Subgroups — C₃₁×#60871 #21517630

Order 7936.

1742 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3243	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3241	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3238	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3226	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3164	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3092	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#555	—	2	1	no	—
19	C₃₁×#553	—	2	1	no	—
20	C₃₁×#553	—	2	1	no	—
21	C₃₁×#551	—	2	2	no	—
22	C₃₁×#547	—	2	1	no	—
23	C₃₁×#546	—	2	2	no	—
24	C₃₁×#544	—	2	2	no	—
25	C₃₁×#544	—	2	1	no	—
26	C₃₁×#544	—	2	1	no	—
27	C₃₁×#544	C₂²	1	2	yes	—
28	C₃₁×#544	C₂²	1	2	yes	—
29	C₃₁×#544	C₂²	1	1	yes	characteristic
30	C₃₁×#544	C₂²	1	4	yes	complemented
31	C₃₁×#542	C₂²	1	2	yes	—
32	C₃₁×#540	C₂²	1	2	yes	—
33	C₃₁×#535	C₂²	1	1	yes	characteristic
34	C₃₁×#532	C₂²	1	2	yes	—
35	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
36	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₂×C₃₁×#125	—	2	1	no	—
39	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
40	C₃₁×#525	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
43	C₃₁×#520	C₂²	1	1	yes	characteristic
44	C₃₁×#518	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	4	yes	complemented
49	C₃₁×#501	C₂²	1	4	yes	complemented
50	C₃₁×#500	C₂²	1	4	yes	complemented
51	C₃₁×#499	C₂²	1	4	yes	complemented
52	C₃₁×#490	C₂²	1	4	yes	complemented
53	C₃₁×#489	C₂²	1	4	yes	complemented
54	C₃₁×#488	C₂²	1	4	yes	complemented
55	C₃₁×#486	C₂²	1	4	yes	complemented
56	C₃₁×#485	C₂²	1	2	yes	complemented
57	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#484	C₂²	1	2	yes	complemented
59	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#483	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	4	yes	—
62	C₃₁×#482	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	2	yes	—
64	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#481	C₂²	1	2	yes	complemented
66	C₃₁×#480	C₂²	1	2	yes	—
67	C₃₁×#480	C₂²	1	2	yes	—
68	C₃₁×#480	C₂²	1	4	yes	—
69	C₃₁×#480	C₂²	1	2	yes	—
70	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#479	C₂²	1	4	yes	complemented
73	C₃₁×#478	C₂²	1	4	yes	complemented
74	C₃₁×#478	C₂²	1	4	yes	complemented
75	C₃₁×#478	C₂²	1	4	yes	complemented
76	C₃₁×#477	C₂²	1	4	yes	complemented
77	C₃₁×#476	C₂²	1	4	yes	complemented
78	C₃₁×#474	C₂²	1	4	yes	complemented
79	C₃₁×#474	C₂²	1	4	yes	complemented
80	C₃₁×#433	C₂²	1	4	yes	complemented
81	C₃₁×#432	C₂²	1	2	yes	complemented
82	C₃₁×#431	C₂²	1	2	yes	complemented
83	C₃₁×#428	C₂²	1	2	yes	—
84	C₃₁×#428	C₂²	1	2	yes	—
85	C₃₁×#427	C₂²	1	2	yes	—
86	C₂×C₃₁×#107	C₂²	1	2	yes	—
87	C₃₁×#424	C₂²	1	2	yes	—
88	C₃₁×#418	C₂²	1	2	yes	—
89	C₃₁×#417	C₂²	1	2	yes	—
90	C₃₁×#416	C₂²	1	2	yes	—
91	C₂×C₃₁×#102	C₂²	1	2	yes	—
92	C₃₁×#407	C₂²	1	1	yes	characteristic
93	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₃₁×#405	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	—	2	2	no	—
98	C₂²×D₄×C₃₁	—	2	1	no	—
