Subgroups — C₃₁×#61839 #21518598

Order 7936.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	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×#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	C₂²	1	2	yes	—
25	Q₈²×C₃₁	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	2	yes	—
29	C₃₁×#556	—	2	2	no	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	1	yes	characteristic
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×#554	C₂²	1	1	yes	characteristic
37	C₃₁×#554	C₂²	1	1	yes	characteristic
38	C₃₁×#552	—	2	1	no	—
39	C₃₁×#552	—	2	1	no	—
40	D₄×Q₈×C₃₁	—	2	1	no	—
41	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#539	—	2	2	no	—
43	C₃₁×#536	—	2	1	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	1	yes	characteristic
48	C₃₁×#533	C₂²	1	2	yes	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	C₂²	1	2	yes	—
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₃₁×#520	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	2	yes	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
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×#500	C₂²	1	1	yes	characteristic
61	C₃₁×#499	C₂²	1	2	yes	—
62	C₃₁×#499	C₂²	1	2	yes	—
63	C₃₁×#498	C₂²	1	1	yes	characteristic
64	C₃₁×#490	C₂²	1	2	yes	—
65	C₃₁×#489	C₂²	1	2	yes	—
66	C₃₁×#489	C₂²	1	2	yes	—
67	C₃₁×#488	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	2	yes	—
72	C₃₁×#485	C₂²	1	2	yes	—
73	C₃₁×#485	C₂²	1	2	yes	—
74	C₃₁×#482	C₂²	1	2	yes	—
75	C₃₁×#482	C₂²	1	1	yes	characteristic
76	C₃₁×#482	C₂²	1	1	yes	characteristic
77	C₃₁×#482	C₂²	1	2	yes	—
78	C₃₁×#479	C₂²	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
89	C₃₁×#477	C₂²	1	2	yes	—
90	C₃₁×#477	C₂²	1	1	yes	characteristic
91	C₃₁×#476	C₂²	1	1	yes	characteristic
92	C₃₁×#476	C₂²	1	1	yes	characteristic
93	C₃₁×#476	C₂²	1	1	yes	characteristic
94	C₃₁×#476	C₂²	1	2	yes	—
95	C₃₁×#476	C₂²	1	1	yes	characteristic
96	C₃₁×#475	C₂²	1	2	yes	—
97	C₃₁×#474	C₂²	1	1	yes	characteristic
98	C₃₁×#474	C₂²	1	1	yes	characteristic
99	C₃₁×#474	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	2	yes	—
101	C₃₁×#464	C₂²	1	2	yes	—
102	C₃₁×#463	C₂²	1	2	yes	—
103	C₃₁×#463	C₂²	1	2	yes	—
104	C₃₁×#462	C₂²	1	1	yes	characteristic
105	C₃₁×#461	C₂²	1	1	yes	characteristic
106	C₃₁×#460	C₂²	1	1	yes	characteristic
107	C₃₁×#459	C₂²	1	1	yes	characteristic
108	C₃₁×#452	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	1	yes	characteristic
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	2	yes	—
114	C₃₁×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₃₁×#442	C₂²	1	2	yes	—
118	C₃₁×#441	C₂²	1	2	yes	—
119	C₃₁×#441	C₂²	1	2	yes	—
120	C₃₁×#440	C₂²	1	2	yes	—
121	C₃₁×#440	C₂²	1	2	yes	—
122	C₃₁×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
128	C₄×D₈×C₃₁	C₂²	1	2	yes	—
129	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
131	C₃₁×#432	C₂²	1	2	yes	—
132	C₃₁×#432	C₂²	1	1	yes	characteristic
133	C₃₁×#431	C₂²	1	2	yes	—
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
139	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
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	2	no	—
148	C₃₁×C₄⋊Q₈	—	2	1	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	2	yes	—
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×#127	C₂³	1	1	yes	characteristic
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#125	—	2	2	no	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	1	no	—
