃₁×#123	—	2	1	no	—
302	C₃₁×#123	—	2	1	no	—
303	C₃₁×#123	—	2	1	no	—
304	C₃₁×#123	—	2	1	no	—
305	C₃₁×#123	—	2	1	no	—
306	C₃₁×#123	—	2	1	no	—
307	C₃₁×#123	—	2	1	no	—
308	C₃₁×#123	—	2	1	no	—
309	C₃₁×#123	—	2	1	no	—
310	C₃₁×#123	—	2	1	no	—
311	C₃₁×#123	—	2	1	no	—
312	C₃₁×#123	—	2	1	no	—
313	C₃₁×#123	—	2	1	no	—
314	C₃₁×#123	—	2	1	no	—
315	C₃₁×#123	—	2	1	no	—
316	C₃₁×#123	D₄	1	1	yes	characteristic
317	C₃₁×#123	D₄	1	1	yes	characteristic
318	C₃₁×C₂²⋊Q₈	—	2	1	no	—
319	C₃₁×C₂²⋊Q₈	—	2	1	no	—
320	C₃₁×C₂²⋊Q₈	—	2	1	no	—
321	C₃₁×C₂²⋊Q₈	—	2	1	no	—
322	C₃₁×C₂²⋊Q₈	—	2	1	no	—
323	C₃₁×C₂²⋊Q₈	—	2	1	no	—
324	C₃₁×C₂²⋊Q₈	—	2	1	no	—
325	C₃₁×C₂²⋊Q₈	—	2	1	no	—
326	C₃₁×C₂²⋊Q₈	—	2	1	no	—
327	C₃₁×C₂²⋊Q₈	—	2	1	no	—
328	C₃₁×C₂²⋊Q₈	—	2	1	no	—
329	C₃₁×C₂²⋊Q₈	—	2	1	no	—
330	C₃₁×C₂²⋊Q₈	—	2	1	no	—
331	C₃₁×C₂²⋊Q₈	—	2	1	no	—
332	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
333	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
334	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
335	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
336	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
337	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
338	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
339	C₃₁×#121	—	2	1	no	—
340	C₃₁×#121	—	2	1	no	—
341	C₃₁×#121	—	2	1	no	—
342	C₃₁×#121	—	2	1	no	—
343	C₃₁×#121	—	2	1	no	—
344	C₃₁×#121	—	2	1	no	—
345	C₃₁×#121	—	2	1	no	—
346	C₃₁×#121	—	2	1	no	—
347	C₃₁×#121	—	2	1	no	—
348	C₃₁×#121	—	2	1	no	—
349	C₃₁×#121	—	2	1	no	—
350	C₃₁×#121	—	2	1	no	—
351	C₃₁×#121	—	2	1	no	—
352	C₃₁×#121	—	2	1	no	—
353	C₃₁×#121	—	2	1	no	—
354	C₃₁×#121	—	2	1	no	—
355	C₃₁×#121	D₄	1	1	yes	characteristic
356	C₃₁×#121	C₂³	1	1	yes	characteristic
357	C₃₁×#121	C₂³	1	1	yes	characteristic
358	C₃₁×#121	C₂³	1	1	yes	characteristic
359	C₃₁×#121	C₂³	1	1	yes	characteristic
360	C₃₁×#121	C₂³	1	1	yes	characteristic
361	C₃₁×#121	C₂³	1	1	yes	characteristic
362	C₄×Q₈×C₃₁	—	2	1	no	—
363	C₄×Q₈×C₃₁	—	2	1	no	—
364	C₄×Q₈×C₃₁	—	2	1	no	—
365	C₄×Q₈×C₃₁	—	2	1	no	—
366	C₄×Q₈×C₃₁	—	2	1	no	—
367	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
370	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
371	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
372	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
373	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
374	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
375	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
376	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
377	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₃₁	—	2	1	no	—
379	C₄×D₄×C₃₁	—	2	1	no	—
380	C₄×D₄×C₃₁	—	2	1	no	—
381	C₄×D₄×C₃₁	—	2	1	no	—
382	C₄×D₄×C₃₁	—	2	1	no	—
383	C₄×D₄×C₃₁	—	2	1	no	—
384	C₄×D₄×C₃₁	—	2	1	no	—
385	C₄×D₄×C₃₁	—	2	1	no	—
386	C₄×D₄×C₃₁	—	2	1	no	—
387	C₄×D₄×C₃₁	—	2	1	no	—
388	C₄×D₄×C₃₁	—	2	1	no	—
389	C₄×D₄×C₃₁	—	2	1	no	—
390	C₄×D₄×C₃₁	—	2	1	no	—
391	C₄×D₄×C₃₁	—	2	1	no	—
392	C₄×D₄×C₃₁	—	2	1	no	—
393	C₄×D₄×C₃₁	—	2	1	no	—
394	C₄×D₄×C₃₁	—	2	1	no	—
395	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
396	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
397	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
398	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
399	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
400	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
401	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
402	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
403	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
404	C₃₁×#117	—	2	1	no	—
405	C₃₁×#117	—	2	1	no	—
406	C₃₁×#117	—	2	1	no	—
407	C₃₁×#117	—	2	1	no	—
408	C₃₁×#117	—	2	1	no	—
409	C₃₁×#117	—	2	1	no	—
410	C₃₁×#117	—	2	1	no	—
411	C₃₁×#117	—	2	1	no	—
412	C₃₁×#117	C₂³	1	1	yes	characteristic
413	C₃₁×#117	C₂³	1	1	yes	characteristic
414	C₃₁×#117	C₂³	1	1	yes	characteristic
415	C₃₁×#117	C₂³	1	1	yes	characteristic
416	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₃₁	—	2	1	no	—
421	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
422	C₃₁×#107	C₂³	1	1	yes	characteristic
423	C₃₁×#107	C₂³	1	1	yes	characteristic
424	C₃₁×#107	C₂³	1	1	yes	characteristic
425	C₃₁×#107	C₂³	1	1	yes	characteristic
426	C₃₁×#106	C₂³	1	1	yes	characteristic
427	C₃₁×#106	C₂³	1	1	yes	characteristic
428	C₃₁×#106	C₂³	1	1	yes	characteristic
429	C₃₁×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
435	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
436	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
437	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
438	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#103	C₂³	1	1	yes	characteristic
451	C₃₁×#103	C₂³	1	1	yes	characteristic
452	C₃₁×#103	C₂³	1	1	yes	characteristic
453	C₃₁×#103	C₂³	1	1	yes	characteristic
454	C₃₁×#103	C₂³	1	1	yes	characteristic
455	C₃₁×#103	C₂³	1	1	yes	characteristic
456	C₃₁×#103	C₂³	1	1	yes	characteristic
457	C₃₁×#103	C₂³	1	1	yes	characteristic
458	C₃₁×#103	C₂³	1	1	yes	characteristic
459	C₃₁×#103	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×#102	C₂³	1	1	yes	characteristic
467	C₃₁×#102	C₂³	1	1	yes	characteristic
468	C₃₁×#102	C₂³	1	1	yes	characteristic
469	C₃₁×#102	C₂³	1	1	yes	characteristic
470	C₃₁×#102	C₂³	1	1	yes	characteristic
471	C₃₁×#102	C₂³	1	1	yes	characteristic
472	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
475	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	C₃₁×#97	C₂³	1	1	yes	characteristic
479	C₃₁×#97	C₂³	1	1	yes	characteristic
480	C₃₁×#97	C₂³	1	1	yes	characteristic
481	C₃₁×#97	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
484	#41×C₃₁	—	2	2	no	—
485	#41×C₃₁	—	2	2	no	—
486	#41×C₃₁	—	4	1	no	—
487	#41×C₃₁	—	4	1	no	—
488	#41×C₃₁	—	4	1	no	—
489	#41×C₃₁	—	4	1	no	—
490	#41×C₃₁	—	4	1	no	—
491	#41×C₃₁	—	4	1	no	—
492	#41×C₃₁	—	4	1	no	—
493	#41×C₃₁	—	4	1	no	—
494	#41×C₃₁	—	4	1	no	—
495	#41×C₃₁	—	4	1	no	—
496	C₂×Q₈×C₃₁	—	2	1	no	—
497	C₂×Q₈×C₃₁	—	2	1	no	—
498	C₂×Q₈×C₃₁	—	2	1	no	—
499	C₂×Q₈×C₃₁	—	2	1	no	—
500	C₂×Q₈×C₃₁	—	2	1	no	—
501	C₂×Q₈×C₃₁	—	2	2	no	—
502	C₂×Q₈×C₃₁	—	4	1	no	—
503	C₂×Q₈×C₃₁	—	4	1	no	—
504	C₂×Q₈×C₃₁	—	4	1	no	—
505	C₂×Q₈×C₃₁	—	4	1	no	—
506	C₂×Q₈×C₃₁	—	4	1	no	—
