Subgroups — C₃₁×#61834 #21518593

Order 7936.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3237	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3116	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3111	C₂	1	2	yes	maximal
21	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic
23	C₃₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#557	C₂²	1	1	yes	characteristic
26	C₃₁×#557	C₂²	1	1	yes	characteristic
27	C₃₁×#557	C₂²	1	2	yes	—
28	C₃₁×#557	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	2	yes	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	2	yes	—
32	C₃₁×#554	—	2	1	no	—
33	C₃₁×#554	—	2	2	no	—
34	C₃₁×#554	C₂²	1	1	yes	characteristic
35	C₃₁×#554	C₂²	1	2	yes	—
36	C₃₁×#552	—	2	1	no	—
37	C₃₁×#552	—	2	2	no	—
38	D₄×Q₈×C₃₁	—	2	1	no	—
39	D₄×Q₈×C₃₁	—	2	1	no	—
40	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#541	—	2	1	no	—
43	C₃₁×#541	—	2	2	no	—
44	C₃₁×#533	—	2	1	no	—
45	C₃₁×#533	—	2	2	no	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#533	C₂²	1	2	yes	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	2	yes	—
50	C₃₁×#529	C₂²	1	1	yes	characteristic
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₃₁×#519	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	2	yes	—
55	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#501	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#501	C₂²	1	2	yes	—
61	C₃₁×#500	C₂²	1	1	yes	characteristic
62	C₃₁×#499	C₂²	1	2	yes	—
63	C₃₁×#498	C₂²	1	1	yes	characteristic
64	C₃₁×#491	C₂²	1	2	yes	—
65	C₃₁×#491	C₂²	1	2	yes	—
66	C₃₁×#489	C₂²	1	2	yes	—
67	C₃₁×#489	C₂²	1	2	yes	—
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#487	C₂²	1	1	yes	characteristic
70	C₃₁×#487	C₂²	1	1	yes	characteristic
71	C₃₁×#485	C₂²	1	1	yes	characteristic
72	C₃₁×#485	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	—
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#485	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	1	yes	characteristic
77	C₃₁×#482	C₂²	1	2	yes	—
78	C₃₁×#479	C₂²	1	1	yes	characteristic
79	C₃₁×#479	C₂²	1	2	yes	—
80	C₃₁×#479	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	—
83	C₃₁×#479	C₂²	1	2	yes	—
84	C₃₁×#478	C₂²	1	1	yes	characteristic
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#478	C₂²	1	2	yes	—
87	C₃₁×#478	C₂²	1	2	yes	—
88	C₃₁×#477	C₂²	1	2	yes	—
89	C₃₁×#477	C₂²	1	2	yes	—
90	C₃₁×#477	C₂²	1	1	yes	characteristic
91	C₃₁×#477	C₂²	1	2	yes	—
92	C₃₁×#476	C₂²	1	1	yes	characteristic
93	C₃₁×#476	C₂²	1	2	yes	—
94	C₃₁×#475	C₂²	1	1	yes	characteristic
95	C₃₁×#475	C₂²	1	2	yes	—
96	C₃₁×#475	C₂²	1	1	yes	characteristic
97	C₃₁×#475	C₂²	1	2	yes	—
98	C₃₁×#474	C₂²	1	1	yes	characteristic
99	C₃₁×#474	C₂²	1	1	yes	characteristic
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#464	C₂²	1	2	yes	—
102	C₃₁×#463	C₂²	1	1	yes	characteristic
103	C₃₁×#463	C₂²	1	2	yes	—
104	C₃₁×#462	C₂²	1	1	yes	characteristic
105	C₃₁×#462	C₂²	1	2	yes	—
106	C₃₁×#461	C₂²	1	1	yes	characteristic
107	C₃₁×#461	C₂²	1	2	yes	—
108	C₃₁×#452	C₂²	1	1	yes	characteristic
109	C₃₁×#452	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₃₁×#446	C₂²	1	1	yes	characteristic
