Subgroups — C₃₁×#62010 #21518769

Order 7936.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3516	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3320	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3312	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3301	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3270	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×#3261	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3225	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3223	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3117	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	C₂×C₃₁×#462	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	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#563	—	2	1	no	—
39	C₃₁×#563	—	2	1	no	—
40	C₃₁×#557	C₂²	1	1	yes	characteristic
41	C₃₁×#557	C₂²	1	1	yes	characteristic
42	C₃₁×#556	—	2	1	no	—
43	C₃₁×#556	C₂²	1	1	yes	characteristic
44	C₃₁×#556	C₂²	1	1	yes	characteristic
45	C₃₁×#554	—	2	1	no	—
46	C₃₁×#554	—	2	1	no	—
47	C₃₁×#554	C₂²	1	1	yes	characteristic
48	C₃₁×#553	—	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	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
54	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
55	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
56	D₄×Q₈×C₃₁	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×#548	C₂²	1	1	yes	characteristic
61	C₃₁×#547	C₂²	1	1	yes	characteristic
62	C₃₁×#544	—	2	1	no	—
63	C₃₁×#542	—	2	1	no	—
64	C₃₁×#542	—	2	1	no	—
65	C₃₁×#542	C₂²	1	1	yes	characteristic
66	C₃₁×#541	—	2	1	no	—
67	C₃₁×#541	C₂²	1	1	yes	characteristic
68	C₃₁×#541	C₂²	1	1	yes	characteristic
69	C₃₁×#541	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	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
75	C₃₁×#529	—	2	1	no	—
76	C₃₁×#529	—	2	1	no	—
77	C₃₁×#529	C₂²	1	1	yes	characteristic
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	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
83	C₃₁×#497	C₂²	1	1	yes	characteristic
84	C₃₁×#497	C₂²	1	1	yes	characteristic
85	C₃₁×#497	C₂²	1	1	yes	characteristic
86	C₃₁×#497	C₂²	1	1	yes	characteristic
87	C₃₁×#495	C₂²	1	1	yes	characteristic
88	C₃₁×#494	C₂²	1	1	yes	characteristic
89	C₃₁×#491	C₂²	1	1	yes	characteristic
90	C₃₁×#491	C₂²	1	1	yes	characteristic
91	C₃₁×#491	C₂²	1	1	yes	characteristic
92	C₃₁×#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×#484	C₂²	1	1	yes	characteristic
98	C₃₁×#484	C₂²	1	1	yes	characteristic
99	C₃₁×#483	C₂²	1	1	yes	characteristic
100	C₃₁×#481	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×#479	C₂²	1	1	yes	characteristic
105	C₃₁×#479	C₂²	1	1	yes	characteristic
106	C₃₁×#479	C₂²	1	1	yes	characteristic
107	C₃₁×#478	C₂²	1	1	yes	characteristic
108	C₃₁×#478	C₂²	1	1	yes	characteristic
109	C₃₁×#477	C₂²	1	1	yes	characteristic
110	C₃₁×#475	C₂²	1	1	yes	characteristic
111	C₃₁×#470	C₂²	1	1	yes	characteristic
112	C₃₁×#470	C₂²	1	1	yes	characteristic
113	C₃₁×#470	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×#467	C₂²	1	1	yes	characteristic
118	C₃₁×#467	C₂²	1	1	yes	characteristic
119	C₃₁×#466	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×#463	C₂²	1	1	yes	characteristic
133	C₃₁×#463	C₂²	1	1	yes	characteristic
134	C₃₁×#463	C₂²	1	1	yes	characteristic
135	C₃₁×#462	C₂²	1	1	yes	characteristic
136	C₃₁×#462	C₂²	1	1	yes	characteristic
137	C₃₁×#462	C₂²	1	1	yes	characteristic
138	C₃₁×#462	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×#462	C₂²	1	1	yes	characteristic
146	C₃₁×#462	C₂²	1	1	yes	characteristic
147	C₃₁×#462	C₂²	1	1	yes	characteristic
148	C₃₁×#462	C₂²	1	1	yes	characteristic
149	C₃₁×#462	C₂²	1	1	yes	characteristic
150	C₃₁×#461	C₂²	1	1	yes	characteristic
151	C₃₁×#461	C₂²	1	1	yes	characteristic
152	C₃₁×#461	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×#451	C₂²	1	1	yes	characteristic
159	C₃₁×#451	C₂²	1	1	yes	characteristic
160	C₃₁×#451	C₂²	1	1	yes	characteristic
161	C₃₁×#451	C₂²	1	1	yes	characteristic
162	C₃₁×#451	C₂²	1	1	yes	characteristic
163	C₃₁×#451	C₂²	1	1	yes	characteristic
164	C₃₁×#451	C₂²	1	1	yes	characteristic
165	C₃₁×#451	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×#441	C₂²	1	1	yes	characteristic
177	C₃₁×#441	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×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
184	C₄×SD₁₆×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	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
201	C₂×C₃₁×#103	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	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×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	C₂×Q₁₆×C₃₁	—	4	2	no	—
216	C₂×Q₁₆×C₃₁	—	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×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×Q₁₆×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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
240	C₂×SD₁₆×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	—	2	1	no	—
251	C₃₁×C₄⋊Q₈	—	2	1	no	—
252	C₃₁×C₄⋊Q₈	—	2	1	no	—
253	C₃₁×C₄⋊Q₈	—	2	1	no	—
254	C₃₁×C₄⋊Q₈	—	2	1	no	—
255	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
256	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
257	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
258	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
260	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
261	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
262	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
263	C₃₁×#126	—	2	1	no	—
264	C₃₁×#126	—	2	1	no	—
265	C₃₁×#126	—	2	1	no	—
266	C₃₁×#126	—	2	1	no	—
267	C₃₁×#126	—	2	1	no	—
268	C₃₁×#126	—	2	1	no	—
269	C₃₁×#126	—	2	1	no	—
270	C₃₁×#126	—	2	1	no	—
271	C₃₁×#126	—	2	1	no	—
272	C₃₁×#126	—	2	1	no	—
273	C₃₁×#126	—	2	1	no	—
274	C₃₁×#126	—	2	1	no	—
275	C₃₁×#126	—	2	1	no	—
276	C₃₁×#126	—	2	1	no	—
277	C₃₁×#126	—	2	1	no	—
278	C₃₁×#126	D₄	1	1	yes	characteristic
279	C₃₁×#126	D₄	1	1	yes	characteristic
