Subgroups — C₃₁×#34521 #21491280

Order 7936.

2008 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#563	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2383	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2373	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2372	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2371	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2369	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2368	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2362	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2359	C₂	1	2	yes	maximal
11	C₃₁×#2335	C₂	1	2	yes	maximal
12	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2330	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2326	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2323	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₃₁×#126	C₂	1	2	yes	maximal, complemented
20	C₃₁×#563	C₄	1	16	yes	complemented
21	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#126	C₂²	1	2	yes	—
24	C₂×C₃₁×#126	C₂²	1	2	yes	—
25	C₂×C₃₁×#125	C₂²	1	2	yes	—
26	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#123	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#117	C₂²	1	2	yes	—
35	C₃₁×#391	C₂²	1	1	yes	characteristic
36	C₃₁×#391	C₂²	1	1	yes	characteristic
37	C₃₁×#391	C₂²	1	2	yes	—
38	C₃₁×#391	C₂²	1	1	yes	characteristic
39	C₃₁×#391	C₂²	1	1	yes	characteristic
40	C₃₁×#391	C₂²	1	1	yes	characteristic
41	C₃₁×#391	C₂²	1	2	yes	—
42	C₃₁×#390	C₂²	1	1	yes	characteristic
43	C₃₁×#389	C₂²	1	2	yes	—
44	C₃₁×#389	C₂²	1	2	yes	—
45	C₃₁×#389	C₂²	1	2	yes	—
46	C₃₁×#389	C₂²	1	2	yes	—
47	C₃₁×#389	C₂²	1	2	yes	—
48	C₃₁×#389	C₂²	1	2	yes	—
49	C₃₁×#389	C₂²	1	2	yes	—
50	C₃₁×#389	C₂²	1	2	yes	—
51	C₃₁×#388	C₂²	1	2	yes	—
52	C₃₁×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	—
62	C₃₁×#387	C₂²	1	2	yes	—
63	C₃₁×#387	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×#385	C₂²	1	2	yes	—
79	C₃₁×#385	C₂²	1	2	yes	—
80	C₃₁×#385	C₂²	1	2	yes	—
81	C₃₁×#385	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#384	C₂²	1	1	yes	characteristic
84	C₃₁×#384	C₂²	1	1	yes	characteristic
85	C₃₁×#383	C₂²	1	2	yes	—
86	C₃₁×#382	C₂²	1	1	yes	characteristic
87	C₃₁×#380	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
96	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₃₁×#376	C₂²	1	1	yes	characteristic
104	C₃₁×#376	C₂²	1	1	yes	characteristic
105	C₃₁×#376	C₂²	1	2	yes	—
106	C₂×C₃₁×#95	C₂²	1	2	yes	—
107	C₄³×C₃₁	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
113	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
114	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
116	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
117	C₃₁×#126	C₂×C₄	1	16	yes	complemented
118	C₃₁×#126	C₂×C₄	1	16	yes	complemented
119	C₃₁×#125	C₂×C₄	1	16	yes	complemented
120	C₃₁×#124	C₂×C₄	1	8	yes	—
121	C₃₁×#123	C₂×C₄	1	16	yes	—
122	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
123	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
124	C₄×Q₈×C₃₁	—	4	2	no	—
125	C₄×Q₈×C₃₁	—	4	2	no	—
126	C₄×Q₈×C₃₁	—	4	2	no	—
127	C₄×D₄×C₃₁	—	4	2	no	—
128	C₃₁×#117	—	4	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄⋊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×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×C₄²×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#95	C₂³	1	2	yes	—
207	C₃₁×#95	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	2	yes	—
209	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₃₁	—	4	1	no	—
211	C₂×Q₈×C₃₁	—	4	1	no	—
