Subgroups — C₃₁×#62129 #21518888

Order 7936.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#557	C₂²	1	1	yes	characteristic
25	C₃₁×#556	—	2	1	no	—
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#555	C₂²	1	2	yes	—
29	C₃₁×#554	C₂²	1	2	yes	—
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#553	C₂²	1	2	yes	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	C₂²	1	1	yes	characteristic
35	C₃₁×#552	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#548	C₂²	1	1	yes	characteristic
40	C₃₁×#548	C₂²	1	1	yes	characteristic
41	C₃₁×#547	—	2	1	no	—
42	C₃₁×#547	—	2	1	no	—
43	C₃₁×#547	C₂²	1	1	yes	characteristic
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#537	—	2	1	no	—
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
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	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃₁×#529	—	2	1	no	—
56	C₃₁×#529	—	2	1	no	—
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#529	C₂²	1	1	yes	characteristic
59	C₃₁×#520	—	2	1	no	—
60	C₄×#41×C₃₁	—	2	1	no	—
61	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
62	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
63	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
65	C₃₁×#501	C₂²	1	2	yes	—
66	C₃₁×#501	C₂²	1	2	yes	—
67	C₃₁×#499	C₂²	1	2	yes	—
68	C₃₁×#491	C₂²	1	2	yes	—
69	C₃₁×#489	C₂²	1	2	yes	—
70	C₃₁×#488	C₂²	1	2	yes	—
71	C₃₁×#485	C₂²	1	2	yes	—
72	C₃₁×#485	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	—
74	C₃₁×#484	C₂²	1	2	yes	—
75	C₃₁×#482	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	—
77	C₃₁×#481	C₂²	1	2	yes	—
78	C₃₁×#481	C₂²	1	2	yes	—
79	C₃₁×#480	C₂²	1	2	yes	—
80	C₃₁×#479	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	—
83	C₃₁×#478	C₂²	1	2	yes	—
84	C₃₁×#478	C₂²	1	2	yes	—
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	1	yes	characteristic
87	C₃₁×#477	C₂²	1	1	yes	characteristic
88	C₃₁×#477	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	1	yes	characteristic
90	C₃₁×#476	C₂²	1	2	yes	—
91	C₃₁×#475	C₂²	1	1	yes	characteristic
92	C₃₁×#475	C₂²	1	1	yes	characteristic
93	C₃₁×#475	C₂²	1	1	yes	characteristic
94	C₃₁×#475	C₂²	1	2	yes	—
95	C₃₁×#475	C₂²	1	1	yes	characteristic
96	C₃₁×#475	C₂²	1	2	yes	—
97	C₃₁×#475	C₂²	1	1	yes	characteristic
98	C₃₁×#475	C₂²	1	1	yes	characteristic
99	C₃₁×#474	C₂²	1	1	yes	characteristic
100	C₃₁×#474	C₂²	1	1	yes	characteristic
101	C₃₁×#469	C₂²	1	2	yes	—
102	C₃₁×#468	C₂²	1	2	yes	—
103	C₃₁×#466	C₂²	1	2	yes	—
104	C₃₁×#465	C₂²	1	2	yes	—
105	C₃₁×#465	C₂²	1	2	yes	—
106	C₃₁×#465	C₂²	1	2	yes	—
107	C₃₁×#463	C₂²	1	2	yes	—
108	C₃₁×#463	C₂²	1	2	yes	—
109	C₃₁×#461	C₂²	1	2	yes	—
110	C₃₁×#460	C₂²	1	1	yes	characteristic
111	C₃₁×#460	C₂²	1	1	yes	characteristic
112	C₃₁×#460	C₂²	1	1	yes	characteristic
113	C₃₁×#459	C₂²	1	1	yes	characteristic
114	C₃₁×#449	C₂²	1	2	yes	—
115	C₃₁×#448	C₂²	1	2	yes	—
116	C₃₁×#448	C₂²	1	2	yes	—
117	C₃₁×#446	C₂²	1	2	yes	—
118	C₃₁×#442	C₂²	1	2	yes	—
119	C₃₁×#440	C₂²	1	2	yes	—
120	C₃₁×#440	C₂²	1	2	yes	—
121	C₃₁×#440	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₃₁	C₂²	1	2	yes	—
127	C₃₁×#432	C₂²	1	1	yes	characteristic
128	C₃₁×#432	C₂²	1	1	yes	characteristic
129	C₃₁×#431	C₂²	1	1	yes	characteristic
130	C₃₁×#428	C₂²	1	2	yes	—
131	C₃₁×#427	C₂²	1	2	yes	—
132	C₂×C₃₁×#106	C₂²	1	2	yes	—
133	C₃₁×#423	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
135	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
136	C₃₁×#419	C₂²	1	2	yes	—
137	C₃₁×#416	C₂²	1	2	yes	—
138	C₂×C₃₁×#103	C₂²	1	2	yes	—
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	D₄	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₃₁	—	2	1	no	—