280	C₃₁×#125	—	2	1	no	—
281	C₃₁×#125	—	2	1	no	—
282	C₃₁×#125	—	2	1	no	—
283	C₃₁×#125	—	2	1	no	—
284	C₃₁×#125	—	2	1	no	—
285	C₃₁×#125	—	2	1	no	—
286	C₃₁×#125	—	2	1	no	—
287	C₃₁×#125	—	2	1	no	—
288	C₃₁×#125	—	2	1	no	—
289	C₃₁×#125	—	2	1	no	—
290	C₃₁×#125	—	2	1	no	—
291	C₃₁×#125	—	2	1	no	—
292	C₃₁×#125	—	2	1	no	—
293	C₃₁×#125	D₄	1	1	yes	characteristic
294	C₃₁×#125	C₂³	1	1	yes	characteristic
295	C₃₁×#125	C₂³	1	1	yes	characteristic
296	C₃₁×#125	C₂³	1	1	yes	characteristic
297	C₃₁×#124	—	2	1	no	—
298	C₃₁×#124	—	2	1	no	—
299	C₃₁×#124	—	2	1	no	—
300	C₃₁×#124	—	2	1	no	—
301	C₃₁×#124	—	2	1	no	—
302	C₃₁×#124	D₄	1	1	yes	characteristic
303	C₃₁×#124	C₂³	1	1	yes	characteristic
304	C₃₁×#124	C₂³	1	1	yes	characteristic
305	C₃₁×#124	C₂³	1	1	yes	characteristic
306	C₃₁×#124	C₂³	1	1	yes	characteristic
307	C₃₁×#124	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
317	C₃₁×#123	—	2	1	no	—
318	C₃₁×#123	—	2	1	no	—
319	C₃₁×#123	D₄	1	1	yes	characteristic
320	C₃₁×#123	D₄	1	1	yes	characteristic
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	—	2	1	no	—
333	C₃₁×C₂²⋊Q₈	—	2	1	no	—
334	C₃₁×C₂²⋊Q₈	—	2	1	no	—
335	C₃₁×C₂²⋊Q₈	—	2	1	no	—
336	C₃₁×C₂²⋊Q₈	—	2	1	no	—
337	C₃₁×C₂²⋊Q₈	—	2	1	no	—
338	C₃₁×C₂²⋊Q₈	—	2	1	no	—
339	C₃₁×C₂²⋊Q₈	—	2	1	no	—
340	C₃₁×C₂²⋊Q₈	—	2	1	no	—
341	C₃₁×C₂²⋊Q₈	—	2	1	no	—
342	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
343	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
344	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
345	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
346	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
347	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
348	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
349	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
350	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
351	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
352	C₃₁×#121	—	2	1	no	—
353	C₃₁×#121	—	2	1	no	—
354	C₃₁×#121	—	2	1	no	—
355	C₃₁×#121	—	2	1	no	—
356	C₃₁×#121	—	2	1	no	—
357	C₃₁×#121	—	2	1	no	—
358	C₃₁×#121	D₄	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	—	2	1	no	—
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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
379	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
380	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
381	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
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	C₃₁×#117	—	2	1	no	—
403	C₃₁×#117	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
411	C₃₁×#117	C₂³	1	1	yes	characteristic
412	C₃₁×#117	C₂³	1	1	yes	characteristic
413	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
461	C₃₁×#103	C₂³	1	1	yes	characteristic
462	C₃₁×#103	C₂³	1	1	yes	characteristic
463	C₃₁×#103	C₂³	1	1	yes	characteristic
464	C₃₁×#103	C₂³	1	1	yes	characteristic
465	C₃₁×#103	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	—	4	1	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	C₂×Q₈×C₃₁	—	2	1	no	—
491	C₂×Q₈×C₃₁	—	2	1	no	—
492	C₂×Q₈×C₃₁	—	2	1	no	—
493	C₂×Q₈×C₃₁	—	2	1	no	—
494	C₂×Q₈×C₃₁	—	2	1	no	—
495	C₂×Q₈×C₃₁	—	2	1	no	—
496	C₂×Q₈×C₃₁	—	2	1	no	—
497	C₂×Q₈×C₃₁	—	2	2	no	—
498	C₂×Q₈×C₃₁	—	2	2	no	—
499	C₂×Q₈×C₃₁	—	4	1	no	—
500	C₂×Q₈×C₃₁	—	4	1	no	—
501	C₂×Q₈×C₃₁	—	4	1	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	—	4	1	no	—
508	C₂×Q₈×C₃₁	—	4	1	no	—
509	C₂×Q₈×C₃₁	C₂×D₄	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×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
515	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
516	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
517	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
525	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
526	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
527	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
528	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
529	C₂²×C₄×C₃₁	—	2	1	no	—
530	C₂²×C₄×C₃₁	—	2	1	no	—
531	C₂²×C₄×C₃₁	—	2	1	no	—
532	C₂²×C₄×C₃₁	—	2	1	no	—
533	C₂²×C₄×C₃₁	—	2	1	no	—
534	C₂²×C₄×C₃₁	—	2	1	no	—
535	C₂²×C₄×C₃₁	—	2	1	no	—
536	C₂²×C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
544	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
545	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
547	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
548	Q₁₆×C₃₁	—	2	2	no	—
549	Q₁₆×C₃₁	—	2	2	no	—
550	Q₁₆×C₃₁	—	2	2	no	—
551	Q₁₆×C₃₁	—	2	2	no	—
552	Q₁₆×C₃₁	—	2	2	no	—
553	Q₁₆×C₃₁	—	4	1	no	—
554	Q₁₆×C₃₁	—	4	1	no	—
555	Q₁₆×C₃₁	—	4	1	no	—
556	Q₁₆×C₃₁	—	4	1	no	—
557	Q₁₆×C₃₁	—	4	1	no	—
558	Q₁₆×C₃₁	—	4	1	no	—
559	Q₁₆×C₃₁	—	4	1	no	—
560	Q₁₆×C₃₁	—	4	1	no	—
561	Q₁₆×C₃₁	—	4	1	no	—
562	Q₁₆×C₃₁	—	4	1	no	—
563	SD₁₆×C₃₁	—	2	2	no	—
564	SD₁₆×C₃₁	—	4	1	no	—
565	SD₁₆×C₃₁	—	4	1	no	—
566	SD₁₆×C₃₁	—	4	1	no	—
567	SD₁₆×C₃₁	—	4	1	no	—
568	SD₁₆×C₃₁	—	4	1	no	—
569	SD₁₆×C₃₁	—	4	1	no	—
570	SD₁₆×C₃₁	—	4	1	no	—
571	D₈×C₃₁	—	4	1	no	—
572	M₁₆×C₃₁	—	4	1	no	—
573	M₁₆×C₃₁	—	4	1	no	—
574	C₂×C₈×C₃₁	—	4	1	no	—
575	C₂×C₈×C₃₁	—	4	1	no	—
576	C₂×C₈×C₃₁	—	4	1	no	—
577	C₂×C₈×C₃₁	—	4	1	no	—
578	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
579	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
580	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
581	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
582	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
583	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
584	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
585	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
586	C₄⋊C₄×C₃₁	—	2	1	no	—
587	C₄⋊C₄×C₃₁	—	2	1	no	—
588	C₄⋊C₄×C₃₁	—	2	1	no	—
589	C₄⋊C₄×C₃₁	—	2	1	no	—
590	C₄⋊C₄×C₃₁	—	2	1	no	—
591	C₄⋊C₄×C₃₁	—	2	1	no	—
592	C₄⋊C₄×C₃₁	—	2	1	no	—
593	C₄⋊C₄×C₃₁	—	2	1	no	—
594	C₄⋊C₄×C₃₁	—	2	1	no	—
595	C₄⋊C₄×C₃₁	—	2	1	no	—
596	C₄⋊C₄×C₃₁	—	2	1	no	—
597	C₄⋊C₄×C₃₁	—	2	1	no	—
598	C₄⋊C₄×C₃₁	—	2	1	no	—