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	1	no	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#124	C₂³	1	2	yes	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	1	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	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	2	no	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	C₂³	1	1	yes	characteristic
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	2	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	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₃₁	D₄	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	C₃₁×#117	—	2	1	no	—
242	C₃₁×#117	—	2	1	no	—
243	C₃₁×#117	—	2	1	no	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	C₂³	1	2	yes	—
249	C₃₁×#117	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
257	C₂×C₄²×C₃₁	—	2	1	no	—
258	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
260	C₃₁×#107	C₂³	1	2	yes	—
261	C₃₁×#107	C₂³	1	1	yes	characteristic
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	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	1	yes	characteristic
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	2	yes	—
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	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	4	4	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	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	4	2	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×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	1	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	2	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	Q₁₆×C₃₁	—	2	4	no	—
351	SD₁₆×C₃₁	—	2	2	no	—
352	SD₁₆×C₃₁	—	2	2	no	—
353	SD₁₆×C₃₁	—	2	4	no	—
354	D₈×C₃₁	—	2	2	no	—
355	D₈×C₃₁	—	2	2	no	—
356	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
361	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	1	no	—
405	C₂²⋊C₄×C₃₁	—	2	1	no	—
406	C₂²⋊C₄×C₃₁	—	2	1	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₄²×C₃₁	—	2	2	no	—
420	C₄²×C₃₁	—	2	1	no	—
421	C₄²×C₃₁	—	2	2	no	—
422	C₄²×C₃₁	—	2	1	no	—
423	C₄²×C₃₁	—	2	2	no	—
424	C₄²×C₃₁	—	2	1	no	—
425	C₄²×C₃₁	—	2	2	no	—
426	C₄²×C₃₁	—	2	2	no	—
427	C₄²×C₃₁	—	2	2	no	—
428	C₄²×C₃₁	C₂×D₄	1	2	yes	—
429	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
434	C₄²×C₃₁	C₂⁴	1	2	yes	—
435	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
436	#61839	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	—	2	1	no	—
440	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₃₁	—	2	2	no	—
442	Q₈×C₃₁	—	2	2	no	—
443	Q₈×C₃₁	—	2	1	no	—
444	Q₈×C₃₁	—	2	2	no	—
445	Q₈×C₃₁	—	2	2	no	—
446	Q₈×C₃₁	—	4	2	no	—
447	Q₈×C₃₁	—	4	4	no	—
448	Q₈×C₃₁	—	4	2	no	—
449	Q₈×C₃₁	—	4	2	no	—
450	Q₈×C₃₁	—	8	2	no	—
451	Q₈×C₃₁	—	8	1	no	—
452	Q₈×C₃₁	—	8	1	no	—
453	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
454	D₄×C₃₁	—	2	4	no	—
455	D₄×C₃₁	—	2	1	no	—
456	D₄×C₃₁	—	2	1	no	—
457	D₄×C₃₁	—	2	1	no	—
458	D₄×C₃₁	—	2	1	no	—
459	D₄×C₃₁	—	2	1	no	—
460	D₄×C₃₁	—	4	2	no	—
461	D₄×C₃₁	—	4	2	no	—
462	D₄×C₃₁	—	4	2	no	—
463	D₄×C₃₁	—	8	1	no	—
464	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
465	C₂×C₄×C₃₁	—	2	4	no	—
466	C₂×C₄×C₃₁	—	2	1	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	4	2	no	—
479	C₂×C₄×C₃₁	—	4	1	no	—
480	C₂×C₄×C₃₁	—	4	2	no	—
481	C₂×C₄×C₃₁	—	4	4	no	—
482	C₂×C₄×C₃₁	—	4	2	no	—
483	C₂×C₄×C₃₁	—	4	2	no	—
484	C₂×C₄×C₃₁	—	4	2	no	—
485	C₂×C₄×C₃₁	—	8	2	no	—
486	C₂×C₄×C₃₁	—	8	2	no	—
487	C₂×C₄×C₃₁	—	8	1	no	—
488	C₂×C₄×C₃₁	—	8	2	no	—
489	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
499	C₈×C₃₁	—	2	1	no	—
