Subgroups — C₃₁×#61052 #21517811

Order 7936.

2722 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3284	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3282	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3269	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3268	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3041	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3008	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#577	—	2	8	no	—
25	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
31	C₂×C₃₁×#135	—	2	8	no	—
32	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
34	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
35	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
36	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
40	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
42	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#550	—	2	2	no	—
44	C₃₁×#550	C₂²	1	4	yes	complemented
45	C₃₁×#548	—	2	2	no	—
46	C₃₁×#548	C₂²	1	4	yes	complemented
47	C₃₁×#547	—	2	2	no	—
48	C₃₁×#547	C₂²	1	4	yes	complemented
49	C₃₁×#546	—	2	2	no	—
50	C₃₁×#546	C₂²	1	4	yes	complemented
51	C₃₁×#536	C₂²	1	1	yes	characteristic
52	C₃₁×#536	C₂²	1	1	yes	characteristic
53	C₃₁×#535	—	2	2	no	—
54	C₃₁×#535	C₂²	1	1	yes	characteristic
55	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#534	—	2	2	no	—
57	C₃₁×#525	—	2	2	no	—
58	C₃₁×#525	C₂²	1	1	yes	characteristic
59	C₃₁×#525	C₂²	1	1	yes	characteristic
60	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃₁×#123	—	2	2	no	—
62	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#518	C₂²	1	1	yes	characteristic
64	C₃₁×#497	C₂²	1	2	yes	complemented
65	C₃₁×#496	C₂²	1	2	yes	complemented
66	C₃₁×#495	C₂²	1	2	yes	complemented
67	C₃₁×#492	C₂²	1	2	yes	complemented
68	C₃₁×#468	C₂²	1	4	yes	complemented
69	C₃₁×#467	C₂²	1	2	yes	complemented
70	C₃₁×#466	C₂²	1	2	yes	complemented
71	C₃₁×#465	C₂²	1	2	yes	complemented
72	C₃₁×#465	C₂²	1	4	yes	complemented
73	C₃₁×#465	C₂²	1	2	yes	complemented
74	C₃₁×#464	C₂²	1	4	yes	complemented
75	C₃₁×#463	C₂²	1	4	yes	complemented
76	C₃₁×#462	C₂²	1	4	yes	complemented
77	C₃₁×#459	C₂²	1	4	yes	complemented
78	C₃₁×#452	C₂²	1	4	yes	complemented
79	C₃₁×#452	C₂²	1	4	yes	complemented
80	C₃₁×#452	C₂²	1	4	yes	complemented
81	C₃₁×#451	C₂²	1	4	yes	complemented
82	C₃₁×#449	C₂²	1	4	yes	complemented
83	C₃₁×#449	C₂²	1	4	yes	complemented
84	C₃₁×#449	C₂²	1	4	yes	complemented
85	C₃₁×#447	C₂²	1	4	yes	complemented
86	C₃₁×#440	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
88	C₃₁×#435	C₂²	1	4	yes	complemented
89	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
90	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#418	C₂²	1	1	yes	characteristic
95	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#416	C₂²	1	1	yes	characteristic
97	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#408	C₂²	1	1	yes	characteristic
99	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×2₋¹⁺⁴	—	2	4	no	—
102	C₃₁×2₋¹⁺⁴	—	4	2	no	—
103	C₃₁×H(5,𝔽₂)	—	2	4	no	—
104	C₃₁×H(5,𝔽₂)	—	4	2	no	—
105	C₂×#41×C₃₁	—	2	1	no	—
106	C₂×#41×C₃₁	—	2	2	no	—
107	C₂×#41×C₃₁	—	2	1	no	—
108	C₂×#41×C₃₁	—	2	2	no	—
109	C₂×#41×C₃₁	—	2	2	no	—
110	C₂×#41×C₃₁	—	2	4	no	—
111	C₂×#41×C₃₁	—	2	4	no	—
112	C₂×#41×C₃₁	—	4	2	no	—
113	C₂×#41×C₃₁	—	4	2	no	—
114	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
115	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
116	C₂×#41×C₃₁	C₂³	1	2	yes	—
117	C₂×#41×C₃₁	C₂³	1	4	yes	—
118	C₂×#41×C₃₁	C₂³	1	4	yes	—
119	C₂×#41×C₃₁	C₂³	1	2	yes	—
120	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₃₁	—	2	1	no	—
122	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₃₁	—	2	1	no	—
126	C₂²×D₄×C₃₁	—	2	1	no	—
127	C₂²×D₄×C₃₁	—	2	2	no	—
128	C₂²×D₄×C₃₁	—	2	1	no	—
129	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
131	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	—	2	1	no	—
133	C₂³×C₄×C₃₁	—	2	1	no	—
134	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₃₁×#137	—	2	4	no	—
136	C₃₁×#137	—	2	8	no	—
