Subgroups — C₃₁×#62097 #21518856

Order 7936.

1738 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3381	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3336	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3302	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3296	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3107	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#557	—	2	1	no	—
19	C₃₁×#557	C₂²	1	2	yes	complemented
20	C₃₁×#556	—	2	1	no	—
21	C₃₁×#556	C₂²	1	1	yes	characteristic
22	C₃₁×#556	C₂²	1	2	yes	complemented
23	C₃₁×#555	C₂²	1	1	yes	characteristic
24	C₃₁×#554	C₂²	1	1	yes	characteristic
25	C₃₁×#553	—	2	1	no	—
26	C₃₁×#552	—	2	1	no	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#552	C₂²	1	2	yes	—
29	C₃₁×#552	C₂²	1	4	yes	—
30	C₃₁×#551	—	2	2	no	—
31	C₃₁×#547	C₂²	1	1	yes	characteristic
32	C₃₁×#546	C₂²	1	2	yes	—
33	C₃₁×#541	—	2	2	no	—
34	C₃₁×#536	—	2	1	no	—
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#533	C₂²	1	2	yes	complemented
38	C₃₁×#533	C₂²	1	2	yes	complemented
39	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₃₁×#529	—	2	2	no	—
41	C₃₁×#529	C₂²	1	2	yes	—
42	C₃₁×#525	—	2	1	no	—
43	C₃₁×#519	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	2	yes	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#117	—	2	1	no	—
48	C₃₁×#499	C₂²	1	4	yes	complemented
49	C₃₁×#498	C₂²	1	2	yes	complemented
50	C₃₁×#488	C₂²	1	4	yes	—
51	C₃₁×#487	C₂²	1	2	yes	complemented
52	C₃₁×#485	C₂²	1	4	yes	complemented
53	C₃₁×#485	C₂²	1	4	yes	complemented
54	C₃₁×#483	C₂²	1	2	yes	—
55	C₃₁×#483	C₂²	1	4	yes	—
56	C₃₁×#482	C₂²	1	4	yes	—
57	C₃₁×#479	C₂²	1	4	yes	complemented
58	C₃₁×#479	C₂²	1	4	yes	complemented
59	C₃₁×#478	C₂²	1	4	yes	—
60	C₃₁×#477	C₂²	1	2	yes	complemented
61	C₃₁×#477	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	1	yes	characteristic
63	C₃₁×#476	C₂²	1	1	yes	characteristic
64	C₃₁×#475	C₂²	1	2	yes	complemented
65	C₃₁×#475	C₂²	1	2	yes	complemented
66	C₃₁×#474	C₂²	1	2	yes	—
67	C₃₁×#474	C₂²	1	2	yes	—
68	C₃₁×#474	C₂²	1	2	yes	—
69	C₃₁×#474	C₂²	1	2	yes	—
70	C₃₁×#467	C₂²	1	4	yes	—
71	C₃₁×#467	C₂²	1	4	yes	complemented
72	C₃₁×#465	C₂²	1	4	yes	—
73	C₃₁×#464	C₂²	1	4	yes	—
74	C₃₁×#462	C₂²	1	2	yes	complemented
75	C₃₁×#462	C₂²	1	2	yes	complemented
76	C₃₁×#461	C₂²	1	1	yes	characteristic
77	C₃₁×#461	C₂²	1	1	yes	characteristic
78	C₃₁×#452	C₂²	1	4	yes	—
79	C₃₁×#450	C₂²	1	2	yes	—
80	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
81	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
83	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
85	C₈×D₄×C₃₁	C₂²	1	4	yes	—
86	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#431	C₂²	1	1	yes	characteristic
88	C₃₁×#431	C₂²	1	2	yes	complemented
89	C₃₁×#427	C₂²	1	4	yes	complemented
90	C₂×C₃₁×#107	C₂²	1	2	yes	—
91	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₃₁×#416	C₂²	1	4	yes	—
94	C₂×C₃₁×#102	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
96	C₂×#41×C₃₁	C₂³	1	2	yes	—
97	C₂²×Q₈×C₃₁	—	2	1	no	—
98	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	—	2	1	no	—
100	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
105	C₃₁×C₄⋊Q₈	—	2	2	no	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×#126	—	2	2	no	—
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#125	—	2	2	no	—
120	C₃₁×#125	—	2	4	no	—
121	C₃₁×#125	—	2	4	no	—
122	C₃₁×#125	—	2	1	no	—
123	C₃₁×#125	—	2	1	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	C₂³	1	4	yes	—
126	C₃₁×#125	C₂³	1	2	yes	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#124	—	2	2	no	—