113	C₃₁×#446	C₂²	1	1	yes	characteristic
114	C₃₁×#446	C₂²	1	1	yes	characteristic
115	C₃₁×#446	C₂²	1	2	yes	—
116	C₃₁×#446	C₂²	1	2	yes	—
117	C₃₁×#442	C₂²	1	2	yes	—
118	C₃₁×#441	C₂²	1	2	yes	—
119	C₃₁×#441	C₂²	1	2	yes	—
120	C₃₁×#441	C₂²	1	2	yes	—
121	C₃₁×#440	C₂²	1	2	yes	—
122	C₃₁×#440	C₂²	1	2	yes	—
123	C₃₁×#440	C₂²	1	2	yes	—
124	C₃₁×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
126	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
130	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
131	C₃₁×#432	C₂²	1	2	yes	—
132	C₃₁×#432	C₂²	1	2	yes	—
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₃₁	—	2	1	no	—
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
139	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₃₁×C₄⋊Q₈	—	2	1	no	—
146	C₃₁×C₄⋊Q₈	—	2	2	no	—
147	C₃₁×C₄⋊Q₈	—	2	1	no	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	1	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#125	C₂³	1	1	yes	characteristic
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#124	C₂³	1	1	yes	characteristic
180	C₃₁×#124	C₂³	1	2	yes	—
181	C₃₁×#123	—	2	1	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×#121	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₃₁	—	2	1	no	—
204	C₄×Q₈×C₃₁	—	2	1	no	—
205	C₄×Q₈×C₃₁	—	2	1	no	—
206	C₄×Q₈×C₃₁	—	2	2	no	—
207	C₄×Q₈×C₃₁	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	D₄	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₃₁×#117	—	2	1	no	—
243	C₃₁×#117	—	2	2	no	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
256	C₂×C₄²×C₃₁	—	2	1	no	—
257	C₂×C₄²×C₃₁	—	2	2	no	—
258	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
260	C₃₁×#107	C₂³	1	1	yes	characteristic
261	C₃₁×#107	C₂³	1	2	yes	—
262	C₃₁×#107	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#106	C₂³	1	1	yes	characteristic
268	C₃₁×#106	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	2	no	—
314	C₂×Q₈×C₃₁	—	2	2	no	—
315	C₂×Q₈×C₃₁	—	2	2	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	4	2	no	—
321	C₂×Q₈×C₃₁	—	4	4	no	—
322	C₂×Q₈×C₃₁	—	4	4	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	—	2	1	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	—	2	1	no	—
336	C₂²×C₄×C₃₁	—	2	2	no	—
337	C₂²×C₄×C₃₁	—	2	1	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	Q₁₆×C₃₁	—	2	2	no	—
346	Q₁₆×C₃₁	—	2	4	no	—
347	SD₁₆×C₃₁	—	2	2	no	—
348	SD₁₆×C₃₁	—	2	2	no	—
349	SD₁₆×C₃₁	—	2	4	no	—
350	D₈×C₃₁	—	2	2	no	—
351	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
353	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
356	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	1	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	1	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	1	no	—
404	C₂²⋊C₄×C₃₁	—	2	1	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	1	no	—
407	C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₄²×C₃₁	—	2	1	no	—
418	C₄²×C₃₁	—	2	2	no	—
419	C₄²×C₃₁	—	2	1	no	—
420	C₄²×C₃₁	—	2	2	no	—
421	C₄²×C₃₁	—	2	2	no	—
422	C₄²×C₃₁	—	2	1	no	—
423	C₄²×C₃₁	—	2	2	no	—
424	C₄²×C₃₁	—	2	2	no	—
425	C₄²×C₃₁	—	2	2	no	—
426	C₄²×C₃₁	—	2	2	no	—
427	C₄²×C₃₁	—	2	1	no	—