599	C₄⋊C₄×C₃₁	—	2	1	no	—
600	C₄⋊C₄×C₃₁	—	2	1	no	—
601	C₄⋊C₄×C₃₁	—	2	1	no	—
602	C₄⋊C₄×C₃₁	—	2	1	no	—
603	C₄⋊C₄×C₃₁	—	2	1	no	—
604	C₄⋊C₄×C₃₁	—	2	1	no	—
605	C₄⋊C₄×C₃₁	—	2	1	no	—
606	C₄⋊C₄×C₃₁	—	2	1	no	—
607	C₄⋊C₄×C₃₁	—	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	—	2	1	no	—
628	C₄⋊C₄×C₃₁	—	2	1	no	—
629	C₄⋊C₄×C₃₁	—	2	1	no	—
630	C₄⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
638	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
639	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
640	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
641	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
642	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
643	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
644	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
645	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
646	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
674	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₃₁	—	2	1	no	—
684	C₄²×C₃₁	—	2	1	no	—
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	#62010	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	C₂²×D₄	1	1	yes	characteristic
707	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
708	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
709	Q₈×C₃₁	—	2	1	no	—
710	Q₈×C₃₁	—	2	1	no	—
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	—	2	1	no	—
723	Q₈×C₃₁	—	2	1	no	—
724	Q₈×C₃₁	—	4	1	no	—
725	Q₈×C₃₁	—	4	2	no	—
726	Q₈×C₃₁	—	4	2	no	—
727	Q₈×C₃₁	—	8	1	no	—
728	Q₈×C₃₁	—	8	1	no	—
729	Q₈×C₃₁	—	8	1	no	—
730	Q₈×C₃₁	—	8	1	no	—
731	Q₈×C₃₁	—	8	1	no	—
732	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
733	D₄×C₃₁	—	2	2	no	—
734	D₄×C₃₁	—	2	2	no	—
735	D₄×C₃₁	—	2	1	no	—
736	D₄×C₃₁	—	2	1	no	—
737	D₄×C₃₁	—	2	1	no	—
738	D₄×C₃₁	—	2	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	C₂×C₄×C₃₁	—	2	2	no	—
747	C₂×C₄×C₃₁	—	2	1	no	—
748	C₂×C₄×C₃₁	—	2	1	no	—
749	C₂×C₄×C₃₁	—	2	1	no	—
750	C₂×C₄×C₃₁	—	2	1	no	—
751	C₂×C₄×C₃₁	—	2	1	no	—
752	C₂×C₄×C₃₁	—	2	1	no	—
753	C₂×C₄×C₃₁	—	2	1	no	—
754	C₂×C₄×C₃₁	—	2	1	no	—
755	C₂×C₄×C₃₁	—	2	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	—	4	1	no	—
768	C₂×C₄×C₃₁	—	4	2	no	—
769	C₂×C₄×C₃₁	—	4	2	no	—
770	C₂×C₄×C₃₁	—	4	2	no	—
771	C₂×C₄×C₃₁	—	4	2	no	—
772	C₂×C₄×C₃₁	—	8	1	no	—
773	C₂×C₄×C₃₁	—	8	1	no	—
774	C₂×C₄×C₃₁	—	8	1	no	—
775	C₂×C₄×C₃₁	—	8	1	no	—
776	C₂×C₄×C₃₁	—	8	1	no	—
777	C₂×C₄×C₃₁	—	8	1	no	—
778	C₂×C₄×C₃₁	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
788	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
789	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
790	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
791	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
792	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
793	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
794	C₈×C₃₁	—	2	1	no	—
795	C₈×C₃₁	—	2	1	no	—
796	C₈×C₃₁	—	2	1	no	—
797	C₈×C₃₁	—	2	1	no	—
798	C₈×C₃₁	—	2	1	no	—
799	C₈×C₃₁	—	2	1	no	—
800	C₈×C₃₁	—	2	1	no	—
801	C₈×C₃₁	—	2	1	no	—
802	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3516	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3402	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3377	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#3320	C₂×C₃₁	1	1	yes	characteristic, complemented
809	#3316	C₂×C₃₁	1	1	yes	characteristic, complemented
810	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
811	#3312	C₂×C₃₁	1	1	yes	characteristic, complemented
812	#3301	C₂×C₃₁	1	1	yes	characteristic, complemented
813	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
814	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
815	#3285	C₂×C₃₁	1	1	yes	characteristic, complemented
816	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
817	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
818	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
819	#3269	C₂×C₃₁	1	1	yes	characteristic, complemented
820	#3261	C₂×C₃₁	1	1	yes	characteristic, complemented
821	#3258	C₂×C₃₁	1	1	yes	characteristic, complemented
822	#3250	C₂×C₃₁	1	1	yes	characteristic, complemented
823	#3225	C₂×C₃₁	1	1	yes	characteristic, complemented
824	#3223	C₂×C₃₁	1	1	yes	characteristic, complemented
825	#3218	C₂×C₃₁	1	1	yes	characteristic, complemented
826	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
827	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
828	#3117	C₂×C₃₁	1	1	yes	characteristic, complemented
829	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
830	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
831	C₂×#462	C₂×C₃₁	1	1	yes	characteristic, complemented
832	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
833	C₂²×C₃₁	—	2	1	no	—
834	C₂²×C₃₁	—	2	1	no	—
835	C₂²×C₃₁	—	2	1	no	—
836	C₂²×C₃₁	—	2	1	no	—
837	C₂²×C₃₁	—	2	1	no	—
838	C₂²×C₃₁	—	2	1	no	—
839	C₂²×C₃₁	—	2	1	no	—
840	C₂²×C₃₁	—	2	1	no	—
841	C₂²×C₃₁	—	4	1	no	—
842	C₂²×C₃₁	—	4	1	no	—
843	C₂²×C₃₁	—	4	1	no	—
844	C₂²×C₃₁	—	4	1	no	—
845	C₂²×C₃₁	—	4	1	no	—
846	C₂²×C₃₁	—	4	1	no	—
847	C₂²×C₃₁	#578	1	2	yes	—
848	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
849	C₄×C₃₁	—	2	1	no	—
850	C₄×C₃₁	—	2	1	no	—
851	C₄×C₃₁	—	2	1	no	—
852	C₄×C₃₁	—	2	1	no	—
853	C₄×C₃₁	—	2	1	no	—
854	C₄×C₃₁	—	2	1	no	—
855	C₄×C₃₁	—	2	1	no	—
856	C₄×C₃₁	—	2	2	no	—
857	C₄×C₃₁	—	2	1	no	—
858	C₄×C₃₁	—	2	1	no	—
859	C₄×C₃₁	—	2	1	no	—
860	C₄×C₃₁	—	2	1	no	—
861	C₄×C₃₁	—	4	1	no	—
862	C₄×C₃₁	—	4	1	no	—
863	C₄×C₃₁	—	4	1	no	—
864	C₄×C₃₁	—	4	1	no	—
865	C₄×C₃₁	—	4	1	no	—
866	C₄×C₃₁	—	4	1	no	—
867	C₄×C₃₁	—	4	1	no	—
868	C₄×C₃₁	—	4	1	no	—
869	C₄×C₃₁	—	4	1	no	—
870	C₄×C₃₁	—	4	1	no	—
871	C₄×C₃₁	—	4	1	no	—
872	C₄×C₃₁	—	4	1	no	—
873	C₄×C₃₁	—	4	1	no	—
874	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
875	C₄×C₃₁	#585	1	1	yes	characteristic
876	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
877	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
878	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