99	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	—	2	1	no	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
104	C₃₁×C₄⋊Q₈	—	2	2	no	—
105	C₃₁×C₄⋊Q₈	—	2	2	no	—
106	C₃₁×C₄⋊Q₈	—	2	4	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	2	no	—
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×#127	C₂³	1	2	yes	—
114	C₃₁×#126	—	2	2	no	—
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#125	—	2	2	no	—
117	C₃₁×#125	—	2	2	no	—
118	C₃₁×#125	—	2	4	no	—
119	C₃₁×#125	—	2	1	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	C₂³	1	4	yes	—
123	C₃₁×#125	C₂³	1	4	yes	—
124	C₃₁×#125	C₂³	1	2	yes	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	C₂³	1	2	yes	—
128	C₃₁×#123	—	2	1	no	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×#121	—	2	1	no	—
142	C₃₁×#121	—	2	1	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	1	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	2	no	—
148	C₃₁×#121	C₂³	1	2	yes	—
149	C₃₁×#121	C₂³	1	2	yes	—
150	C₃₁×#121	C₂³	1	1	yes	characteristic
151	C₃₁×#121	C₂³	1	1	yes	characteristic
152	C₃₁×#120	—	2	1	no	—
153	C₃₁×#120	—	2	2	no	—
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	—	2	1	no	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	—	2	1	no	—
159	C₄×D₄×C₃₁	—	2	1	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₄×D₄×C₃₁	C₂³	1	2	yes	—
165	C₃₁×#117	—	2	1	no	—
166	C₃₁×#117	—	2	1	no	—
167	C₃₁×#117	—	2	1	no	—
168	C₃₁×#117	—	2	2	no	—
169	C₃₁×#117	D₄	1	2	yes	—
170	C₃₁×#117	D₄	1	1	yes	characteristic
171	C₃₁×#117	D₄	1	1	yes	characteristic
172	C₃₁×#117	C₂³	1	2	yes	—
173	C₃₁×#117	C₂³	1	1	yes	characteristic
174	C₃₁×#117	C₂³	1	2	yes	—
175	C₃₁×#117	C₂³	1	1	yes	characteristic
176	C₃₁×#117	C₂³	1	1	yes	characteristic
177	C₃₁×#117	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
181	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
182	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
183	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
184	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
185	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
197	C₂×C₄²×C₃₁	—	2	1	no	—
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₃₁×#107	C₂³	1	4	yes	—
200	C₃₁×#107	C₂³	1	4	yes	—
201	C₃₁×#107	C₂³	1	2	yes	—
202	C₃₁×#107	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#106	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
211	C₃₁×#103	C₂³	1	2	yes	—
212	C₃₁×#103	C₂³	1	2	yes	—
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#102	C₂³	1	4	yes	—
215	C₃₁×#102	C₂³	1	4	yes	—
216	C₃₁×#102	C₂³	1	2	yes	—
217	C₃₁×#102	C₂³	1	2	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₃₁×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	1	no	—
229	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
230	#41×C₃₁	—	2	4	no	—
231	#41×C₃₁	—	8	4	no	—
232	C₂×Q₈×C₃₁	—	2	2	no	—
233	C₂×Q₈×C₃₁	—	2	4	no	—
234	C₂×Q₈×C₃₁	—	2	4	no	—
235	C₂×Q₈×C₃₁	—	8	4	no	—
236	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₃₁	—	2	1	no	—
238	C₂×D₄×C₃₁	—	2	1	no	—
239	C₂×D₄×C₃₁	—	2	2	no	—
240	C₂×D₄×C₃₁	—	2	1	no	—