212	C₂×Q₈×C₃₁	—	4	1	no	—
213	C₂×Q₈×C₃₁	—	4	1	no	—
214	C₂×Q₈×C₃₁	—	4	1	no	—
215	C₂×Q₈×C₃₁	—	4	1	no	—
216	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
217	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
218	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
219	C₂×D₄×C₃₁	—	4	1	no	—
220	C₂×D₄×C₃₁	—	4	1	no	—
221	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
222	C₂²×C₄×C₃₁	—	2	4	no	—
223	C₂²×C₄×C₃₁	—	4	2	no	—
224	C₂²×C₄×C₃₁	—	4	2	no	—
225	C₂²×C₄×C₃₁	—	4	2	no	—
226	C₂²×C₄×C₃₁	—	4	2	no	—
227	C₂²×C₄×C₃₁	—	4	2	no	—
228	C₂²×C₄×C₃₁	—	4	2	no	—
229	C₂²×C₄×C₃₁	—	4	2	no	—
230	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
231	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	4	2	no	—
252	C₄⋊C₄×C₃₁	—	4	2	no	—
253	C₄⋊C₄×C₃₁	—	4	2	no	—
254	C₄⋊C₄×C₃₁	—	4	2	no	—
255	C₄⋊C₄×C₃₁	—	4	2	no	—
256	C₄⋊C₄×C₃₁	—	4	2	no	—
257	C₄⋊C₄×C₃₁	—	4	2	no	—
258	C₄⋊C₄×C₃₁	—	4	1	no	—
259	C₄⋊C₄×C₃₁	—	4	2	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	1	no	—
264	C₄⋊C₄×C₃₁	—	4	1	no	—
265	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
266	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
267	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
268	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
269	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
270	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
271	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
272	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	4	2	no	—
276	C₂²⋊C₄×C₃₁	—	4	2	no	—
277	C₂²⋊C₄×C₃₁	—	4	2	no	—
278	C₂²⋊C₄×C₃₁	—	4	2	no	—
279	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
280	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
281	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
282	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
283	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
284	C₄²×C₃₁	—	2	4	no	—
285	C₄²×C₃₁	—	2	2	no	—
286	C₄²×C₃₁	—	2	2	no	—
287	C₄²×C₃₁	—	2	2	no	—
288	C₄²×C₃₁	—	2	4	no	—
289	C₄²×C₃₁	—	2	4	no	—
290	C₄²×C₃₁	—	4	2	no	—
291	C₄²×C₃₁	—	4	2	no	—
292	C₄²×C₃₁	—	4	1	no	—
293	C₄²×C₃₁	—	4	2	no	—
294	C₄²×C₃₁	—	4	2	no	—
295	C₄²×C₃₁	—	4	2	no	—
296	C₄²×C₃₁	—	4	1	no	—
297	C₄²×C₃₁	—	4	1	no	—
298	C₄²×C₃₁	—	4	2	no	—
299	C₄²×C₃₁	—	4	2	no	—
300	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
301	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
302	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
303	#34521	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
310	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
311	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
312	Q₈×C₃₁	—	4	4	no	—
313	Q₈×C₃₁	—	4	4	no	—
314	Q₈×C₃₁	—	4	4	no	—
315	D₄×C₃₁	—	4	4	no	—
316	C₂×C₄×C₃₁	—	2	2	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	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	1	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	1	no	—
338	C₂×C₄×C₃₁	—	2	1	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	2	no	—
347	C₂×C₄×C₃₁	—	2	2	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	—	4	8	no	—
357	C₂×C₄×C₃₁	—	8	4	no	—
358	C₂×C₄×C₃₁	—	8	4	no	—
359	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
360	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
361	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
362	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
363	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
364	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
365	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