137	C₃₁×#137	—	4	2	no	—
138	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
139	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
140	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
141	C₃₁×#135	—	2	16	no	—
142	C₃₁×#135	—	2	16	no	—
143	C₃₁×#135	—	2	8	no	—
144	C₃₁×#135	—	2	4	no	—
145	C₂×Q₁₆×C₃₁	—	2	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	—	2	8	no	—
151	C₂×SD₁₆×C₃₁	—	2	4	no	—
152	C₂×SD₁₆×C₃₁	D₄	1	8	yes	complemented
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
163	C₂×D₈×C₃₁	—	2	4	no	—
164	C₂×D₈×C₃₁	C₂³	1	4	yes	—
165	C₂×D₈×C₃₁	C₂³	1	2	yes	—
166	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₃₁	C₂³	1	2	yes	—
168	C₃₁×#131	—	2	4	no	—
169	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
172	C₂²×C₈×C₃₁	—	2	4	no	—
173	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
175	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
176	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
177	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₃₁×C₄⋊Q₈	—	2	1	no	—
179	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
180	C₃₁×#127	—	2	4	no	—
181	C₃₁×#127	—	2	1	no	—
182	C₃₁×#127	C₂³	1	2	yes	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	4	no	—
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#124	C₂³	1	2	yes	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	1	no	—
190	C₃₁×#123	—	2	1	no	—
191	C₃₁×#123	—	2	4	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	4	no	—
194	C₃₁×#123	—	2	4	no	—
195	C₃₁×#123	D₄	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	—	2	4	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×#121	—	2	4	no	—
203	C₃₁×#121	—	2	4	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	4	no	—
206	C₃₁×#121	—	2	4	no	—
207	C₃₁×#121	—	2	4	no	—
208	C₃₁×#121	D₄	1	2	yes	—
209	C₃₁×#121	C₂³	1	4	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#120	—	2	1	no	—
213	C₃₁×#120	—	2	1	no	—
214	C₃₁×#120	—	2	2	no	—
215	C₃₁×#120	—	2	4	no	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	D₄	1	2	yes	—
218	C₄×Q₈×C₃₁	—	2	2	no	—
219	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	4	no	—
224	C₄×D₄×C₃₁	—	2	4	no	—
225	C₄×D₄×C₃₁	C₂³	1	4	yes	—
226	C₄×D₄×C₃₁	C₂³	1	4	yes	—
227	C₃₁×#117	—	2	2	no	—
228	C₃₁×#117	C₂³	1	1	yes	characteristic
229	C₃₁×#117	C₂³	1	1	yes	characteristic
230	C₃₁×#117	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
233	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
234	C₃₁×#107	C₂³	1	2	yes	—
235	C₃₁×#106	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
237	C₃₁×#103	C₂³	1	2	yes	—
238	C₃₁×#103	C₂³	1	2	yes	—
239	C₃₁×#103	C₂³	1	4	yes	—
240	C₃₁×#103	C₂³	1	4	yes	—
241	C₃₁×#102	C₂³	1	2	yes	—
242	C₃₁×#102	C₂³	1	2	yes	—
243	C₃₁×#102	C₂³	1	4	yes	—
244	C₃₁×#102	C₂³	1	4	yes	—
245	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
246	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
247	C₃₁×#97	C₂³	1	2	yes	—
248	C₄×C₈×C₃₁	C₂³	1	2	yes	—
249	C₂⁴×C₃₁	—	2	1	no	—
250	C₂⁴×C₃₁	—	2	2	no	—
251	C₂⁴×C₃₁	—	2	1	no	—
252	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
253	#41×C₃₁	—	2	2	no	—
254	#41×C₃₁	—	2	2	no	—
255	#41×C₃₁	—	2	8	no	—
256	#41×C₃₁	—	2	4	no	—
257	#41×C₃₁	—	2	8	no	—
258	#41×C₃₁	—	2	4	no	—
259	#41×C₃₁	—	2	2	no	—
260	#41×C₃₁	—	2	2	no	—
261	#41×C₃₁	—	2	2	no	—
262	#41×C₃₁	—	2	2	no	—
263	#41×C₃₁	—	4	4	no	—
264	#41×C₃₁	—	4	4	no	—
265	#41×C₃₁	—	4	2	no	—
266	#41×C₃₁	—	4	2	no	—
267	#41×C₃₁	—	4	8	no	—
268	#41×C₃₁	—	4	8	no	—
269	#41×C₃₁	—	4	8	no	—
270	#41×C₃₁	—	4	4	no	—
271	#41×C₃₁	—	4	4	no	—
272	C₂×Q₈×C₃₁	—	2	1	no	—
273	C₂×Q₈×C₃₁	—	2	2	no	—
274	C₂×Q₈×C₃₁	—	2	1	no	—
275	C₂×Q₈×C₃₁	—	2	2	no	—
276	C₂×Q₈×C₃₁	—	2	4	no	—
277	C₂×Q₈×C₃₁	—	2	2	no	—
278	C₂×Q₈×C₃₁	—	2	2	no	—
279	C₂×Q₈×C₃₁	—	4	2	no	—
280	C₂×Q₈×C₃₁	—	4	4	no	—
281	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
282	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
285	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
287	C₂×D₄×C₃₁	—	2	4	no	—
288	C₂×D₄×C₃₁	—	2	1	no	—
289	C₂×D₄×C₃₁	—	2	4	no	—
290	C₂×D₄×C₃₁	—	2	1	no	—
