Subgroups — C₃₁×#60805 #21517564

Order 7936.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3219	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3218	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3212	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3211	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3153	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3142	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3037	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3036	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3007	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3006	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₃₁	C₂²	1	2	yes	—
16	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
17	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₃₁×#532	—	2	1	no	—
19	C₃₁×#532	—	2	1	no	—
20	C₃₁×#532	—	2	1	no	—
21	C₃₁×#532	—	2	1	no	—
22	C₃₁×#532	C₂²	1	2	yes	—
23	C₃₁×#532	C₂²	1	2	yes	—
24	C₃₁×#532	C₂²	1	2	yes	complemented
25	C₃₁×#532	C₂²	1	2	yes	complemented
26	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#529	—	2	1	no	—
29	C₃₁×#529	—	2	1	no	—
30	C₃₁×#529	—	2	1	no	—
31	C₃₁×#529	—	2	1	no	—
32	C₃₁×#529	C₂²	1	2	yes	—
33	C₃₁×#529	C₂²	1	2	yes	—
34	C₃₁×#529	C₂²	1	2	yes	complemented
35	C₃₁×#529	C₂²	1	2	yes	complemented
36	C₂×C₃₁×#126	—	2	1	no	—
37	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
40	C₂×C₃₁×#123	—	2	1	no	—
41	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#121	—	2	1	no	—
43	C₂×C₃₁×#121	—	2	1	no	—
44	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₃₁	—	2	1	no	—
47	C₂×C₄×D₄×C₃₁	—	2	1	no	—
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃₁×#117	—	2	1	no	—
51	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
52	C₃₁×#497	C₂²	1	4	yes	complemented
53	C₃₁×#496	C₂²	1	4	yes	complemented
54	C₃₁×#495	C₂²	1	8	yes	complemented
55	C₃₁×#491	C₂²	1	4	yes	complemented
56	C₃₁×#490	C₂²	1	4	yes	complemented
57	C₃₁×#488	C₂²	1	8	yes	complemented
58	C₃₁×#464	C₂²	1	8	yes	complemented
59	C₃₁×#463	C₂²	1	8	yes	complemented
60	C₃₁×#462	C₂²	1	4	yes	complemented
61	C₃₁×#461	C₂²	1	4	yes	complemented
62	C₃₁×#460	C₂²	1	4	yes	complemented
63	C₃₁×#459	C₂²	1	4	yes	complemented
64	C₃₁×#452	C₂²	1	8	yes	complemented
65	C₃₁×#451	C₂²	1	4	yes	complemented
66	C₃₁×#450	C₂²	1	4	yes	complemented
67	C₃₁×#449	C₂²	1	8	yes	complemented
68	C₃₁×#448	C₂²	1	4	yes	—
69	C₃₁×#447	C₂²	1	4	yes	—
70	C₃₁×#432	C₂²	1	2	yes	complemented
71	C₃₁×#432	C₂²	1	2	yes	complemented
72	C₃₁×#431	C₂²	1	2	yes	complemented
73	C₃₁×#431	C₂²	1	2	yes	complemented
74	C₃₁×#423	C₂²	1	2	yes	complemented
75	C₃₁×#417	C₂²	1	4	yes	complemented
76	C₃₁×#417	C₂²	1	4	yes	complemented
77	C₃₁×#407	C₂²	1	2	yes	—
78	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
79	C₂×#41×C₃₁	—	2	2	no	—
80	C₂×#41×C₃₁	—	2	2	no	—
81	C₂×#41×C₃₁	—	4	8	no	—
82	C₂×#41×C₃₁	C₂³	1	4	yes	—
83	C₂×#41×C₃₁	C₂³	1	4	yes	—
84	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₃₁	—	2	1	no	—
87	C₂²×D₄×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	—	2	1	no	—
89	C₂²×D₄×C₃₁	—	2	1	no	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₃₁	—	2	1	no	—
93	C₂³×C₄×C₃₁	—	2	2	no	—
94	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₃₁×#137	—	4	8	no	—
98	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
99	C₂×Q₁₆×C₃₁	C₂³	1	8	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
102	C₂×D₈×C₃₁	C₂³	1	8	yes	—
