Subgroups — C₃₁×#62580 #21519339

Order 7936.

1790 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×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3319	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3311	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3304	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3235	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3135	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	—	2	1	no	—
19	C₃₁×#559	C₂²	1	2	yes	—
20	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₃₁×#556	—	2	2	no	—
22	C₃₁×#556	—	2	1	no	—
23	C₃₁×#556	C₂²	1	2	yes	—
24	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#555	C₂²	1	2	yes	—
26	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#548	—	2	1	no	—
31	C₃₁×#546	—	2	2	no	—
32	C₃₁×#546	C₂²	1	4	yes	—
33	C₃₁×#542	—	2	1	no	—
34	C₃₁×#542	—	2	2	no	—
35	C₃₁×#540	—	2	2	no	—
36	C₃₁×#535	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#533	C₂²	1	2	yes	complemented
40	C₃₁×#532	C₂²	1	2	yes	—
41	C₃₁×#532	C₂²	1	2	yes	—
42	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	1	yes	characteristic
44	C₃₁×#529	C₂²	1	2	yes	complemented
45	C₃₁×#519	—	2	1	no	—
46	C₃₁×#518	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#501	C₂²	1	2	yes	complemented
50	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#496	C₂²	1	2	yes	—
52	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#491	C₂²	1	2	yes	complemented
54	C₃₁×#490	C₂²	1	2	yes	—
55	C₃₁×#490	C₂²	1	2	yes	—
56	C₃₁×#490	C₂²	1	2	yes	—
57	C₃₁×#489	C₂²	1	4	yes	complemented
58	C₃₁×#489	C₂²	1	4	yes	complemented
59	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#486	C₂²	1	2	yes	—
61	C₃₁×#486	C₂²	1	2	yes	—
62	C₃₁×#485	C₂²	1	4	yes	—
63	C₃₁×#482	C₂²	1	4	yes	complemented
64	C₃₁×#482	C₂²	1	4	yes	complemented
65	C₃₁×#477	C₂²	1	2	yes	complemented
66	C₃₁×#476	C₂²	1	4	yes	complemented
67	C₃₁×#475	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	4	yes	complemented
69	C₃₁×#470	C₂²	1	2	yes	—
70	C₃₁×#468	C₂²	1	2	yes	—
71	C₃₁×#466	C₂²	1	4	yes	complemented
72	C₃₁×#465	C₂²	1	4	yes	complemented
73	C₃₁×#464	C₂²	1	4	yes	complemented
74	C₃₁×#463	C₂²	1	4	yes	complemented
75	C₃₁×#460	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	4	yes	complemented
78	C₃₁×#450	C₂²	1	2	yes	—
79	C₃₁×#449	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	2	yes	—
81	C₃₁×#446	C₂²	1	2	yes	complemented
82	C₃₁×#442	C₂²	1	4	yes	complemented
83	C₃₁×#440	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₃₁×#435	C₂²	1	4	yes	—
87	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
88	C₃₁×#432	C₂²	1	1	yes	characteristic
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#418	C₂²	1	4	yes	—
91	C₃₁×#416	C₂²	1	4	yes	complemented
92	C₃₁×#416	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
94	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	4	yes	—
98	C₂²×Q₈×C₃₁	—	2	1	no	—
99	C₂²×D₄×C₃₁	—	2	1	no	—
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×D₈×C₃₁	C₂³	1	4	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×#127	—	2	2	no	—
117	C₃₁×#127	—	2	1	no	—
118	C₃₁×#127	—	2	1	no	—
119	C₃₁×#127	C₂³	1	2	yes	—
120	C₃₁×#127	C₂³	1	2	yes	—
121	C₃₁×#126	—	2	2	no	—
122	C₃₁×#126	—	2	2	no	—
123	C₃₁×#126	—	2	2	no	—
124	C₃₁×#126	—	2	1	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#125	—	2	1	no	—
127	C₃₁×#125	C₂³	1	1	yes	characteristic
128	C₃₁×#125	C₂³	1	2	yes	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#124	—	2	2	no	—
