Subgroups — C₃₁×#61845 #21518604

Order 7936.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1080 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×#3389	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×#3383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3381	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×#3375	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic
20	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	C₂²	1	1	yes	characteristic
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#557	C₂²	1	1	yes	characteristic
28	C₃₁×#557	C₂²	1	2	yes	—
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#557	C₂²	1	1	yes	characteristic
31	C₃₁×#556	—	2	1	no	—
32	C₃₁×#556	—	2	1	no	—
33	C₃₁×#556	C₂²	1	2	yes	—
34	C₃₁×#554	—	2	1	no	—
35	C₃₁×#554	—	2	2	no	—
36	C₃₁×#554	C₂²	1	1	yes	characteristic
37	C₃₁×#554	C₂²	1	2	yes	—
38	C₃₁×#554	C₂²	1	2	yes	—
39	C₃₁×#552	—	2	2	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	2	no	—
45	C₃₁×#533	—	2	1	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×#491	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×#486	C₂²	1	1	yes	characteristic
70	C₃₁×#486	C₂²	1	1	yes	characteristic
71	C₃₁×#485	C₂²	1	2	yes	—
72	C₃₁×#485	C₂²	1	1	yes	characteristic
73	C₃₁×#485	C₂²	1	1	yes	characteristic
74	C₃₁×#485	C₂²	1	2	yes	—
75	C₃₁×#482	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	—
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×#478	C₂²	1	2	yes	—
83	C₃₁×#478	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	1	yes	characteristic
90	C₃₁×#477	C₂²	1	2	yes	—
91	C₃₁×#476	C₂²	1	2	yes	—
92	C₃₁×#475	C₂²	1	1	yes	characteristic
93	C₃₁×#475	C₂²	1	1	yes	characteristic
94	C₃₁×#475	C₂²	1	1	yes	characteristic
95	C₃₁×#475	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	1	yes	characteristic
109	C₃₁×#452	C₂²	1	1	yes	characteristic
110	C₃₁×#449	C₂²	1	2	yes	—
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×#442	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×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
125	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₃₁	C₂²	1	2	yes	—
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	1	yes	characteristic
140	C₂×Q₁₆×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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₃₁	C₂³	1	2	yes	—
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	1	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	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×#127	C₂³	1	1	yes	characteristic
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×#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	2	no	—
168	C₃₁×#125	—	2	1	no	—
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×#125	C₂³	1	2	yes	—
174	C₃₁×#124	—	2	1	no	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#124	C₂³	1	2	yes	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	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	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	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	1	yes	characteristic
200	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	C₂³	1	2	yes	—
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	1	no	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	2	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	1	no	—
213	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₃₁	D₄	1	2	yes	—
