Subgroups — C₃₁×#61512 #21518271

Order 7936.

1760 conjugacy classes of subgroups.

The subgroup lattice has 1662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3524	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3390	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×#3352	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3350	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3348	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3320	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3312	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3270	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3270	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3178	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3174	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3172	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3126	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3121	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3120	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3117	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#2967	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×C₃₁×#137	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	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#559	—	2	1	no	—
36	C₃₁×#559	C₂²	1	1	yes	characteristic
37	C₃₁×#557	—	2	1	no	—
38	C₃₁×#557	C₂²	1	1	yes	characteristic
39	C₃₁×#557	C₂²	1	1	yes	characteristic
40	C₃₁×#557	C₂²	1	1	yes	characteristic
41	C₃₁×#556	—	2	1	no	—
42	C₃₁×#556	C₂²	1	1	yes	characteristic
43	C₃₁×#555	—	2	1	no	—
44	C₃₁×#555	C₂²	1	1	yes	characteristic
45	C₃₁×#553	—	2	1	no	—
46	C₃₁×#553	C₂²	1	1	yes	characteristic
47	C₃₁×#552	—	2	1	no	—
48	C₃₁×#552	—	2	1	no	—
49	C₃₁×#552	—	2	1	no	—
50	C₃₁×#552	C₂²	1	1	yes	characteristic
51	C₃₁×#552	C₂²	1	1	yes	characteristic
52	C₃₁×#552	C₂²	1	1	yes	characteristic
53	C₃₁×#550	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×#542	—	2	1	no	—
60	C₃₁×#542	C₂²	1	1	yes	characteristic
61	C₃₁×#541	—	2	1	no	—
62	C₃₁×#541	—	2	1	no	—
63	C₃₁×#541	C₂²	1	1	yes	characteristic
64	C₃₁×#541	C₂²	1	1	yes	characteristic
65	C₃₁×#540	—	2	1	no	—
66	C₃₁×#540	C₂²	1	1	yes	characteristic
67	C₃₁×#533	—	2	1	no	—
68	C₃₁×#533	C₂²	1	1	yes	characteristic
69	C₃₁×#529	—	2	1	no	—
70	C₃₁×#529	—	2	1	no	—
71	C₃₁×#529	—	2	1	no	—
72	C₃₁×#529	C₂²	1	1	yes	characteristic
73	C₃₁×#529	C₂²	1	1	yes	characteristic
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#519	C₂²	1	1	yes	characteristic
76	C₃₁×#519	C₂²	1	1	yes	characteristic
77	C₃₁×#519	C₂²	1	1	yes	characteristic
78	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
79	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
80	C₃₁×#501	C₂²	1	1	yes	characteristic
81	C₃₁×#501	C₂²	1	1	yes	characteristic
82	C₃₁×#499	C₂²	1	1	yes	characteristic
83	C₃₁×#497	C₂²	1	1	yes	characteristic
84	C₃₁×#497	C₂²	1	1	yes	characteristic
85	C₃₁×#492	C₂²	1	1	yes	characteristic
86	C₃₁×#491	C₂²	1	1	yes	characteristic
87	C₃₁×#491	C₂²	1	1	yes	characteristic
88	C₃₁×#490	C₂²	1	1	yes	characteristic
89	C₃₁×#489	C₂²	1	1	yes	characteristic
90	C₃₁×#488	C₂²	1	1	yes	characteristic
91	C₃₁×#487	C₂²	1	1	yes	characteristic
92	C₃₁×#485	C₂²	1	1	yes	characteristic
93	C₃₁×#485	C₂²	1	1	yes	characteristic
94	C₃₁×#485	C₂²	1	1	yes	characteristic
95	C₃₁×#485	C₂²	1	1	yes	characteristic
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×#482	C₂²	1	1	yes	characteristic
101	C₃₁×#482	C₂²	1	1	yes	characteristic
102	C₃₁×#482	C₂²	1	1	yes	characteristic
103	C₃₁×#481	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×#479	C₂²	1	1	yes	characteristic
108	C₃₁×#479	C₂²	1	1	yes	characteristic
109	C₃₁×#479	C₂²	1	1	yes	characteristic
110	C₃₁×#479	C₂²	1	1	yes	characteristic
111	C₃₁×#478	C₂²	1	1	yes	characteristic
112	C₃₁×#477	C₂²	1	1	yes	characteristic
113	C₃₁×#477	C₂²	1	1	yes	characteristic
114	C₃₁×#476	C₂²	1	1	yes	characteristic
115	C₃₁×#475	C₂²	1	1	yes	characteristic
116	C₃₁×#470	C₂²	1	1	yes	characteristic
117	C₃₁×#470	C₂²	1	1	yes	characteristic
118	C₃₁×#470	C₂²	1	1	yes	characteristic
119	C₃₁×#468	C₂²	1	1	yes	characteristic
120	C₃₁×#468	C₂²	1	1	yes	characteristic
121	C₃₁×#468	C₂²	1	1	yes	characteristic
122	C₃₁×#468	C₂²	1	1	yes	characteristic
123	C₃₁×#468	C₂²	1	1	yes	characteristic
124	C₃₁×#467	C₂²	1	1	yes	characteristic
125	C₃₁×#465	C₂²	1	1	yes	characteristic
126	C₃₁×#465	C₂²	1	1	yes	characteristic
127	C₃₁×#465	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×#462	C₂²	1	1	yes	characteristic
133	C₃₁×#462	C₂²	1	1	yes	characteristic
134	C₃₁×#462	C₂²	1	1	yes	characteristic
135	C₃₁×#462	C₂²	1	1	yes	characteristic
136	C₃₁×#461	C₂²	1	1	yes	characteristic
137	C₃₁×#461	C₂²	1	1	yes	characteristic
138	C₃₁×#460	C₂²	1	1	yes	characteristic
139	C₃₁×#460	C₂²	1	1	yes	characteristic
140	C₃₁×#452	C₂²	1	1	yes	characteristic
141	C₃₁×#452	C₂²	1	1	yes	characteristic
142	C₃₁×#452	C₂²	1	1	yes	characteristic
143	C₃₁×#452	C₂²	1	1	yes	characteristic
144	C₃₁×#451	C₂²	1	1	yes	characteristic
145	C₃₁×#451	C₂²	1	1	yes	characteristic
146	C₃₁×#451	C₂²	1	1	yes	characteristic
147	C₃₁×#451	C₂²	1	1	yes	characteristic
148	C₃₁×#448	C₂²	1	1	yes	characteristic
149	C₃₁×#448	C₂²	1	1	yes	characteristic
150	C₃₁×#448	C₂²	1	1	yes	characteristic
151	C₃₁×#448	C₂²	1	1	yes	characteristic
152	C₃₁×#446	C₂²	1	1	yes	characteristic
153	C₃₁×#446	C₂²	1	1	yes	characteristic
154	C₃₁×#441	C₂²	1	1	yes	characteristic
155	C₃₁×#441	C₂²	1	1	yes	characteristic
156	C₃₁×#441	C₂²	1	1	yes	characteristic
157	C₃₁×#441	C₂²	1	1	yes	characteristic
158	C₃₁×#441	C₂²	1	1	yes	characteristic
159	C₃₁×#441	C₂²	1	1	yes	characteristic
160	C₃₁×#441	C₂²	1	1	yes	characteristic
161	C₃₁×#441	C₂²	1	1	yes	characteristic
162	C₃₁×#441	C₂²	1	1	yes	characteristic
163	C₃₁×#440	C₂²	1	1	yes	characteristic
164	C₃₁×#440	C₂²	1	1	yes	characteristic
165	C₃₁×#440	C₂²	1	1	yes	characteristic
166	C₃₁×#440	C₂²	1	1	yes	characteristic
167	C₃₁×#440	C₂²	1	1	yes	characteristic
168	C₃₁×#440	C₂²	1	1	yes	characteristic
169	C₃₁×#440	C₂²	1	1	yes	characteristic
170	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
171	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
172	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
173	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
174	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
179	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
180	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
181	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
182	C₃₁×#436	C₂²	1	1	yes	characteristic
183	C₃₁×#436	C₂²	1	1	yes	characteristic
184	C₃₁×#435	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×#433	C₂²	1	1	yes	characteristic
189	C₃₁×#433	C₂²	1	1	yes	characteristic
190	C₃₁×#432	C₂²	1	1	yes	characteristic
191	C₃₁×#428	C₂²	1	1	yes	characteristic
192	C₃₁×#428	C₂²	1	1	yes	characteristic
193	C₃₁×#427	C₂²	1	1	yes	characteristic
194	C₃₁×#419	C₂²	1	1	yes	characteristic
