Subgroups — C₃₁×#61516 #21518275

Order 7936.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1708 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, complemented
2	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3371	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3343	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3321	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3316	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3309	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3308	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3277	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3271	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3271	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3179	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3173	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#3124	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#3121	C₂	1	1	yes	maximal, characteristic, complemented
25	C₃₁×#3119	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#3117	C₂	1	1	yes	maximal, characteristic, complemented
27	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#2967	C₂	1	1	yes	maximal, characteristic, complemented
29	C₃₁×#2951	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	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
35	C₃₁×#559	—	2	1	no	—
36	C₃₁×#559	—	2	1	no	—
37	C₃₁×#559	C₂²	1	1	yes	characteristic
38	C₃₁×#559	C₂²	1	1	yes	characteristic
39	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#557	C₂²	1	1	yes	characteristic
41	C₃₁×#555	—	2	1	no	—
42	C₃₁×#555	C₂²	1	1	yes	characteristic
43	C₃₁×#554	—	2	1	no	—
44	C₃₁×#554	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	C₂²	1	1	yes	characteristic
49	C₃₁×#550	C₂²	1	1	yes	characteristic
50	C₃₁×#550	C₂²	1	1	yes	characteristic
51	C₃₁×#548	C₂²	1	1	yes	characteristic
52	C₃₁×#548	C₂²	1	1	yes	characteristic
53	C₃₁×#548	C₂²	1	1	yes	characteristic
54	C₃₁×#548	C₂²	1	1	yes	characteristic
55	C₃₁×#547	—	2	1	no	—
56	C₃₁×#547	—	2	1	no	—
57	C₃₁×#547	C₂²	1	1	yes	characteristic
58	C₃₁×#547	C₂²	1	1	yes	characteristic
59	C₃₁×#542	—	2	1	no	—
60	C₃₁×#542	—	2	1	no	—
61	C₃₁×#542	—	2	1	no	—
62	C₃₁×#542	C₂²	1	1	yes	characteristic
63	C₃₁×#542	C₂²	1	1	yes	characteristic
64	C₃₁×#542	C₂²	1	1	yes	characteristic
65	C₃₁×#540	—	2	1	no	—
66	C₃₁×#540	C₂²	1	1	yes	characteristic
67	C₃₁×#532	—	2	1	no	—
68	C₃₁×#532	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×#520	C₂²	1	1	yes	characteristic
76	C₃₁×#520	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×#498	C₂²	1	1	yes	characteristic
83	C₃₁×#496	C₂²	1	1	yes	characteristic
84	C₃₁×#496	C₂²	1	1	yes	characteristic
85	C₃₁×#495	C₂²	1	1	yes	characteristic
86	C₃₁×#490	C₂²	1	1	yes	characteristic
87	C₃₁×#489	C₂²	1	1	yes	characteristic
88	C₃₁×#489	C₂²	1	1	yes	characteristic
89	C₃₁×#489	C₂²	1	1	yes	characteristic
90	C₃₁×#488	C₂²	1	1	yes	characteristic
91	C₃₁×#486	C₂²	1	1	yes	characteristic
92	C₃₁×#485	C₂²	1	1	yes	characteristic
93	C₃₁×#484	C₂²	1	1	yes	characteristic
94	C₃₁×#484	C₂²	1	1	yes	characteristic
95	C₃₁×#483	C₂²	1	1	yes	characteristic
96	C₃₁×#482	C₂²	1	1	yes	characteristic
97	C₃₁×#482	C₂²	1	1	yes	characteristic
98	C₃₁×#482	C₂²	1	1	yes	characteristic
99	C₃₁×#481	C₂²	1	1	yes	characteristic
100	C₃₁×#481	C₂²	1	1	yes	characteristic
101	C₃₁×#481	C₂²	1	1	yes	characteristic
102	C₃₁×#480	C₂²	1	1	yes	characteristic
103	C₃₁×#480	C₂²	1	1	yes	characteristic
104	C₃₁×#479	C₂²	1	1	yes	characteristic
105	C₃₁×#479	C₂²	1	1	yes	characteristic
106	C₃₁×#479	C₂²	1	1	yes	characteristic
107	C₃₁×#478	C₂²	1	1	yes	characteristic
108	C₃₁×#477	C₂²	1	1	yes	characteristic
109	C₃₁×#477	C₂²	1	1	yes	characteristic
110	C₃₁×#476	C₂²	1	1	yes	characteristic
111	C₃₁×#475	C₂²	1	1	yes	characteristic
112	C₃₁×#475	C₂²	1	1	yes	characteristic
113	C₃₁×#475	C₂²	1	1	yes	characteristic
114	C₃₁×#474	C₂²	1	1	yes	characteristic
115	C₃₁×#474	C₂²	1	1	yes	characteristic
116	C₃₁×#470	C₂²	1	1	yes	characteristic
117	C₃₁×#469	C₂²	1	1	yes	characteristic
118	C₃₁×#469	C₂²	1	1	yes	characteristic
119	C₃₁×#469	C₂²	1	1	yes	characteristic
120	C₃₁×#469	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×#466	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×#464	C₂²	1	1	yes	characteristic
133	C₃₁×#464	C₂²	1	1	yes	characteristic
134	C₃₁×#463	C₂²	1	1	yes	characteristic
135	C₃₁×#463	C₂²	1	1	yes	characteristic
136	C₃₁×#460	C₂²	1	1	yes	characteristic
137	C₃₁×#460	C₂²	1	1	yes	characteristic
138	C₃₁×#459	C₂²	1	1	yes	characteristic
139	C₃₁×#459	C₂²	1	1	yes	characteristic
140	C₃₁×#452	C₂²	1	1	yes	characteristic
141	C₃₁×#452	C₂²	1	1	yes	characteristic
142	C₃₁×#451	C₂²	1	1	yes	characteristic
143	C₃₁×#451	C₂²	1	1	yes	characteristic
144	C₃₁×#449	C₂²	1	1	yes	characteristic
145	C₃₁×#449	C₂²	1	1	yes	characteristic
146	C₃₁×#449	C₂²	1	1	yes	characteristic
147	C₃₁×#449	C₂²	1	1	yes	characteristic
148	C₃₁×#449	C₂²	1	1	yes	characteristic
149	C₃₁×#449	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×#442	C₂²	1	1	yes	characteristic
155	C₃₁×#442	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×#440	C₂²	1	1	yes	characteristic
162	C₃₁×#440	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×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
179	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
180	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
181	C₄×D₈×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	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
194	C₃₁×#419	C₂²	1	1	yes	characteristic
195	C₃₁×#417	C₂²	1	1	yes	characteristic
196	C₃₁×#417	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	—	2	1	no	—
204	C₂×#41×C₃₁	—	2	1	no	—
205	C₂×#41×C₃₁	—	2	1	no	—
206	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
209	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₃₁×#137	—	2	4	no	—
213	C₃₁×#137	—	2	4	no	—
214	C₃₁×#135	—	2	4	no	—
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×SD₁₆×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×D₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
235	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
236	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₃₁×C₄⋊Q₈	—	2	1	no	—
238	C₃₁×C₄⋊Q₈	—	2	1	no	—
239	C₃₁×C₄⋊Q₈	—	2	1	no	—
240	C₃₁×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
245	C₃₁×#127	—	2	1	no	—
246	C₃₁×#127	—	2	1	no	—
247	C₃₁×#127	C₂³	1	1	yes	characteristic