215	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₃₁×#117	—	2	1	no	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	C₂³	1	2	yes	—
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₂×C₄⋊C₄×C₃₁	—	2	2	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	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	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	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	1	yes	characteristic
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	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
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	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
334	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	2	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	Q₁₆×C₃₁	—	2	2	no	—
349	Q₁₆×C₃₁	—	2	2	no	—
350	SD₁₆×C₃₁	—	2	4	no	—
351	SD₁₆×C₃₁	—	2	2	no	—
352	SD₁₆×C₃₁	—	2	2	no	—
353	D₈×C₃₁	—	2	4	no	—
354	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
358	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
368	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	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	2	yes	—
396	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₂²⋊C₄×C₃₁	—	2	1	no	—
403	C₂²⋊C₄×C₃₁	—	2	1	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	1	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₄²×C₃₁	—	2	2	no	—
419	C₄²×C₃₁	—	2	1	no	—
420	C₄²×C₃₁	—	2	2	no	—
421	C₄²×C₃₁	—	2	1	no	—
422	C₄²×C₃₁	—	2	2	no	—
423	C₄²×C₃₁	—	2	1	no	—
424	C₄²×C₃₁	—	2	2	no	—
425	C₄²×C₃₁	—	2	2	no	—
426	C₄²×C₃₁	—	2	1	no	—
427	C₄²×C₃₁	—	2	1	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	2	yes	—
433	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
434	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
435	C₄²×C₃₁	C₂⁴	1	2	yes	—
436	#61845	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂³×C₃₁	—	2	1	no	—
438	C₂³×C₃₁	—	2	2	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	1	no	—
444	Q₈×C₃₁	—	2	1	no	—
445	Q₈×C₃₁	—	2	1	no	—
446	Q₈×C₃₁	—	2	1	no	—
447	Q₈×C₃₁	—	4	2	no	—
448	Q₈×C₃₁	—	4	4	no	—
449	Q₈×C₃₁	—	4	2	no	—
450	Q₈×C₃₁	—	4	2	no	—
451	Q₈×C₃₁	—	8	1	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	2	no	—
458	D₄×C₃₁	—	2	2	no	—
459	D₄×C₃₁	—	4	4	no	—
460	D₄×C₃₁	—	4	2	no	—
461	D₄×C₃₁	—	8	1	no	—
462	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
463	C₂×C₄×C₃₁	—	2	4	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	2	1	no	—
467	C₂×C₄×C₃₁	—	2	1	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	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	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	4	2	no	—
478	C₂×C₄×C₃₁	—	4	1	no	—
479	C₂×C₄×C₃₁	—	4	2	no	—
480	C₂×C₄×C₃₁	—	4	4	no	—
481	C₂×C₄×C₃₁	—	4	4	no	—
482	C₂×C₄×C₃₁	—	4	2	no	—
483	C₂×C₄×C₃₁	—	8	2	no	—
484	C₂×C₄×C₃₁	—	8	2	no	—
485	C₂×C₄×C₃₁	—	8	2	no	—
486	C₂×C₄×C₃₁	—	8	1	no	—
487	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	2	yes	—
492	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
497	C₈×C₃₁	—	2	2	no	—
498	C₈×C₃₁	—	2	2	no	—
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	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
504	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
505	#3389	C₂×C₃₁	1	2	yes	complemented
506	#3388	C₂×C₃₁	1	2	yes	complemented
507	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3377	C₂×C₃₁	1	2	yes	complemented