146	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	1	yes	characteristic
166	C₃₁×#126	—	2	1	no	—
167	C₃₁×#126	—	2	1	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#126	—	2	1	no	—
173	C₃₁×#126	—	2	1	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	—	2	1	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	C₂³	1	1	yes	characteristic
180	C₃₁×#125	C₂³	1	1	yes	characteristic
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	—	2	1	no	—
189	C₃₁×#124	—	2	1	no	—
190	C₃₁×#124	C₂³	1	1	yes	characteristic
191	C₃₁×#124	C₂³	1	1	yes	characteristic
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	1	no	—
194	C₃₁×#123	—	2	1	no	—
195	C₃₁×#123	—	2	1	no	—
196	C₃₁×#123	—	2	1	no	—
197	C₃₁×#123	—	2	1	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	1	no	—
203	C₃₁×C₂²⋊Q₈	—	2	1	no	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	1	no	—
209	C₃₁×C₂²⋊Q₈	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₃₁×#121	—	2	1	no	—
219	C₃₁×#121	—	2	1	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	1	no	—
224	C₃₁×#121	—	2	1	no	—
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	C₂³	1	2	yes	—
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	1	yes	characteristic
230	C₃₁×#121	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	—	2	1	no	—
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	—	2	1	no	—
239	C₄×Q₈×C₃₁	—	2	1	no	—
240	C₄×Q₈×C₃₁	—	2	1	no	—
241	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
242	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	—	2	1	no	—
252	C₄×D₄×C₃₁	—	2	1	no	—
253	C₄×D₄×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	1	no	—
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	1	no	—
257	C₄×D₄×C₃₁	—	2	1	no	—
258	C₄×D₄×C₃₁	—	2	2	no	—
259	C₄×D₄×C₃₁	—	2	2	no	—
260	C₄×D₄×C₃₁	—	2	1	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
264	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
265	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
266	C₄×D₄×C₃₁	C₂³	1	2	yes	—
267	C₄×D₄×C₃₁	C₂³	1	2	yes	—
268	C₄×D₄×C₃₁	C₂³	1	2	yes	—
269	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#117	—	2	1	no	—
275	C₃₁×#117	—	2	1	no	—
276	C₃₁×#117	—	2	2	no	—
277	C₃₁×#117	—	2	1	no	—
278	C₃₁×#117	—	2	1	no	—
279	C₃₁×#117	—	2	1	no	—
280	C₃₁×#117	—	2	1	no	—
281	C₃₁×#117	—	2	1	no	—
282	C₃₁×#117	D₄	1	1	yes	characteristic
283	C₃₁×#117	D₄	1	1	yes	characteristic
284	C₃₁×#117	D₄	1	1	yes	characteristic
285	C₃₁×#117	C₂³	1	2	yes	—
286	C₃₁×#117	C₂³	1	2	yes	—
287	C₃₁×#117	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₃₁	—	2	1	no	—
296	C₂×C₄²×C₃₁	—	2	1	no	—
297	C₂×C₄²×C₃₁	—	2	1	no	—
298	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
301	C₃₁×#107	C₂³	1	2	yes	—
302	C₃₁×#107	C₂³	1	2	yes	—
303	C₃₁×#107	C₂³	1	2	yes	—
304	C₃₁×#107	C₂³	1	2	yes	—
305	C₃₁×#107	C₂³	1	2	yes	—
306	C₃₁×#106	C₂³	1	2	yes	—
307	C₃₁×#106	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×#106	C₂³	1	2	yes	—
313	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
315	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
317	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
318	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
325	C₃₁×#103	C₂³	1	2	yes	—
326	C₃₁×#103	C₂³	1	2	yes	—
327	C₃₁×#103	C₂³	1	2	yes	—
328	C₃₁×#103	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×#102	C₂³	1	2	yes	—
335	C₃₁×#102	C₂³	1	2	yes	—
336	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₃₁×#97	C₂³	1	2	yes	—
341	C₄×C₈×C₃₁	C₂³	1	2	yes	—
342	#41×C₃₁	—	2	2	no	—