507	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
508	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
512	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
513	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
514	C₂×D₄×C₃₁	—	2	1	no	—
515	C₂×D₄×C₃₁	—	2	1	no	—
516	C₂×D₄×C₃₁	—	2	1	no	—
517	C₂×D₄×C₃₁	—	2	1	no	—
518	C₂×D₄×C₃₁	—	2	1	no	—
519	C₂×D₄×C₃₁	—	2	1	no	—
520	C₂×D₄×C₃₁	—	2	1	no	—
521	C₂×D₄×C₃₁	—	2	1	no	—
522	C₂×D₄×C₃₁	—	2	1	no	—
523	C₂×D₄×C₃₁	—	2	1	no	—
524	C₂×D₄×C₃₁	—	2	1	no	—
525	C₂×D₄×C₃₁	—	2	1	no	—
526	C₂×D₄×C₃₁	—	2	1	no	—
527	C₂×D₄×C₃₁	—	2	1	no	—
528	C₂×D₄×C₃₁	—	2	1	no	—
529	C₂×D₄×C₃₁	—	2	1	no	—
530	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
531	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
532	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
533	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
534	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
535	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
536	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₃₁	—	2	1	no	—
538	C₂²×C₄×C₃₁	—	2	1	no	—
539	C₂²×C₄×C₃₁	—	2	1	no	—
540	C₂²×C₄×C₃₁	—	2	1	no	—
541	C₂²×C₄×C₃₁	—	2	1	no	—
542	C₂²×C₄×C₃₁	—	2	1	no	—
543	C₂²×C₄×C₃₁	—	2	1	no	—
544	C₂²×C₄×C₃₁	—	2	1	no	—
545	C₂²×C₄×C₃₁	—	2	1	no	—
546	C₂²×C₄×C₃₁	—	2	1	no	—
547	C₂²×C₄×C₃₁	—	2	1	no	—
548	C₂²×C₄×C₃₁	—	2	1	no	—
549	C₂²×C₄×C₃₁	—	2	1	no	—
550	C₂²×C₄×C₃₁	—	2	1	no	—
551	C₂²×C₄×C₃₁	—	2	1	no	—
552	C₂²×C₄×C₃₁	—	2	1	no	—
553	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
554	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
556	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
557	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
558	Q₁₆×C₃₁	—	2	2	no	—
559	Q₁₆×C₃₁	—	2	2	no	—
560	Q₁₆×C₃₁	—	2	2	no	—
561	Q₁₆×C₃₁	—	2	2	no	—
562	Q₁₆×C₃₁	—	4	1	no	—
563	Q₁₆×C₃₁	—	4	1	no	—
564	Q₁₆×C₃₁	—	4	1	no	—
565	Q₁₆×C₃₁	—	4	1	no	—
566	SD₁₆×C₃₁	—	2	2	no	—
567	SD₁₆×C₃₁	—	2	2	no	—
568	SD₁₆×C₃₁	—	4	1	no	—
569	SD₁₆×C₃₁	—	4	1	no	—
570	SD₁₆×C₃₁	—	4	1	no	—
571	SD₁₆×C₃₁	—	4	1	no	—
572	SD₁₆×C₃₁	—	4	1	no	—
573	SD₁₆×C₃₁	—	4	1	no	—
574	SD₁₆×C₃₁	—	4	1	no	—
575	SD₁₆×C₃₁	—	4	1	no	—
576	SD₁₆×C₃₁	—	4	1	no	—
577	SD₁₆×C₃₁	—	4	1	no	—
578	D₈×C₃₁	—	4	1	no	—
579	D₈×C₃₁	—	4	1	no	—
580	D₈×C₃₁	—	4	1	no	—
581	D₈×C₃₁	—	4	1	no	—
582	M₁₆×C₃₁	—	4	1	no	—
583	M₁₆×C₃₁	—	4	1	no	—
584	C₂×C₈×C₃₁	—	4	1	no	—
585	C₂×C₈×C₃₁	—	4	1	no	—
586	C₂×C₈×C₃₁	—	4	1	no	—
587	C₂×C₈×C₃₁	—	4	1	no	—
588	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
589	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
590	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
591	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
592	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
593	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
594	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
595	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
596	C₄⋊C₄×C₃₁	—	2	1	no	—
597	C₄⋊C₄×C₃₁	—	2	1	no	—
598	C₄⋊C₄×C₃₁	—	2	1	no	—
599	C₄⋊C₄×C₃₁	—	2	1	no	—
600	C₄⋊C₄×C₃₁	—	2	1	no	—
601	C₄⋊C₄×C₃₁	—	2	1	no	—
602	C₄⋊C₄×C₃₁	—	2	1	no	—
603	C₄⋊C₄×C₃₁	—	2	1	no	—
604	C₄⋊C₄×C₃₁	—	2	1	no	—
605	C₄⋊C₄×C₃₁	—	2	1	no	—
606	C₄⋊C₄×C₃₁	—	2	1	no	—
607	C₄⋊C₄×C₃₁	—	2	1	no	—
608	C₄⋊C₄×C₃₁	—	2	1	no	—
609	C₄⋊C₄×C₃₁	—	2	1	no	—
610	C₄⋊C₄×C₃₁	—	2	1	no	—
611	C₄⋊C₄×C₃₁	—	2	1	no	—
612	C₄⋊C₄×C₃₁	—	2	1	no	—
613	C₄⋊C₄×C₃₁	—	2	1	no	—
614	C₄⋊C₄×C₃₁	—	2	1	no	—
615	C₄⋊C₄×C₃₁	—	2	1	no	—
616	C₄⋊C₄×C₃₁	—	2	1	no	—
617	C₄⋊C₄×C₃₁	—	2	1	no	—
618	C₄⋊C₄×C₃₁	—	2	1	no	—
619	C₄⋊C₄×C₃₁	—	2	1	no	—
620	C₄⋊C₄×C₃₁	—	2	1	no	—
621	C₄⋊C₄×C₃₁	—	2	1	no	—
622	C₄⋊C₄×C₃₁	—	2	1	no	—
623	C₄⋊C₄×C₃₁	—	2	1	no	—
624	C₄⋊C₄×C₃₁	—	2	1	no	—
625	C₄⋊C₄×C₃₁	—	2	1	no	—
626	C₄⋊C₄×C₃₁	—	2	1	no	—
627	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
628	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
629	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
630	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
637	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
642	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
643	C₂²⋊C₄×C₃₁	—	2	1	no	—
644	C₂²⋊C₄×C₃₁	—	2	1	no	—
645	C₂²⋊C₄×C₃₁	—	2	1	no	—
646	C₂²⋊C₄×C₃₁	—	2	1	no	—
647	C₂²⋊C₄×C₃₁	—	2	1	no	—
648	C₂²⋊C₄×C₃₁	—	2	1	no	—
649	C₂²⋊C₄×C₃₁	—	2	1	no	—
650	C₂²⋊C₄×C₃₁	—	2	1	no	—
651	C₂²⋊C₄×C₃₁	—	2	1	no	—
652	C₂²⋊C₄×C₃₁	—	2	1	no	—
653	C₂²⋊C₄×C₃₁	—	2	1	no	—
654	C₂²⋊C₄×C₃₁	—	2	1	no	—
655	C₂²⋊C₄×C₃₁	—	2	1	no	—
656	C₂²⋊C₄×C₃₁	—	2	1	no	—
657	C₂²⋊C₄×C₃₁	—	2	1	no	—
658	C₂²⋊C₄×C₃₁	—	2	1	no	—
659	C₂²⋊C₄×C₃₁	—	2	1	no	—
660	C₂²⋊C₄×C₃₁	—	2	1	no	—
661	C₂²⋊C₄×C₃₁	—	2	1	no	—
662	C₂²⋊C₄×C₃₁	—	2	1	no	—
663	C₂²⋊C₄×C₃₁	—	2	1	no	—
664	C₂²⋊C₄×C₃₁	—	2	1	no	—
665	C₂²⋊C₄×C₃₁	—	2	1	no	—
666	C₂²⋊C₄×C₃₁	—	2	1	no	—
667	C₂²⋊C₄×C₃₁	—	2	1	no	—
668	C₂²⋊C₄×C₃₁	—	2	1	no	—
669	C₂²⋊C₄×C₃₁	—	2	1	no	—
670	C₂²⋊C₄×C₃₁	—	2	1	no	—
671	C₂²⋊C₄×C₃₁	—	2	1	no	—
672	C₂²⋊C₄×C₃₁	—	2	1	no	—
673	C₂²⋊C₄×C₃₁	—	2	1	no	—
674	C₂²⋊C₄×C₃₁	—	2	1	no	—
675	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
676	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
677	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
678	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
679	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
680	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
681	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
682	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
684	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
685	C₄²×C₃₁	—	2	1	no	—
686	C₄²×C₃₁	—	2	1	no	—
687	C₄²×C₃₁	—	2	1	no	—
688	C₄²×C₃₁	—	2	1	no	—
689	C₄²×C₃₁	—	2	1	no	—
690	C₄²×C₃₁	—	2	1	no	—
691	C₄²×C₃₁	—	2	1	no	—
692	C₄²×C₃₁	—	2	1	no	—
693	C₄²×C₃₁	—	2	1	no	—
694	C₄²×C₃₁	—	2	1	no	—
695	C₄²×C₃₁	—	2	1	no	—
696	C₄²×C₃₁	—	2	1	no	—
697	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
698	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
699	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
700	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
701	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
702	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
703	#62025	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
