Subgroups — C₃₁×#61866 #21518625

Order 7936.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3383	C₂	1	2	yes	maximal, complemented
7	Q₈×Q₁₆×C₃₁	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×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3243	C₂	1	2	yes	maximal
16	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3121	C₂	1	2	yes	maximal
21	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	Q₈²×C₃₁	—	2	1	no	—
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
27	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#557	—	2	1	no	—
30	C₃₁×#557	—	2	2	no	—
31	C₃₁×#557	C₂²	1	1	yes	characteristic
32	C₃₁×#557	C₂²	1	1	yes	characteristic
33	C₃₁×#557	C₂²	1	2	yes	—
34	C₃₁×#557	C₂²	1	1	yes	characteristic
35	C₃₁×#557	C₂²	1	2	yes	—
36	C₃₁×#557	C₂²	1	2	yes	—
37	C₃₁×#556	—	2	1	no	—
38	C₃₁×#556	C₂²	1	1	yes	characteristic
39	C₃₁×#556	C₂²	1	2	yes	—
40	C₃₁×#554	C₂²	1	1	yes	characteristic
41	C₃₁×#552	—	2	1	no	—
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	—	2	2	no	—
44	C₃₁×#544	C₂²	1	2	yes	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#541	—	2	1	no	—
47	C₃₁×#541	—	2	2	no	—
48	C₃₁×#541	C₂²	1	2	yes	—
49	C₃₁×#533	—	2	1	no	—
50	C₃₁×#533	—	2	1	no	—
51	C₃₁×#533	C₂²	1	1	yes	characteristic
52	C₃₁×#533	C₂²	1	1	yes	characteristic
53	C₃₁×#533	C₂²	1	1	yes	characteristic
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#519	C₂²	1	2	yes	—
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×#500	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×#488	C₂²	1	2	yes	—
67	C₃₁×#488	C₂²	1	2	yes	—
68	C₃₁×#487	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×#484	C₂²	1	2	yes	—
75	C₃₁×#483	C₂²	1	1	yes	characteristic
76	C₃₁×#482	C₂²	1	2	yes	—
77	C₃₁×#480	C₂²	1	1	yes	characteristic
78	C₃₁×#479	C₂²	1	1	yes	characteristic
79	C₃₁×#479	C₂²	1	1	yes	characteristic
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×#479	C₂²	1	2	yes	—
85	C₃₁×#479	C₂²	1	2	yes	—
86	C₃₁×#479	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	1	yes	characteristic
91	C₃₁×#477	C₂²	1	2	yes	—
92	C₃₁×#477	C₂²	1	2	yes	—
93	C₃₁×#477	C₂²	1	2	yes	—
94	C₃₁×#476	C₂²	1	1	yes	characteristic
95	C₃₁×#475	C₂²	1	2	yes	—
96	C₃₁×#475	C₂²	1	1	yes	characteristic
97	C₃₁×#475	C₂²	1	2	yes	—
98	C₃₁×#474	C₂²	1	1	yes	characteristic
99	C₃₁×#474	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#464	C₂²	1	1	yes	characteristic
102	C₃₁×#464	C₂²	1	2	yes	—
103	C₃₁×#464	C₂²	1	2	yes	—
104	C₃₁×#462	C₂²	1	1	yes	characteristic
105	C₃₁×#462	C₂²	1	1	yes	characteristic
106	C₃₁×#462	C₂²	1	2	yes	—
107	C₃₁×#462	C₂²	1	2	yes	—
108	C₃₁×#451	C₂²	1	2	yes	—
109	C₃₁×#451	C₂²	1	1	yes	characteristic
110	C₃₁×#448	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	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
117	C₃₁×#441	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	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
122	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
126	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
127	C₄×Q₁₆×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×SD₁₆×C₃₁	C₂²	1	2	yes	—
131	C₃₁×#433	C₂²	1	2	yes	—
132	C₃₁×#433	C₂²	1	2	yes	—
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊Q₈	—	2	1	no	—
143	C₃₁×C₄⋊Q₈	—	2	1	no	—
144	C₃₁×C₄⋊Q₈	—	2	2	no	—
145	C₃₁×C₄⋊Q₈	—	2	2	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	2	no	—
150	C₃₁×C₄⋊Q₈	—	2	1	no	—
151	C₃₁×C₄⋊Q₈	—	2	2	no	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	2	no	—
183	C₃₁×#125	—	2	2	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	D₄	1	2	yes	—
186	C₃₁×#125	C₂³	1	2	yes	—
187	C₃₁×#125	C₂³	1	2	yes	—
188	C₃₁×#125	C₂³	1	2	yes	—