248	C₃₁×#127	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
256	C₃₁×#126	D₄	1	1	yes	characteristic
257	C₃₁×#125	—	2	1	no	—
258	C₃₁×#125	—	2	1	no	—
259	C₃₁×#125	—	2	1	no	—
260	C₃₁×#125	—	2	1	no	—
261	C₃₁×#125	D₄	1	1	yes	characteristic
262	C₃₁×#125	C₂³	1	1	yes	characteristic
263	C₃₁×#125	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
272	C₃₁×#124	—	2	1	no	—
273	C₃₁×#124	—	2	1	no	—
274	C₃₁×#124	—	2	1	no	—
275	C₃₁×#124	—	2	1	no	—
276	C₃₁×#124	D₄	1	1	yes	characteristic
277	C₃₁×#124	C₂³	1	1	yes	characteristic
278	C₃₁×#124	C₂³	1	1	yes	characteristic
279	C₃₁×#124	C₂³	1	1	yes	characteristic
280	C₃₁×#124	C₂³	1	1	yes	characteristic
281	C₃₁×#123	—	2	1	no	—
282	C₃₁×#123	—	2	1	no	—
283	C₃₁×#123	—	2	1	no	—
284	C₃₁×#123	—	2	1	no	—
285	C₃₁×#123	—	2	1	no	—
286	C₃₁×#123	—	2	1	no	—
287	C₃₁×#123	—	2	1	no	—
288	C₃₁×#123	—	2	1	no	—
289	C₃₁×#123	—	2	1	no	—
290	C₃₁×#123	—	2	1	no	—
291	C₃₁×#123	—	2	1	no	—
292	C₃₁×#123	—	2	1	no	—
293	C₃₁×#123	—	2	1	no	—
294	C₃₁×#123	—	2	1	no	—
295	C₃₁×#123	—	2	1	no	—
296	C₃₁×#123	—	2	1	no	—
297	C₃₁×#123	D₄	1	1	yes	characteristic
298	C₃₁×#123	D₄	1	1	yes	characteristic
299	C₃₁×C₂²⋊Q₈	—	2	1	no	—
300	C₃₁×C₂²⋊Q₈	—	2	1	no	—
301	C₃₁×C₂²⋊Q₈	—	2	1	no	—
302	C₃₁×C₂²⋊Q₈	—	2	1	no	—
303	C₃₁×C₂²⋊Q₈	—	2	1	no	—
304	C₃₁×C₂²⋊Q₈	—	2	1	no	—
305	C₃₁×C₂²⋊Q₈	—	2	1	no	—
306	C₃₁×C₂²⋊Q₈	—	2	1	no	—
307	C₃₁×C₂²⋊Q₈	—	2	1	no	—
308	C₃₁×C₂²⋊Q₈	—	2	1	no	—
309	C₃₁×C₂²⋊Q₈	—	2	1	no	—
310	C₃₁×C₂²⋊Q₈	D₄	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×#121	—	2	1	no	—
316	C₃₁×#121	—	2	1	no	—
317	C₃₁×#121	—	2	1	no	—
318	C₃₁×#121	—	2	1	no	—
319	C₃₁×#121	—	2	1	no	—
320	C₃₁×#121	—	2	1	no	—
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	D₄	1	1	yes	characteristic
329	C₃₁×#121	C₂³	1	1	yes	characteristic
330	C₃₁×#121	C₂³	1	1	yes	characteristic
331	C₃₁×#121	C₂³	1	1	yes	characteristic
332	C₃₁×#121	C₂³	1	1	yes	characteristic
333	C₃₁×#121	C₂³	1	1	yes	characteristic
334	C₃₁×#121	C₂³	1	1	yes	characteristic
335	C₃₁×#121	C₂³	1	1	yes	characteristic
336	C₃₁×#121	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
347	C₄×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×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	—	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	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
385	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
386	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
397	C₃₁×#117	C₂³	1	1	yes	characteristic
398	C₃₁×#117	C₂³	1	1	yes	characteristic
399	C₃₁×#117	C₂³	1	1	yes	characteristic
400	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
405	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	1	yes	characteristic
450	C₃₁×#102	C₂³	1	1	yes	characteristic
451	C₃₁×#102	C₂³	1	1	yes	characteristic
452	C₃₁×#102	C₂³	1	1	yes	characteristic
453	C₃₁×#102	C₂³	1	1	yes	characteristic
454	C₃₁×#102	C₂³	1	1	yes	characteristic
455	C₃₁×#102	C₂³	1	1	yes	characteristic
456	C₃₁×#102	C₂³	1	1	yes	characteristic
457	C₃₁×#102	C₂³	1	1	yes	characteristic
458	C₃₁×#102	C₂³	1	1	yes	characteristic
459	C₃₁×#102	C₂³	1	1	yes	characteristic
460	C₃₁×#102	C₂³	1	1	yes	characteristic
461	C₃₁×#102	C₂³	1	1	yes	characteristic
462	C₃₁×#102	C₂³	1	1	yes	characteristic
463	C₃₁×#102	C₂³	1	1	yes	characteristic
464	C₃₁×#102	C₂³	1	1	yes	characteristic
465	C₃₁×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	—	2	2	no	—
484	#41×C₃₁	—	2	2	no	—
485	#41×C₃₁	—	4	1	no	—
486	#41×C₃₁	—	4	1	no	—
487	#41×C₃₁	—	4	1	no	—
488	#41×C₃₁	—	4	1	no	—
489	#41×C₃₁	—	8	2	no	—
490	#41×C₃₁	—	8	2	no	—
491	#41×C₃₁	—	8	2	no	—
492	C₂×Q₈×C₃₁	—	2	1	no	—
493	C₂×Q₈×C₃₁	—	2	1	no	—
494	C₂×Q₈×C₃₁	—	2	1	no	—
495	C₂×Q₈×C₃₁	—	2	1	no	—
496	C₂×Q₈×C₃₁	—	2	1	no	—
497	C₂×Q₈×C₃₁	—	2	1	no	—
498	C₂×Q₈×C₃₁	—	2	2	no	—
499	C₂×Q₈×C₃₁	—	2	2	no	—
500	C₂×Q₈×C₃₁	—	4	1	no	—
501	C₂×Q₈×C₃₁	—	4	1	no	—
502	C₂×Q₈×C₃₁	C₂×D₄	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×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
515	C₂×D₄×C₃₁	—	2	1	no	—
516	C₂×D₄×C₃₁	—	2	1	no	—
517	C₂×D₄×C₃₁	—	2	1	no	—
518	C₂×D₄×C₃₁	—	2	1	no	—
519	C₂×D₄×C₃₁	—	2	1	no	—
520	C₂×D₄×C₃₁	—	2	1	no	—
521	C₂×D₄×C₃₁	—	2	1	no	—
522	C₂×D₄×C₃₁	—	2	1	no	—
523	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
524	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
525	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
526	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
527	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
528	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
529	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
530	C₂²×C₄×C₃₁	—	2	1	no	—
531	C₂²×C₄×C₃₁	—	2	1	no	—
532	C₂²×C₄×C₃₁	—	2	1	no	—
533	C₂²×C₄×C₃₁	—	2	1	no	—
534	C₂²×C₄×C₃₁	—	2	1	no	—
535	C₂²×C₄×C₃₁	—	2	1	no	—
536	C₂²×C₄×C₃₁	—	2	1	no	—
537	C₂²×C₄×C₃₁	—	2	1	no	—
538	C₂²×C₄×C₃₁	—	2	1	no	—
539	C₂²×C₄×C₃₁	—	2	1	no	—
540	C₂²×C₄×C₃₁	—	2	1	no	—
541	C₂²×C₄×C₃₁	—	2	1	no	—
542	C₂²×C₄×C₃₁	—	2	1	no	—
543	C₂²×C₄×C₃₁	—	2	1	no	—
544	C₂²×C₄×C₃₁	—	2	1	no	—
545	C₂²×C₄×C₃₁	—	2	1	no	—
546	C₂²×C₄×C₃₁	—	2	1	no	—
547	C₂²×C₄×C₃₁	—	2	1	no	—
548	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
549	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
550	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
551	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
552	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
553	Q₁₆×C₃₁	—	2	2	no	—
554	Q₁₆×C₃₁	—	2	2	no	—
555	Q₁₆×C₃₁	—	4	1	no	—
556	Q₁₆×C₃₁	#41	1	4	yes	complemented
557	SD₁₆×C₃₁	—	2	2	no	—
558	SD₁₆×C₃₁	—	2	2	no	—
559	SD₁₆×C₃₁	—	2	2	no	—
560	SD₁₆×C₃₁	—	2	2	no	—
561	SD₁₆×C₃₁	—	2	2	no	—
562	SD₁₆×C₃₁	—	2	2	no	—
563	SD₁₆×C₃₁	—	4	1	no	—
564	SD₁₆×C₃₁	—	4	1	no	—
565	D₈×C₃₁	—	2	2	no	—
566	D₈×C₃₁	—	4	1	no	—
567	D₈×C₃₁	—	4	1	no	—
568	D₈×C₃₁	—	4	1	no	—
569	M₁₆×C₃₁	—	2	2	no	—
570	M₁₆×C₃₁	—	2	2	no	—
571	M₁₆×C₃₁	—	4	1	no	—
572	M₁₆×C₃₁	—	4	1	no	—
573	C₂×C₈×C₃₁	—	2	2	no	—
574	C₂×C₈×C₃₁	—	4	1	no	—
575	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
576	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
577	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
578	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
579	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
580	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
581	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
582	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