195	C₃₁×#419	C₂²	1	1	yes	characteristic
196	C₃₁×#419	C₂²	1	1	yes	characteristic
197	C₃₁×#417	C₂²	1	1	yes	characteristic
198	C₃₁×#416	C₂²	1	1	yes	characteristic
199	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
200	C₃₁×#405	C₂²	1	1	yes	characteristic
201	C₃₁×#405	C₂²	1	1	yes	characteristic
202	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
203	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
205	C₂²×Q₈×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	C₃₁×#137	—	2	4	no	—
210	C₃₁×#137	—	2	4	no	—
211	C₂×Q₁₆×C₃₁	—	2	4	no	—
212	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆×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×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
232	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₃₁×C₄⋊Q₈	—	2	1	no	—
235	C₃₁×C₄⋊Q₈	—	2	1	no	—
236	C₃₁×C₄⋊Q₈	—	2	1	no	—
237	C₃₁×C₄⋊Q₈	—	2	1	no	—
238	C₃₁×C₄⋊Q₈	—	2	1	no	—
239	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
241	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
242	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
243	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
244	C₃₁×#127	—	2	1	no	—
245	C₃₁×#127	C₂³	1	1	yes	characteristic
246	C₃₁×#126	—	2	1	no	—
247	C₃₁×#126	—	2	1	no	—
248	C₃₁×#126	—	2	1	no	—
249	C₃₁×#126	—	2	1	no	—
250	C₃₁×#126	—	2	1	no	—
251	C₃₁×#126	—	2	1	no	—
252	C₃₁×#126	—	2	1	no	—
253	C₃₁×#126	—	2	1	no	—
254	C₃₁×#126	—	2	1	no	—
255	C₃₁×#126	—	2	1	no	—
256	C₃₁×#126	—	2	1	no	—
257	C₃₁×#126	—	2	1	no	—
258	C₃₁×#126	D₄	1	1	yes	characteristic
259	C₃₁×#126	D₄	1	1	yes	characteristic
260	C₃₁×#125	—	2	1	no	—
261	C₃₁×#125	—	2	1	no	—
262	C₃₁×#125	—	2	1	no	—
263	C₃₁×#125	—	2	1	no	—
264	C₃₁×#125	—	2	1	no	—
265	C₃₁×#125	—	2	1	no	—
266	C₃₁×#125	—	2	1	no	—
267	C₃₁×#125	—	2	1	no	—
268	C₃₁×#125	—	2	1	no	—
269	C₃₁×#125	—	2	1	no	—
270	C₃₁×#125	—	2	1	no	—
271	C₃₁×#125	—	2	1	no	—
272	C₃₁×#125	—	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×#125	C₂³	1	1	yes	characteristic
279	C₃₁×#125	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
288	C₃₁×#124	C₂³	1	1	yes	characteristic
289	C₃₁×#124	C₂³	1	1	yes	characteristic
290	C₃₁×#123	—	2	1	no	—
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×#123	—	2	1	no	—
294	C₃₁×#123	—	2	1	no	—
295	C₃₁×#123	—	2	1	no	—
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	D₄	1	1	yes	characteristic
301	C₃₁×#123	D₄	1	1	yes	characteristic
302	C₃₁×C₂²⋊Q₈	—	2	1	no	—
303	C₃₁×C₂²⋊Q₈	—	2	1	no	—
304	C₃₁×C₂²⋊Q₈	—	2	1	no	—
305	C₃₁×C₂²⋊Q₈	—	2	1	no	—
306	C₃₁×C₂²⋊Q₈	—	2	1	no	—
307	C₃₁×C₂²⋊Q₈	—	2	1	no	—
308	C₃₁×C₂²⋊Q₈	—	2	1	no	—
309	C₃₁×C₂²⋊Q₈	—	2	1	no	—
310	C₃₁×C₂²⋊Q₈	—	2	1	no	—
311	C₃₁×C₂²⋊Q₈	—	2	1	no	—
312	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
313	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
319	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
320	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
321	C₃₁×#121	—	2	1	no	—
322	C₃₁×#121	—	2	1	no	—
323	C₃₁×#121	—	2	1	no	—
324	C₃₁×#121	—	2	1	no	—
325	C₃₁×#121	—	2	1	no	—
326	C₃₁×#121	—	2	1	no	—
327	C₃₁×#121	—	2	1	no	—
328	C₃₁×#121	—	2	1	no	—
329	C₃₁×#121	D₄	1	1	yes	characteristic
330	C₃₁×#121	C₂³	1	1	yes	characteristic
331	C₃₁×#121	C₂³	1	1	yes	characteristic
332	C₃₁×#121	C₂³	1	1	yes	characteristic
333	C₃₁×#121	C₂³	1	1	yes	characteristic
334	C₄×Q₈×C₃₁	—	2	1	no	—
335	C₄×Q₈×C₃₁	—	2	1	no	—
336	C₄×Q₈×C₃₁	—	2	1	no	—
337	C₄×Q₈×C₃₁	—	2	1	no	—
338	C₄×Q₈×C₃₁	—	2	1	no	—
339	C₄×Q₈×C₃₁	—	2	1	no	—
340	C₄×Q₈×C₃₁	—	2	1	no	—
341	C₄×Q₈×C₃₁	—	2	1	no	—
342	C₄×Q₈×C₃₁	—	2	1	no	—
343	C₄×Q₈×C₃₁	—	2	1	no	—
344	C₄×Q₈×C₃₁	—	2	1	no	—
345	C₄×Q₈×C₃₁	—	2	1	no	—
346	C₄×Q₈×C₃₁	—	2	1	no	—
347	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
354	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
355	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
356	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
357	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
358	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
359	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
360	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
361	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
362	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
363	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₃₁	—	2	1	no	—
365	C₄×D₄×C₃₁	—	2	1	no	—
366	C₄×D₄×C₃₁	—	2	1	no	—
367	C₄×D₄×C₃₁	—	2	1	no	—
368	C₄×D₄×C₃₁	—	2	1	no	—
369	C₄×D₄×C₃₁	—	2	1	no	—
370	C₄×D₄×C₃₁	—	2	1	no	—
371	C₄×D₄×C₃₁	—	2	1	no	—
372	C₄×D₄×C₃₁	—	2	1	no	—
373	C₄×D₄×C₃₁	—	2	1	no	—
374	C₄×D₄×C₃₁	—	2	1	no	—
375	C₄×D₄×C₃₁	—	2	1	no	—
376	C₄×D₄×C₃₁	—	2	1	no	—
377	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
379	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
381	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
382	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
383	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
384	C₃₁×#117	—	2	1	no	—
385	C₃₁×#117	—	2	1	no	—
386	C₃₁×#117	—	2	1	no	—
387	C₃₁×#117	—	2	1	no	—
388	C₃₁×#117	—	2	1	no	—
389	C₃₁×#117	—	2	1	no	—
390	C₃₁×#117	—	2	1	no	—
391	C₃₁×#117	—	2	1	no	—
392	C₃₁×#117	—	2	1	no	—
393	C₃₁×#117	—	2	1	no	—
394	C₃₁×#117	—	2	1	no	—
395	C₃₁×#117	—	2	1	no	—
396	C₃₁×#117	—	2	1	no	—
397	C₃₁×#117	—	2	1	no	—
398	C₃₁×#117	C₂³	1	1	yes	characteristic
399	C₃₁×#117	C₂³	1	1	yes	characteristic
400	C₃₁×#117	C₂³	1	1	yes	characteristic
401	C₃₁×#117	C₂³	1	1	yes	characteristic
402	C₃₁×#117	C₂³	1	1	yes	characteristic
403	C₃₁×#117	C₂³	1	1	yes	characteristic
404	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
407	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
408	C₂×C₄²×C₃₁	—	2	1	no	—
409	C₂×C₄²×C₃₁	—	2	1	no	—
410	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
411	C₃₁×#107	C₂³	1	1	yes	characteristic
412	C₃₁×#107	C₂³	1	1	yes	characteristic
413	C₃₁×#107	C₂³	1	1	yes	characteristic
414	C₃₁×#107	C₂³	1	1	yes	characteristic
415	C₃₁×#107	C₂³	1	1	yes	characteristic
416	C₃₁×#107	C₂³	1	1	yes	characteristic
417	C₃₁×#107	C₂³	1	1	yes	characteristic
418	C₃₁×#107	C₂³	1	1	yes	characteristic
419	C₃₁×#106	C₂³	1	1	yes	characteristic
420	C₃₁×#106	C₂³	1	1	yes	characteristic
421	C₃₁×#106	C₂³	1	1	yes	characteristic
422	C₃₁×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	C₂³	1	1	yes	characteristic
424	C₃₁×#106	C₂³	1	1	yes	characteristic
425	C₃₁×#106	C₂³	1	1	yes	characteristic
426	C₃₁×#106	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₃₁×#103	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#103	C₂³	1	1	yes	characteristic
451	C₃₁×#103	C₂³	1	1	yes	characteristic
452	C₃₁×#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×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×#102	C₂³	1	1	yes	characteristic
463	C₃₁×#102	C₂³	1	1	yes	characteristic
464	C₃₁×#102	C₂³	1	1	yes	characteristic
465	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₃₁×#97	C₂³	1	1	yes	characteristic
