Subgroups — C₃₁×#34920 #21491679

Order 7936.

1692 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2590	C₂	1	2	yes	maximal
2	C₃₁×#2588	C₂	1	2	yes	maximal
3	C₃₁×#2584	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2581	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2565	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2550	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2520	C₂	1	2	yes	maximal
8	C₃₁×#2508	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2506	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#2462	C₂	1	2	yes	maximal
11	C₃₁×#2453	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2451	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2402	C₂	1	2	yes	maximal
14	C₃₁×#2399	C₂	1	2	yes	maximal
15	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
16	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic
17	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic
18	C₄×C₃₁×#125	C₂	1	2	yes	maximal
19	C₃₁×#2295	C₂	1	2	yes	maximal
20	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic
21	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic
22	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#125	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
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×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#400	C₂²	1	2	yes	—
36	C₃₁×#400	C₂²	1	2	yes	—
37	C₃₁×#400	C₂²	1	2	yes	—
38	C₃₁×#400	C₂²	1	2	yes	—
39	C₃₁×#398	C₂²	1	2	yes	—
40	C₃₁×#398	C₂²	1	2	yes	—
41	C₃₁×#398	C₂²	1	2	yes	—
42	C₃₁×#398	C₂²	1	2	yes	—
43	C₃₁×#398	C₂²	1	2	yes	—
44	C₃₁×#398	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#395	C₂²	1	2	yes	—
48	C₃₁×#395	C₂²	1	2	yes	—
49	C₃₁×#395	C₂²	1	2	yes	—
50	C₃₁×#395	C₂²	1	2	yes	—
51	C₃₁×#391	C₂²	1	2	yes	—
52	C₃₁×#391	C₂²	1	1	yes	characteristic
53	C₃₁×#391	C₂²	1	1	yes	characteristic
54	C₃₁×#391	C₂²	1	1	yes	characteristic
55	C₃₁×#391	C₂²	1	1	yes	characteristic
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	2	yes	—
58	C₃₁×#389	C₂²	1	1	yes	characteristic
59	C₃₁×#389	C₂²	1	1	yes	characteristic
60	C₃₁×#389	C₂²	1	2	yes	—
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	2	yes	—
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	2	yes	—
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	2	yes	—
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	2	yes	—
89	C₃₁×#384	C₂²	1	1	yes	characteristic
90	C₃₁×#382	C₂²	1	1	yes	characteristic
91	C₃₁×#382	C₂²	1	1	yes	characteristic
92	C₃₁×#382	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₃₁×#376	C₂²	1	2	yes	—
118	C₃₁×#376	C₂²	1	2	yes	—
119	C₄³×C₃₁	C₂²	1	1	yes	characteristic
120	C₄³×C₃₁	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	2	yes	—
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
125	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₃₁×C₄⋊Q₈	—	2	4	no	—
127	C₃₁×#125	—	2	8	no	—
128	C₃₁×#125	—	2	4	no	—
129	C₃₁×#125	—	2	4	no	—
130	C₄×Q₈×C₃₁	—	2	4	no	—
131	C₄×Q₈×C₃₁	—	2	4	no	—
132	C₄×Q₈×C₃₁	—	2	4	no	—
133	C₄×Q₈×C₃₁	—	2	8	no	—
134	C₄×Q₈×C₃₁	—	2	4	no	—
135	C₄×Q₈×C₃₁	—	2	4	no	—
136	C₄×Q₈×C₃₁	Q₈	1	8	yes	complemented
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	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×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	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
185	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	1	yes	characteristic
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	1	yes	characteristic
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	1	yes	characteristic
228	C₃₁×#95	C₂³	1	1	yes	characteristic
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	4	no	—
239	C₂×Q₈×C₃₁	—	2	4	no	—
240	C₂×Q₈×C₃₁	—	4	2	no	—
241	C₂×Q₈×C₃₁	C₂×Q₈	1	4	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	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	2	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	4	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	—	2	4	no	—
281	C₄⋊C₄×C₃₁	—	2	4	no	—
282	C₄⋊C₄×C₃₁	—	2	4	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	4	no	—
285	C₄⋊C₄×C₃₁	—	2	4	no	—
286	C₄⋊C₄×C₃₁	—	2	4	no	—
287	C₄⋊C₄×C₃₁	—	2	4	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	4	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	4	2	no	—
