Subgroups — C₃₁×#35099 #21491858

Order 7936.

1674 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2854	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2853	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2646	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2643	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2639	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2533	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2532	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2531	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2530	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2529	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2528	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2527	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2526	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2325	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#376	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#123	C₂²	1	2	yes	—
21	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
24	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#401	C₂²	1	2	yes	—
28	C₃₁×#400	C₂²	1	2	yes	—
29	C₃₁×#400	C₂²	1	2	yes	—
30	C₃₁×#400	C₂²	1	2	yes	—
31	C₃₁×#400	C₂²	1	2	yes	—
32	C₃₁×#400	C₂²	1	2	yes	—
33	C₃₁×#400	C₂²	1	2	yes	—
34	C₃₁×#398	C₂²	1	2	yes	—
35	C₃₁×#398	C₂²	1	2	yes	—
36	C₃₁×#397	C₂²	1	2	yes	—
37	C₃₁×#397	C₂²	1	2	yes	—
38	C₃₁×#397	C₂²	1	2	yes	—
39	C₃₁×#397	C₂²	1	2	yes	—
40	C₃₁×#396	C₂²	1	2	yes	—
41	C₃₁×#394	C₂²	1	2	yes	—
42	C₃₁×#393	C₂²	1	2	yes	—
43	C₃₁×#391	C₂²	1	2	yes	—
44	C₃₁×#391	C₂²	1	1	yes	characteristic
45	C₃₁×#391	C₂²	1	1	yes	characteristic
46	C₃₁×#390	C₂²	1	1	yes	characteristic
47	C₃₁×#390	C₂²	1	1	yes	characteristic
48	C₃₁×#389	C₂²	1	2	yes	—
49	C₃₁×#389	C₂²	1	1	yes	characteristic
50	C₃₁×#389	C₂²	1	1	yes	characteristic
51	C₃₁×#389	C₂²	1	1	yes	characteristic
52	C₃₁×#389	C₂²	1	1	yes	characteristic
53	C₃₁×#388	C₂²	1	2	yes	—
54	C₃₁×#388	C₂²	1	2	yes	—
55	C₃₁×#388	C₂²	1	2	yes	—
56	C₃₁×#388	C₂²	1	2	yes	—
57	C₃₁×#388	C₂²	1	2	yes	—
58	C₃₁×#388	C₂²	1	2	yes	—
59	C₃₁×#388	C₂²	1	2	yes	—
60	C₃₁×#388	C₂²	1	2	yes	—
61	C₃₁×#388	C₂²	1	2	yes	—
62	C₃₁×#388	C₂²	1	2	yes	—
63	C₃₁×#388	C₂²	1	2	yes	—
64	C₃₁×#387	C₂²	1	2	yes	—
65	C₃₁×#387	C₂²	1	2	yes	—
66	C₃₁×#387	C₂²	1	2	yes	—
67	C₃₁×#387	C₂²	1	2	yes	—
68	C₃₁×#387	C₂²	1	2	yes	—
69	C₃₁×#387	C₂²	1	2	yes	—
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#386	C₂²	1	2	yes	—
78	C₃₁×#386	C₂²	1	2	yes	—
79	C₃₁×#386	C₂²	1	2	yes	—
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#386	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#385	C₂²	1	2	yes	—
84	C₃₁×#385	C₂²	1	2	yes	—
85	C₃₁×#385	C₂²	1	2	yes	—
86	C₃₁×#385	C₂²	1	2	yes	—
87	C₃₁×#383	C₂²	1	2	yes	—
88	C₃₁×#382	C₂²	1	2	yes	—
89	C₃₁×#381	C₂²	1	2	yes	—
90	C₃₁×#381	C₂²	1	2	yes	—
91	C₃₁×#380	C₂²	1	2	yes	—
92	C₃₁×#380	C₂²	1	1	yes	characteristic