583	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	—	2	1	no	—
609	C₄⋊C₄×C₃₁	—	2	1	no	—
610	C₄⋊C₄×C₃₁	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
619	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
620	C₄⋊C₄×C₃₁	C₂×D₄	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	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
627	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
628	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
653	C₂²⋊C₄×C₃₁	—	2	1	no	—
654	C₂²⋊C₄×C₃₁	—	2	1	no	—
655	C₂²⋊C₄×C₃₁	—	2	1	no	—
656	C₂²⋊C₄×C₃₁	—	2	1	no	—
657	C₂²⋊C₄×C₃₁	—	2	1	no	—
658	C₂²⋊C₄×C₃₁	—	2	1	no	—
659	C₂²⋊C₄×C₃₁	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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
663	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
664	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
665	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
666	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
667	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
668	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
681	C₄²×C₃₁	—	2	1	no	—
682	C₄²×C₃₁	—	2	1	no	—
683	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
684	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
685	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
686	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
687	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
688	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
689	#61516	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
690	C₂³×C₃₁	—	2	1	no	—
691	C₂³×C₃₁	—	2	1	no	—
692	C₂³×C₃₁	—	2	1	no	—
693	C₂³×C₃₁	—	2	1	no	—
694	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
695	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
696	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
703	Q₈×C₃₁	—	4	1	no	—
704	Q₈×C₃₁	—	4	2	no	—
705	Q₈×C₃₁	—	4	2	no	—
706	Q₈×C₃₁	—	8	1	no	—
707	Q₈×C₃₁	—	8	1	no	—
708	Q₈×C₃₁	—	8	1	no	—
709	Q₈×C₃₁	—	8	1	no	—
710	Q₈×C₃₁	C₂×#41	1	2	yes	—
711	Q₈×C₃₁	C₂×#41	1	2	yes	—
712	D₄×C₃₁	—	2	1	no	—
713	D₄×C₃₁	—	2	1	no	—
714	D₄×C₃₁	—	2	1	no	—
715	D₄×C₃₁	—	2	1	no	—
716	D₄×C₃₁	—	2	1	no	—
717	D₄×C₃₁	—	2	1	no	—
718	D₄×C₃₁	—	2	1	no	—
719	D₄×C₃₁	—	2	1	no	—
720	D₄×C₃₁	—	4	1	no	—
721	D₄×C₃₁	—	4	1	no	—
722	D₄×C₃₁	—	4	1	no	—
723	D₄×C₃₁	—	4	2	no	—
724	D₄×C₃₁	—	4	2	no	—
725	D₄×C₃₁	—	4	2	no	—
726	D₄×C₃₁	—	4	2	no	—
727	D₄×C₃₁	—	4	2	no	—
728	D₄×C₃₁	—	4	2	no	—
729	D₄×C₃₁	—	4	2	no	—
730	D₄×C₃₁	—	8	1	no	—
731	D₄×C₃₁	—	8	1	no	—
732	D₄×C₃₁	—	8	1	no	—
733	D₄×C₃₁	—	8	1	no	—
734	D₄×C₃₁	—	8	1	no	—
735	D₄×C₃₁	—	8	1	no	—
736	D₄×C₃₁	—	8	1	no	—
737	D₄×C₃₁	—	8	1	no	—
738	D₄×C₃₁	—	8	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	—	2	1	no	—
747	C₂×C₄×C₃₁	—	2	1	no	—
748	C₂×C₄×C₃₁	—	2	1	no	—
749	C₂×C₄×C₃₁	—	2	1	no	—
750	C₂×C₄×C₃₁	—	2	1	no	—
751	C₂×C₄×C₃₁	—	2	1	no	—
752	C₂×C₄×C₃₁	—	2	1	no	—
753	C₂×C₄×C₃₁	—	2	1	no	—
754	C₂×C₄×C₃₁	—	2	1	no	—
755	C₂×C₄×C₃₁	—	2	1	no	—
756	C₂×C₄×C₃₁	—	2	1	no	—
757	C₂×C₄×C₃₁	—	4	1	no	—
758	C₂×C₄×C₃₁	—	4	1	no	—
759	C₂×C₄×C₃₁	—	4	2	no	—
760	C₂×C₄×C₃₁	—	4	2	no	—
761	C₂×C₄×C₃₁	—	4	2	no	—
762	C₂×C₄×C₃₁	—	4	2	no	—
763	C₂×C₄×C₃₁	—	4	2	no	—
764	C₂×C₄×C₃₁	—	4	2	no	—
765	C₂×C₄×C₃₁	—	4	2	no	—
766	C₂×C₄×C₃₁	—	8	1	no	—
767	C₂×C₄×C₃₁	—	8	1	no	—
768	C₂×C₄×C₃₁	—	8	1	no	—
769	C₂×C₄×C₃₁	—	8	1	no	—
770	C₂×C₄×C₃₁	—	8	1	no	—
771	C₂×C₄×C₃₁	—	8	1	no	—
772	C₂×C₄×C₃₁	—	8	1	no	—
773	C₂×C₄×C₃₁	—	8	1	no	—
774	C₂×C₄×C₃₁	—	8	1	no	—
775	C₂×C₄×C₃₁	—	8	1	no	—
776	C₂×C₄×C₃₁	—	8	1	no	—
777	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
778	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
779	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
780	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
781	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
782	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
788	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
789	C₈×C₃₁	—	2	1	no	—
790	C₈×C₃₁	—	2	1	no	—
791	C₈×C₃₁	—	2	1	no	—
792	C₈×C₃₁	—	2	1	no	—
793	C₈×C₃₁	—	2	1	no	—
794	C₈×C₃₁	—	2	1	no	—
795	C₈×C₃₁	—	2	1	no	—
796	C₈×C₃₁	C₂×#41	1	2	yes	—
797	#3524	C₂×C₃₁	1	1	yes	characteristic, complemented
798	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
799	#3403	C₂×C₃₁	1	1	yes	characteristic, complemented
800	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
801	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
802	#3371	C₂×C₃₁	1	1	yes	characteristic, complemented
803	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
804	#3346	C₂×C₃₁	1	1	yes	characteristic, complemented
805	#3343	C₂×C₃₁	1	1	yes	characteristic, complemented
806	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
807	#3327	C₂×C₃₁	1	1	yes	characteristic, complemented
808	#3321	C₂×C₃₁	1	1	yes	characteristic, complemented
809	#3316	C₂×C₃₁	1	1	yes	characteristic, complemented
810	#3309	C₂×C₃₁	1	1	yes	characteristic, complemented
811	#3308	C₂×C₃₁	1	1	yes	characteristic, complemented
812	#3277	C₂×C₃₁	1	1	yes	characteristic, complemented
813	#3271	C₂×C₃₁	1	1	yes	characteristic, complemented
814	#3271	C₂×C₃₁	1	1	yes	characteristic, complemented
815	#3179	C₂×C₃₁	1	1	yes	characteristic, complemented
816	#3173	C₂×C₃₁	1	1	yes	characteristic, complemented
817	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
818	#3125	C₂×C₃₁	1	1	yes	characteristic, complemented
819	#3124	C₂×C₃₁	1	1	yes	characteristic, complemented
820	#3121	C₂×C₃₁	1	1	yes	characteristic, complemented
821	#3119	C₂×C₃₁	1	1	yes	characteristic, complemented
822	#3117	C₂×C₃₁	1	1	yes	characteristic, complemented
823	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
824	#2967	C₂×C₃₁	1	1	yes	characteristic, complemented
825	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
826	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
827	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
828	C₂²×C₃₁	—	2	1	no	—
829	C₂²×C₃₁	—	2	1	no	—
830	C₂²×C₃₁	—	2	1	no	—
831	C₂²×C₃₁	—	2	1	no	—
832	C₂²×C₃₁	—	2	1	no	—
833	C₂²×C₃₁	—	2	1	no	—
834	C₂²×C₃₁	—	2	1	no	—
835	C₂²×C₃₁	—	2	1	no	—
836	C₂²×C₃₁	—	2	1	no	—
837	C₂²×C₃₁	—	4	1	no	—
838	C₂²×C₃₁	—	4	1	no	—
839	C₂²×C₃₁	—	4	1	no	—
840	C₂²×C₃₁	—	4	1	no	—
841	C₂²×C₃₁	—	4	1	no	—
842	C₂²×C₃₁	—	4	1	no	—
843	C₂²×C₃₁	—	4	1	no	—
844	C₂²×C₃₁	—	4	1	no	—
845	C₂²×C₃₁	—	4	1	no	—
846	C₂²×C₃₁	—	4	1	no	—
847	C₂²×C₃₁	—	4	1	no	—
848	C₂²×C₃₁	—	4	1	no	—
849	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
