Subgroups — C₃₁×#61781 #21518540

Order 7936.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3541	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3351	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3350	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3349	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3344	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3344	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3316	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3315	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3313	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3312	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3244	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3242	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3202	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3201	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3195	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3121	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
30	C₃₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#563	—	2	1	no	—
33	C₃₁×#562	—	2	1	no	—
34	C₃₁×#556	C₂²	1	1	yes	characteristic
35	C₃₁×#556	C₂²	1	1	yes	characteristic
36	C₃₁×#556	C₂²	1	1	yes	characteristic
37	C₃₁×#554	—	2	1	no	—
38	C₃₁×#554	C₂²	1	1	yes	characteristic
39	C₃₁×#554	C₂²	1	1	yes	characteristic
40	C₃₁×#554	C₂²	1	1	yes	characteristic
41	C₃₁×#553	—	2	1	no	—
42	C₃₁×#553	C₂²	1	1	yes	characteristic
43	C₃₁×#552	—	2	1	no	—
44	C₃₁×#552	—	2	1	no	—
45	C₃₁×#552	C₂²	1	1	yes	characteristic
46	C₃₁×#552	C₂²	1	1	yes	characteristic
47	C₃₁×#552	C₂²	1	1	yes	characteristic
48	C₃₁×#552	C₂²	1	1	yes	characteristic
49	C₃₁×#552	C₂²	1	1	yes	characteristic
50	C₃₁×#551	—	2	1	no	—
51	C₃₁×#551	—	2	1	no	—
52	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
53	C₃₁×#548	C₂²	1	1	yes	characteristic
54	C₃₁×#548	C₂²	1	1	yes	characteristic
55	C₃₁×#547	C₂²	1	1	yes	characteristic
56	C₃₁×#544	C₂²	1	1	yes	characteristic
57	C₃₁×#542	—	2	1	no	—
58	C₃₁×#542	—	2	1	no	—
59	C₃₁×#542	C₂²	1	1	yes	characteristic
60	C₃₁×#541	—	2	1	no	—
61	C₃₁×#541	C₂²	1	1	yes	characteristic
62	C₃₁×#539	—	2	1	no	—
63	C₃₁×#538	—	2	1	no	—
64	C₃₁×#538	—	2	1	no	—
65	C₃₁×#537	C₂²	1	1	yes	characteristic
66	C₃₁×#536	C₂²	1	1	yes	characteristic
67	C₃₁×#536	C₂²	1	1	yes	characteristic
68	C₃₁×#533	—	2	1	no	—
69	C₃₁×#529	—	2	1	no	—
70	C₃₁×#525	C₂²	1	1	yes	characteristic
71	C₃₁×#525	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
74	C₃₁×#520	C₂²	1	1	yes	characteristic
75	C₃₁×#519	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
77	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#485	C₂²	1	1	yes	characteristic
86	C₃₁×#485	C₂²	1	1	yes	characteristic
87	C₃₁×#485	C₂²	1	1	yes	characteristic
88	C₃₁×#485	C₂²	1	1	yes	characteristic
89	C₃₁×#485	C₂²	1	1	yes	characteristic
90	C₃₁×#485	C₂²	1	1	yes	characteristic
91	C₃₁×#485	C₂²	1	1	yes	characteristic
92	C₃₁×#485	C₂²	1	1	yes	characteristic
93	C₃₁×#485	C₂²	1	1	yes	characteristic
94	C₃₁×#485	C₂²	1	1	yes	characteristic
95	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#484	C₂²	1	1	yes	characteristic
101	C₃₁×#484	C₂²	1	1	yes	characteristic
102	C₃₁×#484	C₂²	1	1	yes	characteristic
103	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#483	C₂²	1	1	yes	characteristic
106	C₃₁×#483	C₂²	1	1	yes	characteristic
107	C₃₁×#483	C₂²	1	1	yes	characteristic
108	C₃₁×#483	C₂²	1	1	yes	characteristic
109	C₃₁×#483	C₂²	1	1	yes	characteristic
110	C₃₁×#483	C₂²	1	1	yes	characteristic
111	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#482	C₂²	1	1	yes	characteristic
115	C₃₁×#482	C₂²	1	1	yes	characteristic
116	C₃₁×#482	C₂²	1	1	yes	characteristic
117	C₃₁×#482	C₂²	1	1	yes	characteristic
118	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#481	C₂²	1	1	yes	characteristic
120	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#470	C₂²	1	1	yes	characteristic
134	C₃₁×#470	C₂²	1	1	yes	characteristic
135	C₃₁×#470	C₂²	1	1	yes	characteristic
136	C₃₁×#470	C₂²	1	1	yes	characteristic
137	C₃₁×#470	C₂²	1	1	yes	characteristic
138	C₃₁×#470	C₂²	1	1	yes	characteristic
139	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
140	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
141	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
142	C₃₁×#468	C₂²	1	1	yes	characteristic
143	C₃₁×#468	C₂²	1	1	yes	characteristic
144	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
145	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
146	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
147	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
148	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
149	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
150	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
151	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
152	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
153	C₃₁×#452	C₂²	1	1	yes	characteristic
154	C₃₁×#452	C₂²	1	1	yes	characteristic
155	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
156	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
157	C₃₁×#451	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, complemented
163	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
164	C₃₁×#448	C₂²	1	1	yes	characteristic
165	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
166	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
167	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
168	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
169	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
170	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
171	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
172	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
173	C₃₁×#436	C₂²	1	1	yes	characteristic
174	C₃₁×#436	C₂²	1	1	yes	characteristic
175	C₃₁×#436	C₂²	1	1	yes	characteristic
176	C₃₁×#436	C₂²	1	1	yes	characteristic
177	C₃₁×#435	C₂²	1	1	yes	characteristic
178	C₃₁×#435	C₂²	1	1	yes	characteristic
179	C₃₁×#435	C₂²	1	1	yes	characteristic
