Subgroups — C₃₁×#60994 #21517753

Order 7936.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3221	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3174	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	—	2	1	no	—
25	C₃₁×#559	—	2	1	no	—
26	C₃₁×#550	—	2	1	no	—
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#546	—	2	1	no	—
29	C₃₁×#546	—	2	1	no	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#542	C₂²	1	1	yes	characteristic
35	C₃₁×#542	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#541	—	2	1	no	—
37	C₃₁×#541	C₂²	1	1	yes	characteristic
38	C₃₁×#541	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#540	C₂²	1	2	yes	—
40	C₃₁×#540	C₂²	1	2	yes	—
41	C₃₁×#539	—	2	1	no	—
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#537	C₂²	1	1	yes	characteristic
44	C₃₁×#536	C₂²	1	1	yes	characteristic
45	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#535	C₂²	1	2	yes	—
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
56	C₃₁×#529	—	2	1	no	—
57	C₃₁×#529	—	2	1	no	—
58	C₃₁×#529	—	2	1	no	—
59	C₃₁×#529	C₂²	1	1	yes	characteristic
60	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#518	C₂²	1	2	yes	—
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#501	C₂²	1	2	yes	complemented
66	C₃₁×#499	C₂²	1	2	yes	complemented
67	C₃₁×#496	C₂²	1	2	yes	—
68	C₃₁×#492	C₂²	1	2	yes	—
69	C₃₁×#491	C₂²	1	2	yes	complemented
70	C₃₁×#490	C₂²	1	2	yes	—
71	C₃₁×#488	C₂²	1	2	yes	complemented
72	C₃₁×#486	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	—
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#485	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	—
77	C₃₁×#482	C₂²	1	2	yes	complemented
78	C₃₁×#482	C₂²	1	2	yes	complemented
79	C₃₁×#481	C₂²	1	2	yes	complemented
80	C₃₁×#480	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#476	C₂²	1	2	yes	complemented
88	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#474	C₂²	1	2	yes	complemented
93	C₃₁×#469	C₂²	1	2	yes	complemented
94	C₃₁×#468	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#468	C₂²	1	2	yes	complemented
97	C₃₁×#466	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#465	C₂²	1	2	yes	complemented
101	C₃₁×#463	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	2	yes	complemented
103	C₃₁×#461	C₂²	1	2	yes	complemented
104	C₃₁×#461	C₂²	1	2	yes	complemented
105	C₃₁×#460	C₂²	1	1	yes	characteristic
106	C₃₁×#460	C₂²	1	1	yes	characteristic
107	C₃₁×#460	C₂²	1	1	yes	characteristic
108	C₃₁×#460	C₂²	1	1	yes	characteristic
109	C₃₁×#460	C₂²	1	1	yes	characteristic
110	C₃₁×#460	C₂²	1	1	yes	characteristic
111	C₃₁×#459	C₂²	1	1	yes	characteristic
112	C₃₁×#459	C₂²	1	1	yes	characteristic
113	C₃₁×#450	C₂²	1	2	yes	—
114	C₃₁×#450	C₂²	1	2	yes	—
115	C₃₁×#450	C₂²	1	2	yes	—
116	C₃₁×#449	C₂²	1	2	yes	complemented
117	C₃₁×#449	C₂²	1	2	yes	complemented
118	C₃₁×#448	C₂²	1	2	yes	complemented
119	C₃₁×#448	C₂²	1	2	yes	complemented
120	C₃₁×#447	C₂²	1	2	yes	—
121	C₃₁×#442	C₂²	1	2	yes	complemented
122	C₃₁×#440	C₂²	1	2	yes	complemented
123	C₃₁×#440	C₂²	1	2	yes	complemented
124	C₃₁×#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
128	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
129	C₃₁×#433	C₂²	1	2	yes	—
130	C₃₁×#433	C₂²	1	2	yes	complemented
131	C₃₁×#432	C₂²	1	1	yes	characteristic
132	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#408	C₂²	1	2	yes	—
138	C₃₁×#405	C₂²	1	2	yes	complemented
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	—	2	1	no	—
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	—	2	1	no	—
148	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	—	2	2	no	—
168	C₃₁×#127	—	2	1	no	—
169	C₃₁×#127	—	2	1	no	—
170	C₃₁×#127	C₂³	1	1	yes	characteristic
171	C₃₁×#127	C₂³	1	1	yes	characteristic
172	C₃₁×#127	C₂³	1	2	yes	—
173	C₃₁×#126	—	2	1	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	1	no	—
178	C₃₁×#126	—	2	1	no	—
179	C₃₁×#126	—	2	1	no	—
180	C₃₁×#126	—	2	1	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	—	2	1	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	C₂³	1	1	yes	characteristic
189	C₃₁×#125	C₂³	1	2	yes	—
190	C₃₁×#125	C₂³	1	1	yes	characteristic
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	—	2	1	no	—
197	C₃₁×#124	—	2	1	no	—
198	C₃₁×#124	—	2	1	no	—
199	C₃₁×#124	C₂³	1	1	yes	characteristic
200	C₃₁×#124	C₂³	1	1	yes	characteristic
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	1	no	—
203	C₃₁×#123	—	2	1	no	—
204	C₃₁×#123	—	2	1	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	2	no	—
208	C₃₁×#123	—	2	2	no	—
209	C₃₁×#123	—	2	1	no	—