472	C₃₁×#97	C₂³	1	1	yes	characteristic
473	C₃₁×#97	C₂³	1	1	yes	characteristic
474	C₃₁×#97	C₂³	1	1	yes	characteristic
475	C₃₁×#97	C₂³	1	1	yes	characteristic
476	C₃₁×#97	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
478	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
479	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
480	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
481	#41×C₃₁	—	2	2	no	—
482	#41×C₃₁	—	2	2	no	—
483	#41×C₃₁	—	4	1	no	—
484	#41×C₃₁	—	4	1	no	—
485	C₂×Q₈×C₃₁	—	2	1	no	—
486	C₂×Q₈×C₃₁	—	2	1	no	—
487	C₂×Q₈×C₃₁	—	2	1	no	—
488	C₂×Q₈×C₃₁	—	2	1	no	—
489	C₂×Q₈×C₃₁	—	2	1	no	—
490	C₂×Q₈×C₃₁	—	2	1	no	—
491	C₂×Q₈×C₃₁	—	2	2	no	—
492	C₂×Q₈×C₃₁	—	2	2	no	—
493	C₂×Q₈×C₃₁	—	2	2	no	—
494	C₂×Q₈×C₃₁	—	2	2	no	—
495	C₂×Q₈×C₃₁	—	4	1	no	—
496	C₂×Q₈×C₃₁	—	4	1	no	—
497	C₂×Q₈×C₃₁	—	4	1	no	—
498	C₂×Q₈×C₃₁	—	4	1	no	—
499	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
500	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
501	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
502	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
503	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
504	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
505	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
506	C₂×D₄×C₃₁	—	2	1	no	—
507	C₂×D₄×C₃₁	—	2	1	no	—
508	C₂×D₄×C₃₁	—	2	1	no	—
509	C₂×D₄×C₃₁	—	2	1	no	—
510	C₂×D₄×C₃₁	—	2	1	no	—
511	C₂×D₄×C₃₁	—	2	1	no	—
512	C₂×D₄×C₃₁	—	2	1	no	—
513	C₂×D₄×C₃₁	—	2	1	no	—
514	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
515	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
516	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
517	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
518	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄×C₃₁	—	2	1	no	—
520	C₂²×C₄×C₃₁	—	2	1	no	—
521	C₂²×C₄×C₃₁	—	2	1	no	—
522	C₂²×C₄×C₃₁	—	2	1	no	—
523	C₂²×C₄×C₃₁	—	2	1	no	—
524	C₂²×C₄×C₃₁	—	2	1	no	—
525	C₂²×C₄×C₃₁	—	2	1	no	—
526	C₂²×C₄×C₃₁	—	2	1	no	—
527	C₂²×C₄×C₃₁	—	2	1	no	—
528	C₂²×C₄×C₃₁	—	2	1	no	—
529	C₂²×C₄×C₃₁	—	2	1	no	—
530	C₂²×C₄×C₃₁	—	2	1	no	—
531	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
532	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
533	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
534	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
535	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
536	Q₁₆×C₃₁	—	2	2	no	—
537	Q₁₆×C₃₁	—	2	2	no	—
538	Q₁₆×C₃₁	—	2	2	no	—
539	Q₁₆×C₃₁	—	2	2	no	—
540	Q₁₆×C₃₁	—	2	2	no	—
541	Q₁₆×C₃₁	—	4	1	no	—
542	Q₁₆×C₃₁	—	4	1	no	—
543	Q₁₆×C₃₁	#41	1	4	yes	—
544	SD₁₆×C₃₁	—	2	2	no	—
545	SD₁₆×C₃₁	—	2	2	no	—
546	SD₁₆×C₃₁	—	2	2	no	—
547	SD₁₆×C₃₁	—	2	2	no	—
548	SD₁₆×C₃₁	—	4	1	no	—
549	SD₁₆×C₃₁	—	4	1	no	—
550	SD₁₆×C₃₁	—	4	1	no	—
551	SD₁₆×C₃₁	—	4	1	no	—
552	M₁₆×C₃₁	—	2	2	no	—
553	M₁₆×C₃₁	—	2	2	no	—
554	M₁₆×C₃₁	—	4	1	no	—
555	M₁₆×C₃₁	—	4	1	no	—
556	C₂×C₈×C₃₁	—	2	2	no	—
557	C₂×C₈×C₃₁	—	4	1	no	—
558	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
559	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
560	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
561	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
562	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
563	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
564	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
565	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
566	C₄⋊C₄×C₃₁	—	2	1	no	—
567	C₄⋊C₄×C₃₁	—	2	1	no	—
568	C₄⋊C₄×C₃₁	—	2	1	no	—
569	C₄⋊C₄×C₃₁	—	2	1	no	—
570	C₄⋊C₄×C₃₁	—	2	1	no	—
571	C₄⋊C₄×C₃₁	—	2	1	no	—
572	C₄⋊C₄×C₃₁	—	2	1	no	—
573	C₄⋊C₄×C₃₁	—	2	1	no	—
574	C₄⋊C₄×C₃₁	—	2	1	no	—
575	C₄⋊C₄×C₃₁	—	2	1	no	—
576	C₄⋊C₄×C₃₁	—	2	1	no	—
577	C₄⋊C₄×C₃₁	—	2	1	no	—
578	C₄⋊C₄×C₃₁	—	2	1	no	—
579	C₄⋊C₄×C₃₁	—	2	1	no	—
580	C₄⋊C₄×C₃₁	—	2	1	no	—
581	C₄⋊C₄×C₃₁	—	2	1	no	—
582	C₄⋊C₄×C₃₁	—	2	1	no	—
583	C₄⋊C₄×C₃₁	—	2	1	no	—
584	C₄⋊C₄×C₃₁	—	2	1	no	—
585	C₄⋊C₄×C₃₁	—	2	1	no	—
586	C₄⋊C₄×C₃₁	—	2	1	no	—
587	C₄⋊C₄×C₃₁	—	2	1	no	—
588	C₄⋊C₄×C₃₁	—	2	1	no	—
589	C₄⋊C₄×C₃₁	—	2	1	no	—
590	C₄⋊C₄×C₃₁	—	2	1	no	—
591	C₄⋊C₄×C₃₁	—	2	1	no	—
592	C₄⋊C₄×C₃₁	—	2	1	no	—
593	C₄⋊C₄×C₃₁	—	2	1	no	—
594	C₄⋊C₄×C₃₁	—	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	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
615	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
616	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
617	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
618	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
619	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
620	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
621	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
622	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
623	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
624	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
625	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	—	2	1	no	—
638	C₂²⋊C₄×C₃₁	—	2	1	no	—
639	C₂²⋊C₄×C₃₁	—	2	1	no	—
640	C₂²⋊C₄×C₃₁	—	2	1	no	—
641	C₂²⋊C₄×C₃₁	—	2	1	no	—
642	C₂²⋊C₄×C₃₁	—	2	1	no	—
643	C₂²⋊C₄×C₃₁	—	2	1	no	—
644	C₂²⋊C₄×C₃₁	—	2	1	no	—
645	C₂²⋊C₄×C₃₁	—	2	1	no	—
646	C₂²⋊C₄×C₃₁	—	2	1	no	—
647	C₂²⋊C₄×C₃₁	—	2	1	no	—
648	C₂²⋊C₄×C₃₁	—	2	1	no	—
649	C₂²⋊C₄×C₃₁	—	2	1	no	—
650	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
658	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
659	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
660	C₄²×C₃₁	—	2	1	no	—
661	C₄²×C₃₁	—	2	1	no	—
662	C₄²×C₃₁	—	2	1	no	—
663	C₄²×C₃₁	—	2	1	no	—
664	C₄²×C₃₁	—	2	1	no	—
665	C₄²×C₃₁	—	2	1	no	—
666	C₄²×C₃₁	—	2	1	no	—
667	C₄²×C₃₁	—	2	1	no	—
668	C₄²×C₃₁	—	2	1	no	—
669	C₄²×C₃₁	—	2	1	no	—
670	C₄²×C₃₁	—	2	1	no	—
671	C₄²×C₃₁	—	2	1	no	—
672	C₄²×C₃₁	—	2	1	no	—
673	C₄²×C₃₁	—	2	1	no	—
674	C₄²×C₃₁	—	2	1	no	—
675	C₄²×C₃₁	—	2	1	no	—
676	C₄²×C₃₁	—	2	1	no	—
677	C₄²×C₃₁	—	2	1	no	—
678	C₄²×C₃₁	—	2	1	no	—
679	C₄²×C₃₁	—	2	1	no	—
680	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
681	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
682	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
683	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
684	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
685	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
686	#61512	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
687	C₂³×C₃₁	—	2	1	no	—
688	C₂³×C₃₁	—	2	1	no	—
689	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
690	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
691	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
692	Q₈×C₃₁	—	2	1	no	—
693	Q₈×C₃₁	—	2	1	no	—
694	Q₈×C₃₁	—	2	1	no	—
695	Q₈×C₃₁	—	2	1	no	—
696	Q₈×C₃₁	—	2	1	no	—
697	Q₈×C₃₁	—	2	1	no	—
698	Q₈×C₃₁	—	2	1	no	—
699	Q₈×C₃₁	—	2	1	no	—
700	Q₈×C₃₁	—	2	1	no	—
701	Q₈×C₃₁	—	2	1	no	—
702	Q₈×C₃₁	—	4	1	no	—
703	Q₈×C₃₁	—	4	2	no	—
704	Q₈×C₃₁	—	4	2	no	—
705	Q₈×C₃₁	—	4	2	no	—
706	Q₈×C₃₁	—	4	2	no	—
707	Q₈×C₃₁	—	4	2	no	—
708	Q₈×C₃₁	—	8	1	no	—
709	Q₈×C₃₁	C₂×#41	1	2	yes	—