180	C₃₁×#435	C₂²	1	1	yes	characteristic
181	C₃₁×#433	C₂²	1	1	yes	characteristic
182	C₃₁×#433	C₂²	1	1	yes	characteristic
183	C₃₁×#428	C₂²	1	1	yes	characteristic
184	C₃₁×#428	C₂²	1	1	yes	characteristic
185	C₃₁×#428	C₂²	1	1	yes	characteristic
186	C₃₁×#428	C₂²	1	1	yes	characteristic
187	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
188	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
189	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
190	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
191	C₃₁×#419	C₂²	1	1	yes	characteristic
192	C₃₁×#419	C₂²	1	1	yes	characteristic
193	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
194	C₃₁×#417	C₂²	1	1	yes	characteristic
195	C₃₁×#417	C₂²	1	1	yes	characteristic
196	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
197	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
198	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
199	C₃₁×#408	C₂²	1	1	yes	characteristic
200	C₃₁×#408	C₂²	1	1	yes	characteristic
201	C₃₁×#407	C₂²	1	1	yes	characteristic
202	C₃₁×#407	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	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
220	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×C₄⋊Q₈	—	2	1	no	—
227	C₃₁×C₄⋊Q₈	—	2	1	no	—
228	C₃₁×C₄⋊Q₈	—	2	1	no	—
229	C₃₁×C₄⋊Q₈	—	2	1	no	—
230	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
233	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
234	C₃₁×#126	—	2	1	no	—
235	C₃₁×#126	—	2	1	no	—
236	C₃₁×#126	—	2	1	no	—
237	C₃₁×#126	—	2	1	no	—
238	C₃₁×#126	—	2	1	no	—
239	C₃₁×#126	—	2	1	no	—
240	C₃₁×#126	—	2	1	no	—
241	C₃₁×#126	—	2	1	no	—
242	C₃₁×#126	—	2	1	no	—
243	C₃₁×#126	—	2	1	no	—
244	C₃₁×#126	—	2	1	no	—
245	C₃₁×#126	—	2	1	no	—
246	C₃₁×#126	—	2	1	no	—
247	C₃₁×#126	—	2	1	no	—
248	C₃₁×#126	—	2	1	no	—
249	C₃₁×#125	—	2	1	no	—
250	C₃₁×#125	—	2	1	no	—
251	C₃₁×#125	—	2	1	no	—
252	C₃₁×#125	—	2	1	no	—
253	C₃₁×#125	—	2	1	no	—
254	C₃₁×#125	—	2	1	no	—
255	C₃₁×#125	—	2	1	no	—
256	C₃₁×#125	—	2	1	no	—
257	C₃₁×#125	—	2	1	no	—
258	C₃₁×#125	—	2	1	no	—
259	C₃₁×#125	—	2	1	no	—
260	C₃₁×#125	C₂³	1	1	yes	characteristic
261	C₃₁×#125	C₂³	1	1	yes	characteristic
262	C₃₁×#125	C₂³	1	1	yes	characteristic
263	C₃₁×#124	—	2	1	no	—
264	C₃₁×#124	—	2	1	no	—
265	C₃₁×#124	—	2	1	no	—
266	C₃₁×#124	—	2	1	no	—
267	C₃₁×#124	—	2	1	no	—
268	C₃₁×#124	—	2	1	no	—
269	C₃₁×#124	—	2	1	no	—
270	C₃₁×#124	—	2	1	no	—
271	C₃₁×#124	C₂³	1	1	yes	characteristic
272	C₃₁×#123	—	2	1	no	—
273	C₃₁×#123	—	2	1	no	—
274	C₃₁×#123	—	2	1	no	—
275	C₃₁×#123	—	2	1	no	—
276	C₃₁×#123	—	2	1	no	—
277	C₃₁×#123	—	2	1	no	—
278	C₃₁×#123	—	2	1	no	—
279	C₃₁×#123	—	2	1	no	—
280	C₃₁×#123	—	2	1	no	—
281	C₃₁×#123	—	2	1	no	—
282	C₃₁×#123	—	2	1	no	—
283	C₃₁×#123	—	2	1	no	—
284	C₃₁×#123	—	2	1	no	—
285	C₃₁×#123	—	2	1	no	—
286	C₃₁×#123	D₄	1	1	yes	characteristic
287	C₃₁×#123	D₄	1	1	yes	characteristic
288	C₃₁×C₂²⋊Q₈	—	2	1	no	—
289	C₃₁×C₂²⋊Q₈	—	2	1	no	—
290	C₃₁×C₂²⋊Q₈	—	2	1	no	—
291	C₃₁×C₂²⋊Q₈	—	2	1	no	—
292	C₃₁×C₂²⋊Q₈	—	2	1	no	—
293	C₃₁×C₂²⋊Q₈	—	2	1	no	—
294	C₃₁×C₂²⋊Q₈	—	2	1	no	—
295	C₃₁×C₂²⋊Q₈	—	2	1	no	—
296	C₃₁×C₂²⋊Q₈	—	2	1	no	—
297	C₃₁×C₂²⋊Q₈	—	2	1	no	—
298	C₃₁×C₂²⋊Q₈	—	2	1	no	—
299	C₃₁×C₂²⋊Q₈	—	2	1	no	—
300	C₃₁×C₂²⋊Q₈	—	2	1	no	—
301	C₃₁×C₂²⋊Q₈	—	2	1	no	—
302	C₃₁×C₂²⋊Q₈	—	2	1	no	—
303	C₃₁×C₂²⋊Q₈	—	2	1	no	—
304	C₃₁×C₂²⋊Q₈	—	2	1	no	—
305	C₃₁×C₂²⋊Q₈	—	2	1	no	—
306	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
307	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
308	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
311	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
312	C₃₁×C₂²⋊Q₈	C₂³	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×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
322	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
330	C₃₁×#121	—	2	1	no	—
331	C₃₁×#121	—	2	1	no	—
332	C₃₁×#121	D₄	1	1	yes	characteristic
333	C₃₁×#121	D₄	1	1	yes	characteristic
334	C₃₁×#121	C₂³	1	1	yes	characteristic
335	C₃₁×#121	C₂³	1	1	yes	characteristic
336	C₃₁×#121	C₂³	1	1	yes	characteristic
337	C₃₁×#120	—	2	1	no	—
338	C₃₁×#120	D₄	1	1	yes	characteristic
339	C₃₁×#120	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
347	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
353	C₄×D₄×C₃₁	—	2	1	no	—
354	C₄×D₄×C₃₁	—	2	1	no	—
355	C₄×D₄×C₃₁	—	2	1	no	—
356	C₄×D₄×C₃₁	—	2	1	no	—
357	C₄×D₄×C₃₁	—	2	1	no	—
358	C₄×D₄×C₃₁	—	2	1	no	—
359	C₄×D₄×C₃₁	—	2	1	no	—
360	C₄×D₄×C₃₁	—	2	1	no	—
361	C₄×D₄×C₃₁	—	2	1	no	—
362	C₄×D₄×C₃₁	—	2	1	no	—
363	C₄×D₄×C₃₁	—	2	1	no	—
364	C₄×D₄×C₃₁	—	2	1	no	—
365	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
370	C₃₁×#117	—	2	1	no	—
371	C₃₁×#117	—	2	1	no	—
372	C₃₁×#117	—	2	1	no	—
373	C₃₁×#117	—	2	1	no	—
374	C₃₁×#117	—	2	1	no	—
375	C₃₁×#117	—	2	1	no	—
376	C₃₁×#117	—	2	1	no	—
377	C₃₁×#117	—	2	1	no	—
378	C₃₁×#117	—	2	1	no	—
379	C₃₁×#117	C₂³	1	1	yes	characteristic
380	C₃₁×#117	C₂³	1	1	yes	characteristic
381	C₃₁×#117	C₂³	1	1	yes	characteristic
382	C₃₁×#117	C₂³	1	1	yes	characteristic
383	C₃₁×#117	C₂³	1	1	yes	characteristic
384	C₃₁×#117	C₂³	1	1	yes	characteristic
385	C₃₁×#117	C₂³	1	1	yes	characteristic
386	C₃₁×#117	C₂³	1	1	yes	characteristic
387	C₃₁×#117	C₂³	1	1	yes	characteristic
388	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
396	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
397	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
398	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
399	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
400	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
401	C₂×C₄²×C₃₁	—	2	1	no	—
402	C₃₁×#107	C₂³	1	1	yes	characteristic
403	C₃₁×#107	C₂³	1	1	yes	characteristic
404	C₃₁×#107	C₂³	1	1	yes	characteristic
405	C₃₁×#107	C₂³	1	1	yes	characteristic
406	C₃₁×#107	C₂³	1	1	yes	characteristic
407	C₃₁×#107	C₂³	1	1	yes	characteristic
408	C₃₁×#107	C₂³	1	1	yes	characteristic
409	C₃₁×#107	C₂³	1	1	yes	characteristic
410	C₃₁×#107	C₂³	1	1	yes	characteristic
411	C₃₁×#107	C₂³	1	1	yes	characteristic
412	C₃₁×#106	C₂³	1	1	yes	characteristic
413	C₃₁×#106	C₂³	1	1	yes	characteristic
