Subgroups — C₃₁×#61386 #21518145

Order 7936.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3504	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×#3390	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3383	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3381	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic
16	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic
19	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic
23	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	Q₈²×C₃₁	—	2	1	no	—
26	Q₈²×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#557	—	2	1	no	—
28	C₃₁×#557	—	2	1	no	—
29	C₃₁×#557	—	2	1	no	—
30	C₃₁×#557	C₂²	1	2	yes	—
31	C₃₁×#557	C₂²	1	2	yes	—
32	C₃₁×#557	C₂²	1	2	yes	—
33	C₃₁×#557	C₂²	1	2	yes	—
34	C₃₁×#557	C₂²	1	2	yes	—
35	C₃₁×#554	—	2	2	no	—
36	C₃₁×#554	—	2	2	no	—
37	C₃₁×#554	C₂²	1	2	yes	—
38	C₃₁×#554	C₂²	1	2	yes	—
39	C₃₁×#544	—	2	1	no	—
40	C₃₁×#544	—	2	1	no	—
41	C₃₁×#544	—	2	2	no	—
42	C₃₁×#544	C₂²	1	1	yes	characteristic
43	C₃₁×#544	C₂²	1	1	yes	characteristic
44	C₃₁×#544	C₂²	1	1	yes	characteristic
45	C₃₁×#544	C₂²	1	1	yes	characteristic
46	C₃₁×#533	—	2	1	no	—
47	C₃₁×#533	—	2	2	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#125	—	2	1	no	—
51	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
52	C₃₁×#520	C₂²	1	1	yes	characteristic
53	C₃₁×#520	C₂²	1	1	yes	characteristic
54	C₃₁×#519	C₂²	1	1	yes	characteristic
55	C₃₁×#519	C₂²	1	1	yes	characteristic
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
58	C₃₁×#501	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#501	C₂²	1	2	yes	—
61	C₃₁×#501	C₂²	1	2	yes	—
62	C₃₁×#501	C₂²	1	2	yes	—
63	C₃₁×#501	C₂²	1	2	yes	—
64	C₃₁×#500	C₂²	1	2	yes	—
65	C₃₁×#499	C₂²	1	2	yes	—
66	C₃₁×#499	C₂²	1	2	yes	—
67	C₃₁×#499	C₂²	1	2	yes	—
68	C₃₁×#499	C₂²	1	2	yes	—
69	C₃₁×#498	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×#479	C₂²	1	2	yes	—
74	C₃₁×#479	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	1	yes	characteristic
76	C₃₁×#479	C₂²	1	2	yes	—
77	C₃₁×#479	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	1	yes	characteristic
83	C₃₁×#478	C₂²	1	1	yes	characteristic
84	C₃₁×#478	C₂²	1	2	yes	—
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	1	yes	characteristic
87	C₃₁×#477	C₂²	1	2	yes	—
88	C₃₁×#477	C₂²	1	2	yes	—
89	C₃₁×#477	C₂²	1	2	yes	—
90	C₃₁×#476	C₂²	1	1	yes	characteristic
91	C₃₁×#476	C₂²	1	2	yes	—
92	C₃₁×#475	C₂²	1	1	yes	characteristic
93	C₃₁×#475	C₂²	1	2	yes	—
94	C₃₁×#475	C₂²	1	2	yes	—
95	C₃₁×#475	C₂²	1	2	yes	—
96	C₃₁×#474	C₂²	1	1	yes	characteristic
97	C₃₁×#474	C₂²	1	2	yes	—
98	C₃₁×#446	C₂²	1	2	yes	—
99	C₃₁×#446	C₂²	1	2	yes	—
100	C₃₁×#446	C₂²	1	2	yes	—
101	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
102	C₃₁×#441	C₂²	1	2	yes	—
103	C₃₁×#441	C₂²	1	2	yes	—
104	C₃₁×#441	C₂²	1	2	yes	—
105	C₃₁×#440	C₂²	1	2	yes	—
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
110	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
114	C₃₁×#428	C₂²	1	1	yes	characteristic
115	C₃₁×#428	C₂²	1	1	yes	characteristic
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#428	C₂²	1	1	yes	characteristic
118	C₃₁×#428	C₂²	1	1	yes	characteristic
119	C₃₁×#427	C₂²	1	1	yes	characteristic
120	C₃₁×#427	C₂²	1	1	yes	characteristic
