Subgroups — C₃₁×#61878 #21518637

Order 7936.

1656 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3386	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#563	—	2	1	no	—
22	C₃₁×#559	C₂²	1	2	yes	—
23	Q₈²×C₃₁	C₂²	1	2	yes	—
24	C₃₁×#557	C₂²	1	2	yes	—
25	C₃₁×#557	C₂²	1	2	yes	—
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#554	—	2	2	no	—
29	C₃₁×#554	—	2	2	no	—
30	C₃₁×#554	C₂²	1	2	yes	—
31	C₃₁×#554	C₂²	1	2	yes	—
32	D₄×Q₈×C₃₁	—	2	1	no	—
33	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#544	—	2	1	no	—
35	C₃₁×#544	—	2	1	no	—
36	C₃₁×#544	C₂²	1	1	yes	characteristic
37	C₃₁×#544	C₂²	1	1	yes	characteristic
38	C₃₁×#542	—	2	2	no	—
39	C₃₁×#542	C₂²	1	2	yes	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#536	—	2	2	no	—
42	C₃₁×#533	—	2	1	no	—
43	C₃₁×#533	C₂²	1	1	yes	characteristic
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#532	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#125	—	2	1	no	—
47	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic
49	C₃₁×#520	C₂²	1	1	yes	characteristic
50	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	—
52	C₃₁×#501	C₂²	1	2	yes	—
53	C₃₁×#501	C₂²	1	2	yes	—
54	C₃₁×#501	C₂²	1	2	yes	—
55	C₃₁×#500	C₂²	1	2	yes	—
56	C₃₁×#498	C₂²	1	2	yes	—
57	C₃₁×#491	C₂²	1	2	yes	—
58	C₃₁×#490	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#489	C₂²	1	2	yes	—
61	C₃₁×#488	C₂²	1	2	yes	—
62	C₃₁×#488	C₂²	1	2	yes	—
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#484	C₂²	1	2	yes	—
65	C₃₁×#483	C₂²	1	2	yes	—
66	C₃₁×#482	C₂²	1	2	yes	—
67	C₃₁×#481	C₂²	1	2	yes	—
68	C₃₁×#480	C₂²	1	2	yes	—
69	C₃₁×#479	C₂²	1	2	yes	—
70	C₃₁×#479	C₂²	1	2	yes	—
71	C₃₁×#479	C₂²	1	2	yes	—
72	C₃₁×#479	C₂²	1	2	yes	—
73	C₃₁×#478	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#477	C₂²	1	1	yes	characteristic
78	C₃₁×#477	C₂²	1	2	yes	—
79	C₃₁×#477	C₂²	1	2	yes	—
80	C₃₁×#476	C₂²	1	2	yes	—
81	C₃₁×#476	C₂²	1	1	yes	characteristic
82	C₃₁×#476	C₂²	1	2	yes	—
83	C₃₁×#475	C₂²	1	1	yes	characteristic
84	C₃₁×#475	C₂²	1	2	yes	—
85	C₃₁×#475	C₂²	1	2	yes	—
86	C₃₁×#474	C₂²	1	2	yes	—
87	C₃₁×#474	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	—
90	C₃₁×#464	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#462	C₂²	1	1	yes	characteristic
94	C₃₁×#461	C₂²	1	1	yes	characteristic
95	C₃₁×#460	C₂²	1	1	yes	characteristic
96	C₃₁×#459	C₂²	1	1	yes	characteristic
97	C₃₁×#452	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#446	C₂²	1	2	yes	—
100	C₃₁×#446	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	2	yes	—
102	C₃₁×#446	C₂²	1	2	yes	—
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#441	C₂²	1	2	yes	—
106	C₃₁×#441	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	—
109	C₃₁×#440	C₂²	1	2	yes	—
110	C₃₁×#440	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
114	C₄×D₈×C₃₁	C₂²	1	2	yes	—
115	C₃₁×#433	C₂²	1	2	yes	—
116	C₃₁×#433	C₂²	1	2	yes	—
117	C₃₁×#432	C₂²	1	1	yes	characteristic
118	C₃₁×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₃₁	—	2	2	no	—
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×D₈×C₃₁	C₂³	1	2	yes	—
126	C₃₁×C₄⋊Q₈	—	2	2	no	—
127	C₃₁×C₄⋊Q₈	—	2	2	no	—
128	C₃₁×C₄⋊Q₈	—	2	1	no	—