414	C₃₁×#106	C₂³	1	1	yes	characteristic
415	C₃₁×#106	C₂³	1	1	yes	characteristic
416	C₃₁×#106	C₂³	1	1	yes	characteristic
417	C₃₁×#106	C₂³	1	1	yes	characteristic
418	C₃₁×#106	C₂³	1	1	yes	characteristic
419	C₃₁×#106	C₂³	1	1	yes	characteristic
420	C₃₁×#106	C₂³	1	1	yes	characteristic
421	C₃₁×#106	C₂³	1	1	yes	characteristic
422	C₃₁×#106	C₂³	1	1	yes	characteristic
423	C₃₁×#106	C₂³	1	1	yes	characteristic
424	C₃₁×#106	C₂³	1	1	yes	characteristic
425	C₃₁×#106	C₂³	1	1	yes	characteristic
426	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₃₁×#103	C₂³	1	1	yes	characteristic
431	C₃₁×#103	C₂³	1	1	yes	characteristic
432	C₃₁×#103	C₂³	1	1	yes	characteristic
433	C₃₁×#103	C₂³	1	1	yes	characteristic
434	C₃₁×#103	C₂³	1	1	yes	characteristic
435	C₃₁×#103	C₂³	1	1	yes	characteristic
436	C₃₁×#103	C₂³	1	1	yes	characteristic
437	C₃₁×#103	C₂³	1	1	yes	characteristic
438	C₃₁×#103	C₂³	1	1	yes	characteristic
439	C₃₁×#103	C₂³	1	1	yes	characteristic
440	C₃₁×#103	C₂³	1	1	yes	characteristic
441	C₃₁×#103	C₂³	1	1	yes	characteristic
442	C₃₁×#103	C₂³	1	1	yes	characteristic
443	C₃₁×#103	C₂³	1	1	yes	characteristic
444	C₃₁×#103	C₂³	1	1	yes	characteristic
445	C₃₁×#103	C₂³	1	1	yes	characteristic
446	C₃₁×#103	C₂³	1	1	yes	characteristic
447	C₃₁×#103	C₂³	1	1	yes	characteristic
448	C₃₁×#103	C₂³	1	1	yes	characteristic
449	C₃₁×#103	C₂³	1	1	yes	characteristic
450	C₃₁×#103	C₂³	1	1	yes	characteristic
451	C₃₁×#103	C₂³	1	1	yes	characteristic
452	C₃₁×#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×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₃₁×#97	C₂³	1	1	yes	characteristic
475	C₃₁×#97	C₂³	1	1	yes	characteristic
476	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
478	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
479	#41×C₃₁	—	4	1	no	—
480	#41×C₃₁	—	4	1	no	—
481	#41×C₃₁	—	4	1	no	—
482	#41×C₃₁	—	4	1	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	—	4	1	no	—
492	C₂×Q₈×C₃₁	—	4	1	no	—
493	C₂×Q₈×C₃₁	—	4	1	no	—
494	C₂×Q₈×C₃₁	—	4	1	no	—
495	C₂×Q₈×C₃₁	—	4	1	no	—
496	C₂×Q₈×C₃₁	—	4	1	no	—
497	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
498	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈×C₃₁	C₂⁴	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×D₄×C₃₁	—	2	1	no	—
504	C₂×D₄×C₃₁	—	2	1	no	—
505	C₂×D₄×C₃₁	—	2	1	no	—
506	C₂×D₄×C₃₁	—	2	1	no	—
507	C₂×D₄×C₃₁	—	2	1	no	—
508	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
509	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
510	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
511	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
512	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
513	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
514	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
515	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
516	C₂²×C₄×C₃₁	—	2	1	no	—
517	C₂²×C₄×C₃₁	—	2	1	no	—
518	C₂²×C₄×C₃₁	—	2	1	no	—
519	C₂²×C₄×C₃₁	—	2	1	no	—
520	C₂²×C₄×C₃₁	—	2	1	no	—
521	C₂²×C₄×C₃₁	—	2	1	no	—
522	C₂²×C₄×C₃₁	—	2	1	no	—
523	C₂²×C₄×C₃₁	—	2	1	no	—
524	C₂²×C₄×C₃₁	—	2	1	no	—
525	C₂²×C₄×C₃₁	—	2	1	no	—
526	C₂²×C₄×C₃₁	—	2	1	no	—
527	C₂²×C₄×C₃₁	—	2	1	no	—
528	C₂²×C₄×C₃₁	—	2	1	no	—
529	C₂²×C₄×C₃₁	—	4	1	no	—
530	C₂²×C₄×C₃₁	—	4	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	C₂×D₄	1	1	yes	characteristic
534	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
535	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
536	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
539	Q₁₆×C₃₁	—	4	1	no	—
540	Q₁₆×C₃₁	—	4	1	no	—
541	Q₁₆×C₃₁	—	4	1	no	—
542	Q₁₆×C₃₁	—	4	1	no	—
543	Q₁₆×C₃₁	—	4	1	no	—
544	Q₁₆×C₃₁	—	4	1	no	—
545	SD₁₆×C₃₁	—	4	1	no	—
546	SD₁₆×C₃₁	—	4	1	no	—
547	M₁₆×C₃₁	—	4	1	no	—
548	M₁₆×C₃₁	—	4	1	no	—
549	M₁₆×C₃₁	—	4	1	no	—
550	M₁₆×C₃₁	—	4	1	no	—
551	M₁₆×C₃₁	—	4	1	no	—
552	M₁₆×C₃₁	—	4	1	no	—
553	C₂×C₈×C₃₁	—	4	1	no	—
554	C₂×C₈×C₃₁	—	4	1	no	—
555	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
556	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
557	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	—	2	1	no	—
564	C₄⋊C₄×C₃₁	—	2	1	no	—
565	C₄⋊C₄×C₃₁	—	2	1	no	—
566	C₄⋊C₄×C₃₁	—	2	1	no	—
567	C₄⋊C₄×C₃₁	—	2	1	no	—
568	C₄⋊C₄×C₃₁	—	2	1	no	—
569	C₄⋊C₄×C₃₁	—	2	1	no	—
570	C₄⋊C₄×C₃₁	—	2	1	no	—
571	C₄⋊C₄×C₃₁	—	2	1	no	—
572	C₄⋊C₄×C₃₁	—	2	1	no	—
573	C₄⋊C₄×C₃₁	—	2	1	no	—
574	C₄⋊C₄×C₃₁	—	2	1	no	—
575	C₄⋊C₄×C₃₁	—	2	1	no	—
576	C₄⋊C₄×C₃₁	—	2	1	no	—
577	C₄⋊C₄×C₃₁	—	2	1	no	—
578	C₄⋊C₄×C₃₁	—	2	1	no	—
579	C₄⋊C₄×C₃₁	—	2	1	no	—
580	C₄⋊C₄×C₃₁	—	2	1	no	—
581	C₄⋊C₄×C₃₁	—	2	1	no	—
582	C₄⋊C₄×C₃₁	—	2	1	no	—
583	C₄⋊C₄×C₃₁	—	2	1	no	—
584	C₄⋊C₄×C₃₁	—	2	1	no	—
585	C₄⋊C₄×C₃₁	—	2	1	no	—
586	C₄⋊C₄×C₃₁	—	2	1	no	—
587	C₄⋊C₄×C₃₁	—	2	1	no	—
588	C₄⋊C₄×C₃₁	—	2	1	no	—
589	C₄⋊C₄×C₃₁	—	2	1	no	—
590	C₄⋊C₄×C₃₁	—	2	1	no	—
591	C₄⋊C₄×C₃₁	—	2	1	no	—
592	C₄⋊C₄×C₃₁	—	2	1	no	—
593	C₄⋊C₄×C₃₁	—	2	1	no	—
594	C₄⋊C₄×C₃₁	—	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	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
617	C₄⋊C₄×C₃₁	C₂⁴	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	C₂²⋊C₄×C₃₁	—	2	1	no	—
622	C₂²⋊C₄×C₃₁	—	2	1	no	—
623	C₂²⋊C₄×C₃₁	—	2	1	no	—
624	C₂²⋊C₄×C₃₁	—	2	1	no	—
625	C₂²⋊C₄×C₃₁	—	2	1	no	—
626	C₂²⋊C₄×C₃₁	—	2	1	no	—
627	C₂²⋊C₄×C₃₁	—	2	1	no	—
628	C₂²⋊C₄×C₃₁	—	2	1	no	—
629	C₂²⋊C₄×C₃₁	—	2	1	no	—
630	C₂²⋊C₄×C₃₁	—	2	1	no	—
631	C₂²⋊C₄×C₃₁	—	2	1	no	—
632	C₂²⋊C₄×C₃₁	—	2	1	no	—
633	C₂²⋊C₄×C₃₁	—	2	1	no	—
634	C₂²⋊C₄×C₃₁	—	2	1	no	—
635	C₂²⋊C₄×C₃₁	—	2	1	no	—
636	C₂²⋊C₄×C₃₁	—	2	1	no	—
637	C₂²⋊C₄×C₃₁	—	2	1	no	—
638	C₂²⋊C₄×C₃₁	—	2	1	no	—
639	C₂²⋊C₄×C₃₁	—	2	1	no	—
640	C₂²⋊C₄×C₃₁	—	2	1	no	—
641	C₂²⋊C₄×C₃₁	—	2	1	no	—
642	C₂²⋊C₄×C₃₁	—	2	1	no	—
643	C₂²⋊C₄×C₃₁	—	2	1	no	—
644	C₂²⋊C₄×C₃₁	—	2	1	no	—
645	C₂²⋊C₄×C₃₁	—	2	1	no	—
646	C₂²⋊C₄×C₃₁	—	2	1	no	—
647	C₂²⋊C₄×C₃₁	—	2	1	no	—
648	C₂²⋊C₄×C₃₁	—	2	1	no	—
649	C₂²⋊C₄×C₃₁	—	2	1	no	—
650	C₂²⋊C₄×C₃₁	—	2	1	no	—
651	C₂²⋊C₄×C₃₁	—	2	1	no	—
652	C₂²⋊C₄×C₃₁	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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
661	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
678	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