343	#41×C₃₁	—	4	2	no	—
344	#41×C₃₁	—	4	1	no	—
345	#41×C₃₁	—	4	4	no	—
346	#41×C₃₁	—	4	4	no	—
347	#41×C₃₁	—	8	2	no	—
348	#41×C₃₁	—	8	2	no	—
349	C₂×Q₈×C₃₁	—	2	1	no	—
350	C₂×Q₈×C₃₁	—	2	1	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	2	no	—
356	C₂×Q₈×C₃₁	—	2	2	no	—
357	C₂×Q₈×C₃₁	—	2	2	no	—
358	C₂×Q₈×C₃₁	—	4	1	no	—
359	C₂×Q₈×C₃₁	—	4	1	no	—
360	C₂×Q₈×C₃₁	—	8	2	no	—
361	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₃₁	—	2	2	no	—
366	C₂×D₄×C₃₁	—	2	1	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	—	2	1	no	—
372	C₂×D₄×C₃₁	—	2	1	no	—
373	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₃₁	—	2	1	no	—
379	C₂²×C₄×C₃₁	—	2	1	no	—
380	C₂²×C₄×C₃₁	—	2	1	no	—
381	C₂²×C₄×C₃₁	—	2	1	no	—
382	C₂²×C₄×C₃₁	—	2	2	no	—
383	C₂²×C₄×C₃₁	—	2	1	no	—
384	C₂²×C₄×C₃₁	—	2	1	no	—
385	C₂²×C₄×C₃₁	—	2	1	no	—
386	C₂²×C₄×C₃₁	—	2	2	no	—
387	C₂²×C₄×C₃₁	—	2	2	no	—
388	C₂²×C₄×C₃₁	—	2	2	no	—
389	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	SD₁₆×C₃₁	—	2	4	no	—
399	SD₁₆×C₃₁	—	4	2	no	—
400	SD₁₆×C₃₁	—	4	2	no	—
401	D₈×C₃₁	—	4	2	no	—
402	M₁₆×C₃₁	—	4	2	no	—
403	C₂×C₈×C₃₁	—	4	2	no	—
404	C₂×C₈×C₃₁	—	4	2	no	—
405	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
406	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
407	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
408	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	—	2	1	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	1	no	—
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	2	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	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
452	C₂²⋊C₄×C₃₁	—	2	1	no	—
453	C₂²⋊C₄×C₃₁	—	2	1	no	—
454	C₂²⋊C₄×C₃₁	—	2	1	no	—
455	C₂²⋊C₄×C₃₁	—	2	1	no	—
456	C₂²⋊C₄×C₃₁	—	2	1	no	—
457	C₂²⋊C₄×C₃₁	—	2	2	no	—
458	C₂²⋊C₄×C₃₁	—	2	2	no	—
459	C₂²⋊C₄×C₃₁	—	2	2	no	—
460	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
466	C₂²⋊C₄×C₃₁	—	2	1	no	—
467	C₂²⋊C₄×C₃₁	—	2	1	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	2	no	—
470	C₂²⋊C₄×C₃₁	—	2	2	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	no	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
479	C₄²×C₃₁	—	2	1	no	—
480	C₄²×C₃₁	—	2	1	no	—
481	C₄²×C₃₁	—	2	1	no	—
482	C₄²×C₃₁	—	2	1	no	—
483	C₄²×C₃₁	—	2	1	no	—
484	C₄²×C₃₁	—	2	1	no	—
485	C₄²×C₃₁	—	2	1	no	—
486	C₄²×C₃₁	—	2	1	no	—
487	C₄²×C₃₁	—	2	1	no	—
488	C₄²×C₃₁	—	2	2	no	—
489	C₄²×C₃₁	—	2	2	no	—
490	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
497	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
498	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
499	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
500	#62129	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
501	C₂³×C₃₁	—	2	1	no	—
502	C₂³×C₃₁	—	2	2	no	—
503	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	Q₈×C₃₁	—	2	1	no	—
507	Q₈×C₃₁	—	2	1	no	—
508	Q₈×C₃₁	—	2	1	no	—
509	Q₈×C₃₁	—	2	1	no	—
510	Q₈×C₃₁	—	2	1	no	—
511	Q₈×C₃₁	—	4	1	no	—
512	Q₈×C₃₁	—	4	2	no	—
513	Q₈×C₃₁	—	4	2	no	—
514	Q₈×C₃₁	—	4	2	no	—
515	Q₈×C₃₁	—	4	2	no	—
516	Q₈×C₃₁	—	4	2	no	—
517	Q₈×C₃₁	—	4	2	no	—
518	Q₈×C₃₁	—	8	2	no	—
519	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
520	D₄×C₃₁	—	2	2	no	—
521	D₄×C₃₁	—	2	2	no	—
522	D₄×C₃₁	—	2	2	no	—
523	D₄×C₃₁	—	2	1	no	—
524	D₄×C₃₁	—	2	1	no	—
525	D₄×C₃₁	—	2	2	no	—
526	D₄×C₃₁	—	4	1	no	—
527	D₄×C₃₁	—	4	2	no	—
528	D₄×C₃₁	—	4	2	no	—
529	D₄×C₃₁	—	4	2	no	—
530	D₄×C₃₁	—	4	4	no	—
531	D₄×C₃₁	—	4	2	no	—
532	D₄×C₃₁	—	4	2	no	—
533	D₄×C₃₁	—	8	2	no	—
534	D₄×C₃₁	—	8	2	no	—
535	C₂×C₄×C₃₁	—	2	2	no	—
536	C₂×C₄×C₃₁	—	2	1	no	—
537	C₂×C₄×C₃₁	—	2	2	no	—
538	C₂×C₄×C₃₁	—	2	2	no	—
