Subgroups — C₃₁×#36760 #21493519

Order 7936.

1662 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2798	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2783	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2772	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2754	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2725	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2725	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2721	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2716	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2505	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2480	C₂	1	2	yes	maximal
15	C₃₁×#2480	C₂	1	2	yes	maximal
16	C₃₁×#2473	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃₁×#126	C₂²	1	2	yes	—
22	C₂×C₃₁×#126	C₂²	1	2	yes	—
23	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#400	C₂²	1	2	yes	complemented
33	C₃₁×#400	C₂²	1	2	yes	complemented
34	C₃₁×#400	C₂²	1	2	yes	complemented
35	C₃₁×#400	C₂²	1	2	yes	complemented
36	C₃₁×#399	C₂²	1	2	yes	—
37	C₃₁×#399	C₂²	1	2	yes	—
38	C₃₁×#398	C₂²	1	2	yes	complemented
39	C₃₁×#398	C₂²	1	2	yes	complemented
40	C₃₁×#398	C₂²	1	2	yes	complemented
41	C₃₁×#398	C₂²	1	2	yes	complemented
42	C₃₁×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	—
45	C₃₁×#397	C₂²	1	2	yes	—
46	C₃₁×#397	C₂²	1	2	yes	—
47	C₃₁×#397	C₂²	1	2	yes	—
48	C₃₁×#396	C₂²	1	2	yes	—
49	C₃₁×#396	C₂²	1	2	yes	—
50	C₃₁×#396	C₂²	1	2	yes	—
51	C₃₁×#396	C₂²	1	2	yes	—
52	C₃₁×#396	C₂²	1	2	yes	—
53	C₃₁×#396	C₂²	1	2	yes	—
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	complemented
57	C₃₁×#391	C₂²	1	2	yes	complemented
58	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#389	C₂²	1	2	yes	complemented
61	C₃₁×#389	C₂²	1	2	yes	complemented
62	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#389	C₂²	1	2	yes	complemented
65	C₃₁×#389	C₂²	1	2	yes	complemented
66	C₃₁×#389	C₂²	1	2	yes	complemented
67	C₃₁×#389	C₂²	1	2	yes	complemented
68	C₃₁×#388	C₂²	1	2	yes	—
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#388	C₂²	1	2	yes	—
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	2	yes	—
77	C₃₁×#388	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	complemented
79	C₃₁×#387	C₂²	1	2	yes	complemented
80	C₃₁×#387	C₂²	1	2	yes	complemented
81	C₃₁×#387	C₂²	1	2	yes	complemented
82	C₃₁×#387	C₂²	1	2	yes	complemented
83	C₃₁×#387	C₂²	1	2	yes	complemented
84	C₃₁×#387	C₂²	1	2	yes	complemented
85	C₃₁×#387	C₂²	1	2	yes	complemented
86	C₃₁×#387	C₂²	1	2	yes	complemented
87	C₃₁×#387	C₂²	1	2	yes	complemented
88	C₃₁×#385	C₂²	1	2	yes	—
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#385	C₂²	1	2	yes	—
91	C₃₁×#385	C₂²	1	2	yes	—
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#385	C₂²	1	2	yes	—
94	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#382	C₂²	1	2	yes	complemented
97	C₃₁×#380	C₂²	1	1	yes	characteristic
98	C₃₁×#380	C₂²	1	1	yes	characteristic
99	C₃₁×#380	C₂²	1	2	yes	—
100	C₃₁×#380	C₂²	1	2	yes	—
101	C₃₁×#379	C₂²	1	2	yes	—
102	C₃₁×#379	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
106	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