679	#61781	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
680	C₂³×C₃₁	—	2	1	no	—
681	C₂³×C₃₁	—	4	1	no	—
682	C₂³×C₃₁	—	4	1	no	—
683	C₂³×C₃₁	—	4	1	no	—
684	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
685	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
686	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
687	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
688	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
689	Q₈×C₃₁	—	2	1	no	—
690	Q₈×C₃₁	—	2	1	no	—
691	Q₈×C₃₁	—	2	1	no	—
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	—	4	1	no	—
700	Q₈×C₃₁	—	4	2	no	—
701	Q₈×C₃₁	—	8	1	no	—
702	Q₈×C₃₁	—	8	1	no	—
703	Q₈×C₃₁	—	8	1	no	—
704	Q₈×C₃₁	—	8	1	no	—
705	Q₈×C₃₁	—	8	1	no	—
706	D₄×C₃₁	—	2	1	no	—
707	D₄×C₃₁	—	2	1	no	—
708	D₄×C₃₁	—	4	1	no	—
709	D₄×C₃₁	—	4	1	no	—
710	D₄×C₃₁	—	4	1	no	—
711	D₄×C₃₁	—	4	1	no	—
712	D₄×C₃₁	—	4	1	no	—
713	D₄×C₃₁	—	4	1	no	—
714	D₄×C₃₁	—	4	1	no	—
715	D₄×C₃₁	—	4	2	no	—
716	D₄×C₃₁	—	8	1	no	—
717	D₄×C₃₁	—	8	1	no	—
718	D₄×C₃₁	—	8	1	no	—
719	D₄×C₃₁	—	8	1	no	—
720	C₂×C₄×C₃₁	—	2	1	no	—
721	C₂×C₄×C₃₁	—	2	1	no	—
722	C₂×C₄×C₃₁	—	2	1	no	—
723	C₂×C₄×C₃₁	—	2	1	no	—
724	C₂×C₄×C₃₁	—	2	1	no	—
725	C₂×C₄×C₃₁	—	2	1	no	—
726	C₂×C₄×C₃₁	—	2	1	no	—
727	C₂×C₄×C₃₁	—	2	1	no	—
728	C₂×C₄×C₃₁	—	2	1	no	—
729	C₂×C₄×C₃₁	—	2	1	no	—
730	C₂×C₄×C₃₁	—	2	1	no	—
731	C₂×C₄×C₃₁	—	2	1	no	—
732	C₂×C₄×C₃₁	—	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	—	4	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	—	8	1	no	—
751	C₂×C₄×C₃₁	—	8	1	no	—
752	C₂×C₄×C₃₁	—	8	1	no	—
753	C₂×C₄×C₃₁	—	8	1	no	—
754	C₂×C₄×C₃₁	—	8	1	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	—	8	1	no	—
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	C₂⁵	1	1	yes	characteristic
771	C₈×C₃₁	—	2	1	no	—
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	#3541	C₂×C₃₁	1	1	yes	characteristic
780	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
781	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
782	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
783	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
784	#3351	C₂×C₃₁	1	1	yes	characteristic, complemented
785	#3350	C₂×C₃₁	1	1	yes	characteristic, complemented
786	#3349	C₂×C₃₁	1	1	yes	characteristic, complemented
787	#3344	C₂×C₃₁	1	1	yes	characteristic, complemented
788	#3344	C₂×C₃₁	1	1	yes	characteristic, complemented
789	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
790	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
791	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
792	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
793	#3316	C₂×C₃₁	1	1	yes	characteristic, complemented
794	#3315	C₂×C₃₁	1	1	yes	characteristic, complemented
795	#3313	C₂×C₃₁	1	1	yes	characteristic, complemented
796	#3312	C₂×C₃₁	1	1	yes	characteristic, complemented
797	#3244	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3242	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3202	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3201	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3196	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3195	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3121	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3099	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#3093	C₂×C₃₁	1	1	yes	characteristic, complemented
809	#2978	C₂×C₃₁	1	1	yes	characteristic, complemented
810	C₂²×C₃₁	—	2	1	no	—
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	—	2	1	no	—
821	C₂²×C₃₁	—	2	1	no	—
822	C₂²×C₃₁	—	2	1	no	—
823	C₂²×C₃₁	—	2	1	no	—
824	C₂²×C₃₁	—	2	1	no	—
825	C₂²×C₃₁	—	4	1	no	—
826	C₂²×C₃₁	—	4	1	no	—
827	C₂²×C₃₁	—	4	1	no	—
828	C₂²×C₃₁	—	8	2	no	—
829	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	1	no	—
839	C₄×C₃₁	—	4	1	no	—
840	C₄×C₃₁	—	4	1	no	—
841	C₄×C₃₁	—	4	1	no	—
842	C₄×C₃₁	—	4	1	no	—
843	C₄×C₃₁	—	4	1	no	—
844	C₄×C₃₁	—	4	1	no	—
845	C₄×C₃₁	—	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	—	4	1	no	—
853	C₄×C₃₁	—	4	1	no	—
854	C₄×C₃₁	#585	1	1	yes	characteristic
855	C₄×C₃₁	#585	1	1	yes	characteristic
856	#563	—	2	1	no	—
857	#562	—	2	1	no	—
858	#556	C₂²×C₃₁	1	1	yes	characteristic
859	#556	C₂²×C₃₁	1	1	yes	characteristic
860	#556	C₂²×C₃₁	1	1	yes	characteristic
861	#554	—	2	1	no	—
862	#554	C₂²×C₃₁	1	1	yes	characteristic
863	#554	C₂²×C₃₁	1	1	yes	characteristic
864	#554	C₂²×C₃₁	1	1	yes	characteristic
865	#553	—	2	1	no	—
866	#553	C₂²×C₃₁	1	1	yes	characteristic
867	#552	—	2	1	no	—
868	#552	—	2	1	no	—
869	#552	C₂²×C₃₁	1	1	yes	characteristic
870	#552	C₂²×C₃₁	1	1	yes	characteristic
871	#552	C₂²×C₃₁	1	1	yes	characteristic
872	#552	C₂²×C₃₁	1	1	yes	characteristic
873	#552	C₂²×C₃₁	1	1	yes	characteristic
874	#551	—	2	1	no	—
875	#551	—	2	1	no	—
876	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
877	#548	C₂²×C₃₁	1	1	yes	characteristic
878	#548	C₂²×C₃₁	1	1	yes	characteristic
879	#547	C₂²×C₃₁	1	1	yes	characteristic
880	#544	C₂²×C₃₁	1	1	yes	characteristic
881	#542	—	2	1	no	—
882	#542	—	2	1	no	—
883	#542	C₂²×C₃₁	1	1	yes	characteristic
884	#541	—	2	1	no	—
885	#541	C₂²×C₃₁	1	1	yes	characteristic
886	#539	—	2	1	no	—
887	#538	—	2	1	no	—
888	#538	—	2	1	no	—
889	#537	C₂²×C₃₁	1	1	yes	characteristic
890	#536	C₂²×C₃₁	1	1	yes	characteristic
891	#536	C₂²×C₃₁	1	1	yes	characteristic
892	#533	—	2	1	no	—
893	#529	—	2	1	no	—
894	#525	C₂²×C₃₁	1	1	yes	characteristic
895	#525	C₂²×C₃₁	1	1	yes	characteristic
896	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
897	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
898	#520	C₂²×C₃₁	1	1	yes	characteristic
899	#519	C₂²×C₃₁	1	1	yes	characteristic
900	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
901	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
902	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
903	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
904	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
905	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
906	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