879	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
880	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
881	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
882	#563	—	2	1	no	—
883	#563	—	2	1	no	—
884	#557	C₂²×C₃₁	1	1	yes	characteristic
885	#557	C₂²×C₃₁	1	1	yes	characteristic
886	#556	—	2	1	no	—
887	#556	C₂²×C₃₁	1	1	yes	characteristic
888	#556	C₂²×C₃₁	1	1	yes	characteristic
889	#554	—	2	1	no	—
890	#554	—	2	1	no	—
891	#554	C₂²×C₃₁	1	1	yes	characteristic
892	#553	—	2	1	no	—
893	#553	—	2	1	no	—
894	#553	C₂²×C₃₁	1	1	yes	characteristic
895	#552	—	2	1	no	—
896	#552	C₂²×C₃₁	1	1	yes	characteristic
897	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
898	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
899	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
900	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
901	#548	C₂²×C₃₁	1	1	yes	characteristic
902	#548	C₂²×C₃₁	1	1	yes	characteristic
903	#548	C₂²×C₃₁	1	1	yes	characteristic
904	#548	C₂²×C₃₁	1	1	yes	characteristic
905	#547	C₂²×C₃₁	1	1	yes	characteristic
906	#544	—	2	1	no	—
907	#542	—	2	1	no	—
908	#542	—	2	1	no	—
909	#542	C₂²×C₃₁	1	1	yes	characteristic
910	#541	—	2	1	no	—
911	#541	C₂²×C₃₁	1	1	yes	characteristic
912	#541	C₂²×C₃₁	1	1	yes	characteristic
913	#541	C₂²×C₃₁	1	1	yes	characteristic
914	#539	—	2	1	no	—
915	#539	—	2	1	no	—
916	#536	C₂²×C₃₁	1	1	yes	characteristic
917	#536	C₂²×C₃₁	1	1	yes	characteristic
918	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
919	#529	—	2	1	no	—
920	#529	—	2	1	no	—
921	#529	C₂²×C₃₁	1	1	yes	characteristic
922	#529	C₂²×C₃₁	1	1	yes	characteristic
923	#529	C₂²×C₃₁	1	1	yes	characteristic
924	#520	C₂²×C₃₁	1	1	yes	characteristic
925	#519	C₂²×C₃₁	1	1	yes	characteristic
926	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
927	#497	C₂²×C₃₁	1	1	yes	characteristic
928	#497	C₂²×C₃₁	1	1	yes	characteristic
929	#497	C₂²×C₃₁	1	1	yes	characteristic
930	#497	C₂²×C₃₁	1	1	yes	characteristic
931	#495	C₂²×C₃₁	1	1	yes	characteristic
932	#494	C₂²×C₃₁	1	1	yes	characteristic
933	#491	C₂²×C₃₁	1	1	yes	characteristic
934	#491	C₂²×C₃₁	1	1	yes	characteristic
935	#491	C₂²×C₃₁	1	1	yes	characteristic
936	#489	C₂²×C₃₁	1	1	yes	characteristic
937	#488	C₂²×C₃₁	1	1	yes	characteristic
938	#487	C₂²×C₃₁	1	1	yes	characteristic
939	#485	C₂²×C₃₁	1	1	yes	characteristic
940	#485	C₂²×C₃₁	1	1	yes	characteristic
941	#484	C₂²×C₃₁	1	1	yes	characteristic
942	#484	C₂²×C₃₁	1	1	yes	characteristic
943	#483	C₂²×C₃₁	1	1	yes	characteristic
944	#481	C₂²×C₃₁	1	1	yes	characteristic
945	#479	C₂²×C₃₁	1	1	yes	characteristic
946	#479	C₂²×C₃₁	1	1	yes	characteristic
947	#479	C₂²×C₃₁	1	1	yes	characteristic
948	#479	C₂²×C₃₁	1	1	yes	characteristic
949	#479	C₂²×C₃₁	1	1	yes	characteristic
950	#479	C₂²×C₃₁	1	1	yes	characteristic
951	#478	C₂²×C₃₁	1	1	yes	characteristic
952	#478	C₂²×C₃₁	1	1	yes	characteristic
953	#477	C₂²×C₃₁	1	1	yes	characteristic
954	#475	C₂²×C₃₁	1	1	yes	characteristic
955	#470	C₂²×C₃₁	1	1	yes	characteristic
956	#470	C₂²×C₃₁	1	1	yes	characteristic
957	#470	C₂²×C₃₁	1	1	yes	characteristic
958	#468	C₂²×C₃₁	1	1	yes	characteristic
959	#467	C₂²×C₃₁	1	1	yes	characteristic
960	#467	C₂²×C₃₁	1	1	yes	characteristic
961	#467	C₂²×C₃₁	1	1	yes	characteristic
962	#467	C₂²×C₃₁	1	1	yes	characteristic
963	#466	C₂²×C₃₁	1	1	yes	characteristic
964	#465	C₂²×C₃₁	1	1	yes	characteristic
965	#465	C₂²×C₃₁	1	1	yes	characteristic
966	#465	C₂²×C₃₁	1	1	yes	characteristic
967	#464	C₂²×C₃₁	1	1	yes	characteristic
968	#464	C₂²×C₃₁	1	1	yes	characteristic
969	#464	C₂²×C₃₁	1	1	yes	characteristic
970	#464	C₂²×C₃₁	1	1	yes	characteristic
971	#464	C₂²×C₃₁	1	1	yes	characteristic
972	#464	C₂²×C₃₁	1	1	yes	characteristic
973	#464	C₂²×C₃₁	1	1	yes	characteristic
974	#464	C₂²×C₃₁	1	1	yes	characteristic
975	#464	C₂²×C₃₁	1	1	yes	characteristic
976	#463	C₂²×C₃₁	1	1	yes	characteristic
977	#463	C₂²×C₃₁	1	1	yes	characteristic
978	#463	C₂²×C₃₁	1	1	yes	characteristic
979	#462	C₂²×C₃₁	1	1	yes	characteristic
980	#462	C₂²×C₃₁	1	1	yes	characteristic
981	#462	C₂²×C₃₁	1	1	yes	characteristic
982	#462	C₂²×C₃₁	1	1	yes	characteristic
983	#462	C₂²×C₃₁	1	1	yes	characteristic
984	#462	C₂²×C₃₁	1	1	yes	characteristic
985	#462	C₂²×C₃₁	1	1	yes	characteristic
986	#462	C₂²×C₃₁	1	1	yes	characteristic
987	#462	C₂²×C₃₁	1	1	yes	characteristic
988	#462	C₂²×C₃₁	1	1	yes	characteristic
989	#462	C₂²×C₃₁	1	1	yes	characteristic
990	#462	C₂²×C₃₁	1	1	yes	characteristic
991	#462	C₂²×C₃₁	1	1	yes	characteristic
992	#462	C₂²×C₃₁	1	1	yes	characteristic
993	#462	C₂²×C₃₁	1	1	yes	characteristic
994	#461	C₂²×C₃₁	1	1	yes	characteristic
995	#461	C₂²×C₃₁	1	1	yes	characteristic
996	#461	C₂²×C₃₁	1	1	yes	characteristic
997	#452	C₂²×C₃₁	1	1	yes	characteristic
998	#452	C₂²×C₃₁	1	1	yes	characteristic
999	#452	C₂²×C₃₁	1	1	yes	characteristic
1000	#452	C₂²×C₃₁	1	1	yes	characteristic
1001	#452	C₂²×C₃₁	1	1	yes	characteristic
1002	#451	C₂²×C₃₁	1	1	yes	characteristic
1003	#451	C₂²×C₃₁	1	1	yes	characteristic
1004	#451	C₂²×C₃₁	1	1	yes	characteristic
1005	#451	C₂²×C₃₁	1	1	yes	characteristic
1006	#451	C₂²×C₃₁	1	1	yes	characteristic
1007	#451	C₂²×C₃₁	1	1	yes	characteristic
1008	#451	C₂²×C₃₁	1	1	yes	characteristic
1009	#451	C₂²×C₃₁	1	1	yes	characteristic
1010	#449	C₂²×C₃₁	1	1	yes	characteristic
1011	#448	C₂²×C₃₁	1	1	yes	characteristic
1012	#448	C₂²×C₃₁	1	1	yes	characteristic
1013	#448	C₂²×C₃₁	1	1	yes	characteristic
1014	#448	C₂²×C₃₁	1	1	yes	characteristic
1015	#446	C₂²×C₃₁	1	1	yes	characteristic
1016	#446	C₂²×C₃₁	1	1	yes	characteristic
1017	#441	C₂²×C₃₁	1	1	yes	characteristic
1018	#441	C₂²×C₃₁	1	1	yes	characteristic
1019	#441	C₂²×C₃₁	1	1	yes	characteristic
1020	#441	C₂²×C₃₁	1	1	yes	characteristic
1021	#441	C₂²×C₃₁	1	1	yes	characteristic
1022	#440	C₂²×C₃₁	1	1	yes	characteristic
1023	#440	C₂²×C₃₁	1	1	yes	characteristic
1024	#440	C₂²×C₃₁	1	1	yes	characteristic