129	C₃₁×#124	C₂³	1	2	yes	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	4	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	—	2	1	no	—
138	C₃₁×C₂²⋊Q₈	—	2	1	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₃₁×#121	—	2	1	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	C₂³	1	2	yes	—
151	C₃₁×#120	—	2	2	no	—
152	C₄×Q₈×C₃₁	—	2	2	no	—
153	C₄×Q₈×C₃₁	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	—	2	2	no	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	—	2	1	no	—
158	C₄×Q₈×C₃₁	—	2	2	no	—
159	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
161	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
163	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₃₁	—	2	2	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	D₄	1	2	yes	—
171	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
172	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₃₁	C₂³	1	2	yes	—
175	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₃₁	C₂³	1	2	yes	—
178	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₃₁×#117	—	2	1	no	—
180	C₃₁×#117	—	2	1	no	—
181	C₃₁×#117	—	2	2	no	—
182	C₃₁×#117	—	2	1	no	—
183	C₃₁×#117	—	2	1	no	—
184	C₃₁×#117	—	2	2	no	—
185	C₃₁×#117	—	2	4	no	—
186	C₃₁×#117	—	2	2	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	D₄	1	1	yes	characteristic
189	C₃₁×#117	D₄	1	2	yes	—
190	C₃₁×#117	C₂³	1	4	yes	—
191	C₃₁×#117	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
193	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₄²×C₃₁	—	2	2	no	—
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#107	C₂³	1	4	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	4	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	2	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	1	no	—
229	#41×C₃₁	—	2	4	no	—
230	#41×C₃₁	—	2	4	no	—
231	#41×C₃₁	—	4	2	no	—
232	C₂×Q₈×C₃₁	—	2	1	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	4	4	no	—
237	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
240	C₂×D₄×C₃₁	—	2	2	no	—
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	2	2	no	—
243	C₂×D₄×C₃₁	—	2	1	no	—
244	C₂×D₄×C₃₁	—	4	1	no	—
245	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	—	2	1	no	—
250	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
255	C₂²×C₄×C₃₁	—	2	1	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	4	4	no	—
258	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	Q₁₆×C₃₁	—	4	4	no	—
265	SD₁₆×C₃₁	—	2	4	no	—
266	SD₁₆×C₃₁	—	4	2	no	—
267	C₂×C₈×C₃₁	—	4	4	no	—
268	C₂×C₈×C₃₁	—	4	2	no	—
269	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
270	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
271	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
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	2	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	1	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	4	no	—
286	C₄⋊C₄×C₃₁	—	2	4	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
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	4	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₃₁	—	2	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	1	no	—
313	C₂²⋊C₄×C₃₁	—	2	1	no	—
314	C₂²⋊C₄×C₃₁	—	2	1	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	2	no	—
323	C₄²×C₃₁	—	2	4	no	—
324	C₄²×C₃₁	—	2	4	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	C₂×D₄	1	2	yes	—
327	C₄²×C₃₁	C₂×D₄	1	2	yes	—
328	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₄²×C₃₁	C₂⁴	1	2	yes	—
332	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
333	#62097	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₃₁	—	2	1	no	—