131	C₃₁×#124	—	2	1	no	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	C₂³	1	4	yes	—
137	C₃₁×#124	C₂³	1	1	yes	characteristic
138	C₃₁×#123	—	2	1	no	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×#123	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	1	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	C₂³	1	1	yes	characteristic
160	C₃₁×#121	C₂³	1	2	yes	—
161	C₃₁×#121	C₂³	1	4	yes	—
162	C₃₁×#120	—	2	4	no	—
163	C₄×Q₈×C₃₁	—	2	1	no	—
164	C₄×Q₈×C₃₁	—	2	2	no	—
165	C₄×Q₈×C₃₁	—	2	1	no	—
166	C₄×Q₈×C₃₁	—	2	1	no	—
167	C₄×Q₈×C₃₁	—	2	2	no	—
168	C₄×Q₈×C₃₁	—	2	1	no	—
169	C₄×Q₈×C₃₁	—	2	1	no	—
170	C₄×Q₈×C₃₁	—	2	2	no	—
171	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
173	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
175	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	D₄	1	2	yes	—
184	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₃₁	C₂³	1	4	yes	—
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₃₁	C₂³	1	2	yes	—
190	C₃₁×#117	—	2	1	no	—
191	C₃₁×#117	—	2	2	no	—
192	C₃₁×#117	—	2	1	no	—
193	C₃₁×#117	—	2	1	no	—
194	C₃₁×#117	—	2	2	no	—
195	C₃₁×#117	D₄	1	1	yes	characteristic
196	C₃₁×#117	D₄	1	2	yes	—
197	C₃₁×#117	C₂³	1	2	yes	—
198	C₃₁×#117	C₂³	1	2	yes	—
199	C₃₁×#117	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₃₁×#107	C₂³	1	2	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#106	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
209	C₃₁×#103	C₂³	1	2	yes	—
210	C₃₁×#103	C₂³	1	2	yes	—
211	C₃₁×#103	C₂³	1	4	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
213	C₃₁×#103	C₂³	1	2	yes	—
214	C₃₁×#102	C₂³	1	4	yes	—
215	C₃₁×#102	C₂³	1	4	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
222	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₃₁×#97	C₂³	1	1	yes	characteristic
224	C₃₁×#97	C₂³	1	2	yes	—
225	C₃₁×#97	C₂³	1	4	yes	—
226	C₃₁×#97	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₃₁	C₂³	1	2	yes	—
228	C₂⁴×C₃₁	—	2	2	no	—
229	#41×C₃₁	—	4	2	no	—
230	#41×C₃₁	—	4	4	no	—
231	#41×C₃₁	—	4	4	no	—
232	#41×C₃₁	—	8	4	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	1	no	—
238	C₂×Q₈×C₃₁	—	4	4	no	—
239	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₃₁	—	2	1	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	4	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	4	4	no	—
252	C₂×D₄×C₃₁	—	4	4	no	—
253	C₂×D₄×C₃₁	—	8	2	no	—
254	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
257	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	1	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	4	no	—
262	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₃₁	—	4	2	no	—
269	SD₁₆×C₃₁	—	4	4	no	—
270	SD₁₆×C₃₁	—	4	2	no	—
271	D₈×C₃₁	—	4	4	no	—
272	M₁₆×C₃₁	—	4	2	no	—
273	C₂×C₈×C₃₁	—	4	4	no	—
274	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₃₁	—	2	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	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	4	no	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	2	no	—
326	C₄²×C₃₁	—	2	2	no	—
327	C₄²×C₃₁	—	2	1	no	—
328	C₄²×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₃₁	C₂×D₄	1	2	yes	—
331	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₃₁	C₂⁴	1	2	yes	—
335	#62580	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	4	no	—
338	C₂³×C₃₁	—	4	4	no	—
339	C₂³×C₃₁	—	8	2	no	—
340	C₂³×C₃₁	—	8	2	no	—
341	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	2	no	—
346	Q₈×C₃₁	—	2	2	no	—
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	4	2	no	—
349	Q₈×C₃₁	—	4	2	no	—