1025	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1026	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1027	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1028	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1029	#435	C₂²×C₃₁	1	1	yes	characteristic
1030	#435	C₂²×C₃₁	1	1	yes	characteristic
1031	#435	C₂²×C₃₁	1	1	yes	characteristic
1032	#435	C₂²×C₃₁	1	1	yes	characteristic
1033	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1034	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
1035	#433	C₂²×C₃₁	1	1	yes	characteristic
1036	#433	C₂²×C₃₁	1	1	yes	characteristic
1037	#432	C₂²×C₃₁	1	1	yes	characteristic
1038	#424	C₂²×C₃₁	1	1	yes	characteristic
1039	#424	C₂²×C₃₁	1	1	yes	characteristic
1040	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
1041	#419	C₂²×C₃₁	1	1	yes	characteristic
1042	#417	C₂²×C₃₁	1	1	yes	characteristic
1043	#416	C₂²×C₃₁	1	1	yes	characteristic
1044	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1045	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1046	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1047	C₂×C₃₁	—	2	2	no	—
1048	C₂×C₃₁	—	4	1	no	—
1049	C₂×C₃₁	—	4	1	no	—
1050	C₂×C₃₁	—	8	1	no	—
1051	C₂×C₃₁	—	8	1	no	—
1052	C₂×C₃₁	#3488	1	1	yes	characteristic
1053	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
1054	C₂×C₃₁	#3586	1	1	yes	characteristic
1055	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1059	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1060	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1061	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1062	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1063	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1064	#137	—	4	2	no	—
1065	#137	—	4	2	no	—
1066	#135	—	4	2	no	—
1067	C₂×Q₁₆	—	4	2	no	—
1068	C₂×Q₁₆	—	4	2	no	—
1069	C₂×Q₁₆	—	4	2	no	—
1070	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1071	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1072	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1073	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1074	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1075	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1076	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1077	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1078	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1079	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1080	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1081	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1082	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1083	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1084	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1085	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1086	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1087	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1088	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1089	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1090	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1091	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1092	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1093	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1094	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1095	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1096	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1097	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1098	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1099	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1100	C₄⋊Q₈	—	2	1	no	—
1101	C₄⋊Q₈	—	2	1	no	—
1102	C₄⋊Q₈	—	2	1	no	—
1103	C₄⋊Q₈	—	2	1	no	—
1104	C₄⋊Q₈	—	2	1	no	—
1105	C₄⋊Q₈	—	2	1	no	—
1106	C₄⋊Q₈	—	2	1	no	—
1107	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1108	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1109	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1110	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1111	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1112	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1113	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1114	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1115	#126	—	2	1	no	—
1116	#126	—	2	1	no	—
1117	#126	—	2	1	no	—
1118	#126	—	2	1	no	—
1119	#126	—	2	1	no	—
1120	#126	—	2	1	no	—
1121	#126	—	2	1	no	—
1122	#126	—	2	1	no	—
1123	#126	—	2	1	no	—
1124	#126	—	2	1	no	—
1125	#126	—	2	1	no	—
1126	#126	—	2	1	no	—
1127	#126	—	2	1	no	—
1128	#126	—	2	1	no	—
1129	#126	—	2	1	no	—
1130	#126	D₄×C₃₁	1	1	yes	characteristic
1131	#126	D₄×C₃₁	1	1	yes	characteristic
1132	#125	—	2	1	no	—
1133	#125	—	2	1	no	—
1134	#125	—	2	1	no	—
1135	#125	—	2	1	no	—
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	—	2	1	no	—
1144	#125	—	2	1	no	—
1145	#125	D₄×C₃₁	1	1	yes	characteristic
1146	#125	C₂³×C₃₁	1	1	yes	characteristic
1147	#125	C₂³×C₃₁	1	1	yes	characteristic
1148	#125	C₂³×C₃₁	1	1	yes	characteristic
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	D₄×C₃₁	1	1	yes	characteristic
1155	#124	C₂³×C₃₁	1	1	yes	characteristic
1156	#124	C₂³×C₃₁	1	1	yes	characteristic
1157	#124	C₂³×C₃₁	1	1	yes	characteristic
1158	#124	C₂³×C₃₁	1	1	yes	characteristic
1159	#124	C₂³×C₃₁	1	1	yes	characteristic
1160	#123	—	2	1	no	—
1161	#123	—	2	1	no	—
1162	#123	—	2	1	no	—
1163	#123	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
1172	#123	D₄×C₃₁	1	1	yes	characteristic
1173	C₂²⋊Q₈	—	2	1	no	—
1174	C₂²⋊Q₈	—	2	1	no	—
1175	C₂²⋊Q₈	—	2	1	no	—
1176	C₂²⋊Q₈	—	2	1	no	—
1177	C₂²⋊Q₈	—	2	1	no	—
1178	C₂²⋊Q₈	—	2	1	no	—
1179	C₂²⋊Q₈	—	2	1	no	—
1180	C₂²⋊Q₈	—	2	1	no	—
1181	C₂²⋊Q₈	—	2	1	no	—
1182	C₂²⋊Q₈	—	2	1	no	—
1183	C₂²⋊Q₈	—	2	1	no	—
1184	C₂²⋊Q₈	—	2	1	no	—
1185	C₂²⋊Q₈	—	2	1	no	—
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	D₄×C₃₁	1	1	yes	characteristic