291	C₂×D₄×C₃₁	—	2	2	no	—
292	C₂×D₄×C₃₁	—	2	4	no	—
293	C₂×D₄×C₃₁	—	2	2	no	—
294	C₂×D₄×C₃₁	—	2	2	no	—
295	C₂×D₄×C₃₁	—	2	4	no	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	1	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	2	4	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	4	2	no	—
305	C₂×D₄×C₃₁	—	4	4	no	—
306	C₂×D₄×C₃₁	—	4	4	no	—
307	C₂×D₄×C₃₁	—	4	8	no	—
308	C₂×D₄×C₃₁	—	4	4	no	—
309	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
312	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
313	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₃₁	—	2	1	no	—
318	C₂²×C₄×C₃₁	—	2	2	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	2	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	4	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	2	no	—
325	C₂²×C₄×C₃₁	—	2	1	no	—
326	C₂²×C₄×C₃₁	—	2	4	no	—
327	C₂²×C₄×C₃₁	—	2	1	no	—
328	C₂²×C₄×C₃₁	—	2	4	no	—
329	C₂²×C₄×C₃₁	—	4	4	no	—
330	C₂²×C₄×C₃₁	—	4	4	no	—
331	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	Q₁₆×C₃₁	—	2	8	no	—
337	Q₁₆×C₃₁	—	2	4	no	—
338	Q₁₆×C₃₁	—	2	2	no	—
339	Q₁₆×C₃₁	—	4	2	no	—
340	SD₁₆×C₃₁	—	2	4	no	—
341	SD₁₆×C₃₁	—	2	4	no	—
342	SD₁₆×C₃₁	—	2	2	no	—
343	SD₁₆×C₃₁	—	2	4	no	—
344	SD₁₆×C₃₁	—	2	4	no	—
345	SD₁₆×C₃₁	—	2	2	no	—
346	SD₁₆×C₃₁	—	4	2	no	—
347	SD₁₆×C₃₁	—	4	2	no	—
348	SD₁₆×C₃₁	C₂×D₄	1	8	yes	—
349	SD₁₆×C₃₁	C₂×D₄	1	8	yes	—
350	D₈×C₃₁	—	2	8	no	—
351	D₈×C₃₁	—	2	4	no	—
352	D₈×C₃₁	—	2	2	no	—
353	D₈×C₃₁	—	4	2	no	—
354	M₁₆×C₃₁	—	2	2	no	—
355	M₁₆×C₃₁	—	2	2	no	—
356	M₁₆×C₃₁	—	2	4	no	—
357	C₂×C₈×C₃₁	—	2	2	no	—
358	C₂×C₈×C₃₁	—	2	4	no	—
359	C₂×C₈×C₃₁	—	2	4	no	—
360	C₂×C₈×C₃₁	—	2	4	no	—
361	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
362	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
364	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	4	no	—
369	C₄⋊C₄×C₃₁	—	2	4	no	—
370	C₄⋊C₄×C₃₁	—	2	4	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₃₁	—	2	1	no	—
377	C₂²⋊C₄×C₃₁	—	2	4	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	4	no	—
383	C₂²⋊C₄×C₃₁	—	2	4	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	4	no	—
386	C₂²⋊C₄×C₃₁	—	2	4	no	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
390	C₄²×C₃₁	—	2	4	no	—
391	C₄²×C₃₁	—	2	1	no	—
392	C₄²×C₃₁	—	2	1	no	—
393	C₄²×C₃₁	C₂⁴	1	2	yes	—
394	#61052	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂³×C₃₁	—	2	2	no	—
396	C₂³×C₃₁	—	2	2	no	—
397	C₂³×C₃₁	—	2	4	no	—
398	C₂³×C₃₁	—	2	1	no	—
399	C₂³×C₃₁	—	2	2	no	—
400	C₂³×C₃₁	—	2	1	no	—
401	C₂³×C₃₁	—	4	2	no	—
402	C₂³×C₃₁	—	4	4	no	—
403	C₂³×C₃₁	—	4	2	no	—
404	C₂³×C₃₁	—	8	2	no	—
405	C₂³×C₃₁	—	8	2	no	—
406	C₂³×C₃₁	—	8	4	no	—
407	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
408	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
409	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₃₁	—	2	4	no	—
411	Q₈×C₃₁	—	2	2	no	—
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	2	1	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	2	1	no	—
416	Q₈×C₃₁	—	2	1	no	—
417	Q₈×C₃₁	—	2	2	no	—
418	Q₈×C₃₁	—	2	1	no	—
419	Q₈×C₃₁	—	4	4	no	—
420	Q₈×C₃₁	—	4	2	no	—
421	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
422	D₄×C₃₁	—	2	4	no	—
423	D₄×C₃₁	—	2	4	no	—
424	D₄×C₃₁	—	2	2	no	—
425	D₄×C₃₁	—	2	1	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	1	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	1	no	—
430	D₄×C₃₁	—	2	2	no	—
431	D₄×C₃₁	—	2	1	no	—
432	D₄×C₃₁	—	4	4	no	—
433	D₄×C₃₁	—	4	4	no	—
434	D₄×C₃₁	—	4	8	no	—
435	D₄×C₃₁	—	4	4	no	—
436	D₄×C₃₁	—	4	4	no	—
437	D₄×C₃₁	—	4	8	no	—
438	D₄×C₃₁	—	4	2	no	—
439	D₄×C₃₁	—	4	2	no	—
440	D₄×C₃₁	—	4	2	no	—
441	D₄×C₃₁	—	8	4	no	—
442	D₄×C₃₁	—	8	2	no	—
443	D₄×C₃₁	—	8	4	no	—
444	D₄×C₃₁	—	8	2	no	—
445	D₄×C₃₁	C₂²×D₄	1	4	yes	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	4	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	4	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	4	8	no	—
460	C₂×C₄×C₃₁	—	4	4	no	—
461	C₂×C₄×C₃₁	—	4	8	no	—
462	C₂×C₄×C₃₁	—	4	4	no	—
463	C₂×C₄×C₃₁	—	4	4	no	—
464	C₂×C₄×C₃₁	—	4	2	no	—
465	C₂×C₄×C₃₁	—	4	2	no	—