107	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×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	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	—	4	2	no	—
117	C₃₁×#126	—	4	4	no	—
118	C₃₁×#126	—	4	4	no	—
119	C₃₁×#125	—	4	2	no	—
120	C₃₁×#125	—	4	4	no	—
121	C₃₁×C₂²⋊Q₈	—	2	4	no	—
122	C₃₁×C₂²⋊Q₈	—	2	4	no	—
123	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
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	1	yes	characteristic
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
151	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
152	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₃₁	—	4	2	no	—
172	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₃₁	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	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	2	yes	—
206	C₂⁴×C₃₁	—	2	2	no	—
207	C₂⁴×C₃₁	—	2	2	no	—
208	C₂⁴×C₃₁	—	2	2	no	—
209	C₂⁴×C₃₁	—	4	1	no	—
210	C₂⁴×C₃₁	—	4	1	no	—
211	C₂⁴×C₃₁	—	4	1	no	—
212	C₂⁴×C₃₁	—	4	1	no	—
213	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
214	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂×Q₈×C₃₁	—	2	2	no	—
216	C₂×Q₈×C₃₁	—	2	2	no	—
217	C₂×Q₈×C₃₁	—	4	1	no	—
218	C₂×Q₈×C₃₁	—	4	1	no	—
219	C₂×Q₈×C₃₁	—	4	1	no	—
220	C₂×Q₈×C₃₁	—	4	1	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	2	no	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
232	C₂²×C₄×C₃₁	—	4	1	no	—
233	C₂²×C₄×C₃₁	—	4	1	no	—
234	C₂²×C₄×C₃₁	—	4	1	no	—
235	C₂²×C₄×C₃₁	—	4	1	no	—
236	C₂²×C₄×C₃₁	—	4	1	no	—
237	C₂²×C₄×C₃₁	—	4	1	no	—
238	C₂²×C₄×C₃₁	#41	1	4	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	4	no	—
260	C₄⋊C₄×C₃₁	—	2	4	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	—	2	4	no	—
263	C₄⋊C₄×C₃₁	—	2	4	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	4	2	no	—
266	C₄⋊C₄×C₃₁	—	4	1	no	—
267	C₄⋊C₄×C₃₁	—	4	1	no	—
268	C₄⋊C₄×C₃₁	—	4	2	no	—
269	C₄⋊C₄×C₃₁	—	4	2	no	—
270	C₄⋊C₄×C₃₁	—	4	2	no	—
271	C₄⋊C₄×C₃₁	—	4	2	no	—
272	C₄⋊C₄×C₃₁	—	4	2	no	—
273	C₄⋊C₄×C₃₁	—	4	1	no	—
274	C₄⋊C₄×C₃₁	—	4	1	no	—
275	C₄⋊C₄×C₃₁	—	4	2	no	—
276	C₄⋊C₄×C₃₁	—	4	2	no	—
277	C₄⋊C₄×C₃₁	—	4	2	no	—
278	C₄⋊C₄×C₃₁	—	4	2	no	—
279	C₄⋊C₄×C₃₁	—	4	2	no	—
280	C₄⋊C₄×C₃₁	—	4	2	no	—
281	C₄⋊C₄×C₃₁	—	4	2	no	—
282	C₂²⋊C₄×C₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	4	2	no	—
291	C₂²⋊C₄×C₃₁	—	4	2	no	—
292	C₂²⋊C₄×C₃₁	—	4	2	no	—
293	C₂²⋊C₄×C₃₁	—	4	2	no	—
294	C₂²⋊C₄×C₃₁	—	4	2	no	—
295	C₂²⋊C₄×C₃₁	—	4	2	no	—
296	C₂²⋊C₄×C₃₁	—	4	2	no	—
297	C₂²⋊C₄×C₃₁	—	4	2	no	—
298	C₂²⋊C₄×C₃₁	—	4	2	no	—
299	C₂²⋊C₄×C₃₁	—	4	2	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	—	4	1	no	—
303	C₄²×C₃₁	—	4	1	no	—
304	C₄²×C₃₁	—	4	2	no	—
305	C₄²×C₃₁	—	4	2	no	—
306	C₄²×C₃₁	—	4	2	no	—
307	C₄²×C₃₁	—	4	2	no	—
308	#36760	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂³×C₃₁	—	2	1	no	—
310	C₂³×C₃₁	—	2	1	no	—
311	C₂³×C₃₁	—	2	1	no	—
312	C₂³×C₃₁	—	2	1	no	—
313	C₂³×C₃₁	—	2	2	no	—
314	C₂³×C₃₁	—	2	2	no	—
315	C₂³×C₃₁	—	2	2	no	—
316	C₂³×C₃₁	—	2	2	no	—
317	C₂³×C₃₁	—	2	2	no	—
318	C₂³×C₃₁	—	2	2	no	—
319	C₂³×C₃₁	—	2	2	no	—
320	C₂³×C₃₁	—	4	4	no	—
321	C₂³×C₃₁	—	4	4	no	—
322	C₂³×C₃₁	—	4	4	no	—
323	C₂³×C₃₁	—	8	2	no	—
324	C₂³×C₃₁	—	8	2	no	—
325	C₂³×C₃₁	—	8	2	no	—
326	C₂³×C₃₁	—	8	2	no	—