539	C₂×C₄×C₃₁	—	2	2	no	—
540	C₂×C₄×C₃₁	—	2	1	no	—
541	C₂×C₄×C₃₁	—	2	1	no	—
542	C₂×C₄×C₃₁	—	2	1	no	—
543	C₂×C₄×C₃₁	—	2	1	no	—
544	C₂×C₄×C₃₁	—	2	1	no	—
545	C₂×C₄×C₃₁	—	2	1	no	—
546	C₂×C₄×C₃₁	—	2	1	no	—
547	C₂×C₄×C₃₁	—	2	1	no	—
548	C₂×C₄×C₃₁	—	2	1	no	—
549	C₂×C₄×C₃₁	—	2	1	no	—
550	C₂×C₄×C₃₁	—	2	2	no	—
551	C₂×C₄×C₃₁	—	2	1	no	—
552	C₂×C₄×C₃₁	—	2	1	no	—
553	C₂×C₄×C₃₁	—	2	2	no	—
554	C₂×C₄×C₃₁	—	2	2	no	—
555	C₂×C₄×C₃₁	—	4	1	no	—
556	C₂×C₄×C₃₁	—	4	1	no	—
557	C₂×C₄×C₃₁	—	4	2	no	—
558	C₂×C₄×C₃₁	—	4	2	no	—
559	C₂×C₄×C₃₁	—	4	2	no	—
560	C₂×C₄×C₃₁	—	4	4	no	—
561	C₂×C₄×C₃₁	—	4	2	no	—
562	C₂×C₄×C₃₁	—	4	2	no	—
563	C₂×C₄×C₃₁	—	4	2	no	—
564	C₂×C₄×C₃₁	—	4	2	no	—
565	C₂×C₄×C₃₁	—	8	2	no	—
566	C₂×C₄×C₃₁	—	8	2	no	—
567	C₂×C₄×C₃₁	—	8	2	no	—
568	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
580	C₈×C₃₁	—	2	2	no	—
581	C₈×C₃₁	—	2	2	no	—
582	C₈×C₃₁	—	2	2	no	—
583	C₈×C₃₁	—	2	2	no	—
584	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
585	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#3388	C₂×C₃₁	1	2	yes	complemented
587	#3376	C₂×C₃₁	1	2	yes	complemented
588	#3348	C₂×C₃₁	1	2	yes	complemented
589	#3345	C₂×C₃₁	1	2	yes	complemented
590	#3337	C₂×C₃₁	1	2	yes	complemented
591	#3321	C₂×C₃₁	1	2	yes	complemented
592	#3320	C₂×C₃₁	1	2	yes	complemented
593	#3301	C₂×C₃₁	1	2	yes	complemented
594	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
595	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
596	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
597	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
598	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
599	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
600	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
601	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
602	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
603	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
604	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
605	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
607	C₂²×C₃₁	—	2	1	no	—
608	C₂²×C₃₁	—	2	1	no	—
609	C₂²×C₃₁	—	2	1	no	—
610	C₂²×C₃₁	—	2	1	no	—
611	C₂²×C₃₁	—	2	1	no	—
612	C₂²×C₃₁	—	2	1	no	—
613	C₂²×C₃₁	—	2	1	no	—
614	C₂²×C₃₁	—	2	1	no	—
615	C₂²×C₃₁	—	4	1	no	—
616	C₂²×C₃₁	—	4	2	no	—
617	C₂²×C₃₁	—	4	2	no	—
618	C₂²×C₃₁	—	4	1	no	—
619	C₂²×C₃₁	—	4	1	no	—
620	C₂²×C₃₁	—	4	2	no	—
621	C₂²×C₃₁	#575	1	2	yes	—
622	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
623	C₄×C₃₁	—	2	1	no	—
624	C₄×C₃₁	—	2	1	no	—
625	C₄×C₃₁	—	2	1	no	—
626	C₄×C₃₁	—	2	2	no	—
627	C₄×C₃₁	—	2	1	no	—
628	C₄×C₃₁	—	2	1	no	—
629	C₄×C₃₁	—	2	1	no	—
630	C₄×C₃₁	—	2	1	no	—
631	C₄×C₃₁	—	2	1	no	—
632	C₄×C₃₁	—	2	1	no	—
633	C₄×C₃₁	—	2	1	no	—
634	C₄×C₃₁	—	4	1	no	—
635	C₄×C₃₁	—	4	1	no	—
636	C₄×C₃₁	—	4	1	no	—
637	C₄×C₃₁	—	4	2	no	—
638	C₄×C₃₁	—	4	1	no	—
639	C₄×C₃₁	—	4	1	no	—
640	C₄×C₃₁	—	4	1	no	—
641	C₄×C₃₁	—	4	2	no	—
642	C₄×C₃₁	—	4	2	no	—
643	C₄×C₃₁	#577	1	2	yes	—
644	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
645	C₄×C₃₁	#585	1	1	yes	characteristic
646	#557	C₂²×C₃₁	1	1	yes	characteristic
647	#556	—	2	1	no	—
648	#556	—	2	1	no	—
649	#556	C₂²×C₃₁	1	1	yes	characteristic
650	#555	C₂²×C₃₁	1	2	yes	—
651	#554	C₂²×C₃₁	1	2	yes	—
652	#553	C₂²×C₃₁	1	2	yes	—
653	#553	C₂²×C₃₁	1	2	yes	—
654	#552	—	2	1	no	—
655	#552	—	2	1	no	—
656	#552	C₂²×C₃₁	1	1	yes	characteristic
657	#552	C₂²×C₃₁	1	1	yes	characteristic
658	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
659	#548	—	2	1	no	—
660	#548	—	2	1	no	—
661	#548	C₂²×C₃₁	1	1	yes	characteristic
662	#548	C₂²×C₃₁	1	1	yes	characteristic