500	C₈×C₃₁	—	2	1	no	—
501	C₈×C₃₁	—	2	1	no	—
502	C₈×C₃₁	—	2	1	no	—
503	C₈×C₃₁	—	2	2	no	—
504	C₈×C₃₁	—	2	2	no	—
505	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
506	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3390	C₂×C₃₁	1	2	yes	complemented
508	#3388	C₂×C₃₁	1	2	yes	complemented
509	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3371	C₂×C₃₁	1	2	yes	complemented
514	#3370	C₂×C₃₁	1	2	yes	complemented
515	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3240	C₂×C₃₁	1	2	yes	complemented
520	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3233	C₂×C₃₁	1	2	yes	complemented
522	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3111	C₂×C₃₁	1	2	yes	complemented
525	#3106	C₂×C₃₁	1	1	yes	characteristic
526	#3102	C₂×C₃₁	1	2	yes	complemented
527	#2984	C₂×C₃₁	1	1	yes	characteristic, complemented
528	C₂²×C₃₁	—	2	1	no	—
529	C₂²×C₃₁	—	2	1	no	—
530	C₂²×C₃₁	—	2	2	no	—
531	C₂²×C₃₁	—	2	1	no	—
532	C₂²×C₃₁	—	4	1	no	—
533	C₂²×C₃₁	—	4	1	no	—
534	C₂²×C₃₁	—	4	1	no	—
535	C₂²×C₃₁	—	4	1	no	—
536	C₂²×C₃₁	—	4	1	no	—
537	C₂²×C₃₁	—	4	1	no	—
538	C₂²×C₃₁	—	4	1	no	—
539	C₂²×C₃₁	—	4	1	no	—
540	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₃₁	—	2	2	no	—
542	C₄×C₃₁	—	2	1	no	—
543	C₄×C₃₁	—	2	2	no	—
544	C₄×C₃₁	—	2	1	no	—
545	C₄×C₃₁	—	2	1	no	—
546	C₄×C₃₁	—	2	2	no	—
547	C₄×C₃₁	—	2	1	no	—
548	C₄×C₃₁	—	2	2	no	—
549	C₄×C₃₁	—	2	2	no	—
550	C₄×C₃₁	—	4	2	no	—
551	C₄×C₃₁	—	4	2	no	—
552	C₄×C₃₁	—	4	1	no	—
553	C₄×C₃₁	—	4	2	no	—
554	C₄×C₃₁	—	4	1	no	—
555	C₄×C₃₁	—	4	1	no	—
556	C₄×C₃₁	—	4	2	no	—
557	C₄×C₃₁	—	4	1	no	—
558	C₄×C₃₁	#575	1	2	yes	—
559	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
560	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	#559	C₂²×C₃₁	1	2	yes	—
562	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
563	#557	C₂²×C₃₁	1	1	yes	characteristic
564	#557	C₂²×C₃₁	1	2	yes	—
565	#557	C₂²×C₃₁	1	2	yes	—
566	#556	—	2	2	no	—
567	#556	C₂²×C₃₁	1	1	yes	characteristic
568	#556	C₂²×C₃₁	1	1	yes	characteristic
569	#554	—	2	1	no	—
570	#554	—	2	2	no	—
571	#554	C₂²×C₃₁	1	1	yes	characteristic
572	#554	C₂²×C₃₁	1	2	yes	—
573	#554	C₂²×C₃₁	1	1	yes	characteristic
574	#554	C₂²×C₃₁	1	1	yes	characteristic
575	#552	—	2	1	no	—
576	#552	—	2	1	no	—
577	D₄×Q₈	—	2	1	no	—
578	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
579	#539	—	2	2	no	—
580	#536	—	2	1	no	—
581	#533	—	2	1	no	—
582	#533	—	2	2	no	—
583	#533	C₂²×C₃₁	1	1	yes	characteristic
584	#533	C₂²×C₃₁	1	1	yes	characteristic
585	#533	C₂²×C₃₁	1	2	yes	—
586	#532	C₂²×C₃₁	1	1	yes	characteristic
587	#529	C₂²×C₃₁	1	2	yes	—
588	#529	C₂²×C₃₁	1	2	yes	—
589	#520	—	2	1	no	—
590	C₄×#41	C₂²×C₃₁	1	2	yes	—
591	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
592	C₂×C₄×Q₈	—	2	1	no	—
593	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
594	#501	C₂²×C₃₁	1	2	yes	—
595	#501	C₂²×C₃₁	1	2	yes	—
596	#501	C₂²×C₃₁	1	2	yes	—
597	#500	C₂²×C₃₁	1	1	yes	characteristic
598	#499	C₂²×C₃₁	1	2	yes	—
599	#499	C₂²×C₃₁	1	2	yes	—
600	#498	C₂²×C₃₁	1	1	yes	characteristic
601	#490	C₂²×C₃₁	1	2	yes	—
602	#489	C₂²×C₃₁	1	2	yes	—
603	#489	C₂²×C₃₁	1	2	yes	—
604	#488	C₂²×C₃₁	1	2	yes	—
605	#488	C₂²×C₃₁	1	2	yes	—
606	#487	C₂²×C₃₁	1	1	yes	characteristic
607	#487	C₂²×C₃₁	1	1	yes	characteristic
608	#485	C₂²×C₃₁	1	2	yes	—
609	#485	C₂²×C₃₁	1	2	yes	—
610	#485	C₂²×C₃₁	1	2	yes	—
611	#482	C₂²×C₃₁	1	2	yes	—
612	#482	C₂²×C₃₁	1	1	yes	characteristic
613	#482	C₂²×C₃₁	1	1	yes	characteristic
614	#482	C₂²×C₃₁	1	2	yes	—
615	#479	C₂²×C₃₁	1	2	yes	—
616	#479	C₂²×C₃₁	1	2	yes	—