327	C₂³×C₃₁	C₂×#41	1	2	yes	—
328	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
329	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
330	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
331	Q₈×C₃₁	—	8	2	no	—
332	Q₈×C₃₁	—	8	2	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	1	no	—
338	C₂×C₄×C₃₁	—	2	1	no	—
339	C₂×C₄×C₃₁	—	2	1	no	—
340	C₂×C₄×C₃₁	—	2	1	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	1	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	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	4	4	no	—
381	C₂×C₄×C₃₁	—	4	4	no	—
382	C₂×C₄×C₃₁	—	4	4	no	—
383	C₂×C₄×C₃₁	—	4	4	no	—
384	C₂×C₄×C₃₁	—	8	2	no	—
385	C₂×C₄×C₃₁	—	8	2	no	—
386	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
387	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
388	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
389	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
390	#2857	C₂×C₃₁	1	1	yes	characteristic, complemented
391	#2851	C₂×C₃₁	1	1	yes	characteristic, complemented
392	#2798	C₂×C₃₁	1	2	yes	complemented
393	#2783	C₂×C₃₁	1	2	yes	complemented
394	#2772	C₂×C₃₁	1	2	yes	complemented
395	#2754	C₂×C₃₁	1	2	yes	complemented
396	#2725	C₂×C₃₁	1	2	yes	complemented
397	#2725	C₂×C₃₁	1	2	yes	complemented
398	#2721	C₂×C₃₁	1	2	yes	complemented
399	#2716	C₂×C₃₁	1	2	yes	complemented
400	#2626	C₂×C₃₁	1	1	yes	characteristic
401	#2626	C₂×C₃₁	1	1	yes	characteristic
402	#2505	C₂×C₃₁	1	2	yes	complemented
403	#2480	C₂×C₃₁	1	2	yes	—
404	#2480	C₂×C₃₁	1	2	yes	—
405	#2473	C₂×C₃₁	1	2	yes	complemented
406	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
408	C₂×#388	C₂×C₃₁	1	1	yes	characteristic
409	C₂²×C₃₁	—	2	2	no	—
410	C₂²×C₃₁	—	2	2	no	—
411	C₂²×C₃₁	—	2	2	no	—
412	C₂²×C₃₁	—	2	2	no	—
413	C₂²×C₃₁	—	2	2	no	—
414	C₂²×C₃₁	—	2	2	no	—
415	C₂²×C₃₁	—	4	2	no	—
416	C₂²×C₃₁	—	4	2	no	—
417	C₂²×C₃₁	—	4	2	no	—
418	C₂²×C₃₁	—	4	2	no	—
419	C₂²×C₃₁	—	4	2	no	—
420	C₂²×C₃₁	—	4	2	no	—
421	C₂²×C₃₁	—	4	2	no	—
422	C₂²×C₃₁	—	8	8	no	—
423	C₂²×C₃₁	#541	1	4	yes	—
424	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
429	C₂²×C₃₁	#585	1	1	yes	characteristic
430	C₂²×C₃₁	#585	1	1	yes	characteristic
431	C₄×C₃₁	—	2	2	no	—
432	C₄×C₃₁	—	2	2	no	—
433	C₄×C₃₁	—	2	2	no	—
434	C₄×C₃₁	—	2	2	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	2	no	—
437	C₄×C₃₁	—	4	2	no	—
438	C₄×C₃₁	—	4	2	no	—
439	C₄×C₃₁	—	4	2	no	—
440	C₄×C₃₁	—	4	2	no	—
441	C₄×C₃₁	—	4	1	no	—
442	C₄×C₃₁	—	4	2	no	—
443	C₄×C₃₁	—	4	1	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	—	4	2	no	—
446	C₄×C₃₁	—	4	2	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
449	C₂×#126	C₂²×C₃₁	1	2	yes	—
450	C₂×#126	C₂²×C₃₁	1	2	yes	—
451	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
453	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
455	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
457	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
458	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
459	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
460	#400	C₂²×C₃₁	1	2	yes	complemented
461	#400	C₂²×C₃₁	1	2	yes	complemented
462	#400	C₂²×C₃₁	1	2	yes	complemented
463	#400	C₂²×C₃₁	1	2	yes	complemented