129	C₃₁×C₄⋊Q₈	—	2	1	no	—
130	C₃₁×C₄⋊Q₈	—	2	2	no	—
131	C₃₁×C₄⋊Q₈	—	2	2	no	—
132	C₃₁×C₄⋊Q₈	—	2	2	no	—
133	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
134	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×#127	C₂³	1	1	yes	characteristic
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#125	—	2	1	no	—
148	C₃₁×#125	—	2	1	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	—	2	1	no	—
154	C₃₁×#125	—	2	1	no	—
155	C₃₁×#125	—	2	1	no	—
156	C₃₁×#125	D₄	1	1	yes	characteristic
157	C₃₁×#125	D₄	1	1	yes	characteristic
158	C₃₁×#125	C₂³	1	2	yes	—
159	C₃₁×#125	C₂³	1	2	yes	—
160	C₃₁×#125	C₂³	1	2	yes	—
161	C₃₁×#125	C₂³	1	2	yes	—
162	C₃₁×#124	—	2	2	no	—
163	C₃₁×#124	—	2	2	no	—
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	1	no	—
166	C₃₁×#124	C₂³	1	2	yes	—
167	C₃₁×#124	C₂³	1	2	yes	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	2	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	1	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	2	yes	—
188	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×#121	—	2	1	no	—
191	C₃₁×#121	C₂³	1	2	yes	—
192	C₄×Q₈×C₃₁	—	2	2	no	—
193	C₄×Q₈×C₃₁	—	2	2	no	—
194	C₄×Q₈×C₃₁	—	2	2	no	—
195	C₄×Q₈×C₃₁	—	2	1	no	—
196	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
197	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
198	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
199	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
200	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
202	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×D₄×C₃₁	—	2	1	no	—
206	C₄×D₄×C₃₁	—	2	1	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	C₂³	1	2	yes	—
212	C₄×D₄×C₃₁	C₂³	1	2	yes	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₃₁×#117	—	2	1	no	—
219	C₃₁×#117	—	2	1	no	—
220	C₃₁×#117	—	2	1	no	—
221	C₃₁×#117	—	2	2	no	—
222	C₃₁×#117	—	2	1	no	—
223	C₃₁×#117	C₂³	1	1	yes	characteristic
224	C₃₁×#117	C₂³	1	1	yes	characteristic
225	C₃₁×#117	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
227	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
231	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₃₁	—	2	1	no	—
235	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#107	C₂³	1	2	yes	—
237	C₃₁×#107	C₂³	1	2	yes	—
238	C₃₁×#107	C₂³	1	2	yes	—
239	C₃₁×#107	C₂³	1	2	yes	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#106	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	2	yes	—
275	C₃₁×#97	C₂³	1	2	yes	—
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	#41×C₃₁	—	2	2	no	—
281	#41×C₃₁	—	2	2	no	—
282	#41×C₃₁	—	8	2	no	—
283	C₂×Q₈×C₃₁	—	2	1	no	—
284	C₂×Q₈×C₃₁	—	2	2	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	—	8	4	no	—
290	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
291	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
292	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₃₁	—	2	1	no	—
295	C₂×D₄×C₃₁	—	2	2	no	—
296	C₂×D₄×C₃₁	—	2	1	no	—
297	C₂×D₄×C₃₁	—	2	1	no	—
298	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	—	2	1	no	—
301	C₂²×C₄×C₃₁	—	2	1	no	—
302	C₂²×C₄×C₃₁	—	2	1	no	—
303	C₂²×C₄×C₃₁	—	2	2	no	—