210	C₃₁×#123	—	2	1	no	—
211	C₃₁×#123	—	2	1	no	—
212	C₃₁×#123	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	1	no	—
217	C₃₁×C₂²⋊Q₈	—	2	1	no	—
218	C₃₁×C₂²⋊Q₈	—	2	1	no	—
219	C₃₁×C₂²⋊Q₈	—	2	1	no	—
220	C₃₁×C₂²⋊Q₈	—	2	1	no	—
221	C₃₁×C₂²⋊Q₈	—	2	1	no	—
222	C₃₁×C₂²⋊Q₈	—	2	1	no	—
223	C₃₁×C₂²⋊Q₈	—	2	1	no	—
224	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	1	no	—
232	C₃₁×#121	—	2	1	no	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	1	no	—
235	C₃₁×#121	—	2	1	no	—
236	C₃₁×#121	—	2	1	no	—
237	C₃₁×#121	—	2	2	no	—
238	C₃₁×#121	—	2	2	no	—
239	C₃₁×#121	—	2	2	no	—
240	C₃₁×#121	—	2	2	no	—
241	C₃₁×#121	C₂³	1	1	yes	characteristic
242	C₃₁×#121	C₂³	1	2	yes	—
243	C₃₁×#121	C₂³	1	2	yes	—
244	C₃₁×#121	C₂³	1	2	yes	—
245	C₃₁×#121	C₂³	1	2	yes	—
246	C₃₁×#121	C₂³	1	1	yes	characteristic
247	C₃₁×#120	—	2	2	no	—
248	C₃₁×#120	—	2	2	no	—
249	C₄×Q₈×C₃₁	—	2	1	no	—
250	C₄×Q₈×C₃₁	—	2	1	no	—
251	C₄×Q₈×C₃₁	—	2	1	no	—
252	C₄×Q₈×C₃₁	—	2	1	no	—
253	C₄×Q₈×C₃₁	—	2	1	no	—
254	C₄×Q₈×C₃₁	—	2	1	no	—
255	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
257	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
260	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
261	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₃₁	—	2	1	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	—	2	1	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	—	2	2	no	—
268	C₄×D₄×C₃₁	—	2	2	no	—
269	C₄×D₄×C₃₁	—	2	1	no	—
270	C₄×D₄×C₃₁	—	2	1	no	—
271	C₄×D₄×C₃₁	—	2	1	no	—
272	C₄×D₄×C₃₁	—	2	1	no	—
273	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
274	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
275	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
276	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
277	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
278	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
279	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₃₁	C₂³	1	2	yes	—
281	C₄×D₄×C₃₁	C₂³	1	2	yes	—
282	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₃₁	C₂³	1	2	yes	—
284	C₄×D₄×C₃₁	C₂³	1	2	yes	—
285	C₃₁×#117	—	2	1	no	—
286	C₃₁×#117	—	2	1	no	—
287	C₃₁×#117	—	2	1	no	—
288	C₃₁×#117	—	2	1	no	—
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	C₂³	1	2	yes	—
291	C₃₁×#117	C₂³	1	1	yes	characteristic
292	C₃₁×#117	C₂³	1	1	yes	characteristic
293	C₃₁×#117	C₂³	1	1	yes	characteristic
294	C₃₁×#117	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂×C₄²×C₃₁	—	2	1	no	—
300	C₂×C₄²×C₃₁	—	2	1	no	—
301	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
304	C₃₁×#107	C₂³	1	2	yes	—
305	C₃₁×#107	C₂³	1	2	yes	—
306	C₃₁×#107	C₂³	1	2	yes	—
307	C₃₁×#107	C₂³	1	2	yes	—
308	C₃₁×#106	C₂³	1	2	yes	—
309	C₃₁×#106	C₂³	1	2	yes	—
310	C₃₁×#106	C₂³	1	2	yes	—
311	C₃₁×#106	C₂³	1	2	yes	—
312	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
313	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
315	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
318	C₃₁×#103	C₂³	1	2	yes	—
319	C₃₁×#103	C₂³	1	2	yes	—
320	C₃₁×#103	C₂³	1	2	yes	—
321	C₃₁×#103	C₂³	1	2	yes	—
322	C₃₁×#103	C₂³	1	2	yes	—
323	C₃₁×#103	C₂³	1	2	yes	—
324	C₃₁×#102	C₂³	1	2	yes	—
325	C₃₁×#102	C₂³	1	2	yes	—
326	C₃₁×#102	C₂³	1	2	yes	—
327	C₃₁×#102	C₂³	1	2	yes	—
328	C₃₁×#102	C₂³	1	2	yes	—
329	C₃₁×#102	C₂³	1	2	yes	—
330	C₃₁×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×#102	C₂³	1	2	yes	—
333	C₃₁×#102	C₂³	1	2	yes	—
334	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃₁×#97	C₂³	1	2	yes	—
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₃₁	C₂³	1	2	yes	—
341	C₄×C₈×C₃₁	C₂³	1	2	yes	—
342	C₂⁴×C₃₁	—	2	2	no	—
343	#41×C₃₁	—	4	1	no	—
344	#41×C₃₁	—	4	1	no	—
345	#41×C₃₁	—	4	1	no	—
346	#41×C₃₁	—	4	1	no	—
347	#41×C₃₁	—	8	2	no	—
348	#41×C₃₁	—	8	2	no	—
349	#41×C₃₁	—	8	2	no	—
350	#41×C₃₁	—	8	2	no	—
351	C₂×Q₈×C₃₁	—	2	1	no	—
352	C₂×Q₈×C₃₁	—	2	1	no	—
353	C₂×Q₈×C₃₁	—	2	1	no	—
354	C₂×Q₈×C₃₁	—	2	1	no	—
355	C₂×Q₈×C₃₁	—	2	1	no	—
356	C₂×Q₈×C₃₁	—	4	1	no	—
357	C₂×Q₈×C₃₁	—	4	1	no	—
358	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₃₁	—	2	1	no	—
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	2	1	no	—
365	C₂×D₄×C₃₁	—	2	2	no	—
366	C₂×D₄×C₃₁	—	2	2	no	—
367	C₂×D₄×C₃₁	—	2	2	no	—
368	C₂×D₄×C₃₁	—	2	2	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	1	no	—
371	C₂×D₄×C₃₁	—	2	1	no	—
372	C₂×D₄×C₃₁	—	2	1	no	—
373	C₂×D₄×C₃₁	—	2	1	no	—
374	C₂×D₄×C₃₁	—	2	2	no	—
375	C₂×D₄×C₃₁	—	2	2	no	—
376	C₂×D₄×C₃₁	—	4	2	no	—
377	C₂×D₄×C₃₁	—	4	2	no	—
378	C₂×D₄×C₃₁	—	8	2	no	—
379	C₂×D₄×C₃₁	—	8	2	no	—
380	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