366	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
367	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
368	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
369	C₂×#563	C₂×C₃₁	1	1	yes	characteristic
370	#2383	C₂×C₃₁	1	2	yes	complemented
371	#2381	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#2373	C₂×C₃₁	1	2	yes	complemented
373	#2372	C₂×C₃₁	1	1	yes	characteristic
374	#2371	C₂×C₃₁	1	2	yes	complemented
375	#2369	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#2368	C₂×C₃₁	1	2	yes	complemented
377	#2362	C₂×C₃₁	1	2	yes	complemented
378	#2359	C₂×C₃₁	1	2	yes	—
379	#2335	C₂×C₃₁	1	2	yes	—
380	#2334	C₂×C₃₁	1	2	yes	complemented
381	#2330	C₂×C₃₁	1	2	yes	complemented
382	#2329	C₂×C₃₁	1	2	yes	complemented
383	#2327	C₂×C₃₁	1	1	yes	characteristic, complemented
384	#2326	C₂×C₃₁	1	1	yes	characteristic
385	#2323	C₂×C₃₁	1	2	yes	complemented
386	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
387	C₄×#126	C₂×C₃₁	1	2	yes	complemented
388	C₂²×C₃₁	—	2	4	no	—
389	C₂²×C₃₁	—	2	4	no	—
390	C₂²×C₃₁	—	2	4	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	4	2	no	—
393	C₂²×C₃₁	—	4	2	no	—
394	C₂²×C₃₁	—	4	2	no	—
395	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
396	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
398	C₂²×C₃₁	#585	1	1	yes	characteristic
399	C₂²×C₃₁	#585	1	2	yes	—
400	C₄×C₃₁	—	2	4	no	—
401	C₄×C₃₁	—	2	4	no	—
402	C₄×C₃₁	—	2	2	no	—
403	C₄×C₃₁	—	2	2	no	—
404	C₄×C₃₁	—	2	2	no	—
405	C₄×C₃₁	—	2	4	no	—
406	C₄×C₃₁	—	2	4	no	—
407	C₄×C₃₁	—	2	4	no	—
408	C₄×C₃₁	—	2	2	no	—
409	C₄×C₃₁	—	2	4	no	—
410	C₄×C₃₁	—	4	2	no	—
411	C₄×C₃₁	—	4	1	no	—
412	C₄×C₃₁	—	4	2	no	—
413	C₄×C₃₁	—	4	1	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	1	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	2	no	—
418	#563	C₄×C₃₁	1	16	yes	complemented
419	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
420	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
421	C₂×#126	C₂²×C₃₁	1	2	yes	—
422	C₂×#126	C₂²×C₃₁	1	2	yes	—
423	C₂×#125	C₂²×C₃₁	1	2	yes	—
424	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
425	C₂×#123	C₂²×C₃₁	1	2	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
427	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
428	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×#117	C₂²×C₃₁	1	2	yes	—
433	#391	C₂²×C₃₁	1	1	yes	characteristic
434	#391	C₂²×C₃₁	1	1	yes	characteristic
435	#391	C₂²×C₃₁	1	2	yes	—
436	#391	C₂²×C₃₁	1	1	yes	characteristic
437	#391	C₂²×C₃₁	1	1	yes	characteristic
438	#391	C₂²×C₃₁	1	1	yes	characteristic
439	#391	C₂²×C₃₁	1	2	yes	—
440	#390	C₂²×C₃₁	1	1	yes	characteristic
441	#389	C₂²×C₃₁	1	2	yes	—
442	#389	C₂²×C₃₁	1	2	yes	—
443	#389	C₂²×C₃₁	1	2	yes	—
444	#389	C₂²×C₃₁	1	2	yes	—
445	#389	C₂²×C₃₁	1	2	yes	—
446	#389	C₂²×C₃₁	1	2	yes	—
447	#389	C₂²×C₃₁	1	2	yes	—
448	#389	C₂²×C₃₁	1	2	yes	—
449	#388	C₂²×C₃₁	1	2	yes	—
450	#388	C₂²×C₃₁	1	2	yes	—
451	#388	C₂²×C₃₁	1	2	yes	—
452	#388	C₂²×C₃₁	1	2	yes	—
453	#388	C₂²×C₃₁	1	2	yes	—
454	#388	C₂²×C₃₁	1	2	yes	—
455	#388	C₂²×C₃₁	1	2	yes	—
456	#388	C₂²×C₃₁	1	2	yes	—
457	#388	C₂²×C₃₁	1	2	yes	—
458	#388	C₂²×C₃₁	1	2	yes	—
459	#387	C₂²×C₃₁	1	2	yes	—
460	#387	C₂²×C₃₁	1	2	yes	—
461	#387	C₂²×C₃₁	1	2	yes	—
462	#387	C₂²×C₃₁	1	2	yes	—
463	#387	C₂²×C₃₁	1	2	yes	—
464	#387	C₂²×C₃₁	1	2	yes	—
465	#387	C₂²×C₃₁	1	2	yes	—
466	#387	C₂²×C₃₁	1	2	yes	—
467	#387	C₂²×C₃₁	1	2	yes	—
468	#387	C₂²×C₃₁	1	2	yes	—
469	#387	C₂²×C₃₁	1	2	yes	—
470	#387	C₂²×C₃₁	1	2	yes	—
471	#387	C₂²×C₃₁	1	2	yes	—
472	#387	C₂²×C₃₁	1	2	yes	—
473	#387	C₂²×C₃₁	1	2	yes	—
474	#387	C₂²×C₃₁	1	2	yes	—
475	#386	C₂²×C₃₁	1	2	yes	—