304	C₂²×C₄×C₃₁	—	2	1	no	—
305	C₂²×C₄×C₃₁	—	2	1	no	—
306	C₂²×C₄×C₃₁	—	2	2	no	—
307	C₂²×C₄×C₃₁	—	2	2	no	—
308	C₂²×C₄×C₃₁	—	2	2	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	Q₁₆×C₃₁	—	2	4	no	—
314	SD₁₆×C₃₁	—	2	4	no	—
315	SD₁₆×C₃₁	—	2	4	no	—
316	D₈×C₃₁	—	2	4	no	—
317	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
318	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
319	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
320	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	1	no	—
324	C₄⋊C₄×C₃₁	—	2	1	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	1	no	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₄⋊C₄×C₃₁	—	2	1	no	—
337	C₄⋊C₄×C₃₁	—	2	1	no	—
338	C₄⋊C₄×C₃₁	—	2	1	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	1	no	—
365	C₂²⋊C₄×C₃₁	—	2	1	no	—
366	C₂²⋊C₄×C₃₁	—	2	1	no	—
367	C₂²⋊C₄×C₃₁	—	2	2	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₄²×C₃₁	—	2	1	no	—
380	C₄²×C₃₁	—	2	1	no	—
381	C₄²×C₃₁	—	2	1	no	—
382	C₄²×C₃₁	—	2	2	no	—
383	C₄²×C₃₁	—	2	2	no	—
384	C₄²×C₃₁	—	2	2	no	—
385	C₄²×C₃₁	—	2	2	no	—
386	C₄²×C₃₁	—	2	2	no	—
387	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₃₁	C₂⁴	1	2	yes	—
390	C₄²×C₃₁	C₂⁴	1	2	yes	—
391	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
393	#61878	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂³×C₃₁	—	2	1	no	—
395	C₂³×C₃₁	—	2	2	no	—
396	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	Q₈×C₃₁	—	2	1	no	—
398	Q₈×C₃₁	—	2	2	no	—
399	Q₈×C₃₁	—	2	2	no	—
400	Q₈×C₃₁	—	4	2	no	—
401	Q₈×C₃₁	—	4	2	no	—
402	Q₈×C₃₁	—	4	2	no	—
403	Q₈×C₃₁	—	8	2	no	—
404	Q₈×C₃₁	—	8	2	no	—
405	Q₈×C₃₁	—	8	2	no	—
406	Q₈×C₃₁	—	8	2	no	—
407	Q₈×C₃₁	—	8	1	no	—
408	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
409	D₄×C₃₁	—	2	4	no	—
410	D₄×C₃₁	—	2	1	no	—
411	D₄×C₃₁	—	2	2	no	—
412	D₄×C₃₁	—	2	2	no	—
413	D₄×C₃₁	—	4	2	no	—
414	D₄×C₃₁	—	8	1	no	—
415	D₄×C₃₁	—	8	2	no	—
416	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
417	C₂×C₄×C₃₁	—	2	4	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	1	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	4	1	no	—
429	C₂×C₄×C₃₁	—	4	1	no	—
430	C₂×C₄×C₃₁	—	4	4	no	—
431	C₂×C₄×C₃₁	—	8	1	no	—
432	C₂×C₄×C₃₁	—	8	2	no	—
433	C₂×C₄×C₃₁	—	8	1	no	—
434	C₂×C₄×C₃₁	—	8	2	no	—
435	C₂×C₄×C₃₁	—	8	2	no	—
436	C₂×C₄×C₃₁	—	8	2	no	—
437	C₂×C₄×C₃₁	—	8	1	no	—
438	C₂×C₄×C₃₁	—	8	1	no	—
439	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
449	C₈×C₃₁	—	2	2	no	—
450	C₈×C₃₁	—	2	2	no	—
451	C₈×C₃₁	—	2	2	no	—
452	C₈×C₃₁	—	2	2	no	—
453	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#3387	C₂×C₃₁	1	2	yes	complemented
456	#3386	C₂×C₃₁	1	2	yes	complemented
457	#3385	C₂×C₃₁	1	2	yes	complemented
458	#3384	C₂×C₃₁	1	2	yes	complemented
459	#3377	C₂×C₃₁	1	2	yes	complemented
460	#3376	C₂×C₃₁	1	2	yes	complemented
461	#3371	C₂×C₃₁	1	2	yes	complemented
462	#3370	C₂×C₃₁	1	2	yes	complemented
463	#3244	C₂×C₃₁	1	2	yes	complemented
464	#3243	C₂×C₃₁	1	2	yes	complemented
465	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
466	#3234	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#3125	C₂×C₃₁	1	2	yes	complemented
468	#3124	C₂×C₃₁	1	2	yes	complemented