103	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
104	C₃₁×C₄⋊Q₈	—	2	1	no	—
105	C₃₁×C₄⋊Q₈	—	2	1	no	—
106	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₃₁×#127	—	2	1	no	—
109	C₃₁×#127	—	2	1	no	—
110	C₃₁×#127	C₂³	1	2	yes	—
111	C₃₁×#127	C₂³	1	2	yes	—
112	C₃₁×#126	—	2	2	no	—
113	C₃₁×#126	—	2	2	no	—
114	C₃₁×#126	—	2	2	no	—
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#125	—	2	1	no	—
117	C₃₁×#125	—	2	1	no	—
118	C₃₁×#125	C₂³	1	2	yes	—
119	C₃₁×#125	C₂³	1	2	yes	—
120	C₃₁×#124	—	2	1	no	—
121	C₃₁×#124	—	2	1	no	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	—	2	2	no	—
124	C₃₁×#124	C₂³	1	4	yes	—
125	C₃₁×#124	C₂³	1	4	yes	—
126	C₃₁×#124	C₂³	1	2	yes	—
127	C₃₁×#124	C₂³	1	2	yes	—
128	C₃₁×#123	—	2	2	no	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	1	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	2	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	1	no	—
146	C₃₁×#121	C₂³	1	2	yes	—
147	C₃₁×#121	C₂³	1	2	yes	—
148	C₄×Q₈×C₃₁	—	2	1	no	—
149	C₄×Q₈×C₃₁	—	2	1	no	—
150	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	2	no	—
155	C₄×D₄×C₃₁	—	2	2	no	—
156	C₄×D₄×C₃₁	—	2	2	no	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₃₁×#117	—	2	2	no	—
169	C₃₁×#117	—	2	2	no	—
170	C₃₁×#117	—	2	2	no	—
171	C₃₁×#117	—	2	2	no	—
172	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
173	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
174	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
175	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
184	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
185	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
187	C₂×C₄²×C₃₁	—	2	1	no	—
188	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
201	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	8	yes	—
203	C₃₁×#103	C₂³	1	8	yes	—
204	C₃₁×#102	C₂³	1	8	yes	—
205	C₃₁×#102	C₂³	1	8	yes	—
206	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₃₁×#97	C₂³	1	4	yes	—
209	C₄×C₈×C₃₁	C₂³	1	4	yes	—
210	C₂⁴×C₃₁	—	2	1	no	—
211	C₂⁴×C₃₁	—	2	2	no	—
212	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
213	#41×C₃₁	—	2	8	no	—
214	#41×C₃₁	—	2	8	no	—
215	#41×C₃₁	—	4	4	no	—
216	#41×C₃₁	—	4	4	no	—
217	#41×C₃₁	—	4	8	no	—
218	#41×C₃₁	—	4	8	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	2	no	—
221	C₂×Q₈×C₃₁	—	2	4	no	—
222	C₂×Q₈×C₃₁	—	4	4	no	—
223	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
224	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
225	C₂×D₄×C₃₁	—	2	2	no	—
226	C₂×D₄×C₃₁	—	2	2	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	2	4	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	2	2	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	2	no	—
234	C₂×D₄×C₃₁	—	2	2	no	—
235	C₂×D₄×C₃₁	—	2	4	no	—
236	C₂×D₄×C₃₁	—	4	4	no	—
237	C₂×D₄×C₃₁	—	4	4	no	—
238	C₂×D₄×C₃₁	—	4	4	no	—
239	C₂×D₄×C₃₁	—	4	4	no	—
240	C₂×D₄×C₃₁	—	4	8	no	—
241	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
242	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	—	2	4	no	—
244	C₂²×C₄×C₃₁	—	2	1	no	—
245	C₂²×C₄×C₃₁	—	2	1	no	—
246	C₂²×C₄×C₃₁	—	2	1	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	4	no	—
251	C₂²×C₄×C₃₁	—	2	4	no	—
252	C₂²×C₄×C₃₁	—	4	2	no	—
253	C₂²×C₄×C₃₁	—	4	2	no	—
254	C₂²×C₄×C₃₁	—	4	4	no	—
255	C₂²×C₄×C₃₁	—	4	8	no	—
256	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	Q₁₆×C₃₁	—	4	8	no	—
275	SD₁₆×C₃₁	—	4	8	no	—
276	SD₁₆×C₃₁	—	4	8	no	—
277	D₈×C₃₁	—	4	8	no	—