121	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
122	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
123	C₃₁×#424	C₂²	1	1	yes	characteristic
124	C₃₁×#424	C₂²	1	1	yes	characteristic
125	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₃₁×#419	C₂²	1	1	yes	characteristic
127	C₃₁×#417	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₃₁×#416	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
132	C₃₁×#405	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₃₁×#137	Q₈	1	8	yes	complemented
138	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
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	2	no	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	—	2	1	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	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
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	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×#125	—	2	1	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	2	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	1	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	D₄	1	1	yes	characteristic
181	C₃₁×#125	D₄	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	1	yes	characteristic
183	C₃₁×#125	C₂³	1	1	yes	characteristic
184	C₃₁×#125	C₂³	1	2	yes	—
185	C₃₁×#125	C₂³	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	2	yes	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
204	C₄×Q₈×C₃₁	—	2	2	no	—
205	C₄×Q₈×C₃₁	—	2	1	no	—
206	C₄×Q₈×C₃₁	—	2	1	no	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	2	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₃₁×#117	—	2	1	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	1	no	—
243	C₃₁×#117	C₂³	1	1	yes	characteristic
244	C₃₁×#117	C₂³	1	1	yes	characteristic
245	C₃₁×#117	C₂³	1	1	yes	characteristic
246	C₃₁×#117	C₂³	1	1	yes	characteristic
247	C₃₁×#117	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₃₁	—	2	1	no	—
259	C₂×C₄²×C₃₁	—	2	1	no	—
260	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
261	C₃₁×#107	C₂³	1	2	yes	—
262	C₃₁×#107	C₂³	1	2	yes	—
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
288	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
289	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
290	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#103	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₄×C₈×C₃₁	C₂³	1	2	yes	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	C₂×Q₈	1	4	yes	—
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	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₃₁	C₂×Q₈	1	4	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	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	1	no	—
334	C₂²×C₄×C₃₁	—	2	1	no	—
335	C₂²×C₄×C₃₁	—	2	1	no	—
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	2	no	—
339	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	Q₁₆×C₃₁	C₂×Q₈	1	8	yes	—
343	SD₁₆×C₃₁	C₂×Q₈	1	8	yes	—
344	M₁₆×C₃₁	—	2	2	no	—
345	M₁₆×C₃₁	C₂×Q₈	1	4	yes	—
346	C₂×C₈×C₃₁	—	2	2	no	—
347	C₂×C₈×C₃₁	—	2	2	no	—
348	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
351	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	1	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	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	2	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	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₄²×C₃₁	—	2	1	no	—