512	#3376	C₂×C₃₁	1	2	yes	complemented
513	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3240	C₂×C₃₁	1	2	yes	complemented
518	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3233	C₂×C₃₁	1	2	yes	complemented
520	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3115	C₂×C₃₁	1	1	yes	characteristic
522	#3111	C₂×C₃₁	1	2	yes	complemented
523	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3102	C₂×C₃₁	1	2	yes	complemented
525	#2984	C₂×C₃₁	1	1	yes	characteristic, complemented
526	C₂²×C₃₁	—	2	1	no	—
527	C₂²×C₃₁	—	2	1	no	—
528	C₂²×C₃₁	—	2	2	no	—
529	C₂²×C₃₁	—	2	1	no	—
530	C₂²×C₃₁	—	4	1	no	—
531	C₂²×C₃₁	—	4	1	no	—
532	C₂²×C₃₁	—	4	2	no	—
533	C₂²×C₃₁	—	4	2	no	—
534	C₂²×C₃₁	—	4	2	no	—
535	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
536	C₄×C₃₁	—	2	2	no	—
537	C₄×C₃₁	—	2	2	no	—
538	C₄×C₃₁	—	2	1	no	—
539	C₄×C₃₁	—	2	1	no	—
540	C₄×C₃₁	—	2	1	no	—
541	C₄×C₃₁	—	2	2	no	—
542	C₄×C₃₁	—	2	1	no	—
543	C₄×C₃₁	—	2	2	no	—
544	C₄×C₃₁	—	2	2	no	—
545	C₄×C₃₁	—	4	1	no	—
546	C₄×C₃₁	—	4	1	no	—
547	C₄×C₃₁	—	4	2	no	—
548	C₄×C₃₁	—	4	1	no	—
549	C₄×C₃₁	—	4	1	no	—
550	C₄×C₃₁	—	4	1	no	—
551	C₄×C₃₁	—	4	2	no	—
552	C₄×C₃₁	—	4	2	no	—
553	C₄×C₃₁	—	4	1	no	—
554	C₄×C₃₁	#575	1	2	yes	—
555	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
556	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
557	#559	C₂²×C₃₁	1	1	yes	characteristic
558	#559	C₂²×C₃₁	1	1	yes	characteristic
559	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
560	#557	C₂²×C₃₁	1	1	yes	characteristic
561	#557	C₂²×C₃₁	1	2	yes	—
562	#557	C₂²×C₃₁	1	1	yes	characteristic
563	#557	C₂²×C₃₁	1	1	yes	characteristic
564	#556	—	2	1	no	—
565	#556	—	2	1	no	—
566	#556	C₂²×C₃₁	1	2	yes	—
567	#554	—	2	1	no	—
568	#554	—	2	2	no	—
569	#554	C₂²×C₃₁	1	1	yes	characteristic
570	#554	C₂²×C₃₁	1	2	yes	—
571	#554	C₂²×C₃₁	1	2	yes	—
572	#552	—	2	2	no	—
573	D₄×Q₈	—	2	1	no	—
574	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
575	#539	—	2	2	no	—
576	#536	—	2	1	no	—
577	#533	—	2	2	no	—
578	#533	—	2	1	no	—
579	#533	C₂²×C₃₁	1	1	yes	characteristic
580	#533	C₂²×C₃₁	1	1	yes	characteristic
581	#533	C₂²×C₃₁	1	2	yes	—
582	#532	C₂²×C₃₁	1	1	yes	characteristic
583	#529	C₂²×C₃₁	1	2	yes	—
584	#529	C₂²×C₃₁	1	2	yes	—
585	#520	—	2	1	no	—
586	C₄×#41	C₂²×C₃₁	1	2	yes	—
587	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
588	C₂×C₄×Q₈	—	2	1	no	—
589	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
590	#501	C₂²×C₃₁	1	2	yes	—
591	#501	C₂²×C₃₁	1	2	yes	—
592	#501	C₂²×C₃₁	1	2	yes	—
593	#500	C₂²×C₃₁	1	1	yes	characteristic
594	#499	C₂²×C₃₁	1	2	yes	—
595	#499	C₂²×C₃₁	1	2	yes	—
596	#498	C₂²×C₃₁	1	1	yes	characteristic
597	#491	C₂²×C₃₁	1	2	yes	—
598	#489	C₂²×C₃₁	1	2	yes	—
599	#489	C₂²×C₃₁	1	2	yes	—
600	#488	C₂²×C₃₁	1	2	yes	—
601	#488	C₂²×C₃₁	1	2	yes	—
602	#486	C₂²×C₃₁	1	1	yes	characteristic
603	#486	C₂²×C₃₁	1	1	yes	characteristic
604	#485	C₂²×C₃₁	1	2	yes	—
605	#485	C₂²×C₃₁	1	1	yes	characteristic
606	#485	C₂²×C₃₁	1	1	yes	characteristic
607	#485	C₂²×C₃₁	1	2	yes	—
608	#482	C₂²×C₃₁	1	2	yes	—
609	#482	C₂²×C₃₁	1	2	yes	—
610	#482	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	#479	C₂²×C₃₁	1	2	yes	—
615	#478	C₂²×C₃₁	1	2	yes	—
616	#478	C₂²×C₃₁	1	2	yes	—
617	#478	C₂²×C₃₁	1	2	yes	—
618	#478	C₂²×C₃₁	1	2	yes	—
619	#478	C₂²×C₃₁	1	2	yes	—
620	#478	C₂²×C₃₁	1	2	yes	—
621	#477	C₂²×C₃₁	1	1	yes	characteristic
622	#477	C₂²×C₃₁	1	1	yes	characteristic