278	M₁₆×C₃₁	—	2	8	no	—
279	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	—	2	2	no	—
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	4	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₄²×C₃₁	—	2	2	no	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
328	#60805	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₃₁	—	2	2	no	—
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	4	no	—
333	C₂³×C₃₁	—	4	1	no	—
334	C₂³×C₃₁	—	4	4	no	—
335	C₂³×C₃₁	—	4	2	no	—
336	C₂³×C₃₁	—	4	4	no	—
337	C₂³×C₃₁	—	4	2	no	—
338	C₂³×C₃₁	—	4	2	no	—
339	C₂³×C₃₁	—	4	4	no	—
340	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₃₁	—	2	4	no	—
344	Q₈×C₃₁	—	2	4	no	—
345	Q₈×C₃₁	—	2	4	no	—
346	Q₈×C₃₁	—	4	4	no	—
347	Q₈×C₃₁	—	4	2	no	—
348	D₄×C₃₁	—	2	4	no	—
349	D₄×C₃₁	—	2	4	no	—
350	D₄×C₃₁	—	2	4	no	—
351	D₄×C₃₁	—	4	4	no	—
352	D₄×C₃₁	—	4	4	no	—
353	D₄×C₃₁	—	4	4	no	—
354	D₄×C₃₁	—	4	4	no	—
355	D₄×C₃₁	—	4	4	no	—
356	D₄×C₃₁	—	4	8	no	—
357	D₄×C₃₁	—	4	8	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	4	2	no	—
360	D₄×C₃₁	—	4	4	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	4	no	—
375	C₂×C₄×C₃₁	—	4	1	no	—
376	C₂×C₄×C₃₁	—	4	1	no	—
377	C₂×C₄×C₃₁	—	4	1	no	—
378	C₂×C₄×C₃₁	—	4	1	no	—
379	C₂×C₄×C₃₁	—	4	1	no	—
380	C₂×C₄×C₃₁	—	4	1	no	—
381	C₂×C₄×C₃₁	—	4	1	no	—
382	C₂×C₄×C₃₁	—	4	4	no	—
383	C₂×C₄×C₃₁	—	4	8	no	—
384	C₂×C₄×C₃₁	—	4	2	no	—
385	C₂×C₄×C₃₁	—	4	4	no	—
386	C₂×C₄×C₃₁	—	4	2	no	—
387	C₂×C₄×C₃₁	—	4	2	no	—
388	C₂×C₄×C₃₁	—	4	8	no	—
389	C₂×C₄×C₃₁	—	4	4	no	—
390	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
402	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
403	C₈×C₃₁	—	2	8	no	—
404	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
405	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3219	C₂×C₃₁	1	4	yes	complemented
407	#3218	C₂×C₃₁	1	2	yes	complemented
408	#3217	C₂×C₃₁	1	2	yes	complemented
409	#3212	C₂×C₃₁	1	4	yes	complemented
410	#3211	C₂×C₃₁	1	4	yes	complemented
411	#3153	C₂×C₃₁	1	2	yes	complemented
412	#3142	C₂×C₃₁	1	2	yes	complemented
413	#3037	C₂×C₃₁	1	2	yes	complemented
414	#3036	C₂×C₃₁	1	2	yes	complemented
415	#3007	C₂×C₃₁	1	2	yes	complemented
416	#3006	C₂×C₃₁	1	2	yes	complemented
417	#2920	C₂×C₃₁	1	1	yes	characteristic, complemented
418	C₂²×C₃₁	—	2	1	no	—
419	C₂²×C₃₁	—	2	1	no	—
420	C₂²×C₃₁	—	2	1	no	—
421	C₂²×C₃₁	—	2	1	no	—
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	2	1	no	—
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	4	4	no	—
426	C₂²×C₃₁	—	4	4	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	4	2	no	—
429	C₂²×C₃₁	—	4	4	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	4	no	—
432	C₂²×C₃₁	—	8	8	no	—
433	C₂²×C₃₁	—	8	4	no	—
434	C₂²×C₃₁	#535	1	2	yes	—
435	C₂²×C₃₁	#575	1	2	yes	—
436	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₃₁	—	2	1	no	—
438	C₄×C₃₁	—	2	1	no	—
439	C₄×C₃₁	—	2	1	no	—
440	C₄×C₃₁	—	2	1	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	1	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	1	no	—
445	C₄×C₃₁	—	2	1	no	—
446	C₄×C₃₁	—	4	4	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	2	no	—
449	C₄×C₃₁	—	4	2	no	—
450	C₄×C₃₁	#535	1	2	yes	—
451	C₄×C₃₁	#575	1	2	yes	—
452	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
453	C₂²×#41	C₂²×C₃₁	1	2	yes	—
454	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
455	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
456	#532	—	2	1	no	—
457	#532	—	2	1	no	—
458	#532	—	2	1	no	—