466	C₂×C₄×C₃₁	—	4	2	no	—
467	C₂×C₄×C₃₁	—	8	4	no	—
468	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
469	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
474	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
475	C₈×C₃₁	—	2	2	no	—
476	C₈×C₃₁	—	2	2	no	—
477	C₈×C₃₁	—	2	2	no	—
478	C₈×C₃₁	C₂²×D₄	1	2	yes	—
479	C₈×C₃₁	C₂²×D₄	1	2	yes	—
480	C₂×#577	C₂×C₃₁	1	1	yes	characteristic, complemented
481	C₂²×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#3487	C₂×C₃₁	1	1	yes	characteristic, complemented
483	#3485	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#3284	C₂×C₃₁	1	4	yes	complemented
485	#3282	C₂×C₃₁	1	4	yes	complemented
486	#3269	C₂×C₃₁	1	4	yes	complemented
487	#3268	C₂×C₃₁	1	4	yes	complemented
488	#3154	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#3057	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
491	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
492	#3041	C₂×C₃₁	1	1	yes	characteristic, complemented
493	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#3008	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3005	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#3005	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#2949	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#2929	C₂×C₃₁	1	1	yes	characteristic, complemented
499	C₂²×C₃₁	—	2	2	no	—
500	C₂²×C₃₁	—	2	2	no	—
501	C₂²×C₃₁	—	2	4	no	—
502	C₂²×C₃₁	—	2	2	no	—
503	C₂²×C₃₁	—	2	2	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	4	no	—
506	C₂²×C₃₁	—	4	4	no	—
507	C₂²×C₃₁	—	4	4	no	—
508	C₂²×C₃₁	—	4	2	no	—
509	C₂²×C₃₁	—	4	4	no	—
510	C₂²×C₃₁	—	4	2	no	—
511	C₂²×C₃₁	—	4	1	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	1	no	—
514	C₂²×C₃₁	—	8	4	no	—
515	C₂²×C₃₁	—	8	4	no	—
516	C₂²×C₃₁	—	16	4	no	—
517	C₂²×C₃₁	D₄²	1	2	yes	—
518	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₃₁	—	2	4	no	—
520	C₄×C₃₁	—	2	2	no	—
521	C₄×C₃₁	—	2	4	no	—
522	C₄×C₃₁	—	2	2	no	—
523	C₄×C₃₁	—	4	2	no	—
524	C₄×C₃₁	—	4	2	no	—
525	C₄×C₃₁	—	4	1	no	—
526	C₄×C₃₁	—	4	2	no	—
527	C₄×C₃₁	—	4	1	no	—
528	C₄×C₃₁	D₄²	1	2	yes	—
529	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
530	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
532	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
533	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
534	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
535	#577	—	2	8	no	—
536	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
537	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
538	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
539	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
540	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
541	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
542	C₂×#135	—	2	8	no	—
543	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
545	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
546	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
547	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
549	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
550	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
551	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
552	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
553	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#550	—	2	2	no	—
555	#550	C₂²×C₃₁	1	4	yes	complemented
556	#548	—	2	2	no	—
557	#548	C₂²×C₃₁	1	4	yes	complemented
558	#547	—	2	2	no	—
559	#547	C₂²×C₃₁	1	4	yes	complemented
560	#546	—	2	2	no	—
561	#546	C₂²×C₃₁	1	4	yes	complemented
562	#536	C₂²×C₃₁	1	1	yes	characteristic
563	#536	C₂²×C₃₁	1	1	yes	characteristic
564	#535	—	2	2	no	—
565	#535	C₂²×C₃₁	1	1	yes	characteristic
566	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
567	#534	—	2	2	no	—
568	#525	—	2	2	no	—
569	#525	C₂²×C₃₁	1	1	yes	characteristic
570	#525	C₂²×C₃₁	1	1	yes	characteristic
571	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	C₂×#123	—	2	2	no	—
573	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#518	C₂²×C₃₁	1	1	yes	characteristic