623	#477	C₂²×C₃₁	1	2	yes	—
624	#476	C₂²×C₃₁	1	2	yes	—
625	#475	C₂²×C₃₁	1	1	yes	characteristic
626	#475	C₂²×C₃₁	1	1	yes	characteristic
627	#475	C₂²×C₃₁	1	1	yes	characteristic
628	#475	C₂²×C₃₁	1	1	yes	characteristic
629	#475	C₂²×C₃₁	1	2	yes	—
630	#474	C₂²×C₃₁	1	1	yes	characteristic
631	#474	C₂²×C₃₁	1	1	yes	characteristic
632	#474	C₂²×C₃₁	1	2	yes	—
633	#464	C₂²×C₃₁	1	2	yes	—
634	#464	C₂²×C₃₁	1	2	yes	—
635	#463	C₂²×C₃₁	1	2	yes	—
636	#463	C₂²×C₃₁	1	2	yes	—
637	#462	C₂²×C₃₁	1	1	yes	characteristic
638	#461	C₂²×C₃₁	1	1	yes	characteristic
639	#460	C₂²×C₃₁	1	1	yes	characteristic
640	#459	C₂²×C₃₁	1	1	yes	characteristic
641	#452	C₂²×C₃₁	1	1	yes	characteristic
642	#452	C₂²×C₃₁	1	1	yes	characteristic
643	#449	C₂²×C₃₁	1	2	yes	—
644	#446	C₂²×C₃₁	1	1	yes	characteristic
645	#446	C₂²×C₃₁	1	1	yes	characteristic
646	#446	C₂²×C₃₁	1	2	yes	—
647	#446	C₂²×C₃₁	1	2	yes	—
648	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
649	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
650	#442	C₂²×C₃₁	1	2	yes	—
651	#442	C₂²×C₃₁	1	2	yes	—
652	#441	C₂²×C₃₁	1	2	yes	—
653	#440	C₂²×C₃₁	1	2	yes	—
654	#440	C₂²×C₃₁	1	2	yes	—
655	#440	C₂²×C₃₁	1	2	yes	—
656	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
657	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
658	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
659	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
660	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
661	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
662	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
663	C₄×D₈	C₂²×C₃₁	1	2	yes	—
664	#432	C₂²×C₃₁	1	2	yes	—
665	#432	C₂²×C₃₁	1	1	yes	characteristic
666	#431	C₂²×C₃₁	1	2	yes	—
667	#431	C₂²×C₃₁	1	1	yes	characteristic
668	C₂×C₃₁	—	4	1	no	—
669	C₂×C₃₁	—	4	2	no	—
670	C₂×C₃₁	—	8	2	no	—
671	C₂×C₃₁	#3486	1	1	yes	characteristic
672	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
673	C₂×C₃₁	#3584	1	1	yes	characteristic
674	C₂×#41	—	2	1	no	—
675	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
676	C₂²×Q₈	—	2	1	no	—
677	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
678	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×D₈	C₂³×C₃₁	1	2	yes	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	2	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	1	no	—
689	C₄⋊Q₈	—	2	2	no	—
690	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	#127	C₂³×C₃₁	1	1	yes	characteristic
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	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	2	no	—
707	#125	—	2	1	no	—
708	#125	C₂³×C₃₁	1	2	yes	—
709	#125	C₂³×C₃₁	1	2	yes	—
710	#125	C₂³×C₃₁	1	2	yes	—
711	#125	C₂³×C₃₁	1	2	yes	—
712	#125	C₂³×C₃₁	1	2	yes	—
713	#124	—	2	1	no	—
714	#124	—	2	1	no	—
715	#124	—	2	1	no	—
716	#124	C₂³×C₃₁	1	2	yes	—
717	#124	C₂³×C₃₁	1	2	yes	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
740	#121	—	2	1	no	—
741	#121	C₂³×C₃₁	1	2	yes	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	2	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
753	C₄×Q₈	D₄×C₃₁	1	2	yes	—
754	C₄×Q₈	D₄×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	1	yes	characteristic
758	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
759	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
765	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
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	1	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₃₁	1	2	yes	—