459	#532	—	2	1	no	—
460	#532	C₂²×C₃₁	1	2	yes	—
461	#532	C₂²×C₃₁	1	2	yes	—
462	#532	C₂²×C₃₁	1	2	yes	complemented
463	#532	C₂²×C₃₁	1	2	yes	complemented
464	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
466	#529	—	2	1	no	—
467	#529	—	2	1	no	—
468	#529	—	2	1	no	—
469	#529	—	2	1	no	—
470	#529	C₂²×C₃₁	1	2	yes	—
471	#529	C₂²×C₃₁	1	2	yes	—
472	#529	C₂²×C₃₁	1	2	yes	complemented
473	#529	C₂²×C₃₁	1	2	yes	complemented
474	C₂×#126	—	2	1	no	—
475	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
476	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
478	C₂×#123	—	2	1	no	—
479	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×#121	—	2	1	no	—
481	C₂×#121	—	2	1	no	—
482	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
483	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
484	C₂×C₄×D₄	—	2	1	no	—
485	C₂×C₄×D₄	—	2	1	no	—
486	C₂×C₄×D₄	—	2	1	no	—
487	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
488	C₂×#117	—	2	1	no	—
489	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
490	#497	C₂²×C₃₁	1	4	yes	complemented
491	#496	C₂²×C₃₁	1	4	yes	complemented
492	#495	C₂²×C₃₁	1	8	yes	complemented
493	#491	C₂²×C₃₁	1	4	yes	complemented
494	#490	C₂²×C₃₁	1	4	yes	complemented
495	#488	C₂²×C₃₁	1	8	yes	complemented
496	#464	C₂²×C₃₁	1	8	yes	complemented
497	#463	C₂²×C₃₁	1	8	yes	complemented
498	#462	C₂²×C₃₁	1	4	yes	complemented
499	#461	C₂²×C₃₁	1	4	yes	complemented
500	#460	C₂²×C₃₁	1	4	yes	complemented
501	#459	C₂²×C₃₁	1	4	yes	complemented
502	#452	C₂²×C₃₁	1	8	yes	complemented
503	#451	C₂²×C₃₁	1	4	yes	complemented
504	#450	C₂²×C₃₁	1	4	yes	complemented
505	#449	C₂²×C₃₁	1	8	yes	complemented
506	#448	C₂²×C₃₁	1	4	yes	—
507	#447	C₂²×C₃₁	1	4	yes	—
508	#432	C₂²×C₃₁	1	2	yes	complemented
509	#432	C₂²×C₃₁	1	2	yes	complemented
510	#431	C₂²×C₃₁	1	2	yes	complemented
511	#431	C₂²×C₃₁	1	2	yes	complemented
512	#423	C₂²×C₃₁	1	2	yes	complemented
513	#417	C₂²×C₃₁	1	4	yes	complemented
514	#417	C₂²×C₃₁	1	4	yes	complemented
515	#407	C₂²×C₃₁	1	2	yes	—
516	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
517	C₂×C₃₁	—	2	2	no	—
518	C₂×C₃₁	—	2	2	no	—
519	C₂×C₃₁	—	4	1	no	—
520	C₂×C₃₁	—	8	4	no	—
521	C₂×C₃₁	—	8	2	no	—
522	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
523	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
524	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
525	C₂×#41	—	2	2	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	—	4	8	no	—
528	C₂×#41	C₂³×C₃₁	1	4	yes	—
529	C₂×#41	C₂³×C₃₁	1	4	yes	—
530	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	—	2	2	no	—
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
538	C₂³×C₄	—	2	1	no	—
539	C₂³×C₄	—	2	2	no	—
540	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
541	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
543	#137	—	4	8	no	—
544	AGL(1,ℤ/8)	—	4	8	no	—
545	C₂×Q₁₆	C₂³×C₃₁	1	8	yes	—
546	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
547	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
548	C₂×D₈	C₂³×C₃₁	1	8	yes	—
549	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
554	#127	—	2	1	no	—
555	#127	—	2	1	no	—
556	#127	C₂³×C₃₁	1	2	yes	—
557	#127	C₂³×C₃₁	1	2	yes	—
558	#126	—	2	2	no	—
559	#126	—	2	2	no	—
560	#126	—	2	2	no	—
561	#126	—	2	2	no	—
562	#125	—	2	1	no	—
563	#125	—	2	1	no	—
564	#125	C₂³×C₃₁	1	2	yes	—
565	#125	C₂³×C₃₁	1	2	yes	—
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	C₂³×C₃₁	1	2	yes	—