385	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₃₁	—	2	1	no	—
387	C₂²×C₄×C₃₁	—	2	1	no	—
388	C₂²×C₄×C₃₁	—	2	1	no	—
389	C₂²×C₄×C₃₁	—	2	1	no	—
390	C₂²×C₄×C₃₁	—	2	1	no	—
391	C₂²×C₄×C₃₁	—	2	2	no	—
392	C₂²×C₄×C₃₁	—	2	2	no	—
393	C₂²×C₄×C₃₁	—	2	2	no	—
394	C₂²×C₄×C₃₁	—	2	2	no	—
395	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	SD₁₆×C₃₁	—	4	2	no	—
405	SD₁₆×C₃₁	—	4	2	no	—
406	SD₁₆×C₃₁	—	4	2	no	—
407	SD₁₆×C₃₁	—	4	2	no	—
408	SD₁₆×C₃₁	—	4	2	no	—
409	SD₁₆×C₃₁	—	4	2	no	—
410	D₈×C₃₁	—	4	2	no	—
411	D₈×C₃₁	—	4	2	no	—
412	M₁₆×C₃₁	—	4	2	no	—
413	C₂×C₈×C₃₁	—	4	2	no	—
414	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
415	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
416	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
417	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	—	2	1	no	—
424	C₄⋊C₄×C₃₁	—	2	1	no	—
425	C₄⋊C₄×C₃₁	—	2	1	no	—
426	C₄⋊C₄×C₃₁	—	2	1	no	—
427	C₄⋊C₄×C₃₁	—	2	1	no	—
428	C₄⋊C₄×C₃₁	—	2	1	no	—
429	C₄⋊C₄×C₃₁	—	2	1	no	—
430	C₄⋊C₄×C₃₁	—	2	1	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	1	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	—	2	1	no	—
435	C₄⋊C₄×C₃₁	—	2	1	no	—
436	C₄⋊C₄×C₃₁	—	2	1	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	2	no	—
439	C₄⋊C₄×C₃₁	—	2	1	no	—
440	C₄⋊C₄×C₃₁	—	2	1	no	—
441	C₄⋊C₄×C₃₁	—	2	1	no	—
442	C₄⋊C₄×C₃₁	—	2	1	no	—
443	C₄⋊C₄×C₃₁	—	2	1	no	—
444	C₄⋊C₄×C₃₁	—	2	1	no	—
445	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
457	C₂²⋊C₄×C₃₁	—	2	2	no	—
458	C₂²⋊C₄×C₃₁	—	2	1	no	—
459	C₂²⋊C₄×C₃₁	—	2	1	no	—
460	C₂²⋊C₄×C₃₁	—	2	1	no	—
461	C₂²⋊C₄×C₃₁	—	2	1	no	—
462	C₂²⋊C₄×C₃₁	—	2	1	no	—
463	C₂²⋊C₄×C₃₁	—	2	1	no	—
464	C₂²⋊C₄×C₃₁	—	2	1	no	—
465	C₂²⋊C₄×C₃₁	—	2	2	no	—
466	C₂²⋊C₄×C₃₁	—	2	2	no	—
467	C₂²⋊C₄×C₃₁	—	2	2	no	—
468	C₂²⋊C₄×C₃₁	—	2	2	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	1	no	—
474	C₂²⋊C₄×C₃₁	—	2	1	no	—
475	C₂²⋊C₄×C₃₁	—	2	2	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	2	no	—
478	C₂²⋊C₄×C₃₁	—	2	2	no	—
479	C₂²⋊C₄×C₃₁	—	2	1	no	—
480	C₂²⋊C₄×C₃₁	—	2	1	no	—
481	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
487	C₄²×C₃₁	—	2	1	no	—
488	C₄²×C₃₁	—	2	1	no	—
489	C₄²×C₃₁	—	2	1	no	—
490	C₄²×C₃₁	—	2	1	no	—
491	C₄²×C₃₁	—	2	1	no	—
492	C₄²×C₃₁	—	2	1	no	—
493	C₄²×C₃₁	—	2	1	no	—
494	C₄²×C₃₁	—	2	2	no	—
495	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
501	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
502	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
503	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
504	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
505	#60994	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
506	C₂³×C₃₁	—	2	1	no	—
507	C₂³×C₃₁	—	2	2	no	—
508	C₂³×C₃₁	—	2	2	no	—
509	C₂³×C₃₁	—	4	4	no	—
510	C₂³×C₃₁	—	8	2	no	—
511	C₂³×C₃₁	—	8	2	no	—
512	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	Q₈×C₃₁	—	2	1	no	—
516	Q₈×C₃₁	—	2	1	no	—
517	Q₈×C₃₁	—	2	1	no	—
518	Q₈×C₃₁	—	2	1	no	—
519	Q₈×C₃₁	—	2	1	no	—
520	Q₈×C₃₁	—	2	1	no	—
521	Q₈×C₃₁	—	4	1	no	—
522	Q₈×C₃₁	—	4	2	no	—
523	Q₈×C₃₁	—	4	2	no	—
524	Q₈×C₃₁	—	4	2	no	—
525	Q₈×C₃₁	—	8	1	no	—
526	Q₈×C₃₁	—	8	1	no	—
527	D₄×C₃₁	—	2	1	no	—
528	D₄×C₃₁	—	2	1	no	—
529	D₄×C₃₁	—	2	2	no	—
530	D₄×C₃₁	—	2	2	no	—
531	D₄×C₃₁	—	2	2	no	—
532	D₄×C₃₁	—	2	2	no	—
533	D₄×C₃₁	—	4	1	no	—
534	D₄×C₃₁	—	4	1	no	—
535	D₄×C₃₁	—	4	1	no	—
536	D₄×C₃₁	—	4	4	no	—
537	D₄×C₃₁	—	4	2	no	—
538	D₄×C₃₁	—	4	2	no	—
539	D₄×C₃₁	—	4	2	no	—
540	D₄×C₃₁	—	4	2	no	—
541	D₄×C₃₁	—	4	2	no	—
542	D₄×C₃₁	—	8	2	no	—
543	D₄×C₃₁	—	8	2	no	—
544	D₄×C₃₁	—	8	1	no	—
545	D₄×C₃₁	—	8	1	no	—
546	D₄×C₃₁	—	8	2	no	—
547	D₄×C₃₁	—	8	2	no	—
548	D₄×C₃₁	—	8	2	no	—
549	D₄×C₃₁	—	8	2	no	—
550	C₂×C₄×C₃₁	—	2	2	no	—
551	C₂×C₄×C₃₁	—	2	2	no	—
552	C₂×C₄×C₃₁	—	2	2	no	—
553	C₂×C₄×C₃₁	—	2	1	no	—
554	C₂×C₄×C₃₁	—	2	1	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	1	no	—
560	C₂×C₄×C₃₁	—	2	1	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	1	no	—
566	C₂×C₄×C₃₁	—	2	2	no	—
567	C₂×C₄×C₃₁	—	2	2	no	—
568	C₂×C₄×C₃₁	—	4	1	no	—
569	C₂×C₄×C₃₁	—	4	1	no	—
570	C₂×C₄×C₃₁	—	4	1	no	—
571	C₂×C₄×C₃₁	—	4	2	no	—
572	C₂×C₄×C₃₁	—	4	2	no	—
573	C₂×C₄×C₃₁	—	4	2	no	—
574	C₂×C₄×C₃₁	—	8	1	no	—
575	C₂×C₄×C₃₁	—	8	2	no	—
576	C₂×C₄×C₃₁	—	8	2	no	—
577	C₂×C₄×C₃₁	—	8	2	no	—
578	C₂×C₄×C₃₁	—	8	2	no	—
579	C₂×C₄×C₃₁	—	8	1	no	—
580	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
592	C₈×C₃₁	—	2	2	no	—
593	C₈×C₃₁	—	2	2	no	—
594	C₈×C₃₁	—	2	2	no	—
595	C₈×C₃₁	—	2	2	no	—
596	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3461	C₂×C₃₁	1	1	yes	characteristic, complemented
598	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