428	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
429	C₄²×C₃₁	C₂×D₄	1	2	yes	—
430	C₄²×C₃₁	C₂×D₄	1	2	yes	—
431	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
433	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
434	C₄²×C₃₁	C₂⁴	1	2	yes	—
435	C₄²×C₃₁	C₂⁴	1	2	yes	—
436	#61834	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂³×C₃₁	—	2	1	no	—
438	C₂³×C₃₁	—	2	1	no	—
439	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
440	Q₈×C₃₁	—	2	2	no	—
441	Q₈×C₃₁	—	2	2	no	—
442	Q₈×C₃₁	—	2	1	no	—
443	Q₈×C₃₁	—	2	2	no	—
444	Q₈×C₃₁	—	2	1	no	—
445	Q₈×C₃₁	—	2	2	no	—
446	Q₈×C₃₁	—	2	1	no	—
447	Q₈×C₃₁	—	4	2	no	—
448	Q₈×C₃₁	—	4	4	no	—
449	Q₈×C₃₁	—	4	4	no	—
450	Q₈×C₃₁	—	4	2	no	—
451	Q₈×C₃₁	—	4	2	no	—
452	Q₈×C₃₁	—	8	2	no	—
453	Q₈×C₃₁	—	8	1	no	—
454	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
455	D₄×C₃₁	—	2	4	no	—
456	D₄×C₃₁	—	2	1	no	—
457	D₄×C₃₁	—	2	1	no	—
458	D₄×C₃₁	—	2	1	no	—
459	D₄×C₃₁	—	4	2	no	—
460	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
461	C₂×C₄×C₃₁	—	2	4	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	2	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	4	1	no	—
476	C₂×C₄×C₃₁	—	4	2	no	—
477	C₂×C₄×C₃₁	—	4	2	no	—
478	C₂×C₄×C₃₁	—	4	4	no	—
479	C₂×C₄×C₃₁	—	4	4	no	—
480	C₂×C₄×C₃₁	—	4	2	no	—
481	C₂×C₄×C₃₁	—	4	2	no	—
482	C₂×C₄×C₃₁	—	8	1	no	—
483	C₂×C₄×C₃₁	—	8	2	no	—
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
494	C₈×C₃₁	—	2	1	no	—
495	C₈×C₃₁	—	2	1	no	—
496	C₈×C₃₁	—	2	1	no	—
497	C₈×C₃₁	—	2	2	no	—
498	C₈×C₃₁	—	2	1	no	—
499	C₈×C₃₁	—	2	2	no	—
500	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
501	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#3390	C₂×C₃₁	1	2	yes	complemented
503	#3388	C₂×C₃₁	1	2	yes	complemented
504	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
505	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
506	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3377	C₂×C₃₁	1	2	yes	complemented
509	#3376	C₂×C₃₁	1	2	yes	complemented
510	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3240	C₂×C₃₁	1	2	yes	complemented
515	#3237	C₂×C₃₁	1	2	yes	complemented
516	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3116	C₂×C₃₁	1	2	yes	complemented
519	#3111	C₂×C₃₁	1	2	yes	—
520	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3102	C₂×C₃₁	1	1	yes	characteristic
522	#2983	C₂×C₃₁	1	1	yes	characteristic, complemented
523	C₂²×C₃₁	—	2	1	no	—
524	C₂²×C₃₁	—	2	1	no	—
525	C₂²×C₃₁	—	2	2	no	—
526	C₂²×C₃₁	—	2	1	no	—
527	C₂²×C₃₁	—	4	1	no	—
528	C₂²×C₃₁	—	4	1	no	—
529	C₂²×C₃₁	—	4	1	no	—
530	C₂²×C₃₁	—	4	1	no	—
531	C₂²×C₃₁	—	4	1	no	—
532	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₃₁	—	2	1	no	—
534	C₄×C₃₁	—	2	2	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	2	1	no	—
537	C₄×C₃₁	—	2	1	no	—
538	C₄×C₃₁	—	2	2	no	—
539	C₄×C₃₁	—	2	1	no	—
540	C₄×C₃₁	—	2	2	no	—
541	C₄×C₃₁	—	2	2	no	—
542	C₄×C₃₁	—	4	2	no	—
543	C₄×C₃₁	—	4	1	no	—
544	C₄×C₃₁	—	4	1	no	—
545	C₄×C₃₁	—	4	2	no	—
546	C₄×C₃₁	—	4	1	no	—
547	C₄×C₃₁	—	4	2	no	—
548	C₄×C₃₁	—	4	2	no	—
549	C₄×C₃₁	—	4	1	no	—
550	C₄×C₃₁	—	4	1	no	—
551	C₄×C₃₁	#575	1	2	yes	—