617	#479	C₂²×C₃₁	1	2	yes	—
618	#479	C₂²×C₃₁	1	2	yes	—
619	#479	C₂²×C₃₁	1	2	yes	—
620	#479	C₂²×C₃₁	1	2	yes	—
621	#478	C₂²×C₃₁	1	2	yes	—
622	#478	C₂²×C₃₁	1	2	yes	—
623	#478	C₂²×C₃₁	1	2	yes	—
624	#478	C₂²×C₃₁	1	2	yes	—
625	#477	C₂²×C₃₁	1	1	yes	characteristic
626	#477	C₂²×C₃₁	1	2	yes	—
627	#477	C₂²×C₃₁	1	1	yes	characteristic
628	#476	C₂²×C₃₁	1	1	yes	characteristic
629	#476	C₂²×C₃₁	1	1	yes	characteristic
630	#476	C₂²×C₃₁	1	1	yes	characteristic
631	#476	C₂²×C₃₁	1	2	yes	—
632	#476	C₂²×C₃₁	1	1	yes	characteristic
633	#475	C₂²×C₃₁	1	2	yes	—
634	#474	C₂²×C₃₁	1	1	yes	characteristic
635	#474	C₂²×C₃₁	1	1	yes	characteristic
636	#474	C₂²×C₃₁	1	2	yes	—
637	#464	C₂²×C₃₁	1	2	yes	—
638	#464	C₂²×C₃₁	1	2	yes	—
639	#463	C₂²×C₃₁	1	2	yes	—
640	#463	C₂²×C₃₁	1	2	yes	—
641	#462	C₂²×C₃₁	1	1	yes	characteristic
642	#461	C₂²×C₃₁	1	1	yes	characteristic
643	#460	C₂²×C₃₁	1	1	yes	characteristic
644	#459	C₂²×C₃₁	1	1	yes	characteristic
645	#452	C₂²×C₃₁	1	2	yes	—
646	#449	C₂²×C₃₁	1	1	yes	characteristic
647	#449	C₂²×C₃₁	1	1	yes	characteristic
648	#446	C₂²×C₃₁	1	1	yes	characteristic
649	#446	C₂²×C₃₁	1	1	yes	characteristic
650	#446	C₂²×C₃₁	1	2	yes	—
651	#446	C₂²×C₃₁	1	2	yes	—
652	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
653	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
654	#442	C₂²×C₃₁	1	2	yes	—
655	#441	C₂²×C₃₁	1	2	yes	—
656	#441	C₂²×C₃₁	1	2	yes	—
657	#440	C₂²×C₃₁	1	2	yes	—
658	#440	C₂²×C₃₁	1	2	yes	—
659	#440	C₂²×C₃₁	1	2	yes	—
660	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
661	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
662	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
663	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
665	C₄×D₈	C₂²×C₃₁	1	2	yes	—
666	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
668	#432	C₂²×C₃₁	1	2	yes	—
669	#432	C₂²×C₃₁	1	1	yes	characteristic
670	#431	C₂²×C₃₁	1	2	yes	—
671	#431	C₂²×C₃₁	1	1	yes	characteristic
672	C₂×C₃₁	—	4	1	no	—
673	C₂×C₃₁	—	4	2	no	—
674	C₂×C₃₁	—	8	1	no	—
675	C₂×C₃₁	—	8	1	no	—
676	C₂×C₃₁	#3486	1	1	yes	characteristic
677	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
678	C₂×C₃₁	#3584	1	1	yes	characteristic
679	C₂×#41	—	2	1	no	—
680	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
681	C₂²×Q₈	—	2	1	no	—
682	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
683	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
687	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
698	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
701	#127	C₂³×C₃₁	1	1	yes	characteristic
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	1	no	—
712	#125	C₂³×C₃₁	1	2	yes	—
713	#125	C₂³×C₃₁	1	2	yes	—
714	#125	C₂³×C₃₁	1	2	yes	—
715	#125	C₂³×C₃₁	1	2	yes	—
716	#125	C₂³×C₃₁	1	2	yes	—
717	#124	—	2	2	no	—
718	#124	—	2	1	no	—
719	#124	C₂³×C₃₁	1	2	yes	—
720	#124	C₂³×C₃₁	1	2	yes	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	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	1	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
744	#121	—	2	1	no	—
745	#121	C₂³×C₃₁	1	1	yes	characteristic
746	#121	C₂³×C₃₁	1	1	yes	characteristic
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	2	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
757	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
758	C₄×Q₈	D₄×C₃₁	1	2	yes	—
759	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
763	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
764	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