294	C₄⋊C₄×C₃₁	—	4	2	no	—
295	C₄⋊C₄×C₃₁	—	4	2	no	—
296	C₄⋊C₄×C₃₁	—	4	2	no	—
297	C₄⋊C₄×C₃₁	C₂×Q₈	1	8	yes	—
298	C₄⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
299	C₄⋊C₄×C₃₁	#41	1	4	yes	—
300	C₄⋊C₄×C₃₁	#41	1	4	yes	—
301	C₄²×C₃₁	—	2	2	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	—	2	4	no	—
304	C₄²×C₃₁	—	2	2	no	—
305	C₄²×C₃₁	—	2	2	no	—
306	C₄²×C₃₁	—	2	4	no	—
307	C₄²×C₃₁	—	2	2	no	—
308	C₄²×C₃₁	—	2	2	no	—
309	C₄²×C₃₁	—	2	2	no	—
310	C₄²×C₃₁	—	2	2	no	—
311	C₄²×C₃₁	—	2	4	no	—
312	C₄²×C₃₁	—	2	4	no	—
313	C₄²×C₃₁	—	2	4	no	—
314	C₄²×C₃₁	—	2	2	no	—
315	C₄²×C₃₁	—	2	2	no	—
316	C₄²×C₃₁	—	2	2	no	—
317	C₄²×C₃₁	—	2	2	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	4	no	—
320	C₄²×C₃₁	—	4	1	no	—
321	C₄²×C₃₁	—	4	2	no	—
322	C₄²×C₃₁	—	4	1	no	—
323	C₄²×C₃₁	—	4	1	no	—
324	C₄²×C₃₁	C₂×Q₈	1	8	yes	—
325	C₄²×C₃₁	C₂×Q₈	1	4	yes	—
326	C₄²×C₃₁	#41	1	4	yes	—
327	C₄²×C₃₁	#41	1	4	yes	—
328	#34920	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
330	Q₈×C₃₁	—	2	8	no	—
331	Q₈×C₃₁	—	2	8	no	—
332	Q₈×C₃₁	—	4	8	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	1	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	1	no	—
343	C₂×C₄×C₃₁	—	2	1	no	—
344	C₂×C₄×C₃₁	—	2	1	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	1	no	—
349	C₂×C₄×C₃₁	—	2	1	no	—
350	C₂×C₄×C₃₁	—	2	1	no	—
351	C₂×C₄×C₃₁	—	2	1	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	1	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	1	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	2	1	no	—
364	C₂×C₄×C₃₁	—	2	1	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	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
386	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
387	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
388	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
389	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
390	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
391	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
392	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
393	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
394	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
395	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
396	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
397	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
398	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
399	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
400	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
401	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
402	#2590	C₂×C₃₁	1	2	yes	—
403	#2588	C₂×C₃₁	1	2	yes	—
404	#2584	C₂×C₃₁	1	1	yes	characteristic
405	#2581	C₂×C₃₁	1	1	yes	characteristic
406	#2565	C₂×C₃₁	1	1	yes	characteristic
407	#2550	C₂×C₃₁	1	1	yes	characteristic
408	#2520	C₂×C₃₁	1	2	yes	—
409	#2508	C₂×C₃₁	1	1	yes	characteristic
410	#2506	C₂×C₃₁	1	1	yes	characteristic
411	#2462	C₂×C₃₁	1	2	yes	—
412	#2453	C₂×C₃₁	1	1	yes	characteristic
413	#2451	C₂×C₃₁	1	1	yes	characteristic
414	#2402	C₂×C₃₁	1	2	yes	—
415	#2399	C₂×C₃₁	1	2	yes	—
416	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
417	C₄×#125	C₂×C₃₁	1	1	yes	characteristic
418	C₄×#125	C₂×C₃₁	1	1	yes	characteristic
419	C₄×#125	C₂×C₃₁	1	2	yes	—
420	#2295	C₂×C₃₁	1	2	yes	—
421	#2295	C₂×C₃₁	1	1	yes	characteristic
422	#2295	C₂×C₃₁	1	1	yes	characteristic
423	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic
424	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic
425	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
426	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
427	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
428	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
431	C₂²×C₃₁	#585	1	1	yes	characteristic
432	C₄×C₃₁	—	2	4	no	—
433	C₄×C₃₁	—	2	2	no	—
434	C₄×C₃₁	—	2	2	no	—
435	C₄×C₃₁	—	2	2	no	—
436	C₄×C₃₁	—	2	2	no	—
437	C₄×C₃₁	—	2	4	no	—
438	C₄×C₃₁	—	2	2	no	—
439	C₄×C₃₁	—	2	2	no	—
440	C₄×C₃₁	—	2	4	no	—
441	C₄×C₃₁	—	2	2	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	4	2	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	1	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	1	no	—
450	C₄×C₃₁	—	4	2	no	—
451	C₄×C₃₁	—	4	1	no	—