663	#547	—	2	1	no	—
664	#547	—	2	1	no	—
665	#547	C₂²×C₃₁	1	1	yes	characteristic
666	#542	—	2	1	no	—
667	#542	—	2	1	no	—
668	#537	—	2	1	no	—
669	#533	—	2	1	no	—
670	#533	C₂²×C₃₁	1	1	yes	characteristic
671	#533	C₂²×C₃₁	1	1	yes	characteristic
672	#533	C₂²×C₃₁	1	1	yes	characteristic
673	#532	C₂²×C₃₁	1	1	yes	characteristic
674	#532	C₂²×C₃₁	1	1	yes	characteristic
675	#532	C₂²×C₃₁	1	1	yes	characteristic
676	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
677	#529	—	2	1	no	—
678	#529	—	2	1	no	—
679	#529	C₂²×C₃₁	1	1	yes	characteristic
680	#529	C₂²×C₃₁	1	1	yes	characteristic
681	#520	—	2	1	no	—
682	C₄×#41	—	2	1	no	—
683	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
684	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
685	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
686	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
687	#501	C₂²×C₃₁	1	2	yes	—
688	#501	C₂²×C₃₁	1	2	yes	—
689	#499	C₂²×C₃₁	1	2	yes	—
690	#491	C₂²×C₃₁	1	2	yes	—
691	#489	C₂²×C₃₁	1	2	yes	—
692	#488	C₂²×C₃₁	1	2	yes	—
693	#485	C₂²×C₃₁	1	2	yes	—
694	#485	C₂²×C₃₁	1	2	yes	—
695	#485	C₂²×C₃₁	1	2	yes	—
696	#484	C₂²×C₃₁	1	2	yes	—
697	#482	C₂²×C₃₁	1	2	yes	—
698	#482	C₂²×C₃₁	1	2	yes	—
699	#481	C₂²×C₃₁	1	2	yes	—
700	#481	C₂²×C₃₁	1	2	yes	—
701	#480	C₂²×C₃₁	1	2	yes	—
702	#479	C₂²×C₃₁	1	2	yes	—
703	#479	C₂²×C₃₁	1	2	yes	—
704	#479	C₂²×C₃₁	1	2	yes	—
705	#478	C₂²×C₃₁	1	2	yes	—
706	#478	C₂²×C₃₁	1	2	yes	—
707	#478	C₂²×C₃₁	1	2	yes	—
708	#477	C₂²×C₃₁	1	1	yes	characteristic
709	#477	C₂²×C₃₁	1	1	yes	characteristic
710	#477	C₂²×C₃₁	1	1	yes	characteristic
711	#476	C₂²×C₃₁	1	1	yes	characteristic
712	#476	C₂²×C₃₁	1	2	yes	—
713	#475	C₂²×C₃₁	1	1	yes	characteristic
714	#475	C₂²×C₃₁	1	1	yes	characteristic
715	#475	C₂²×C₃₁	1	2	yes	—
716	#475	C₂²×C₃₁	1	2	yes	—
717	#475	C₂²×C₃₁	1	1	yes	characteristic
718	#475	C₂²×C₃₁	1	1	yes	characteristic
719	#475	C₂²×C₃₁	1	1	yes	characteristic
720	#475	C₂²×C₃₁	1	1	yes	characteristic
721	#474	C₂²×C₃₁	1	1	yes	characteristic
722	#474	C₂²×C₃₁	1	1	yes	characteristic
723	#469	C₂²×C₃₁	1	2	yes	—
724	#468	C₂²×C₃₁	1	2	yes	—
725	#466	C₂²×C₃₁	1	2	yes	—
726	#465	C₂²×C₃₁	1	2	yes	—
727	#465	C₂²×C₃₁	1	2	yes	—
728	#465	C₂²×C₃₁	1	2	yes	—
729	#463	C₂²×C₃₁	1	2	yes	—
730	#463	C₂²×C₃₁	1	2	yes	—
731	#461	C₂²×C₃₁	1	2	yes	—
732	#460	C₂²×C₃₁	1	1	yes	characteristic
733	#460	C₂²×C₃₁	1	1	yes	characteristic
734	#460	C₂²×C₃₁	1	1	yes	characteristic
735	#459	C₂²×C₃₁	1	1	yes	characteristic
736	#449	C₂²×C₃₁	1	2	yes	—
737	#448	C₂²×C₃₁	1	2	yes	—
738	#448	C₂²×C₃₁	1	2	yes	—
739	#446	C₂²×C₃₁	1	2	yes	—
740	#442	C₂²×C₃₁	1	2	yes	—
741	#440	C₂²×C₃₁	1	2	yes	—
742	#440	C₂²×C₃₁	1	2	yes	—
743	#440	C₂²×C₃₁	1	2	yes	—
744	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
745	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
746	#435	C₂²×C₃₁	1	2	yes	—
747	#435	C₂²×C₃₁	1	2	yes	—
748	C₈×D₄	C₂²×C₃₁	1	2	yes	—
749	#432	C₂²×C₃₁	1	1	yes	characteristic
750	#432	C₂²×C₃₁	1	1	yes	characteristic
751	#431	C₂²×C₃₁	1	1	yes	characteristic
752	#428	C₂²×C₃₁	1	2	yes	—
753	#427	C₂²×C₃₁	1	2	yes	—
754	C₂×#106	C₂²×C₃₁	1	2	yes	—
755	#423	C₂²×C₃₁	1	1	yes	characteristic
756	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
757	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
758	#419	C₂²×C₃₁	1	2	yes	—
759	#416	C₂²×C₃₁	1	2	yes	—
760	C₂×#103	C₂²×C₃₁	1	2	yes	—
761	C₂×C₃₁	—	2	2	no	—
762	C₂×C₃₁	—	4	1	no	—
763	C₂×C₃₁	—	4	1	no	—
764	C₂×C₃₁	—	8	1	no	—
765	C₂×C₃₁	—	8	2	no	—
766	C₂×C₃₁	#3489	1	1	yes	characteristic
767	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
768	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