335	C₂³×C₃₁	—	2	1	no	—
336	C₂³×C₃₁	—	4	2	no	—
337	C₂³×C₃₁	—	4	2	no	—
338	C₂³×C₃₁	—	8	1	no	—
339	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
340	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₃₁	—	2	2	no	—
342	Q₈×C₃₁	—	2	2	no	—
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	2	no	—
346	Q₈×C₃₁	—	4	2	no	—
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	4	4	no	—
349	Q₈×C₃₁	—	8	1	no	—
350	D₄×C₃₁	—	2	4	no	—
351	D₄×C₃₁	—	2	2	no	—
352	D₄×C₃₁	—	2	1	no	—
353	D₄×C₃₁	—	2	1	no	—
354	D₄×C₃₁	—	2	1	no	—
355	D₄×C₃₁	—	4	2	no	—
356	D₄×C₃₁	—	4	4	no	—
357	D₄×C₃₁	—	8	2	no	—
358	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
359	C₂×C₄×C₃₁	—	2	4	no	—
360	C₂×C₄×C₃₁	—	2	1	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	1	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	4	no	—
370	C₂×C₄×C₃₁	—	2	1	no	—
371	C₂×C₄×C₃₁	—	4	2	no	—
372	C₂×C₄×C₃₁	—	4	1	no	—
373	C₂×C₄×C₃₁	—	4	4	no	—
374	C₂×C₄×C₃₁	—	4	2	no	—
375	C₂×C₄×C₃₁	—	4	4	no	—
376	C₂×C₄×C₃₁	—	4	2	no	—
377	C₂×C₄×C₃₁	—	4	2	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	2	no	—
380	C₂×C₄×C₃₁	—	8	2	no	—
381	C₂×C₄×C₃₁	#135	1	4	yes	—
382	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
391	C₈×C₃₁	—	2	2	no	—
392	C₈×C₃₁	—	2	2	no	—
393	C₈×C₃₁	—	2	4	no	—
394	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
395	#3475	C₂×C₃₁	1	1	yes	characteristic
396	#3381	C₂×C₃₁	1	2	yes	complemented
397	#3364	C₂×C₃₁	1	2	yes	complemented
398	#3340	C₂×C₃₁	1	2	yes	complemented
399	#3336	C₂×C₃₁	1	4	yes	complemented
400	#3302	C₂×C₃₁	1	2	yes	complemented
401	#3296	C₂×C₃₁	1	4	yes	complemented
402	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3248	C₂×C₃₁	1	2	yes	complemented
404	#3233	C₂×C₃₁	1	2	yes	complemented
405	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3107	C₂×C₃₁	1	2	yes	complemented
407	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3076	C₂×C₃₁	1	2	yes	complemented
409	C₂×#474	C₂×C₃₁	1	1	yes	characteristic, complemented
410	#2988	C₂×C₃₁	1	1	yes	characteristic, complemented
411	C₂²×C₃₁	—	2	1	no	—
412	C₂²×C₃₁	—	2	1	no	—
413	C₂²×C₃₁	—	2	2	no	—
414	C₂²×C₃₁	—	2	2	no	—
415	C₂²×C₃₁	—	2	2	no	—
416	C₂²×C₃₁	—	2	2	no	—
417	C₂²×C₃₁	—	4	1	no	—
418	C₂²×C₃₁	—	4	1	no	—
419	C₂²×C₃₁	—	4	1	no	—
420	C₂²×C₃₁	—	4	1	no	—
421	C₂²×C₃₁	—	4	1	no	—
422	C₂²×C₃₁	—	8	4	no	—
423	C₂²×C₃₁	C₂×#135	1	2	yes	—
424	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
425	C₄×C₃₁	—	2	1	no	—
426	C₄×C₃₁	—	2	2	no	—
427	C₄×C₃₁	—	2	1	no	—
428	C₄×C₃₁	—	2	2	no	—
429	C₄×C₃₁	—	2	1	no	—
430	C₄×C₃₁	—	2	2	no	—
431	C₄×C₃₁	—	4	2	no	—
432	C₄×C₃₁	—	4	2	no	—
433	C₄×C₃₁	—	4	2	no	—
434	C₄×C₃₁	—	4	2	no	—
435	C₄×C₃₁	—	4	1	no	—
436	C₄×C₃₁	—	4	1	no	—
437	C₄×C₃₁	—	4	4	no	—
438	C₄×C₃₁	C₂×#135	1	2	yes	—
439	C₄×C₃₁	C₂×#135	1	2	yes	—
440	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₄×C₃₁	#585	1	1	yes	characteristic
442	#557	—	2	1	no	—
443	#557	C₂²×C₃₁	1	2	yes	complemented
444	#556	—	2	1	no	—
445	#556	C₂²×C₃₁	1	1	yes	characteristic
446	#556	C₂²×C₃₁	1	2	yes	complemented
447	#555	C₂²×C₃₁	1	1	yes	characteristic
448	#554	C₂²×C₃₁	1	1	yes	characteristic
449	#553	—	2	1	no	—
450	#552	—	2	1	no	—
451	#552	—	2	2	no	—
452	#552	C₂²×C₃₁	1	2	yes	—
453	#552	C₂²×C₃₁	1	4	yes	—
454	#551	—	2	2	no	—
455	#547	C₂²×C₃₁	1	1	yes	characteristic
456	#546	C₂²×C₃₁	1	2	yes	—
457	#541	—	2	2	no	—
458	#536	—	2	1	no	—
459	#533	C₂²×C₃₁	1	1	yes	characteristic
460	#533	C₂²×C₃₁	1	1	yes	characteristic
461	#533	C₂²×C₃₁	1	2	yes	complemented
462	#533	C₂²×C₃₁	1	2	yes	complemented