571	#124	C₂³×C₃₁	1	2	yes	—
572	#124	C₂³×C₃₁	1	4	yes	—
573	#124	C₂³×C₃₁	1	4	yes	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
582	#121	—	2	2	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	C₂³×C₃₁	1	2	yes	—
593	#121	C₂³×C₃₁	1	2	yes	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
597	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	C₂³×C₃₁	1	2	yes	—
613	C₄×D₄	C₂³×C₃₁	1	2	yes	—
614	#117	—	2	2	no	—
615	#117	—	2	2	no	—
616	#117	—	2	2	no	—
617	#117	—	2	2	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
635	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
636	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
637	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
638	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
639	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
646	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
647	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
648	#103	C₂³×C₃₁	1	8	yes	—
649	#103	C₂³×C₃₁	1	8	yes	—
650	#102	C₂³×C₃₁	1	8	yes	—
651	#102	C₂³×C₃₁	1	8	yes	—
652	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
654	#97	C₂³×C₃₁	1	4	yes	—
655	C₄×C₈	C₂³×C₃₁	1	4	yes	—
656	C₃₁	#60805	1	1	yes	characteristic, direct product factor, Sylow
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	2	no	—
659	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
660	#41	—	2	8	no	—
661	#41	—	2	8	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	4	8	no	—
665	#41	—	4	8	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	4	4	no	—
670	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
671	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	8	no	—
688	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
689	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	4	no	—
702	C₂²×C₄	—	4	8	no	—
703	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
721	Q₁₆	—	4	8	no	—
722	SD₁₆	—	4	8	no	—
723	SD₁₆	—	4	8	no	—
724	D₈	—	4	8	no	—
725	M₁₆	—	2	8	no	—
726	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
771	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
774	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	4	2	no	—
785	C₂³	—	4	4	no	—
786	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
787	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
788	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
789	Q₈	—	2	4	no	—
790	Q₈	—	2	4	no	—
791	Q₈	—	2	4	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
847	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
848	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
849	C₈	—	2	8	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	4	4	no	—
858	C₂²	—	4	4	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	8	8	no	—
865	C₂²	—	8	4	no	—
866	C₂²	C₃₁×#535	1	2	yes	—
867	C₂²	C₃₁×#575	1	2	yes	—
868	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	4	4	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	C₃₁×#535	1	2	yes	—
883	C₄	C₃₁×#575	1	2	yes	—
884	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	4	no	—
889	C₂	—	8	2	no	—
890	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
891	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
892	C₂	C₂×C₃₁×#575	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 ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#532	C₂	semidirect
2. C₂×C₃₁×#529	C₂	semidirect
3. C₃₁×#3219	C₂	semidirect