418	C₄²×C₃₁	—	2	1	no	—
419	C₄²×C₃₁	—	2	1	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	—	2	2	no	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
433	C₄²×C₃₁	C₂⁴	1	2	yes	—
434	C₄²×C₃₁	C₂⁴	1	2	yes	—
435	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
436	#61386	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂³×C₃₁	—	2	1	no	—
438	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
439	Q₈×C₃₁	—	2	4	no	—
440	Q₈×C₃₁	—	2	2	no	—
441	Q₈×C₃₁	—	2	1	no	—
442	Q₈×C₃₁	—	4	2	no	—
443	Q₈×C₃₁	—	4	2	no	—
444	Q₈×C₃₁	—	4	2	no	—
445	Q₈×C₃₁	—	8	1	no	—
446	Q₈×C₃₁	—	8	2	no	—
447	Q₈×C₃₁	—	8	2	no	—
448	Q₈×C₃₁	—	8	2	no	—
449	Q₈×C₃₁	—	8	2	no	—
450	Q₈×C₃₁	C₂²×Q₈	1	4	yes	—
451	Q₈×C₃₁	C₂²×Q₈	1	2	yes	—
452	D₄×C₃₁	—	2	4	no	—
453	D₄×C₃₁	—	2	1	no	—
454	D₄×C₃₁	C₂²×Q₈	1	2	yes	—
455	C₂×C₄×C₃₁	—	2	4	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	4	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	1	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	4	1	no	—
469	C₂×C₄×C₃₁	—	4	1	no	—
470	C₂×C₄×C₃₁	—	8	1	no	—
471	C₂×C₄×C₃₁	—	8	2	no	—
472	C₂×C₄×C₃₁	—	8	1	no	—
473	C₂×C₄×C₃₁	—	8	2	no	—
474	C₂×C₄×C₃₁	—	8	1	no	—
475	C₂×C₄×C₃₁	—	8	1	no	—
476	C₂×C₄×C₃₁	—	8	1	no	—
477	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
482	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
487	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
488	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
489	C₈×C₃₁	—	2	1	no	—
490	C₈×C₃₁	—	2	1	no	—
491	C₈×C₃₁	—	2	1	no	—
492	C₈×C₃₁	—	2	1	no	—
493	C₈×C₃₁	—	2	2	no	—
494	C₈×C₃₁	C₂²×Q₈	1	4	yes	—
495	#3504	C₂×C₃₁	1	1	yes	characteristic
496	#3502	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#3390	C₂×C₃₁	1	2	yes	complemented
498	#3390	C₂×C₃₁	1	2	yes	complemented
499	#3388	C₂×C₃₁	1	2	yes	complemented
500	#3388	C₂×C₃₁	1	2	yes	complemented
501	#3387	C₂×C₃₁	1	2	yes	complemented
502	#3385	C₂×C₃₁	1	2	yes	complemented
503	#3383	C₂×C₃₁	1	2	yes	complemented
504	#3381	C₂×C₃₁	1	2	yes	complemented
505	#3166	C₂×C₃₁	1	1	yes	characteristic, complemented
506	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3084	C₂×C₃₁	1	1	yes	characteristic
509	#3083	C₂×C₃₁	1	1	yes	characteristic
510	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3076	C₂×C₃₁	1	1	yes	characteristic
513	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#2962	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#2947	C₂×C₃₁	1	1	yes	characteristic
516	#2947	C₂×C₃₁	1	1	yes	characteristic
517	C₄×#137	C₂×C₃₁	1	1	yes	characteristic
518	C₂²×C₃₁	—	2	1	no	—
519	C₂²×C₃₁	—	2	1	no	—
520	C₂²×C₃₁	—	2	2	no	—
521	C₂²×C₃₁	—	4	1	no	—
522	C₂²×C₃₁	—	4	1	no	—
523	C₂²×C₃₁	D₄×Q₈	1	2	yes	—
524	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
525	C₄×C₃₁	—	2	1	no	—
526	C₄×C₃₁	—	2	1	no	—
527	C₄×C₃₁	—	2	2	no	—
528	C₄×C₃₁	—	2	2	no	—
529	C₄×C₃₁	—	2	1	no	—
530	C₄×C₃₁	—	2	1	no	—
531	C₄×C₃₁	—	2	2	no	—
532	C₄×C₃₁	—	2	2	no	—
533	C₄×C₃₁	—	2	2	no	—
534	C₄×C₃₁	—	2	4	no	—
535	C₄×C₃₁	—	4	2	no	—
536	C₄×C₃₁	—	4	1	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	—	4	1	no	—
542	C₄×C₃₁	—	4	1	no	—
543	C₄×C₃₁	—	4	1	no	—