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	2	1	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	4	no	—
246	C₂×D₄×C₃₁	—	8	2	no	—
247	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	—	2	4	no	—
250	C₂²×C₄×C₃₁	—	2	1	no	—
251	C₂²×C₄×C₃₁	—	2	1	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	1	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	8	2	no	—
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
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	2	yes	—
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	M₁₆×C₃₁	—	2	4	no	—
270	C₂×C₈×C₃₁	—	2	4	no	—
271	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
272	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
273	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	—	2	4	no	—
281	C₄⋊C₄×C₃₁	—	2	4	no	—
282	C₄⋊C₄×C₃₁	—	2	4	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	4	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
292	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₃₁	—	2	1	no	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	1	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	1	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
322	C₄²×C₃₁	—	2	2	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	1	no	—
326	C₄²×C₃₁	C₂×D₄	1	2	yes	—
327	C₄²×C₃₁	C₂×D₄	1	2	yes	—
328	C₄²×C₃₁	C₂⁴	1	2	yes	—
329	C₄²×C₃₁	C₂⁴	1	2	yes	—
330	#60871	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	2	no	—
333	C₂³×C₃₁	—	2	2	no	—
334	C₂³×C₃₁	—	2	1	no	—
335	C₂³×C₃₁	—	4	1	no	—
336	C₂³×C₃₁	—	4	2	no	—
337	C₂³×C₃₁	—	8	1	no	—
338	C₂³×C₃₁	—	8	1	no	—
339	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₃₁	—	2	2	no	—
343	Q₈×C₃₁	—	8	4	no	—
344	Q₈×C₃₁	—	8	4	no	—
345	Q₈×C₃₁	—	8	2	no	—
346	D₄×C₃₁	—	2	4	no	—
347	D₄×C₃₁	—	2	2	no	—
348	D₄×C₃₁	—	4	2	no	—
349	D₄×C₃₁	—	4	4	no	—
350	D₄×C₃₁	—	4	2	no	—
351	D₄×C₃₁	—	4	2	no	—
352	D₄×C₃₁	—	8	2	no	—
353	D₄×C₃₁	—	8	2	no	—
354	D₄×C₃₁	—	8	1	no	—
355	D₄×C₃₁	—	8	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	4	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	4	no	—
369	C₂×C₄×C₃₁	—	4	2	no	—
370	C₂×C₄×C₃₁	—	4	2	no	—
371	C₂×C₄×C₃₁	—	4	4	no	—
372	C₂×C₄×C₃₁	—	4	2	no	—
373	C₂×C₄×C₃₁	—	4	2	no	—
374	C₂×C₄×C₃₁	—	8	2	no	—
375	C₂×C₄×C₃₁	—	8	2	no	—
376	C₂×C₄×C₃₁	—	8	2	no	—
377	C₂×C₄×C₃₁	—	8	2	no	—
378	C₂×C₄×C₃₁	—	8	2	no	—
379	C₂×C₄×C₃₁	—	8	1	no	—
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
388	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
389	C₈×C₃₁	—	2	2	no	—
390	C₈×C₃₁	—	2	2	no	—
391	C₈×C₃₁	—	2	4	no	—
392	#3494	C₂×C₃₁	1	1	yes	characteristic
393	C₂×#544	C₂×C₃₁	1	1	yes	characteristic, complemented
394	#3243	C₂×C₃₁	1	4	yes	complemented
395	#3241	C₂×C₃₁	1	4	yes	complemented
396	#3238	C₂×C₃₁	1	2	yes	complemented
397	#3234	C₂×C₃₁	1	2	yes	complemented
398	#3232	C₂×C₃₁	1	2	yes	complemented
399	#3226	C₂×C₃₁	1	2	yes	complemented
400	#3164	C₂×C₃₁	1	2	yes	complemented
401	#3136	C₂×C₃₁	1	2	yes	complemented
402	#3094	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3092	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