350	Q₈×C₃₁	—	8	2	no	—
351	Q₈×C₃₁	—	8	1	no	—
352	D₄×C₃₁	—	2	2	no	—
353	D₄×C₃₁	—	2	2	no	—
354	D₄×C₃₁	—	2	4	no	—
355	D₄×C₃₁	—	2	4	no	—
356	D₄×C₃₁	—	4	2	no	—
357	D₄×C₃₁	—	4	4	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	8	2	no	—
361	D₄×C₃₁	—	8	2	no	—
362	D₄×C₃₁	—	8	2	no	—
363	D₄×C₃₁	—	8	1	no	—
364	D₄×C₃₁	—	8	4	no	—
365	D₄×C₃₁	—	8	4	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	4	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	1	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	4	1	no	—
377	C₂×C₄×C₃₁	—	4	2	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	4	no	—
380	C₂×C₄×C₃₁	—	4	2	no	—
381	C₂×C₄×C₃₁	—	8	4	no	—
382	C₂×C₄×C₃₁	—	8	4	no	—
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	2	yes	—
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
392	C₈×C₃₁	—	2	2	no	—
393	C₈×C₃₁	—	2	4	no	—
394	C₈×C₃₁	—	2	2	no	—
395	#3518	C₂×C₃₁	1	1	yes	characteristic, complemented
396	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
397	#3375	C₂×C₃₁	1	2	yes	complemented
398	#3373	C₂×C₃₁	1	2	yes	complemented
399	#3319	C₂×C₃₁	1	4	yes	complemented
400	#3311	C₂×C₃₁	1	4	yes	complemented
401	#3305	C₂×C₃₁	1	2	yes	complemented
402	#3304	C₂×C₃₁	1	2	yes	complemented
403	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#3235	C₂×C₃₁	1	2	yes	complemented
405	#3219	C₂×C₃₁	1	2	yes	complemented
406	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3180	C₂×C₃₁	1	2	yes	complemented
408	#3172	C₂×C₃₁	1	1	yes	characteristic, complemented
409	#3138	C₂×C₃₁	1	1	yes	characteristic, complemented
410	#3135	C₂×C₃₁	1	2	yes	complemented
411	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
412	C₂²×C₃₁	—	2	2	no	—
413	C₂²×C₃₁	—	2	1	no	—
414	C₂²×C₃₁	—	2	2	no	—
415	C₂²×C₃₁	—	2	1	no	—
416	C₂²×C₃₁	—	2	1	no	—
417	C₂²×C₃₁	—	2	2	no	—
418	C₂²×C₃₁	—	4	4	no	—
419	C₂²×C₃₁	—	4	1	no	—
420	C₂²×C₃₁	—	4	4	no	—
421	C₂²×C₃₁	—	4	1	no	—
422	C₂²×C₃₁	—	4	1	no	—
423	C₂²×C₃₁	—	4	4	no	—
424	C₂²×C₃₁	—	16	4	no	—
425	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₃₁	—	2	1	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	1	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	1	no	—
431	C₄×C₃₁	—	2	1	no	—
432	C₄×C₃₁	—	2	2	no	—
433	C₄×C₃₁	—	4	2	no	—
434	C₄×C₃₁	—	4	2	no	—
435	C₄×C₃₁	—	4	1	no	—
436	C₄×C₃₁	—	4	2	no	—
437	C₄×C₃₁	—	4	1	no	—
438	C₄×C₃₁	—	4	2	no	—
439	C₄×C₃₁	—	4	1	no	—
440	C₄×C₃₁	#575	1	2	yes	—
441	C₄×C₃₁	#585	1	2	yes	—
442	#559	—	2	1	no	—
443	#559	C₂²×C₃₁	1	2	yes	—
444	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	#556	—	2	2	no	—
446	#556	—	2	1	no	—
447	#556	C₂²×C₃₁	1	2	yes	—
448	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
449	#555	C₂²×C₃₁	1	2	yes	—
450	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	#550	—	2	1	no	—
452	#550	C₂²×C₃₁	1	2	yes	—
453	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	#548	—	2	1	no	—
455	#546	—	2	2	no	—
456	#546	C₂²×C₃₁	1	4	yes	—
457	#542	—	2	1	no	—
458	#542	—	2	2	no	—
459	#540	—	2	2	no	—
460	#535	—	2	1	no	—
461	#533	C₂²×C₃₁	1	1	yes	characteristic
462	#533	C₂²×C₃₁	1	1	yes	characteristic
463	#533	C₂²×C₃₁	1	2	yes	complemented
464	#532	C₂²×C₃₁	1	2	yes	—
465	#532	C₂²×C₃₁	1	2	yes	—
466	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
467	#529	C₂²×C₃₁	1	1	yes	characteristic
468	#529	C₂²×C₃₁	1	2	yes	complemented
469	#519	—	2	1	no	—
470	#518	—	2	1	no	—
471	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
472	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
473	#501	C₂²×C₃₁	1	2	yes	complemented