1195	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1196	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1197	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1198	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1199	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1200	C₂²⋊Q₈	C₂³×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	#121	—	2	1	no	—
1205	#121	—	2	1	no	—
1206	#121	—	2	1	no	—
1207	#121	—	2	1	no	—
1208	#121	—	2	1	no	—
1209	#121	—	2	1	no	—
1210	#121	D₄×C₃₁	1	1	yes	characteristic
1211	#121	C₂³×C₃₁	1	1	yes	characteristic
1212	#121	C₂³×C₃₁	1	1	yes	characteristic
1213	#121	C₂³×C₃₁	1	1	yes	characteristic
1214	C₄×Q₈	—	2	1	no	—
1215	C₄×Q₈	—	2	1	no	—
1216	C₄×Q₈	—	2	1	no	—
1217	C₄×Q₈	—	2	1	no	—
1218	C₄×Q₈	—	2	1	no	—
1219	C₄×Q₈	—	2	1	no	—
1220	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1221	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1222	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1223	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1224	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1225	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1226	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1227	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1228	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1229	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1230	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1231	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1232	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1233	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1234	C₄×D₄	—	2	1	no	—
1235	C₄×D₄	—	2	1	no	—
1236	C₄×D₄	—	2	1	no	—
1237	C₄×D₄	—	2	1	no	—
1238	C₄×D₄	—	2	1	no	—
1239	C₄×D₄	—	2	1	no	—
1240	C₄×D₄	—	2	1	no	—
1241	C₄×D₄	—	2	1	no	—
1242	C₄×D₄	—	2	1	no	—
1243	C₄×D₄	—	2	1	no	—
1244	C₄×D₄	—	2	1	no	—
1245	C₄×D₄	—	2	1	no	—
1246	C₄×D₄	—	2	1	no	—
1247	C₄×D₄	—	2	1	no	—
1248	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1249	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1250	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1251	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1252	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1253	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1254	#117	—	2	1	no	—
1255	#117	—	2	1	no	—
1256	#117	—	2	1	no	—
1257	#117	—	2	1	no	—
1258	#117	—	2	1	no	—
1259	#117	—	2	1	no	—
1260	#117	—	2	1	no	—
1261	#117	—	2	1	no	—
1262	#117	C₂³×C₃₁	1	1	yes	characteristic
1263	#117	C₂³×C₃₁	1	1	yes	characteristic
1264	#117	C₂³×C₃₁	1	1	yes	characteristic
1265	C₂×C₄⋊C₄	—	2	1	no	—
1266	C₂×C₄⋊C₄	—	2	1	no	—
1267	C₂×C₄⋊C₄	—	2	1	no	—
1268	C₂×C₄⋊C₄	—	2	1	no	—
1269	C₂×C₄⋊C₄	—	2	1	no	—
1270	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1271	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1272	C₂×C₄²	—	2	1	no	—
1273	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1274	#107	C₂³×C₃₁	1	1	yes	characteristic
1275	#107	C₂³×C₃₁	1	1	yes	characteristic
1276	#107	C₂³×C₃₁	1	1	yes	characteristic
1277	#107	C₂³×C₃₁	1	1	yes	characteristic
1278	#106	C₂³×C₃₁	1	1	yes	characteristic
1279	#106	C₂³×C₃₁	1	1	yes	characteristic
1280	#106	C₂³×C₃₁	1	1	yes	characteristic
1281	#106	C₂³×C₃₁	1	1	yes	characteristic
1282	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1283	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1284	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1285	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1286	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1287	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1288	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1289	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1290	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1291	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1292	#103	C₂³×C₃₁	1	1	yes	characteristic
1293	#103	C₂³×C₃₁	1	1	yes	characteristic
1294	#103	C₂³×C₃₁	1	1	yes	characteristic
1295	#103	C₂³×C₃₁	1	1	yes	characteristic
1296	#103	C₂³×C₃₁	1	1	yes	characteristic
1297	#103	C₂³×C₃₁	1	1	yes	characteristic
1298	#103	C₂³×C₃₁	1	1	yes	characteristic
1299	#103	C₂³×C₃₁	1	1	yes	characteristic
1300	#103	C₂³×C₃₁	1	1	yes	characteristic
1301	#103	C₂³×C₃₁	1	1	yes	characteristic
1302	#103	C₂³×C₃₁	1	1	yes	characteristic
1303	#103	C₂³×C₃₁	1	1	yes	characteristic
1304	#103	C₂³×C₃₁	1	1	yes	characteristic
1305	#103	C₂³×C₃₁	1	1	yes	characteristic
1306	#103	C₂³×C₃₁	1	1	yes	characteristic
1307	#103	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	#102	C₂³×C₃₁	1	1	yes	characteristic
1319	#102	C₂³×C₃₁	1	1	yes	characteristic
1320	#102	C₂³×C₃₁	1	1	yes	characteristic
1321	#102	C₂³×C₃₁	1	1	yes	characteristic
1322	#102	C₂³×C₃₁	1	1	yes	characteristic
1323	#102	C₂³×C₃₁	1	1	yes	characteristic
1324	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1325	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1326	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1327	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1328	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1329	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1330	#97	C₂³×C₃₁	1	1	yes	characteristic
1331	#97	C₂³×C₃₁	1	1	yes	characteristic
1332	#97	C₂³×C₃₁	1	1	yes	characteristic
1333	#97	C₂³×C₃₁	1	1	yes	characteristic
1334	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1335	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1336	C₃₁	#62010	1	1	yes	characteristic, direct product factor, Sylow
1337	#41	—	2	2	no	—
1338	#41	—	4	1	no	—
1339	#41	—	4	1	no	—
1340	#41	—	4	1	no	—
1341	#41	—	4	1	no	—
1342	#41	—	4	1	no	—
1343	C₂×Q₈	—	2	1	no	—
1344	C₂×Q₈	—	2	1	no	—
1345	C₂×Q₈	—	2	1	no	—
1346	C₂×Q₈	—	2	1	no	—
1347	C₂×Q₈	—	2	1	no	—
1348	C₂×Q₈	—	2	1	no	—
1349	C₂×Q₈	—	2	1	no	—
1350	C₂×Q₈	—	2	2	no	—
1351	C₂×Q₈	—	2	2	no	—
1352	C₂×Q₈	—	4	1	no	—
1353	C₂×Q₈	—	4	1	no	—
1354	C₂×Q₈	—	4	1	no	—
1355	C₂×Q₈	—	4	1	no	—
1356	C₂×Q₈	—	4	1	no	—
1357	C₂×Q₈	—	4	1	no	—
1358	C₂×Q₈	—	4	1	no	—
1359	C₂×Q₈	—	4	1	no	—