405	C₂×#480	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3083	C₂×C₃₁	1	2	yes	complemented
407	#3081	C₂×C₃₁	1	2	yes	complemented
408	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
409	C₂²×C₃₁	—	2	1	no	—
410	C₂²×C₃₁	—	2	1	no	—
411	C₂²×C₃₁	—	2	1	no	—
412	C₂²×C₃₁	—	2	1	no	—
413	C₂²×C₃₁	—	2	1	no	—
414	C₂²×C₃₁	—	2	1	no	—
415	C₂²×C₃₁	—	2	1	no	—
416	C₂²×C₃₁	—	4	4	no	—
417	C₂²×C₃₁	—	4	2	no	—
418	C₂²×C₃₁	—	4	1	no	—
419	C₂²×C₃₁	—	4	1	no	—
420	C₂²×C₃₁	—	4	2	no	—
421	C₂²×C₃₁	—	4	1	no	—
422	C₂²×C₃₁	—	4	2	no	—
423	C₂²×C₃₁	—	16	2	no	—
424	C₂²×C₃₁	#536	1	2	yes	—
425	C₂²×C₃₁	#576	1	2	yes	—
426	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	2	no	—
429	C₄×C₃₁	—	2	1	no	—
430	C₄×C₃₁	—	2	1	no	—
431	C₄×C₃₁	—	2	2	no	—
432	C₄×C₃₁	—	2	2	no	—
433	C₄×C₃₁	—	4	2	no	—
434	C₄×C₃₁	—	4	1	no	—
435	C₄×C₃₁	—	4	1	no	—
436	C₄×C₃₁	—	4	4	no	—
437	C₄×C₃₁	—	4	2	no	—
438	C₄×C₃₁	—	4	2	no	—
439	C₄×C₃₁	—	4	1	no	—
440	C₄×C₃₁	#536	1	2	yes	—
441	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
442	#555	—	2	1	no	—
443	#553	—	2	1	no	—
444	#553	—	2	1	no	—
445	#551	—	2	2	no	—
446	#547	—	2	1	no	—
447	#546	—	2	2	no	—
448	#544	—	2	2	no	—
449	#544	—	2	1	no	—
450	#544	—	2	1	no	—
451	#544	C₂²×C₃₁	1	2	yes	—
452	#544	C₂²×C₃₁	1	2	yes	—
453	#544	C₂²×C₃₁	1	1	yes	characteristic
454	#544	C₂²×C₃₁	1	4	yes	complemented
455	#542	C₂²×C₃₁	1	2	yes	—
456	#540	C₂²×C₃₁	1	2	yes	—
457	#535	C₂²×C₃₁	1	1	yes	characteristic
458	#532	C₂²×C₃₁	1	2	yes	—
459	C₂×C₄⋊Q₈	—	2	1	no	—
460	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
461	#529	C₂²×C₃₁	1	2	yes	—
462	C₂×#125	—	2	1	no	—
463	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
464	#525	C₂²×C₃₁	1	1	yes	characteristic
465	C₂×C₂²⋊Q₈	—	2	2	no	—
466	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
467	#520	C₂²×C₃₁	1	1	yes	characteristic
468	#518	C₂²×C₃₁	1	1	yes	characteristic
469	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
470	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
471	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
472	#501	C₂²×C₃₁	1	4	yes	complemented
473	#501	C₂²×C₃₁	1	4	yes	complemented
474	#500	C₂²×C₃₁	1	4	yes	complemented
475	#499	C₂²×C₃₁	1	4	yes	complemented
476	#490	C₂²×C₃₁	1	4	yes	complemented
477	#489	C₂²×C₃₁	1	4	yes	complemented
478	#488	C₂²×C₃₁	1	4	yes	complemented
479	#486	C₂²×C₃₁	1	4	yes	complemented
480	#485	C₂²×C₃₁	1	2	yes	complemented
481	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
482	#484	C₂²×C₃₁	1	2	yes	complemented
483	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
484	#483	C₂²×C₃₁	1	2	yes	complemented
485	#482	C₂²×C₃₁	1	4	yes	—
486	#482	C₂²×C₃₁	1	2	yes	complemented
487	#481	C₂²×C₃₁	1	2	yes	—
488	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#481	C₂²×C₃₁	1	2	yes	complemented
490	#480	C₂²×C₃₁	1	2	yes	—
491	#480	C₂²×C₃₁	1	2	yes	—
492	#480	C₂²×C₃₁	1	4	yes	—
493	#480	C₂²×C₃₁	1	2	yes	—
494	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
495	#480	C₂²×C₃₁	1	2	yes	complemented