600	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
601	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3241	C₂×C₃₁	1	2	yes	complemented
603	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
605	#3221	C₂×C₃₁	1	2	yes	complemented
606	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
608	#3200	C₂×C₃₁	1	2	yes	complemented
609	#3198	C₂×C₃₁	1	2	yes	complemented
610	#3179	C₂×C₃₁	1	2	yes	complemented
611	#3174	C₂×C₃₁	1	2	yes	complemented
612	#3123	C₂×C₃₁	1	2	yes	complemented
613	#3118	C₂×C₃₁	1	2	yes	complemented
614	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
615	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
616	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
617	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
618	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
619	C₂²×C₃₁	—	2	1	no	—
620	C₂²×C₃₁	—	2	1	no	—
621	C₂²×C₃₁	—	2	1	no	—
622	C₂²×C₃₁	—	2	1	no	—
623	C₂²×C₃₁	—	2	1	no	—
624	C₂²×C₃₁	—	2	1	no	—
625	C₂²×C₃₁	—	2	1	no	—
626	C₂²×C₃₁	—	2	1	no	—
627	C₂²×C₃₁	—	2	1	no	—
628	C₂²×C₃₁	—	4	2	no	—
629	C₂²×C₃₁	—	4	2	no	—
630	C₂²×C₃₁	—	4	1	no	—
631	C₂²×C₃₁	—	4	1	no	—
632	C₂²×C₃₁	—	4	2	no	—
633	C₂²×C₃₁	—	4	2	no	—
634	C₂²×C₃₁	—	4	1	no	—
635	C₂²×C₃₁	—	4	2	no	—
636	C₂²×C₃₁	—	4	2	no	—
637	C₂²×C₃₁	—	16	4	no	—
638	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
639	C₄×C₃₁	—	2	1	no	—
640	C₄×C₃₁	—	2	1	no	—
641	C₄×C₃₁	—	2	1	no	—
642	C₄×C₃₁	—	2	1	no	—
643	C₄×C₃₁	—	2	1	no	—
644	C₄×C₃₁	—	2	1	no	—
645	C₄×C₃₁	—	2	1	no	—
646	C₄×C₃₁	—	2	1	no	—
647	C₄×C₃₁	—	2	1	no	—
648	C₄×C₃₁	—	2	1	no	—
649	C₄×C₃₁	—	4	2	no	—
650	C₄×C₃₁	—	4	1	no	—
651	C₄×C₃₁	—	4	1	no	—
652	C₄×C₃₁	—	4	1	no	—
653	C₄×C₃₁	—	4	1	no	—
654	C₄×C₃₁	—	4	1	no	—
655	C₄×C₃₁	—	4	1	no	—
656	C₄×C₃₁	—	4	1	no	—
657	C₄×C₃₁	—	4	2	no	—
658	C₄×C₃₁	#577	1	2	yes	—
659	C₄×C₃₁	#585	1	1	yes	characteristic
660	C₄×C₃₁	#585	1	1	yes	characteristic
661	#559	—	2	1	no	—
662	#559	—	2	1	no	—
663	#550	—	2	1	no	—
664	#550	—	2	1	no	—
665	#546	—	2	1	no	—
666	#546	—	2	1	no	—
667	#546	—	2	1	no	—
668	#546	—	2	1	no	—
669	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#542	—	2	1	no	—
671	#542	C₂²×C₃₁	1	1	yes	characteristic
672	#542	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#541	—	2	1	no	—
674	#541	C₂²×C₃₁	1	1	yes	characteristic
675	#541	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#540	C₂²×C₃₁	1	2	yes	—
677	#540	C₂²×C₃₁	1	2	yes	—
678	#539	—	2	1	no	—
679	#539	—	2	1	no	—
680	#537	C₂²×C₃₁	1	1	yes	characteristic
681	#536	C₂²×C₃₁	1	1	yes	characteristic
682	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#535	C₂²×C₃₁	1	2	yes	—
684	#533	—	2	1	no	—
685	#533	C₂²×C₃₁	1	1	yes	characteristic
686	#533	C₂²×C₃₁	1	1	yes	characteristic
687	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#532	C₂²×C₃₁	1	1	yes	characteristic
689	#532	C₂²×C₃₁	1	1	yes	characteristic
690	#532	C₂²×C₃₁	1	1	yes	characteristic
691	#532	C₂²×C₃₁	1	1	yes	characteristic
692	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
693	#529	—	2	1	no	—
694	#529	—	2	1	no	—
695	#529	—	2	1	no	—
696	#529	C₂²×C₃₁	1	1	yes	characteristic
697	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#518	C₂²×C₃₁	1	2	yes	—
699	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
700	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#501	C₂²×C₃₁	1	2	yes	complemented
703	#499	C₂²×C₃₁	1	2	yes	complemented
704	#496	C₂²×C₃₁	1	2	yes	—
705	#492	C₂²×C₃₁	1	2	yes	—
706	#491	C₂²×C₃₁	1	2	yes	complemented
707	#490	C₂²×C₃₁	1	2	yes	—
708	#488	C₂²×C₃₁	1	2	yes	complemented
709	#486	C₂²×C₃₁	1	2	yes	—
710	#485	C₂²×C₃₁	1	2	yes	—
711	#485	C₂²×C₃₁	1	2	yes	—
712	#485	C₂²×C₃₁	1	2	yes	—
713	#482	C₂²×C₃₁	1	2	yes	—
714	#482	C₂²×C₃₁	1	2	yes	complemented
715	#482	C₂²×C₃₁	1	2	yes	complemented
716	#481	C₂²×C₃₁	1	2	yes	complemented
717	#480	C₂²×C₃₁	1	2	yes	complemented
718	#478	C₂²×C₃₁	1	2	yes	complemented
719	#478	C₂²×C₃₁	1	2	yes	complemented
720	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
722	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
723	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
724	#476	C₂²×C₃₁	1	2	yes	complemented
725	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
729	#474	C₂²×C₃₁	1	2	yes	complemented
730	#469	C₂²×C₃₁	1	2	yes	complemented
731	#468	C₂²×C₃₁	1	2	yes	complemented
732	#468	C₂²×C₃₁	1	2	yes	complemented
733	#468	C₂²×C₃₁	1	2	yes	complemented
734	#466	C₂²×C₃₁	1	2	yes	complemented
735	#465	C₂²×C₃₁	1	2	yes	complemented
736	#465	C₂²×C₃₁	1	2	yes	complemented
737	#465	C₂²×C₃₁	1	2	yes	complemented