463	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
464	#529	—	2	2	no	—
465	#529	C₂²×C₃₁	1	2	yes	—
466	#525	—	2	1	no	—
467	#519	—	2	1	no	—
468	C₄×#41	C₂²×C₃₁	1	2	yes	—
469	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
471	C₂×#117	—	2	1	no	—
472	#499	C₂²×C₃₁	1	4	yes	complemented
473	#498	C₂²×C₃₁	1	2	yes	complemented
474	#488	C₂²×C₃₁	1	4	yes	—
475	#487	C₂²×C₃₁	1	2	yes	complemented
476	#485	C₂²×C₃₁	1	4	yes	complemented
477	#485	C₂²×C₃₁	1	4	yes	complemented
478	#483	C₂²×C₃₁	1	2	yes	—
479	#483	C₂²×C₃₁	1	4	yes	—
480	#482	C₂²×C₃₁	1	4	yes	—
481	#479	C₂²×C₃₁	1	4	yes	complemented
482	#479	C₂²×C₃₁	1	4	yes	complemented
483	#478	C₂²×C₃₁	1	4	yes	—
484	#477	C₂²×C₃₁	1	2	yes	complemented
485	#477	C₂²×C₃₁	1	2	yes	complemented
486	#476	C₂²×C₃₁	1	1	yes	characteristic
487	#476	C₂²×C₃₁	1	1	yes	characteristic
488	#475	C₂²×C₃₁	1	2	yes	complemented
489	#475	C₂²×C₃₁	1	2	yes	complemented
490	#474	C₂²×C₃₁	1	2	yes	—
491	#474	C₂²×C₃₁	1	2	yes	—
492	#474	C₂²×C₃₁	1	2	yes	—
493	#474	C₂²×C₃₁	1	2	yes	—
494	#467	C₂²×C₃₁	1	4	yes	—
495	#467	C₂²×C₃₁	1	4	yes	complemented
496	#465	C₂²×C₃₁	1	4	yes	—
497	#464	C₂²×C₃₁	1	4	yes	—
498	#462	C₂²×C₃₁	1	2	yes	complemented
499	#462	C₂²×C₃₁	1	2	yes	complemented
500	#461	C₂²×C₃₁	1	1	yes	characteristic
501	#461	C₂²×C₃₁	1	1	yes	characteristic
502	#452	C₂²×C₃₁	1	4	yes	—
503	#450	C₂²×C₃₁	1	2	yes	—
504	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
505	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
506	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
507	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
508	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
509	C₈×D₄	C₂²×C₃₁	1	4	yes	—
510	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
511	#431	C₂²×C₃₁	1	1	yes	characteristic
512	#431	C₂²×C₃₁	1	2	yes	complemented
513	#427	C₂²×C₃₁	1	4	yes	complemented
514	C₂×#107	C₂²×C₃₁	1	2	yes	—
515	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
517	#416	C₂²×C₃₁	1	4	yes	—
518	C₂×#102	C₂²×C₃₁	1	2	yes	—
519	C₂×C₃₁	—	2	2	no	—
520	C₂×C₃₁	—	4	2	no	—
521	C₂×C₃₁	—	4	2	no	—
522	C₂×C₃₁	—	8	1	no	—
523	C₂×C₃₁	#3489	1	1	yes	characteristic
524	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
525	C₂×C₃₁	#3586	1	1	yes	characteristic
526	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
527	C₂×#41	C₂³×C₃₁	1	2	yes	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
530	C₂³×C₄	—	2	1	no	—
531	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
532	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
533	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
534	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
535	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#126	—	2	4	no	—
548	#126	—	2	4	no	—
549	#126	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	4	no	—
552	#125	—	2	4	no	—
553	#125	—	2	1	no	—
554	#125	—	2	1	no	—
555	#125	—	2	2	no	—
556	#125	C₂³×C₃₁	1	2	yes	—
557	#125	C₂³×C₃₁	1	4	yes	—
558	#124	—	2	2	no	—
559	#124	—	2	2	no	—
560	#124	C₂³×C₃₁	1	2	yes	—
561	#123	—	2	2	no	—
562	#123	—	2	4	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
575	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
576	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	2	no	—
581	#121	C₂³×C₃₁	1	2	yes	—
582	#120	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
592	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
593	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
594	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
595	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	D₄×C₃₁	1	2	yes	—