850	C₄×C₃₁	—	2	1	no	—
851	C₄×C₃₁	—	2	1	no	—
852	C₄×C₃₁	—	2	1	no	—
853	C₄×C₃₁	—	2	1	no	—
854	C₄×C₃₁	—	2	1	no	—
855	C₄×C₃₁	—	2	1	no	—
856	C₄×C₃₁	—	2	1	no	—
857	C₄×C₃₁	—	2	1	no	—
858	C₄×C₃₁	—	2	1	no	—
859	C₄×C₃₁	—	2	1	no	—
860	C₄×C₃₁	—	2	1	no	—
861	C₄×C₃₁	—	2	2	no	—
862	C₄×C₃₁	—	2	2	no	—
863	C₄×C₃₁	—	4	1	no	—
864	C₄×C₃₁	—	4	1	no	—
865	C₄×C₃₁	—	4	1	no	—
866	C₄×C₃₁	—	4	1	no	—
867	C₄×C₃₁	—	4	1	no	—
868	C₄×C₃₁	—	4	1	no	—
869	C₄×C₃₁	—	4	1	no	—
870	C₄×C₃₁	—	4	1	no	—
871	C₄×C₃₁	—	4	1	no	—
872	C₄×C₃₁	—	4	1	no	—
873	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
874	C₄×C₃₁	#585	1	1	yes	characteristic
875	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
876	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
877	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
878	#559	—	2	1	no	—
879	#559	—	2	1	no	—
880	#559	C₂²×C₃₁	1	1	yes	characteristic
881	#559	C₂²×C₃₁	1	1	yes	characteristic
882	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
883	#557	C₂²×C₃₁	1	1	yes	characteristic
884	#555	—	2	1	no	—
885	#555	C₂²×C₃₁	1	1	yes	characteristic
886	#554	—	2	1	no	—
887	#554	C₂²×C₃₁	1	1	yes	characteristic
888	#553	—	2	1	no	—
889	#553	C₂²×C₃₁	1	1	yes	characteristic
890	#552	—	2	1	no	—
891	#552	C₂²×C₃₁	1	1	yes	characteristic
892	#550	C₂²×C₃₁	1	1	yes	characteristic
893	#550	C₂²×C₃₁	1	1	yes	characteristic
894	#548	C₂²×C₃₁	1	1	yes	characteristic
895	#548	C₂²×C₃₁	1	1	yes	characteristic
896	#548	C₂²×C₃₁	1	1	yes	characteristic
897	#548	C₂²×C₃₁	1	1	yes	characteristic
898	#547	—	2	1	no	—
899	#547	—	2	1	no	—
900	#547	C₂²×C₃₁	1	1	yes	characteristic
901	#547	C₂²×C₃₁	1	1	yes	characteristic
902	#542	—	2	1	no	—
903	#542	—	2	1	no	—
904	#542	—	2	1	no	—
905	#542	C₂²×C₃₁	1	1	yes	characteristic
906	#542	C₂²×C₃₁	1	1	yes	characteristic
907	#542	C₂²×C₃₁	1	1	yes	characteristic
908	#540	—	2	1	no	—
909	#540	C₂²×C₃₁	1	1	yes	characteristic
910	#532	—	2	1	no	—
911	#532	C₂²×C₃₁	1	1	yes	characteristic
912	#529	—	2	1	no	—
913	#529	—	2	1	no	—
914	#529	—	2	1	no	—
915	#529	C₂²×C₃₁	1	1	yes	characteristic
916	#529	C₂²×C₃₁	1	1	yes	characteristic
917	#520	C₂²×C₃₁	1	1	yes	characteristic
918	#520	C₂²×C₃₁	1	1	yes	characteristic
919	#520	C₂²×C₃₁	1	1	yes	characteristic
920	#519	C₂²×C₃₁	1	1	yes	characteristic
921	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
922	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
923	#501	C₂²×C₃₁	1	1	yes	characteristic
924	#501	C₂²×C₃₁	1	1	yes	characteristic
925	#498	C₂²×C₃₁	1	1	yes	characteristic
926	#496	C₂²×C₃₁	1	1	yes	characteristic
927	#496	C₂²×C₃₁	1	1	yes	characteristic
928	#495	C₂²×C₃₁	1	1	yes	characteristic
929	#490	C₂²×C₃₁	1	1	yes	characteristic
930	#489	C₂²×C₃₁	1	1	yes	characteristic
931	#489	C₂²×C₃₁	1	1	yes	characteristic
932	#489	C₂²×C₃₁	1	1	yes	characteristic
933	#488	C₂²×C₃₁	1	1	yes	characteristic
934	#486	C₂²×C₃₁	1	1	yes	characteristic
935	#485	C₂²×C₃₁	1	1	yes	characteristic
936	#484	C₂²×C₃₁	1	1	yes	characteristic
937	#484	C₂²×C₃₁	1	1	yes	characteristic
938	#483	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	#481	C₂²×C₃₁	1	1	yes	characteristic
943	#481	C₂²×C₃₁	1	1	yes	characteristic
944	#481	C₂²×C₃₁	1	1	yes	characteristic
945	#480	C₂²×C₃₁	1	1	yes	characteristic
946	#480	C₂²×C₃₁	1	1	yes	characteristic
947	#479	C₂²×C₃₁	1	1	yes	characteristic
948	#479	C₂²×C₃₁	1	1	yes	characteristic
949	#479	C₂²×C₃₁	1	1	yes	characteristic
950	#478	C₂²×C₃₁	1	1	yes	characteristic
951	#477	C₂²×C₃₁	1	1	yes	characteristic
952	#477	C₂²×C₃₁	1	1	yes	characteristic
953	#476	C₂²×C₃₁	1	1	yes	characteristic
954	#475	C₂²×C₃₁	1	1	yes	characteristic
955	#475	C₂²×C₃₁	1	1	yes	characteristic
956	#475	C₂²×C₃₁	1	1	yes	characteristic
957	#474	C₂²×C₃₁	1	1	yes	characteristic
958	#474	C₂²×C₃₁	1	1	yes	characteristic
959	#470	C₂²×C₃₁	1	1	yes	characteristic
960	#469	C₂²×C₃₁	1	1	yes	characteristic
961	#469	C₂²×C₃₁	1	1	yes	characteristic
962	#469	C₂²×C₃₁	1	1	yes	characteristic
963	#469	C₂²×C₃₁	1	1	yes	characteristic
964	#468	C₂²×C₃₁	1	1	yes	characteristic
965	#468	C₂²×C₃₁	1	1	yes	characteristic
966	#468	C₂²×C₃₁	1	1	yes	characteristic
967	#466	C₂²×C₃₁	1	1	yes	characteristic
968	#465	C₂²×C₃₁	1	1	yes	characteristic
969	#465	C₂²×C₃₁	1	1	yes	characteristic
970	#465	C₂²×C₃₁	1	1	yes	characteristic
971	#464	C₂²×C₃₁	1	1	yes	characteristic
972	#464	C₂²×C₃₁	1	1	yes	characteristic
973	#464	C₂²×C₃₁	1	1	yes	characteristic
974	#464	C₂²×C₃₁	1	1	yes	characteristic
975	#464	C₂²×C₃₁	1	1	yes	characteristic
976	#464	C₂²×C₃₁	1	1	yes	characteristic
977	#463	C₂²×C₃₁	1	1	yes	characteristic
978	#463	C₂²×C₃₁	1	1	yes	characteristic
979	#460	C₂²×C₃₁	1	1	yes	characteristic
980	#460	C₂²×C₃₁	1	1	yes	characteristic
981	#459	C₂²×C₃₁	1	1	yes	characteristic
982	#459	C₂²×C₃₁	1	1	yes	characteristic
983	#452	C₂²×C₃₁	1	1	yes	characteristic
984	#452	C₂²×C₃₁	1	1	yes	characteristic
985	#451	C₂²×C₃₁	1	1	yes	characteristic
986	#451	C₂²×C₃₁	1	1	yes	characteristic
987	#449	C₂²×C₃₁	1	1	yes	characteristic
988	#449	C₂²×C₃₁	1	1	yes	characteristic
989	#449	C₂²×C₃₁	1	1	yes	characteristic
990	#449	C₂²×C₃₁	1	1	yes	characteristic
991	#449	C₂²×C₃₁	1	1	yes	characteristic
992	#449	C₂²×C₃₁	1	1	yes	characteristic
993	#448	C₂²×C₃₁	1	1	yes	characteristic
994	#448	C₂²×C₃₁	1	1	yes	characteristic
995	#446	C₂²×C₃₁	1	1	yes	characteristic
996	#446	C₂²×C₃₁	1	1	yes	characteristic
997	#442	C₂²×C₃₁	1	1	yes	characteristic
998	#442	C₂²×C₃₁	1	1	yes	characteristic
999	#441	C₂²×C₃₁	1	1	yes	characteristic
1000	#441	C₂²×C₃₁	1	1	yes	characteristic
1001	#441	C₂²×C₃₁	1	1	yes	characteristic
1002	#441	C₂²×C₃₁	1	1	yes	characteristic
1003	#441	C₂²×C₃₁	1	1	yes	characteristic
1004	#440	C₂²×C₃₁	1	1	yes	characteristic
1005	#440	C₂²×C₃₁	1	1	yes	characteristic
1006	#440	C₂²×C₃₁	1	1	yes	characteristic
1007	#440	C₂²×C₃₁	1	1	yes	characteristic
1008	#440	C₂²×C₃₁	1	1	yes	characteristic
1009	#440	C₂²×C₃₁	1	1	yes	characteristic
1010	#440	C₂²×C₃₁	1	1	yes	characteristic
1011	#440	C₂²×C₃₁	1	1	yes	characteristic
1012	#440	C₂²×C₃₁	1	1	yes	characteristic
1013	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1014	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1015	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1016	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
1017	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1018	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1019	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1020	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1021	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