469	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#3115	C₂×C₃₁	1	1	yes	characteristic
471	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
472	C₂²×C₃₁	—	2	1	no	—
473	C₂²×C₃₁	—	2	1	no	—
474	C₂²×C₃₁	—	2	1	no	—
475	C₂²×C₃₁	—	2	2	no	—
476	C₂²×C₃₁	—	4	1	no	—
477	C₂²×C₃₁	—	4	1	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
482	C₄×C₃₁	—	2	1	no	—
483	C₄×C₃₁	—	2	1	no	—
484	C₄×C₃₁	—	2	2	no	—
485	C₄×C₃₁	—	2	2	no	—
486	C₄×C₃₁	—	2	1	no	—
487	C₄×C₃₁	—	2	1	no	—
488	C₄×C₃₁	—	2	2	no	—
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	2	1	no	—
491	C₄×C₃₁	—	2	2	no	—
492	C₄×C₃₁	—	4	2	no	—
493	C₄×C₃₁	—	4	2	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	1	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	1	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
500	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	#563	—	2	1	no	—
502	#563	—	2	1	no	—
503	#559	C₂²×C₃₁	1	2	yes	—
504	Q₈²	C₂²×C₃₁	1	2	yes	—
505	#557	C₂²×C₃₁	1	2	yes	—
506	#557	C₂²×C₃₁	1	2	yes	—
507	#556	—	2	1	no	—
508	#556	C₂²×C₃₁	1	2	yes	—
509	#554	—	2	2	no	—
510	#554	—	2	2	no	—
511	#554	C₂²×C₃₁	1	2	yes	—
512	#554	C₂²×C₃₁	1	2	yes	—
513	D₄×Q₈	—	2	1	no	—
514	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
515	#544	—	2	1	no	—
516	#544	—	2	1	no	—
517	#544	C₂²×C₃₁	1	1	yes	characteristic
518	#544	C₂²×C₃₁	1	1	yes	characteristic
519	#542	—	2	2	no	—
520	#542	C₂²×C₃₁	1	2	yes	—
521	#542	C₂²×C₃₁	1	2	yes	—
522	#536	—	2	2	no	—
523	#533	—	2	1	no	—
524	#533	C₂²×C₃₁	1	1	yes	characteristic
525	#533	C₂²×C₃₁	1	1	yes	characteristic
526	#532	C₂²×C₃₁	1	1	yes	characteristic
527	C₂×#125	—	2	1	no	—
528	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
529	#520	C₂²×C₃₁	1	1	yes	characteristic
530	#520	C₂²×C₃₁	1	1	yes	characteristic
531	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
532	#501	C₂²×C₃₁	1	2	yes	—
533	#501	C₂²×C₃₁	1	2	yes	—
534	#501	C₂²×C₃₁	1	2	yes	—
535	#501	C₂²×C₃₁	1	2	yes	—
536	#500	C₂²×C₃₁	1	2	yes	—
537	#498	C₂²×C₃₁	1	2	yes	—
538	#491	C₂²×C₃₁	1	2	yes	—
539	#490	C₂²×C₃₁	1	2	yes	—
540	#489	C₂²×C₃₁	1	2	yes	—
541	#489	C₂²×C₃₁	1	2	yes	—
542	#488	C₂²×C₃₁	1	2	yes	—
543	#488	C₂²×C₃₁	1	2	yes	—
544	#485	C₂²×C₃₁	1	2	yes	—
545	#484	C₂²×C₃₁	1	2	yes	—
546	#483	C₂²×C₃₁	1	2	yes	—
547	#482	C₂²×C₃₁	1	2	yes	—
548	#481	C₂²×C₃₁	1	2	yes	—
549	#480	C₂²×C₃₁	1	2	yes	—
550	#479	C₂²×C₃₁	1	2	yes	—
551	#479	C₂²×C₃₁	1	2	yes	—
552	#479	C₂²×C₃₁	1	2	yes	—
553	#479	C₂²×C₃₁	1	2	yes	—
554	#478	C₂²×C₃₁	1	2	yes	—
555	#478	C₂²×C₃₁	1	2	yes	—
556	#478	C₂²×C₃₁	1	2	yes	—
557	#478	C₂²×C₃₁	1	2	yes	—
558	#477	C₂²×C₃₁	1	1	yes	characteristic
559	#477	C₂²×C₃₁	1	2	yes	—
560	#477	C₂²×C₃₁	1	2	yes	—
561	#476	C₂²×C₃₁	1	2	yes	—
562	#476	C₂²×C₃₁	1	1	yes	characteristic
563	#476	C₂²×C₃₁	1	2	yes	—
564	#475	C₂²×C₃₁	1	1	yes	characteristic
565	#475	C₂²×C₃₁	1	2	yes	—
566	#475	C₂²×C₃₁	1	2	yes	—
567	#474	C₂²×C₃₁	1	2	yes	—
568	#474	C₂²×C₃₁	1	1	yes	characteristic
569	#474	C₂²×C₃₁	1	2	yes	—
570	#464	C₂²×C₃₁	1	2	yes	—
571	#464	C₂²×C₃₁	1	2	yes	—
572	#463	C₂²×C₃₁	1	2	yes	—
573	#463	C₂²×C₃₁	1	2	yes	—
574	#462	C₂²×C₃₁	1	1	yes	characteristic
575	#461	C₂²×C₃₁	1	1	yes	characteristic