704	C₂³×C₃₁	—	2	1	no	—
705	C₂³×C₃₁	—	2	1	no	—
706	C₂³×C₃₁	—	2	1	no	—
707	C₂³×C₃₁	—	2	1	no	—
708	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
709	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
710	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
711	Q₈×C₃₁	—	2	1	no	—
712	Q₈×C₃₁	—	2	1	no	—
713	Q₈×C₃₁	—	2	1	no	—
714	Q₈×C₃₁	—	2	1	no	—
715	Q₈×C₃₁	—	2	1	no	—
716	Q₈×C₃₁	—	2	1	no	—
717	Q₈×C₃₁	—	2	1	no	—
718	Q₈×C₃₁	—	2	1	no	—
719	Q₈×C₃₁	—	2	1	no	—
720	Q₈×C₃₁	—	2	1	no	—
721	Q₈×C₃₁	—	2	1	no	—
722	Q₈×C₃₁	—	4	1	no	—
723	Q₈×C₃₁	—	4	2	no	—
724	Q₈×C₃₁	—	8	1	no	—
725	Q₈×C₃₁	—	8	1	no	—
726	Q₈×C₃₁	—	8	1	no	—
727	Q₈×C₃₁	—	8	1	no	—
728	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
729	D₄×C₃₁	—	2	1	no	—
730	D₄×C₃₁	—	2	1	no	—
731	D₄×C₃₁	—	2	1	no	—
732	D₄×C₃₁	—	2	1	no	—
733	D₄×C₃₁	—	2	1	no	—
734	D₄×C₃₁	—	2	1	no	—
735	D₄×C₃₁	—	2	1	no	—
736	D₄×C₃₁	—	2	1	no	—
737	D₄×C₃₁	—	4	1	no	—
738	D₄×C₃₁	—	4	1	no	—
739	D₄×C₃₁	—	4	1	no	—
740	D₄×C₃₁	—	4	2	no	—
741	D₄×C₃₁	—	4	2	no	—
742	D₄×C₃₁	—	4	2	no	—
743	D₄×C₃₁	—	8	1	no	—
744	D₄×C₃₁	—	8	1	no	—
745	D₄×C₃₁	—	8	1	no	—
746	D₄×C₃₁	—	8	1	no	—
747	D₄×C₃₁	—	8	1	no	—
748	D₄×C₃₁	—	8	1	no	—
749	D₄×C₃₁	—	8	1	no	—
750	D₄×C₃₁	—	8	1	no	—
751	D₄×C₃₁	—	8	1	no	—
752	D₄×C₃₁	—	8	1	no	—
753	D₄×C₃₁	—	8	1	no	—
754	D₄×C₃₁	—	8	1	no	—
755	D₄×C₃₁	—	8	1	no	—
756	C₂×C₄×C₃₁	—	2	1	no	—
757	C₂×C₄×C₃₁	—	2	1	no	—
758	C₂×C₄×C₃₁	—	2	1	no	—
759	C₂×C₄×C₃₁	—	2	1	no	—
760	C₂×C₄×C₃₁	—	2	1	no	—
761	C₂×C₄×C₃₁	—	2	1	no	—
762	C₂×C₄×C₃₁	—	2	1	no	—
763	C₂×C₄×C₃₁	—	2	1	no	—
764	C₂×C₄×C₃₁	—	2	1	no	—
765	C₂×C₄×C₃₁	—	2	1	no	—
766	C₂×C₄×C₃₁	—	2	1	no	—
767	C₂×C₄×C₃₁	—	2	1	no	—
768	C₂×C₄×C₃₁	—	2	1	no	—
769	C₂×C₄×C₃₁	—	2	1	no	—
770	C₂×C₄×C₃₁	—	2	1	no	—
771	C₂×C₄×C₃₁	—	2	1	no	—
772	C₂×C₄×C₃₁	—	2	1	no	—
773	C₂×C₄×C₃₁	—	2	1	no	—
774	C₂×C₄×C₃₁	—	4	1	no	—
775	C₂×C₄×C₃₁	—	4	1	no	—
776	C₂×C₄×C₃₁	—	4	2	no	—
777	C₂×C₄×C₃₁	—	4	2	no	—
778	C₂×C₄×C₃₁	—	4	2	no	—
779	C₂×C₄×C₃₁	—	8	1	no	—
780	C₂×C₄×C₃₁	—	8	1	no	—
781	C₂×C₄×C₃₁	—	8	1	no	—
782	C₂×C₄×C₃₁	—	8	1	no	—
783	C₂×C₄×C₃₁	—	8	1	no	—
784	C₂×C₄×C₃₁	—	8	1	no	—
785	C₂×C₄×C₃₁	—	8	1	no	—
786	C₂×C₄×C₃₁	—	8	1	no	—
787	C₂×C₄×C₃₁	—	8	1	no	—
788	C₂×C₄×C₃₁	—	8	1	no	—
789	C₂×C₄×C₃₁	—	8	1	no	—
790	C₂×C₄×C₃₁	—	8	1	no	—
791	C₂×C₄×C₃₁	—	8	1	no	—
792	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
793	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
794	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
795	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
796	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
797	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
798	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
800	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
802	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
803	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
804	C₈×C₃₁	—	2	1	no	—
805	C₈×C₃₁	—	2	1	no	—
806	C₈×C₃₁	—	2	1	no	—
807	C₈×C₃₁	—	2	1	no	—
808	C₈×C₃₁	—	2	1	no	—
809	C₈×C₃₁	—	2	1	no	—
810	C₈×C₃₁	—	2	1	no	—
811	C₈×C₃₁	—	2	1	no	—
812	#3554	C₂×C₃₁	1	1	yes	characteristic, complemented
813	#3524	C₂×C₃₁	1	1	yes	characteristic, complemented
814	#3403	C₂×C₃₁	1	1	yes	characteristic, complemented
815	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
816	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
817	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
818	#3321	C₂×C₃₁	1	1	yes	characteristic, complemented
819	#3320	C₂×C₃₁	1	1	yes	characteristic, complemented
820	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
821	#3309	C₂×C₃₁	1	1	yes	characteristic, complemented
822	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
823	#3300	C₂×C₃₁	1	1	yes	characteristic, complemented
824	#3285	C₂×C₃₁	1	1	yes	characteristic, complemented
825	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
826	#3271	C₂×C₃₁	1	1	yes	characteristic, complemented
827	#3271	C₂×C₃₁	1	1	yes	characteristic, complemented
828	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
829	#3269	C₂×C₃₁	1	1	yes	characteristic, complemented
830	#3263	C₂×C₃₁	1	1	yes	characteristic, complemented
831	#3257	C₂×C₃₁	1	1	yes	characteristic, complemented
832	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
833	#3225	C₂×C₃₁	1	1	yes	characteristic, complemented
834	#3221	C₂×C₃₁	1	1	yes	characteristic, complemented
835	#3219	C₂×C₃₁	1	1	yes	characteristic, complemented
836	#3124	C₂×C₃₁	1	1	yes	characteristic, complemented
837	#3121	C₂×C₃₁	1	1	yes	characteristic, complemented
838	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
839	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
840	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
841	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
842	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
843	C₂²×C₃₁	—	2	1	no	—
844	C₂²×C₃₁	—	2	1	no	—
845	C₂²×C₃₁	—	2	1	no	—
846	C₂²×C₃₁	—	2	1	no	—
847	C₂²×C₃₁	—	2	1	no	—
848	C₂²×C₃₁	—	2	1	no	—
849	C₂²×C₃₁	—	2	1	no	—
850	C₂²×C₃₁	—	2	1	no	—
851	C₂²×C₃₁	—	2	1	no	—
852	C₂²×C₃₁	—	4	1	no	—
853	C₂²×C₃₁	—	4	1	no	—
854	C₂²×C₃₁	—	4	1	no	—
855	C₂²×C₃₁	—	4	1	no	—
856	C₂²×C₃₁	—	4	1	no	—
857	C₂²×C₃₁	—	4	1	no	—
858	C₂²×C₃₁	—	4	1	no	—
859	C₂²×C₃₁	—	4	1	no	—
860	C₂²×C₃₁	—	4	1	no	—
861	C₂²×C₃₁	—	4	1	no	—
862	C₂²×C₃₁	—	4	1	no	—
863	C₂²×C₃₁	—	4	1	no	—
864	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
865	C₄×C₃₁	—	2	1	no	—
866	C₄×C₃₁	—	2	1	no	—
867	C₄×C₃₁	—	2	1	no	—
868	C₄×C₃₁	—	2	1	no	—
869	C₄×C₃₁	—	2	1	no	—
870	C₄×C₃₁	—	2	1	no	—
871	C₄×C₃₁	—	2	1	no	—
872	C₄×C₃₁	—	2	1	no	—
873	C₄×C₃₁	—	2	1	no	—
874	C₄×C₃₁	—	2	1	no	—
875	C₄×C₃₁	—	2	1	no	—
876	C₄×C₃₁	—	2	2	no	—
877	C₄×C₃₁	—	4	1	no	—
878	C₄×C₃₁	—	4	1	no	—
879	C₄×C₃₁	—	4	1	no	—
880	C₄×C₃₁	—	4	1	no	—
881	C₄×C₃₁	—	4	1	no	—
882	C₄×C₃₁	—	4	1	no	—
883	C₄×C₃₁	—	4	1	no	—
884	C₄×C₃₁	—	4	1	no	—
885	C₄×C₃₁	—	4	1	no	—
886	C₄×C₃₁	—	4	1	no	—
887	C₄×C₃₁	—	4	1	no	—
888	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
889	C₄×C₃₁	#585	1	1	yes	characteristic
890	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
891	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
892	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