1360	C₂×Q₈	—	4	1	no	—
1361	C₂×Q₈	—	4	1	no	—
1362	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1363	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1364	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1365	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1366	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1367	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1368	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1369	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1370	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1371	C₂×D₄	—	2	1	no	—
1372	C₂×D₄	—	2	1	no	—
1373	C₂×D₄	—	2	1	no	—
1374	C₂×D₄	—	2	1	no	—
1375	C₂×D₄	—	2	1	no	—
1376	C₂×D₄	—	2	1	no	—
1377	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1378	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1379	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1380	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1381	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1382	C₂²×C₄	—	2	1	no	—
1383	C₂²×C₄	—	2	1	no	—
1384	C₂²×C₄	—	2	1	no	—
1385	C₂²×C₄	—	2	1	no	—
1386	C₂²×C₄	—	2	1	no	—
1387	C₂²×C₄	—	2	1	no	—
1388	C₂²×C₄	—	2	1	no	—
1389	C₂²×C₄	—	2	1	no	—
1390	C₂²×C₄	—	2	1	no	—
1391	C₂²×C₄	—	2	1	no	—
1392	C₂²×C₄	—	2	1	no	—
1393	C₂²×C₄	—	2	1	no	—
1394	C₂²×C₄	—	2	1	no	—
1395	C₂²×C₄	—	2	1	no	—
1396	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1397	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1398	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1399	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1400	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1401	Q₁₆	—	2	2	no	—
1402	Q₁₆	—	2	2	no	—
1403	Q₁₆	—	2	2	no	—
1404	Q₁₆	—	2	2	no	—
1405	Q₁₆	—	2	2	no	—
1406	Q₁₆	—	4	1	no	—
1407	Q₁₆	—	4	1	no	—
1408	Q₁₆	—	4	1	no	—
1409	Q₁₆	—	4	1	no	—
1410	Q₁₆	—	4	1	no	—
1411	Q₁₆	—	4	1	no	—
1412	Q₁₆	—	4	1	no	—
1413	Q₁₆	—	4	1	no	—
1414	Q₁₆	—	4	1	no	—
1415	Q₁₆	—	4	1	no	—
1416	SD₁₆	—	2	2	no	—
1417	SD₁₆	—	4	1	no	—
1418	SD₁₆	—	4	1	no	—
1419	SD₁₆	—	4	1	no	—
1420	SD₁₆	—	4	1	no	—
1421	SD₁₆	—	4	1	no	—
1422	SD₁₆	—	4	1	no	—
1423	SD₁₆	—	4	1	no	—
1424	D₈	—	4	1	no	—
1425	M₁₆	—	4	1	no	—
1426	M₁₆	—	4	1	no	—
1427	C₂×C₈	—	4	1	no	—
1428	C₂×C₈	—	4	1	no	—
1429	C₂×C₈	—	4	1	no	—
1430	C₂×C₈	—	4	1	no	—
1431	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1432	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1433	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1434	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1435	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1436	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1437	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1438	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	—	2	1	no	—
1448	C₄⋊C₄	—	2	1	no	—
1449	C₄⋊C₄	—	2	1	no	—
1450	C₄⋊C₄	—	2	1	no	—
1451	C₄⋊C₄	—	2	1	no	—
1452	C₄⋊C₄	—	2	1	no	—
1453	C₄⋊C₄	—	2	1	no	—
1454	C₄⋊C₄	—	2	1	no	—
1455	C₄⋊C₄	—	2	1	no	—
1456	C₄⋊C₄	—	2	1	no	—
1457	C₄⋊C₄	—	2	1	no	—
1458	C₄⋊C₄	—	2	1	no	—
1459	C₄⋊C₄	—	2	1	no	—
1460	C₄⋊C₄	—	2	1	no	—
1461	C₄⋊C₄	—	2	1	no	—
1462	C₄⋊C₄	—	2	1	no	—
1463	C₄⋊C₄	—	2	1	no	—
1464	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1485	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1486	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1487	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1488	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1489	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1490	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1491	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1492	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1493	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1494	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1495	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1496	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1497	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1498	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1499	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1500	C₂²⋊C₄	—	2	1	no	—
1501	C₂²⋊C₄	—	2	1	no	—
1502	C₂²⋊C₄	—	2	1	no	—
1503	C₂²⋊C₄	—	2	1	no	—
1504	C₂²⋊C₄	—	2	1	no	—
1505	C₂²⋊C₄	—	2	1	no	—
1506	C₂²⋊C₄	—	2	1	no	—
1507	C₂²⋊C₄	—	2	1	no	—
1508	C₂²⋊C₄	—	2	1	no	—
1509	C₂²⋊C₄	—	2	1	no	—
1510	C₂²⋊C₄	—	2	1	no	—
1511	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
1527	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1528	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1529	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1530	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1531	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1532	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1533	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1534	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1535	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1536	C₄²	—	2	1	no	—
1537	C₄²	—	2	1	no	—
1538	C₄²	—	2	1	no	—
1539	C₄²	—	2	1	no	—
1540	C₄²	—	2	1	no	—
1541	C₄²	—	2	1	no	—
1542	C₄²	—	2	1	no	—
1543	C₄²	—	2	1	no	—
1544	C₄²	—	2	1	no	—
1545	C₄²	—	2	1	no	—
1546	C₄²	—	2	1	no	—
1547	C₄²	—	2	1	no	—
1548	C₄²	—	2	1	no	—
1549	C₄²	—	2	1	no	—
1550	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1551	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1552	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1553	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1554	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1555	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1556	C₂³	—	2	1	no	—
1557	C₂³	—	2	1	no	—
1558	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1559	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1560	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1561	Q₈	—	2	1	no	—
1562	Q₈	—	2	1	no	—
1563	Q₈	—	2	1	no	—
1564	Q₈	—	2	1	no	—
1565	Q₈	—	2	1	no	—
1566	Q₈	—	2	1	no	—
1567	Q₈	—	2	1	no	—
1568	Q₈	—	2	1	no	—