93	C₃₁×#380	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₃₁×#376	C₂²	1	2	yes	—
100	C₃₁×#376	C₂²	1	2	yes	—
101	C₃₁×#376	C₂²	1	2	yes	—
102	C₃₁×#376	C₂²	1	2	yes	—
103	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
104	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
105	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
106	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₃₁×#123	—	2	8	no	—
119	C₃₁×C₂²⋊Q₈	—	2	4	no	—
120	C₃₁×#121	—	2	4	no	—
121	C₄×D₄×C₃₁	—	2	8	no	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄²×C₃₁	—	2	4	no	—
156	C₂×C₄²×C₃₁	—	2	4	no	—
157	C₂×C₄²×C₃₁	—	2	4	no	—
158	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
169	C₃₁×#95	C₂³	1	2	yes	—
170	C₃₁×#95	C₂³	1	2	yes	—
171	C₃₁×#95	C₂³	1	2	yes	—
172	C₃₁×#95	C₂³	1	2	yes	—
173	C₃₁×#95	C₂³	1	2	yes	—
174	C₃₁×#95	C₂³	1	2	yes	—
175	C₃₁×#95	C₂³	1	2	yes	—
176	C₃₁×#95	C₂³	1	2	yes	—
177	C₃₁×#95	C₂³	1	2	yes	—
178	C₃₁×#95	C₂³	1	2	yes	—
179	C₃₁×#95	C₂³	1	2	yes	—
180	C₃₁×#95	C₂³	1	2	yes	—
181	C₃₁×#95	C₂³	1	2	yes	—
182	C₃₁×#95	C₂³	1	2	yes	—
183	C₃₁×#95	C₂³	1	2	yes	—
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	2	yes	—
187	C₃₁×#95	C₂³	1	2	yes	—
188	C₃₁×#95	C₂³	1	2	yes	—
189	C₃₁×#95	C₂³	1	2	yes	—
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	2	yes	—
192	C₃₁×#95	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	2	yes	—
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
202	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₃₁	—	2	2	no	—
204	C₂×Q₈×C₃₁	—	4	1	no	—
205	C₂×Q₈×C₃₁	—	4	1	no	—
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	4	1	no	—
211	C₂×D₄×C₃₁	—	4	1	no	—
212	C₂²×C₄×C₃₁	—	2	2	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	2	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	4	1	no	—
220	C₂²×C₄×C₃₁	—	4	1	no	—
221	C₂²×C₄×C₃₁	—	4	1	no	—
222	C₂²×C₄×C₃₁	—	4	1	no	—
223	C₂²×C₄×C₃₁	—	4	1	no	—
224	C₂²×C₄×C₃₁	—	4	1	no	—
225	C₂²×C₄×C₃₁	—	4	1	no	—
226	C₂²×C₄×C₃₁	—	4	1	no	—
227	C₂²×C₄×C₃₁	—	4	1	no	—
228	C₂²×C₄×C₃₁	—	4	1	no	—
229	C₂²×C₄×C₃₁	—	4	1	no	—
230	C₂²×C₄×C₃₁	—	4	1	no	—
231	C₂²×C₄×C₃₁	—	4	2	no	—
232	C₂²×C₄×C₃₁	—	4	2	no	—
233	C₂²×C₄×C₃₁	#41	1	4	yes	—
234	C₂²×C₄×C₃₁	#41	1	4	yes	—
235	C₂²×C₄×C₃₁	#41	1	4	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	4	1	no	—
260	C₄⋊C₄×C₃₁	—	4	1	no	—
261	C₄⋊C₄×C₃₁	—	4	1	no	—
262	C₄⋊C₄×C₃₁	—	4	1	no	—
263	C₄⋊C₄×C₃₁	—	4	2	no	—
264	C₄⋊C₄×C₃₁	—	4	2	no	—
265	C₄⋊C₄×C₃₁	—	4	2	no	—
266	C₄⋊C₄×C₃₁	—	4	2	no	—
267	C₄⋊C₄×C₃₁	—	4	2	no	—
268	C₄⋊C₄×C₃₁	—	4	2	no	—
269	C₄⋊C₄×C₃₁	—	4	2	no	—
270	C₄⋊C₄×C₃₁	—	4	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	—	4	2	no	—
279	C₂²⋊C₄×C₃₁	—	4	2	no	—
280	C₂²⋊C₄×C₃₁	—	4	2	no	—
281	C₂²⋊C₄×C₃₁	—	4	2	no	—
282	C₂²⋊C₄×C₃₁	—	4	2	no	—
283	C₂²⋊C₄×C₃₁	—	4	2	no	—
284	C₂²⋊C₄×C₃₁	—	4	2	no	—
285	C₂²⋊C₄×C₃₁	—	4	2	no	—
286	C₄²×C₃₁	—	2	4	no	—
287	C₄²×C₃₁	—	2	4	no	—
288	C₄²×C₃₁	—	2	2	no	—
289	C₄²×C₃₁	—	2	2	no	—
290	C₄²×C₃₁	—	2	2	no	—
291	C₄²×C₃₁	—	2	2	no	—
292	C₄²×C₃₁	—	2	4	no	—