907	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
908	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
909	#485	C₂²×C₃₁	1	1	yes	characteristic
910	#485	C₂²×C₃₁	1	1	yes	characteristic
911	#485	C₂²×C₃₁	1	1	yes	characteristic
912	#485	C₂²×C₃₁	1	1	yes	characteristic
913	#485	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	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
920	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
921	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
922	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
923	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
924	#484	C₂²×C₃₁	1	1	yes	characteristic
925	#484	C₂²×C₃₁	1	1	yes	characteristic
926	#484	C₂²×C₃₁	1	1	yes	characteristic
927	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
928	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
929	#483	C₂²×C₃₁	1	1	yes	characteristic
930	#483	C₂²×C₃₁	1	1	yes	characteristic
931	#483	C₂²×C₃₁	1	1	yes	characteristic
932	#483	C₂²×C₃₁	1	1	yes	characteristic
933	#483	C₂²×C₃₁	1	1	yes	characteristic
934	#483	C₂²×C₃₁	1	1	yes	characteristic
935	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
936	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
937	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
938	#482	C₂²×C₃₁	1	1	yes	characteristic
939	#482	C₂²×C₃₁	1	1	yes	characteristic
940	#482	C₂²×C₃₁	1	1	yes	characteristic
941	#482	C₂²×C₃₁	1	1	yes	characteristic
942	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
943	#481	C₂²×C₃₁	1	1	yes	characteristic
944	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
945	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
946	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
947	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
948	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
949	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
950	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
951	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
952	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
953	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
954	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
955	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
956	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
957	#470	C₂²×C₃₁	1	1	yes	characteristic
958	#470	C₂²×C₃₁	1	1	yes	characteristic
959	#470	C₂²×C₃₁	1	1	yes	characteristic
960	#470	C₂²×C₃₁	1	1	yes	characteristic
961	#470	C₂²×C₃₁	1	1	yes	characteristic
962	#470	C₂²×C₃₁	1	1	yes	characteristic
963	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
964	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
965	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
966	#468	C₂²×C₃₁	1	1	yes	characteristic
967	#468	C₂²×C₃₁	1	1	yes	characteristic
968	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
969	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
970	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
971	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
972	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
973	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
974	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
975	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
976	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
977	#452	C₂²×C₃₁	1	1	yes	characteristic
978	#452	C₂²×C₃₁	1	1	yes	characteristic
979	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
980	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
981	#451	C₂²×C₃₁	1	1	yes	characteristic
982	#451	C₂²×C₃₁	1	1	yes	characteristic
983	#451	C₂²×C₃₁	1	1	yes	characteristic
984	#451	C₂²×C₃₁	1	1	yes	characteristic
985	#451	C₂²×C₃₁	1	1	yes	characteristic
986	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
987	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
988	#448	C₂²×C₃₁	1	1	yes	characteristic
989	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
990	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
991	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
992	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
993	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
994	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
995	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
996	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
997	#436	C₂²×C₃₁	1	1	yes	characteristic
998	#436	C₂²×C₃₁	1	1	yes	characteristic
999	#436	C₂²×C₃₁	1	1	yes	characteristic
1000	#436	C₂²×C₃₁	1	1	yes	characteristic
1001	#435	C₂²×C₃₁	1	1	yes	characteristic
1002	#435	C₂²×C₃₁	1	1	yes	characteristic
1003	#435	C₂²×C₃₁	1	1	yes	characteristic
1004	#435	C₂²×C₃₁	1	1	yes	characteristic
1005	#433	C₂²×C₃₁	1	1	yes	characteristic
1006	#433	C₂²×C₃₁	1	1	yes	characteristic
1007	#428	C₂²×C₃₁	1	1	yes	characteristic
1008	#428	C₂²×C₃₁	1	1	yes	characteristic
1009	#428	C₂²×C₃₁	1	1	yes	characteristic
1010	#428	C₂²×C₃₁	1	1	yes	characteristic
1011	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1012	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
1013	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
1014	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
1015	#419	C₂²×C₃₁	1	1	yes	characteristic
1016	#419	C₂²×C₃₁	1	1	yes	characteristic
1017	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
1018	#417	C₂²×C₃₁	1	1	yes	characteristic
1019	#417	C₂²×C₃₁	1	1	yes	characteristic
1020	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
1021	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
1022	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
1023	#408	C₂²×C₃₁	1	1	yes	characteristic
1024	#408	C₂²×C₃₁	1	1	yes	characteristic
1025	#407	C₂²×C₃₁	1	1	yes	characteristic
1026	#407	C₂²×C₃₁	1	1	yes	characteristic
1027	C₂×C₃₁	—	4	1	no	—
1028	C₂×C₃₁	—	4	1	no	—
1029	C₂×C₃₁	—	4	1	no	—
1030	C₂×C₃₁	—	4	1	no	—
1031	C₂×C₃₁	—	4	1	no	—
1032	C₂×C₃₁	—	8	1	no	—
1033	C₂×C₃₁	#3485	1	1	yes	characteristic
1034	C₂×C₃₁	#3586	1	1	yes	characteristic