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#125	C₂³	1	2	yes	—
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	C₂³	1	1	yes	characteristic
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#123	—	2	1	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	2	no	—
217	C₄×Q₈×C₃₁	—	2	2	no	—
218	C₄×Q₈×C₃₁	—	2	2	no	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₃₁	—	2	1	no	—
259	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
260	C₃₁×#107	C₂³	1	2	yes	—
261	C₃₁×#107	C₂³	1	2	yes	—
262	C₃₁×#107	C₂³	1	2	yes	—
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	1	yes	characteristic
266	C₃₁×#107	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	2	yes	—
283	C₃₁×#103	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
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	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂×Q₈×C₃₁	—	2	2	no	—
313	C₂×Q₈×C₃₁	—	2	2	no	—
314	C₂×Q₈×C₃₁	—	2	1	no	—
315	C₂×Q₈×C₃₁	—	2	1	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₃₁	—	2	1	no	—
331	C₂²×C₄×C₃₁	—	2	1	no	—
332	C₂²×C₄×C₃₁	—	2	1	no	—
333	C₂²×C₄×C₃₁	—	2	2	no	—
334	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	Q₁₆×C₃₁	—	2	4	no	—
338	Q₁₆×C₃₁	—	2	2	no	—
339	Q₁₆×C₃₁	—	2	4	no	—
340	Q₁₆×C₃₁	—	2	2	no	—
341	SD₁₆×C₃₁	—	2	2	no	—
342	SD₁₆×C₃₁	—	2	2	no	—
343	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
345	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
348	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	1	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
386	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	1	no	—
404	C₂²⋊C₄×C₃₁	—	2	1	no	—
405	C₂²⋊C₄×C₃₁	—	2	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	C₂×D₄	1	2	yes	—
412	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₄²×C₃₁	—	2	1	no	—
414	C₄²×C₃₁	—	2	1	no	—
415	C₄²×C₃₁	—	2	1	no	—
416	C₄²×C₃₁	—	2	1	no	—
417	C₄²×C₃₁	—	2	2	no	—
418	C₄²×C₃₁	—	2	1	no	—
419	C₄²×C₃₁	—	2	2	no	—
420	C₄²×C₃₁	—	2	2	no	—
421	C₄²×C₃₁	—	2	2	no	—
422	C₄²×C₃₁	—	2	2	no	—
423	C₄²×C₃₁	—	2	2	no	—
424	C₄²×C₃₁	—	2	2	no	—
425	C₄²×C₃₁	—	2	2	no	—
426	C₄²×C₃₁	—	2	2	no	—
427	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
428	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
429	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
431	C₄²×C₃₁	C₂⁴	1	2	yes	—
432	C₄²×C₃₁	C₂⁴	1	2	yes	—
433	#61866	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂³×C₃₁	—	2	1	no	—
435	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
436	Q₈×C₃₁	—	2	4	no	—
437	Q₈×C₃₁	—	2	2	no	—
438	Q₈×C₃₁	—	2	2	no	—
439	Q₈×C₃₁	—	2	1	no	—
440	Q₈×C₃₁	—	2	1	no	—
441	Q₈×C₃₁	—	2	2	no	—
442	Q₈×C₃₁	—	2	1	no	—
443	Q₈×C₃₁	—	2	2	no	—
444	Q₈×C₃₁	—	2	1	no	—
445	Q₈×C₃₁	—	4	2	no	—
446	Q₈×C₃₁	—	4	2	no	—
447	Q₈×C₃₁	—	8	1	no	—
448	Q₈×C₃₁	—	8	1	no	—
449	Q₈×C₃₁	—	8	2	no	—
450	Q₈×C₃₁	—	8	2	no	—
451	Q₈×C₃₁	—	8	2	no	—
452	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
453	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
454	D₄×C₃₁	—	2	1	no	—
455	D₄×C₃₁	—	2	1	no	—
456	D₄×C₃₁	—	8	1	no	—
457	C₂×C₄×C₃₁	—	2	4	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	2	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	2	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	2	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	4	1	no	—
473	C₂×C₄×C₃₁	—	4	2	no	—
474	C₂×C₄×C₃₁	—	8	2	no	—
475	C₂×C₄×C₃₁	—	8	1	no	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
486	C₈×C₃₁	—	2	1	no	—
487	C₈×C₃₁	—	2	1	no	—
488	C₈×C₃₁	—	2	1	no	—
489	C₈×C₃₁	—	2	2	no	—
490	C₈×C₃₁	—	2	1	no	—
491	C₈×C₃₁	—	2	2	no	—
492	#3555	C₂×C₃₁	1	1	yes	characteristic
493	#3502	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#3390	C₂×C₃₁	1	2	yes	complemented