293	C₄²×C₃₁	—	2	4	no	—
294	C₄²×C₃₁	—	2	4	no	—
295	C₄²×C₃₁	—	4	2	no	—
296	C₄²×C₃₁	—	4	2	no	—
297	#35099	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂³×C₃₁	—	2	1	no	—
299	C₂³×C₃₁	—	2	1	no	—
300	C₂³×C₃₁	—	2	1	no	—
301	C₂³×C₃₁	—	2	1	no	—
302	C₂³×C₃₁	—	2	2	no	—
303	C₂³×C₃₁	—	2	2	no	—
304	C₂³×C₃₁	—	2	2	no	—
305	C₂³×C₃₁	—	2	2	no	—
306	C₂³×C₃₁	—	2	2	no	—
307	C₂³×C₃₁	—	2	2	no	—
308	C₂³×C₃₁	—	2	2	no	—
309	C₂³×C₃₁	C₂×#41	1	2	yes	—
310	C₂³×C₃₁	C₂×#41	1	2	yes	—
311	C₂³×C₃₁	C₂×#41	1	2	yes	—
312	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
313	Q₈×C₃₁	—	8	2	no	—
314	D₄×C₃₁	—	4	8	no	—
315	D₄×C₃₁	—	8	2	no	—
316	C₂×C₄×C₃₁	—	2	8	no	—
317	C₂×C₄×C₃₁	—	2	1	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	1	no	—
320	C₂×C₄×C₃₁	—	2	1	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	1	no	—
324	C₂×C₄×C₃₁	—	2	1	no	—
325	C₂×C₄×C₃₁	—	2	1	no	—
326	C₂×C₄×C₃₁	—	2	1	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	1	no	—
330	C₂×C₄×C₃₁	—	2	1	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	1	no	—
347	C₂×C₄×C₃₁	—	2	1	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	4	4	no	—
364	C₂×C₄×C₃₁	—	4	4	no	—
365	C₂×C₄×C₃₁	—	4	4	no	—
366	C₂×C₄×C₃₁	—	4	4	no	—
367	C₂×C₄×C₃₁	—	4	4	no	—
368	C₂×C₄×C₃₁	—	4	4	no	—
369	C₂×C₄×C₃₁	—	8	4	no	—
370	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
371	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
372	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
373	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
374	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
375	#2855	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#2854	C₂×C₃₁	1	1	yes	characteristic
377	#2853	C₂×C₃₁	1	2	yes	complemented
378	#2646	C₂×C₃₁	1	1	yes	characteristic, complemented
379	#2643	C₂×C₃₁	1	2	yes	complemented
380	#2639	C₂×C₃₁	1	1	yes	characteristic
381	#2533	C₂×C₃₁	1	2	yes	complemented
382	#2532	C₂×C₃₁	1	2	yes	complemented
383	#2531	C₂×C₃₁	1	2	yes	complemented
384	#2530	C₂×C₃₁	1	2	yes	complemented
385	#2529	C₂×C₃₁	1	2	yes	complemented
386	#2528	C₂×C₃₁	1	2	yes	complemented
387	#2527	C₂×C₃₁	1	2	yes	complemented
388	#2526	C₂×C₃₁	1	2	yes	complemented
389	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#2325	C₂×C₃₁	1	1	yes	characteristic
391	#2318	C₂×C₃₁	1	2	yes	complemented
392	C₄×#123	C₂×C₃₁	1	2	yes	complemented
393	C₂×#376	C₂×C₃₁	1	1	yes	characteristic, complemented
394	C₂²×C₃₁	—	2	2	no	—
395	C₂²×C₃₁	—	2	2	no	—
396	C₂²×C₃₁	—	2	2	no	—
397	C₂²×C₃₁	—	2	2	no	—
398	C₂²×C₃₁	—	2	2	no	—
399	C₂²×C₃₁	—	2	2	no	—
400	C₂²×C₃₁	—	4	2	no	—
401	C₂²×C₃₁	—	4	2	no	—
402	C₂²×C₃₁	—	4	2	no	—
403	C₂²×C₃₁	—	4	2	no	—
404	C₂²×C₃₁	—	4	2	no	—
405	C₂²×C₃₁	—	4	2	no	—
406	C₂²×C₃₁	—	4	2	no	—
407	C₂²×C₃₁	#529	1	4	yes	—
408	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
409	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₃₁	#585	1	1	yes	characteristic
412	C₂²×C₃₁	#585	1	1	yes	characteristic