777	C₄×D₄	C₂³×C₃₁	1	2	yes	—
778	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₃₁	1	2	yes	—
780	C₄×D₄	C₂³×C₃₁	1	2	yes	—
781	C₄×D₄	C₂³×C₃₁	1	2	yes	—
782	#117	—	2	1	no	—
783	#117	—	2	2	no	—
784	#117	—	2	2	no	—
785	#117	—	2	1	no	—
786	#117	—	2	2	no	—
787	#117	—	2	2	no	—
788	#117	C₂³×C₃₁	1	2	yes	—
789	#117	C₂³×C₃₁	1	1	yes	characteristic
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	—	2	2	no	—
792	C₂×C₄⋊C₄	—	2	2	no	—
793	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
794	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
795	C₂×C₄²	—	2	2	no	—
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
798	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
799	#107	C₂³×C₃₁	1	2	yes	—
800	#107	C₂³×C₃₁	1	1	yes	characteristic
801	#107	C₂³×C₃₁	1	1	yes	characteristic
802	#107	C₂³×C₃₁	1	2	yes	—
803	#107	C₂³×C₃₁	1	2	yes	—
804	#107	C₂³×C₃₁	1	2	yes	—
805	#107	C₂³×C₃₁	1	2	yes	—
806	#106	C₂³×C₃₁	1	1	yes	characteristic
807	#106	C₂³×C₃₁	1	2	yes	—
808	#106	C₂³×C₃₁	1	1	yes	characteristic
809	#106	C₂³×C₃₁	1	2	yes	—
810	#106	C₂³×C₃₁	1	2	yes	—
811	#106	C₂³×C₃₁	1	2	yes	—
812	#106	C₂³×C₃₁	1	2	yes	—
813	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
816	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
817	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
820	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	1	yes	characteristic
822	#103	C₂³×C₃₁	1	1	yes	characteristic
823	#103	C₂³×C₃₁	1	1	yes	characteristic
824	#103	C₂³×C₃₁	1	2	yes	—
825	#103	C₂³×C₃₁	1	1	yes	characteristic
826	#103	C₂³×C₃₁	1	2	yes	—
827	#103	C₂³×C₃₁	1	1	yes	characteristic
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	#102	C₂³×C₃₁	1	1	yes	characteristic
833	#102	C₂³×C₃₁	1	2	yes	—
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	#102	C₂³×C₃₁	1	2	yes	—
839	#102	C₂³×C₃₁	1	2	yes	—
840	#102	C₂³×C₃₁	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
844	#97	C₂³×C₃₁	1	2	yes	—
845	#97	C₂³×C₃₁	1	2	yes	—
846	#97	C₂³×C₃₁	1	2	yes	—
847	C₄×C₈	C₂³×C₃₁	1	2	yes	—
848	C₄×C₈	C₂³×C₃₁	1	2	yes	—
849	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₃₁	#61845	1	1	yes	characteristic, direct product factor, Sylow
852	#41	—	2	2	no	—
853	#41	—	2	2	no	—
854	#41	—	4	4	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	4	2	no	—
862	C₂×Q₈	—	4	4	no	—
863	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
864	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
865	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
874	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
884	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
885	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
888	Q₁₆	—	2	2	no	—
889	Q₁₆	—	2	2	no	—
890	SD₁₆	—	2	4	no	—
891	SD₁₆	—	2	2	no	—
892	SD₁₆	—	2	2	no	—
893	D₈	—	2	4	no	—
894	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
898	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
930	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
931	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
933	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
934	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	C₂×D₄×C₃₁	1	2	yes	—
969	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
970	C₄²	C₂×D₄×C₃₁	1	2	yes	—
971	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
972	C₄²	C₂⁴×C₃₁	1	2	yes	—