496	#479	C₂²×C₃₁	1	4	yes	complemented
497	#478	C₂²×C₃₁	1	4	yes	complemented
498	#478	C₂²×C₃₁	1	4	yes	complemented
499	#478	C₂²×C₃₁	1	4	yes	complemented
500	#477	C₂²×C₃₁	1	4	yes	complemented
501	#476	C₂²×C₃₁	1	4	yes	complemented
502	#474	C₂²×C₃₁	1	4	yes	complemented
503	#474	C₂²×C₃₁	1	4	yes	complemented
504	#433	C₂²×C₃₁	1	4	yes	complemented
505	#432	C₂²×C₃₁	1	2	yes	complemented
506	#431	C₂²×C₃₁	1	2	yes	complemented
507	#428	C₂²×C₃₁	1	2	yes	—
508	#428	C₂²×C₃₁	1	2	yes	—
509	#427	C₂²×C₃₁	1	2	yes	—
510	C₂×#107	C₂²×C₃₁	1	2	yes	—
511	#424	C₂²×C₃₁	1	2	yes	—
512	#418	C₂²×C₃₁	1	2	yes	—
513	#417	C₂²×C₃₁	1	2	yes	—
514	#416	C₂²×C₃₁	1	2	yes	—
515	C₂×#102	C₂²×C₃₁	1	2	yes	—
516	#407	C₂²×C₃₁	1	1	yes	characteristic
517	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
518	#405	C₂²×C₃₁	1	2	yes	—
519	C₂×C₃₁	—	2	2	no	—
520	C₂×C₃₁	—	2	2	no	—
521	C₂×C₃₁	—	4	1	no	—
522	C₂×C₃₁	—	8	1	no	—
523	C₂×C₃₁	—	8	2	no	—
524	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
525	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
526	C₂×C₃₁	#3586	1	1	yes	characteristic
527	C₂×#41	—	2	2	no	—
528	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
529	C₂²×Q₈	—	2	2	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
535	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	4	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
543	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
544	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
545	#127	C₂³×C₃₁	1	2	yes	—
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#125	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	—	2	4	no	—
551	#125	—	2	1	no	—
552	#125	—	2	2	no	—
553	#125	—	2	2	no	—
554	#125	C₂³×C₃₁	1	4	yes	—
555	#125	C₂³×C₃₁	1	4	yes	—
556	#125	C₂³×C₃₁	1	2	yes	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	C₂³×C₃₁	1	2	yes	—
560	#123	—	2	1	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
573	#121	—	2	1	no	—
574	#121	—	2	1	no	—
575	#121	—	2	2	no	—
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	C₂³×C₃₁	1	2	yes	—
581	#121	C₂³×C₃₁	1	2	yes	—
582	#121	C₂³×C₃₁	1	1	yes	characteristic
583	#121	C₂³×C₃₁	1	1	yes	characteristic
584	#120	—	2	1	no	—
585	#120	—	2	2	no	—
586	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	C₂³×C₃₁	1	2	yes	—
595	C₄×D₄	C₂³×C₃₁	1	2	yes	—
596	C₄×D₄	C₂³×C₃₁	1	2	yes	—
597	#117	—	2	1	no	—
598	#117	—	2	1	no	—
599	#117	—	2	1	no	—
600	#117	—	2	2	no	—
601	#117	D₄×C₃₁	1	2	yes	—
602	#117	D₄×C₃₁	1	1	yes	characteristic
603	#117	D₄×C₃₁	1	1	yes	characteristic
604	#117	C₂³×C₃₁	1	2	yes	—
605	#117	C₂³×C₃₁	1	2	yes	—
606	#117	C₂³×C₃₁	1	1	yes	characteristic
607	#117	C₂³×C₃₁	1	1	yes	characteristic
608	#117	C₂³×C₃₁	1	1	yes	characteristic
609	#117	C₂³×C₃₁	1	2	yes	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	2	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
618	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
629	C₂×C₄²	—	2	1	no	—
630	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
631	#107	C₂³×C₃₁	1	4	yes	—
632	#107	C₂³×C₃₁	1	4	yes	—