4. C₃₁×#3218	C₂	semidirect
5. C₃₁×#3217	C₂	semidirect
6. C₃₁×#3212	C₂	semidirect
7. C₃₁×#3211	C₂	semidirect
8. C₃₁×#3153	C₂	semidirect
9. C₃₁×#3142	C₂	semidirect
10. C₃₁×#3037	C₂	semidirect
11. C₃₁×#3036	C₂	semidirect
12. C₃₁×#3007	C₂	semidirect
13. C₃₁×#3006	C₂	semidirect
14. C₃₁×#2920	C₂	semidirect
16. C₂×C₃₁×#137	C₂²	semidirect
17. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
24. C₃₁×#532	C₂²	semidirect
25. C₃₁×#532	C₂²	semidirect
26. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₃₁×#127	C₂²	semidirect
34. C₃₁×#529	C₂²	semidirect
35. C₃₁×#529	C₂²	semidirect
37. C₂×C₃₁×#125	C₂²	semidirect
38. C₂×C₃₁×#124	C₂²	semidirect
39. C₂×C₃₁×#124	C₂²	semidirect
45. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
52. C₃₁×#497	C₂²	semidirect
53. C₃₁×#496	C₂²	semidirect
54. C₃₁×#495	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#488	C₂²	semidirect
58. C₃₁×#464	C₂²	semidirect
59. C₃₁×#463	C₂²	semidirect
60. C₃₁×#462	C₂²	semidirect
61. C₃₁×#461	C₂²	semidirect
62. C₃₁×#460	C₂²	semidirect
63. C₃₁×#459	C₂²	semidirect
64. C₃₁×#452	C₂²	semidirect
65. C₃₁×#451	C₂²	semidirect
66. C₃₁×#450	C₂²	semidirect
67. C₃₁×#449	C₂²	semidirect
70. C₃₁×#432	C₂²	semidirect
71. C₃₁×#432	C₂²	semidirect
72. C₃₁×#431	C₂²	semidirect
73. C₃₁×#431	C₂²	semidirect
74. C₃₁×#423	C₂²	semidirect
75. C₃₁×#417	C₂²	semidirect
76. C₃₁×#417	C₂²	semidirect
78. C₄×M₁₆×C₃₁	C₂²	semidirect
328. #60805	C₃₁	direct (N × H)
404. C₂×#532	C₂×C₃₁	semidirect
405. C₂×#529	C₂×C₃₁	semidirect
406. #3219	C₂×C₃₁	semidirect
407. #3218	C₂×C₃₁	semidirect
408. #3217	C₂×C₃₁	semidirect
409. #3212	C₂×C₃₁	semidirect
410. #3211	C₂×C₃₁	semidirect
411. #3153	C₂×C₃₁	semidirect
412. #3142	C₂×C₃₁	semidirect
413. #3037	C₂×C₃₁	semidirect
414. #3036	C₂×C₃₁	semidirect
415. #3007	C₂×C₃₁	semidirect
416. #3006	C₂×C₃₁	semidirect
417. #2920	C₂×C₃₁	semidirect
454. C₂×#137	C₂²×C₃₁	semidirect
455. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
462. #532	C₂²×C₃₁	semidirect
463. #532	C₂²×C₃₁	semidirect
464. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
465. C₂×#127	C₂²×C₃₁	semidirect
472. #529	C₂²×C₃₁	semidirect
473. #529	C₂²×C₃₁	semidirect
475. C₂×#125	C₂²×C₃₁	semidirect
476. C₂×#124	C₂²×C₃₁	semidirect
477. C₂×#124	C₂²×C₃₁	semidirect
483. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
487. C₂×C₄×D₄	C₂²×C₃₁	semidirect
490. #497	C₂²×C₃₁	semidirect
491. #496	C₂²×C₃₁	semidirect
492. #495	C₂²×C₃₁	semidirect
493. #491	C₂²×C₃₁	semidirect
494. #490	C₂²×C₃₁	semidirect
495. #488	C₂²×C₃₁	semidirect
496. #464	C₂²×C₃₁	semidirect
497. #463	C₂²×C₃₁	semidirect
498. #462	C₂²×C₃₁	semidirect
499. #461	C₂²×C₃₁	semidirect
500. #460	C₂²×C₃₁	semidirect
501. #459	C₂²×C₃₁	semidirect
502. #452	C₂²×C₃₁	semidirect
503. #451	C₂²×C₃₁	semidirect
504. #450	C₂²×C₃₁	semidirect
505. #449	C₂²×C₃₁	semidirect
508. #432	C₂²×C₃₁	semidirect
509. #432	C₂²×C₃₁	semidirect
510. #431	C₂²×C₃₁	semidirect
511. #431	C₂²×C₃₁	semidirect
512. #423	C₂²×C₃₁	semidirect
513. #417	C₂²×C₃₁	semidirect
514. #417	C₂²×C₃₁	semidirect
516. C₄×M₁₆	C₂²×C₃₁	semidirect
656. C₃₁	#60805	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×#532	2
C₂×C₃₁×#529	2
C₃₁×#3219	2
C₃₁×#3218	2
C₃₁×#3217	2
C₃₁×#3212	2
C₃₁×#3211	2
C₃₁×#3153	2
C₃₁×#3142	2
C₃₁×#3037	2
C₃₁×#3036	2
C₃₁×#3007	2
C₃₁×#3006	2
C₃₁×#2920	2
#60805	31

Subgroups — C31×#60805 #21517564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60805 #21517564