474	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	#496	C₂²×C₃₁	1	2	yes	—
476	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	#491	C₂²×C₃₁	1	2	yes	complemented
478	#490	C₂²×C₃₁	1	2	yes	—
479	#490	C₂²×C₃₁	1	2	yes	—
480	#490	C₂²×C₃₁	1	2	yes	—
481	#489	C₂²×C₃₁	1	4	yes	complemented
482	#489	C₂²×C₃₁	1	4	yes	complemented
483	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
484	#486	C₂²×C₃₁	1	2	yes	—
485	#486	C₂²×C₃₁	1	2	yes	—
486	#485	C₂²×C₃₁	1	4	yes	—
487	#482	C₂²×C₃₁	1	4	yes	complemented
488	#482	C₂²×C₃₁	1	4	yes	complemented
489	#477	C₂²×C₃₁	1	2	yes	complemented
490	#476	C₂²×C₃₁	1	4	yes	complemented
491	#475	C₂²×C₃₁	1	2	yes	complemented
492	#474	C₂²×C₃₁	1	4	yes	complemented
493	#470	C₂²×C₃₁	1	2	yes	—
494	#468	C₂²×C₃₁	1	2	yes	—
495	#466	C₂²×C₃₁	1	4	yes	complemented
496	#465	C₂²×C₃₁	1	4	yes	complemented
497	#464	C₂²×C₃₁	1	4	yes	complemented
498	#463	C₂²×C₃₁	1	4	yes	complemented
499	#460	C₂²×C₃₁	1	2	yes	—
500	#459	C₂²×C₃₁	1	2	yes	—
501	#452	C₂²×C₃₁	1	4	yes	complemented
502	#450	C₂²×C₃₁	1	2	yes	—
503	#449	C₂²×C₃₁	1	4	yes	complemented
504	#447	C₂²×C₃₁	1	2	yes	—
505	#446	C₂²×C₃₁	1	2	yes	complemented
506	#442	C₂²×C₃₁	1	4	yes	complemented
507	#440	C₂²×C₃₁	1	4	yes	complemented
508	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
509	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
510	#435	C₂²×C₃₁	1	4	yes	—
511	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
512	#432	C₂²×C₃₁	1	1	yes	characteristic
513	#432	C₂²×C₃₁	1	2	yes	complemented
514	#418	C₂²×C₃₁	1	4	yes	—
515	#416	C₂²×C₃₁	1	4	yes	complemented
516	#416	C₂²×C₃₁	1	4	yes	complemented
517	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
519	C₂×C₃₁	—	4	2	no	—
520	C₂×C₃₁	—	4	1	no	—
521	C₂×C₃₁	—	8	1	no	—
522	C₂×C₃₁	—	8	4	no	—
523	C₂×C₃₁	#3500	1	1	yes	characteristic
524	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
525	C₂×C₃₁	#3585	1	1	yes	characteristic
526	C₂×#41	—	2	2	no	—
527	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
528	C₂×#41	C₂³×C₃₁	1	4	yes	—
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
533	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
534	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
536	C₂×D₈	C₂³×C₃₁	1	4	yes	—
537	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
538	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
547	#127	—	2	2	no	—
548	#127	—	2	1	no	—
549	#127	—	2	1	no	—
550	#127	C₂³×C₃₁	1	2	yes	—
551	#127	C₂³×C₃₁	1	2	yes	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#126	—	2	1	no	—
556	#126	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	C₂³×C₃₁	1	1	yes	characteristic
559	#125	C₂³×C₃₁	1	2	yes	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	1	no	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	2	no	—
567	#124	C₂³×C₃₁	1	1	yes	characteristic
568	#124	C₂³×C₃₁	1	4	yes	—
569	#123	—	2	1	no	—
570	#123	—	2	2	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	4	no	—
590	#121	C₂³×C₃₁	1	1	yes	characteristic
591	#121	C₂³×C₃₁	1	2	yes	—
592	#121	C₂³×C₃₁	1	4	yes	—
593	#120	—	2	4	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
605	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
606	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	D₄×C₃₁	1	2	yes	—
615	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₃₁	1	2	yes	—
618	C₄×D₄	C₂³×C₃₁	1	4	yes	—
619	C₄×D₄	C₂³×C₃₁	1	2	yes	—
620	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	#117	—	2	1	no	—
624	#117	—	2	1	no	—
625	#117	—	2	2	no	—