769	C₂×#41	—	2	1	no	—
770	C₂×#41	—	2	1	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	—	2	1	no	—
773	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
774	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
775	C₂²×Q₈	—	2	1	no	—
776	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
781	C₂×D₈	C₂³×C₃₁	1	2	yes	—
782	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
783	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
784	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
785	C₄⋊Q₈	—	2	1	no	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
793	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	#127	C₂³×C₃₁	1	1	yes	characteristic
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	2	no	—
799	#126	—	2	2	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	2	1	no	—
803	#126	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	C₂³×C₃₁	1	1	yes	characteristic
810	#125	C₂³×C₃₁	1	1	yes	characteristic
811	#125	C₂³×C₃₁	1	2	yes	—
812	#125	C₂³×C₃₁	1	2	yes	—
813	#124	—	2	1	no	—
814	#124	—	2	1	no	—
815	#124	—	2	2	no	—
816	#124	—	2	2	no	—
817	#124	—	2	1	no	—
818	#124	—	2	1	no	—
819	#124	—	2	1	no	—
820	#124	C₂³×C₃₁	1	1	yes	characteristic
821	#124	C₂³×C₃₁	1	1	yes	characteristic
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	1	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	2	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	2	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
845	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
848	#121	—	2	1	no	—
849	#121	—	2	1	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	—	2	1	no	—
854	#121	—	2	1	no	—
855	#121	—	2	1	no	—
856	#121	C₂³×C₃₁	1	1	yes	characteristic
857	#121	C₂³×C₃₁	1	1	yes	characteristic
858	#121	C₂³×C₃₁	1	2	yes	—
859	#121	C₂³×C₃₁	1	2	yes	—
860	#121	C₂³×C₃₁	1	2	yes	—
861	C₄×Q₈	—	2	1	no	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×Q₈	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
872	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	—	2	2	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
894	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
895	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
896	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
897	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
898	C₄×D₄	C₂³×C₃₁	1	2	yes	—
899	C₄×D₄	C₂³×C₃₁	1	2	yes	—
900	C₄×D₄	C₂³×C₃₁	1	2	yes	—
901	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
902	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
903	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
904	#117	—	2	1	no	—
905	#117	—	2	1	no	—
906	#117	—	2	2	no	—
907	#117	—	2	1	no	—
908	#117	—	2	1	no	—
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	D₄×C₃₁	1	1	yes	characteristic
913	#117	D₄×C₃₁	1	1	yes	characteristic
914	#117	D₄×C₃₁	1	1	yes	characteristic
915	#117	C₂³×C₃₁	1	1	yes	characteristic
916	#117	C₂³×C₃₁	1	2	yes	—
917	#117	C₂³×C₃₁	1	2	yes	—
918	C₂×C₄⋊C₄	—	2	1	no	—
919	C₂×C₄⋊C₄	—	2	1	no	—
920	C₂×C₄⋊C₄	—	2	1	no	—
921	C₂×C₄⋊C₄	—	2	2	no	—
922	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
925	C₂×C₄²	—	2	1	no	—
926	C₂×C₄²	—	2	1	no	—
927	C₂×C₄²	—	2	1	no	—
928	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
929	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
930	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
931	#107	C₂³×C₃₁	1	2	yes	—
932	#107	C₂³×C₃₁	1	2	yes	—
933	#107	C₂³×C₃₁	1	2	yes	—
934	#107	C₂³×C₃₁	1	2	yes	—
935	#107	C₂³×C₃₁	1	2	yes	—
936	#106	C₂³×C₃₁	1	2	yes	—
937	#106	C₂³×C₃₁	1	2	yes	—