710	Q₈×C₃₁	C₂×#41	1	2	yes	—
711	D₄×C₃₁	—	2	1	no	—
712	D₄×C₃₁	—	2	1	no	—
713	D₄×C₃₁	—	2	1	no	—
714	D₄×C₃₁	—	2	1	no	—
715	D₄×C₃₁	—	4	1	no	—
716	D₄×C₃₁	—	4	1	no	—
717	D₄×C₃₁	—	4	1	no	—
718	D₄×C₃₁	—	4	2	no	—
719	D₄×C₃₁	—	4	2	no	—
720	D₄×C₃₁	—	8	1	no	—
721	D₄×C₃₁	—	8	1	no	—
722	D₄×C₃₁	—	8	1	no	—
723	D₄×C₃₁	—	8	1	no	—
724	D₄×C₃₁	—	8	1	no	—
725	D₄×C₃₁	—	8	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	2	1	no	—
728	C₂×C₄×C₃₁	—	2	1	no	—
729	C₂×C₄×C₃₁	—	2	1	no	—
730	C₂×C₄×C₃₁	—	2	1	no	—
731	C₂×C₄×C₃₁	—	2	1	no	—
732	C₂×C₄×C₃₁	—	2	1	no	—
733	C₂×C₄×C₃₁	—	2	1	no	—
734	C₂×C₄×C₃₁	—	2	1	no	—
735	C₂×C₄×C₃₁	—	2	1	no	—
736	C₂×C₄×C₃₁	—	2	1	no	—
737	C₂×C₄×C₃₁	—	2	1	no	—
738	C₂×C₄×C₃₁	—	2	1	no	—
739	C₂×C₄×C₃₁	—	2	1	no	—
740	C₂×C₄×C₃₁	—	2	1	no	—
741	C₂×C₄×C₃₁	—	2	1	no	—
742	C₂×C₄×C₃₁	—	2	1	no	—
743	C₂×C₄×C₃₁	—	2	1	no	—
744	C₂×C₄×C₃₁	—	2	1	no	—
745	C₂×C₄×C₃₁	—	2	1	no	—
746	C₂×C₄×C₃₁	—	4	1	no	—
747	C₂×C₄×C₃₁	—	4	1	no	—
748	C₂×C₄×C₃₁	—	4	2	no	—
749	C₂×C₄×C₃₁	—	4	2	no	—
750	C₂×C₄×C₃₁	—	4	2	no	—
751	C₂×C₄×C₃₁	—	4	2	no	—
752	C₂×C₄×C₃₁	—	4	2	no	—
753	C₂×C₄×C₃₁	—	4	2	no	—
754	C₂×C₄×C₃₁	—	4	2	no	—
755	C₂×C₄×C₃₁	—	8	1	no	—
756	C₂×C₄×C₃₁	—	8	1	no	—
757	C₂×C₄×C₃₁	—	8	1	no	—
758	C₂×C₄×C₃₁	—	8	1	no	—
759	C₂×C₄×C₃₁	—	8	1	no	—
760	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
763	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
764	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
765	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
766	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
770	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
771	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
772	C₈×C₃₁	—	2	1	no	—
773	C₈×C₃₁	—	2	1	no	—
774	C₈×C₃₁	—	2	1	no	—
775	C₈×C₃₁	—	2	1	no	—
776	C₈×C₃₁	—	2	1	no	—
777	C₈×C₃₁	—	2	1	no	—
778	C₈×C₃₁	—	2	1	no	—
779	C₈×C₃₁	C₂×#41	1	2	yes	—
780	#3524	C₂×C₃₁	1	1	yes	characteristic
781	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3390	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3350	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3348	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3320	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3317	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3313	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3312	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3278	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3270	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3178	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3174	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3172	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3126	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3121	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3120	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3117	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#2967	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#2950	C₂×C₃₁	1	1	yes	characteristic, complemented
809	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
810	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
811	C₂²×C₃₁	—	2	1	no	—
812	C₂²×C₃₁	—	2	1	no	—
813	C₂²×C₃₁	—	2	1	no	—
814	C₂²×C₃₁	—	2	1	no	—
815	C₂²×C₃₁	—	2	1	no	—
816	C₂²×C₃₁	—	2	1	no	—
817	C₂²×C₃₁	—	2	1	no	—
818	C₂²×C₃₁	—	2	1	no	—
819	C₂²×C₃₁	—	2	1	no	—
820	C₂²×C₃₁	—	4	1	no	—
821	C₂²×C₃₁	—	4	1	no	—
822	C₂²×C₃₁	—	4	1	no	—
823	C₂²×C₃₁	—	4	1	no	—
824	C₂²×C₃₁	—	4	1	no	—
825	C₂²×C₃₁	—	4	1	no	—
826	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
827	C₄×C₃₁	—	2	1	no	—
828	C₄×C₃₁	—	2	1	no	—
829	C₄×C₃₁	—	2	1	no	—
830	C₄×C₃₁	—	2	1	no	—
831	C₄×C₃₁	—	2	1	no	—
832	C₄×C₃₁	—	2	1	no	—
833	C₄×C₃₁	—	2	1	no	—
834	C₄×C₃₁	—	2	1	no	—
835	C₄×C₃₁	—	2	1	no	—
836	C₄×C₃₁	—	2	1	no	—
837	C₄×C₃₁	—	2	1	no	—
838	C₄×C₃₁	—	2	2	no	—
839	C₄×C₃₁	—	2	2	no	—
840	C₄×C₃₁	—	4	1	no	—
841	C₄×C₃₁	—	4	1	no	—
842	C₄×C₃₁	—	4	1	no	—
843	C₄×C₃₁	—	4	1	no	—
844	C₄×C₃₁	—	4	1	no	—
845	C₄×C₃₁	—	4	1	no	—
846	C₄×C₃₁	—	4	1	no	—
847	C₄×C₃₁	—	4	1	no	—
848	C₄×C₃₁	—	4	1	no	—
849	C₄×C₃₁	—	4	1	no	—
850	C₄×C₃₁	—	4	1	no	—
851	C₄×C₃₁	—	4	1	no	—
852	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
853	C₄×C₃₁	#585	1	1	yes	characteristic
854	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
855	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
856	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
857	#559	—	2	1	no	—
858	#559	C₂²×C₃₁	1	1	yes	characteristic
859	#557	—	2	1	no	—
860	#557	C₂²×C₃₁	1	1	yes	characteristic
861	#557	C₂²×C₃₁	1	1	yes	characteristic
862	#557	C₂²×C₃₁	1	1	yes	characteristic
863	#556	—	2	1	no	—
864	#556	C₂²×C₃₁	1	1	yes	characteristic
865	#555	—	2	1	no	—
866	#555	C₂²×C₃₁	1	1	yes	characteristic
867	#553	—	2	1	no	—
868	#553	C₂²×C₃₁	1	1	yes	characteristic
869	#552	—	2	1	no	—
870	#552	—	2	1	no	—
871	#552	—	2	1	no	—
872	#552	C₂²×C₃₁	1	1	yes	characteristic
873	#552	C₂²×C₃₁	1	1	yes	characteristic
874	#552	C₂²×C₃₁	1	1	yes	characteristic
875	#550	C₂²×C₃₁	1	1	yes	characteristic
876	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
877	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
878	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
879	#548	C₂²×C₃₁	1	1	yes	characteristic
880	#548	C₂²×C₃₁	1	1	yes	characteristic
881	#542	—	2	1	no	—
882	#542	C₂²×C₃₁	1	1	yes	characteristic
883	#541	—	2	1	no	—
884	#541	—	2	1	no	—
885	#541	C₂²×C₃₁	1	1	yes	characteristic
886	#541	C₂²×C₃₁	1	1	yes	characteristic
887	#540	—	2	1	no	—
888	#540	C₂²×C₃₁	1	1	yes	characteristic
889	#533	—	2	1	no	—
890	#533	C₂²×C₃₁	1	1	yes	characteristic
891	#529	—	2	1	no	—
892	#529	—	2	1	no	—
893	#529	—	2	1	no	—
894	#529	C₂²×C₃₁	1	1	yes	characteristic
895	#529	C₂²×C₃₁	1	1	yes	characteristic
896	#520	C₂²×C₃₁	1	1	yes	characteristic
897	#519	C₂²×C₃₁	1	1	yes	characteristic
898	#519	C₂²×C₃₁	1	1	yes	characteristic
899	#519	C₂²×C₃₁	1	1	yes	characteristic
900	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
901	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
902	#501	C₂²×C₃₁	1	1	yes	characteristic
903	#501	C₂²×C₃₁	1	1	yes	characteristic
904	#499	C₂²×C₃₁	1	1	yes	characteristic
905	#497	C₂²×C₃₁	1	1	yes	characteristic
906	#497	C₂²×C₃₁	1	1	yes	characteristic
907	#492	C₂²×C₃₁	1	1	yes	characteristic
908	#491	C₂²×C₃₁	1	1	yes	characteristic
909	#491	C₂²×C₃₁	1	1	yes	characteristic
910	#490	C₂²×C₃₁	1	1	yes	characteristic
911	#489	C₂²×C₃₁	1	1	yes	characteristic
912	#488	C₂²×C₃₁	1	1	yes	characteristic
913	#487	C₂²×C₃₁	1	1	yes	characteristic
914	#485	C₂²×C₃₁	1	1	yes	characteristic
915	#485	C₂²×C₃₁	1	1	yes	characteristic
916	#485	C₂²×C₃₁	1	1	yes	characteristic
917	#485	C₂²×C₃₁	1	1	yes	characteristic
918	#485	C₂²×C₃₁	1	1	yes	characteristic
919	#484	C₂²×C₃₁	1	1	yes	characteristic
920	#484	C₂²×C₃₁	1	1	yes	characteristic
921	#483	C₂²×C₃₁	1	1	yes	characteristic
922	#482	C₂²×C₃₁	1	1	yes	characteristic
923	#482	C₂²×C₃₁	1	1	yes	characteristic