495	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#3383	C₂×C₃₁	1	2	yes	complemented
498	Q₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3377	C₂×C₃₁	1	2	yes	complemented
501	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#3364	C₂×C₃₁	1	2	yes	complemented
505	#3363	C₂×C₃₁	1	1	yes	characteristic, complemented
506	#3243	C₂×C₃₁	1	2	yes	—
507	#3242	C₂×C₃₁	1	2	yes	complemented
508	#3233	C₂×C₃₁	1	1	yes	characteristic
509	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3127	C₂×C₃₁	1	2	yes	complemented
511	#3121	C₂×C₃₁	1	2	yes	—
512	#3108	C₂×C₃₁	1	1	yes	characteristic
513	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
515	C₂²×C₃₁	—	2	1	no	—
516	C₂²×C₃₁	—	2	1	no	—
517	C₂²×C₃₁	—	2	1	no	—
518	C₂²×C₃₁	—	4	1	no	—
519	C₂²×C₃₁	—	4	1	no	—
520	C₂²×C₃₁	—	4	1	no	—
521	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₃₁	—	2	1	no	—
523	C₄×C₃₁	—	2	1	no	—
524	C₄×C₃₁	—	2	2	no	—
525	C₄×C₃₁	—	2	2	no	—
526	C₄×C₃₁	—	2	2	no	—
527	C₄×C₃₁	—	2	2	no	—
528	C₄×C₃₁	—	2	1	no	—
529	C₄×C₃₁	—	2	1	no	—
530	C₄×C₃₁	—	2	2	no	—
531	C₄×C₃₁	—	2	2	no	—
532	C₄×C₃₁	—	4	2	no	—
533	C₄×C₃₁	—	4	1	no	—
534	C₄×C₃₁	—	4	1	no	—
535	C₄×C₃₁	—	4	1	no	—
536	C₄×C₃₁	—	4	2	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₄×C₃₁	—	4	1	no	—
539	C₄×C₃₁	—	4	1	no	—
540	C₄×C₃₁	—	4	2	no	—
541	C₄×C₃₁	#578	1	2	yes	—
542	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
544	#563	—	2	2	no	—
545	Q₈²	—	2	1	no	—
546	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
547	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
548	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
549	#557	—	2	1	no	—
550	#557	—	2	2	no	—
551	#557	C₂²×C₃₁	1	1	yes	characteristic
552	#557	C₂²×C₃₁	1	1	yes	characteristic
553	#557	C₂²×C₃₁	1	2	yes	—
554	#557	C₂²×C₃₁	1	1	yes	characteristic
555	#557	C₂²×C₃₁	1	2	yes	—
556	#557	C₂²×C₃₁	1	2	yes	—
557	#556	—	2	1	no	—
558	#556	C₂²×C₃₁	1	1	yes	characteristic
559	#556	C₂²×C₃₁	1	2	yes	—
560	#554	C₂²×C₃₁	1	1	yes	characteristic
561	#552	—	2	1	no	—
562	#544	—	2	1	no	—
563	#544	—	2	2	no	—
564	#544	C₂²×C₃₁	1	2	yes	—
565	#542	C₂²×C₃₁	1	2	yes	—
566	#541	—	2	1	no	—
567	#541	—	2	2	no	—
568	#541	C₂²×C₃₁	1	2	yes	—
569	#533	—	2	1	no	—
570	#533	—	2	1	no	—
571	#533	C₂²×C₃₁	1	1	yes	characteristic
572	#533	C₂²×C₃₁	1	1	yes	characteristic
573	#533	C₂²×C₃₁	1	1	yes	characteristic
574	#529	C₂²×C₃₁	1	1	yes	characteristic
575	#519	C₂²×C₃₁	1	2	yes	—
576	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
577	#501	C₂²×C₃₁	1	2	yes	—
578	#501	C₂²×C₃₁	1	2	yes	—
579	#500	C₂²×C₃₁	1	2	yes	—
580	#500	C₂²×C₃₁	1	1	yes	characteristic
581	#499	C₂²×C₃₁	1	2	yes	—
582	#499	C₂²×C₃₁	1	2	yes	—
583	#498	C₂²×C₃₁	1	1	yes	characteristic
584	#491	C₂²×C₃₁	1	2	yes	—
585	#489	C₂²×C₃₁	1	2	yes	—
586	#488	C₂²×C₃₁	1	2	yes	—
587	#488	C₂²×C₃₁	1	2	yes	—
588	#487	C₂²×C₃₁	1	2	yes	—
589	#487	C₂²×C₃₁	1	1	yes	characteristic
590	#487	C₂²×C₃₁	1	1	yes	characteristic
591	#485	C₂²×C₃₁	1	2	yes	—
592	#485	C₂²×C₃₁	1	2	yes	—
593	#485	C₂²×C₃₁	1	2	yes	—
594	#484	C₂²×C₃₁	1	2	yes	—
595	#483	C₂²×C₃₁	1	1	yes	characteristic
596	#482	C₂²×C₃₁	1	2	yes	—
597	#480	C₂²×C₃₁	1	1	yes	characteristic
598	#479	C₂²×C₃₁	1	1	yes	characteristic
599	#479	C₂²×C₃₁	1	1	yes	characteristic
600	#479	C₂²×C₃₁	1	2	yes	—
601	#479	C₂²×C₃₁	1	2	yes	—
602	#479	C₂²×C₃₁	1	2	yes	—
603	#479	C₂²×C₃₁	1	2	yes	—
604	#479	C₂²×C₃₁	1	2	yes	—
605	#479	C₂²×C₃₁	1	2	yes	—
606	#479	C₂²×C₃₁	1	2	yes	—
607	#478	C₂²×C₃₁	1	2	yes	—
608	#477	C₂²×C₃₁	1	1	yes	characteristic
609	#477	C₂²×C₃₁	1	1	yes	characteristic
610	#477	C₂²×C₃₁	1	1	yes	characteristic
611	#477	C₂²×C₃₁	1	2	yes	—
612	#477	C₂²×C₃₁	1	2	yes	—
613	#477	C₂²×C₃₁	1	2	yes	—
614	#476	C₂²×C₃₁	1	1	yes	characteristic