893	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
894	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
895	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
896	#562	—	2	1	no	—
897	#562	—	2	1	no	—
898	#559	—	2	1	no	—
899	#559	—	2	1	no	—
900	#559	C₂²×C₃₁	1	1	yes	characteristic
901	#559	C₂²×C₃₁	1	1	yes	characteristic
902	#557	C₂²×C₃₁	1	1	yes	characteristic
903	#557	C₂²×C₃₁	1	1	yes	characteristic
904	#555	—	2	1	no	—
905	#555	C₂²×C₃₁	1	1	yes	characteristic
906	#554	—	2	1	no	—
907	#553	—	2	1	no	—
908	#553	C₂²×C₃₁	1	1	yes	characteristic
909	#552	—	2	1	no	—
910	#552	C₂²×C₃₁	1	1	yes	characteristic
911	#550	C₂²×C₃₁	1	1	yes	characteristic
912	#550	C₂²×C₃₁	1	1	yes	characteristic
913	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
914	#548	C₂²×C₃₁	1	1	yes	characteristic
915	#548	C₂²×C₃₁	1	1	yes	characteristic
916	#548	C₂²×C₃₁	1	1	yes	characteristic
917	#548	C₂²×C₃₁	1	1	yes	characteristic
918	#547	C₂²×C₃₁	1	1	yes	characteristic
919	#547	C₂²×C₃₁	1	1	yes	characteristic
920	#542	—	2	1	no	—
921	#542	—	2	1	no	—
922	#542	C₂²×C₃₁	1	1	yes	characteristic
923	#542	C₂²×C₃₁	1	1	yes	characteristic
924	#542	C₂²×C₃₁	1	1	yes	characteristic
925	#540	—	2	1	no	—
926	#540	—	2	1	no	—
927	#540	C₂²×C₃₁	1	1	yes	characteristic
928	#539	—	2	1	no	—
929	#539	—	2	1	no	—
930	#536	C₂²×C₃₁	1	1	yes	characteristic
931	#536	C₂²×C₃₁	1	1	yes	characteristic
932	#533	C₂²×C₃₁	1	1	yes	characteristic
933	#532	C₂²×C₃₁	1	1	yes	characteristic
934	#529	—	2	1	no	—
935	#529	—	2	1	no	—
936	#529	C₂²×C₃₁	1	1	yes	characteristic
937	#529	C₂²×C₃₁	1	1	yes	characteristic
938	#520	C₂²×C₃₁	1	1	yes	characteristic
939	#519	C₂²×C₃₁	1	1	yes	characteristic
940	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
941	#497	C₂²×C₃₁	1	1	yes	characteristic
942	#497	C₂²×C₃₁	1	1	yes	characteristic
943	#496	C₂²×C₃₁	1	1	yes	characteristic
944	#496	C₂²×C₃₁	1	1	yes	characteristic
945	#495	C₂²×C₃₁	1	1	yes	characteristic
946	#492	C₂²×C₃₁	1	1	yes	characteristic
947	#491	C₂²×C₃₁	1	1	yes	characteristic
948	#491	C₂²×C₃₁	1	1	yes	characteristic
949	#490	C₂²×C₃₁	1	1	yes	characteristic
950	#489	C₂²×C₃₁	1	1	yes	characteristic
951	#488	C₂²×C₃₁	1	1	yes	characteristic
952	#487	C₂²×C₃₁	1	1	yes	characteristic
953	#485	C₂²×C₃₁	1	1	yes	characteristic
954	#485	C₂²×C₃₁	1	1	yes	characteristic
955	#485	C₂²×C₃₁	1	1	yes	characteristic
956	#484	C₂²×C₃₁	1	1	yes	characteristic
957	#482	C₂²×C₃₁	1	1	yes	characteristic
958	#480	C₂²×C₃₁	1	1	yes	characteristic
959	#479	C₂²×C₃₁	1	1	yes	characteristic
960	#479	C₂²×C₃₁	1	1	yes	characteristic
961	#479	C₂²×C₃₁	1	1	yes	characteristic
962	#478	C₂²×C₃₁	1	1	yes	characteristic
963	#477	C₂²×C₃₁	1	1	yes	characteristic
964	#476	C₂²×C₃₁	1	1	yes	characteristic
965	#476	C₂²×C₃₁	1	1	yes	characteristic
966	#475	C₂²×C₃₁	1	1	yes	characteristic
967	#475	C₂²×C₃₁	1	1	yes	characteristic
968	#474	C₂²×C₃₁	1	1	yes	characteristic
969	#470	C₂²×C₃₁	1	1	yes	characteristic
970	#469	C₂²×C₃₁	1	1	yes	characteristic
971	#469	C₂²×C₃₁	1	1	yes	characteristic
972	#468	C₂²×C₃₁	1	1	yes	characteristic
973	#467	C₂²×C₃₁	1	1	yes	characteristic
974	#467	C₂²×C₃₁	1	1	yes	characteristic
975	#466	C₂²×C₃₁	1	1	yes	characteristic
976	#465	C₂²×C₃₁	1	1	yes	characteristic
977	#465	C₂²×C₃₁	1	1	yes	characteristic
978	#465	C₂²×C₃₁	1	1	yes	characteristic
979	#465	C₂²×C₃₁	1	1	yes	characteristic
980	#465	C₂²×C₃₁	1	1	yes	characteristic
981	#464	C₂²×C₃₁	1	1	yes	characteristic
982	#464	C₂²×C₃₁	1	1	yes	characteristic
983	#464	C₂²×C₃₁	1	1	yes	characteristic
984	#464	C₂²×C₃₁	1	1	yes	characteristic
985	#464	C₂²×C₃₁	1	1	yes	characteristic
986	#464	C₂²×C₃₁	1	1	yes	characteristic
987	#464	C₂²×C₃₁	1	1	yes	characteristic
988	#464	C₂²×C₃₁	1	1	yes	characteristic
989	#464	C₂²×C₃₁	1	1	yes	characteristic
990	#464	C₂²×C₃₁	1	1	yes	characteristic
991	#463	C₂²×C₃₁	1	1	yes	characteristic
992	#463	C₂²×C₃₁	1	1	yes	characteristic
993	#463	C₂²×C₃₁	1	1	yes	characteristic
994	#463	C₂²×C₃₁	1	1	yes	characteristic
995	#463	C₂²×C₃₁	1	1	yes	characteristic
996	#463	C₂²×C₃₁	1	1	yes	characteristic
997	#462	C₂²×C₃₁	1	1	yes	characteristic
998	#462	C₂²×C₃₁	1	1	yes	characteristic
999	#462	C₂²×C₃₁	1	1	yes	characteristic
1000	#462	C₂²×C₃₁	1	1	yes	characteristic
1001	#462	C₂²×C₃₁	1	1	yes	characteristic
1002	#462	C₂²×C₃₁	1	1	yes	characteristic
1003	#461	C₂²×C₃₁	1	1	yes	characteristic
1004	#461	C₂²×C₃₁	1	1	yes	characteristic
1005	#461	C₂²×C₃₁	1	1	yes	characteristic
1006	#461	C₂²×C₃₁	1	1	yes	characteristic
1007	#460	C₂²×C₃₁	1	1	yes	characteristic
1008	#460	C₂²×C₃₁	1	1	yes	characteristic
1009	#459	C₂²×C₃₁	1	1	yes	characteristic
1010	#459	C₂²×C₃₁	1	1	yes	characteristic
1011	#452	C₂²×C₃₁	1	1	yes	characteristic
1012	#452	C₂²×C₃₁	1	1	yes	characteristic
1013	#452	C₂²×C₃₁	1	1	yes	characteristic
1014	#452	C₂²×C₃₁	1	1	yes	characteristic
1015	#452	C₂²×C₃₁	1	1	yes	characteristic
1016	#452	C₂²×C₃₁	1	1	yes	characteristic
1017	#451	C₂²×C₃₁	1	1	yes	characteristic
1018	#451	C₂²×C₃₁	1	1	yes	characteristic
1019	#449	C₂²×C₃₁	1	1	yes	characteristic
1020	#449	C₂²×C₃₁	1	1	yes	characteristic
1021	#449	C₂²×C₃₁	1	1	yes	characteristic
1022	#449	C₂²×C₃₁	1	1	yes	characteristic
1023	#449	C₂²×C₃₁	1	1	yes	characteristic
1024	#449	C₂²×C₃₁	1	1	yes	characteristic
1025	#448	C₂²×C₃₁	1	1	yes	characteristic
1026	#448	C₂²×C₃₁	1	1	yes	characteristic
1027	#448	C₂²×C₃₁	1	1	yes	characteristic
1028	#448	C₂²×C₃₁	1	1	yes	characteristic
1029	#446	C₂²×C₃₁	1	1	yes	characteristic
1030	#446	C₂²×C₃₁	1	1	yes	characteristic
1031	#441	C₂²×C₃₁	1	1	yes	characteristic
1032	#441	C₂²×C₃₁	1	1	yes	characteristic
1033	#441	C₂²×C₃₁	1	1	yes	characteristic
1034	#440	C₂²×C₃₁	1	1	yes	characteristic
1035	#440	C₂²×C₃₁	1	1	yes	characteristic
1036	#440	C₂²×C₃₁	1	1	yes	characteristic
1037	#440	C₂²×C₃₁	1	1	yes	characteristic
1038	#440	C₂²×C₃₁	1	1	yes	characteristic
1039	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1040	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1041	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1042	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1043	#435	C₂²×C₃₁	1	1	yes	characteristic
1044	#435	C₂²×C₃₁	1	1	yes	characteristic
1045	#435	C₂²×C₃₁	1	1	yes	characteristic