575	#497	C₂²×C₃₁	1	2	yes	complemented
576	#496	C₂²×C₃₁	1	2	yes	complemented
577	#495	C₂²×C₃₁	1	2	yes	complemented
578	#492	C₂²×C₃₁	1	2	yes	complemented
579	#468	C₂²×C₃₁	1	4	yes	complemented
580	#467	C₂²×C₃₁	1	2	yes	complemented
581	#466	C₂²×C₃₁	1	2	yes	complemented
582	#465	C₂²×C₃₁	1	2	yes	complemented
583	#465	C₂²×C₃₁	1	4	yes	complemented
584	#465	C₂²×C₃₁	1	2	yes	complemented
585	#464	C₂²×C₃₁	1	4	yes	complemented
586	#463	C₂²×C₃₁	1	4	yes	complemented
587	#462	C₂²×C₃₁	1	4	yes	complemented
588	#459	C₂²×C₃₁	1	4	yes	complemented
589	#452	C₂²×C₃₁	1	4	yes	complemented
590	#452	C₂²×C₃₁	1	4	yes	complemented
591	#452	C₂²×C₃₁	1	4	yes	complemented
592	#451	C₂²×C₃₁	1	4	yes	complemented
593	#449	C₂²×C₃₁	1	4	yes	complemented
594	#449	C₂²×C₃₁	1	4	yes	complemented
595	#449	C₂²×C₃₁	1	4	yes	complemented
596	#447	C₂²×C₃₁	1	4	yes	complemented
597	#440	C₂²×C₃₁	1	4	yes	complemented
598	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
599	#435	C₂²×C₃₁	1	4	yes	complemented
600	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
601	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#418	C₂²×C₃₁	1	1	yes	characteristic
606	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	#416	C₂²×C₃₁	1	1	yes	characteristic
608	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#408	C₂²×C₃₁	1	1	yes	characteristic
610	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	C₂×C₃₁	—	2	2	no	—
613	C₂×C₃₁	—	4	2	no	—
614	C₂×C₃₁	—	4	2	no	—
615	C₂×C₃₁	—	4	4	no	—
616	C₂×C₃₁	—	8	1	no	—
617	C₂×C₃₁	—	8	2	no	—
618	C₂×C₃₁	—	8	1	no	—
619	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
620	C₂×C₃₁	#3584	1	2	yes	—
621	2₋¹⁺⁴	—	2	4	no	—
622	2₋¹⁺⁴	—	4	2	no	—
623	H(5,𝔽₂)	—	2	4	no	—
624	H(5,𝔽₂)	—	4	2	no	—
625	C₂×#41	—	2	1	no	—
626	C₂×#41	—	2	2	no	—
627	C₂×#41	—	2	1	no	—
628	C₂×#41	—	2	2	no	—
629	C₂×#41	—	2	2	no	—
630	C₂×#41	—	2	4	no	—
631	C₂×#41	—	2	4	no	—
632	C₂×#41	—	4	2	no	—
633	C₂×#41	—	4	2	no	—
634	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×#41	C₂³×C₃₁	1	4	yes	—
637	C₂×#41	C₂³×C₃₁	1	2	yes	—
638	C₂×#41	C₂³×C₃₁	1	4	yes	—
639	C₂×#41	C₂³×C₃₁	1	2	yes	—
640	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
641	C₂²×Q₈	—	2	1	no	—
642	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
643	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
644	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
645	C₂²×D₄	—	2	1	no	—
646	C₂²×D₄	—	2	1	no	—
647	C₂²×D₄	—	2	2	no	—
648	C₂²×D₄	—	2	1	no	—
649	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
651	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
652	C₂³×C₄	—	2	1	no	—
653	C₂³×C₄	—	2	1	no	—
654	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
655	#137	—	2	4	no	—
656	#137	—	2	8	no	—
657	#137	—	4	2	no	—
658	AGL(1,ℤ/8)	—	2	4	no	—
659	AGL(1,ℤ/8)	—	2	8	no	—
660	AGL(1,ℤ/8)	—	4	2	no	—
661	#135	—	2	16	no	—
662	#135	—	2	16	no	—
663	#135	—	2	8	no	—
664	#135	—	2	4	no	—
665	C₂×Q₁₆	—	2	4	no	—
666	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
667	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
668	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
670	C₂×SD₁₆	—	2	8	no	—
671	C₂×SD₁₆	—	2	4	no	—
672	C₂×SD₁₆	D₄×C₃₁	1	8	yes	complemented
673	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
681	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
683	C₂×D₈	—	2	4	no	—
684	C₂×D₈	C₂³×C₃₁	1	4	yes	—
685	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×D₈	C₂³×C₃₁	1	2	yes	—
687	C₂×D₈	C₂³×C₃₁	1	2	yes	—
688	#131	—	2	4	no	—
689	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
691	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
692	C₂²×C₈	—	2	4	no	—
693	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
694	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
695	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
696	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
697	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
700	#127	—	2	4	no	—
701	#127	—	2	1	no	—
702	#127	C₂³×C₃₁	1	2	yes	—
703	#124	—	2	1	no	—