633	#107	C₂³×C₃₁	1	2	yes	—
634	#107	C₂³×C₃₁	1	2	yes	—
635	#107	C₂³×C₃₁	1	4	yes	—
636	#107	C₂³×C₃₁	1	4	yes	—
637	#106	C₂³×C₃₁	1	2	yes	—
638	#106	C₂³×C₃₁	1	2	yes	—
639	#106	C₂³×C₃₁	1	4	yes	—
640	#106	C₂³×C₃₁	1	4	yes	—
641	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
642	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
643	#103	C₂³×C₃₁	1	2	yes	—
644	#103	C₂³×C₃₁	1	2	yes	—
645	#103	C₂³×C₃₁	1	4	yes	—
646	#102	C₂³×C₃₁	1	4	yes	—
647	#102	C₂³×C₃₁	1	4	yes	—
648	#102	C₂³×C₃₁	1	2	yes	—
649	#102	C₂³×C₃₁	1	2	yes	—
650	#102	C₂³×C₃₁	1	4	yes	—
651	#102	C₂³×C₃₁	1	4	yes	—
652	#102	C₂³×C₃₁	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
654	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
655	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
656	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
658	#97	C₂³×C₃₁	1	4	yes	—
659	C₄×C₈	C₂³×C₃₁	1	4	yes	—
660	C₃₁	#60871	1	1	yes	characteristic, direct product factor, Sylow
661	C₂⁴	—	2	1	no	—
662	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
663	#41	—	2	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	4	no	—
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	8	4	no	—
669	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	8	2	no	—
680	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
681	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
702	M₁₆	—	2	4	no	—
703	C₂×C₈	—	2	4	no	—
704	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
705	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
706	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
730	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
733	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
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	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	1	no	—
759	C₄²	C₂×D₄×C₃₁	1	2	yes	—
760	C₄²	C₂×D₄×C₃₁	1	2	yes	—
761	C₄²	C₂⁴×C₃₁	1	2	yes	—
762	C₄²	C₂⁴×C₃₁	1	2	yes	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
772	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
774	Q₈	—	2	2	no	—
775	Q₈	—	8	4	no	—
776	Q₈	—	8	4	no	—
777	Q₈	—	8	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	2	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	D₄	—	8	1	no	—
787	D₄	—	8	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
819	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
820	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	—	2	4	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	16	2	no	—
839	C₂²	C₃₁×#536	1	2	yes	—
840	C₂²	C₃₁×#576	1	2	yes	—
841	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	C₃₁×#536	1	2	yes	—
856	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
857	C₂	—	2	2	no	—
858	C₂	—	2	2	no	—
859	C₂	—	4	1	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
863	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
864	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#544	C₂	semidirect
3. C₃₁×#3243	C₂	semidirect
4. C₃₁×#3241	C₂	semidirect
5. C₃₁×#3238	C₂	semidirect