626	#117	D₄×C₃₁	1	1	yes	characteristic
627	#117	D₄×C₃₁	1	2	yes	—
628	#117	C₂³×C₃₁	1	2	yes	—
629	#117	C₂³×C₃₁	1	2	yes	—
630	#117	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
634	#107	C₂³×C₃₁	1	2	yes	—
635	#107	C₂³×C₃₁	1	4	yes	—
636	#106	C₂³×C₃₁	1	2	yes	—
637	#106	C₂³×C₃₁	1	4	yes	—
638	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
639	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
640	#103	C₂³×C₃₁	1	2	yes	—
641	#103	C₂³×C₃₁	1	2	yes	—
642	#103	C₂³×C₃₁	1	4	yes	—
643	#103	C₂³×C₃₁	1	4	yes	—
644	#103	C₂³×C₃₁	1	2	yes	—
645	#102	C₂³×C₃₁	1	4	yes	—
646	#102	C₂³×C₃₁	1	4	yes	—
647	#102	C₂³×C₃₁	1	4	yes	—
648	#102	C₂³×C₃₁	1	4	yes	—
649	#102	C₂³×C₃₁	1	4	yes	—
650	#102	C₂³×C₃₁	1	4	yes	—
651	#102	C₂³×C₃₁	1	2	yes	—
652	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
654	#97	C₂³×C₃₁	1	1	yes	characteristic
655	#97	C₂³×C₃₁	1	2	yes	—
656	#97	C₂³×C₃₁	1	4	yes	—
657	#97	C₂³×C₃₁	1	1	yes	characteristic
658	C₄×C₈	C₂³×C₃₁	1	2	yes	—
659	C₃₁	#62580	1	1	yes	characteristic, direct product factor, Sylow
660	C₂⁴	—	2	2	no	—
661	#41	—	4	2	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
672	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	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	2	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	8	2	no	—
686	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
687	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
688	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
689	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	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	2	yes	—
697	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	Q₁₆	—	4	2	no	—
701	SD₁₆	—	4	4	no	—
702	SD₁₆	—	4	2	no	—
703	D₈	—	4	4	no	—
704	M₁₆	—	4	2	no	—
705	C₂×C₈	—	4	4	no	—
706	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
707	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
708	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	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	4	no	—
748	C₂²⋊C₄	—	2	4	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	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₃₁	1	2	yes	—
761	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₃₁	1	2	yes	—
763	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
764	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₄²	C₂⁴×C₃₁	1	2	yes	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	8	2	no	—
771	C₂³	—	8	2	no	—
772	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	4	4	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	8	2	no	—
782	Q₈	—	8	1	no	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	4	2	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	8	2	no	—
792	D₄	—	8	2	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	1	no	—
795	D₄	—	8	4	no	—
796	D₄	—	8	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	4	no	—
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	2	yes	—
817	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
822	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₈	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	16	4	no	—
839	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	C₃₁×#575	1	2	yes	—
855	C₄	C₃₁×#585	1	2	yes	—
856	C₂	—	4	1	no	—
857	C₂	—	4	2	no	—
858	C₂	—	8	4	no	—
859	C₂	—	8	1	no	—
860	C₂	C₃₁×#3500	1	1	yes	characteristic
861	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
862	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3518	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3375	C₂	semidirect