938	#106	C₂³×C₃₁	1	2	yes	—
939	#106	C₂³×C₃₁	1	2	yes	—
940	#106	C₂³×C₃₁	1	2	yes	—
941	#106	C₂³×C₃₁	1	2	yes	—
942	#106	C₂³×C₃₁	1	2	yes	—
943	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
944	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
945	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
946	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
947	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
948	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
949	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
950	#103	C₂³×C₃₁	1	2	yes	—
951	#103	C₂³×C₃₁	1	2	yes	—
952	#103	C₂³×C₃₁	1	2	yes	—
953	#103	C₂³×C₃₁	1	2	yes	—
954	#103	C₂³×C₃₁	1	2	yes	—
955	#103	C₂³×C₃₁	1	2	yes	—
956	#103	C₂³×C₃₁	1	2	yes	—
957	#103	C₂³×C₃₁	1	2	yes	—
958	#103	C₂³×C₃₁	1	2	yes	—
959	#102	C₂³×C₃₁	1	2	yes	—
960	#102	C₂³×C₃₁	1	2	yes	—
961	#102	C₂³×C₃₁	1	2	yes	—
962	#102	C₂³×C₃₁	1	2	yes	—
963	#102	C₂³×C₃₁	1	2	yes	—
964	#102	C₂³×C₃₁	1	2	yes	—
965	#102	C₂³×C₃₁	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
967	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
968	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
969	#97	C₂³×C₃₁	1	2	yes	—
970	#97	C₂³×C₃₁	1	2	yes	—
971	C₄×C₈	C₂³×C₃₁	1	2	yes	—
972	C₃₁	#62129	1	1	yes	characteristic, direct product factor, Sylow
973	#41	—	2	2	no	—
974	#41	—	4	2	no	—
975	#41	—	4	1	no	—
976	#41	—	4	4	no	—
977	#41	—	4	4	no	—
978	#41	—	8	2	no	—
979	#41	—	8	2	no	—
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	2	1	no	—
985	C₂×Q₈	—	2	1	no	—
986	C₂×Q₈	—	2	2	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	4	1	no	—
990	C₂×Q₈	—	4	1	no	—
991	C₂×Q₈	—	8	2	no	—
992	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1025	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1029	SD₁₆	—	2	4	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	D₈	—	4	2	no	—
1033	M₁₆	—	4	2	no	—
1034	C₂×C₈	—	4	2	no	—
1035	C₂×C₈	—	4	2	no	—
1036	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1038	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1039	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1071	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1072	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1073	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1078	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1079	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1080	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1081	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1105	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1106	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1107	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1108	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1109	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	1	no	—
1117	C₄²	—	2	1	no	—
1118	C₄²	—	2	1	no	—
1119	C₄²	—	2	2	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1122	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1123	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1124	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1125	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1126	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1127	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1128	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1129	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1131	C₂³	—	2	1	no	—
1132	C₂³	—	2	2	no	—
1133	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1134	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1135	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	1	no	—