924	#482	C₂²×C₃₁	1	1	yes	characteristic
925	#481	C₂²×C₃₁	1	1	yes	characteristic
926	#479	C₂²×C₃₁	1	1	yes	characteristic
927	#479	C₂²×C₃₁	1	1	yes	characteristic
928	#479	C₂²×C₃₁	1	1	yes	characteristic
929	#479	C₂²×C₃₁	1	1	yes	characteristic
930	#479	C₂²×C₃₁	1	1	yes	characteristic
931	#479	C₂²×C₃₁	1	1	yes	characteristic
932	#479	C₂²×C₃₁	1	1	yes	characteristic
933	#478	C₂²×C₃₁	1	1	yes	characteristic
934	#477	C₂²×C₃₁	1	1	yes	characteristic
935	#477	C₂²×C₃₁	1	1	yes	characteristic
936	#476	C₂²×C₃₁	1	1	yes	characteristic
937	#475	C₂²×C₃₁	1	1	yes	characteristic
938	#470	C₂²×C₃₁	1	1	yes	characteristic
939	#470	C₂²×C₃₁	1	1	yes	characteristic
940	#470	C₂²×C₃₁	1	1	yes	characteristic
941	#468	C₂²×C₃₁	1	1	yes	characteristic
942	#468	C₂²×C₃₁	1	1	yes	characteristic
943	#468	C₂²×C₃₁	1	1	yes	characteristic
944	#468	C₂²×C₃₁	1	1	yes	characteristic
945	#468	C₂²×C₃₁	1	1	yes	characteristic
946	#467	C₂²×C₃₁	1	1	yes	characteristic
947	#465	C₂²×C₃₁	1	1	yes	characteristic
948	#465	C₂²×C₃₁	1	1	yes	characteristic
949	#465	C₂²×C₃₁	1	1	yes	characteristic
950	#464	C₂²×C₃₁	1	1	yes	characteristic
951	#464	C₂²×C₃₁	1	1	yes	characteristic
952	#464	C₂²×C₃₁	1	1	yes	characteristic
953	#464	C₂²×C₃₁	1	1	yes	characteristic
954	#462	C₂²×C₃₁	1	1	yes	characteristic
955	#462	C₂²×C₃₁	1	1	yes	characteristic
956	#462	C₂²×C₃₁	1	1	yes	characteristic
957	#462	C₂²×C₃₁	1	1	yes	characteristic
958	#461	C₂²×C₃₁	1	1	yes	characteristic
959	#461	C₂²×C₃₁	1	1	yes	characteristic
960	#460	C₂²×C₃₁	1	1	yes	characteristic
961	#460	C₂²×C₃₁	1	1	yes	characteristic
962	#452	C₂²×C₃₁	1	1	yes	characteristic
963	#452	C₂²×C₃₁	1	1	yes	characteristic
964	#452	C₂²×C₃₁	1	1	yes	characteristic
965	#452	C₂²×C₃₁	1	1	yes	characteristic
966	#451	C₂²×C₃₁	1	1	yes	characteristic
967	#451	C₂²×C₃₁	1	1	yes	characteristic
968	#451	C₂²×C₃₁	1	1	yes	characteristic
969	#451	C₂²×C₃₁	1	1	yes	characteristic
970	#448	C₂²×C₃₁	1	1	yes	characteristic
971	#448	C₂²×C₃₁	1	1	yes	characteristic
972	#448	C₂²×C₃₁	1	1	yes	characteristic
973	#448	C₂²×C₃₁	1	1	yes	characteristic
974	#446	C₂²×C₃₁	1	1	yes	characteristic
975	#446	C₂²×C₃₁	1	1	yes	characteristic
976	#441	C₂²×C₃₁	1	1	yes	characteristic
977	#441	C₂²×C₃₁	1	1	yes	characteristic
978	#441	C₂²×C₃₁	1	1	yes	characteristic
979	#441	C₂²×C₃₁	1	1	yes	characteristic
980	#441	C₂²×C₃₁	1	1	yes	characteristic
981	#441	C₂²×C₃₁	1	1	yes	characteristic
982	#441	C₂²×C₃₁	1	1	yes	characteristic
983	#441	C₂²×C₃₁	1	1	yes	characteristic
984	#441	C₂²×C₃₁	1	1	yes	characteristic
985	#440	C₂²×C₃₁	1	1	yes	characteristic
986	#440	C₂²×C₃₁	1	1	yes	characteristic
987	#440	C₂²×C₃₁	1	1	yes	characteristic
988	#440	C₂²×C₃₁	1	1	yes	characteristic
989	#440	C₂²×C₃₁	1	1	yes	characteristic
990	#440	C₂²×C₃₁	1	1	yes	characteristic
991	#440	C₂²×C₃₁	1	1	yes	characteristic
992	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
993	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
994	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
995	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
996	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
997	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
998	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
999	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1000	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1001	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1002	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1003	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1004	#436	C₂²×C₃₁	1	1	yes	characteristic
1005	#436	C₂²×C₃₁	1	1	yes	characteristic
1006	#435	C₂²×C₃₁	1	1	yes	characteristic
1007	#435	C₂²×C₃₁	1	1	yes	characteristic
1008	#435	C₂²×C₃₁	1	1	yes	characteristic
1009	#435	C₂²×C₃₁	1	1	yes	characteristic
1010	#433	C₂²×C₃₁	1	1	yes	characteristic
1011	#433	C₂²×C₃₁	1	1	yes	characteristic
1012	#432	C₂²×C₃₁	1	1	yes	characteristic
1013	#428	C₂²×C₃₁	1	1	yes	characteristic
1014	#428	C₂²×C₃₁	1	1	yes	characteristic
1015	#427	C₂²×C₃₁	1	1	yes	characteristic
1016	#419	C₂²×C₃₁	1	1	yes	characteristic
1017	#419	C₂²×C₃₁	1	1	yes	characteristic
1018	#419	C₂²×C₃₁	1	1	yes	characteristic
1019	#417	C₂²×C₃₁	1	1	yes	characteristic
1020	#416	C₂²×C₃₁	1	1	yes	characteristic
1021	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1022	#405	C₂²×C₃₁	1	1	yes	characteristic
1023	#405	C₂²×C₃₁	1	1	yes	characteristic
1024	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
1025	C₂×C₃₁	—	4	1	no	—
1026	C₂×C₃₁	—	4	1	no	—
1027	C₂×C₃₁	—	4	1	no	—
1028	C₂×C₃₁	—	8	1	no	—
1029	C₂×C₃₁	—	8	1	no	—
1030	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
1031	C₂×C₃₁	#3586	1	1	yes	characteristic
1032	C₂×C₃₁	#3586	1	1	yes	characteristic
1033	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1034	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1035	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1036	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1037	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1038	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1039	#137	—	2	4	no	—
1040	#137	—	2	4	no	—
1041	C₂×Q₁₆	—	2	4	no	—
1042	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1043	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1044	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1045	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1046	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1047	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1048	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1049	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1055	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1059	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1060	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1061	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1062	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1063	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1064	C₄⋊Q₈	—	2	1	no	—
1065	C₄⋊Q₈	—	2	1	no	—
1066	C₄⋊Q₈	—	2	1	no	—
1067	C₄⋊Q₈	—	2	1	no	—
1068	C₄⋊Q₈	—	2	1	no	—
1069	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1070	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1071	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1072	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1073	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1074	#127	—	2	1	no	—
1075	#127	C₂³×C₃₁	1	1	yes	characteristic
1076	#126	—	2	1	no	—
1077	#126	—	2	1	no	—
1078	#126	—	2	1	no	—
1079	#126	—	2	1	no	—
1080	#126	—	2	1	no	—
1081	#126	—	2	1	no	—
1082	#126	—	2	1	no	—
1083	#126	—	2	1	no	—
1084	#126	—	2	1	no	—
1085	#126	—	2	1	no	—
1086	#126	—	2	1	no	—
1087	#126	—	2	1	no	—
1088	#126	D₄×C₃₁	1	1	yes	characteristic
1089	#126	D₄×C₃₁	1	1	yes	characteristic
1090	#125	—	2	1	no	—
1091	#125	—	2	1	no	—
1092	#125	—	2	1	no	—
1093	#125	—	2	1	no	—
1094	#125	—	2	1	no	—
1095	#125	—	2	1	no	—
1096	#125	—	2	1	no	—
1097	#125	—	2	1	no	—