544	C₄×C₃₁	D₄×Q₈	1	2	yes	—
545	C₄×C₃₁	C₂³×Q₈	1	1	yes	characteristic
546	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
548	Q₈²	—	2	1	no	—
549	Q₈²	C₂²×C₃₁	1	2	yes	—
550	#557	—	2	1	no	—
551	#557	—	2	1	no	—
552	#557	—	2	1	no	—
553	#557	C₂²×C₃₁	1	2	yes	—
554	#557	C₂²×C₃₁	1	2	yes	—
555	#557	C₂²×C₃₁	1	2	yes	—
556	#557	C₂²×C₃₁	1	2	yes	—
557	#557	C₂²×C₃₁	1	2	yes	—
558	#554	—	2	2	no	—
559	#554	—	2	2	no	—
560	#554	C₂²×C₃₁	1	2	yes	—
561	#554	C₂²×C₃₁	1	2	yes	—
562	#544	—	2	1	no	—
563	#544	—	2	1	no	—
564	#544	—	2	2	no	—
565	#544	C₂²×C₃₁	1	1	yes	characteristic
566	#544	C₂²×C₃₁	1	1	yes	characteristic
567	#544	C₂²×C₃₁	1	1	yes	characteristic
568	#544	C₂²×C₃₁	1	1	yes	characteristic
569	#533	—	2	1	no	—
570	#533	—	2	2	no	—
571	#533	C₂²×C₃₁	1	1	yes	characteristic
572	#533	C₂²×C₃₁	1	1	yes	characteristic
573	C₂×#125	—	2	1	no	—
574	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
575	#520	C₂²×C₃₁	1	1	yes	characteristic
576	#520	C₂²×C₃₁	1	1	yes	characteristic
577	#519	C₂²×C₃₁	1	1	yes	characteristic
578	#519	C₂²×C₃₁	1	1	yes	characteristic
579	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
580	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
581	#501	C₂²×C₃₁	1	2	yes	—
582	#501	C₂²×C₃₁	1	2	yes	—
583	#501	C₂²×C₃₁	1	2	yes	—
584	#501	C₂²×C₃₁	1	2	yes	—
585	#501	C₂²×C₃₁	1	2	yes	—
586	#501	C₂²×C₃₁	1	2	yes	—
587	#500	C₂²×C₃₁	1	2	yes	—
588	#499	C₂²×C₃₁	1	2	yes	—
589	#499	C₂²×C₃₁	1	2	yes	—
590	#499	C₂²×C₃₁	1	2	yes	—
591	#499	C₂²×C₃₁	1	2	yes	—
592	#498	C₂²×C₃₁	1	2	yes	—
593	#479	C₂²×C₃₁	1	2	yes	—
594	#479	C₂²×C₃₁	1	2	yes	—
595	#479	C₂²×C₃₁	1	2	yes	—
596	#479	C₂²×C₃₁	1	2	yes	—
597	#479	C₂²×C₃₁	1	1	yes	characteristic
598	#479	C₂²×C₃₁	1	1	yes	characteristic
599	#479	C₂²×C₃₁	1	2	yes	—
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	#478	C₂²×C₃₁	1	1	yes	characteristic
606	#478	C₂²×C₃₁	1	1	yes	characteristic
607	#478	C₂²×C₃₁	1	2	yes	—
608	#478	C₂²×C₃₁	1	2	yes	—
609	#477	C₂²×C₃₁	1	1	yes	characteristic
610	#477	C₂²×C₃₁	1	2	yes	—
611	#477	C₂²×C₃₁	1	2	yes	—
612	#477	C₂²×C₃₁	1	2	yes	—
613	#476	C₂²×C₃₁	1	1	yes	characteristic
614	#476	C₂²×C₃₁	1	2	yes	—
615	#475	C₂²×C₃₁	1	1	yes	characteristic
616	#475	C₂²×C₃₁	1	2	yes	—
617	#475	C₂²×C₃₁	1	2	yes	—
618	#475	C₂²×C₃₁	1	2	yes	—
619	#474	C₂²×C₃₁	1	1	yes	characteristic
620	#474	C₂²×C₃₁	1	2	yes	—
621	#446	C₂²×C₃₁	1	2	yes	—
622	#446	C₂²×C₃₁	1	2	yes	—
623	#446	C₂²×C₃₁	1	2	yes	—
624	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
625	#441	C₂²×C₃₁	1	2	yes	—
626	#441	C₂²×C₃₁	1	2	yes	—
627	#441	C₂²×C₃₁	1	2	yes	—
628	#440	C₂²×C₃₁	1	2	yes	—
629	#440	C₂²×C₃₁	1	2	yes	—
630	#440	C₂²×C₃₁	1	2	yes	—
631	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
632	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
633	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
634	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
635	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
636	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
637	#428	C₂²×C₃₁	1	1	yes	characteristic
638	#428	C₂²×C₃₁	1	1	yes	characteristic
639	#428	C₂²×C₃₁	1	1	yes	characteristic
640	#428	C₂²×C₃₁	1	1	yes	characteristic
641	#428	C₂²×C₃₁	1	1	yes	characteristic
642	#427	C₂²×C₃₁	1	1	yes	characteristic
643	#427	C₂²×C₃₁	1	1	yes	characteristic