464	#399	C₂²×C₃₁	1	2	yes	—
465	#399	C₂²×C₃₁	1	2	yes	—
466	#398	C₂²×C₃₁	1	2	yes	complemented
467	#398	C₂²×C₃₁	1	2	yes	complemented
468	#398	C₂²×C₃₁	1	2	yes	complemented
469	#398	C₂²×C₃₁	1	2	yes	complemented
470	#397	C₂²×C₃₁	1	2	yes	—
471	#397	C₂²×C₃₁	1	2	yes	—
472	#397	C₂²×C₃₁	1	2	yes	—
473	#397	C₂²×C₃₁	1	2	yes	—
474	#397	C₂²×C₃₁	1	2	yes	—
475	#397	C₂²×C₃₁	1	2	yes	—
476	#396	C₂²×C₃₁	1	2	yes	—
477	#396	C₂²×C₃₁	1	2	yes	—
478	#396	C₂²×C₃₁	1	2	yes	—
479	#396	C₂²×C₃₁	1	2	yes	—
480	#396	C₂²×C₃₁	1	2	yes	—
481	#396	C₂²×C₃₁	1	2	yes	—
482	#393	C₂²×C₃₁	1	2	yes	—
483	#393	C₂²×C₃₁	1	2	yes	—
484	#391	C₂²×C₃₁	1	2	yes	complemented
485	#391	C₂²×C₃₁	1	2	yes	complemented
486	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
487	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
488	#389	C₂²×C₃₁	1	2	yes	complemented
489	#389	C₂²×C₃₁	1	2	yes	complemented
490	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
491	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
492	#389	C₂²×C₃₁	1	2	yes	complemented
493	#389	C₂²×C₃₁	1	2	yes	complemented
494	#389	C₂²×C₃₁	1	2	yes	complemented
495	#389	C₂²×C₃₁	1	2	yes	complemented
496	#388	C₂²×C₃₁	1	2	yes	—
497	#388	C₂²×C₃₁	1	2	yes	—
498	#388	C₂²×C₃₁	1	2	yes	—
499	#388	C₂²×C₃₁	1	2	yes	—
500	#388	C₂²×C₃₁	1	2	yes	—
501	#388	C₂²×C₃₁	1	2	yes	—
502	#388	C₂²×C₃₁	1	2	yes	—
503	#388	C₂²×C₃₁	1	2	yes	—
504	#388	C₂²×C₃₁	1	2	yes	—
505	#388	C₂²×C₃₁	1	2	yes	—
506	#387	C₂²×C₃₁	1	2	yes	complemented
507	#387	C₂²×C₃₁	1	2	yes	complemented
508	#387	C₂²×C₃₁	1	2	yes	complemented
509	#387	C₂²×C₃₁	1	2	yes	complemented
510	#387	C₂²×C₃₁	1	2	yes	complemented
511	#387	C₂²×C₃₁	1	2	yes	complemented
512	#387	C₂²×C₃₁	1	2	yes	complemented
513	#387	C₂²×C₃₁	1	2	yes	complemented
514	#387	C₂²×C₃₁	1	2	yes	complemented
515	#387	C₂²×C₃₁	1	2	yes	complemented
516	#385	C₂²×C₃₁	1	2	yes	—
517	#385	C₂²×C₃₁	1	2	yes	—
518	#385	C₂²×C₃₁	1	2	yes	—
519	#385	C₂²×C₃₁	1	2	yes	—
520	#385	C₂²×C₃₁	1	2	yes	—
521	#385	C₂²×C₃₁	1	2	yes	—
522	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
523	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
524	#382	C₂²×C₃₁	1	2	yes	complemented
525	#380	C₂²×C₃₁	1	1	yes	characteristic
526	#380	C₂²×C₃₁	1	1	yes	characteristic
527	#380	C₂²×C₃₁	1	2	yes	—
528	#380	C₂²×C₃₁	1	2	yes	—
529	#379	C₂²×C₃₁	1	2	yes	—
530	#379	C₂²×C₃₁	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
533	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
534	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
535	C₂×C₃₁	—	2	4	no	—
536	C₂×C₃₁	—	8	2	no	—
537	C₂×C₃₁	C₂×#541	1	1	yes	characteristic
538	C₂×C₃₁	#3505	1	1	yes	characteristic
539	C₂×C₃₁	#3506	1	1	yes	characteristic
540	C₂×C₃₁	#3535	1	1	yes	characteristic
541	C₂×C₃₁	#3536	1	1	yes	characteristic
542	C₂×C₃₁	#3561	1	1	yes	characteristic
543	C₂×C₃₁	#3564	1	1	yes	characteristic
544	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
553	C₄⋊Q₈	—	4	2	no	—
554	#126	—	4	4	no	—
555	#126	—	4	4	no	—
556	#125	—	4	2	no	—
557	#125	—	4	4	no	—
558	C₂²⋊Q₈	—	2	4	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂×C₄⋊C₄	—	4	2	no	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₂²⋊C₄	—	2	4	no	—