615	#475	C₂²×C₃₁	1	2	yes	—
616	#475	C₂²×C₃₁	1	1	yes	characteristic
617	#475	C₂²×C₃₁	1	2	yes	—
618	#474	C₂²×C₃₁	1	1	yes	characteristic
619	#474	C₂²×C₃₁	1	2	yes	—
620	#464	C₂²×C₃₁	1	1	yes	characteristic
621	#464	C₂²×C₃₁	1	1	yes	characteristic
622	#464	C₂²×C₃₁	1	2	yes	—
623	#464	C₂²×C₃₁	1	2	yes	—
624	#462	C₂²×C₃₁	1	1	yes	characteristic
625	#462	C₂²×C₃₁	1	1	yes	characteristic
626	#462	C₂²×C₃₁	1	2	yes	—
627	#462	C₂²×C₃₁	1	2	yes	—
628	#451	C₂²×C₃₁	1	2	yes	—
629	#451	C₂²×C₃₁	1	1	yes	characteristic
630	#448	C₂²×C₃₁	1	1	yes	characteristic
631	#446	C₂²×C₃₁	1	1	yes	characteristic
632	#446	C₂²×C₃₁	1	1	yes	characteristic
633	#446	C₂²×C₃₁	1	2	yes	—
634	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
635	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
636	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
637	#441	C₂²×C₃₁	1	2	yes	—
638	#441	C₂²×C₃₁	1	2	yes	—
639	#441	C₂²×C₃₁	1	2	yes	—
640	#440	C₂²×C₃₁	1	2	yes	—
641	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
642	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
643	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
644	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
645	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
646	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
647	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
648	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
649	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
650	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
651	#433	C₂²×C₃₁	1	2	yes	—
652	#433	C₂²×C₃₁	1	2	yes	—
653	#431	C₂²×C₃₁	1	1	yes	characteristic
654	#431	C₂²×C₃₁	1	1	yes	characteristic
655	C₂×C₃₁	—	4	1	no	—
656	C₂×C₃₁	—	8	1	no	—
657	C₂×C₃₁	#3486	1	1	yes	characteristic
658	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
659	C₂×C₃₁	#3584	1	1	yes	characteristic
660	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
662	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
663	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
667	C₄⋊Q₈	—	2	1	no	—
668	C₄⋊Q₈	—	2	1	no	—
669	C₄⋊Q₈	—	2	2	no	—
670	C₄⋊Q₈	—	2	2	no	—
671	C₄⋊Q₈	—	2	2	no	—
672	C₄⋊Q₈	—	2	1	no	—
673	C₄⋊Q₈	—	2	1	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	1	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	2	no	—
678	C₄⋊Q₈	—	2	2	no	—
679	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
680	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
681	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
682	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
683	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
684	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
685	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	1	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	1	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	1	no	—
710	#125	D₄×C₃₁	1	2	yes	—
711	#125	C₂³×C₃₁	1	1	yes	characteristic
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	#124	—	2	2	no	—
717	#124	C₂³×C₃₁	1	1	yes	characteristic
718	#124	C₂³×C₃₁	1	2	yes	—
719	#123	—	2	1	no	—
720	#123	—	2	2	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
732	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
733	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
735	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
736	#121	C₂³×C₃₁	1	1	yes	characteristic
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	—	2	2	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	1	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
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	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	2	yes	—