765	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
766	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₃₁	1	2	yes	—
779	C₄×D₄	C₂³×C₃₁	1	2	yes	—
780	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₃₁	1	2	yes	—
782	C₄×D₄	C₂³×C₃₁	1	2	yes	—
783	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
785	#117	—	2	1	no	—
786	#117	—	2	1	no	—
787	#117	—	2	1	no	—
788	#117	—	2	2	no	—
789	#117	—	2	1	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	C₂³×C₃₁	1	2	yes	—
793	#117	C₂³×C₃₁	1	1	yes	characteristic
794	C₂×C₄⋊C₄	—	2	1	no	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	—	2	1	no	—
798	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
799	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
800	C₂×C₄²	—	2	2	no	—
801	C₂×C₄²	—	2	1	no	—
802	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
803	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
804	#107	C₂³×C₃₁	1	2	yes	—
805	#107	C₂³×C₃₁	1	1	yes	characteristic
806	#107	C₂³×C₃₁	1	1	yes	characteristic
807	#107	C₂³×C₃₁	1	2	yes	—
808	#107	C₂³×C₃₁	1	2	yes	—
809	#107	C₂³×C₃₁	1	2	yes	—
810	#107	C₂³×C₃₁	1	2	yes	—
811	#106	C₂³×C₃₁	1	1	yes	characteristic
812	#106	C₂³×C₃₁	1	2	yes	—
813	#106	C₂³×C₃₁	1	2	yes	—
814	#106	C₂³×C₃₁	1	1	yes	characteristic
815	#106	C₂³×C₃₁	1	2	yes	—
816	#106	C₂³×C₃₁	1	2	yes	—
817	#106	C₂³×C₃₁	1	2	yes	—
818	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
821	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
822	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
825	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
826	#103	C₂³×C₃₁	1	1	yes	characteristic
827	#103	C₂³×C₃₁	1	2	yes	—
828	#103	C₂³×C₃₁	1	1	yes	characteristic
829	#103	C₂³×C₃₁	1	2	yes	—
830	#103	C₂³×C₃₁	1	2	yes	—
831	#103	C₂³×C₃₁	1	2	yes	—
832	#103	C₂³×C₃₁	1	2	yes	—
833	#103	C₂³×C₃₁	1	2	yes	—
834	#103	C₂³×C₃₁	1	2	yes	—
835	#102	C₂³×C₃₁	1	1	yes	characteristic
836	#102	C₂³×C₃₁	1	1	yes	characteristic
837	#102	C₂³×C₃₁	1	2	yes	—
838	#102	C₂³×C₃₁	1	1	yes	characteristic
839	#102	C₂³×C₃₁	1	1	yes	characteristic
840	#102	C₂³×C₃₁	1	2	yes	—
841	#102	C₂³×C₃₁	1	1	yes	characteristic
842	#102	C₂³×C₃₁	1	1	yes	characteristic
843	#102	C₂³×C₃₁	1	2	yes	—
844	#102	C₂³×C₃₁	1	2	yes	—
845	#102	C₂³×C₃₁	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
849	#97	C₂³×C₃₁	1	2	yes	—
850	#97	C₂³×C₃₁	1	2	yes	—
851	#97	C₂³×C₃₁	1	2	yes	—
852	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₃₁	1	2	yes	—
855	C₄×C₈	C₂³×C₃₁	1	2	yes	—
856	C₃₁	#61839	1	1	yes	characteristic, direct product factor, Sylow
857	#41	—	2	2	no	—
858	#41	—	2	2	no	—
859	#41	—	4	4	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	—	4	4	no	—
868	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
869	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
870	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
871	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
872	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
893	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
895	Q₁₆	—	2	4	no	—
896	SD₁₆	—	2	2	no	—
897	SD₁₆	—	2	2	no	—
898	SD₁₆	—	2	4	no	—
899	D₈	—	2	2	no	—
900	D₈	—	2	2	no	—
901	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
904	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
906	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
936	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
937	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
940	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