413	C₂²×C₃₁	#585	1	1	yes	characteristic
414	C₂²×C₃₁	#585	1	1	yes	characteristic
415	C₄×C₃₁	—	2	2	no	—
416	C₄×C₃₁	—	2	2	no	—
417	C₄×C₃₁	—	2	4	no	—
418	C₄×C₃₁	—	2	2	no	—
419	C₄×C₃₁	—	2	2	no	—
420	C₄×C₃₁	—	4	2	no	—
421	C₄×C₃₁	—	4	2	no	—
422	C₄×C₃₁	—	4	2	no	—
423	C₄×C₃₁	—	4	2	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	—	4	2	no	—
426	C₄×C₃₁	—	4	2	no	—
427	C₄×C₃₁	—	4	2	no	—
428	C₄×C₃₁	—	4	2	no	—
429	C₄×C₃₁	—	4	1	no	—
430	C₄×C₃₁	—	4	1	no	—
431	C₄×C₃₁	—	4	2	no	—
432	C₂×#123	C₂²×C₃₁	1	2	yes	—
433	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
436	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
438	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
439	#401	C₂²×C₃₁	1	2	yes	—
440	#400	C₂²×C₃₁	1	2	yes	—
441	#400	C₂²×C₃₁	1	2	yes	—
442	#400	C₂²×C₃₁	1	2	yes	—
443	#400	C₂²×C₃₁	1	2	yes	—
444	#400	C₂²×C₃₁	1	2	yes	—
445	#400	C₂²×C₃₁	1	2	yes	—
446	#398	C₂²×C₃₁	1	2	yes	—
447	#398	C₂²×C₃₁	1	2	yes	—
448	#397	C₂²×C₃₁	1	2	yes	—
449	#397	C₂²×C₃₁	1	2	yes	—
450	#397	C₂²×C₃₁	1	2	yes	—
451	#397	C₂²×C₃₁	1	2	yes	—
452	#396	C₂²×C₃₁	1	2	yes	—
453	#394	C₂²×C₃₁	1	2	yes	—
454	#393	C₂²×C₃₁	1	2	yes	—
455	#391	C₂²×C₃₁	1	2	yes	—
456	#391	C₂²×C₃₁	1	1	yes	characteristic
457	#391	C₂²×C₃₁	1	1	yes	characteristic
458	#390	C₂²×C₃₁	1	1	yes	characteristic
459	#390	C₂²×C₃₁	1	1	yes	characteristic
460	#389	C₂²×C₃₁	1	2	yes	—
461	#389	C₂²×C₃₁	1	1	yes	characteristic
462	#389	C₂²×C₃₁	1	1	yes	characteristic
463	#389	C₂²×C₃₁	1	1	yes	characteristic
464	#389	C₂²×C₃₁	1	1	yes	characteristic
465	#388	C₂²×C₃₁	1	2	yes	—
466	#388	C₂²×C₃₁	1	2	yes	—
467	#388	C₂²×C₃₁	1	2	yes	—
468	#388	C₂²×C₃₁	1	2	yes	—
469	#388	C₂²×C₃₁	1	2	yes	—
470	#388	C₂²×C₃₁	1	2	yes	—
471	#388	C₂²×C₃₁	1	2	yes	—
472	#388	C₂²×C₃₁	1	2	yes	—
473	#388	C₂²×C₃₁	1	2	yes	—
474	#388	C₂²×C₃₁	1	2	yes	—
475	#388	C₂²×C₃₁	1	2	yes	—
476	#387	C₂²×C₃₁	1	2	yes	—
477	#387	C₂²×C₃₁	1	2	yes	—
478	#387	C₂²×C₃₁	1	2	yes	—
479	#387	C₂²×C₃₁	1	2	yes	—
480	#387	C₂²×C₃₁	1	2	yes	—
481	#387	C₂²×C₃₁	1	2	yes	—
482	#387	C₂²×C₃₁	1	2	yes	—
483	#387	C₂²×C₃₁	1	2	yes	—
484	#387	C₂²×C₃₁	1	2	yes	—
485	#387	C₂²×C₃₁	1	2	yes	—
486	#387	C₂²×C₃₁	1	2	yes	—
487	#387	C₂²×C₃₁	1	2	yes	—
488	#387	C₂²×C₃₁	1	2	yes	—
489	#386	C₂²×C₃₁	1	2	yes	—
490	#386	C₂²×C₃₁	1	2	yes	—
491	#386	C₂²×C₃₁	1	2	yes	—
492	#386	C₂²×C₃₁	1	2	yes	—
493	#386	C₂²×C₃₁	1	2	yes	—
494	#385	C₂²×C₃₁	1	2	yes	—
495	#385	C₂²×C₃₁	1	2	yes	—
496	#385	C₂²×C₃₁	1	2	yes	—
497	#385	C₂²×C₃₁	1	2	yes	—
498	#385	C₂²×C₃₁	1	2	yes	—
499	#383	C₂²×C₃₁	1	2	yes	—
500	#382	C₂²×C₃₁	1	2	yes	—
501	#381	C₂²×C₃₁	1	2	yes	—
502	#381	C₂²×C₃₁	1	2	yes	—
503	#380	C₂²×C₃₁	1	2	yes	—
504	#380	C₂²×C₃₁	1	1	yes	characteristic
505	#380	C₂²×C₃₁	1	1	yes	characteristic
506	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
507	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
510	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
511	#376	C₂²×C₃₁	1	2	yes	—
512	#376	C₂²×C₃₁	1	2	yes	—