4. C₃₁×#3373	C₂	semidirect
5. C₃₁×#3319	C₂	semidirect
6. C₃₁×#3311	C₂	semidirect
7. C₃₁×#3305	C₂	semidirect
8. C₃₁×#3304	C₂	semidirect
9. C₃₁×#3237	C₂	semidirect
10. C₃₁×#3235	C₂	semidirect
11. C₃₁×#3219	C₂	semidirect
12. C₃₁×#3217	C₂	semidirect
13. C₃₁×#3180	C₂	semidirect
14. C₃₁×#3172	C₂	semidirect
15. C₃₁×#3138	C₂	semidirect
16. C₃₁×#3135	C₂	semidirect
17. C₃₁×#2970	C₂	semidirect
20. Q₈²×C₃₁	C₂²	semidirect
24. C₃₁×#556	C₂²	semidirect
26. C₃₁×#555	C₂²	semidirect
29. D₄×Q₈×C₃₁	C₂²	semidirect
39. C₃₁×#533	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#497	C₂²	semidirect
52. C₃₁×#491	C₂²	semidirect
53. C₃₁×#491	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#489	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
63. C₃₁×#482	C₂²	semidirect
64. C₃₁×#482	C₂²	semidirect
65. C₃₁×#477	C₂²	semidirect
66. C₃₁×#476	C₂²	semidirect
67. C₃₁×#475	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
71. C₃₁×#466	C₂²	semidirect
72. C₃₁×#465	C₂²	semidirect
73. C₃₁×#464	C₂²	semidirect
74. C₃₁×#463	C₂²	semidirect
77. C₃₁×#452	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
81. C₃₁×#446	C₂²	semidirect
82. C₃₁×#442	C₂²	semidirect
83. C₃₁×#440	C₂²	semidirect
84. C₄×Q₁₆×C₃₁	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
87. C₈×D₄×C₃₁	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
91. C₃₁×#416	C₂²	semidirect
92. C₃₁×#416	C₂²	semidirect
94. C₂×C₃₁×#97	C₂²	semidirect
335. #62580	C₃₁	direct (N × H)
395. #3518	C₂×C₃₁	semidirect
396. #3508	C₂×C₃₁	semidirect
397. #3375	C₂×C₃₁	semidirect
398. #3373	C₂×C₃₁	semidirect
399. #3319	C₂×C₃₁	semidirect
400. #3311	C₂×C₃₁	semidirect
401. #3305	C₂×C₃₁	semidirect
402. #3304	C₂×C₃₁	semidirect
403. #3237	C₂×C₃₁	semidirect
404. #3235	C₂×C₃₁	semidirect
405. #3219	C₂×C₃₁	semidirect
406. #3217	C₂×C₃₁	semidirect
407. #3180	C₂×C₃₁	semidirect
408. #3172	C₂×C₃₁	semidirect
409. #3138	C₂×C₃₁	semidirect
410. #3135	C₂×C₃₁	semidirect
411. #2970	C₂×C₃₁	semidirect
444. Q₈²	C₂²×C₃₁	semidirect
448. #556	C₂²×C₃₁	semidirect
450. #555	C₂²×C₃₁	semidirect
453. D₄×Q₈	C₂²×C₃₁	semidirect
463. #533	C₂²×C₃₁	semidirect
468. #529	C₂²×C₃₁	semidirect
472. #501	C₂²×C₃₁	semidirect
473. #501	C₂²×C₃₁	semidirect
474. #497	C₂²×C₃₁	semidirect
476. #491	C₂²×C₃₁	semidirect
477. #491	C₂²×C₃₁	semidirect
481. #489	C₂²×C₃₁	semidirect
482. #489	C₂²×C₃₁	semidirect
483. #489	C₂²×C₃₁	semidirect
487. #482	C₂²×C₃₁	semidirect
488. #482	C₂²×C₃₁	semidirect
489. #477	C₂²×C₃₁	semidirect
490. #476	C₂²×C₃₁	semidirect
491. #475	C₂²×C₃₁	semidirect
492. #474	C₂²×C₃₁	semidirect
495. #466	C₂²×C₃₁	semidirect
496. #465	C₂²×C₃₁	semidirect
497. #464	C₂²×C₃₁	semidirect
498. #463	C₂²×C₃₁	semidirect
501. #452	C₂²×C₃₁	semidirect
503. #449	C₂²×C₃₁	semidirect
505. #446	C₂²×C₃₁	semidirect
506. #442	C₂²×C₃₁	semidirect
507. #440	C₂²×C₃₁	semidirect
508. C₄×Q₁₆	C₂²×C₃₁	semidirect
509. C₄×SD₁₆	C₂²×C₃₁	semidirect
511. C₈×D₄	C₂²×C₃₁	semidirect
513. #432	C₂²×C₃₁	semidirect
515. #416	C₂²×C₃₁	semidirect
516. #416	C₂²×C₃₁	semidirect
518. C₂×#97	C₂²×C₃₁	semidirect
659. C₃₁	#62580	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×#3518	2
C₃₁×#3508	2
C₃₁×#3375	2
C₃₁×#3373	2
C₃₁×#3319	2
C₃₁×#3311	2
C₃₁×#3305	2
C₃₁×#3304	2
C₃₁×#3237	2
C₃₁×#3235	2
C₃₁×#3219	2
C₃₁×#3217	2
C₃₁×#3180	2
C₃₁×#3172	2
C₃₁×#3138	2
C₃₁×#3135	2
C₃₁×#2970	2
#62580	31

Subgroups — C31×#62580 #21519339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62580 #21519339