452	C₄×C₃₁	—	4	2	no	—
453	C₄×C₃₁	#533	1	4	yes	—
454	C₄×C₃₁	#557	1	4	yes	—
455	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
456	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
457	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×#125	C₂²×C₃₁	1	2	yes	—
459	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
460	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
461	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
463	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
464	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
465	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
466	#400	C₂²×C₃₁	1	2	yes	—
467	#400	C₂²×C₃₁	1	2	yes	—
468	#400	C₂²×C₃₁	1	2	yes	—
469	#400	C₂²×C₃₁	1	2	yes	—
470	#398	C₂²×C₃₁	1	2	yes	—
471	#398	C₂²×C₃₁	1	2	yes	—
472	#398	C₂²×C₃₁	1	2	yes	—
473	#398	C₂²×C₃₁	1	2	yes	—
474	#398	C₂²×C₃₁	1	2	yes	—
475	#398	C₂²×C₃₁	1	2	yes	—
476	#398	C₂²×C₃₁	1	2	yes	—
477	#398	C₂²×C₃₁	1	2	yes	—
478	#395	C₂²×C₃₁	1	2	yes	—
479	#395	C₂²×C₃₁	1	2	yes	—
480	#395	C₂²×C₃₁	1	2	yes	—
481	#395	C₂²×C₃₁	1	2	yes	—
482	#391	C₂²×C₃₁	1	2	yes	—
483	#391	C₂²×C₃₁	1	1	yes	characteristic
484	#391	C₂²×C₃₁	1	1	yes	characteristic
485	#391	C₂²×C₃₁	1	1	yes	characteristic
486	#391	C₂²×C₃₁	1	1	yes	characteristic
487	#391	C₂²×C₃₁	1	2	yes	—
488	#391	C₂²×C₃₁	1	2	yes	—
489	#389	C₂²×C₃₁	1	1	yes	characteristic
490	#389	C₂²×C₃₁	1	2	yes	—
491	#389	C₂²×C₃₁	1	1	yes	characteristic
492	#389	C₂²×C₃₁	1	2	yes	—
493	#389	C₂²×C₃₁	1	1	yes	characteristic
494	#389	C₂²×C₃₁	1	1	yes	characteristic
495	#389	C₂²×C₃₁	1	1	yes	characteristic
496	#389	C₂²×C₃₁	1	1	yes	characteristic
497	#389	C₂²×C₃₁	1	2	yes	—
498	#389	C₂²×C₃₁	1	2	yes	—
499	#389	C₂²×C₃₁	1	1	yes	characteristic
500	#389	C₂²×C₃₁	1	1	yes	characteristic
501	#389	C₂²×C₃₁	1	2	yes	—
502	#389	C₂²×C₃₁	1	1	yes	characteristic
503	#389	C₂²×C₃₁	1	1	yes	characteristic
504	#387	C₂²×C₃₁	1	2	yes	—
505	#387	C₂²×C₃₁	1	2	yes	—
506	#387	C₂²×C₃₁	1	2	yes	—
507	#387	C₂²×C₃₁	1	2	yes	—
508	#387	C₂²×C₃₁	1	2	yes	—
509	#387	C₂²×C₃₁	1	2	yes	—
510	#387	C₂²×C₃₁	1	2	yes	—
511	#387	C₂²×C₃₁	1	2	yes	—
512	#387	C₂²×C₃₁	1	2	yes	—
513	#387	C₂²×C₃₁	1	2	yes	—
514	#387	C₂²×C₃₁	1	2	yes	—
515	#387	C₂²×C₃₁	1	2	yes	—
516	#387	C₂²×C₃₁	1	2	yes	—
517	#387	C₂²×C₃₁	1	2	yes	—
518	#387	C₂²×C₃₁	1	2	yes	—
519	#387	C₂²×C₃₁	1	2	yes	—
520	#384	C₂²×C₃₁	1	1	yes	characteristic
521	#382	C₂²×C₃₁	1	1	yes	characteristic
522	#382	C₂²×C₃₁	1	1	yes	characteristic
523	#382	C₂²×C₃₁	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
525	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
526	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
527	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
532	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
533	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
534	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
539	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
542	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
543	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
545	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
546	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
547	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
548	#376	C₂²×C₃₁	1	2	yes	—
549	#376	C₂²×C₃₁	1	2	yes	—
550	C₄³	C₂²×C₃₁	1	1	yes	characteristic
551	C₄³	C₂²×C₃₁	1	2	yes	—
552	C₄³	C₂²×C₃₁	1	1	yes	characteristic
553	C₄³	C₂²×C₃₁	1	1	yes	characteristic
554	C₂×C₃₁	C₂×#533	1	1	yes	characteristic
555	C₂×C₃₁	#3444	1	1	yes	characteristic
556	C₂×C₃₁	#3461	1	1	yes	characteristic
557	C₂×C₃₁	#3475	1	1	yes	characteristic
558	C₂×C₃₁	C₂×#557	1	1	yes	characteristic
559	C₂×C₃₁	Q₈×#41	1	1	yes	characteristic
560	C₂×C₃₁	#3482	1	1	yes	characteristic
561	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
563	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	C₄⋊Q₈	—	2	4	no	—
565	#125	—	2	8	no	—
566	#125	—	2	4	no	—
567	#125	—	2	4	no	—
568	C₄×Q₈	—	2	4	no	—
569	C₄×Q₈	—	2	4	no	—
570	C₄×Q₈	—	2	4	no	—
571	C₄×Q₈	—	2	8	no	—
572	C₄×Q₈	—	2	4	no	—
573	C₄×Q₈	—	2	4	no	—
574	C₄×Q₈	Q₈×C₃₁	1	8	yes	complemented
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
612	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
618	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