1098	#125	—	2	1	no	—
1099	#125	—	2	1	no	—
1100	#125	—	2	1	no	—
1101	#125	—	2	1	no	—
1102	#125	—	2	1	no	—
1103	#125	—	2	1	no	—
1104	#125	—	2	1	no	—
1105	#125	D₄×C₃₁	1	1	yes	characteristic
1106	#125	C₂³×C₃₁	1	1	yes	characteristic
1107	#125	C₂³×C₃₁	1	1	yes	characteristic
1108	#125	C₂³×C₃₁	1	1	yes	characteristic
1109	#125	C₂³×C₃₁	1	1	yes	characteristic
1110	#124	—	2	1	no	—
1111	#124	—	2	1	no	—
1112	#124	—	2	1	no	—
1113	#124	—	2	1	no	—
1114	#124	—	2	1	no	—
1115	#124	—	2	1	no	—
1116	#124	—	2	1	no	—
1117	#124	D₄×C₃₁	1	1	yes	characteristic
1118	#124	C₂³×C₃₁	1	1	yes	characteristic
1119	#124	C₂³×C₃₁	1	1	yes	characteristic
1120	#123	—	2	1	no	—
1121	#123	—	2	1	no	—
1122	#123	—	2	1	no	—
1123	#123	—	2	1	no	—
1124	#123	—	2	1	no	—
1125	#123	—	2	1	no	—
1126	#123	—	2	1	no	—
1127	#123	—	2	1	no	—
1128	#123	—	2	1	no	—
1129	#123	—	2	1	no	—
1130	#123	D₄×C₃₁	1	1	yes	characteristic
1131	#123	D₄×C₃₁	1	1	yes	characteristic
1132	C₂²⋊Q₈	—	2	1	no	—
1133	C₂²⋊Q₈	—	2	1	no	—
1134	C₂²⋊Q₈	—	2	1	no	—
1135	C₂²⋊Q₈	—	2	1	no	—
1136	C₂²⋊Q₈	—	2	1	no	—
1137	C₂²⋊Q₈	—	2	1	no	—
1138	C₂²⋊Q₈	—	2	1	no	—
1139	C₂²⋊Q₈	—	2	1	no	—
1140	C₂²⋊Q₈	—	2	1	no	—
1141	C₂²⋊Q₈	—	2	1	no	—
1142	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1143	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1144	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1145	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1146	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1147	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1148	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1149	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1150	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1151	#121	—	2	1	no	—
1152	#121	—	2	1	no	—
1153	#121	—	2	1	no	—
1154	#121	—	2	1	no	—
1155	#121	—	2	1	no	—
1156	#121	—	2	1	no	—
1157	#121	—	2	1	no	—
1158	#121	—	2	1	no	—
1159	#121	D₄×C₃₁	1	1	yes	characteristic
1160	#121	C₂³×C₃₁	1	1	yes	characteristic
1161	#121	C₂³×C₃₁	1	1	yes	characteristic
1162	#121	C₂³×C₃₁	1	1	yes	characteristic
1163	#121	C₂³×C₃₁	1	1	yes	characteristic
1164	C₄×Q₈	—	2	1	no	—
1165	C₄×Q₈	—	2	1	no	—
1166	C₄×Q₈	—	2	1	no	—
1167	C₄×Q₈	—	2	1	no	—
1168	C₄×Q₈	—	2	1	no	—
1169	C₄×Q₈	—	2	1	no	—
1170	C₄×Q₈	—	2	1	no	—
1171	C₄×Q₈	—	2	1	no	—
1172	C₄×Q₈	—	2	1	no	—
1173	C₄×Q₈	—	2	1	no	—
1174	C₄×Q₈	—	2	1	no	—
1175	C₄×Q₈	—	2	1	no	—
1176	C₄×Q₈	—	2	1	no	—
1177	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1178	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1179	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1180	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1181	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1182	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1183	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1184	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1185	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1186	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1187	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1188	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1189	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1190	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1191	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1192	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1193	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1194	C₄×D₄	—	2	1	no	—
1195	C₄×D₄	—	2	1	no	—
1196	C₄×D₄	—	2	1	no	—
1197	C₄×D₄	—	2	1	no	—
1198	C₄×D₄	—	2	1	no	—
1199	C₄×D₄	—	2	1	no	—
1200	C₄×D₄	—	2	1	no	—
1201	C₄×D₄	—	2	1	no	—
1202	C₄×D₄	—	2	1	no	—
1203	C₄×D₄	—	2	1	no	—
1204	C₄×D₄	—	2	1	no	—
1205	C₄×D₄	—	2	1	no	—
1206	C₄×D₄	—	2	1	no	—
1207	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1208	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1209	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1210	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1211	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1212	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1213	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1214	#117	—	2	1	no	—
1215	#117	—	2	1	no	—
1216	#117	—	2	1	no	—
1217	#117	—	2	1	no	—
1218	#117	—	2	1	no	—
1219	#117	—	2	1	no	—
1220	#117	—	2	1	no	—
1221	#117	—	2	1	no	—
1222	#117	—	2	1	no	—
1223	#117	—	2	1	no	—
1224	#117	—	2	1	no	—
1225	#117	—	2	1	no	—
1226	#117	—	2	1	no	—
1227	#117	—	2	1	no	—
1228	#117	C₂³×C₃₁	1	1	yes	characteristic
1229	#117	C₂³×C₃₁	1	1	yes	characteristic
1230	#117	C₂³×C₃₁	1	1	yes	characteristic
1231	#117	C₂³×C₃₁	1	1	yes	characteristic
1232	#117	C₂³×C₃₁	1	1	yes	characteristic
1233	#117	C₂³×C₃₁	1	1	yes	characteristic
1234	C₂×C₄⋊C₄	—	2	1	no	—
1235	C₂×C₄⋊C₄	—	2	1	no	—
1236	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1237	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1238	C₂×C₄²	—	2	1	no	—
1239	C₂×C₄²	—	2	1	no	—
1240	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1241	#107	C₂³×C₃₁	1	1	yes	characteristic
1242	#107	C₂³×C₃₁	1	1	yes	characteristic
1243	#107	C₂³×C₃₁	1	1	yes	characteristic
1244	#107	C₂³×C₃₁	1	1	yes	characteristic
1245	#107	C₂³×C₃₁	1	1	yes	characteristic
1246	#107	C₂³×C₃₁	1	1	yes	characteristic
1247	#107	C₂³×C₃₁	1	1	yes	characteristic
1248	#107	C₂³×C₃₁	1	1	yes	characteristic
1249	#106	C₂³×C₃₁	1	1	yes	characteristic
1250	#106	C₂³×C₃₁	1	1	yes	characteristic
1251	#106	C₂³×C₃₁	1	1	yes	characteristic
1252	#106	C₂³×C₃₁	1	1	yes	characteristic
1253	#106	C₂³×C₃₁	1	1	yes	characteristic
1254	#106	C₂³×C₃₁	1	1	yes	characteristic
1255	#106	C₂³×C₃₁	1	1	yes	characteristic
1256	#106	C₂³×C₃₁	1	1	yes	characteristic
1257	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1258	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1259	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1260	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1261	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1262	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1263	#103	C₂³×C₃₁	1	1	yes	characteristic
1264	#103	C₂³×C₃₁	1	1	yes	characteristic
1265	#103	C₂³×C₃₁	1	1	yes	characteristic
1266	#103	C₂³×C₃₁	1	1	yes	characteristic
1267	#103	C₂³×C₃₁	1	1	yes	characteristic
1268	#103	C₂³×C₃₁	1	1	yes	characteristic
1269	#103	C₂³×C₃₁	1	1	yes	characteristic
1270	#103	C₂³×C₃₁	1	1	yes	characteristic
1271	#103	C₂³×C₃₁	1	1	yes	characteristic
1272	#103	C₂³×C₃₁	1	1	yes	characteristic
1273	#103	C₂³×C₃₁	1	1	yes	characteristic
1274	#103	C₂³×C₃₁	1	1	yes	characteristic
1275	#103	C₂³×C₃₁	1	1	yes	characteristic
1276	#103	C₂³×C₃₁	1	1	yes	characteristic
1277	#103	C₂³×C₃₁	1	1	yes	characteristic
1278	#103	C₂³×C₃₁	1	1	yes	characteristic
1279	#103	C₂³×C₃₁	1	1	yes	characteristic
1280	#103	C₂³×C₃₁	1	1	yes	characteristic
1281	#103	C₂³×C₃₁	1	1	yes	characteristic
1282	#103	C₂³×C₃₁	1	1	yes	characteristic
1283	#103	C₂³×C₃₁	1	1	yes	characteristic
1284	#103	C₂³×C₃₁	1	1	yes	characteristic
1285	#103	C₂³×C₃₁	1	1	yes	characteristic