1046	#435	C₂²×C₃₁	1	1	yes	characteristic
1047	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1048	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1049	#433	C₂²×C₃₁	1	1	yes	characteristic
1050	#433	C₂²×C₃₁	1	1	yes	characteristic
1051	#432	C₂²×C₃₁	1	1	yes	characteristic
1052	#424	C₂²×C₃₁	1	1	yes	characteristic
1053	#424	C₂²×C₃₁	1	1	yes	characteristic
1054	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
1055	#419	C₂²×C₃₁	1	1	yes	characteristic
1056	#417	C₂²×C₃₁	1	1	yes	characteristic
1057	#416	C₂²×C₃₁	1	1	yes	characteristic
1058	#416	C₂²×C₃₁	1	1	yes	characteristic
1059	#416	C₂²×C₃₁	1	1	yes	characteristic
1060	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1061	C₂×C₃₁	—	4	1	no	—
1062	C₂×C₃₁	—	4	1	no	—
1063	C₂×C₃₁	—	4	1	no	—
1064	C₂×C₃₁	—	8	1	no	—
1065	C₂×C₃₁	—	8	1	no	—
1066	C₂×C₃₁	—	8	1	no	—
1067	C₂×C₃₁	—	8	1	no	—
1068	C₂×C₃₁	#3488	1	1	yes	characteristic
1069	C₂×C₃₁	#3584	1	1	yes	characteristic
1070	C₂×C₃₁	#3586	1	1	yes	characteristic
1071	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1072	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1073	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1074	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1075	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1076	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1077	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1078	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1079	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1080	#137	—	4	2	no	—
1081	#137	—	4	2	no	—
1082	#135	—	4	2	no	—
1083	#135	—	4	2	no	—
1084	#135	—	4	2	no	—
1085	C₂×Q₁₆	—	4	2	no	—
1086	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1087	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1088	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1089	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1090	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1091	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1092	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1093	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1094	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1095	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1096	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1097	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1098	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1099	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1100	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1101	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1102	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1103	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1104	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1105	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1106	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1107	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1108	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1109	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1110	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1111	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1112	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1113	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1114	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1115	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1116	C₄⋊Q₈	—	2	1	no	—
1117	C₄⋊Q₈	—	2	1	no	—
1118	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	#127	—	2	1	no	—
1125	#127	—	2	1	no	—
1126	#127	C₂³×C₃₁	1	1	yes	characteristic
1127	#127	C₂³×C₃₁	1	1	yes	characteristic
1128	#126	—	2	1	no	—
1129	#126	—	2	1	no	—
1130	#126	—	2	1	no	—
1131	#126	—	2	1	no	—
1132	#126	—	2	1	no	—
1133	#126	—	2	1	no	—
1134	#126	D₄×C₃₁	1	1	yes	characteristic
1135	#126	D₄×C₃₁	1	1	yes	characteristic
1136	#125	—	2	1	no	—
1137	#125	—	2	1	no	—
1138	#125	—	2	1	no	—
1139	#125	—	2	1	no	—
1140	#125	—	2	1	no	—
1141	#125	—	2	1	no	—
1142	#125	—	2	1	no	—
1143	#125	D₄×C₃₁	1	1	yes	characteristic
1144	#125	C₂³×C₃₁	1	1	yes	characteristic
1145	#125	C₂³×C₃₁	1	1	yes	characteristic
1146	#124	—	2	1	no	—
1147	#124	—	2	1	no	—
1148	#124	—	2	1	no	—
1149	#124	—	2	1	no	—
1150	#124	—	2	1	no	—
1151	#124	—	2	1	no	—
1152	#124	—	2	1	no	—
1153	#124	—	2	1	no	—
1154	#124	—	2	1	no	—
1155	#124	—	2	1	no	—
1156	#124	—	2	1	no	—
1157	#124	D₄×C₃₁	1	1	yes	characteristic
1158	#124	C₂³×C₃₁	1	1	yes	characteristic
1159	#124	C₂³×C₃₁	1	1	yes	characteristic
1160	#124	C₂³×C₃₁	1	1	yes	characteristic
1161	#124	C₂³×C₃₁	1	1	yes	characteristic
1162	#124	C₂³×C₃₁	1	1	yes	characteristic
1163	#124	C₂³×C₃₁	1	1	yes	characteristic
1164	#123	—	2	1	no	—
1165	#123	—	2	1	no	—
1166	#123	—	2	1	no	—
1167	#123	—	2	1	no	—
1168	#123	—	2	1	no	—
1169	#123	—	2	1	no	—
1170	#123	—	2	1	no	—
1171	#123	—	2	1	no	—
1172	#123	—	2	1	no	—
1173	#123	—	2	1	no	—
1174	#123	—	2	1	no	—
1175	#123	—	2	1	no	—
1176	#123	—	2	1	no	—
1177	#123	—	2	1	no	—
1178	#123	—	2	1	no	—
1179	#123	—	2	1	no	—
1180	#123	—	2	1	no	—
1181	#123	—	2	1	no	—
1182	#123	—	2	1	no	—
1183	#123	—	2	1	no	—
1184	#123	D₄×C₃₁	1	1	yes	characteristic
1185	#123	D₄×C₃₁	1	1	yes	characteristic
1186	C₂²⋊Q₈	—	2	1	no	—
1187	C₂²⋊Q₈	—	2	1	no	—
1188	C₂²⋊Q₈	—	2	1	no	—
1189	C₂²⋊Q₈	—	2	1	no	—
1190	C₂²⋊Q₈	—	2	1	no	—
1191	C₂²⋊Q₈	—	2	1	no	—
1192	C₂²⋊Q₈	—	2	1	no	—
1193	C₂²⋊Q₈	—	2	1	no	—
1194	C₂²⋊Q₈	—	2	1	no	—
1195	C₂²⋊Q₈	—	2	1	no	—
1196	C₂²⋊Q₈	—	2	1	no	—
1197	C₂²⋊Q₈	—	2	1	no	—
1198	C₂²⋊Q₈	—	2	1	no	—
1199	C₂²⋊Q₈	—	2	1	no	—
1200	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1201	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1202	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1203	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1204	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1205	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1206	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1207	#121	—	2	1	no	—
1208	#121	—	2	1	no	—
1209	#121	—	2	1	no	—
1210	#121	—	2	1	no	—
1211	#121	—	2	1	no	—
1212	#121	—	2	1	no	—
1213	#121	—	2	1	no	—
1214	#121	—	2	1	no	—
1215	#121	—	2	1	no	—