588	C₂×C₂²⋊C₄	—	4	2	no	—
589	C₂×C₂²⋊C₄	—	4	2	no	—
590	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
608	C₂×C₄²	—	4	2	no	—
609	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
612	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
614	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	#95	C₂³×C₃₁	1	2	yes	—
623	#95	C₂³×C₃₁	1	2	yes	—
624	#95	C₂³×C₃₁	1	2	yes	—
625	#95	C₂³×C₃₁	1	2	yes	—
626	#95	C₂³×C₃₁	1	2	yes	—
627	#95	C₂³×C₃₁	1	2	yes	—
628	#95	C₂³×C₃₁	1	2	yes	—
629	#95	C₂³×C₃₁	1	2	yes	—
630	#95	C₂³×C₃₁	1	2	yes	—
631	#95	C₂³×C₃₁	1	2	yes	—
632	#95	C₂³×C₃₁	1	2	yes	—
633	#95	C₂³×C₃₁	1	2	yes	—
634	#95	C₂³×C₃₁	1	2	yes	—
635	#95	C₂³×C₃₁	1	2	yes	—
636	#95	C₂³×C₃₁	1	2	yes	—
637	#95	C₂³×C₃₁	1	2	yes	—
638	#95	C₂³×C₃₁	1	2	yes	—
639	#95	C₂³×C₃₁	1	2	yes	—
640	#95	C₂³×C₃₁	1	2	yes	—
641	#95	C₂³×C₃₁	1	2	yes	—
642	#95	C₂³×C₃₁	1	2	yes	—
643	C₃₁	#36760	1	1	yes	characteristic, direct product factor, Sylow
644	C₂⁴	—	2	2	no	—
645	C₂⁴	—	2	2	no	—
646	C₂⁴	—	2	2	no	—
647	C₂⁴	—	4	1	no	—
648	C₂⁴	—	4	1	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	—	4	1	no	—
651	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
652	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	4	1	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂×Q₈	—	4	1	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	#41×C₃₁	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	1	no	—
712	C₄⋊C₄	—	4	1	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	4	1	no	—
741	C₄²	—	4	1	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	2	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	2	no	—
763	C₂³	—	8	2	no	—
764	C₂³	C₂×#41×C₃₁	1	2	yes	—
765	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
766	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
767	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
768	Q₈	—	8	2	no	—
769	Q₈	—	8	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	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	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
824	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
825	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
826	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	8	no	—
841	C₂²	C₃₁×#541	1	4	yes	—
842	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
843	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
845	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
847	C₂²	C₃₁×#585	1	1	yes	characteristic
848	C₂²	C₃₁×#585	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₂	—	2	4	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₃₁×#541	1	1	yes	characteristic
869	C₂	C₃₁×#3505	1	1	yes	characteristic
870	C₂	C₃₁×#3506	1	1	yes	characteristic
871	C₂	C₃₁×#3535	1	1	yes	characteristic
872	C₂	C₃₁×#3536	1	1	yes	characteristic
873	C₂	C₃₁×#3561	1	1	yes	characteristic
874	C₂	C₃₁×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
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×#2857	C₂	semidirect
2. C₃₁×#2851	C₂	semidirect
3. C₃₁×#2798	C₂	semidirect
4. C₃₁×#2783	C₂	semidirect
5. C₃₁×#2772	C₂	semidirect
6. C₃₁×#2754	C₂	semidirect
7. C₃₁×#2725	C₂	semidirect
8. C₃₁×#2725	C₂	semidirect