768	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₃₁	1	2	yes	—
772	#117	—	2	1	no	—
773	#117	—	2	2	no	—
774	#117	—	2	1	no	—
775	#117	—	2	2	no	—
776	#117	—	2	2	no	—
777	#117	—	2	1	no	—
778	#117	C₂³×C₃₁	1	2	yes	—
779	#117	C₂³×C₃₁	1	2	yes	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×C₄²	—	2	1	no	—
784	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
785	#107	C₂³×C₃₁	1	2	yes	—
786	#107	C₂³×C₃₁	1	2	yes	—
787	#107	C₂³×C₃₁	1	2	yes	—
788	#107	C₂³×C₃₁	1	2	yes	—
789	#107	C₂³×C₃₁	1	2	yes	—
790	#107	C₂³×C₃₁	1	1	yes	characteristic
791	#107	C₂³×C₃₁	1	1	yes	characteristic
792	#107	C₂³×C₃₁	1	2	yes	—
793	#106	C₂³×C₃₁	1	1	yes	characteristic
794	#106	C₂³×C₃₁	1	2	yes	—
795	#106	C₂³×C₃₁	1	1	yes	characteristic
796	#106	C₂³×C₃₁	1	2	yes	—
797	#106	C₂³×C₃₁	1	2	yes	—
798	#106	C₂³×C₃₁	1	2	yes	—
799	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
804	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
805	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
806	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
807	#103	C₂³×C₃₁	1	2	yes	—
808	#103	C₂³×C₃₁	1	1	yes	characteristic
809	#103	C₂³×C₃₁	1	1	yes	characteristic
810	#103	C₂³×C₃₁	1	1	yes	characteristic
811	#103	C₂³×C₃₁	1	2	yes	—
812	#103	C₂³×C₃₁	1	1	yes	characteristic
813	#103	C₂³×C₃₁	1	2	yes	—
814	#103	C₂³×C₃₁	1	2	yes	—
815	#103	C₂³×C₃₁	1	2	yes	—
816	#103	C₂³×C₃₁	1	2	yes	—
817	#103	C₂³×C₃₁	1	2	yes	—
818	#103	C₂³×C₃₁	1	1	yes	characteristic
819	#103	C₂³×C₃₁	1	1	yes	characteristic
820	#103	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	2	yes	—
822	#103	C₂³×C₃₁	1	2	yes	—
823	#102	C₂³×C₃₁	1	1	yes	characteristic
824	#102	C₂³×C₃₁	1	2	yes	—
825	#102	C₂³×C₃₁	1	1	yes	characteristic
826	#102	C₂³×C₃₁	1	2	yes	—
827	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
828	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
829	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
830	#97	C₂³×C₃₁	1	2	yes	—
831	#97	C₂³×C₃₁	1	2	yes	—
832	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄×C₈	C₂³×C₃₁	1	2	yes	—
835	C₄×C₈	C₂³×C₃₁	1	2	yes	—
836	C₄×C₈	C₂³×C₃₁	1	2	yes	—
837	C₃₁	#61866	1	1	yes	characteristic, direct product factor, Sylow
838	C₂×Q₈	—	2	2	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
848	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
849	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
850	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
851	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
852	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
853	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
863	Q₁₆	—	2	4	no	—
864	Q₁₆	—	2	2	no	—
865	Q₁₆	—	2	4	no	—
866	Q₁₆	—	2	2	no	—
867	SD₁₆	—	2	2	no	—
868	SD₁₆	—	2	2	no	—
869	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
871	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
872	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
873	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
874	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
913	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
915	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
917	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
919	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
920	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
921	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
924	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
925	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
926	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	1	no	—