704	#124	—	2	1	no	—
705	#124	—	2	4	no	—
706	#124	C₂³×C₃₁	1	2	yes	—
707	#124	C₂³×C₃₁	1	2	yes	—
708	#123	—	2	2	no	—
709	#123	—	2	1	no	—
710	#123	—	2	1	no	—
711	#123	—	2	4	no	—
712	#123	—	2	2	no	—
713	#123	—	2	4	no	—
714	#123	—	2	4	no	—
715	#123	D₄×C₃₁	1	2	yes	—
716	C₂²⋊Q₈	—	2	4	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
719	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
720	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
722	#121	—	2	4	no	—
723	#121	—	2	4	no	—
724	#121	—	2	2	no	—
725	#121	—	2	4	no	—
726	#121	—	2	4	no	—
727	#121	—	2	4	no	—
728	#121	D₄×C₃₁	1	2	yes	—
729	#121	C₂³×C₃₁	1	2	yes	—
730	#121	C₂³×C₃₁	1	2	yes	—
731	#121	C₂³×C₃₁	1	4	yes	—
732	#120	—	2	1	no	—
733	#120	—	2	1	no	—
734	#120	—	2	2	no	—
735	#120	—	2	4	no	—
736	#120	—	2	2	no	—
737	#120	D₄×C₃₁	1	2	yes	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
740	C₄×D₄	—	2	2	no	—
741	C₄×D₄	—	2	2	no	—
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	4	no	—
744	C₄×D₄	—	2	4	no	—
745	C₄×D₄	C₂³×C₃₁	1	4	yes	—
746	C₄×D₄	C₂³×C₃₁	1	4	yes	—
747	#117	—	2	2	no	—
748	#117	C₂³×C₃₁	1	1	yes	characteristic
749	#117	C₂³×C₃₁	1	1	yes	characteristic
750	#117	C₂³×C₃₁	1	1	yes	characteristic
751	C₂×C₄⋊C₄	—	2	4	no	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₂²⋊C₄	—	2	4	no	—
754	#107	C₂³×C₃₁	1	2	yes	—
755	#106	C₂³×C₃₁	1	2	yes	—
756	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#103	C₂³×C₃₁	1	4	yes	—
760	#103	C₂³×C₃₁	1	4	yes	—
761	#102	C₂³×C₃₁	1	2	yes	—
762	#102	C₂³×C₃₁	1	2	yes	—
763	#102	C₂³×C₃₁	1	4	yes	—
764	#102	C₂³×C₃₁	1	4	yes	—
765	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
766	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
767	#97	C₂³×C₃₁	1	2	yes	—
768	C₄×C₈	C₂³×C₃₁	1	2	yes	—
769	C₃₁	#61052	1	1	yes	characteristic, direct product factor, Sylow
770	C₂⁴	—	2	1	no	—
771	C₂⁴	—	2	2	no	—
772	C₂⁴	—	2	1	no	—
773	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
774	#41	—	2	2	no	—
775	#41	—	2	2	no	—
776	#41	—	2	8	no	—
777	#41	—	2	4	no	—
778	#41	—	2	8	no	—
779	#41	—	2	4	no	—
780	#41	—	2	2	no	—
781	#41	—	2	2	no	—
782	#41	—	2	2	no	—
783	#41	—	2	2	no	—
784	#41	—	4	4	no	—
785	#41	—	4	4	no	—
786	#41	—	4	2	no	—
787	#41	—	4	2	no	—
788	#41	—	4	8	no	—
789	#41	—	4	8	no	—
790	#41	—	4	8	no	—
791	#41	—	4	4	no	—
792	#41	—	4	4	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	4	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	—	4	4	no	—
802	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
803	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
804	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
805	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
807	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	4	no	—
827	C₂×D₄	—	4	4	no	—
828	C₂×D₄	—	4	8	no	—
829	C₂×D₄	—	4	4	no	—
830	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
831	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
832	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
833	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
834	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
835	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
836	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
837	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	4	no	—
850	C₂²×C₄	—	4	4	no	—
851	C₂²×C₄	—	4	4	no	—
852	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
853	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
857	Q₁₆	—	2	8	no	—
858	Q₁₆	—	2	4	no	—
859	Q₁₆	—	2	2	no	—
860	Q₁₆	—	4	2	no	—
861	SD₁₆	—	2	4	no	—
862	SD₁₆	—	2	4	no	—
863	SD₁₆	—	2	2	no	—
864	SD₁₆	—	2	4	no	—
865	SD₁₆	—	2	4	no	—
866	SD₁₆	—	2	2	no	—
867	SD₁₆	—	4	2	no	—
868	SD₁₆	—	4	2	no	—
869	SD₁₆	C₂×D₄×C₃₁	1	8	yes	—
870	SD₁₆	C₂×D₄×C₃₁	1	8	yes	—
871	D₈	—	2	8	no	—
872	D₈	—	2	4	no	—
873	D₈	—	2	2	no	—
874	D₈	—	4	2	no	—
875	M₁₆	—	2	2	no	—
876	M₁₆	—	2	2	no	—
877	M₁₆	—	2	4	no	—
878	C₂×C₈	—	2	2	no	—
879	C₂×C₈	—	2	4	no	—
880	C₂×C₈	—	2	4	no	—
881	C₂×C₈	—	2	4	no	—
882	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