738	#463	C₂²×C₃₁	1	2	yes	complemented
739	#463	C₂²×C₃₁	1	2	yes	complemented
740	#461	C₂²×C₃₁	1	2	yes	complemented
741	#461	C₂²×C₃₁	1	2	yes	complemented
742	#460	C₂²×C₃₁	1	1	yes	characteristic
743	#460	C₂²×C₃₁	1	1	yes	characteristic
744	#460	C₂²×C₃₁	1	1	yes	characteristic
745	#460	C₂²×C₃₁	1	1	yes	characteristic
746	#460	C₂²×C₃₁	1	1	yes	characteristic
747	#460	C₂²×C₃₁	1	1	yes	characteristic
748	#459	C₂²×C₃₁	1	1	yes	characteristic
749	#459	C₂²×C₃₁	1	1	yes	characteristic
750	#450	C₂²×C₃₁	1	2	yes	—
751	#450	C₂²×C₃₁	1	2	yes	—
752	#450	C₂²×C₃₁	1	2	yes	—
753	#449	C₂²×C₃₁	1	2	yes	complemented
754	#449	C₂²×C₃₁	1	2	yes	complemented
755	#448	C₂²×C₃₁	1	2	yes	complemented
756	#448	C₂²×C₃₁	1	2	yes	complemented
757	#447	C₂²×C₃₁	1	2	yes	—
758	#442	C₂²×C₃₁	1	2	yes	complemented
759	#440	C₂²×C₃₁	1	2	yes	complemented
760	#440	C₂²×C₃₁	1	2	yes	complemented
761	#440	C₂²×C₃₁	1	2	yes	complemented
762	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
763	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
764	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
765	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
766	#433	C₂²×C₃₁	1	2	yes	—
767	#433	C₂²×C₃₁	1	2	yes	complemented
768	#432	C₂²×C₃₁	1	1	yes	characteristic
769	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	#431	C₂²×C₃₁	1	1	yes	characteristic
771	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
772	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
773	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
774	#408	C₂²×C₃₁	1	2	yes	—
775	#405	C₂²×C₃₁	1	2	yes	complemented
776	C₂×C₃₁	—	4	1	no	—
777	C₂×C₃₁	—	4	1	no	—
778	C₂×C₃₁	—	4	1	no	—
779	C₂×C₃₁	—	8	1	no	—
780	C₂×C₃₁	—	8	2	no	—
781	C₂×C₃₁	—	8	2	no	—
782	C₂×C₃₁	#3449	1	1	yes	characteristic
783	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
784	C₂×C₃₁	#3585	1	1	yes	characteristic
785	C₂×#41	—	2	1	no	—
786	C₂×#41	—	2	1	no	—
787	C₂×#41	—	2	1	no	—
788	C₂×#41	—	2	1	no	—
789	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
790	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
791	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₂²×D₄	—	2	1	no	—
793	C₂²×D₄	—	2	1	no	—
794	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
795	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
796	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
797	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
798	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
799	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
800	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
801	C₂×D₈	C₂³×C₃₁	1	2	yes	—
802	C₂×D₈	C₂³×C₃₁	1	2	yes	—
803	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
804	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
805	C₄⋊Q₈	—	2	1	no	—
806	C₄⋊Q₈	—	2	1	no	—
807	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
813	#127	—	2	2	no	—
814	#127	—	2	1	no	—
815	#127	—	2	1	no	—
816	#127	C₂³×C₃₁	1	1	yes	characteristic
817	#127	C₂³×C₃₁	1	1	yes	characteristic
818	#127	C₂³×C₃₁	1	2	yes	—
819	#126	—	2	1	no	—
820	#126	—	2	1	no	—
821	#126	—	2	1	no	—
822	#126	—	2	1	no	—
823	#126	—	2	1	no	—
824	#126	—	2	1	no	—
825	#126	—	2	1	no	—
826	#126	—	2	1	no	—
827	#125	—	2	1	no	—
828	#125	—	2	1	no	—
829	#125	—	2	1	no	—
830	#125	—	2	1	no	—
831	#125	—	2	1	no	—
832	#125	—	2	1	no	—
833	#125	—	2	1	no	—
834	#125	C₂³×C₃₁	1	1	yes	characteristic
835	#125	C₂³×C₃₁	1	1	yes	characteristic
836	#125	C₂³×C₃₁	1	2	yes	—
837	#124	—	2	2	no	—
838	#124	—	2	1	no	—
839	#124	—	2	1	no	—
840	#124	—	2	1	no	—
841	#124	—	2	1	no	—
842	#124	—	2	1	no	—
843	#124	—	2	1	no	—
844	#124	—	2	1	no	—
845	#124	C₂³×C₃₁	1	1	yes	characteristic
846	#124	C₂³×C₃₁	1	1	yes	characteristic
847	#123	—	2	1	no	—
848	#123	—	2	1	no	—
849	#123	—	2	1	no	—
850	#123	—	2	1	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	#123	—	2	2	no	—
854	#123	—	2	2	no	—
855	#123	—	2	1	no	—
856	#123	—	2	1	no	—
857	#123	—	2	1	no	—
858	#123	—	2	1	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	—	2	1	no	—
862	C₂²⋊Q₈	—	2	1	no	—
863	C₂²⋊Q₈	—	2	1	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	1	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	—	2	1	no	—
880	#121	—	2	1	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	2	no	—
884	#121	—	2	2	no	—
885	#121	—	2	2	no	—
886	#121	—	2	2	no	—
887	#121	C₂³×C₃₁	1	1	yes	characteristic
888	#121	C₂³×C₃₁	1	1	yes	characteristic
889	#121	C₂³×C₃₁	1	2	yes	—
890	#121	C₂³×C₃₁	1	2	yes	—
891	#121	C₂³×C₃₁	1	2	yes	—
892	#121	C₂³×C₃₁	1	2	yes	—
893	#120	—	2	2	no	—