6. C₃₁×#3234	C₂	semidirect
7. C₃₁×#3232	C₂	semidirect
8. C₃₁×#3226	C₂	semidirect
9. C₃₁×#3164	C₂	semidirect
10. C₃₁×#3136	C₂	semidirect
11. C₃₁×#3094	C₂	semidirect
12. C₃₁×#3092	C₂	semidirect
13. C₃₁×#3091	C₂	semidirect
14. C₂×C₃₁×#480	C₂	semidirect
15. C₃₁×#3083	C₂	semidirect
16. C₃₁×#3081	C₂	semidirect
17. C₃₁×#2924	C₂	semidirect
30. C₃₁×#544	C₂²	semidirect
36. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₃₁×#125	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#500	C₂²	semidirect
51. C₃₁×#499	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
53. C₃₁×#489	C₂²	semidirect
54. C₃₁×#488	C₂²	semidirect
55. C₃₁×#486	C₂²	semidirect
56. C₃₁×#485	C₂²	semidirect
57. C₃₁×#484	C₂²	semidirect
58. C₃₁×#484	C₂²	semidirect
59. C₃₁×#483	C₂²	semidirect
60. C₃₁×#483	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
64. C₃₁×#481	C₂²	semidirect
65. C₃₁×#481	C₂²	semidirect
70. C₃₁×#480	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#478	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
79. C₃₁×#474	C₂²	semidirect
80. C₃₁×#433	C₂²	semidirect
81. C₃₁×#432	C₂²	semidirect
82. C₃₁×#431	C₂²	semidirect
330. #60871	C₃₁	direct (N × H)
393. C₂×#544	C₂×C₃₁	semidirect
394. #3243	C₂×C₃₁	semidirect
395. #3241	C₂×C₃₁	semidirect
396. #3238	C₂×C₃₁	semidirect
397. #3234	C₂×C₃₁	semidirect
398. #3232	C₂×C₃₁	semidirect
399. #3226	C₂×C₃₁	semidirect
400. #3164	C₂×C₃₁	semidirect
401. #3136	C₂×C₃₁	semidirect
402. #3094	C₂×C₃₁	semidirect
403. #3092	C₂×C₃₁	semidirect
404. #3091	C₂×C₃₁	semidirect
405. C₂×#480	C₂×C₃₁	semidirect
406. #3083	C₂×C₃₁	semidirect
407. #3081	C₂×C₃₁	semidirect
408. #2924	C₂×C₃₁	semidirect
454. #544	C₂²×C₃₁	semidirect
460. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
463. C₂×#125	C₂²×C₃₁	semidirect
472. #501	C₂²×C₃₁	semidirect
473. #501	C₂²×C₃₁	semidirect
474. #500	C₂²×C₃₁	semidirect
475. #499	C₂²×C₃₁	semidirect
476. #490	C₂²×C₃₁	semidirect
477. #489	C₂²×C₃₁	semidirect
478. #488	C₂²×C₃₁	semidirect
479. #486	C₂²×C₃₁	semidirect
480. #485	C₂²×C₃₁	semidirect
481. #484	C₂²×C₃₁	semidirect
482. #484	C₂²×C₃₁	semidirect
483. #483	C₂²×C₃₁	semidirect
484. #483	C₂²×C₃₁	semidirect
486. #482	C₂²×C₃₁	semidirect
488. #481	C₂²×C₃₁	semidirect
489. #481	C₂²×C₃₁	semidirect
494. #480	C₂²×C₃₁	semidirect
495. #480	C₂²×C₃₁	semidirect
496. #479	C₂²×C₃₁	semidirect
497. #478	C₂²×C₃₁	semidirect
498. #478	C₂²×C₃₁	semidirect
499. #478	C₂²×C₃₁	semidirect
500. #477	C₂²×C₃₁	semidirect
501. #476	C₂²×C₃₁	semidirect
502. #474	C₂²×C₃₁	semidirect
503. #474	C₂²×C₃₁	semidirect
504. #433	C₂²×C₃₁	semidirect
505. #432	C₂²×C₃₁	semidirect
506. #431	C₂²×C₃₁	semidirect
660. C₃₁	#60871	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×#3494	2
C₂×C₃₁×#544	2
C₃₁×#3243	2
C₃₁×#3241	2
C₃₁×#3238	2
C₃₁×#3234	2
C₃₁×#3232	2
C₃₁×#3226	2
C₃₁×#3164	2
C₃₁×#3136	2
C₃₁×#3094	2
C₃₁×#3092	2
C₃₁×#3091	2
C₂×C₃₁×#480	2
C₃₁×#3083	2
C₃₁×#3081	2
C₃₁×#2924	2
#60871	31

Subgroups — C31×#60871 #21517630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60871 #21517630