9. C₃₁×#2721	C₂	semidirect
10. C₃₁×#2716	C₂	semidirect
13. C₃₁×#2505	C₂	semidirect
16. C₃₁×#2473	C₂	semidirect
17. C₃₁×#2329	C₂	semidirect
18. C₃₁×#2329	C₂	semidirect
20. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₃₁×#125	C₂²	semidirect
24. C₂×C₃₁×#125	C₂²	semidirect
32. C₃₁×#400	C₂²	semidirect
33. C₃₁×#400	C₂²	semidirect
34. C₃₁×#400	C₂²	semidirect
35. C₃₁×#400	C₂²	semidirect
38. C₃₁×#398	C₂²	semidirect
39. C₃₁×#398	C₂²	semidirect
40. C₃₁×#398	C₂²	semidirect
41. C₃₁×#398	C₂²	semidirect
56. C₃₁×#391	C₂²	semidirect
57. C₃₁×#391	C₂²	semidirect
58. C₃₁×#391	C₂²	semidirect
59. C₃₁×#391	C₂²	semidirect
60. C₃₁×#389	C₂²	semidirect
61. C₃₁×#389	C₂²	semidirect
62. C₃₁×#389	C₂²	semidirect
63. C₃₁×#389	C₂²	semidirect
64. C₃₁×#389	C₂²	semidirect
65. C₃₁×#389	C₂²	semidirect
66. C₃₁×#389	C₂²	semidirect
67. C₃₁×#389	C₂²	semidirect
78. C₃₁×#387	C₂²	semidirect
79. C₃₁×#387	C₂²	semidirect
80. C₃₁×#387	C₂²	semidirect
81. C₃₁×#387	C₂²	semidirect
82. C₃₁×#387	C₂²	semidirect
83. C₃₁×#387	C₂²	semidirect
84. C₃₁×#387	C₂²	semidirect
85. C₃₁×#387	C₂²	semidirect
86. C₃₁×#387	C₂²	semidirect
87. C₃₁×#387	C₂²	semidirect
94. C₃₁×#384	C₂²	semidirect
95. C₃₁×#382	C₂²	semidirect
96. C₃₁×#382	C₂²	semidirect
308. #36760	C₃₁	direct (N × H)
390. #2857	C₂×C₃₁	semidirect
391. #2851	C₂×C₃₁	semidirect
392. #2798	C₂×C₃₁	semidirect
393. #2783	C₂×C₃₁	semidirect
394. #2772	C₂×C₃₁	semidirect
395. #2754	C₂×C₃₁	semidirect
396. #2725	C₂×C₃₁	semidirect
397. #2725	C₂×C₃₁	semidirect
398. #2721	C₂×C₃₁	semidirect
399. #2716	C₂×C₃₁	semidirect
402. #2505	C₂×C₃₁	semidirect
405. #2473	C₂×C₃₁	semidirect
406. #2329	C₂×C₃₁	semidirect
407. #2329	C₂×C₃₁	semidirect
448. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
451. C₂×#125	C₂²×C₃₁	semidirect
452. C₂×#125	C₂²×C₃₁	semidirect
460. #400	C₂²×C₃₁	semidirect
461. #400	C₂²×C₃₁	semidirect
462. #400	C₂²×C₃₁	semidirect
463. #400	C₂²×C₃₁	semidirect
466. #398	C₂²×C₃₁	semidirect
467. #398	C₂²×C₃₁	semidirect
468. #398	C₂²×C₃₁	semidirect
469. #398	C₂²×C₃₁	semidirect
484. #391	C₂²×C₃₁	semidirect
485. #391	C₂²×C₃₁	semidirect
486. #391	C₂²×C₃₁	semidirect
487. #391	C₂²×C₃₁	semidirect
488. #389	C₂²×C₃₁	semidirect
489. #389	C₂²×C₃₁	semidirect
490. #389	C₂²×C₃₁	semidirect
491. #389	C₂²×C₃₁	semidirect
492. #389	C₂²×C₃₁	semidirect
493. #389	C₂²×C₃₁	semidirect
494. #389	C₂²×C₃₁	semidirect
495. #389	C₂²×C₃₁	semidirect
506. #387	C₂²×C₃₁	semidirect
507. #387	C₂²×C₃₁	semidirect
508. #387	C₂²×C₃₁	semidirect
509. #387	C₂²×C₃₁	semidirect
510. #387	C₂²×C₃₁	semidirect
511. #387	C₂²×C₃₁	semidirect
512. #387	C₂²×C₃₁	semidirect
513. #387	C₂²×C₃₁	semidirect
514. #387	C₂²×C₃₁	semidirect
515. #387	C₂²×C₃₁	semidirect
522. #384	C₂²×C₃₁	semidirect
523. #382	C₂²×C₃₁	semidirect
524. #382	C₂²×C₃₁	semidirect
643. C₃₁	#36760	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×#2857	2
C₃₁×#2851	2
C₃₁×#2798	2
C₃₁×#2783	2
C₃₁×#2772	2
C₃₁×#2754	2
C₃₁×#2725	2
C₃₁×#2721	2
C₃₁×#2716	2
C₃₁×#2626	2
C₃₁×#2505	2
C₃₁×#2480	2
C₃₁×#2473	2
C₃₁×#2329	2
C₂×C₃₁×#388	2
#36760	31

Subgroups — C31×#36760 #21493519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36760 #21493519