602	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₃₁	1	2	yes	—
608	C₄×D₄	C₂³×C₃₁	1	2	yes	—
609	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
610	#117	—	2	1	no	—
611	#117	—	2	1	no	—
612	#117	—	2	2	no	—
613	#117	—	2	1	no	—
614	#117	—	2	1	no	—
615	#117	—	2	2	no	—
616	#117	—	2	4	no	—
617	#117	—	2	2	no	—
618	#117	—	2	2	no	—
619	#117	D₄×C₃₁	1	1	yes	characteristic
620	#117	D₄×C₃₁	1	2	yes	—
621	#117	C₂³×C₃₁	1	2	yes	—
622	#117	C₂³×C₃₁	1	4	yes	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₄²	—	2	2	no	—
631	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
633	#107	C₂³×C₃₁	1	4	yes	—
634	#107	C₂³×C₃₁	1	4	yes	—
635	#107	C₂³×C₃₁	1	4	yes	—
636	#106	C₂³×C₃₁	1	2	yes	—
637	#106	C₂³×C₃₁	1	4	yes	—
638	#106	C₂³×C₃₁	1	4	yes	—
639	#106	C₂³×C₃₁	1	2	yes	—
640	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
641	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
642	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
643	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
644	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
645	#103	C₂³×C₃₁	1	4	yes	—
646	#103	C₂³×C₃₁	1	4	yes	—
647	#103	C₂³×C₃₁	1	2	yes	—
648	#103	C₂³×C₃₁	1	2	yes	—
649	#103	C₂³×C₃₁	1	4	yes	—
650	#103	C₂³×C₃₁	1	4	yes	—
651	#102	C₂³×C₃₁	1	4	yes	—
652	#102	C₂³×C₃₁	1	4	yes	—
653	#102	C₂³×C₃₁	1	2	yes	—
654	#102	C₂³×C₃₁	1	2	yes	—
655	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
656	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
657	C₄×C₈	C₂³×C₃₁	1	2	yes	—
658	C₄×C₈	C₂³×C₃₁	1	4	yes	—
659	C₃₁	#62097	1	1	yes	characteristic, direct product factor, Sylow
660	C₂⁴	—	2	1	no	—
661	#41	—	2	4	no	—
662	#41	—	2	4	no	—
663	#41	—	4	2	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
670	C₂×Q₈	C₂⁴×C₃₁	1	2	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	2	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	4	1	no	—
677	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
678	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
679	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
680	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	4	4	no	—
690	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
693	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
696	Q₁₆	—	4	4	no	—
697	SD₁₆	—	2	4	no	—
698	SD₁₆	—	4	2	no	—
699	C₂×C₈	—	4	4	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
702	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
703	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
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	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	2	no	—
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	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
731	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
750	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
751	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	2	no	—
758	C₄²	C₂×D₄×C₃₁	1	2	yes	—
759	C₄²	C₂×D₄×C₃₁	1	2	yes	—
760	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₄²	C₂⁴×C₃₁	1	2	yes	—
764	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	8	1	no	—
770	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
771	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	4	2	no	—
778	Q₈	—	4	4	no	—
779	Q₈	—	4	4	no	—
780	Q₈	—	8	1	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	1	no	—
784	D₄	—	2	1	no	—
785	D₄	—	2	1	no	—
786	D₄	—	4	2	no	—
787	D₄	—	4	4	no	—
788	D₄	—	8	2	no	—
789	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	8	2	no	—
812	C₂×C₄	C₃₁×#135	1	4	yes	—