1286	#103	C₂³×C₃₁	1	1	yes	characteristic
1287	#102	C₂³×C₃₁	1	1	yes	characteristic
1288	#102	C₂³×C₃₁	1	1	yes	characteristic
1289	#102	C₂³×C₃₁	1	1	yes	characteristic
1290	#102	C₂³×C₃₁	1	1	yes	characteristic
1291	#102	C₂³×C₃₁	1	1	yes	characteristic
1292	#102	C₂³×C₃₁	1	1	yes	characteristic
1293	#102	C₂³×C₃₁	1	1	yes	characteristic
1294	#102	C₂³×C₃₁	1	1	yes	characteristic
1295	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1296	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1297	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1298	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1299	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1300	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1301	#97	C₂³×C₃₁	1	1	yes	characteristic
1302	#97	C₂³×C₃₁	1	1	yes	characteristic
1303	#97	C₂³×C₃₁	1	1	yes	characteristic
1304	#97	C₂³×C₃₁	1	1	yes	characteristic
1305	#97	C₂³×C₃₁	1	1	yes	characteristic
1306	#97	C₂³×C₃₁	1	1	yes	characteristic
1307	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1308	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1309	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1310	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1311	C₃₁	#61512	1	1	yes	characteristic, direct product factor, Sylow
1312	#41	—	2	2	no	—
1313	#41	—	2	2	no	—
1314	#41	—	4	1	no	—
1315	#41	—	4	1	no	—
1316	C₂×Q₈	—	2	1	no	—
1317	C₂×Q₈	—	2	1	no	—
1318	C₂×Q₈	—	2	1	no	—
1319	C₂×Q₈	—	2	1	no	—
1320	C₂×Q₈	—	2	1	no	—
1321	C₂×Q₈	—	2	1	no	—
1322	C₂×Q₈	—	2	2	no	—
1323	C₂×Q₈	—	2	2	no	—
1324	C₂×Q₈	—	2	2	no	—
1325	C₂×Q₈	—	2	2	no	—
1326	C₂×Q₈	—	4	1	no	—
1327	C₂×Q₈	—	4	1	no	—
1328	C₂×Q₈	—	4	1	no	—
1329	C₂×Q₈	—	4	1	no	—
1330	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1331	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1332	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1333	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1334	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1335	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1336	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1337	C₂×D₄	—	2	1	no	—
1338	C₂×D₄	—	2	1	no	—
1339	C₂×D₄	—	2	1	no	—
1340	C₂×D₄	—	2	1	no	—
1341	C₂×D₄	—	2	1	no	—
1342	C₂×D₄	—	2	1	no	—
1343	C₂×D₄	—	2	1	no	—
1344	C₂×D₄	—	2	1	no	—
1345	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1346	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1347	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1348	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1349	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1350	C₂²×C₄	—	2	1	no	—
1351	C₂²×C₄	—	2	1	no	—
1352	C₂²×C₄	—	2	1	no	—
1353	C₂²×C₄	—	2	1	no	—
1354	C₂²×C₄	—	2	1	no	—
1355	C₂²×C₄	—	2	1	no	—
1356	C₂²×C₄	—	2	1	no	—
1357	C₂²×C₄	—	2	1	no	—
1358	C₂²×C₄	—	2	1	no	—
1359	C₂²×C₄	—	2	1	no	—
1360	C₂²×C₄	—	2	1	no	—
1361	C₂²×C₄	—	2	1	no	—
1362	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1363	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1364	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1365	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1366	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1367	Q₁₆	—	2	2	no	—
1368	Q₁₆	—	2	2	no	—
1369	Q₁₆	—	2	2	no	—
1370	Q₁₆	—	2	2	no	—
1371	Q₁₆	—	2	2	no	—
1372	Q₁₆	—	4	1	no	—
1373	Q₁₆	—	4	1	no	—
1374	Q₁₆	#41×C₃₁	1	4	yes	—
1375	SD₁₆	—	2	2	no	—
1376	SD₁₆	—	2	2	no	—
1377	SD₁₆	—	2	2	no	—
1378	SD₁₆	—	2	2	no	—
1379	SD₁₆	—	4	1	no	—
1380	SD₁₆	—	4	1	no	—
1381	SD₁₆	—	4	1	no	—
1382	SD₁₆	—	4	1	no	—
1383	M₁₆	—	2	2	no	—
1384	M₁₆	—	2	2	no	—
1385	M₁₆	—	4	1	no	—
1386	M₁₆	—	4	1	no	—
1387	C₂×C₈	—	2	2	no	—
1388	C₂×C₈	—	4	1	no	—
1389	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1390	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1391	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1392	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1393	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1394	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1395	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1396	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	—	2	1	no	—
1400	C₄⋊C₄	—	2	1	no	—
1401	C₄⋊C₄	—	2	1	no	—
1402	C₄⋊C₄	—	2	1	no	—
1403	C₄⋊C₄	—	2	1	no	—
1404	C₄⋊C₄	—	2	1	no	—
1405	C₄⋊C₄	—	2	1	no	—
1406	C₄⋊C₄	—	2	1	no	—
1407	C₄⋊C₄	—	2	1	no	—
1408	C₄⋊C₄	—	2	1	no	—
1409	C₄⋊C₄	—	2	1	no	—
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	—	2	1	no	—
1413	C₄⋊C₄	—	2	1	no	—
1414	C₄⋊C₄	—	2	1	no	—
1415	C₄⋊C₄	—	2	1	no	—
1416	C₄⋊C₄	—	2	1	no	—
1417	C₄⋊C₄	—	2	1	no	—
1418	C₄⋊C₄	—	2	1	no	—
1419	C₄⋊C₄	—	2	1	no	—
1420	C₄⋊C₄	—	2	1	no	—
1421	C₄⋊C₄	—	2	1	no	—
1422	C₄⋊C₄	—	2	1	no	—
1423	C₄⋊C₄	—	2	1	no	—
1424	C₄⋊C₄	—	2	1	no	—
1425	C₄⋊C₄	—	2	1	no	—
1426	C₄⋊C₄	—	2	1	no	—
1427	C₄⋊C₄	—	2	1	no	—
1428	C₄⋊C₄	—	2	1	no	—
1429	C₄⋊C₄	—	2	1	no	—
1430	C₄⋊C₄	—	2	1	no	—
1431	C₄⋊C₄	—	2	1	no	—
1432	C₄⋊C₄	—	2	1	no	—
1433	C₄⋊C₄	—	2	1	no	—
1434	C₄⋊C₄	—	2	1	no	—
1435	C₄⋊C₄	—	2	1	no	—
1436	C₄⋊C₄	—	2	1	no	—
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1440	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1441	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1442	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1443	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1444	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1445	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1446	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1447	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1448	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1449	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1450	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1451	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1452	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1453	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1454	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1455	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1456	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1457	C₂²⋊C₄	—	2	1	no	—
1458	C₂²⋊C₄	—	2	1	no	—
1459	C₂²⋊C₄	—	2	1	no	—
1460	C₂²⋊C₄	—	2	1	no	—
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	—	2	1	no	—
1476	C₂²⋊C₄	—	2	1	no	—
1477	C₂²⋊C₄	—	2	1	no	—
1478	C₂²⋊C₄	—	2	1	no	—
1479	C₂²⋊C₄	—	2	1	no	—
1480	C₂²⋊C₄	—	2	1	no	—
1481	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1482	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1483	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1484	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1485	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1486	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1487	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1488	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1489	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1490	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1491	C₄²	—	2	1	no	—