513	#376	C₂²×C₃₁	1	2	yes	—
514	#376	C₂²×C₃₁	1	2	yes	—
515	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
517	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×C₃₁	—	2	4	no	—
520	C₂×C₃₁	—	8	2	no	—
521	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
522	C₂×C₃₁	#3455	1	1	yes	characteristic
523	C₂×C₃₁	#3455	1	1	yes	characteristic
524	C₂×C₃₁	#3491	1	1	yes	characteristic
525	C₂×C₃₁	#3491	1	1	yes	characteristic
526	C₂×C₃₁	#3493	1	1	yes	characteristic
527	C₂×C₃₁	#3493	1	1	yes	characteristic
528	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
530	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
533	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
539	#123	—	2	8	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	#121	—	2	4	no	—
542	C₄×D₄	—	2	8	no	—
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄²	—	2	4	no	—
577	C₂×C₄²	—	2	4	no	—
578	C₂×C₄²	—	2	4	no	—
579	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
581	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
582	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
584	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
589	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
590	#95	C₂³×C₃₁	1	2	yes	—
591	#95	C₂³×C₃₁	1	2	yes	—
592	#95	C₂³×C₃₁	1	2	yes	—
593	#95	C₂³×C₃₁	1	2	yes	—
594	#95	C₂³×C₃₁	1	2	yes	—
595	#95	C₂³×C₃₁	1	2	yes	—
596	#95	C₂³×C₃₁	1	2	yes	—
597	#95	C₂³×C₃₁	1	2	yes	—
598	#95	C₂³×C₃₁	1	2	yes	—
599	#95	C₂³×C₃₁	1	2	yes	—
600	#95	C₂³×C₃₁	1	2	yes	—
601	#95	C₂³×C₃₁	1	2	yes	—
602	#95	C₂³×C₃₁	1	2	yes	—
603	#95	C₂³×C₃₁	1	2	yes	—
604	#95	C₂³×C₃₁	1	2	yes	—
605	#95	C₂³×C₃₁	1	2	yes	—
606	#95	C₂³×C₃₁	1	2	yes	—
607	#95	C₂³×C₃₁	1	2	yes	—
608	#95	C₂³×C₃₁	1	2	yes	—
609	#95	C₂³×C₃₁	1	2	yes	—
610	#95	C₂³×C₃₁	1	2	yes	—
611	#95	C₂³×C₃₁	1	2	yes	—
612	#95	C₂³×C₃₁	1	2	yes	—
613	#95	C₂³×C₃₁	1	2	yes	—
614	#95	C₂³×C₃₁	1	2	yes	—
615	#95	C₂³×C₃₁	1	2	yes	—
616	#95	C₂³×C₃₁	1	2	yes	—
617	#95	C₂³×C₃₁	1	2	yes	—
618	#95	C₂³×C₃₁	1	2	yes	—
619	#95	C₂³×C₃₁	1	2	yes	—
620	#95	C₂³×C₃₁	1	2	yes	—
621	#95	C₂³×C₃₁	1	2	yes	—
622	C₃₁	#35099	1	1	yes	characteristic, direct product factor, Sylow
623	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
624	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	4	1	no	—
627	C₂×Q₈	—	4	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	4	1	no	—
633	C₂×D₄	—	4	1	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	4	1	no	—
642	C₂²×C₄	—	4	1	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	—	4	1	no	—
645	C₂²×C₄	—	4	1	no	—
646	C₂²×C₄	—	4	1	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	1	no	—
652	C₂²×C₄	—	4	1	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	#41×C₃₁	1	4	yes	—
656	C₂²×C₄	#41×C₃₁	1	4	yes	—
657	C₂²×C₄	#41×C₃₁	1	4	yes	—
658	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	4	1	no	—
682	C₄⋊C₄	—	4	1	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	1	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	2	no	—