894	#120	—	2	2	no	—
895	C₄×Q₈	—	2	1	no	—
896	C₄×Q₈	—	2	1	no	—
897	C₄×Q₈	—	2	1	no	—
898	C₄×Q₈	—	2	1	no	—
899	C₄×Q₈	—	2	1	no	—
900	C₄×Q₈	—	2	1	no	—
901	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
902	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
903	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
904	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
905	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
906	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
907	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
908	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	—	2	1	no	—
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	2	no	—
914	C₄×D₄	—	2	2	no	—
915	C₄×D₄	—	2	1	no	—
916	C₄×D₄	—	2	1	no	—
917	C₄×D₄	—	2	1	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
920	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
921	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
922	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
923	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
924	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
925	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
926	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
927	C₄×D₄	C₂³×C₃₁	1	2	yes	—
928	C₄×D₄	C₂³×C₃₁	1	2	yes	—
929	C₄×D₄	C₂³×C₃₁	1	2	yes	—
930	C₄×D₄	C₂³×C₃₁	1	2	yes	—
931	#117	—	2	1	no	—
932	#117	—	2	1	no	—
933	#117	—	2	1	no	—
934	#117	—	2	1	no	—
935	#117	—	2	1	no	—
936	#117	C₂³×C₃₁	1	1	yes	characteristic
937	#117	C₂³×C₃₁	1	2	yes	—
938	#117	C₂³×C₃₁	1	1	yes	characteristic
939	#117	C₂³×C₃₁	1	1	yes	characteristic
940	#117	C₂³×C₃₁	1	1	yes	characteristic
941	C₂×C₄⋊C₄	—	2	1	no	—
942	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×C₂²⋊C₄	—	2	2	no	—
944	C₂×C₂²⋊C₄	—	2	2	no	—
945	C₂×C₄²	—	2	1	no	—
946	C₂×C₄²	—	2	1	no	—
947	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
948	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
949	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
950	#107	C₂³×C₃₁	1	2	yes	—
951	#107	C₂³×C₃₁	1	2	yes	—
952	#107	C₂³×C₃₁	1	2	yes	—
953	#107	C₂³×C₃₁	1	2	yes	—
954	#106	C₂³×C₃₁	1	2	yes	—
955	#106	C₂³×C₃₁	1	2	yes	—
956	#106	C₂³×C₃₁	1	2	yes	—
957	#106	C₂³×C₃₁	1	2	yes	—
958	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
959	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
960	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
961	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
962	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
963	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
964	#103	C₂³×C₃₁	1	2	yes	—
965	#103	C₂³×C₃₁	1	2	yes	—
966	#103	C₂³×C₃₁	1	2	yes	—
967	#103	C₂³×C₃₁	1	2	yes	—
968	#103	C₂³×C₃₁	1	2	yes	—
969	#103	C₂³×C₃₁	1	2	yes	—
970	#102	C₂³×C₃₁	1	2	yes	—
971	#102	C₂³×C₃₁	1	2	yes	—
972	#102	C₂³×C₃₁	1	2	yes	—
973	#102	C₂³×C₃₁	1	2	yes	—
974	#102	C₂³×C₃₁	1	2	yes	—
975	#102	C₂³×C₃₁	1	2	yes	—
976	#102	C₂³×C₃₁	1	2	yes	—
977	#102	C₂³×C₃₁	1	2	yes	—
978	#102	C₂³×C₃₁	1	2	yes	—
979	#102	C₂³×C₃₁	1	2	yes	—
980	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
981	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
982	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
983	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
984	#97	C₂³×C₃₁	1	2	yes	—
985	#97	C₂³×C₃₁	1	2	yes	—
986	C₄×C₈	C₂³×C₃₁	1	2	yes	—
987	C₄×C₈	C₂³×C₃₁	1	2	yes	—
988	C₃₁	#60994	1	1	yes	characteristic, direct product factor, Sylow
989	C₂⁴	—	2	2	no	—
990	#41	—	4	1	no	—
991	#41	—	4	1	no	—
992	#41	—	4	1	no	—
993	#41	—	4	1	no	—
994	#41	—	8	2	no	—
995	#41	—	8	2	no	—
996	#41	—	8	2	no	—
997	#41	—	8	2	no	—
998	C₂×Q₈	—	2	1	no	—
999	C₂×Q₈	—	2	1	no	—
1000	C₂×Q₈	—	2	1	no	—
1001	C₂×Q₈	—	2	1	no	—
1002	C₂×Q₈	—	2	1	no	—
1003	C₂×Q₈	—	4	1	no	—
1004	C₂×Q₈	—	4	1	no	—
1005	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	4	2	no	—
1024	C₂×D₄	—	4	2	no	—
1025	C₂×D₄	—	8	2	no	—
1026	C₂×D₄	—	8	2	no	—
1027	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1028	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1043	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1044	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1047	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1048	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1051	SD₁₆	—	4	2	no	—
1052	SD₁₆	—	4	2	no	—
1053	SD₁₆	—	4	2	no	—
1054	SD₁₆	—	4	2	no	—
1055	SD₁₆	—	4	2	no	—
1056	SD₁₆	—	4	2	no	—
1057	D₈	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	M₁₆	—	4	2	no	—
1060	C₂×C₈	—	4	2	no	—