1035	C₂×C₃₁	#3586	1	1	yes	characteristic
1036	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1037	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1038	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1039	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1040	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1041	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1042	C₂³×C₄	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×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1050	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1051	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1052	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1053	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1054	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1055	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1056	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1059	C₄⋊Q₈	—	2	1	no	—
1060	C₄⋊Q₈	—	2	1	no	—
1061	C₄⋊Q₈	—	2	1	no	—
1062	C₄⋊Q₈	—	2	1	no	—
1063	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1064	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1065	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1066	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1067	#126	—	2	1	no	—
1068	#126	—	2	1	no	—
1069	#126	—	2	1	no	—
1070	#126	—	2	1	no	—
1071	#126	—	2	1	no	—
1072	#126	—	2	1	no	—
1073	#126	—	2	1	no	—
1074	#126	—	2	1	no	—
1075	#126	—	2	1	no	—
1076	#126	—	2	1	no	—
1077	#126	—	2	1	no	—
1078	#126	—	2	1	no	—
1079	#126	—	2	1	no	—
1080	#126	—	2	1	no	—
1081	#126	—	2	1	no	—
1082	#125	—	2	1	no	—
1083	#125	—	2	1	no	—
1084	#125	—	2	1	no	—
1085	#125	—	2	1	no	—
1086	#125	—	2	1	no	—
1087	#125	—	2	1	no	—
1088	#125	—	2	1	no	—
1089	#125	—	2	1	no	—
1090	#125	—	2	1	no	—
1091	#125	—	2	1	no	—
1092	#125	—	2	1	no	—
1093	#125	C₂³×C₃₁	1	1	yes	characteristic
1094	#125	C₂³×C₃₁	1	1	yes	characteristic
1095	#125	C₂³×C₃₁	1	1	yes	characteristic
1096	#124	—	2	1	no	—
1097	#124	—	2	1	no	—
1098	#124	—	2	1	no	—
1099	#124	—	2	1	no	—
1100	#124	—	2	1	no	—
1101	#124	—	2	1	no	—
1102	#124	—	2	1	no	—
1103	#124	—	2	1	no	—
1104	#124	C₂³×C₃₁	1	1	yes	characteristic
1105	#123	—	2	1	no	—
1106	#123	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	—	2	1	no	—
1109	#123	—	2	1	no	—
1110	#123	—	2	1	no	—
1111	#123	—	2	1	no	—
1112	#123	—	2	1	no	—
1113	#123	—	2	1	no	—
1114	#123	—	2	1	no	—
1115	#123	—	2	1	no	—
1116	#123	—	2	1	no	—
1117	#123	—	2	1	no	—
1118	#123	—	2	1	no	—
1119	#123	D₄×C₃₁	1	1	yes	characteristic
1120	#123	D₄×C₃₁	1	1	yes	characteristic
1121	C₂²⋊Q₈	—	2	1	no	—
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	—	2	1	no	—
1125	C₂²⋊Q₈	—	2	1	no	—
1126	C₂²⋊Q₈	—	2	1	no	—
1127	C₂²⋊Q₈	—	2	1	no	—
1128	C₂²⋊Q₈	—	2	1	no	—
1129	C₂²⋊Q₈	—	2	1	no	—
1130	C₂²⋊Q₈	—	2	1	no	—
1131	C₂²⋊Q₈	—	2	1	no	—
1132	C₂²⋊Q₈	—	2	1	no	—
1133	C₂²⋊Q₈	—	2	1	no	—
1134	C₂²⋊Q₈	—	2	1	no	—
1135	C₂²⋊Q₈	—	2	1	no	—
1136	C₂²⋊Q₈	—	2	1	no	—
1137	C₂²⋊Q₈	—	2	1	no	—
1138	C₂²⋊Q₈	—	2	1	no	—
1139	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1140	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1141	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1142	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1143	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1144	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1145	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1146	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1147	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1148	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	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1152	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1153	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1154	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1155	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1156	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1157	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1158	#121	—	2	1	no	—
1159	#121	—	2	1	no	—
1160	#121	—	2	1	no	—
1161	#121	—	2	1	no	—
1162	#121	—	2	1	no	—
1163	#121	—	2	1	no	—
1164	#121	—	2	1	no	—
1165	#121	D₄×C₃₁	1	1	yes	characteristic
1166	#121	D₄×C₃₁	1	1	yes	characteristic
1167	#121	C₂³×C₃₁	1	1	yes	characteristic
1168	#121	C₂³×C₃₁	1	1	yes	characteristic
1169	#121	C₂³×C₃₁	1	1	yes	characteristic
1170	#120	—	2	1	no	—
1171	#120	D₄×C₃₁	1	1	yes	characteristic
1172	#120	D₄×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1178	C₄×Q₈	—	2	1	no	—
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×D₄	—	2	1	no	—
1187	C₄×D₄	—	2	1	no	—
1188	C₄×D₄	—	2	1	no	—
1189	C₄×D₄	—	2	1	no	—
1190	C₄×D₄	—	2	1	no	—
1191	C₄×D₄	—	2	1	no	—
1192	C₄×D₄	—	2	1	no	—
1193	C₄×D₄	—	2	1	no	—
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	C₂³×C₃₁	1	1	yes	characteristic
1199	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1200	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1201	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1202	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1203	#117	—	2	1	no	—
1204	#117	—	2	1	no	—
1205	#117	—	2	1	no	—
1206	#117	—	2	1	no	—
1207	#117	—	2	1	no	—
1208	#117	—	2	1	no	—
1209	#117	—	2	1	no	—
1210	#117	—	2	1	no	—
1211	#117	—	2	1	no	—
1212	#117	C₂³×C₃₁	1	1	yes	characteristic
1213	#117	C₂³×C₃₁	1	1	yes	characteristic
1214	#117	C₂³×C₃₁	1	1	yes	characteristic
1215	#117	C₂³×C₃₁	1	1	yes	characteristic
1216	#117	C₂³×C₃₁	1	1	yes	characteristic
1217	#117	C₂³×C₃₁	1	1	yes	characteristic
1218	#117	C₂³×C₃₁	1	1	yes	characteristic
1219	#117	C₂³×C₃₁	1	1	yes	characteristic
1220	#117	C₂³×C₃₁	1	1	yes	characteristic
1221	C₂×C₄⋊C₄	—	2	1	no	—
1222	C₂×C₄⋊C₄	—	2	1	no	—
1223	C₂×C₄⋊C₄	—	2	1	no	—
1224	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1225	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1226	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1227	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1228	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1229	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1230	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1231	C₂×C₂²⋊C₄	—	2	1	no	—