644	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
645	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
646	#424	C₂²×C₃₁	1	1	yes	characteristic
647	#424	C₂²×C₃₁	1	1	yes	characteristic
648	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
649	#419	C₂²×C₃₁	1	1	yes	characteristic
650	#417	C₂²×C₃₁	1	1	yes	characteristic
651	#416	C₂²×C₃₁	1	1	yes	characteristic
652	#416	C₂²×C₃₁	1	1	yes	characteristic
653	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
654	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
655	#405	C₂²×C₃₁	1	1	yes	characteristic
656	#405	C₂²×C₃₁	1	1	yes	characteristic
657	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
658	C₂×C₃₁	—	2	2	no	—
659	C₂×C₃₁	—	4	2	no	—
660	C₂×C₃₁	C₂×D₄×Q₈	1	1	yes	characteristic
661	C₂×C₃₁	#3584	1	1	yes	characteristic
662	C₂×C₃₁	#3586	1	1	yes	characteristic
663	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
664	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
665	#137	Q₈×C₃₁	1	8	yes	complemented
666	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
667	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
668	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
670	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
671	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
672	C₄⋊Q₈	—	2	2	no	—
673	C₄⋊Q₈	—	2	2	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	2	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	1	no	—
678	C₄⋊Q₈	—	2	1	no	—
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	—	2	1	no	—
684	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
685	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	#125	—	2	1	no	—
693	#125	—	2	1	no	—
694	#125	—	2	2	no	—
695	#125	—	2	2	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	2	no	—
704	#125	—	2	1	no	—
705	#125	—	2	1	no	—
706	#125	—	2	1	no	—
707	#125	—	2	1	no	—
708	#125	D₄×C₃₁	1	1	yes	characteristic
709	#125	D₄×C₃₁	1	1	yes	characteristic
710	#125	C₂³×C₃₁	1	2	yes	—
711	#125	C₂³×C₃₁	1	2	yes	—
712	#125	C₂³×C₃₁	1	1	yes	characteristic
713	#125	C₂³×C₃₁	1	1	yes	characteristic
714	#125	C₂³×C₃₁	1	2	yes	—
715	#125	C₂³×C₃₁	1	2	yes	—
716	#125	C₂³×C₃₁	1	2	yes	—
717	#125	C₂³×C₃₁	1	2	yes	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
731	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	2	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	2	no	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
747	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
748	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
749	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
751	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
752	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
753	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
754	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
755	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
756	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
763	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
764	C₄×D₄	C₂³×C₃₁	1	2	yes	—
765	C₄×D₄	C₂³×C₃₁	1	2	yes	—
766	#117	—	2	1	no	—
767	#117	—	2	1	no	—
768	#117	—	2	2	no	—
769	#117	—	2	2	no	—
770	#117	—	2	1	no	—
771	#117	C₂³×C₃₁	1	1	yes	characteristic