1061	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1062	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1063	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1064	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1094	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1096	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1097	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1101	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1103	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1129	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1132	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1133	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1134	C₄²	—	2	1	no	—
1135	C₄²	—	2	1	no	—
1136	C₄²	—	2	1	no	—
1137	C₄²	—	2	1	no	—
1138	C₄²	—	2	1	no	—
1139	C₄²	—	2	1	no	—
1140	C₄²	—	2	1	no	—
1141	C₄²	—	2	2	no	—
1142	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1143	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1144	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1145	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1146	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1147	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1148	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1149	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1150	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1151	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1152	C₂³	—	2	1	no	—
1153	C₂³	—	2	2	no	—
1154	C₂³	—	2	2	no	—
1155	C₂³	—	4	4	no	—
1156	C₂³	—	8	2	no	—
1157	C₂³	—	8	2	no	—
1158	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1159	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1160	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1161	Q₈	—	2	1	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	2	1	no	—
1165	Q₈	—	2	1	no	—
1166	Q₈	—	2	1	no	—
1167	Q₈	—	4	1	no	—
1168	Q₈	—	4	2	no	—
1169	Q₈	—	4	2	no	—
1170	Q₈	—	4	2	no	—
1171	Q₈	—	8	1	no	—
1172	Q₈	—	8	1	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	2	1	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	4	1	no	—
1180	D₄	—	4	1	no	—
1181	D₄	—	4	1	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	1	no	—
1191	D₄	—	8	1	no	—
1192	D₄	—	8	2	no	—
1193	D₄	—	8	2	no	—
1194	D₄	—	8	2	no	—
1195	D₄	—	8	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	4	1	no	—
1215	C₂×C₄	—	4	1	no	—
1216	C₂×C₄	—	4	1	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	8	1	no	—
1221	C₂×C₄	—	8	2	no	—
1222	C₂×C₄	—	8	2	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	—	8	2	no	—
1225	C₂×C₄	—	8	1	no	—
1226	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1228	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1232	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1233	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1234	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1235	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1236	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1237	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1238	C₈	—	2	2	no	—
1239	C₈	—	2	2	no	—
1240	C₈	—	2	2	no	—
1241	C₈	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	2	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	16	4	no	—
1261	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	2	no	—
1277	C₄	—	4	2	no	—
1278	C₄	—	4	1	no	—
1279	C₄	—	4	1	no	—
1280	C₄	—	4	1	no	—
1281	C₄	C₃₁×#577	1	2	yes	—
1282	C₄	C₃₁×#585	1	1	yes	characteristic
1283	C₄	C₃₁×#585	1	1	yes	characteristic
1284	C₂	—	4	1	no	—
1285	C₂	—	4	1	no	—
1286	C₂	—	4	1	no	—
1287	C₂	—	8	2	no	—
1288	C₂	—	8	2	no	—
1289	C₂	—	8	1	no	—
1290	C₂	C₃₁×#3449	1	1	yes	characteristic
1291	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1292	C₂	C₃₁×#3585	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3461	C₂	semidirect
3. C₃₁×#3254	C₂	semidirect
4. C₃₁×#3251	C₂	semidirect
5. C₃₁×#3247	C₂	semidirect
6. C₃₁×#3246	C₂	semidirect
7. C₃₁×#3241	C₂	semidirect
8. C₃₁×#3237	C₂	semidirect
9. C₃₁×#3233	C₂	semidirect
10. C₃₁×#3221	C₂	semidirect
11. C₃₁×#3217	C₂	semidirect
12. C₃₁×#3208	C₂	semidirect
13. C₃₁×#3200	C₂	semidirect
14. C₃₁×#3198	C₂	semidirect
15. C₃₁×#3179	C₂	semidirect
16. C₃₁×#3174	C₂	semidirect
17. C₃₁×#3123	C₂	semidirect
18. C₃₁×#3118	C₂	semidirect
19. C₃₁×#3115	C₂	semidirect
20. C₃₁×#3112	C₂	semidirect
21. C₃₁×#3106	C₂	semidirect
22. C₃₁×#3103	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
32. C₃₁×#544	C₂²	semidirect
35. C₃₁×#542	C₂²	semidirect
38. C₃₁×#541	C₂²	semidirect