1232	C₂×C₂²⋊C₄	—	2	1	no	—
1233	C₂×C₂²⋊C₄	—	2	1	no	—
1234	C₂×C₄²	—	2	1	no	—
1235	#107	C₂³×C₃₁	1	1	yes	characteristic
1236	#107	C₂³×C₃₁	1	1	yes	characteristic
1237	#107	C₂³×C₃₁	1	1	yes	characteristic
1238	#107	C₂³×C₃₁	1	1	yes	characteristic
1239	#107	C₂³×C₃₁	1	1	yes	characteristic
1240	#107	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	#106	C₂³×C₃₁	1	1	yes	characteristic
1246	#106	C₂³×C₃₁	1	1	yes	characteristic
1247	#106	C₂³×C₃₁	1	1	yes	characteristic
1248	#106	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	#106	C₂³×C₃₁	1	1	yes	characteristic
1258	#106	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	#103	C₂³×C₃₁	1	1	yes	characteristic
1288	#103	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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1302	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1303	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1304	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1305	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1306	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1307	#97	C₂³×C₃₁	1	1	yes	characteristic
1308	#97	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	#61781	1	1	yes	characteristic, direct product factor, Sylow
1312	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
1313	#41	—	4	1	no	—
1314	#41	—	4	1	no	—
1315	#41	—	4	1	no	—
1316	#41	—	4	1	no	—
1317	#41	—	4	1	no	—
1318	#41	—	4	1	no	—
1319	C₂×Q₈	—	2	1	no	—
1320	C₂×Q₈	—	2	1	no	—
1321	C₂×Q₈	—	2	1	no	—
1322	C₂×Q₈	—	2	1	no	—
1323	C₂×Q₈	—	2	1	no	—
1324	C₂×Q₈	—	2	1	no	—
1325	C₂×Q₈	—	4	1	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	—	4	1	no	—
1331	C₂×Q₈	C₂×D₄×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	C₂×D₄×C₃₁	1	1	yes	characteristic
1343	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1344	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂×D₄×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	—	2	1	no	—
1363	C₂²×C₄	—	4	1	no	—
1364	C₂²×C₄	—	4	1	no	—
1365	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1366	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1367	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1368	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1369	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1370	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1371	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1372	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1373	Q₁₆	—	4	1	no	—
1374	Q₁₆	—	4	1	no	—
1375	Q₁₆	—	4	1	no	—
1376	Q₁₆	—	4	1	no	—
1377	Q₁₆	—	4	1	no	—
1378	Q₁₆	—	4	1	no	—
1379	SD₁₆	—	4	1	no	—
1380	SD₁₆	—	4	1	no	—
1381	M₁₆	—	4	1	no	—
1382	M₁₆	—	4	1	no	—
1383	M₁₆	—	4	1	no	—
1384	M₁₆	—	4	1	no	—
1385	M₁₆	—	4	1	no	—
1386	M₁₆	—	4	1	no	—
1387	C₂×C₈	—	4	1	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	C₂⁴×C₃₁	1	1	yes	characteristic
1446	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1447	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1448	C₄⋊C₄	C₂⁴×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	C₂²⋊C₄	—	2	1	no	—
1456	C₂²⋊C₄	—	2	1	no	—
1457	C₂²⋊C₄	—	2	1	no	—
1458	C₂²⋊C₄	—	2	1	no	—
1459	C₂²⋊C₄	—	2	1	no	—
1460	C₂²⋊C₄	—	2	1	no	—
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	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	—	2	1	no	—
1482	C₂²⋊C₄	—	2	1	no	—
1483	C₂²⋊C₄	—	2	1	no	—
1484	C₂²⋊C₄	—	2	1	no	—
1485	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1492	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1493	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1494	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1495	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁴×C₃₁	1	1	yes	characteristic
1512	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1513	C₂³	—	2	1	no	—
1514	C₂³	—	4	1	no	—
1515	C₂³	—	4	1	no	—
1516	C₂³	—	4	1	no	—
1517	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1518	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	—	8	1	no	—
1535	Q₈	—	8	1	no	—
1536	Q₈	—	8	1	no	—
1537	Q₈	—	8	1	no	—
1538	Q₈	—	8	1	no	—
1539	D₄	—	2	1	no	—
1540	D₄	—	2	1	no	—
1541	D₄	—	4	1	no	—
1542	D₄	—	4	1	no	—
1543	D₄	—	4	1	no	—
1544	D₄	—	4	1	no	—
1545	D₄	—	4	1	no	—
1546	D₄	—	4	1	no	—
1547	D₄	—	4	1	no	—
1548	D₄	—	4	2	no	—
1549	D₄	—	8	1	no	—
1550	D₄	—	8	1	no	—
1551	D₄	—	8	1	no	—
1552	D₄	—	8	1	no	—
1553	C₂×C₄	—	2	1	no	—
1554	C₂×C₄	—	2	1	no	—
1555	C₂×C₄	—	2	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	—	2	1	no	—
1577	C₂×C₄	—	2	1	no	—
1578	C₂×C₄	—	4	1	no	—
1579	C₂×C₄	—	4	1	no	—
1580	C₂×C₄	—	4	1	no	—
1581	C₂×C₄	—	4	2	no	—
1582	C₂×C₄	—	4	2	no	—
1583	C₂×C₄	—	8	1	no	—
1584	C₂×C₄	—	8	1	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	—	8	1	no	—
1591	C₂×C₄	—	8	1	no	—
1592	C₂×C₄	—	8	1	no	—
1593	C₂×C₄	—	8	1	no	—
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	C₂²×D₄×C₃₁	1	1	yes	characteristic
1602	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1603	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1610	C₈	—	2	1	no	—
1611	C₈	—	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	—	2	1	no	—
1620	C₂²	—	2	1	no	—
1621	C₂²	—	2	1	no	—
1622	C₂²	—	2	1	no	—
1623	C₂²	—	2	1	no	—
1624	C₂²	—	2	1	no	—
1625	C₂²	—	2	1	no	—
1626	C₂²	—	2	1	no	—
1627	C₂²	—	4	1	no	—
1628	C₂²	—	4	1	no	—
1629	C₂²	—	4	1	no	—
1630	C₂²	—	8	2	no	—
1631	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
1640	C₄	—	2	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	—	4	1	no	—
1652	C₄	—	4	1	no	—
1653	C₄	—	4	1	no	—
1654	C₄	—	4	1	no	—
1655	C₄	—	4	1	no	—
1656	C₄	C₃₁×#585	1	1	yes	characteristic
1657	C₄	C₃₁×#585	1	1	yes	characteristic
1658	C₂	—	4	1	no	—
1659	C₂	—	4	1	no	—
1660	C₂	—	4	1	no	—
1661	C₂	—	4	1	no	—
1662	C₂	—	4	1	no	—
1663	C₂	—	8	1	no	—
1664	C₂	C₃₁×#3485	1	1	yes	characteristic
1665	C₂	C₃₁×#3586	1	1	yes	characteristic
1666	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×#3541	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3495	C₂	semidirect
3. C₃₁×#3356	C₂	semidirect
4. C₃₁×#3356	C₂	semidirect