552	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
555	#557	C₂²×C₃₁	1	1	yes	characteristic
556	#557	C₂²×C₃₁	1	1	yes	characteristic
557	#557	C₂²×C₃₁	1	2	yes	—
558	#557	C₂²×C₃₁	1	1	yes	characteristic
559	#557	C₂²×C₃₁	1	2	yes	—
560	#556	C₂²×C₃₁	1	1	yes	characteristic
561	#556	C₂²×C₃₁	1	2	yes	—
562	#554	—	2	1	no	—
563	#554	—	2	2	no	—
564	#554	C₂²×C₃₁	1	1	yes	characteristic
565	#554	C₂²×C₃₁	1	2	yes	—
566	#552	—	2	1	no	—
567	#552	—	2	2	no	—
568	D₄×Q₈	—	2	1	no	—
569	D₄×Q₈	—	2	1	no	—
570	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
571	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
572	#541	—	2	1	no	—
573	#541	—	2	2	no	—
574	#533	—	2	1	no	—
575	#533	—	2	2	no	—
576	#533	C₂²×C₃₁	1	1	yes	characteristic
577	#533	C₂²×C₃₁	1	2	yes	—
578	#533	C₂²×C₃₁	1	1	yes	characteristic
579	#533	C₂²×C₃₁	1	2	yes	—
580	#529	C₂²×C₃₁	1	1	yes	characteristic
581	#529	C₂²×C₃₁	1	2	yes	—
582	#519	—	2	1	no	—
583	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
584	C₄×#41	C₂²×C₃₁	1	2	yes	—
585	C₂×C₄×Q₈	—	2	1	no	—
586	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
587	#501	C₂²×C₃₁	1	2	yes	—
588	#501	C₂²×C₃₁	1	2	yes	—
589	#501	C₂²×C₃₁	1	2	yes	—
590	#501	C₂²×C₃₁	1	2	yes	—
591	#500	C₂²×C₃₁	1	1	yes	characteristic
592	#499	C₂²×C₃₁	1	2	yes	—
593	#498	C₂²×C₃₁	1	1	yes	characteristic
594	#491	C₂²×C₃₁	1	2	yes	—
595	#491	C₂²×C₃₁	1	2	yes	—
596	#489	C₂²×C₃₁	1	2	yes	—
597	#489	C₂²×C₃₁	1	2	yes	—
598	#488	C₂²×C₃₁	1	2	yes	—
599	#487	C₂²×C₃₁	1	1	yes	characteristic
600	#487	C₂²×C₃₁	1	1	yes	characteristic
601	#485	C₂²×C₃₁	1	1	yes	characteristic
602	#485	C₂²×C₃₁	1	2	yes	—
603	#485	C₂²×C₃₁	1	2	yes	—
604	#485	C₂²×C₃₁	1	2	yes	—
605	#485	C₂²×C₃₁	1	2	yes	—
606	#482	C₂²×C₃₁	1	1	yes	characteristic
607	#482	C₂²×C₃₁	1	2	yes	—
608	#479	C₂²×C₃₁	1	1	yes	characteristic
609	#479	C₂²×C₃₁	1	2	yes	—
610	#479	C₂²×C₃₁	1	2	yes	—
611	#479	C₂²×C₃₁	1	2	yes	—
612	#479	C₂²×C₃₁	1	2	yes	—
613	#479	C₂²×C₃₁	1	2	yes	—
614	#478	C₂²×C₃₁	1	1	yes	characteristic
615	#478	C₂²×C₃₁	1	2	yes	—
616	#478	C₂²×C₃₁	1	2	yes	—
617	#478	C₂²×C₃₁	1	2	yes	—
618	#477	C₂²×C₃₁	1	2	yes	—
619	#477	C₂²×C₃₁	1	2	yes	—
620	#477	C₂²×C₃₁	1	1	yes	characteristic
621	#477	C₂²×C₃₁	1	2	yes	—
622	#476	C₂²×C₃₁	1	1	yes	characteristic
623	#476	C₂²×C₃₁	1	2	yes	—
624	#475	C₂²×C₃₁	1	1	yes	characteristic
625	#475	C₂²×C₃₁	1	2	yes	—
626	#475	C₂²×C₃₁	1	1	yes	characteristic
627	#475	C₂²×C₃₁	1	2	yes	—
628	#474	C₂²×C₃₁	1	1	yes	characteristic
629	#474	C₂²×C₃₁	1	1	yes	characteristic
630	#464	C₂²×C₃₁	1	1	yes	characteristic
631	#464	C₂²×C₃₁	1	2	yes	—
632	#463	C₂²×C₃₁	1	1	yes	characteristic
633	#463	C₂²×C₃₁	1	2	yes	—
634	#462	C₂²×C₃₁	1	1	yes	characteristic
635	#462	C₂²×C₃₁	1	2	yes	—
636	#461	C₂²×C₃₁	1	1	yes	characteristic
637	#461	C₂²×C₃₁	1	2	yes	—
638	#452	C₂²×C₃₁	1	1	yes	characteristic
639	#452	C₂²×C₃₁	1	2	yes	—
640	#449	C₂²×C₃₁	1	1	yes	characteristic
641	#446	C₂²×C₃₁	1	1	yes	characteristic
642	#446	C₂²×C₃₁	1	1	yes	characteristic
643	#446	C₂²×C₃₁	1	1	yes	characteristic
644	#446	C₂²×C₃₁	1	1	yes	characteristic
645	#446	C₂²×C₃₁	1	2	yes	—
646	#446	C₂²×C₃₁	1	2	yes	—
647	#442	C₂²×C₃₁	1	2	yes	—
648	#441	C₂²×C₃₁	1	2	yes	—