1216	#121	—	2	1	no	—
1217	#121	—	2	1	no	—
1218	#121	—	2	1	no	—
1219	#121	—	2	1	no	—
1220	#121	—	2	1	no	—
1221	#121	—	2	1	no	—
1222	#121	—	2	1	no	—
1223	#121	D₄×C₃₁	1	1	yes	characteristic
1224	#121	C₂³×C₃₁	1	1	yes	characteristic
1225	#121	C₂³×C₃₁	1	1	yes	characteristic
1226	#121	C₂³×C₃₁	1	1	yes	characteristic
1227	#121	C₂³×C₃₁	1	1	yes	characteristic
1228	#121	C₂³×C₃₁	1	1	yes	characteristic
1229	#121	C₂³×C₃₁	1	1	yes	characteristic
1230	C₄×Q₈	—	2	1	no	—
1231	C₄×Q₈	—	2	1	no	—
1232	C₄×Q₈	—	2	1	no	—
1233	C₄×Q₈	—	2	1	no	—
1234	C₄×Q₈	—	2	1	no	—
1235	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1236	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1237	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1238	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1239	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1240	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1241	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1242	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1243	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1244	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1245	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1246	C₄×D₄	—	2	1	no	—
1247	C₄×D₄	—	2	1	no	—
1248	C₄×D₄	—	2	1	no	—
1249	C₄×D₄	—	2	1	no	—
1250	C₄×D₄	—	2	1	no	—
1251	C₄×D₄	—	2	1	no	—
1252	C₄×D₄	—	2	1	no	—
1253	C₄×D₄	—	2	1	no	—
1254	C₄×D₄	—	2	1	no	—
1255	C₄×D₄	—	2	1	no	—
1256	C₄×D₄	—	2	1	no	—
1257	C₄×D₄	—	2	1	no	—
1258	C₄×D₄	—	2	1	no	—
1259	C₄×D₄	—	2	1	no	—
1260	C₄×D₄	—	2	1	no	—
1261	C₄×D₄	—	2	1	no	—
1262	C₄×D₄	—	2	1	no	—
1263	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1264	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1265	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1266	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1267	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1268	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1269	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1270	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1271	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1272	#117	—	2	1	no	—
1273	#117	—	2	1	no	—
1274	#117	—	2	1	no	—
1275	#117	—	2	1	no	—
1276	#117	—	2	1	no	—
1277	#117	—	2	1	no	—
1278	#117	—	2	1	no	—
1279	#117	—	2	1	no	—
1280	#117	C₂³×C₃₁	1	1	yes	characteristic
1281	#117	C₂³×C₃₁	1	1	yes	characteristic
1282	#117	C₂³×C₃₁	1	1	yes	characteristic
1283	#117	C₂³×C₃₁	1	1	yes	characteristic
1284	C₂×C₄⋊C₄	—	2	1	no	—
1285	C₂×C₄⋊C₄	—	2	1	no	—
1286	C₂×C₄⋊C₄	—	2	1	no	—
1287	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1288	C₂×C₄²	—	2	1	no	—
1289	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1290	#107	C₂³×C₃₁	1	1	yes	characteristic
1291	#107	C₂³×C₃₁	1	1	yes	characteristic
1292	#107	C₂³×C₃₁	1	1	yes	characteristic
1293	#107	C₂³×C₃₁	1	1	yes	characteristic
1294	#106	C₂³×C₃₁	1	1	yes	characteristic
1295	#106	C₂³×C₃₁	1	1	yes	characteristic
1296	#106	C₂³×C₃₁	1	1	yes	characteristic
1297	#106	C₂³×C₃₁	1	1	yes	characteristic
1298	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1299	C₄⋊C₈	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1303	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1304	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1305	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1306	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1307	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1308	#103	C₂³×C₃₁	1	1	yes	characteristic
1309	#103	C₂³×C₃₁	1	1	yes	characteristic
1310	#103	C₂³×C₃₁	1	1	yes	characteristic
1311	#103	C₂³×C₃₁	1	1	yes	characteristic
1312	#103	C₂³×C₃₁	1	1	yes	characteristic
1313	#103	C₂³×C₃₁	1	1	yes	characteristic
1314	#103	C₂³×C₃₁	1	1	yes	characteristic
1315	#103	C₂³×C₃₁	1	1	yes	characteristic
1316	#103	C₂³×C₃₁	1	1	yes	characteristic
1317	#103	C₂³×C₃₁	1	1	yes	characteristic
1318	#103	C₂³×C₃₁	1	1	yes	characteristic
1319	#103	C₂³×C₃₁	1	1	yes	characteristic
1320	#103	C₂³×C₃₁	1	1	yes	characteristic
1321	#103	C₂³×C₃₁	1	1	yes	characteristic
1322	#103	C₂³×C₃₁	1	1	yes	characteristic
1323	#103	C₂³×C₃₁	1	1	yes	characteristic
1324	#103	C₂³×C₃₁	1	1	yes	characteristic
1325	#103	C₂³×C₃₁	1	1	yes	characteristic
1326	#103	C₂³×C₃₁	1	1	yes	characteristic
1327	#103	C₂³×C₃₁	1	1	yes	characteristic
1328	#102	C₂³×C₃₁	1	1	yes	characteristic
1329	#102	C₂³×C₃₁	1	1	yes	characteristic
1330	#102	C₂³×C₃₁	1	1	yes	characteristic
1331	#102	C₂³×C₃₁	1	1	yes	characteristic
1332	#102	C₂³×C₃₁	1	1	yes	characteristic
1333	#102	C₂³×C₃₁	1	1	yes	characteristic
1334	#102	C₂³×C₃₁	1	1	yes	characteristic
1335	#102	C₂³×C₃₁	1	1	yes	characteristic
1336	#102	C₂³×C₃₁	1	1	yes	characteristic
1337	#102	C₂³×C₃₁	1	1	yes	characteristic
1338	#102	C₂³×C₃₁	1	1	yes	characteristic
1339	#102	C₂³×C₃₁	1	1	yes	characteristic
1340	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1341	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1342	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1343	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1344	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1345	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1346	#97	C₂³×C₃₁	1	1	yes	characteristic
1347	#97	C₂³×C₃₁	1	1	yes	characteristic
1348	#97	C₂³×C₃₁	1	1	yes	characteristic
1349	#97	C₂³×C₃₁	1	1	yes	characteristic
1350	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1351	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1352	C₃₁	#62025	1	1	yes	characteristic, direct product factor, Sylow
1353	#41	—	2	2	no	—
1354	#41	—	2	2	no	—
1355	#41	—	4	1	no	—
1356	#41	—	4	1	no	—
1357	#41	—	4	1	no	—
1358	#41	—	4	1	no	—
1359	#41	—	4	1	no	—
1360	#41	—	4	1	no	—
1361	#41	—	4	1	no	—
1362	#41	—	4	1	no	—
1363	#41	—	4	1	no	—
1364	#41	—	4	1	no	—
1365	C₂×Q₈	—	2	1	no	—
1366	C₂×Q₈	—	2	1	no	—
1367	C₂×Q₈	—	2	1	no	—
1368	C₂×Q₈	—	2	1	no	—
1369	C₂×Q₈	—	2	1	no	—
1370	C₂×Q₈	—	2	2	no	—
1371	C₂×Q₈	—	4	1	no	—
1372	C₂×Q₈	—	4	1	no	—
1373	C₂×Q₈	—	4	1	no	—
1374	C₂×Q₈	—	4	1	no	—
1375	C₂×Q₈	—	4	1	no	—