576	#460	C₂²×C₃₁	1	1	yes	characteristic
577	#459	C₂²×C₃₁	1	1	yes	characteristic
578	#452	C₂²×C₃₁	1	2	yes	—
579	#449	C₂²×C₃₁	1	2	yes	—
580	#446	C₂²×C₃₁	1	2	yes	—
581	#446	C₂²×C₃₁	1	2	yes	—
582	#446	C₂²×C₃₁	1	2	yes	—
583	#446	C₂²×C₃₁	1	2	yes	—
584	#442	C₂²×C₃₁	1	2	yes	—
585	#442	C₂²×C₃₁	1	2	yes	—
586	#441	C₂²×C₃₁	1	2	yes	—
587	#441	C₂²×C₃₁	1	2	yes	—
588	#440	C₂²×C₃₁	1	2	yes	—
589	#440	C₂²×C₃₁	1	2	yes	—
590	#440	C₂²×C₃₁	1	2	yes	—
591	#440	C₂²×C₃₁	1	2	yes	—
592	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
593	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
594	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
595	C₄×D₈	C₂²×C₃₁	1	2	yes	—
596	#433	C₂²×C₃₁	1	2	yes	—
597	#433	C₂²×C₃₁	1	2	yes	—
598	#432	C₂²×C₃₁	1	1	yes	characteristic
599	#432	C₂²×C₃₁	1	1	yes	characteristic
600	C₂×C₃₁	—	4	1	no	—
601	C₂×C₃₁	—	4	2	no	—
602	C₂×C₃₁	—	8	2	no	—
603	C₂×C₃₁	#3486	1	1	yes	characteristic
604	C₂×C₃₁	#3585	1	1	yes	characteristic
605	C₂×C₃₁	#3586	1	1	yes	characteristic
606	C₂×#41	—	2	1	no	—
607	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
608	C₂²×Q₈	—	2	2	no	—
609	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
612	C₂×D₈	C₂³×C₃₁	1	2	yes	—
613	C₄⋊Q₈	—	2	2	no	—
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	—	2	1	no	—
616	C₄⋊Q₈	—	2	1	no	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	—	2	2	no	—
620	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
621	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
626	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
628	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
629	#127	C₂³×C₃₁	1	1	yes	characteristic
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#125	—	2	1	no	—
635	#125	—	2	1	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	1	no	—
641	#125	—	2	1	no	—
642	#125	—	2	1	no	—
643	#125	D₄×C₃₁	1	1	yes	characteristic
644	#125	D₄×C₃₁	1	1	yes	characteristic
645	#125	C₂³×C₃₁	1	2	yes	—
646	#125	C₂³×C₃₁	1	2	yes	—
647	#125	C₂³×C₃₁	1	2	yes	—
648	#125	C₂³×C₃₁	1	2	yes	—
649	#124	—	2	2	no	—
650	#124	—	2	2	no	—
651	#124	—	2	2	no	—
652	#124	—	2	1	no	—
653	#124	C₂³×C₃₁	1	2	yes	—
654	#124	C₂³×C₃₁	1	2	yes	—
655	#123	—	2	2	no	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	1	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
675	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
676	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
677	#121	—	2	1	no	—
678	#121	C₂³×C₃₁	1	2	yes	—
679	C₄×Q₈	—	2	2	no	—
680	C₄×Q₈	—	2	2	no	—
681	C₄×Q₈	—	2	2	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
684	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
685	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
686	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
687	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
688	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
689	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
690	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
691	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	1	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
699	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