649	#441	C₂²×C₃₁	1	2	yes	—
650	#441	C₂²×C₃₁	1	2	yes	—
651	#440	C₂²×C₃₁	1	2	yes	—
652	#440	C₂²×C₃₁	1	2	yes	—
653	#440	C₂²×C₃₁	1	2	yes	—
654	#440	C₂²×C₃₁	1	2	yes	—
655	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
656	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
657	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
658	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
659	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
660	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
661	#432	C₂²×C₃₁	1	2	yes	—
662	#432	C₂²×C₃₁	1	2	yes	—
663	#431	C₂²×C₃₁	1	1	yes	characteristic
664	#431	C₂²×C₃₁	1	1	yes	characteristic
665	C₂×C₃₁	—	4	1	no	—
666	C₂×C₃₁	—	4	2	no	—
667	C₂×C₃₁	—	8	1	no	—
668	C₂×C₃₁	#3486	1	1	yes	characteristic
669	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
670	C₂×C₃₁	#3586	1	1	yes	characteristic
671	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
672	C₂²×Q₈	—	2	1	no	—
673	C₂²×Q₈	—	2	1	no	—
674	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
675	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
678	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
680	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	2	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
688	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
689	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
692	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	1	no	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	1	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	1	no	—
710	#125	C₂³×C₃₁	1	1	yes	characteristic
711	#125	C₂³×C₃₁	1	2	yes	—
712	#125	C₂³×C₃₁	1	2	yes	—
713	#125	C₂³×C₃₁	1	2	yes	—
714	#125	C₂³×C₃₁	1	2	yes	—
715	#124	C₂³×C₃₁	1	1	yes	characteristic
716	#124	C₂³×C₃₁	1	2	yes	—
717	#123	—	2	1	no	—
718	#123	—	2	2	no	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
738	#121	C₂³×C₃₁	1	1	yes	characteristic
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	—	2	2	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
752	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
753	C₄×Q₈	D₄×C₃₁	1	2	yes	—
754	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
756	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
758	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
762	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
763	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₃₁	1	2	yes	—
774	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
775	C₄×D₄	C₂³×C₃₁	1	2	yes	—
776	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
777	C₄×D₄	C₂³×C₃₁	1	2	yes	—
778	#117	—	2	1	no	—
779	#117	—	2	2	no	—
780	#117	—	2	2	no	—
781	#117	—	2	1	no	—
782	#117	—	2	2	no	—
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	—	2	2	no	—
786	#117	C₂³×C₃₁	1	1	yes	characteristic
787	#117	C₂³×C₃₁	1	2	yes	—
788	C₂×C₄⋊C₄	—	2	1	no	—
789	C₂×C₄⋊C₄	—	2	2	no	—
790	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
791	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
792	C₂×C₄²	—	2	1	no	—
793	C₂×C₄²	—	2	2	no	—
794	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