476	#385	C₂²×C₃₁	1	2	yes	—
477	#385	C₂²×C₃₁	1	2	yes	—
478	#385	C₂²×C₃₁	1	2	yes	—
479	#385	C₂²×C₃₁	1	2	yes	—
480	#385	C₂²×C₃₁	1	2	yes	—
481	#384	C₂²×C₃₁	1	1	yes	characteristic
482	#384	C₂²×C₃₁	1	1	yes	characteristic
483	#383	C₂²×C₃₁	1	2	yes	—
484	#382	C₂²×C₃₁	1	1	yes	characteristic
485	#380	C₂²×C₃₁	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
492	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
501	#376	C₂²×C₃₁	1	1	yes	characteristic
502	#376	C₂²×C₃₁	1	1	yes	characteristic
503	#376	C₂²×C₃₁	1	2	yes	—
504	C₂×#95	C₂²×C₃₁	1	2	yes	—
505	C₄³	C₂²×C₃₁	1	1	yes	characteristic
506	C₂×C₃₁	—	4	4	no	—
507	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂×C₃₁	C₄×2₋¹⁺⁴	1	2	yes	—
509	C₂×C₃₁	#3544	1	1	yes	characteristic
510	C₂×C₃₁	#3551	1	1	yes	characteristic
511	C₂×C₃₁	#3564	1	2	yes	—
512	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
517	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
518	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
519	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
520	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
521	#126	C₂×C₄×C₃₁	1	16	yes	complemented
522	#126	C₂×C₄×C₃₁	1	16	yes	complemented
523	#125	C₂×C₄×C₃₁	1	16	yes	complemented
524	#124	C₂×C₄×C₃₁	1	8	yes	—
525	#123	C₂×C₄×C₃₁	1	16	yes	—
526	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
527	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
528	C₄×Q₈	—	4	2	no	—
529	C₄×Q₈	—	4	2	no	—
530	C₄×Q₈	—	4	2	no	—
531	C₄×D₄	—	4	2	no	—
532	#117	—	4	4	no	—
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
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	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₂²⋊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×C₄²	C₂³×C₃₁	1	2	yes	—
569	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
573	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
575	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
578	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	#95	C₂³×C₃₁	1	2	yes	—
588	#95	C₂³×C₃₁	1	2	yes	—
589	#95	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	C₃₁	#34521	1	1	yes	characteristic, direct product factor, Sylow
614	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
615	C₂×Q₈	—	4	1	no	—
616	C₂×Q₈	—	4	1	no	—
617	C₂×Q₈	—	4	1	no	—
618	C₂×Q₈	—	4	1	no	—
619	C₂×Q₈	—	4	1	no	—
620	C₂×Q₈	—	4	1	no	—
621	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
622	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
623	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
624	C₂×D₄	—	4	1	no	—
625	C₂×D₄	—	4	1	no	—
626	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
636	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	1	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	1	no	—
668	C₄⋊C₄	—	4	1	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
671	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
672	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
673	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
674	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
675	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
676	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
677	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
688	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	1	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	1	no	—
702	C₄²	—	4	1	no	—
703	C₄²	—	4	2	no	—
704	C₄²	—	4	2	no	—
705	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
706	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