772	#117	C₂³×C₃₁	1	1	yes	characteristic
773	#117	C₂³×C₃₁	1	1	yes	characteristic
774	#117	C₂³×C₃₁	1	1	yes	characteristic
775	#117	C₂³×C₃₁	1	1	yes	characteristic
776	C₂×C₄⋊C₄	—	2	1	no	—
777	C₂×C₄⋊C₄	—	2	1	no	—
778	C₂×C₄⋊C₄	—	2	1	no	—
779	C₂×C₄⋊C₄	—	2	1	no	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	2	2	no	—
782	C₂×C₄⋊C₄	—	2	2	no	—
783	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₂×C₄²	—	2	1	no	—
787	C₂×C₄²	—	2	1	no	—
788	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
789	#107	C₂³×C₃₁	1	2	yes	—
790	#107	C₂³×C₃₁	1	2	yes	—
791	#107	C₂³×C₃₁	1	1	yes	characteristic
792	#107	C₂³×C₃₁	1	1	yes	characteristic
793	#107	C₂³×C₃₁	1	1	yes	characteristic
794	#107	C₂³×C₃₁	1	1	yes	characteristic
795	#107	C₂³×C₃₁	1	2	yes	—
796	#107	C₂³×C₃₁	1	2	yes	—
797	#107	C₂³×C₃₁	1	2	yes	—
798	#107	C₂³×C₃₁	1	2	yes	—
799	#107	C₂³×C₃₁	1	2	yes	—
800	#106	C₂³×C₃₁	1	2	yes	—
801	#106	C₂³×C₃₁	1	2	yes	—
802	#106	C₂³×C₃₁	1	1	yes	characteristic
803	#106	C₂³×C₃₁	1	1	yes	characteristic
804	#106	C₂³×C₃₁	1	1	yes	characteristic
805	#106	C₂³×C₃₁	1	1	yes	characteristic
806	#106	C₂³×C₃₁	1	2	yes	—
807	#106	C₂³×C₃₁	1	2	yes	—
808	#106	C₂³×C₃₁	1	2	yes	—
809	#106	C₂³×C₃₁	1	2	yes	—
810	#106	C₂³×C₃₁	1	2	yes	—
811	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₃₁	1	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	2	yes	—
818	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
819	#103	C₂³×C₃₁	1	2	yes	—
820	#103	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	2	yes	—
822	#103	C₂³×C₃₁	1	2	yes	—
823	#103	C₂³×C₃₁	1	1	yes	characteristic
824	#103	C₂³×C₃₁	1	1	yes	characteristic
825	#103	C₂³×C₃₁	1	1	yes	characteristic
826	#103	C₂³×C₃₁	1	1	yes	characteristic
827	#103	C₂³×C₃₁	1	2	yes	—
828	#103	C₂³×C₃₁	1	2	yes	—
829	#103	C₂³×C₃₁	1	2	yes	—
830	#102	C₂³×C₃₁	1	1	yes	characteristic
831	#102	C₂³×C₃₁	1	1	yes	characteristic
832	#102	C₂³×C₃₁	1	1	yes	characteristic
833	#102	C₂³×C₃₁	1	1	yes	characteristic
834	#102	C₂³×C₃₁	1	2	yes	—
835	#97	C₂³×C₃₁	1	2	yes	—
836	#97	C₂³×C₃₁	1	2	yes	—
837	#97	C₂³×C₃₁	1	2	yes	—
838	C₄×C₈	C₂³×C₃₁	1	2	yes	—
839	C₄×C₈	C₂³×C₃₁	1	2	yes	—
840	C₄×C₈	C₂³×C₃₁	1	2	yes	—
841	C₃₁	#61386	1	1	yes	characteristic, direct product factor, Sylow
842	#41	—	2	2	no	—
843	#41	C₂×Q₈×C₃₁	1	4	yes	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
853	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
854	C₂×Q₈	C₂×Q₈×C₃₁	1	4	yes	—
855	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
856	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	Q₁₆	C₂×Q₈×C₃₁	1	8	yes	—
872	SD₁₆	C₂×Q₈×C₃₁	1	8	yes	—
873	M₁₆	—	2	2	no	—
874	M₁₆	C₂×Q₈×C₃₁	1	4	yes	—
875	C₂×C₈	—	2	2	no	—
876	C₂×C₈	—	2	2	no	—
877	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
880	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
921	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
922	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₄²	—	2	1	no	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₄²	C₂⁴×C₃₁	1	2	yes	—
963	C₄²	C₂⁴×C₃₁	1	2	yes	—
964	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂³	—	2	1	no	—
966	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
967	Q₈	—	2	4	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	1	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	4	2	no	—