1022	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1023	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1024	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
1025	#436	C₂²×C₃₁	1	1	yes	characteristic
1026	#436	C₂²×C₃₁	1	1	yes	characteristic
1027	#435	C₂²×C₃₁	1	1	yes	characteristic
1028	#435	C₂²×C₃₁	1	1	yes	characteristic
1029	#435	C₂²×C₃₁	1	1	yes	characteristic
1030	#435	C₂²×C₃₁	1	1	yes	characteristic
1031	#433	C₂²×C₃₁	1	1	yes	characteristic
1032	#433	C₂²×C₃₁	1	1	yes	characteristic
1033	#432	C₂²×C₃₁	1	1	yes	characteristic
1034	#428	C₂²×C₃₁	1	1	yes	characteristic
1035	#428	C₂²×C₃₁	1	1	yes	characteristic
1036	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
1037	#419	C₂²×C₃₁	1	1	yes	characteristic
1038	#417	C₂²×C₃₁	1	1	yes	characteristic
1039	#417	C₂²×C₃₁	1	1	yes	characteristic
1040	#417	C₂²×C₃₁	1	1	yes	characteristic
1041	#416	C₂²×C₃₁	1	1	yes	characteristic
1042	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
1043	#405	C₂²×C₃₁	1	1	yes	characteristic
1044	#405	C₂²×C₃₁	1	1	yes	characteristic
1045	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
1046	C₂×C₃₁	—	4	1	no	—
1047	C₂×C₃₁	—	4	1	no	—
1048	C₂×C₃₁	—	4	1	no	—
1049	C₂×C₃₁	—	8	1	no	—
1050	C₂×C₃₁	—	8	1	no	—
1051	C₂×C₃₁	—	8	1	no	—
1052	C₂×C₃₁	—	8	1	no	—
1053	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
1054	C₂×C₃₁	#3585	1	1	yes	characteristic
1055	C₂×C₃₁	#3586	1	1	yes	characteristic
1056	C₂×#41	—	2	1	no	—
1057	C₂×#41	—	2	1	no	—
1058	C₂×#41	—	2	1	no	—
1059	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1060	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1061	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1062	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
1063	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1064	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1065	#137	—	2	4	no	—
1066	#137	—	2	4	no	—
1067	#135	—	2	4	no	—
1068	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1069	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1070	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1071	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
1072	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1073	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1074	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1075	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1076	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1077	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1078	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1079	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
1080	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1081	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1082	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1083	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
1084	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1085	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1086	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1087	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1088	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1089	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
1090	C₄⋊Q₈	—	2	1	no	—
1091	C₄⋊Q₈	—	2	1	no	—
1092	C₄⋊Q₈	—	2	1	no	—
1093	C₄⋊Q₈	—	2	1	no	—
1094	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1095	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1096	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1097	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1098	#127	—	2	1	no	—
1099	#127	—	2	1	no	—
1100	#127	C₂³×C₃₁	1	1	yes	characteristic
1101	#127	C₂³×C₃₁	1	1	yes	characteristic
1102	#126	—	2	1	no	—
1103	#126	—	2	1	no	—
1104	#126	—	2	1	no	—
1105	#126	—	2	1	no	—
1106	#126	—	2	1	no	—
1107	#126	—	2	1	no	—
1108	#126	D₄×C₃₁	1	1	yes	characteristic
1109	#126	D₄×C₃₁	1	1	yes	characteristic
1110	#125	—	2	1	no	—
1111	#125	—	2	1	no	—
1112	#125	—	2	1	no	—
1113	#125	—	2	1	no	—
1114	#125	D₄×C₃₁	1	1	yes	characteristic
1115	#125	C₂³×C₃₁	1	1	yes	characteristic
1116	#125	C₂³×C₃₁	1	1	yes	characteristic
1117	#124	—	2	1	no	—
1118	#124	—	2	1	no	—
1119	#124	—	2	1	no	—
1120	#124	—	2	1	no	—
1121	#124	—	2	1	no	—
1122	#124	—	2	1	no	—
1123	#124	—	2	1	no	—
1124	#124	—	2	1	no	—
1125	#124	—	2	1	no	—
1126	#124	—	2	1	no	—
1127	#124	—	2	1	no	—
1128	#124	—	2	1	no	—
1129	#124	D₄×C₃₁	1	1	yes	characteristic
1130	#124	C₂³×C₃₁	1	1	yes	characteristic
1131	#124	C₂³×C₃₁	1	1	yes	characteristic
1132	#124	C₂³×C₃₁	1	1	yes	characteristic
1133	#124	C₂³×C₃₁	1	1	yes	characteristic
1134	#123	—	2	1	no	—
1135	#123	—	2	1	no	—
1136	#123	—	2	1	no	—
1137	#123	—	2	1	no	—
1138	#123	—	2	1	no	—
1139	#123	—	2	1	no	—
1140	#123	—	2	1	no	—
1141	#123	—	2	1	no	—
1142	#123	—	2	1	no	—
1143	#123	—	2	1	no	—
1144	#123	—	2	1	no	—
1145	#123	—	2	1	no	—
1146	#123	—	2	1	no	—
1147	#123	—	2	1	no	—
1148	#123	—	2	1	no	—
1149	#123	—	2	1	no	—
1150	#123	D₄×C₃₁	1	1	yes	characteristic
1151	#123	D₄×C₃₁	1	1	yes	characteristic
1152	C₂²⋊Q₈	—	2	1	no	—
1153	C₂²⋊Q₈	—	2	1	no	—
1154	C₂²⋊Q₈	—	2	1	no	—
1155	C₂²⋊Q₈	—	2	1	no	—
1156	C₂²⋊Q₈	—	2	1	no	—
1157	C₂²⋊Q₈	—	2	1	no	—
1158	C₂²⋊Q₈	—	2	1	no	—
1159	C₂²⋊Q₈	—	2	1	no	—
1160	C₂²⋊Q₈	—	2	1	no	—
1161	C₂²⋊Q₈	—	2	1	no	—
1162	C₂²⋊Q₈	—	2	1	no	—
1163	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
1164	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1165	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1166	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1167	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1168	#121	—	2	1	no	—
1169	#121	—	2	1	no	—
1170	#121	—	2	1	no	—
1171	#121	—	2	1	no	—
1172	#121	—	2	1	no	—
1173	#121	—	2	1	no	—
1174	#121	—	2	1	no	—
1175	#121	—	2	1	no	—
1176	#121	—	2	1	no	—
1177	#121	—	2	1	no	—
1178	#121	—	2	1	no	—
1179	#121	—	2	1	no	—
1180	#121	—	2	1	no	—
1181	#121	D₄×C₃₁	1	1	yes	characteristic
1182	#121	C₂³×C₃₁	1	1	yes	characteristic
1183	#121	C₂³×C₃₁	1	1	yes	characteristic
1184	#121	C₂³×C₃₁	1	1	yes	characteristic
1185	#121	C₂³×C₃₁	1	1	yes	characteristic
1186	#121	C₂³×C₃₁	1	1	yes	characteristic
1187	#121	C₂³×C₃₁	1	1	yes	characteristic
1188	#121	C₂³×C₃₁	1	1	yes	characteristic
1189	#121	C₂³×C₃₁	1	1	yes	characteristic
1190	C₄×Q₈	—	2	1	no	—
1191	C₄×Q₈	—	2	1	no	—