813	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
821	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
822	C₈	—	2	2	no	—
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	8	4	no	—
837	C₂²	C₂×C₃₁×#135	1	2	yes	—
838	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
839	C₄	—	2	2	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	C₂×C₃₁×#135	1	2	yes	—
853	C₄	C₂×C₃₁×#135	1	2	yes	—
854	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
855	C₄	C₃₁×#585	1	1	yes	characteristic
856	C₂	—	2	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	4	2	no	—
859	C₂	—	8	1	no	—
860	C₂	C₃₁×#3489	1	1	yes	characteristic
861	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
862	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×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3381	C₂	semidirect
4. C₃₁×#3364	C₂	semidirect
5. C₃₁×#3340	C₂	semidirect
6. C₃₁×#3336	C₂	semidirect
7. C₃₁×#3302	C₂	semidirect
8. C₃₁×#3296	C₂	semidirect
9. C₃₁×#3249	C₂	semidirect
10. C₃₁×#3248	C₂	semidirect
11. C₃₁×#3233	C₂	semidirect
12. C₃₁×#3229	C₂	semidirect
13. C₃₁×#3107	C₂	semidirect
14. C₃₁×#3101	C₂	semidirect
15. C₃₁×#3076	C₂	semidirect
16. C₂×C₃₁×#474	C₂	semidirect
17. C₃₁×#2988	C₂	semidirect
19. C₃₁×#557	C₂²	semidirect
22. C₃₁×#556	C₂²	semidirect
37. C₃₁×#533	C₂²	semidirect
38. C₃₁×#533	C₂²	semidirect
48. C₃₁×#499	C₂²	semidirect
49. C₃₁×#498	C₂²	semidirect
51. C₃₁×#487	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
57. C₃₁×#479	C₂²	semidirect
58. C₃₁×#479	C₂²	semidirect
60. C₃₁×#477	C₂²	semidirect
61. C₃₁×#477	C₂²	semidirect
64. C₃₁×#475	C₂²	semidirect
65. C₃₁×#475	C₂²	semidirect
71. C₃₁×#467	C₂²	semidirect
74. C₃₁×#462	C₂²	semidirect
75. C₃₁×#462	C₂²	semidirect
80. C₈×Q₈×C₃₁	C₂²	semidirect
81. C₄×Q₁₆×C₃₁	C₂²	semidirect
86. C₈×D₄×C₃₁	C₂²	semidirect
88. C₃₁×#431	C₂²	semidirect
89. C₃₁×#427	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
333. #62097	C₃₁	direct (N × H)
394. #3509	C₂×C₃₁	semidirect
396. #3381	C₂×C₃₁	semidirect
397. #3364	C₂×C₃₁	semidirect
398. #3340	C₂×C₃₁	semidirect
399. #3336	C₂×C₃₁	semidirect
400. #3302	C₂×C₃₁	semidirect
401. #3296	C₂×C₃₁	semidirect
402. #3249	C₂×C₃₁	semidirect
403. #3248	C₂×C₃₁	semidirect
404. #3233	C₂×C₃₁	semidirect
405. #3229	C₂×C₃₁	semidirect
406. #3107	C₂×C₃₁	semidirect
407. #3101	C₂×C₃₁	semidirect
408. #3076	C₂×C₃₁	semidirect
409. C₂×#474	C₂×C₃₁	semidirect
410. #2988	C₂×C₃₁	semidirect
443. #557	C₂²×C₃₁	semidirect
446. #556	C₂²×C₃₁	semidirect
461. #533	C₂²×C₃₁	semidirect
462. #533	C₂²×C₃₁	semidirect
472. #499	C₂²×C₃₁	semidirect
473. #498	C₂²×C₃₁	semidirect
475. #487	C₂²×C₃₁	semidirect
476. #485	C₂²×C₃₁	semidirect
477. #485	C₂²×C₃₁	semidirect
481. #479	C₂²×C₃₁	semidirect
482. #479	C₂²×C₃₁	semidirect
484. #477	C₂²×C₃₁	semidirect
485. #477	C₂²×C₃₁	semidirect
488. #475	C₂²×C₃₁	semidirect
489. #475	C₂²×C₃₁	semidirect
495. #467	C₂²×C₃₁	semidirect
498. #462	C₂²×C₃₁	semidirect
499. #462	C₂²×C₃₁	semidirect
504. C₈×Q₈	C₂²×C₃₁	semidirect
505. C₄×Q₁₆	C₂²×C₃₁	semidirect
510. C₈×D₄	C₂²×C₃₁	semidirect
512. #431	C₂²×C₃₁	semidirect
513. #427	C₂²×C₃₁	semidirect
516. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
659. C₃₁	#62097	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×#3509	2
C₃₁×#3475	2
C₃₁×#3381	2
C₃₁×#3364	2
C₃₁×#3340	2
C₃₁×#3336	2
C₃₁×#3302	2
C₃₁×#3296	2
C₃₁×#3249	2
C₃₁×#3248	2
C₃₁×#3233	2
C₃₁×#3229	2
C₃₁×#3107	2
C₃₁×#3101	2
C₃₁×#3076	2
C₂×C₃₁×#474	2
C₃₁×#2988	2
#62097	31

Subgroups — C31×#62097 #21518856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62097 #21518856