973	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄²	C₂⁴×C₃₁	1	2	yes	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	2	no	—
978	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
979	Q₈	—	2	2	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	2	1	no	—
984	Q₈	—	2	1	no	—
985	Q₈	—	2	1	no	—
986	Q₈	—	4	2	no	—
987	Q₈	—	4	4	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	8	1	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	1	no	—
993	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
994	D₄	—	2	4	no	—
995	D₄	—	2	1	no	—
996	D₄	—	2	2	no	—
997	D₄	—	2	2	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	8	1	no	—
1001	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	1	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	1	no	—
1026	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1029	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1030	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1031	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1033	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1035	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1036	C₈	—	2	2	no	—
1037	C₈	—	2	2	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	C₃₁×#575	1	2	yes	—
1071	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1072	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1073	C₂	—	4	1	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	8	2	no	—
1076	C₂	C₃₁×#3486	1	1	yes	characteristic
1077	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1078	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×#3115	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×#3389	C₂	semidirect
4. C₃₁×#3388	C₂	semidirect
5. C₃₁×#3387	C₂	semidirect
6. C₃₁×#3386	C₂	semidirect
7. C₃₁×#3383	C₂	semidirect
8. C₃₁×#3381	C₂	semidirect
9. C₃₁×#3377	C₂	semidirect
10. C₃₁×#3376	C₂	semidirect
11. C₃₁×#3375	C₂	semidirect
12. C₃₁×#3373	C₂	semidirect
13. C₃₁×#3365	C₂	semidirect
14. C₃₁×#3361	C₂	semidirect
15. C₃₁×#3240	C₂	semidirect
16. C₃₁×#3237	C₂	semidirect
17. C₃₁×#3233	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
20. C₃₁×#3111	C₂	semidirect
21. C₃₁×#3107	C₂	semidirect
22. C₃₁×#3102	C₂	semidirect
23. C₃₁×#2984	C₂	semidirect
436. #61845	C₃₁	direct (N × H)
503. #3507	C₂×C₃₁	semidirect
504. Q₈×#41	C₂×C₃₁	semidirect
505. #3389	C₂×C₃₁	semidirect
506. #3388	C₂×C₃₁	semidirect
507. #3387	C₂×C₃₁	semidirect
508. #3386	C₂×C₃₁	semidirect
509. #3383	C₂×C₃₁	semidirect
510. #3381	C₂×C₃₁	semidirect
511. #3377	C₂×C₃₁	semidirect
512. #3376	C₂×C₃₁	semidirect
513. #3375	C₂×C₃₁	semidirect
514. #3373	C₂×C₃₁	semidirect
515. #3365	C₂×C₃₁	semidirect
516. #3361	C₂×C₃₁	semidirect
517. #3240	C₂×C₃₁	semidirect
518. #3237	C₂×C₃₁	semidirect
519. #3233	C₂×C₃₁	semidirect
520. #3228	C₂×C₃₁	semidirect
522. #3111	C₂×C₃₁	semidirect
523. #3107	C₂×C₃₁	semidirect
524. #3102	C₂×C₃₁	semidirect
525. #2984	C₂×C₃₁	semidirect
851. C₃₁	#61845	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×#3389	2
C₃₁×#3388	2
C₃₁×#3387	2
C₃₁×#3386	2
C₃₁×#3383	2
C₃₁×#3381	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3375	2
C₃₁×#3373	2
C₃₁×#3365	2
C₃₁×#3361	2
C₃₁×#3240	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3228	2
C₃₁×#3115	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#3102	2
C₃₁×#2984	2
#61845	31

Subgroups — C31×#61845 #21518604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61845 #21518604