700	C₄×D₄	C₂³×C₃₁	1	2	yes	—
701	C₄×D₄	C₂³×C₃₁	1	2	yes	—
702	C₄×D₄	C₂³×C₃₁	1	2	yes	—
703	C₄×D₄	C₂³×C₃₁	1	2	yes	—
704	C₄×D₄	C₂³×C₃₁	1	2	yes	—
705	#117	—	2	1	no	—
706	#117	—	2	1	no	—
707	#117	—	2	1	no	—
708	#117	—	2	2	no	—
709	#117	—	2	1	no	—
710	#117	C₂³×C₃₁	1	1	yes	characteristic
711	#117	C₂³×C₃₁	1	1	yes	characteristic
712	#117	C₂³×C₃₁	1	1	yes	characteristic
713	C₂×C₄⋊C₄	—	2	1	no	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	—	2	2	no	—
718	C₂×C₄⋊C₄	—	2	2	no	—
719	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×C₄²	—	2	1	no	—
722	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
723	#107	C₂³×C₃₁	1	2	yes	—
724	#107	C₂³×C₃₁	1	2	yes	—
725	#107	C₂³×C₃₁	1	2	yes	—
726	#107	C₂³×C₃₁	1	2	yes	—
727	#107	C₂³×C₃₁	1	2	yes	—
728	#107	C₂³×C₃₁	1	2	yes	—
729	#106	C₂³×C₃₁	1	2	yes	—
730	#106	C₂³×C₃₁	1	2	yes	—
731	#106	C₂³×C₃₁	1	2	yes	—
732	#106	C₂³×C₃₁	1	2	yes	—
733	#106	C₂³×C₃₁	1	2	yes	—
734	#106	C₂³×C₃₁	1	2	yes	—
735	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
740	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
741	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
742	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
743	#103	C₂³×C₃₁	1	2	yes	—
744	#103	C₂³×C₃₁	1	2	yes	—
745	#103	C₂³×C₃₁	1	2	yes	—
746	#103	C₂³×C₃₁	1	2	yes	—
747	#103	C₂³×C₃₁	1	2	yes	—
748	#103	C₂³×C₃₁	1	2	yes	—
749	#103	C₂³×C₃₁	1	2	yes	—
750	#103	C₂³×C₃₁	1	2	yes	—
751	#102	C₂³×C₃₁	1	2	yes	—
752	#102	C₂³×C₃₁	1	2	yes	—
753	#102	C₂³×C₃₁	1	2	yes	—
754	#102	C₂³×C₃₁	1	2	yes	—
755	#102	C₂³×C₃₁	1	2	yes	—
756	#102	C₂³×C₃₁	1	2	yes	—
757	#102	C₂³×C₃₁	1	2	yes	—
758	#102	C₂³×C₃₁	1	2	yes	—
759	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
761	#97	C₂³×C₃₁	1	2	yes	—
762	#97	C₂³×C₃₁	1	2	yes	—
763	#97	C₂³×C₃₁	1	2	yes	—
764	#97	C₂³×C₃₁	1	2	yes	—
765	C₄×C₈	C₂³×C₃₁	1	2	yes	—
766	C₄×C₈	C₂³×C₃₁	1	2	yes	—
767	C₃₁	#61878	1	1	yes	characteristic, direct product factor, Sylow
768	#41	—	2	2	no	—
769	#41	—	2	2	no	—
770	#41	—	8	2	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	8	4	no	—
778	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
779	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
787	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
801	Q₁₆	—	2	4	no	—
802	SD₁₆	—	2	4	no	—
803	SD₁₆	—	2	4	no	—
804	D₈	—	2	4	no	—
805	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
806	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
807	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
808	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
836	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
838	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
839	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
841	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
842	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
843	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
844	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
848	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
849	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