883	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
884	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
885	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
886	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
894	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
895	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
897	C₂²⋊C₄	—	2	1	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	1	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
910	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
911	C₄²	—	2	4	no	—
912	C₄²	—	2	1	no	—
913	C₄²	—	2	1	no	—
914	C₄²	C₂⁴×C₃₁	1	2	yes	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	4	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	4	2	no	—
922	C₂³	—	4	4	no	—
923	C₂³	—	4	2	no	—
924	C₂³	—	8	2	no	—
925	C₂³	—	8	2	no	—
926	C₂³	—	8	4	no	—
927	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
928	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
929	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
930	Q₈	—	2	4	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	2	2	no	—
933	Q₈	—	2	1	no	—
934	Q₈	—	2	2	no	—
935	Q₈	—	2	1	no	—
936	Q₈	—	2	1	no	—
937	Q₈	—	2	2	no	—
938	Q₈	—	2	1	no	—
939	Q₈	—	4	4	no	—
940	Q₈	—	4	2	no	—
941	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
942	D₄	—	2	4	no	—
943	D₄	—	2	4	no	—
944	D₄	—	2	2	no	—
945	D₄	—	2	1	no	—
946	D₄	—	2	2	no	—
947	D₄	—	2	1	no	—
948	D₄	—	2	2	no	—
949	D₄	—	2	1	no	—
950	D₄	—	2	2	no	—
951	D₄	—	2	1	no	—
952	D₄	—	4	4	no	—
953	D₄	—	4	4	no	—
954	D₄	—	4	8	no	—
955	D₄	—	4	4	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	2	no	—
960	D₄	—	4	2	no	—
961	D₄	—	8	4	no	—
962	D₄	—	8	2	no	—
963	D₄	—	8	4	no	—
964	D₄	—	8	2	no	—
965	D₄	C₂²×D₄×C₃₁	1	4	yes	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	4	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	2	no	—
985	C₂×C₄	—	4	2	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	8	4	no	—
988	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
989	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
990	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
991	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
992	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
993	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
994	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
995	C₈	—	2	2	no	—
996	C₈	—	2	2	no	—
997	C₈	—	2	2	no	—
998	C₈	C₂²×D₄×C₃₁	1	2	yes	—
999	C₈	C₂²×D₄×C₃₁	1	2	yes	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	4	4	no	—
1008	C₂²	—	4	4	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	8	4	no	—
1016	C₂²	—	8	4	no	—
1017	C₂²	—	16	4	no	—
1018	C₂²	D₄²×C₃₁	1	2	yes	—
1019	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1020	C₄	—	2	2	no	—
1021	C₄	—	2	4	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	4	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	D₄²×C₃₁	1	2	yes	—
1030	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1031	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂	—	2	2	no	—
1033	C₂	—	4	2	no	—
1034	C₂	—	4	2	no	—
1035	C₂	—	4	4	no	—
1036	C₂	—	8	2	no	—
1037	C₂	—	8	1	no	—
1038	C₂	—	8	1	no	—
1039	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1040	C₂	C₃₁×#3584	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#577	C₂	semidirect
2. C₂²×C₃₁×#135	C₂	semidirect
3. C₃₁×#3487	C₂	semidirect
4. C₃₁×#3485	C₂	semidirect
5. C₃₁×#3284	C₂	semidirect
6. C₃₁×#3282	C₂	semidirect
7. C₃₁×#3269	C₂	semidirect
8. C₃₁×#3268	C₂	semidirect
9. C₃₁×#3154	C₂	semidirect
10. C₃₁×#3057	C₂	semidirect
11. C₃₁×#3050	C₂	semidirect
12. C₃₁×#3044	C₂	semidirect
13. C₃₁×#3041	C₂	semidirect
14. C₃₁×#3011	C₂	semidirect
15. C₃₁×#3008	C₂	semidirect
16. C₃₁×#3005	C₂	semidirect
17. C₃₁×#3005	C₂	semidirect
18. C₃₁×#2949	C₂	semidirect
19. C₃₁×#2929	C₂	semidirect
23. C₂²×#41×C₃₁	C₂²	semidirect
26. C₂×C₃₁×#137	C₂²	semidirect
27. C₂×C₃₁×#137	C₂²	semidirect
30. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
33. C₂×C₃₁×#135	C₂²	semidirect
34. C₂×C₃₁×#135	C₂²	semidirect