973	Q₈	—	8	1	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	2	no	—
977	Q₈	—	8	2	no	—
978	Q₈	C₂²×Q₈×C₃₁	1	4	yes	—
979	Q₈	C₂²×Q₈×C₃₁	1	2	yes	—
980	D₄	—	2	4	no	—
981	D₄	—	2	1	no	—
982	D₄	C₂²×Q₈×C₃₁	1	2	yes	—
983	C₂×C₄	—	2	4	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	4	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	4	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	8	1	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	1	no	—
1001	C₂×C₄	—	8	2	no	—
1002	C₂×C₄	—	8	1	no	—
1003	C₂×C₄	—	8	1	no	—
1004	C₂×C₄	—	8	1	no	—
1005	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1007	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1008	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1009	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1010	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1011	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1012	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1014	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
1015	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1016	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	—	2	1	no	—
1021	C₈	—	2	2	no	—
1022	C₈	C₂²×Q₈×C₃₁	1	4	yes	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	D₄×Q₈×C₃₁	1	2	yes	—
1029	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1030	C₄	—	2	2	no	—
1031	C₄	—	2	4	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	D₄×Q₈×C₃₁	1	2	yes	—
1050	C₄	C₂³×Q₈×C₃₁	1	1	yes	characteristic
1051	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1052	C₂	—	2	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	C₂×D₄×Q₈×C₃₁	1	1	yes	characteristic
1055	C₂	C₃₁×#3584	1	1	yes	characteristic
1056	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	C₂×#41×C₃₁	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×#3390	C₂	semidirect
5. C₃₁×#3388	C₂	semidirect
6. C₃₁×#3388	C₂	semidirect
7. C₃₁×#3387	C₂	semidirect
8. C₃₁×#3385	C₂	semidirect
9. C₃₁×#3383	C₂	semidirect
10. C₃₁×#3381	C₂	semidirect
11. C₃₁×#3166	C₂	semidirect
12. C₃₁×#3164	C₂	semidirect
13. C₃₁×#3163	C₂	semidirect
16. C₃₁×#3082	C₂	semidirect
17. C₃₁×#3082	C₂	semidirect
19. C₂×C₃₁×#479	C₂	semidirect
20. C₃₁×#2962	C₂	semidirect
137. C₃₁×#137	Q₈	semidirect
436. #61386	C₃₁	direct (N × H)
496. #3502	C₂×C₃₁	semidirect
497. #3390	C₂×C₃₁	semidirect
498. #3390	C₂×C₃₁	semidirect
499. #3388	C₂×C₃₁	semidirect
500. #3388	C₂×C₃₁	semidirect
501. #3387	C₂×C₃₁	semidirect
502. #3385	C₂×C₃₁	semidirect
503. #3383	C₂×C₃₁	semidirect
504. #3381	C₂×C₃₁	semidirect
505. #3166	C₂×C₃₁	semidirect
506. #3164	C₂×C₃₁	semidirect
507. #3163	C₂×C₃₁	semidirect
510. #3082	C₂×C₃₁	semidirect
511. #3082	C₂×C₃₁	semidirect
513. C₂×#479	C₂×C₃₁	semidirect
514. #2962	C₂×C₃₁	semidirect
665. #137	Q₈×C₃₁	semidirect
841. C₃₁	#61386	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×#3504	2
C₃₁×#3502	2
C₃₁×#3390	2
C₃₁×#3388	2
C₃₁×#3387	2
C₃₁×#3385	2
C₃₁×#3383	2
C₃₁×#3381	2
C₃₁×#3166	2
C₃₁×#3164	2
C₃₁×#3163	2
C₃₁×#3084	2
C₃₁×#3083	2
C₃₁×#3082	2
C₃₁×#3076	2
C₂×C₃₁×#479	2
C₃₁×#2962	2
C₃₁×#2947	2
C₄×C₃₁×#137	2
#61386	31

Subgroups — C31×#61386 #21518145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61386 #21518145