796	#107	C₂³×C₃₁	1	1	yes	characteristic
797	#107	C₂³×C₃₁	1	2	yes	—
798	#107	C₂³×C₃₁	1	1	yes	characteristic
799	#107	C₂³×C₃₁	1	2	yes	—
800	#107	C₂³×C₃₁	1	2	yes	—
801	#107	C₂³×C₃₁	1	2	yes	—
802	#107	C₂³×C₃₁	1	2	yes	—
803	#106	C₂³×C₃₁	1	1	yes	characteristic
804	#106	C₂³×C₃₁	1	2	yes	—
805	#106	C₂³×C₃₁	1	1	yes	characteristic
806	#106	C₂³×C₃₁	1	2	yes	—
807	#106	C₂³×C₃₁	1	2	yes	—
808	#106	C₂³×C₃₁	1	2	yes	—
809	#106	C₂³×C₃₁	1	2	yes	—
810	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
815	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
816	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
817	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
818	#103	C₂³×C₃₁	1	1	yes	characteristic
819	#103	C₂³×C₃₁	1	2	yes	—
820	#103	C₂³×C₃₁	1	1	yes	characteristic
821	#103	C₂³×C₃₁	1	2	yes	—
822	#103	C₂³×C₃₁	1	1	yes	characteristic
823	#103	C₂³×C₃₁	1	2	yes	—
824	#103	C₂³×C₃₁	1	1	yes	characteristic
825	#103	C₂³×C₃₁	1	2	yes	—
826	#103	C₂³×C₃₁	1	2	yes	—
827	#103	C₂³×C₃₁	1	2	yes	—
828	#103	C₂³×C₃₁	1	2	yes	—
829	#103	C₂³×C₃₁	1	2	yes	—
830	#103	C₂³×C₃₁	1	2	yes	—
831	#102	C₂³×C₃₁	1	1	yes	characteristic
832	#102	C₂³×C₃₁	1	1	yes	characteristic
833	#102	C₂³×C₃₁	1	1	yes	characteristic
834	#102	C₂³×C₃₁	1	2	yes	—
835	#102	C₂³×C₃₁	1	1	yes	characteristic
836	#102	C₂³×C₃₁	1	2	yes	—
837	#102	C₂³×C₃₁	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
841	#97	C₂³×C₃₁	1	2	yes	—
842	#97	C₂³×C₃₁	1	2	yes	—
843	#97	C₂³×C₃₁	1	2	yes	—
844	#97	C₂³×C₃₁	1	2	yes	—
845	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₄×C₈	C₂³×C₃₁	1	2	yes	—
848	C₃₁	#61834	1	1	yes	characteristic, direct product factor, Sylow
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	4	2	no	—
858	C₂×Q₈	—	4	4	no	—
859	C₂×Q₈	—	4	4	no	—
860	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
862	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
863	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
864	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
865	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	—	2	1	no	—
868	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
869	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
878	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
879	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
880	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
882	Q₁₆	—	2	2	no	—
883	Q₁₆	—	2	4	no	—
884	SD₁₆	—	2	2	no	—
885	SD₁₆	—	2	2	no	—
886	SD₁₆	—	2	4	no	—
887	D₈	—	2	2	no	—
888	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
890	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
893	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
929	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
930	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
931	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
938	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₄²	—	2	1	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	1	no	—
965	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
966	C₄²	C₂×D₄×C₃₁	1	2	yes	—
967	C₄²	C₂×D₄×C₃₁	1	2	yes	—