942	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	C₂×D₄×C₃₁	1	2	yes	—
974	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
975	C₄²	C₂×D₄×C₃₁	1	2	yes	—
976	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
977	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄²	C₂⁴×C₃₁	1	2	yes	—
979	C₄²	C₂⁴×C₃₁	1	2	yes	—
980	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
985	Q₈	—	2	2	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	2	2	no	—
989	Q₈	—	2	2	no	—
990	Q₈	—	4	2	no	—
991	Q₈	—	4	4	no	—
992	Q₈	—	4	2	no	—
993	Q₈	—	4	2	no	—
994	Q₈	—	8	2	no	—
995	Q₈	—	8	1	no	—
996	Q₈	—	8	1	no	—
997	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
998	D₄	—	2	4	no	—
999	D₄	—	2	1	no	—
1000	D₄	—	2	1	no	—
1001	D₄	—	2	1	no	—
1002	D₄	—	2	1	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	4	2	no	—
1005	D₄	—	4	2	no	—
1006	D₄	—	4	2	no	—
1007	D₄	—	8	1	no	—
1008	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	4	2	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	4	2	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	8	1	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1035	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1042	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	2	no	—
1048	C₈	—	2	2	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	1	no	—
1079	C₄	C₃₁×#575	1	2	yes	—
1080	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	2	no	—
1084	C₂	—	8	1	no	—
1085	C₂	—	8	1	no	—
1086	C₂	C₃₁×#3486	1	1	yes	characteristic
1087	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1088	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3106	C₂
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×#3507	C₂	semidirect
2. Q₈×#41×C₃₁	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3388	C₂	semidirect
5. C₃₁×#3385	C₂	semidirect
6. C₃₁×#3384	C₂	semidirect
7. C₃₁×#3381	C₂	semidirect
8. C₃₁×#3380	C₂	semidirect
9. C₃₁×#3371	C₂	semidirect
10. C₃₁×#3370	C₂	semidirect
11. C₃₁×#3369	C₂	semidirect
12. C₃₁×#3367	C₂	semidirect
13. C₃₁×#3364	C₂	semidirect
14. C₃₁×#3360	C₂	semidirect
15. C₃₁×#3240	C₂	semidirect
16. C₃₁×#3235	C₂	semidirect
17. C₃₁×#3233	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3116	C₂	semidirect
20. C₃₁×#3111	C₂	semidirect
22. C₃₁×#3102	C₂	semidirect
23. C₃₁×#2984	C₂	semidirect
436. #61839	C₃₁	direct (N × H)
505. #3507	C₂×C₃₁	semidirect
506. Q₈×#41	C₂×C₃₁	semidirect
507. #3390	C₂×C₃₁	semidirect
508. #3388	C₂×C₃₁	semidirect
509. #3385	C₂×C₃₁	semidirect
510. #3384	C₂×C₃₁	semidirect
511. #3381	C₂×C₃₁	semidirect
512. #3380	C₂×C₃₁	semidirect
513. #3371	C₂×C₃₁	semidirect
514. #3370	C₂×C₃₁	semidirect
515. #3369	C₂×C₃₁	semidirect
516. #3367	C₂×C₃₁	semidirect
517. #3364	C₂×C₃₁	semidirect
518. #3360	C₂×C₃₁	semidirect
519. #3240	C₂×C₃₁	semidirect
520. #3235	C₂×C₃₁	semidirect
521. #3233	C₂×C₃₁	semidirect
522. #3231	C₂×C₃₁	semidirect
523. #3116	C₂×C₃₁	semidirect
524. #3111	C₂×C₃₁	semidirect
526. #3102	C₂×C₃₁	semidirect
527. #2984	C₂×C₃₁	semidirect
856. C₃₁	#61839	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×#3507	2
Q₈×#41×C₃₁	2
C₃₁×#3390	2
C₃₁×#3388	2
C₃₁×#3385	2
C₃₁×#3384	2
C₃₁×#3381	2
C₃₁×#3380	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3369	2
C₃₁×#3367	2
C₃₁×#3364	2
C₃₁×#3360	2
C₃₁×#3240	2
C₃₁×#3235	2
C₃₁×#3233	2
C₃₁×#3231	2
C₃₁×#3116	2
C₃₁×#3111	2
C₃₁×#3106	2
C₃₁×#3102	2
C₃₁×#2984	2
#61839	31

Subgroups — C31×#61839 #21518598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61839 #21518598