5. C₃₁×#3352	C₂	semidirect
6. C₃₁×#3351	C₂	semidirect
7. C₃₁×#3350	C₂	semidirect
8. C₃₁×#3349	C₂	semidirect
9. C₃₁×#3344	C₂	semidirect
10. C₃₁×#3344	C₂	semidirect
11. C₃₁×#3331	C₂	semidirect
12. C₃₁×#3328	C₂	semidirect
13. C₃₁×#3327	C₂	semidirect
14. C₃₁×#3327	C₂	semidirect
15. C₃₁×#3316	C₂	semidirect
16. C₃₁×#3315	C₂	semidirect
17. C₃₁×#3313	C₂	semidirect
18. C₃₁×#3312	C₂	semidirect
19. C₃₁×#3244	C₂	semidirect
20. C₃₁×#3242	C₂	semidirect
21. C₃₁×#3202	C₂	semidirect
22. C₃₁×#3201	C₂	semidirect
23. C₃₁×#3196	C₂	semidirect
24. C₃₁×#3195	C₂	semidirect
25. C₃₁×#3127	C₂	semidirect
26. C₃₁×#3121	C₂	semidirect
27. C₃₁×#3099	C₂	semidirect
28. C₃₁×#3097	C₂	semidirect
29. C₃₁×#3095	C₂	semidirect
30. C₃₁×#3093	C₂	semidirect
31. C₃₁×#2978	C₂	semidirect
77. C₃₁×#501	C₂²	semidirect
78. C₃₁×#501	C₂²	semidirect
79. C₃₁×#499	C₂²	semidirect
80. C₃₁×#498	C₂²	semidirect
81. C₃₁×#491	C₂²	semidirect
82. C₃₁×#489	C₂²	semidirect
83. C₃₁×#488	C₂²	semidirect
84. C₃₁×#487	C₂²	semidirect
95. C₃₁×#485	C₂²	semidirect
96. C₃₁×#485	C₂²	semidirect
97. C₃₁×#485	C₂²	semidirect
98. C₃₁×#485	C₂²	semidirect
99. C₃₁×#485	C₂²	semidirect
103. C₃₁×#484	C₂²	semidirect
104. C₃₁×#484	C₂²	semidirect
111. C₃₁×#483	C₂²	semidirect
112. C₃₁×#483	C₂²	semidirect
113. C₃₁×#483	C₂²	semidirect
118. C₃₁×#482	C₂²	semidirect
120. C₃₁×#481	C₂²	semidirect
121. C₃₁×#479	C₂²	semidirect
122. C₃₁×#479	C₂²	semidirect
123. C₃₁×#479	C₂²	semidirect
124. C₃₁×#479	C₂²	semidirect
125. C₃₁×#479	C₂²	semidirect
126. C₃₁×#478	C₂²	semidirect
127. C₃₁×#477	C₂²	semidirect
128. C₃₁×#477	C₂²	semidirect
129. C₃₁×#476	C₂²	semidirect
130. C₃₁×#475	C₂²	semidirect
131. C₃₁×#475	C₂²	semidirect
132. C₃₁×#475	C₂²	semidirect
139. C₃₁×#470	C₂²	semidirect
140. C₃₁×#470	C₂²	semidirect
141. C₃₁×#470	C₂²	semidirect
144. C₃₁×#468	C₂²	semidirect
145. C₃₁×#467	C₂²	semidirect
146. C₃₁×#467	C₂²	semidirect
147. C₃₁×#467	C₂²	semidirect
148. C₃₁×#465	C₂²	semidirect
149. C₃₁×#464	C₂²	semidirect
150. C₃₁×#464	C₂²	semidirect
151. C₃₁×#462	C₂²	semidirect
152. C₃₁×#462	C₂²	semidirect
155. C₃₁×#452	C₂²	semidirect
156. C₃₁×#452	C₂²	semidirect
162. C₃₁×#451	C₂²	semidirect
163. C₃₁×#451	C₂²	semidirect
165. C₃₁×#441	C₂²	semidirect
166. C₃₁×#441	C₂²	semidirect
167. C₃₁×#441	C₂²	semidirect
168. C₃₁×#440	C₂²	semidirect
169. C₄×Q₁₆×C₃₁	C₂²	semidirect
170. C₄×Q₁₆×C₃₁	C₂²	semidirect
171. C₄×Q₁₆×C₃₁	C₂²	semidirect
172. C₄×SD₁₆×C₃₁	C₂²	semidirect
187. C₃₁×#428	C₂²	semidirect
188. C₃₁×#428	C₂²	semidirect
189. C₃₁×#427	C₂²	semidirect
190. C₂×C₃₁×#106	C₂²	semidirect
193. C₃₁×#419	C₂²	semidirect
196. C₃₁×#417	C₂²	semidirect
197. C₃₁×#416	C₂²	semidirect
198. C₂×C₃₁×#103	C₂²	semidirect
679. #61781	C₃₁	direct (N × H)
780. #3495	C₂×C₃₁	semidirect
781. #3356	C₂×C₃₁	semidirect
782. #3356	C₂×C₃₁	semidirect
783. #3352	C₂×C₃₁	semidirect
784. #3351	C₂×C₃₁	semidirect
785. #3350	C₂×C₃₁	semidirect
786. #3349	C₂×C₃₁	semidirect
787. #3344	C₂×C₃₁	semidirect
788. #3344	C₂×C₃₁	semidirect
789. #3331	C₂×C₃₁	semidirect
790. #3328	C₂×C₃₁	semidirect
791. #3327	C₂×C₃₁	semidirect
792. #3327	C₂×C₃₁	semidirect
793. #3316	C₂×C₃₁	semidirect
794. #3315	C₂×C₃₁	semidirect
795. #3313	C₂×C₃₁	semidirect
796. #3312	C₂×C₃₁	semidirect
797. #3244	C₂×C₃₁	semidirect
798. #3242	C₂×C₃₁	semidirect
799. #3202	C₂×C₃₁	semidirect
800. #3201	C₂×C₃₁	semidirect
801. #3196	C₂×C₃₁	semidirect
802. #3195	C₂×C₃₁	semidirect
803. #3127	C₂×C₃₁	semidirect
804. #3121	C₂×C₃₁	semidirect
805. #3099	C₂×C₃₁	semidirect
806. #3097	C₂×C₃₁	semidirect
807. #3095	C₂×C₃₁	semidirect
808. #3093	C₂×C₃₁	semidirect
809. #2978	C₂×C₃₁	semidirect
901. #501	C₂²×C₃₁	semidirect
902. #501	C₂²×C₃₁	semidirect
903. #499	C₂²×C₃₁	semidirect
904. #498	C₂²×C₃₁	semidirect
905. #491	C₂²×C₃₁	semidirect
906. #489	C₂²×C₃₁	semidirect
907. #488	C₂²×C₃₁	semidirect
908. #487	C₂²×C₃₁	semidirect
919. #485	C₂²×C₃₁	semidirect
920. #485	C₂²×C₃₁	semidirect
921. #485	C₂²×C₃₁	semidirect
922. #485	C₂²×C₃₁	semidirect
923. #485	C₂²×C₃₁	semidirect
927. #484	C₂²×C₃₁	semidirect
928. #484	C₂²×C₃₁	semidirect
935. #483	C₂²×C₃₁	semidirect
936. #483	C₂²×C₃₁	semidirect
937. #483	C₂²×C₃₁	semidirect
942. #482	C₂²×C₃₁	semidirect
944. #481	C₂²×C₃₁	semidirect
945. #479	C₂²×C₃₁	semidirect
946. #479	C₂²×C₃₁	semidirect
947. #479	C₂²×C₃₁	semidirect
948. #479	C₂²×C₃₁	semidirect
949. #479	C₂²×C₃₁	semidirect
950. #478	C₂²×C₃₁	semidirect
951. #477	C₂²×C₃₁	semidirect
952. #477	C₂²×C₃₁	semidirect
953. #476	C₂²×C₃₁	semidirect
954. #475	C₂²×C₃₁	semidirect
955. #475	C₂²×C₃₁	semidirect
956. #475	C₂²×C₃₁	semidirect
963. #470	C₂²×C₃₁	semidirect
964. #470	C₂²×C₃₁	semidirect
965. #470	C₂²×C₃₁	semidirect
968. #468	C₂²×C₃₁	semidirect
969. #467	C₂²×C₃₁	semidirect
970. #467	C₂²×C₃₁	semidirect
971. #467	C₂²×C₃₁	semidirect
972. #465	C₂²×C₃₁	semidirect
973. #464	C₂²×C₃₁	semidirect
974. #464	C₂²×C₃₁	semidirect
975. #462	C₂²×C₃₁	semidirect
976. #462	C₂²×C₃₁	semidirect
979. #452	C₂²×C₃₁	semidirect
980. #452	C₂²×C₃₁	semidirect
986. #451	C₂²×C₃₁	semidirect
987. #451	C₂²×C₃₁	semidirect
989. #441	C₂²×C₃₁	semidirect
990. #441	C₂²×C₃₁	semidirect
991. #441	C₂²×C₃₁	semidirect
992. #440	C₂²×C₃₁	semidirect
993. C₄×Q₁₆	C₂²×C₃₁	semidirect
994. C₄×Q₁₆	C₂²×C₃₁	semidirect
995. C₄×Q₁₆	C₂²×C₃₁	semidirect
996. C₄×SD₁₆	C₂²×C₃₁	semidirect
1011. #428	C₂²×C₃₁	semidirect
1012. #428	C₂²×C₃₁	semidirect
1013. #427	C₂²×C₃₁	semidirect
1014. C₂×#106	C₂²×C₃₁	semidirect
1017. #419	C₂²×C₃₁	semidirect
1020. #417	C₂²×C₃₁	semidirect
1021. #416	C₂²×C₃₁	semidirect
1022. C₂×#103	C₂²×C₃₁	semidirect
1311. C₃₁	#61781	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×#3541	2
C₃₁×#3495	2
C₃₁×#3356	2
C₃₁×#3352	2
C₃₁×#3351	2
C₃₁×#3350	2
C₃₁×#3349	2
C₃₁×#3344	2
C₃₁×#3331	2
C₃₁×#3328	2
C₃₁×#3327	2
C₃₁×#3316	2
C₃₁×#3315	2
C₃₁×#3313	2
C₃₁×#3312	2
C₃₁×#3244	2
C₃₁×#3242	2
C₃₁×#3202	2
C₃₁×#3201	2
C₃₁×#3196	2
C₃₁×#3195	2
C₃₁×#3127	2
C₃₁×#3121	2
C₃₁×#3099	2
C₃₁×#3097	2
C₃₁×#3095	2
C₃₁×#3093	2
C₃₁×#2978	2
#61781	31

Subgroups — C31×#61781 #21518540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61781 #21518540