1192	C₄×Q₈	—	2	1	no	—
1193	C₄×Q₈	—	2	1	no	—
1194	C₄×Q₈	—	2	1	no	—
1195	C₄×Q₈	—	2	1	no	—
1196	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1197	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1198	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1199	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1200	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1201	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1202	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1203	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1204	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1205	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1206	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1207	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1208	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1209	C₄×D₄	—	2	1	no	—
1210	C₄×D₄	—	2	1	no	—
1211	C₄×D₄	—	2	1	no	—
1212	C₄×D₄	—	2	1	no	—
1213	C₄×D₄	—	2	1	no	—
1214	C₄×D₄	—	2	1	no	—
1215	C₄×D₄	—	2	1	no	—
1216	C₄×D₄	—	2	1	no	—
1217	C₄×D₄	—	2	1	no	—
1218	C₄×D₄	—	2	1	no	—
1219	C₄×D₄	—	2	1	no	—
1220	C₄×D₄	—	2	1	no	—
1221	C₄×D₄	—	2	1	no	—
1222	C₄×D₄	—	2	1	no	—
1223	C₄×D₄	—	2	1	no	—
1224	C₄×D₄	—	2	1	no	—
1225	C₄×D₄	—	2	1	no	—
1226	C₄×D₄	—	2	1	no	—
1227	C₄×D₄	—	2	1	no	—
1228	C₄×D₄	—	2	1	no	—
1229	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1230	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1231	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1232	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1233	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1234	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1235	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1236	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1237	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1238	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1239	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1240	#117	—	2	1	no	—
1241	#117	—	2	1	no	—
1242	#117	—	2	1	no	—
1243	#117	—	2	1	no	—
1244	#117	—	2	1	no	—
1245	#117	—	2	1	no	—
1246	#117	—	2	1	no	—
1247	#117	—	2	1	no	—
1248	#117	—	2	1	no	—
1249	#117	C₂³×C₃₁	1	1	yes	characteristic
1250	#117	C₂³×C₃₁	1	1	yes	characteristic
1251	#117	C₂³×C₃₁	1	1	yes	characteristic
1252	#117	C₂³×C₃₁	1	1	yes	characteristic
1253	C₂×C₄⋊C₄	—	2	1	no	—
1254	C₂×C₄⋊C₄	—	2	1	no	—
1255	C₂×C₄⋊C₄	—	2	1	no	—
1256	C₂×C₄⋊C₄	—	2	1	no	—
1257	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1258	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1259	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1260	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1261	C₂×C₄²	—	2	1	no	—
1262	C₂×C₄²	—	2	1	no	—
1263	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1264	#107	C₂³×C₃₁	1	1	yes	characteristic
1265	#107	C₂³×C₃₁	1	1	yes	characteristic
1266	#107	C₂³×C₃₁	1	1	yes	characteristic
1267	#107	C₂³×C₃₁	1	1	yes	characteristic
1268	#107	C₂³×C₃₁	1	1	yes	characteristic
1269	#107	C₂³×C₃₁	1	1	yes	characteristic
1270	#107	C₂³×C₃₁	1	1	yes	characteristic
1271	#107	C₂³×C₃₁	1	1	yes	characteristic
1272	#106	C₂³×C₃₁	1	1	yes	characteristic
1273	#106	C₂³×C₃₁	1	1	yes	characteristic
1274	#106	C₂³×C₃₁	1	1	yes	characteristic
1275	#106	C₂³×C₃₁	1	1	yes	characteristic
1276	#106	C₂³×C₃₁	1	1	yes	characteristic
1277	#106	C₂³×C₃₁	1	1	yes	characteristic
1278	#106	C₂³×C₃₁	1	1	yes	characteristic
1279	#106	C₂³×C₃₁	1	1	yes	characteristic
1280	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1281	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1282	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1283	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1284	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1285	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1286	#103	C₂³×C₃₁	1	1	yes	characteristic
1287	#103	C₂³×C₃₁	1	1	yes	characteristic
1288	#103	C₂³×C₃₁	1	1	yes	characteristic
1289	#103	C₂³×C₃₁	1	1	yes	characteristic
1290	#103	C₂³×C₃₁	1	1	yes	characteristic
1291	#103	C₂³×C₃₁	1	1	yes	characteristic
1292	#103	C₂³×C₃₁	1	1	yes	characteristic
1293	#103	C₂³×C₃₁	1	1	yes	characteristic
1294	#103	C₂³×C₃₁	1	1	yes	characteristic
1295	#103	C₂³×C₃₁	1	1	yes	characteristic
1296	#103	C₂³×C₃₁	1	1	yes	characteristic
1297	#103	C₂³×C₃₁	1	1	yes	characteristic
1298	#103	C₂³×C₃₁	1	1	yes	characteristic
1299	#103	C₂³×C₃₁	1	1	yes	characteristic
1300	#103	C₂³×C₃₁	1	1	yes	characteristic
1301	#103	C₂³×C₃₁	1	1	yes	characteristic
1302	#102	C₂³×C₃₁	1	1	yes	characteristic
1303	#102	C₂³×C₃₁	1	1	yes	characteristic
1304	#102	C₂³×C₃₁	1	1	yes	characteristic
1305	#102	C₂³×C₃₁	1	1	yes	characteristic
1306	#102	C₂³×C₃₁	1	1	yes	characteristic
1307	#102	C₂³×C₃₁	1	1	yes	characteristic
1308	#102	C₂³×C₃₁	1	1	yes	characteristic
1309	#102	C₂³×C₃₁	1	1	yes	characteristic
1310	#102	C₂³×C₃₁	1	1	yes	characteristic
1311	#102	C₂³×C₃₁	1	1	yes	characteristic
1312	#102	C₂³×C₃₁	1	1	yes	characteristic
1313	#102	C₂³×C₃₁	1	1	yes	characteristic
1314	#102	C₂³×C₃₁	1	1	yes	characteristic
1315	#102	C₂³×C₃₁	1	1	yes	characteristic
1316	#102	C₂³×C₃₁	1	1	yes	characteristic
1317	#102	C₂³×C₃₁	1	1	yes	characteristic
1318	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1319	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1320	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1321	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1322	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1323	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1324	#97	C₂³×C₃₁	1	1	yes	characteristic
1325	#97	C₂³×C₃₁	1	1	yes	characteristic
1326	#97	C₂³×C₃₁	1	1	yes	characteristic
1327	#97	C₂³×C₃₁	1	1	yes	characteristic
1328	#97	C₂³×C₃₁	1	1	yes	characteristic
1329	#97	C₂³×C₃₁	1	1	yes	characteristic
1330	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1331	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1332	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1333	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
1334	C₃₁	#61516	1	1	yes	characteristic, direct product factor, Sylow
1335	#41	—	2	2	no	—
1336	#41	—	2	2	no	—
1337	#41	—	2	2	no	—
1338	#41	—	2	2	no	—
1339	#41	—	4	1	no	—
1340	#41	—	4	1	no	—
1341	#41	—	4	1	no	—
1342	#41	—	4	1	no	—
1343	#41	—	8	2	no	—
1344	#41	—	8	2	no	—
1345	#41	—	8	2	no	—
1346	C₂×Q₈	—	2	1	no	—
1347	C₂×Q₈	—	2	1	no	—
1348	C₂×Q₈	—	2	1	no	—
1349	C₂×Q₈	—	2	1	no	—
1350	C₂×Q₈	—	2	1	no	—