35. C₂×C₃₁×#135	C₂²	semidirect
36. C₂²×Q₁₆×C₃₁	C₂²	semidirect
38. C₂²×SD₁₆×C₃₁	C₂²	semidirect
39. C₂²×SD₁₆×C₃₁	C₂²	semidirect
42. C₂³×C₈×C₃₁	C₂²	semidirect
44. C₃₁×#550	C₂²	semidirect
46. C₃₁×#548	C₂²	semidirect
48. C₃₁×#547	C₂²	semidirect
50. C₃₁×#546	C₂²	semidirect
55. C₃₁×#535	C₂²	semidirect
60. C₃₁×#525	C₂²	semidirect
62. C₃₁×#519	C₂²	semidirect
64. C₃₁×#497	C₂²	semidirect
65. C₃₁×#496	C₂²	semidirect
66. C₃₁×#495	C₂²	semidirect
67. C₃₁×#492	C₂²	semidirect
68. C₃₁×#468	C₂²	semidirect
69. C₃₁×#467	C₂²	semidirect
70. C₃₁×#466	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#465	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
74. C₃₁×#464	C₂²	semidirect
75. C₃₁×#463	C₂²	semidirect
76. C₃₁×#462	C₂²	semidirect
77. C₃₁×#459	C₂²	semidirect
78. C₃₁×#452	C₂²	semidirect
79. C₃₁×#452	C₂²	semidirect
80. C₃₁×#452	C₂²	semidirect
81. C₃₁×#451	C₂²	semidirect
82. C₃₁×#449	C₂²	semidirect
83. C₃₁×#449	C₂²	semidirect
84. C₃₁×#449	C₂²	semidirect
85. C₃₁×#447	C₂²	semidirect
86. C₃₁×#440	C₂²	semidirect
87. C₄×SD₁₆×C₃₁	C₂²	semidirect
88. C₃₁×#435	C₂²	semidirect
89. C₈×D₄×C₃₁	C₂²	semidirect
90. C₃₁×#427	C₂²	semidirect
91. C₃₁×#424	C₂²	semidirect
92. C₃₁×#419	C₂²	semidirect
93. C₃₁×#419	C₂²	semidirect
95. C₃₁×#418	C₂²	semidirect
97. C₃₁×#416	C₂²	semidirect
99. C₃₁×#407	C₂²	semidirect
100. C₃₁×#405	C₂²	semidirect
152. C₂×SD₁₆×C₃₁	D₄	semidirect
394. #61052	C₃₁	direct (N × H)
480. C₂×#577	C₂×C₃₁	semidirect
481. C₂²×#135	C₂×C₃₁	semidirect
482. #3487	C₂×C₃₁	semidirect
483. #3485	C₂×C₃₁	semidirect
484. #3284	C₂×C₃₁	semidirect
485. #3282	C₂×C₃₁	semidirect
486. #3269	C₂×C₃₁	semidirect
487. #3268	C₂×C₃₁	semidirect
488. #3154	C₂×C₃₁	semidirect
489. #3057	C₂×C₃₁	semidirect
490. #3050	C₂×C₃₁	semidirect
491. #3044	C₂×C₃₁	semidirect
492. #3041	C₂×C₃₁	semidirect
493. #3011	C₂×C₃₁	semidirect
494. #3008	C₂×C₃₁	semidirect
495. #3005	C₂×C₃₁	semidirect
496. #3005	C₂×C₃₁	semidirect
497. #2949	C₂×C₃₁	semidirect
498. #2929	C₂×C₃₁	semidirect
534. C₂²×#41	C₂²×C₃₁	semidirect
537. C₂×#137	C₂²×C₃₁	semidirect
538. C₂×#137	C₂²×C₃₁	semidirect
541. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
544. C₂×#135	C₂²×C₃₁	semidirect
545. C₂×#135	C₂²×C₃₁	semidirect
546. C₂×#135	C₂²×C₃₁	semidirect
547. C₂²×Q₁₆	C₂²×C₃₁	semidirect
549. C₂²×SD₁₆	C₂²×C₃₁	semidirect
550. C₂²×SD₁₆	C₂²×C₃₁	semidirect
553. C₂³×C₈	C₂²×C₃₁	semidirect
555. #550	C₂²×C₃₁	semidirect
557. #548	C₂²×C₃₁	semidirect
559. #547	C₂²×C₃₁	semidirect
561. #546	C₂²×C₃₁	semidirect
566. #535	C₂²×C₃₁	semidirect
571. #525	C₂²×C₃₁	semidirect
573. #519	C₂²×C₃₁	semidirect
575. #497	C₂²×C₃₁	semidirect
576. #496	C₂²×C₃₁	semidirect
577. #495	C₂²×C₃₁	semidirect
578. #492	C₂²×C₃₁	semidirect
579. #468	C₂²×C₃₁	semidirect
580. #467	C₂²×C₃₁	semidirect
581. #466	C₂²×C₃₁	semidirect
582. #465	C₂²×C₃₁	semidirect
583. #465	C₂²×C₃₁	semidirect
584. #465	C₂²×C₃₁	semidirect
585. #464	C₂²×C₃₁	semidirect
586. #463	C₂²×C₃₁	semidirect
587. #462	C₂²×C₃₁	semidirect
588. #459	C₂²×C₃₁	semidirect
589. #452	C₂²×C₃₁	semidirect
590. #452	C₂²×C₃₁	semidirect
591. #452	C₂²×C₃₁	semidirect
592. #451	C₂²×C₃₁	semidirect
593. #449	C₂²×C₃₁	semidirect
594. #449	C₂²×C₃₁	semidirect
595. #449	C₂²×C₃₁	semidirect
596. #447	C₂²×C₃₁	semidirect
597. #440	C₂²×C₃₁	semidirect
598. C₄×SD₁₆	C₂²×C₃₁	semidirect
599. #435	C₂²×C₃₁	semidirect
600. C₈×D₄	C₂²×C₃₁	semidirect
601. #427	C₂²×C₃₁	semidirect
602. #424	C₂²×C₃₁	semidirect
603. #419	C₂²×C₃₁	semidirect
604. #419	C₂²×C₃₁	semidirect
606. #418	C₂²×C₃₁	semidirect
608. #416	C₂²×C₃₁	semidirect
610. #407	C₂²×C₃₁	semidirect
611. #405	C₂²×C₃₁	semidirect
672. C₂×SD₁₆	D₄×C₃₁	semidirect
769. C₃₁	#61052	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#577	2
C₂²×C₃₁×#135	2
C₃₁×#3487	2
C₃₁×#3485	2
C₃₁×#3284	2
C₃₁×#3282	2
C₃₁×#3269	2
C₃₁×#3268	2
C₃₁×#3154	2
C₃₁×#3057	2
C₃₁×#3050	2
C₃₁×#3044	2
C₃₁×#3041	2
C₃₁×#3011	2
C₃₁×#3008	2
C₃₁×#3005	2
C₃₁×#2949	2
C₃₁×#2929	2
#61052	31

Subgroups — C31×#61052 #21517811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61052 #21517811