623	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
624	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
630	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
636	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	#95	C₂³×C₃₁	1	2	yes	—
644	#95	C₂³×C₃₁	1	2	yes	—
645	#95	C₂³×C₃₁	1	2	yes	—
646	#95	C₂³×C₃₁	1	1	yes	characteristic
647	#95	C₂³×C₃₁	1	1	yes	characteristic
648	#95	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	1	yes	characteristic
650	#95	C₂³×C₃₁	1	1	yes	characteristic
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	1	yes	characteristic
653	#95	C₂³×C₃₁	1	2	yes	—
654	#95	C₂³×C₃₁	1	1	yes	characteristic
655	#95	C₂³×C₃₁	1	2	yes	—
656	#95	C₂³×C₃₁	1	2	yes	—
657	#95	C₂³×C₃₁	1	2	yes	—
658	#95	C₂³×C₃₁	1	2	yes	—
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	2	yes	—
661	#95	C₂³×C₃₁	1	2	yes	—
662	#95	C₂³×C₃₁	1	2	yes	—
663	#95	C₂³×C₃₁	1	2	yes	—
664	#95	C₂³×C₃₁	1	2	yes	—
665	#95	C₂³×C₃₁	1	2	yes	—
666	#95	C₂³×C₃₁	1	2	yes	—
667	#95	C₂³×C₃₁	1	2	yes	—
668	#95	C₂³×C₃₁	1	2	yes	—
669	#95	C₂³×C₃₁	1	2	yes	—
670	#95	C₂³×C₃₁	1	2	yes	—
671	C₃₁	#34920	1	1	yes	characteristic, direct product factor, Sylow
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	C₂×Q₈×C₃₁	1	4	yes	—
681	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	C₂×Q₈×C₃₁	1	8	yes	—
737	C₄⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
738	C₄⋊C₄	#41×C₃₁	1	4	yes	—
739	C₄⋊C₄	#41×C₃₁	1	4	yes	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	4	1	no	—
760	C₄²	—	4	2	no	—
761	C₄²	—	4	1	no	—
762	C₄²	—	4	1	no	—
763	C₄²	C₂×Q₈×C₃₁	1	8	yes	—
764	C₄²	C₂×Q₈×C₃₁	1	4	yes	—
765	C₄²	#41×C₃₁	1	4	yes	—
766	C₄²	#41×C₃₁	1	4	yes	—
767	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
768	Q₈	—	2	8	no	—
769	Q₈	—	2	8	no	—
770	Q₈	—	4	8	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	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	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
824	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
825	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
826	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
827	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
828	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
829	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
830	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
831	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
832	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
833	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
834	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
835	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
836	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
837	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
838	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
839	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
840	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
841	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
842	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
843	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
844	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
845	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂²	C₃₁×#585	1	1	yes	characteristic
847	C₄	—	2	4	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	C₃₁×#533	1	4	yes	—
869	C₄	C₃₁×#557	1	4	yes	—
870	C₂	C₂×C₃₁×#533	1	1	yes	characteristic
871	C₂	C₃₁×#3444	1	1	yes	characteristic
872	C₂	C₃₁×#3461	1	1	yes	characteristic
873	C₂	C₃₁×#3475	1	1	yes	characteristic
874	C₂	C₂×C₃₁×#557	1	1	yes	characteristic
875	C₂	Q₈×#41×C₃₁	1	1	yes	characteristic
876	C₂	C₃₁×#3482	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
136. C₄×Q₈×C₃₁	Q₈	semidirect
328. #34920	C₃₁	direct (N × H)
574. C₄×Q₈	Q₈×C₃₁	semidirect
671. C₃₁	#34920	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×#2590	2
C₃₁×#2588	2
C₃₁×#2584	2
C₃₁×#2581	2
C₃₁×#2565	2
C₃₁×#2550	2
C₃₁×#2520	2
C₃₁×#2508	2
C₃₁×#2506	2
C₃₁×#2462	2
C₃₁×#2453	2
C₃₁×#2451	2
C₃₁×#2402	2
C₃₁×#2399	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#125	2
C₃₁×#2295	2
C₄²×Q₈×C₃₁	2
#34920	31

Subgroups — C31×#34920 #21491679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34920 #21491679