1351	C₂×Q₈	—	2	1	no	—
1352	C₂×Q₈	—	2	2	no	—
1353	C₂×Q₈	—	2	2	no	—
1354	C₂×Q₈	—	4	1	no	—
1355	C₂×Q₈	—	4	1	no	—
1356	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1357	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1358	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1359	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1360	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1361	C₂×D₄	—	2	1	no	—
1362	C₂×D₄	—	2	1	no	—
1363	C₂×D₄	—	2	1	no	—
1364	C₂×D₄	—	2	1	no	—
1365	C₂×D₄	—	2	1	no	—
1366	C₂×D₄	—	2	1	no	—
1367	C₂×D₄	—	2	1	no	—
1368	C₂×D₄	—	2	1	no	—
1369	C₂×D₄	—	2	1	no	—
1370	C₂×D₄	—	2	1	no	—
1371	C₂×D₄	—	2	1	no	—
1372	C₂×D₄	—	2	1	no	—
1373	C₂×D₄	—	2	1	no	—
1374	C₂×D₄	—	2	1	no	—
1375	C₂×D₄	—	2	1	no	—
1376	C₂×D₄	—	2	1	no	—
1377	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1378	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1379	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1380	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1381	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1382	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1383	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1384	C₂²×C₄	—	2	1	no	—
1385	C₂²×C₄	—	2	1	no	—
1386	C₂²×C₄	—	2	1	no	—
1387	C₂²×C₄	—	2	1	no	—
1388	C₂²×C₄	—	2	1	no	—
1389	C₂²×C₄	—	2	1	no	—
1390	C₂²×C₄	—	2	1	no	—
1391	C₂²×C₄	—	2	1	no	—
1392	C₂²×C₄	—	2	1	no	—
1393	C₂²×C₄	—	2	1	no	—
1394	C₂²×C₄	—	2	1	no	—
1395	C₂²×C₄	—	2	1	no	—
1396	C₂²×C₄	—	2	1	no	—
1397	C₂²×C₄	—	2	1	no	—
1398	C₂²×C₄	—	2	1	no	—
1399	C₂²×C₄	—	2	1	no	—
1400	C₂²×C₄	—	2	1	no	—
1401	C₂²×C₄	—	2	1	no	—
1402	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1403	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1404	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1405	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1406	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1407	Q₁₆	—	2	2	no	—
1408	Q₁₆	—	2	2	no	—
1409	Q₁₆	—	4	1	no	—
1410	Q₁₆	#41×C₃₁	1	4	yes	complemented
1411	SD₁₆	—	2	2	no	—
1412	SD₁₆	—	2	2	no	—
1413	SD₁₆	—	2	2	no	—
1414	SD₁₆	—	2	2	no	—
1415	SD₁₆	—	2	2	no	—
1416	SD₁₆	—	2	2	no	—
1417	SD₁₆	—	4	1	no	—
1418	SD₁₆	—	4	1	no	—
1419	D₈	—	2	2	no	—
1420	D₈	—	4	1	no	—
1421	D₈	—	4	1	no	—
1422	D₈	—	4	1	no	—
1423	M₁₆	—	2	2	no	—
1424	M₁₆	—	2	2	no	—
1425	M₁₆	—	4	1	no	—
1426	M₁₆	—	4	1	no	—
1427	C₂×C₈	—	2	2	no	—
1428	C₂×C₈	—	4	1	no	—
1429	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1430	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1431	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1432	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1433	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1434	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1435	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1436	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	—	2	1	no	—
1448	C₄⋊C₄	—	2	1	no	—
1449	C₄⋊C₄	—	2	1	no	—
1450	C₄⋊C₄	—	2	1	no	—
1451	C₄⋊C₄	—	2	1	no	—
1452	C₄⋊C₄	—	2	1	no	—
1453	C₄⋊C₄	—	2	1	no	—
1454	C₄⋊C₄	—	2	1	no	—
1455	C₄⋊C₄	—	2	1	no	—
1456	C₄⋊C₄	—	2	1	no	—
1457	C₄⋊C₄	—	2	1	no	—
1458	C₄⋊C₄	—	2	1	no	—
1459	C₄⋊C₄	—	2	1	no	—
1460	C₄⋊C₄	—	2	1	no	—
1461	C₄⋊C₄	—	2	1	no	—
1462	C₄⋊C₄	—	2	1	no	—
1463	C₄⋊C₄	—	2	1	no	—
1464	C₄⋊C₄	—	2	1	no	—
1465	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1466	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1467	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1468	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1469	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1470	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1471	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1472	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1473	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1474	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1475	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1476	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1477	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1478	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1479	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1480	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1481	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1482	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1483	C₂²⋊C₄	—	2	1	no	—
1484	C₂²⋊C₄	—	2	1	no	—
1485	C₂²⋊C₄	—	2	1	no	—
1486	C₂²⋊C₄	—	2	1	no	—
1487	C₂²⋊C₄	—	2	1	no	—
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	—	2	1	no	—
1496	C₂²⋊C₄	—	2	1	no	—
1497	C₂²⋊C₄	—	2	1	no	—
1498	C₂²⋊C₄	—	2	1	no	—
1499	C₂²⋊C₄	—	2	1	no	—
1500	C₂²⋊C₄	—	2	1	no	—
1501	C₂²⋊C₄	—	2	1	no	—
1502	C₂²⋊C₄	—	2	1	no	—
1503	C₂²⋊C₄	—	2	1	no	—
1504	C₂²⋊C₄	—	2	1	no	—
1505	C₂²⋊C₄	—	2	1	no	—
1506	C₂²⋊C₄	—	2	1	no	—
1507	C₂²⋊C₄	—	2	1	no	—
1508	C₂²⋊C₄	—	2	1	no	—
1509	C₂²⋊C₄	—	2	1	no	—
1510	C₂²⋊C₄	—	2	1	no	—
1511	C₂²⋊C₄	—	2	1	no	—
1512	C₂²⋊C₄	—	2	1	no	—
1513	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1514	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1515	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1516	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1517	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1518	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1519	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1520	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1521	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1522	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1523	C₄²	—	2	1	no	—
1524	C₄²	—	2	1	no	—
1525	C₄²	—	2	1	no	—
1526	C₄²	—	2	1	no	—
1527	C₄²	—	2	1	no	—
1528	C₄²	—	2	1	no	—
1529	C₄²	—	2	1	no	—
1530	C₄²	—	2	1	no	—
1531	C₄²	—	2	1	no	—
1532	C₄²	—	2	1	no	—
1533	C₄²	—	2	1	no	—
1534	C₄²	—	2	1	no	—
1535	C₄²	—	2	1	no	—
1536	C₄²	—	2	1	no	—
1537	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1538	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1539	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1540	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1541	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1542	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1543	C₂³	—	2	1	no	—
1544	C₂³	—	2	1	no	—
1545	C₂³	—	2	1	no	—
1546	C₂³	—	2	1	no	—
1547	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1548	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1549	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1550	Q₈	—	2	1	no	—