45. C₃₁×#536	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
60. C₃₁×#529	C₂²	semidirect
63. C₄×#41×C₃₁	C₂²	semidirect
64. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
65. C₃₁×#501	C₂²	semidirect
66. C₃₁×#499	C₂²	semidirect
69. C₃₁×#491	C₂²	semidirect
71. C₃₁×#488	C₂²	semidirect
77. C₃₁×#482	C₂²	semidirect
78. C₃₁×#482	C₂²	semidirect
79. C₃₁×#481	C₂²	semidirect
80. C₃₁×#480	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
84. C₃₁×#477	C₂²	semidirect
85. C₃₁×#477	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#475	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#469	C₂²	semidirect
94. C₃₁×#468	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
96. C₃₁×#468	C₂²	semidirect
97. C₃₁×#466	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
100. C₃₁×#465	C₂²	semidirect
101. C₃₁×#463	C₂²	semidirect
102. C₃₁×#463	C₂²	semidirect
103. C₃₁×#461	C₂²	semidirect
104. C₃₁×#461	C₂²	semidirect
116. C₃₁×#449	C₂²	semidirect
117. C₃₁×#449	C₂²	semidirect
118. C₃₁×#448	C₂²	semidirect
119. C₃₁×#448	C₂²	semidirect
121. C₃₁×#442	C₂²	semidirect
122. C₃₁×#440	C₂²	semidirect
123. C₃₁×#440	C₂²	semidirect
124. C₃₁×#440	C₂²	semidirect
125. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₄×SD₁₆×C₃₁	C₂²	semidirect
127. C₄×SD₁₆×C₃₁	C₂²	semidirect
128. C₄×D₈×C₃₁	C₂²	semidirect
130. C₃₁×#433	C₂²	semidirect
132. C₃₁×#432	C₂²	semidirect
134. C₃₁×#431	C₂²	semidirect
135. C₃₁×#423	C₂²	semidirect
136. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
138. C₃₁×#405	C₂²	semidirect
505. #60994	C₃₁	direct (N × H)
596. #3508	C₂×C₃₁	semidirect
597. #3461	C₂×C₃₁	semidirect
598. #3254	C₂×C₃₁	semidirect
599. #3251	C₂×C₃₁	semidirect
600. #3247	C₂×C₃₁	semidirect
601. #3246	C₂×C₃₁	semidirect
602. #3241	C₂×C₃₁	semidirect
603. #3237	C₂×C₃₁	semidirect
604. #3233	C₂×C₃₁	semidirect
605. #3221	C₂×C₃₁	semidirect
606. #3217	C₂×C₃₁	semidirect
607. #3208	C₂×C₃₁	semidirect
608. #3200	C₂×C₃₁	semidirect
609. #3198	C₂×C₃₁	semidirect
610. #3179	C₂×C₃₁	semidirect
611. #3174	C₂×C₃₁	semidirect
612. #3123	C₂×C₃₁	semidirect
613. #3118	C₂×C₃₁	semidirect
614. #3115	C₂×C₃₁	semidirect
615. #3112	C₂×C₃₁	semidirect
616. #3106	C₂×C₃₁	semidirect
617. #3103	C₂×C₃₁	semidirect
618. #2925	C₂×C₃₁	semidirect
669. #544	C₂²×C₃₁	semidirect
672. #542	C₂²×C₃₁	semidirect
675. #541	C₂²×C₃₁	semidirect
682. #536	C₂²×C₃₁	semidirect
687. #533	C₂²×C₃₁	semidirect
697. #529	C₂²×C₃₁	semidirect
700. C₄×#41	C₂²×C₃₁	semidirect
701. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
702. #501	C₂²×C₃₁	semidirect
703. #499	C₂²×C₃₁	semidirect
706. #491	C₂²×C₃₁	semidirect
708. #488	C₂²×C₃₁	semidirect
714. #482	C₂²×C₃₁	semidirect
715. #482	C₂²×C₃₁	semidirect
716. #481	C₂²×C₃₁	semidirect
717. #480	C₂²×C₃₁	semidirect
718. #478	C₂²×C₃₁	semidirect
719. #478	C₂²×C₃₁	semidirect
720. #477	C₂²×C₃₁	semidirect
721. #477	C₂²×C₃₁	semidirect
722. #477	C₂²×C₃₁	semidirect
723. #476	C₂²×C₃₁	semidirect
724. #476	C₂²×C₃₁	semidirect
725. #475	C₂²×C₃₁	semidirect
726. #475	C₂²×C₃₁	semidirect
727. #475	C₂²×C₃₁	semidirect
728. #474	C₂²×C₃₁	semidirect
729. #474	C₂²×C₃₁	semidirect
730. #469	C₂²×C₃₁	semidirect
731. #468	C₂²×C₃₁	semidirect
732. #468	C₂²×C₃₁	semidirect
733. #468	C₂²×C₃₁	semidirect
734. #466	C₂²×C₃₁	semidirect
735. #465	C₂²×C₃₁	semidirect
736. #465	C₂²×C₃₁	semidirect
737. #465	C₂²×C₃₁	semidirect
738. #463	C₂²×C₃₁	semidirect
739. #463	C₂²×C₃₁	semidirect
740. #461	C₂²×C₃₁	semidirect
741. #461	C₂²×C₃₁	semidirect
753. #449	C₂²×C₃₁	semidirect
754. #449	C₂²×C₃₁	semidirect
755. #448	C₂²×C₃₁	semidirect
756. #448	C₂²×C₃₁	semidirect
758. #442	C₂²×C₃₁	semidirect
759. #440	C₂²×C₃₁	semidirect
760. #440	C₂²×C₃₁	semidirect
761. #440	C₂²×C₃₁	semidirect
762. C₄×SD₁₆	C₂²×C₃₁	semidirect
763. C₄×SD₁₆	C₂²×C₃₁	semidirect
764. C₄×SD₁₆	C₂²×C₃₁	semidirect
765. C₄×D₈	C₂²×C₃₁	semidirect
767. #433	C₂²×C₃₁	semidirect
769. #432	C₂²×C₃₁	semidirect
771. #431	C₂²×C₃₁	semidirect
772. #423	C₂²×C₃₁	semidirect
773. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
775. #405	C₂²×C₃₁	semidirect
988. C₃₁	#60994	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×#3508	2
C₃₁×#3461	2
C₃₁×#3254	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3246	2
C₃₁×#3241	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3221	2
C₃₁×#3217	2
C₃₁×#3208	2
C₃₁×#3200	2
C₃₁×#3198	2
C₃₁×#3179	2
C₃₁×#3174	2
C₃₁×#3123	2
C₃₁×#3118	2
C₃₁×#3115	2
C₃₁×#3112	2
C₃₁×#3106	2
C₃₁×#3103	2
C₃₁×#2925	2
#60994	31

Subgroups — C31×#60994 #21517753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60994 #21517753