1569	Q₈	—	2	1	no	—
1570	Q₈	—	2	1	no	—
1571	Q₈	—	2	1	no	—
1572	Q₈	—	2	1	no	—
1573	Q₈	—	2	1	no	—
1574	Q₈	—	2	1	no	—
1575	Q₈	—	2	1	no	—
1576	Q₈	—	4	1	no	—
1577	Q₈	—	4	2	no	—
1578	Q₈	—	4	2	no	—
1579	Q₈	—	8	1	no	—
1580	Q₈	—	8	1	no	—
1581	Q₈	—	8	1	no	—
1582	Q₈	—	8	1	no	—
1583	Q₈	—	8	1	no	—
1584	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1585	D₄	—	2	2	no	—
1586	D₄	—	2	2	no	—
1587	D₄	—	2	1	no	—
1588	D₄	—	2	1	no	—
1589	D₄	—	2	1	no	—
1590	D₄	—	2	1	no	—
1591	D₄	—	4	1	no	—
1592	D₄	—	4	2	no	—
1593	D₄	—	4	2	no	—
1594	D₄	—	4	2	no	—
1595	D₄	—	8	1	no	—
1596	D₄	—	8	1	no	—
1597	D₄	—	8	1	no	—
1598	C₂×C₄	—	2	2	no	—
1599	C₂×C₄	—	2	1	no	—
1600	C₂×C₄	—	2	1	no	—
1601	C₂×C₄	—	2	1	no	—
1602	C₂×C₄	—	2	1	no	—
1603	C₂×C₄	—	2	1	no	—
1604	C₂×C₄	—	2	1	no	—
1605	C₂×C₄	—	2	1	no	—
1606	C₂×C₄	—	2	1	no	—
1607	C₂×C₄	—	2	1	no	—
1608	C₂×C₄	—	2	1	no	—
1609	C₂×C₄	—	2	1	no	—
1610	C₂×C₄	—	2	1	no	—
1611	C₂×C₄	—	2	1	no	—
1612	C₂×C₄	—	2	1	no	—
1613	C₂×C₄	—	2	1	no	—
1614	C₂×C₄	—	2	1	no	—
1615	C₂×C₄	—	2	1	no	—
1616	C₂×C₄	—	2	1	no	—
1617	C₂×C₄	—	2	1	no	—
1618	C₂×C₄	—	2	1	no	—
1619	C₂×C₄	—	4	1	no	—
1620	C₂×C₄	—	4	2	no	—
1621	C₂×C₄	—	4	2	no	—
1622	C₂×C₄	—	4	2	no	—
1623	C₂×C₄	—	4	2	no	—
1624	C₂×C₄	—	8	1	no	—
1625	C₂×C₄	—	8	1	no	—
1626	C₂×C₄	—	8	1	no	—
1627	C₂×C₄	—	8	1	no	—
1628	C₂×C₄	—	8	1	no	—
1629	C₂×C₄	—	8	1	no	—
1630	C₂×C₄	—	8	1	no	—
1631	C₂×C₄	—	8	1	no	—
1632	C₂×C₄	—	8	1	no	—
1633	C₂×C₄	—	8	1	no	—
1634	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1635	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1636	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1637	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1638	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1639	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1640	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1641	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1642	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1643	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1644	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1645	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1646	C₈	—	2	1	no	—
1647	C₈	—	2	1	no	—
1648	C₈	—	2	1	no	—
1649	C₈	—	2	1	no	—
1650	C₈	—	2	1	no	—
1651	C₈	—	2	1	no	—
1652	C₈	—	2	1	no	—
1653	C₈	—	2	1	no	—
1654	C₂²	—	2	1	no	—
1655	C₂²	—	2	1	no	—
1656	C₂²	—	2	1	no	—
1657	C₂²	—	2	1	no	—
1658	C₂²	—	2	1	no	—
1659	C₂²	—	2	1	no	—
1660	C₂²	—	2	1	no	—
1661	C₂²	—	2	1	no	—
1662	C₂²	—	4	1	no	—
1663	C₂²	—	4	1	no	—
1664	C₂²	—	4	1	no	—
1665	C₂²	—	4	1	no	—
1666	C₂²	—	4	1	no	—
1667	C₂²	—	4	1	no	—
1668	C₂²	C₃₁×#578	1	2	yes	—
1669	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1670	C₄	—	2	1	no	—
1671	C₄	—	2	1	no	—
1672	C₄	—	2	1	no	—
1673	C₄	—	2	2	no	—
1674	C₄	—	2	1	no	—
1675	C₄	—	2	1	no	—
1676	C₄	—	2	1	no	—
1677	C₄	—	2	1	no	—
1678	C₄	—	2	1	no	—
1679	C₄	—	2	1	no	—
1680	C₄	—	2	1	no	—
1681	C₄	—	2	1	no	—
1682	C₄	—	4	1	no	—
1683	C₄	—	4	1	no	—
1684	C₄	—	4	1	no	—
1685	C₄	—	4	1	no	—
1686	C₄	—	4	1	no	—
1687	C₄	—	4	1	no	—
1688	C₄	—	4	1	no	—
1689	C₄	—	4	1	no	—
1690	C₄	—	4	1	no	—
1691	C₄	—	4	1	no	—
1692	C₄	—	4	1	no	—
1693	C₄	—	4	1	no	—
1694	C₄	—	4	1	no	—
1695	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1696	C₄	C₃₁×#585	1	1	yes	characteristic
1697	C₂	—	2	2	no	—
1698	C₂	—	4	1	no	—
1699	C₂	—	4	1	no	—
1700	C₂	—	8	1	no	—
1701	C₂	—	8	1	no	—
1702	C₂	C₃₁×#3488	1	1	yes	characteristic
1703	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1704	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×#3552	C₂	semidirect
2. C₃₁×#3516	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3398	C₂	semidirect
5. C₃₁×#3377	C₂	semidirect
6. C₃₁×#3374	C₂	semidirect
7. C₃₁×#3320	C₂	semidirect
8. C₃₁×#3316	C₂	semidirect
9. C₃₁×#3315	C₂	semidirect
10. C₃₁×#3312	C₂	semidirect
11. C₃₁×#3301	C₂	semidirect
12. C₃₁×#3299	C₂	semidirect
13. D₄×Q₁₆×C₃₁	C₂	semidirect
14. C₃₁×#3285	C₂	semidirect
15. C₃₁×#3270	C₂	semidirect
16. C₃₁×#3270	C₂	semidirect
17. C₃₁×#3270	C₂	semidirect
18. C₃₁×#3269	C₂	semidirect
19. C₃₁×#3261	C₂	semidirect
20. C₃₁×#3258	C₂	semidirect
21. C₃₁×#3250	C₂	semidirect
22. C₃₁×#3225	C₂	semidirect
23. C₃₁×#3223	C₂	semidirect
24. C₃₁×#3218	C₂	semidirect
25. C₃₁×#3127	C₂	semidirect
26. C₃₁×#3120	C₂	semidirect
27. C₃₁×#3117	C₂	semidirect
28. C₃₁×#3046	C₂	semidirect
29. C₃₁×#3044	C₂	semidirect
30. C₂×C₃₁×#462	C₂	semidirect
31. C₃₁×#2992	C₂	semidirect
703. #62010	C₃₁	direct (N × H)
802. #3552	C₂×C₃₁	semidirect
803. #3516	C₂×C₃₁	semidirect
804. #3402	C₂×C₃₁	semidirect
805. #3398	C₂×C₃₁	semidirect
806. #3377	C₂×C₃₁	semidirect
807. #3374	C₂×C₃₁	semidirect
808. #3320	C₂×C₃₁	semidirect
809. #3316	C₂×C₃₁	semidirect
810. #3315	C₂×C₃₁	semidirect
811. #3312	C₂×C₃₁	semidirect
812. #3301	C₂×C₃₁	semidirect
813. #3299	C₂×C₃₁	semidirect
814. D₄×Q₁₆	C₂×C₃₁	semidirect
815. #3285	C₂×C₃₁	semidirect
816. #3270	C₂×C₃₁	semidirect
817. #3270	C₂×C₃₁	semidirect
818. #3270	C₂×C₃₁	semidirect
819. #3269	C₂×C₃₁	semidirect
820. #3261	C₂×C₃₁	semidirect
821. #3258	C₂×C₃₁	semidirect
822. #3250	C₂×C₃₁	semidirect
823. #3225	C₂×C₃₁	semidirect
824. #3223	C₂×C₃₁	semidirect
825. #3218	C₂×C₃₁	semidirect
826. #3127	C₂×C₃₁	semidirect
827. #3120	C₂×C₃₁	semidirect
828. #3117	C₂×C₃₁	semidirect
829. #3046	C₂×C₃₁	semidirect
830. #3044	C₂×C₃₁	semidirect
831. C₂×#462	C₂×C₃₁	semidirect
832. #2992	C₂×C₃₁	semidirect
1336. C₃₁	#62010	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×#3552	2
C₃₁×#3516	2
C₃₁×#3402	2
C₃₁×#3398	2
C₃₁×#3377	2
C₃₁×#3374	2
C₃₁×#3320	2
C₃₁×#3316	2
C₃₁×#3315	2
C₃₁×#3312	2
C₃₁×#3301	2
C₃₁×#3299	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3285	2
C₃₁×#3270	2
C₃₁×#3269	2
C₃₁×#3261	2
C₃₁×#3258	2
C₃₁×#3250	2
C₃₁×#3225	2
C₃₁×#3223	2
C₃₁×#3218	2
C₃₁×#3127	2
C₃₁×#3120	2
C₃₁×#3117	2
C₃₁×#3046	2
C₃₁×#3044	2
C₂×C₃₁×#462	2
C₃₁×#2992	2
#62010	31

Subgroups — C31×#62010 #21518769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62010 #21518769