712	C₄²	—	2	2	no	—
713	C₄²	—	2	2	no	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	4	2	no	—
718	C₄²	—	4	2	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	C₂×#41×C₃₁	1	2	yes	—
731	C₂³	C₂×#41×C₃₁	1	2	yes	—
732	C₂³	C₂×#41×C₃₁	1	2	yes	—
733	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
734	Q₈	—	8	2	no	—
735	D₄	—	4	8	no	—
736	D₄	—	8	2	no	—
737	C₂×C₄	—	2	8	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
792	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
793	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
794	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
795	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	C₃₁×#529	1	4	yes	—
810	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
811	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
812	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
813	C₂²	C₃₁×#585	1	1	yes	characteristic
814	C₂²	C₃₁×#585	1	1	yes	characteristic
815	C₂²	C₃₁×#585	1	1	yes	characteristic
816	C₂²	C₃₁×#585	1	1	yes	characteristic
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	4	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₂	—	2	4	no	—
835	C₂	—	8	2	no	—
836	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
837	C₂	C₃₁×#3455	1	1	yes	characteristic
838	C₂	C₃₁×#3455	1	1	yes	characteristic
839	C₂	C₃₁×#3491	1	1	yes	characteristic
840	C₂	C₃₁×#3491	1	1	yes	characteristic
841	C₂	C₃₁×#3493	1	1	yes	characteristic
842	C₂	C₃₁×#3493	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2855	C₂	semidirect
3. C₃₁×#2853	C₂	semidirect
4. C₃₁×#2646	C₂	semidirect
5. C₃₁×#2643	C₂	semidirect
7. C₃₁×#2533	C₂	semidirect
8. C₃₁×#2532	C₂	semidirect
9. C₃₁×#2531	C₂	semidirect
10. C₃₁×#2530	C₂	semidirect
11. C₃₁×#2529	C₂	semidirect
12. C₃₁×#2528	C₂	semidirect
13. C₃₁×#2527	C₂	semidirect
14. C₃₁×#2526	C₂	semidirect
15. C₃₁×#2329	C₂	semidirect
17. C₃₁×#2318	C₂	semidirect
18. C₄×C₃₁×#123	C₂	semidirect
19. C₂×C₃₁×#376	C₂	semidirect
297. #35099	C₃₁	direct (N × H)
375. #2855	C₂×C₃₁	semidirect
377. #2853	C₂×C₃₁	semidirect
378. #2646	C₂×C₃₁	semidirect
379. #2643	C₂×C₃₁	semidirect
381. #2533	C₂×C₃₁	semidirect
382. #2532	C₂×C₃₁	semidirect
383. #2531	C₂×C₃₁	semidirect
384. #2530	C₂×C₃₁	semidirect
385. #2529	C₂×C₃₁	semidirect
386. #2528	C₂×C₃₁	semidirect
387. #2527	C₂×C₃₁	semidirect
388. #2526	C₂×C₃₁	semidirect
389. #2329	C₂×C₃₁	semidirect
391. #2318	C₂×C₃₁	semidirect
392. C₄×#123	C₂×C₃₁	semidirect
393. C₂×#376	C₂×C₃₁	semidirect
622. C₃₁	#35099	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×#2855	2
C₃₁×#2854	2
C₃₁×#2853	2
C₃₁×#2646	2
C₃₁×#2643	2
C₃₁×#2639	2
C₃₁×#2533	2
C₃₁×#2532	2
C₃₁×#2531	2
C₃₁×#2530	2
C₃₁×#2529	2
C₃₁×#2528	2
C₃₁×#2527	2
C₃₁×#2526	2
C₃₁×#2329	2
C₃₁×#2325	2
C₃₁×#2318	2
C₄×C₃₁×#123	2
C₂×C₃₁×#376	2
#35099	31

Subgroups — C31×#35099 #21491858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35099 #21491858