1492	C₄²	—	2	1	no	—
1493	C₄²	—	2	1	no	—
1494	C₄²	—	2	1	no	—
1495	C₄²	—	2	1	no	—
1496	C₄²	—	2	1	no	—
1497	C₄²	—	2	1	no	—
1498	C₄²	—	2	1	no	—
1499	C₄²	—	2	1	no	—
1500	C₄²	—	2	1	no	—
1501	C₄²	—	2	1	no	—
1502	C₄²	—	2	1	no	—
1503	C₄²	—	2	1	no	—
1504	C₄²	—	2	1	no	—
1505	C₄²	—	2	1	no	—
1506	C₄²	—	2	1	no	—
1507	C₄²	—	2	1	no	—
1508	C₄²	—	2	1	no	—
1509	C₄²	—	2	1	no	—
1510	C₄²	—	2	1	no	—
1511	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1512	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1513	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1514	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1515	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1516	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1517	C₂³	—	2	1	no	—
1518	C₂³	—	2	1	no	—
1519	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1520	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1521	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1522	Q₈	—	2	1	no	—
1523	Q₈	—	2	1	no	—
1524	Q₈	—	2	1	no	—
1525	Q₈	—	2	1	no	—
1526	Q₈	—	2	1	no	—
1527	Q₈	—	2	1	no	—
1528	Q₈	—	2	1	no	—
1529	Q₈	—	2	1	no	—
1530	Q₈	—	2	1	no	—
1531	Q₈	—	2	1	no	—
1532	Q₈	—	4	1	no	—
1533	Q₈	—	4	2	no	—
1534	Q₈	—	4	2	no	—
1535	Q₈	—	4	2	no	—
1536	Q₈	—	4	2	no	—
1537	Q₈	—	4	2	no	—
1538	Q₈	—	8	1	no	—
1539	Q₈	C₂×#41×C₃₁	1	2	yes	—
1540	Q₈	C₂×#41×C₃₁	1	2	yes	—
1541	D₄	—	2	1	no	—
1542	D₄	—	2	1	no	—
1543	D₄	—	2	1	no	—
1544	D₄	—	2	1	no	—
1545	D₄	—	4	1	no	—
1546	D₄	—	4	1	no	—
1547	D₄	—	4	1	no	—
1548	D₄	—	4	2	no	—
1549	D₄	—	4	2	no	—
1550	D₄	—	8	1	no	—
1551	D₄	—	8	1	no	—
1552	D₄	—	8	1	no	—
1553	D₄	—	8	1	no	—
1554	D₄	—	8	1	no	—
1555	D₄	—	8	1	no	—
1556	C₂×C₄	—	2	1	no	—
1557	C₂×C₄	—	2	1	no	—
1558	C₂×C₄	—	2	1	no	—
1559	C₂×C₄	—	2	1	no	—
1560	C₂×C₄	—	2	1	no	—
1561	C₂×C₄	—	2	1	no	—
1562	C₂×C₄	—	2	1	no	—
1563	C₂×C₄	—	2	1	no	—
1564	C₂×C₄	—	2	1	no	—
1565	C₂×C₄	—	2	1	no	—
1566	C₂×C₄	—	2	1	no	—
1567	C₂×C₄	—	2	1	no	—
1568	C₂×C₄	—	2	1	no	—
1569	C₂×C₄	—	2	1	no	—
1570	C₂×C₄	—	2	1	no	—
1571	C₂×C₄	—	2	1	no	—
1572	C₂×C₄	—	2	1	no	—
1573	C₂×C₄	—	2	1	no	—
1574	C₂×C₄	—	2	1	no	—
1575	C₂×C₄	—	2	1	no	—
1576	C₂×C₄	—	4	1	no	—
1577	C₂×C₄	—	4	1	no	—
1578	C₂×C₄	—	4	2	no	—
1579	C₂×C₄	—	4	2	no	—
1580	C₂×C₄	—	4	2	no	—
1581	C₂×C₄	—	4	2	no	—
1582	C₂×C₄	—	4	2	no	—
1583	C₂×C₄	—	4	2	no	—
1584	C₂×C₄	—	4	2	no	—
1585	C₂×C₄	—	8	1	no	—
1586	C₂×C₄	—	8	1	no	—
1587	C₂×C₄	—	8	1	no	—
1588	C₂×C₄	—	8	1	no	—
1589	C₂×C₄	—	8	1	no	—
1590	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1591	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1592	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1593	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1594	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1595	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1596	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1597	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1598	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1599	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1600	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1601	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1602	C₈	—	2	1	no	—
1603	C₈	—	2	1	no	—
1604	C₈	—	2	1	no	—
1605	C₈	—	2	1	no	—
1606	C₈	—	2	1	no	—
1607	C₈	—	2	1	no	—
1608	C₈	—	2	1	no	—
1609	C₈	C₂×#41×C₃₁	1	2	yes	—
1610	C₂²	—	2	1	no	—
1611	C₂²	—	2	1	no	—
1612	C₂²	—	2	1	no	—
1613	C₂²	—	2	1	no	—
1614	C₂²	—	2	1	no	—
1615	C₂²	—	2	1	no	—
1616	C₂²	—	2	1	no	—
1617	C₂²	—	2	1	no	—
1618	C₂²	—	2	1	no	—
1619	C₂²	—	4	1	no	—
1620	C₂²	—	4	1	no	—
1621	C₂²	—	4	1	no	—
1622	C₂²	—	4	1	no	—
1623	C₂²	—	4	1	no	—
1624	C₂²	—	4	1	no	—
1625	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1626	C₄	—	2	1	no	—
1627	C₄	—	2	1	no	—
1628	C₄	—	2	1	no	—
1629	C₄	—	2	2	no	—
1630	C₄	—	2	2	no	—
1631	C₄	—	2	1	no	—
1632	C₄	—	2	1	no	—
1633	C₄	—	2	1	no	—
1634	C₄	—	2	1	no	—
1635	C₄	—	2	1	no	—
1636	C₄	—	2	1	no	—
1637	C₄	—	2	1	no	—
1638	C₄	—	2	1	no	—
1639	C₄	—	4	1	no	—
1640	C₄	—	4	1	no	—
1641	C₄	—	4	1	no	—
1642	C₄	—	4	1	no	—
1643	C₄	—	4	1	no	—
1644	C₄	—	4	1	no	—
1645	C₄	—	4	1	no	—
1646	C₄	—	4	1	no	—
1647	C₄	—	4	1	no	—
1648	C₄	—	4	1	no	—
1649	C₄	—	4	1	no	—
1650	C₄	—	4	1	no	—
1651	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1652	C₄	C₃₁×#585	1	1	yes	characteristic
1653	C₂	—	4	1	no	—
1654	C₂	—	4	1	no	—
1655	C₂	—	4	1	no	—
1656	C₂	—	8	1	no	—
1657	C₂	—	8	1	no	—
1658	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1659	C₂	C₃₁×#3586	1	1	yes	characteristic
1660	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3524	C₂
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
2. C₃₁×#3523	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3390	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3371	C₂	semidirect
7. C₃₁×#3352	C₂	semidirect
8. C₃₁×#3350	C₂	semidirect
9. C₃₁×#3348	C₂	semidirect
10. C₃₁×#3329	C₂	semidirect
11. C₃₁×#3327	C₂	semidirect
12. C₃₁×#3320	C₂	semidirect
13. C₃₁×#3317	C₂	semidirect
14. C₃₁×#3313	C₂	semidirect
15. C₃₁×#3312	C₂	semidirect
16. C₃₁×#3278	C₂	semidirect
17. C₃₁×#3270	C₂	semidirect
18. C₃₁×#3270	C₂	semidirect
19. C₃₁×#3178	C₂	semidirect
20. C₃₁×#3174	C₂	semidirect
21. C₃₁×#3172	C₂	semidirect
22. C₃₁×#3127	C₂	semidirect
23. C₃₁×#3126	C₂	semidirect
24. C₃₁×#3121	C₂	semidirect
25. C₃₁×#3120	C₂	semidirect
26. C₃₁×#3117	C₂	semidirect
27. C₃₁×#3116	C₂	semidirect
28. C₃₁×#2967	C₂	semidirect
29. C₃₁×#2950	C₂	semidirect
30. C₃₁×#2947	C₂	semidirect
31. C₄×C₃₁×#137	C₂	semidirect
686. #61512	C₃₁	direct (N × H)
781. #3523	C₂×C₃₁	semidirect
782. #3400	C₂×C₃₁	semidirect
783. #3390	C₂×C₃₁	semidirect
784. #3374	C₂×C₃₁	semidirect
785. #3371	C₂×C₃₁	semidirect
786. #3352	C₂×C₃₁	semidirect
787. #3350	C₂×C₃₁	semidirect
788. #3348	C₂×C₃₁	semidirect
789. #3329	C₂×C₃₁	semidirect
790. #3327	C₂×C₃₁	semidirect
791. #3320	C₂×C₃₁	semidirect
792. #3317	C₂×C₃₁	semidirect
793. #3313	C₂×C₃₁	semidirect
794. #3312	C₂×C₃₁	semidirect
795. #3278	C₂×C₃₁	semidirect
796. #3270	C₂×C₃₁	semidirect
797. #3270	C₂×C₃₁	semidirect
798. #3178	C₂×C₃₁	semidirect
799. #3174	C₂×C₃₁	semidirect
800. #3172	C₂×C₃₁	semidirect
801. #3127	C₂×C₃₁	semidirect
802. #3126	C₂×C₃₁	semidirect
803. #3121	C₂×C₃₁	semidirect
804. #3120	C₂×C₃₁	semidirect
805. #3117	C₂×C₃₁	semidirect
806. #3116	C₂×C₃₁	semidirect
807. #2967	C₂×C₃₁	semidirect
808. #2950	C₂×C₃₁	semidirect
809. #2947	C₂×C₃₁	semidirect
810. C₄×#137	C₂×C₃₁	semidirect
1311. C₃₁	#61512	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×#3524	2
C₃₁×#3523	2
C₃₁×#3400	2
C₃₁×#3390	2
C₃₁×#3374	2
C₃₁×#3371	2
C₃₁×#3352	2
C₃₁×#3350	2
C₃₁×#3348	2
C₃₁×#3329	2
C₃₁×#3327	2
C₃₁×#3320	2
C₃₁×#3317	2
C₃₁×#3313	2
C₃₁×#3312	2
C₃₁×#3278	2
C₃₁×#3270	2
C₃₁×#3178	2
C₃₁×#3174	2
C₃₁×#3172	2
C₃₁×#3127	2
C₃₁×#3126	2
C₃₁×#3121	2
C₃₁×#3120	2
C₃₁×#3117	2
C₃₁×#3116	2
C₃₁×#2967	2
C₃₁×#2950	2
C₃₁×#2947	2
C₄×C₃₁×#137	2
#61512	31

Subgroups — C31×#61512 #21518271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61512 #21518271