1551	Q₈	—	2	1	no	—
1552	Q₈	—	2	1	no	—
1553	Q₈	—	2	1	no	—
1554	Q₈	—	2	1	no	—
1555	Q₈	—	2	1	no	—
1556	Q₈	—	4	1	no	—
1557	Q₈	—	4	2	no	—
1558	Q₈	—	4	2	no	—
1559	Q₈	—	8	1	no	—
1560	Q₈	—	8	1	no	—
1561	Q₈	—	8	1	no	—
1562	Q₈	—	8	1	no	—
1563	Q₈	C₂×#41×C₃₁	1	2	yes	—
1564	Q₈	C₂×#41×C₃₁	1	2	yes	—
1565	D₄	—	2	1	no	—
1566	D₄	—	2	1	no	—
1567	D₄	—	2	1	no	—
1568	D₄	—	2	1	no	—
1569	D₄	—	2	1	no	—
1570	D₄	—	2	1	no	—
1571	D₄	—	2	1	no	—
1572	D₄	—	2	1	no	—
1573	D₄	—	4	1	no	—
1574	D₄	—	4	1	no	—
1575	D₄	—	4	1	no	—
1576	D₄	—	4	2	no	—
1577	D₄	—	4	2	no	—
1578	D₄	—	4	2	no	—
1579	D₄	—	4	2	no	—
1580	D₄	—	4	2	no	—
1581	D₄	—	4	2	no	—
1582	D₄	—	4	2	no	—
1583	D₄	—	8	1	no	—
1584	D₄	—	8	1	no	—
1585	D₄	—	8	1	no	—
1586	D₄	—	8	1	no	—
1587	D₄	—	8	1	no	—
1588	D₄	—	8	1	no	—
1589	D₄	—	8	1	no	—
1590	D₄	—	8	1	no	—
1591	D₄	—	8	1	no	—
1592	C₂×C₄	—	2	1	no	—
1593	C₂×C₄	—	2	1	no	—
1594	C₂×C₄	—	2	1	no	—
1595	C₂×C₄	—	2	1	no	—
1596	C₂×C₄	—	2	1	no	—
1597	C₂×C₄	—	2	1	no	—
1598	C₂×C₄	—	2	1	no	—
1599	C₂×C₄	—	2	1	no	—
1600	C₂×C₄	—	2	1	no	—
1601	C₂×C₄	—	2	1	no	—
1602	C₂×C₄	—	2	1	no	—
1603	C₂×C₄	—	2	1	no	—
1604	C₂×C₄	—	2	1	no	—
1605	C₂×C₄	—	2	1	no	—
1606	C₂×C₄	—	2	1	no	—
1607	C₂×C₄	—	2	1	no	—
1608	C₂×C₄	—	2	1	no	—
1609	C₂×C₄	—	2	1	no	—
1610	C₂×C₄	—	4	1	no	—
1611	C₂×C₄	—	4	1	no	—
1612	C₂×C₄	—	4	2	no	—
1613	C₂×C₄	—	4	2	no	—
1614	C₂×C₄	—	4	2	no	—
1615	C₂×C₄	—	4	2	no	—
1616	C₂×C₄	—	4	2	no	—
1617	C₂×C₄	—	4	2	no	—
1618	C₂×C₄	—	4	2	no	—
1619	C₂×C₄	—	8	1	no	—
1620	C₂×C₄	—	8	1	no	—
1621	C₂×C₄	—	8	1	no	—
1622	C₂×C₄	—	8	1	no	—
1623	C₂×C₄	—	8	1	no	—
1624	C₂×C₄	—	8	1	no	—
1625	C₂×C₄	—	8	1	no	—
1626	C₂×C₄	—	8	1	no	—
1627	C₂×C₄	—	8	1	no	—
1628	C₂×C₄	—	8	1	no	—
1629	C₂×C₄	—	8	1	no	—
1630	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1631	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1632	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1633	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1634	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1635	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1636	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1637	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1638	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1639	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1640	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1641	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1642	C₈	—	2	1	no	—
1643	C₈	—	2	1	no	—
1644	C₈	—	2	1	no	—
1645	C₈	—	2	1	no	—
1646	C₈	—	2	1	no	—
1647	C₈	—	2	1	no	—
1648	C₈	—	2	1	no	—
1649	C₈	C₂×#41×C₃₁	1	2	yes	—
1650	C₂²	—	2	1	no	—
1651	C₂²	—	2	1	no	—
1652	C₂²	—	2	1	no	—
1653	C₂²	—	2	1	no	—
1654	C₂²	—	2	1	no	—
1655	C₂²	—	2	1	no	—
1656	C₂²	—	2	1	no	—
1657	C₂²	—	2	1	no	—
1658	C₂²	—	2	1	no	—
1659	C₂²	—	4	1	no	—
1660	C₂²	—	4	1	no	—
1661	C₂²	—	4	1	no	—
1662	C₂²	—	4	1	no	—
1663	C₂²	—	4	1	no	—
1664	C₂²	—	4	1	no	—
1665	C₂²	—	4	1	no	—
1666	C₂²	—	4	1	no	—
1667	C₂²	—	4	1	no	—
1668	C₂²	—	4	1	no	—
1669	C₂²	—	4	1	no	—
1670	C₂²	—	4	1	no	—
1671	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1672	C₄	—	2	1	no	—
1673	C₄	—	2	1	no	—
1674	C₄	—	2	1	no	—
1675	C₄	—	2	2	no	—
1676	C₄	—	2	2	no	—
1677	C₄	—	2	1	no	—
1678	C₄	—	2	1	no	—
1679	C₄	—	2	1	no	—
1680	C₄	—	2	1	no	—
1681	C₄	—	2	1	no	—
1682	C₄	—	2	1	no	—
1683	C₄	—	2	1	no	—
1684	C₄	—	2	1	no	—
1685	C₄	—	4	1	no	—
1686	C₄	—	4	1	no	—
1687	C₄	—	4	1	no	—
1688	C₄	—	4	1	no	—
1689	C₄	—	4	1	no	—
1690	C₄	—	4	1	no	—
1691	C₄	—	4	1	no	—
1692	C₄	—	4	1	no	—
1693	C₄	—	4	1	no	—
1694	C₄	—	4	1	no	—
1695	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1696	C₄	C₃₁×#585	1	1	yes	characteristic
1697	C₂	—	4	1	no	—
1698	C₂	—	4	1	no	—
1699	C₂	—	4	1	no	—
1700	C₂	—	8	1	no	—
1701	C₂	—	8	1	no	—
1702	C₂	—	8	1	no	—
1703	C₂	—	8	1	no	—
1704	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1705	C₂	C₃₁×#3585	1	1	yes	characteristic
1706	C₂	C₃₁×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3524	C₂	semidirect
2. C₃₁×#3522	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3387	C₂	semidirect
5. C₃₁×#3375	C₂	semidirect
6. C₃₁×#3371	C₂	semidirect
7. C₃₁×#3354	C₂	semidirect
8. C₃₁×#3346	C₂	semidirect
9. C₃₁×#3343	C₂	semidirect
10. C₃₁×#3332	C₂	semidirect
11. C₃₁×#3327	C₂	semidirect
12. C₃₁×#3321	C₂	semidirect
13. C₃₁×#3316	C₂	semidirect
14. C₃₁×#3309	C₂	semidirect
15. C₃₁×#3308	C₂	semidirect
16. C₃₁×#3277	C₂	semidirect
17. C₃₁×#3271	C₂	semidirect
18. C₃₁×#3271	C₂	semidirect
19. C₃₁×#3179	C₂	semidirect
20. C₃₁×#3173	C₂	semidirect
21. C₃₁×#3171	C₂	semidirect
22. C₃₁×#3125	C₂	semidirect
23. C₃₁×#3124	C₂	semidirect
24. C₃₁×#3121	C₂	semidirect
25. C₃₁×#3119	C₂	semidirect
26. C₃₁×#3117	C₂	semidirect
27. C₃₁×#3115	C₂	semidirect
28. C₃₁×#2967	C₂	semidirect
29. C₃₁×#2951	C₂	semidirect
30. C₃₁×#2947	C₂	semidirect
31. C₄×C₃₁×#137	C₂	semidirect
556. Q₁₆×C₃₁	#41	semidirect
689. #61516	C₃₁	direct (N × H)
797. #3524	C₂×C₃₁	semidirect
798. #3522	C₂×C₃₁	semidirect
799. #3403	C₂×C₃₁	semidirect
800. #3387	C₂×C₃₁	semidirect
801. #3375	C₂×C₃₁	semidirect
802. #3371	C₂×C₃₁	semidirect
803. #3354	C₂×C₃₁	semidirect
804. #3346	C₂×C₃₁	semidirect
805. #3343	C₂×C₃₁	semidirect
806. #3332	C₂×C₃₁	semidirect
807. #3327	C₂×C₃₁	semidirect
808. #3321	C₂×C₃₁	semidirect
809. #3316	C₂×C₃₁	semidirect
810. #3309	C₂×C₃₁	semidirect
811. #3308	C₂×C₃₁	semidirect
812. #3277	C₂×C₃₁	semidirect
813. #3271	C₂×C₃₁	semidirect
814. #3271	C₂×C₃₁	semidirect
815. #3179	C₂×C₃₁	semidirect
816. #3173	C₂×C₃₁	semidirect
817. #3171	C₂×C₃₁	semidirect
818. #3125	C₂×C₃₁	semidirect
819. #3124	C₂×C₃₁	semidirect
820. #3121	C₂×C₃₁	semidirect
821. #3119	C₂×C₃₁	semidirect
822. #3117	C₂×C₃₁	semidirect
823. #3115	C₂×C₃₁	semidirect
824. #2967	C₂×C₃₁	semidirect
825. #2951	C₂×C₃₁	semidirect
826. #2947	C₂×C₃₁	semidirect
827. C₄×#137	C₂×C₃₁	semidirect
1334. C₃₁	#61516	direct (N × H)
1410. Q₁₆	#41×C₃₁	semidirect

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×#3522	2
C₃₁×#3403	2
C₃₁×#3387	2
C₃₁×#3375	2
C₃₁×#3371	2
C₃₁×#3354	2
C₃₁×#3346	2
C₃₁×#3343	2
C₃₁×#3332	2
C₃₁×#3327	2
C₃₁×#3321	2
C₃₁×#3316	2
C₃₁×#3309	2
C₃₁×#3308	2
C₃₁×#3277	2
C₃₁×#3271	2
C₃₁×#3179	2
C₃₁×#3173	2
C₃₁×#3171	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3121	2
C₃₁×#3119	2
C₃₁×#3117	2
C₃₁×#3115	2
C₃₁×#2967	2
C₃₁×#2951	2
C₃₁×#2947	2
C₄×C₃₁×#137	2
#61516	31

Subgroups — C31×#61516 #21518275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61516 #21518275