930	C₂²⋊C₄	—	2	1	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	1	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	1	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
938	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	1	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
954	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
955	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₄²	C₂⁴×C₃₁	1	2	yes	—
958	C₄²	C₂⁴×C₃₁	1	2	yes	—
959	C₂³	—	2	1	no	—
960	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
961	Q₈	—	2	4	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	1	no	—
965	Q₈	—	2	1	no	—
966	Q₈	—	2	2	no	—
967	Q₈	—	2	1	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	1	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	8	1	no	—
973	Q₈	—	8	1	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	2	no	—
977	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
978	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
979	D₄	—	2	1	no	—
980	D₄	—	2	1	no	—
981	D₄	—	8	1	no	—
982	C₂×C₄	—	2	4	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	4	2	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	1	no	—
1001	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1004	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1005	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1006	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1007	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1008	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1009	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1010	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1011	C₈	—	2	1	no	—
1012	C₈	—	2	1	no	—
1013	C₈	—	2	1	no	—
1014	C₈	—	2	2	no	—
1015	C₈	—	2	1	no	—
1016	C₈	—	2	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	C₃₁×#578	1	2	yes	—
1044	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1045	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	8	1	no	—
1048	C₂	C₃₁×#3486	1	1	yes	characteristic
1049	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1050	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×#121	C₂³
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
2. C₃₁×#3502	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3387	C₂	semidirect
5. C₃₁×#3385	C₂	semidirect
6. C₃₁×#3383	C₂	semidirect
7. Q₈×Q₁₆×C₃₁	C₂	semidirect
8. C₃₁×#3381	C₂	semidirect
9. C₃₁×#3377	C₂	semidirect
10. C₃₁×#3374	C₂	semidirect
11. C₃₁×#3369	C₂	semidirect
12. C₃₁×#3364	C₂	semidirect
13. C₃₁×#3364	C₂	semidirect
14. C₃₁×#3363	C₂	semidirect
16. C₃₁×#3242	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3127	C₂	semidirect
22. C₃₁×#3104	C₂	semidirect
23. C₃₁×#2986	C₂	semidirect
433. #61866	C₃₁	direct (N × H)
493. #3502	C₂×C₃₁	semidirect
494. #3390	C₂×C₃₁	semidirect
495. #3387	C₂×C₃₁	semidirect
496. #3385	C₂×C₃₁	semidirect
497. #3383	C₂×C₃₁	semidirect
498. Q₈×Q₁₆	C₂×C₃₁	semidirect
499. #3381	C₂×C₃₁	semidirect
500. #3377	C₂×C₃₁	semidirect
501. #3374	C₂×C₃₁	semidirect
502. #3369	C₂×C₃₁	semidirect
503. #3364	C₂×C₃₁	semidirect
504. #3364	C₂×C₃₁	semidirect
505. #3363	C₂×C₃₁	semidirect
507. #3242	C₂×C₃₁	semidirect
509. #3231	C₂×C₃₁	semidirect
510. #3127	C₂×C₃₁	semidirect
513. #3104	C₂×C₃₁	semidirect
514. #2986	C₂×C₃₁	semidirect
837. C₃₁	#61866	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×#3555	2
C₃₁×#3502	2
C₃₁×#3390	2
C₃₁×#3387	2
C₃₁×#3385	2
C₃₁×#3383	2
Q₈×Q₁₆×C₃₁	2
C₃₁×#3381	2
C₃₁×#3377	2
C₃₁×#3374	2
C₃₁×#3369	2
C₃₁×#3364	2
C₃₁×#3363	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3233	2
C₃₁×#3231	2
C₃₁×#3127	2
C₃₁×#3121	2
C₃₁×#3108	2
C₃₁×#3104	2
C₃₁×#2986	2
#61866	31

Subgroups — C31×#61866 #21518625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61866 #21518625