850	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	1	no	—
854	C₂²⋊C₄	—	2	1	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
866	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₄²	—	2	1	no	—
868	C₄²	—	2	1	no	—
869	C₄²	—	2	1	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₄²	C₂⁴×C₃₁	1	2	yes	—
878	C₄²	C₂⁴×C₃₁	1	2	yes	—
879	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
884	Q₈	—	2	1	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	2	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	4	2	no	—
890	Q₈	—	8	2	no	—
891	Q₈	—	8	2	no	—
892	Q₈	—	8	2	no	—
893	Q₈	—	8	2	no	—
894	Q₈	—	8	1	no	—
895	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
896	D₄	—	2	4	no	—
897	D₄	—	2	1	no	—
898	D₄	—	2	2	no	—
899	D₄	—	2	2	no	—
900	D₄	—	4	2	no	—
901	D₄	—	8	1	no	—
902	D₄	—	8	2	no	—
903	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	8	1	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	—	8	1	no	—
925	C₂×C₄	—	8	1	no	—
926	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
928	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
933	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
935	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
936	C₈	—	2	2	no	—
937	C₈	—	2	2	no	—
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
950	C₄	—	2	1	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
968	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
969	C₂	—	4	1	no	—
970	C₂	—	4	2	no	—
971	C₂	—	8	2	no	—
972	C₂	C₃₁×#3486	1	1	yes	characteristic
973	C₂	C₃₁×#3585	1	1	yes	characteristic
974	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×#3115	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3550	C₂	semidirect
2. C₃₁×#3504	C₂	semidirect
3. C₃₁×#3387	C₂	semidirect
4. C₃₁×#3386	C₂	semidirect
5. C₃₁×#3385	C₂	semidirect
6. C₃₁×#3384	C₂	semidirect
7. C₃₁×#3377	C₂	semidirect
8. C₃₁×#3376	C₂	semidirect
9. C₃₁×#3371	C₂	semidirect
10. C₃₁×#3370	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3243	C₂	semidirect
13. C₃₁×#3236	C₂	semidirect
14. C₃₁×#3234	C₂	semidirect
15. C₃₁×#3125	C₂	semidirect
16. C₃₁×#3124	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
19. C₃₁×#2987	C₂	semidirect
393. #61878	C₃₁	direct (N × H)
453. #3550	C₂×C₃₁	semidirect
454. #3504	C₂×C₃₁	semidirect
455. #3387	C₂×C₃₁	semidirect
456. #3386	C₂×C₃₁	semidirect
457. #3385	C₂×C₃₁	semidirect
458. #3384	C₂×C₃₁	semidirect
459. #3377	C₂×C₃₁	semidirect
460. #3376	C₂×C₃₁	semidirect
461. #3371	C₂×C₃₁	semidirect
462. #3370	C₂×C₃₁	semidirect
463. #3244	C₂×C₃₁	semidirect
464. #3243	C₂×C₃₁	semidirect
465. #3236	C₂×C₃₁	semidirect
466. #3234	C₂×C₃₁	semidirect
467. #3125	C₂×C₃₁	semidirect
468. #3124	C₂×C₃₁	semidirect
469. #3116	C₂×C₃₁	semidirect
471. #2987	C₂×C₃₁	semidirect
767. C₃₁	#61878	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×#3550	2
C₃₁×#3504	2
C₃₁×#3387	2
C₃₁×#3386	2
C₃₁×#3385	2
C₃₁×#3384	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3236	2
C₃₁×#3234	2
C₃₁×#3125	2
C₃₁×#3124	2
C₃₁×#3116	2
C₃₁×#3115	2
C₃₁×#2987	2
#61878	31

Subgroups — C31×#61878 #21518637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61878 #21518637