707	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
715	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
716	Q₈	—	4	4	no	—
717	Q₈	—	4	4	no	—
718	Q₈	—	4	4	no	—
719	D₄	—	4	4	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	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	—	4	8	no	—
761	C₂×C₄	—	8	4	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
764	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
765	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
766	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
767	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
768	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
769	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
770	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
771	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
772	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
781	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
782	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
783	C₂²	C₃₁×#585	1	1	yes	characteristic
784	C₂²	C₃₁×#585	1	2	yes	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	4	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₂	—	4	4	no	—
804	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
805	C₂	C₄×C₃₁×2₋¹⁺⁴	1	2	yes	—
806	C₂	C₃₁×#3544	1	1	yes	characteristic
807	C₂	C₃₁×#3551	1	1	yes	characteristic
808	C₂	C₃₁×#3564	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2383	C₂	semidirect
3. C₃₁×#2381	C₂	semidirect
4. C₃₁×#2373	C₂	semidirect
6. C₃₁×#2371	C₂	semidirect
7. C₃₁×#2369	C₂	semidirect
8. C₃₁×#2368	C₂	semidirect
9. C₃₁×#2362	C₂	semidirect
12. C₃₁×#2334	C₂	semidirect
13. C₃₁×#2330	C₂	semidirect
14. C₃₁×#2329	C₂	semidirect
15. C₃₁×#2327	C₂	semidirect
17. C₃₁×#2323	C₂	semidirect
18. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
19. C₄×C₃₁×#126	C₂	semidirect
20. C₃₁×#563	C₄	semidirect
115. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
116. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
117. C₃₁×#126	C₂×C₄	semidirect
118. C₃₁×#126	C₂×C₄	semidirect
119. C₃₁×#125	C₂×C₄	semidirect
122. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
123. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
303. #34521	C₃₁	direct (N × H)
370. #2383	C₂×C₃₁	semidirect
371. #2381	C₂×C₃₁	semidirect
372. #2373	C₂×C₃₁	semidirect
374. #2371	C₂×C₃₁	semidirect
375. #2369	C₂×C₃₁	semidirect
376. #2368	C₂×C₃₁	semidirect
377. #2362	C₂×C₃₁	semidirect
380. #2334	C₂×C₃₁	semidirect
381. #2330	C₂×C₃₁	semidirect
382. #2329	C₂×C₃₁	semidirect
383. #2327	C₂×C₃₁	semidirect
385. #2323	C₂×C₃₁	semidirect
386. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
387. C₄×#126	C₂×C₃₁	semidirect
418. #563	C₄×C₃₁	semidirect
519. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
520. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
521. #126	C₂×C₄×C₃₁	semidirect
522. #126	C₂×C₄×C₃₁	semidirect
523. #125	C₂×C₄×C₃₁	semidirect
526. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
527. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
613. C₃₁	#34521	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#563	2
C₃₁×#2383	2
C₃₁×#2381	2
C₃₁×#2373	2
C₃₁×#2372	2
C₃₁×#2371	2
C₃₁×#2369	2
C₃₁×#2368	2
C₃₁×#2362	2
C₃₁×#2359	2
C₃₁×#2335	2
C₃₁×#2334	2
C₃₁×#2330	2
C₃₁×#2329	2
C₃₁×#2327	2
C₃₁×#2326	2
C₃₁×#2323	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#126	2
#34521	31

Subgroups — C31×#34521 #21491280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34521 #21491280