1376	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1377	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1378	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1379	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1380	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1381	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1382	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1383	C₂×D₄	—	2	1	no	—
1384	C₂×D₄	—	2	1	no	—
1385	C₂×D₄	—	2	1	no	—
1386	C₂×D₄	—	2	1	no	—
1387	C₂×D₄	—	2	1	no	—
1388	C₂×D₄	—	2	1	no	—
1389	C₂×D₄	—	2	1	no	—
1390	C₂×D₄	—	2	1	no	—
1391	C₂×D₄	—	2	1	no	—
1392	C₂×D₄	—	2	1	no	—
1393	C₂×D₄	—	2	1	no	—
1394	C₂×D₄	—	2	1	no	—
1395	C₂×D₄	—	2	1	no	—
1396	C₂×D₄	—	2	1	no	—
1397	C₂×D₄	—	2	1	no	—
1398	C₂×D₄	—	2	1	no	—
1399	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1400	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1401	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1402	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1403	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1404	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1405	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1417	C₂²×C₄	—	2	1	no	—
1418	C₂²×C₄	—	2	1	no	—
1419	C₂²×C₄	—	2	1	no	—
1420	C₂²×C₄	—	2	1	no	—
1421	C₂²×C₄	—	2	1	no	—
1422	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1423	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1424	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1425	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1426	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1427	Q₁₆	—	2	2	no	—
1428	Q₁₆	—	2	2	no	—
1429	Q₁₆	—	2	2	no	—
1430	Q₁₆	—	2	2	no	—
1431	Q₁₆	—	4	1	no	—
1432	Q₁₆	—	4	1	no	—
1433	Q₁₆	—	4	1	no	—
1434	Q₁₆	—	4	1	no	—
1435	SD₁₆	—	2	2	no	—
1436	SD₁₆	—	2	2	no	—
1437	SD₁₆	—	4	1	no	—
1438	SD₁₆	—	4	1	no	—
1439	SD₁₆	—	4	1	no	—
1440	SD₁₆	—	4	1	no	—
1441	SD₁₆	—	4	1	no	—
1442	SD₁₆	—	4	1	no	—
1443	SD₁₆	—	4	1	no	—
1444	SD₁₆	—	4	1	no	—
1445	SD₁₆	—	4	1	no	—
1446	SD₁₆	—	4	1	no	—
1447	D₈	—	4	1	no	—
1448	D₈	—	4	1	no	—
1449	D₈	—	4	1	no	—
1450	D₈	—	4	1	no	—
1451	M₁₆	—	4	1	no	—
1452	M₁₆	—	4	1	no	—
1453	C₂×C₈	—	4	1	no	—
1454	C₂×C₈	—	4	1	no	—
1455	C₂×C₈	—	4	1	no	—
1456	C₂×C₈	—	4	1	no	—
1457	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1458	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1459	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1460	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1461	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1462	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1463	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1464	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1465	C₄⋊C₄	—	2	1	no	—
1466	C₄⋊C₄	—	2	1	no	—
1467	C₄⋊C₄	—	2	1	no	—
1468	C₄⋊C₄	—	2	1	no	—
1469	C₄⋊C₄	—	2	1	no	—
1470	C₄⋊C₄	—	2	1	no	—
1471	C₄⋊C₄	—	2	1	no	—
1472	C₄⋊C₄	—	2	1	no	—
1473	C₄⋊C₄	—	2	1	no	—
1474	C₄⋊C₄	—	2	1	no	—
1475	C₄⋊C₄	—	2	1	no	—
1476	C₄⋊C₄	—	2	1	no	—
1477	C₄⋊C₄	—	2	1	no	—
1478	C₄⋊C₄	—	2	1	no	—
1479	C₄⋊C₄	—	2	1	no	—
1480	C₄⋊C₄	—	2	1	no	—
1481	C₄⋊C₄	—	2	1	no	—
1482	C₄⋊C₄	—	2	1	no	—
1483	C₄⋊C₄	—	2	1	no	—
1484	C₄⋊C₄	—	2	1	no	—
1485	C₄⋊C₄	—	2	1	no	—
1486	C₄⋊C₄	—	2	1	no	—
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	2	1	no	—
1492	C₄⋊C₄	—	2	1	no	—
1493	C₄⋊C₄	—	2	1	no	—
1494	C₄⋊C₄	—	2	1	no	—
1495	C₄⋊C₄	—	2	1	no	—
1496	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1497	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1498	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1499	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1500	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1501	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1502	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1503	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1504	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1505	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1506	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1507	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1508	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1509	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1510	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1511	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1512	C₂²⋊C₄	—	2	1	no	—
1513	C₂²⋊C₄	—	2	1	no	—
1514	C₂²⋊C₄	—	2	1	no	—
1515	C₂²⋊C₄	—	2	1	no	—
1516	C₂²⋊C₄	—	2	1	no	—
1517	C₂²⋊C₄	—	2	1	no	—
1518	C₂²⋊C₄	—	2	1	no	—
1519	C₂²⋊C₄	—	2	1	no	—
1520	C₂²⋊C₄	—	2	1	no	—
1521	C₂²⋊C₄	—	2	1	no	—
1522	C₂²⋊C₄	—	2	1	no	—
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	—	2	1	no	—
1542	C₂²⋊C₄	—	2	1	no	—
1543	C₂²⋊C₄	—	2	1	no	—
1544	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1545	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1546	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1547	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1548	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1549	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1550	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1551	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1552	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1553	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1554	C₄²	—	2	1	no	—
1555	C₄²	—	2	1	no	—
1556	C₄²	—	2	1	no	—
1557	C₄²	—	2	1	no	—
1558	C₄²	—	2	1	no	—
1559	C₄²	—	2	1	no	—
1560	C₄²	—	2	1	no	—
1561	C₄²	—	2	1	no	—
1562	C₄²	—	2	1	no	—
1563	C₄²	—	2	1	no	—
1564	C₄²	—	2	1	no	—
1565	C₄²	—	2	1	no	—
1566	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1567	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1568	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1569	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1570	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1571	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1572	C₂³	—	2	1	no	—
1573	C₂³	—	2	1	no	—
1574	C₂³	—	2	1	no	—
1575	C₂³	—	2	1	no	—
1576	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1577	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1578	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1579	Q₈	—	2	1	no	—
1580	Q₈	—	2	1	no	—
1581	Q₈	—	2	1	no	—
1582	Q₈	—	2	1	no	—
1583	Q₈	—	2	1	no	—
1584	Q₈	—	2	1	no	—
1585	Q₈	—	2	1	no	—
1586	Q₈	—	2	1	no	—