968	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
969	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₄²	C₂⁴×C₃₁	1	2	yes	—
972	C₄²	C₂⁴×C₃₁	1	2	yes	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
976	Q₈	—	2	2	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	4	4	no	—
985	Q₈	—	4	4	no	—
986	Q₈	—	4	2	no	—
987	Q₈	—	4	2	no	—
988	Q₈	—	8	2	no	—
989	Q₈	—	8	1	no	—
990	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
991	D₄	—	2	4	no	—
992	D₄	—	2	1	no	—
993	D₄	—	2	1	no	—
994	D₄	—	2	1	no	—
995	D₄	—	4	2	no	—
996	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
997	C₂×C₄	—	2	4	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	—	8	1	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1023	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1025	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	2	no	—
1034	C₈	—	2	1	no	—
1035	C₈	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	1	no	—
1064	C₄	C₃₁×#575	1	2	yes	—
1065	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1066	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1067	C₂	—	4	1	no	—
1068	C₂	—	4	2	no	—
1069	C₂	—	8	1	no	—
1070	C₂	C₃₁×#3486	1	1	yes	characteristic
1071	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1072	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×#449	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3523	C₂	semidirect
2. Q₈×#41×C₃₁	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3388	C₂	semidirect
5. C₃₁×#3387	C₂	semidirect
6. C₃₁×#3386	C₂	semidirect
7. C₃₁×#3386	C₂	semidirect
8. C₃₁×#3384	C₂	semidirect
9. C₃₁×#3377	C₂	semidirect
10. C₃₁×#3376	C₂	semidirect
11. C₃₁×#3374	C₂	semidirect
12. C₃₁×#3372	C₂	semidirect
13. C₃₁×#3369	C₂	semidirect
14. C₃₁×#3367	C₂	semidirect
15. C₃₁×#3240	C₂	semidirect
16. C₃₁×#3237	C₂	semidirect
17. C₃₁×#3233	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3116	C₂	semidirect
21. C₃₁×#3107	C₂	semidirect
23. C₃₁×#2983	C₂	semidirect
436. #61834	C₃₁	direct (N × H)
500. #3523	C₂×C₃₁	semidirect
501. Q₈×#41	C₂×C₃₁	semidirect
502. #3390	C₂×C₃₁	semidirect
503. #3388	C₂×C₃₁	semidirect
504. #3387	C₂×C₃₁	semidirect
505. #3386	C₂×C₃₁	semidirect
506. #3386	C₂×C₃₁	semidirect
507. #3384	C₂×C₃₁	semidirect
508. #3377	C₂×C₃₁	semidirect
509. #3376	C₂×C₃₁	semidirect
510. #3374	C₂×C₃₁	semidirect
511. #3372	C₂×C₃₁	semidirect
512. #3369	C₂×C₃₁	semidirect
513. #3367	C₂×C₃₁	semidirect
514. #3240	C₂×C₃₁	semidirect
515. #3237	C₂×C₃₁	semidirect
516. #3233	C₂×C₃₁	semidirect
517. #3231	C₂×C₃₁	semidirect
518. #3116	C₂×C₃₁	semidirect
520. #3107	C₂×C₃₁	semidirect
522. #2983	C₂×C₃₁	semidirect
848. C₃₁	#61834	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×#3523	2
Q₈×#41×C₃₁	2
C₃₁×#3390	2
C₃₁×#3388	2
C₃₁×#3387	2
C₃₁×#3386	2
C₃₁×#3384	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3374	2
C₃₁×#3372	2
C₃₁×#3369	2
C₃₁×#3367	2
C₃₁×#3240	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3231	2
C₃₁×#3116	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#3102	2
C₃₁×#2983	2
#61834	31

Subgroups — C31×#61834 #21518593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61834 #21518593