1138	Q₈	—	2	1	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	4	1	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	4	2	no	—
1145	Q₈	—	4	2	no	—
1146	Q₈	—	4	2	no	—
1147	Q₈	—	4	2	no	—
1148	Q₈	—	8	2	no	—
1149	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
1150	D₄	—	2	2	no	—
1151	D₄	—	2	2	no	—
1152	D₄	—	2	2	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	2	1	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	4	1	no	—
1157	D₄	—	4	2	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	4	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	8	2	no	—
1196	C₂×C₄	—	8	2	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1199	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1200	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1207	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1208	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1209	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1210	C₈	—	2	2	no	—
1211	C₈	—	2	2	no	—
1212	C₈	—	2	2	no	—
1213	C₈	—	2	2	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	C₃₁×#575	1	2	yes	—
1229	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	2	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	2	no	—
1250	C₄	C₃₁×#577	1	2	yes	—
1251	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1252	C₄	C₃₁×#585	1	1	yes	characteristic
1253	C₂	—	2	2	no	—
1254	C₂	—	4	1	no	—
1255	C₂	—	4	1	no	—
1256	C₂	—	8	1	no	—
1257	C₂	—	8	2	no	—
1258	C₂	C₃₁×#3489	1	1	yes	characteristic
1259	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1260	C₂	C₂×C₃₁×#577	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×#3511	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3388	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3348	C₂	semidirect
6. C₃₁×#3345	C₂	semidirect
7. C₃₁×#3337	C₂	semidirect
8. C₃₁×#3321	C₂	semidirect
9. C₃₁×#3320	C₂	semidirect
10. C₃₁×#3301	C₂	semidirect
11. C₃₁×#3251	C₂	semidirect
12. C₃₁×#3247	C₂	semidirect
13. C₃₁×#3246	C₂	semidirect
14. C₃₁×#3239	C₂	semidirect
15. C₃₁×#3237	C₂	semidirect
16. C₃₁×#3233	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3112	C₂	semidirect
19. C₃₁×#3103	C₂	semidirect
20. C₃₁×#3078	C₂	semidirect
21. C₃₁×#3076	C₂	semidirect
22. C₂×C₃₁×#475	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
500. #62129	C₃₁	direct (N × H)
584. #3511	C₂×C₃₁	semidirect
585. #3482	C₂×C₃₁	semidirect
586. #3388	C₂×C₃₁	semidirect
587. #3376	C₂×C₃₁	semidirect
588. #3348	C₂×C₃₁	semidirect
589. #3345	C₂×C₃₁	semidirect
590. #3337	C₂×C₃₁	semidirect
591. #3321	C₂×C₃₁	semidirect
592. #3320	C₂×C₃₁	semidirect
593. #3301	C₂×C₃₁	semidirect
594. #3251	C₂×C₃₁	semidirect
595. #3247	C₂×C₃₁	semidirect
596. #3246	C₂×C₃₁	semidirect
597. #3239	C₂×C₃₁	semidirect
598. #3237	C₂×C₃₁	semidirect
599. #3233	C₂×C₃₁	semidirect
600. #3115	C₂×C₃₁	semidirect
601. #3112	C₂×C₃₁	semidirect
602. #3103	C₂×C₃₁	semidirect
603. #3078	C₂×C₃₁	semidirect
604. #3076	C₂×C₃₁	semidirect
605. C₂×#475	C₂×C₃₁	semidirect
606. #2990	C₂×C₃₁	semidirect
972. C₃₁	#62129	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×#3511	2
C₃₁×#3482	2
C₃₁×#3388	2
C₃₁×#3376	2
C₃₁×#3348	2
C₃₁×#3345	2
C₃₁×#3337	2
C₃₁×#3321	2
C₃₁×#3320	2
C₃₁×#3301	2
C₃₁×#3251	2
C₃₁×#3247	2
C₃₁×#3246	2
C₃₁×#3239	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3115	2
C₃₁×#3112	2
C₃₁×#3103	2
C₃₁×#3078	2
C₃₁×#3076	2
C₂×C₃₁×#475	2
C₃₁×#2990	2
#62129	31

Subgroups — C31×#62129 #21518888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62129 #21518888