1587	Q₈	—	2	1	no	—
1588	Q₈	—	2	1	no	—
1589	Q₈	—	2	1	no	—
1590	Q₈	—	4	1	no	—
1591	Q₈	—	4	2	no	—
1592	Q₈	—	8	1	no	—
1593	Q₈	—	8	1	no	—
1594	Q₈	—	8	1	no	—
1595	Q₈	—	8	1	no	—
1596	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1597	D₄	—	2	1	no	—
1598	D₄	—	2	1	no	—
1599	D₄	—	2	1	no	—
1600	D₄	—	2	1	no	—
1601	D₄	—	2	1	no	—
1602	D₄	—	2	1	no	—
1603	D₄	—	2	1	no	—
1604	D₄	—	2	1	no	—
1605	D₄	—	4	1	no	—
1606	D₄	—	4	1	no	—
1607	D₄	—	4	1	no	—
1608	D₄	—	4	2	no	—
1609	D₄	—	4	2	no	—
1610	D₄	—	4	2	no	—
1611	D₄	—	8	1	no	—
1612	D₄	—	8	1	no	—
1613	D₄	—	8	1	no	—
1614	D₄	—	8	1	no	—
1615	D₄	—	8	1	no	—
1616	D₄	—	8	1	no	—
1617	D₄	—	8	1	no	—
1618	D₄	—	8	1	no	—
1619	D₄	—	8	1	no	—
1620	D₄	—	8	1	no	—
1621	D₄	—	8	1	no	—
1622	D₄	—	8	1	no	—
1623	D₄	—	8	1	no	—
1624	C₂×C₄	—	2	1	no	—
1625	C₂×C₄	—	2	1	no	—
1626	C₂×C₄	—	2	1	no	—
1627	C₂×C₄	—	2	1	no	—
1628	C₂×C₄	—	2	1	no	—
1629	C₂×C₄	—	2	1	no	—
1630	C₂×C₄	—	2	1	no	—
1631	C₂×C₄	—	2	1	no	—
1632	C₂×C₄	—	2	1	no	—
1633	C₂×C₄	—	2	1	no	—
1634	C₂×C₄	—	2	1	no	—
1635	C₂×C₄	—	2	1	no	—
1636	C₂×C₄	—	2	1	no	—
1637	C₂×C₄	—	2	1	no	—
1638	C₂×C₄	—	2	1	no	—
1639	C₂×C₄	—	2	1	no	—
1640	C₂×C₄	—	2	1	no	—
1641	C₂×C₄	—	2	1	no	—
1642	C₂×C₄	—	4	1	no	—
1643	C₂×C₄	—	4	1	no	—
1644	C₂×C₄	—	4	2	no	—
1645	C₂×C₄	—	4	2	no	—
1646	C₂×C₄	—	4	2	no	—
1647	C₂×C₄	—	8	1	no	—
1648	C₂×C₄	—	8	1	no	—
1649	C₂×C₄	—	8	1	no	—
1650	C₂×C₄	—	8	1	no	—
1651	C₂×C₄	—	8	1	no	—
1652	C₂×C₄	—	8	1	no	—
1653	C₂×C₄	—	8	1	no	—
1654	C₂×C₄	—	8	1	no	—
1655	C₂×C₄	—	8	1	no	—
1656	C₂×C₄	—	8	1	no	—
1657	C₂×C₄	—	8	1	no	—
1658	C₂×C₄	—	8	1	no	—
1659	C₂×C₄	—	8	1	no	—
1660	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1661	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1662	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1663	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1664	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1665	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1666	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1667	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1668	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1669	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1670	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1671	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1672	C₈	—	2	1	no	—
1673	C₈	—	2	1	no	—
1674	C₈	—	2	1	no	—
1675	C₈	—	2	1	no	—
1676	C₈	—	2	1	no	—
1677	C₈	—	2	1	no	—
1678	C₈	—	2	1	no	—
1679	C₈	—	2	1	no	—
1680	C₂²	—	2	1	no	—
1681	C₂²	—	2	1	no	—
1682	C₂²	—	2	1	no	—
1683	C₂²	—	2	1	no	—
1684	C₂²	—	2	1	no	—
1685	C₂²	—	2	1	no	—
1686	C₂²	—	2	1	no	—
1687	C₂²	—	2	1	no	—
1688	C₂²	—	2	1	no	—
1689	C₂²	—	4	1	no	—
1690	C₂²	—	4	1	no	—
1691	C₂²	—	4	1	no	—
1692	C₂²	—	4	1	no	—
1693	C₂²	—	4	1	no	—
1694	C₂²	—	4	1	no	—
1695	C₂²	—	4	1	no	—
1696	C₂²	—	4	1	no	—
1697	C₂²	—	4	1	no	—
1698	C₂²	—	4	1	no	—
1699	C₂²	—	4	1	no	—
1700	C₂²	—	4	1	no	—
1701	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1702	C₄	—	2	1	no	—
1703	C₄	—	2	1	no	—
1704	C₄	—	2	1	no	—
1705	C₄	—	2	2	no	—
1706	C₄	—	2	1	no	—
1707	C₄	—	2	1	no	—
1708	C₄	—	2	1	no	—
1709	C₄	—	2	1	no	—
1710	C₄	—	2	1	no	—
1711	C₄	—	2	1	no	—
1712	C₄	—	2	1	no	—
1713	C₄	—	2	1	no	—
1714	C₄	—	4	1	no	—
1715	C₄	—	4	1	no	—
1716	C₄	—	4	1	no	—
1717	C₄	—	4	1	no	—
1718	C₄	—	4	1	no	—
1719	C₄	—	4	1	no	—
1720	C₄	—	4	1	no	—
1721	C₄	—	4	1	no	—
1722	C₄	—	4	1	no	—
1723	C₄	—	4	1	no	—
1724	C₄	—	4	1	no	—
1725	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1726	C₄	C₃₁×#585	1	1	yes	characteristic
1727	C₂	—	4	1	no	—
1728	C₂	—	4	1	no	—
1729	C₂	—	4	1	no	—
1730	C₂	—	8	1	no	—
1731	C₂	—	8	1	no	—
1732	C₂	—	8	1	no	—
1733	C₂	—	8	1	no	—
1734	C₂	C₃₁×#3488	1	1	yes	characteristic
1735	C₂	C₃₁×#3584	1	1	yes	characteristic
1736	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×#3554	C₂	semidirect
2. C₃₁×#3524	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3400	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3371	C₂	semidirect
7. C₃₁×#3321	C₂	semidirect
8. C₃₁×#3320	C₂	semidirect
9. C₃₁×#3315	C₂	semidirect
10. C₃₁×#3309	C₂	semidirect
11. C₃₁×#3303	C₂	semidirect
12. C₃₁×#3300	C₂	semidirect
13. C₃₁×#3285	C₂	semidirect
14. C₃₁×#3284	C₂	semidirect
15. C₃₁×#3271	C₂	semidirect
16. C₃₁×#3271	C₂	semidirect
17. C₃₁×#3270	C₂	semidirect
18. C₃₁×#3269	C₂	semidirect
19. C₃₁×#3263	C₂	semidirect
20. C₃₁×#3257	C₂	semidirect
21. C₃₁×#3248	C₂	semidirect
22. C₃₁×#3225	C₂	semidirect
23. C₃₁×#3221	C₂	semidirect
24. C₃₁×#3219	C₂	semidirect
25. C₃₁×#3124	C₂	semidirect
26. C₃₁×#3121	C₂	semidirect
27. C₃₁×#3116	C₂	semidirect
28. C₃₁×#3046	C₂	semidirect
29. C₃₁×#3044	C₂	semidirect
30. C₃₁×#3035	C₂	semidirect
31. C₃₁×#2992	C₂	semidirect
703. #62025	C₃₁	direct (N × H)
812. #3554	C₂×C₃₁	semidirect
813. #3524	C₂×C₃₁	semidirect
814. #3403	C₂×C₃₁	semidirect
815. #3400	C₂×C₃₁	semidirect
816. #3374	C₂×C₃₁	semidirect
817. #3371	C₂×C₃₁	semidirect
818. #3321	C₂×C₃₁	semidirect
819. #3320	C₂×C₃₁	semidirect
820. #3315	C₂×C₃₁	semidirect
821. #3309	C₂×C₃₁	semidirect
822. #3303	C₂×C₃₁	semidirect
823. #3300	C₂×C₃₁	semidirect
824. #3285	C₂×C₃₁	semidirect
825. #3284	C₂×C₃₁	semidirect
826. #3271	C₂×C₃₁	semidirect
827. #3271	C₂×C₃₁	semidirect
828. #3270	C₂×C₃₁	semidirect
829. #3269	C₂×C₃₁	semidirect
830. #3263	C₂×C₃₁	semidirect
831. #3257	C₂×C₃₁	semidirect
832. #3248	C₂×C₃₁	semidirect
833. #3225	C₂×C₃₁	semidirect
834. #3221	C₂×C₃₁	semidirect
835. #3219	C₂×C₃₁	semidirect
836. #3124	C₂×C₃₁	semidirect
837. #3121	C₂×C₃₁	semidirect
838. #3116	C₂×C₃₁	semidirect
839. #3046	C₂×C₃₁	semidirect
840. #3044	C₂×C₃₁	semidirect
841. #3035	C₂×C₃₁	semidirect
842. #2992	C₂×C₃₁	semidirect
1352. C₃₁	#62025	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×#3554	2
C₃₁×#3524	2
C₃₁×#3403	2
C₃₁×#3400	2
C₃₁×#3374	2
C₃₁×#3371	2
C₃₁×#3321	2
C₃₁×#3320	2
C₃₁×#3315	2
C₃₁×#3309	2
C₃₁×#3303	2
C₃₁×#3300	2
C₃₁×#3285	2
C₃₁×#3284	2
C₃₁×#3271	2
C₃₁×#3270	2
C₃₁×#3269	2
C₃₁×#3263	2
C₃₁×#3257	2
C₃₁×#3248	2
C₃₁×#3225	2
C₃₁×#3221	2
C₃₁×#3219	2
C₃₁×#3124	2
C₃₁×#3121	2
C₃₁×#3116	2
C₃₁×#3046	2
C₃₁×#3044	2
C₃₁×#3035	2
C₃₁×#2992	2
#62025	31

Subgroups — C31×#62025 #21518784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62025 #21518784