Subgroups — C₃₁×#34975 #21491734

Order 7936.

1738 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2533	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2528	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2514	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2506	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2496	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2489	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2478	C₂	1	2	yes	maximal
8	C₃₁×#2475	C₂	1	2	yes	maximal
9	C₃₁×#2453	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2429	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2421	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2402	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2401	C₂	1	2	yes	maximal
15	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×#125	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#126	C₂	1	2	yes	maximal
19	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
20	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
21	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#126	C₂²	1	2	yes	—
26	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#125	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×C₂²⋊Q₈	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×C₃₁×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#401	C₂²	1	2	yes	—
38	C₃₁×#400	C₂²	1	2	yes	—
39	C₃₁×#400	C₂²	1	2	yes	—
40	C₃₁×#400	C₂²	1	2	yes	—
41	C₃₁×#400	C₂²	1	2	yes	—
42	C₃₁×#400	C₂²	1	2	yes	—
43	C₃₁×#400	C₂²	1	2	yes	—
44	C₃₁×#400	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#398	C₂²	1	2	yes	—
48	C₃₁×#398	C₂²	1	2	yes	—
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#397	C₂²	1	2	yes	—
51	C₃₁×#397	C₂²	1	2	yes	—
52	C₃₁×#396	C₂²	1	2	yes	—
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	1	yes	characteristic
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#389	C₂²	1	2	yes	—
60	C₃₁×#389	C₂²	1	2	yes	—
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	2	yes	—
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#388	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×#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×#385	C₂²	1	2	yes	—
86	C₃₁×#385	C₂²	1	2	yes	—
87	C₃₁×#384	C₂²	1	1	yes	characteristic
88	C₃₁×#383	C₂²	1	2	yes	—
89	C₃₁×#382	C₂²	1	1	yes	characteristic
90	C₃₁×#382	C₂²	1	2	yes	—
91	C₃₁×#380	C₂²	1	1	yes	characteristic
92	C₃₁×#380	C₂²	1	1	yes	characteristic
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×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₃₁×#376	C₂²	1	2	yes	—
118	C₃₁×#376	C₂²	1	1	yes	characteristic
119	C₃₁×#376	C₂²	1	1	yes	characteristic
120	C₄³×C₃₁	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	2	yes	—
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₃₁×C₄⋊Q₈	—	2	4	no	—
129	C₃₁×#126	—	2	8	no	—
130	C₃₁×#125	—	2	8	no	—
131	C₃₁×#125	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₄×Q₈×C₃₁	—	2	4	no	—
135	C₄×Q₈×C₃₁	—	2	4	no	—
136	C₄×Q₈×C₃₁	—	2	4	no	—
137	C₄×Q₈×C₃₁	—	2	4	no	—
138	C₃₁×#117	—	2	4	no	—
139	C₃₁×#117	—	2	4	no	—
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	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	—	2	4	no	—
177	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
189	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
193	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
217	C₃₁×#95	C₂³	1	1	yes	characteristic
218	C₃₁×#95	C₂³	1	1	yes	characteristic
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
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	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	#41	1	4	yes	—
242	C₂²×C₄×C₃₁	—	2	2	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
259	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	4	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	4	no	—
283	C₄⋊C₄×C₃₁	—	2	2	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	4	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	4	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	2	4	no	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	—	2	4	no	—
299	C₄⋊C₄×C₃₁	#41	1	4	yes	—
300	C₄⋊C₄×C₃₁	#41	1	4	yes	—
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	4	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
309	C₄²×C₃₁	—	2	2	no	—
310	C₄²×C₃₁	—	2	2	no	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	—	2	2	no	—
313	C₄²×C₃₁	—	2	2	no	—
314	C₄²×C₃₁	—	2	2	no	—
315	C₄²×C₃₁	—	2	2	no	—
316	C₄²×C₃₁	—	2	4	no	—
317	C₄²×C₃₁	—	2	4	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	2	4	no	—
321	C₄²×C₃₁	—	2	4	no	—
322	C₄²×C₃₁	—	2	4	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	2	4	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	2	no	—
327	C₄²×C₃₁	—	2	2	no	—
328	C₄²×C₃₁	—	2	2	no	—
329	C₄²×C₃₁	—	2	4	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	—	2	4	no	—
332	C₄²×C₃₁	#41	1	4	yes	—
333	#34975	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₃₁	—	2	1	no	—
335	C₂³×C₃₁	—	2	1	no	—
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	1	no	—
338	C₂³×C₃₁	—	2	1	no	—
339	C₂³×C₃₁	—	2	1	no	—
340	C₂³×C₃₁	C₂×#41	1	2	yes	—
341	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
342	Q₈×C₃₁	—	2	8	no	—
343	Q₈×C₃₁	—	4	4	no	—
344	C₂×C₄×C₃₁	—	2	8	no	—
345	C₂×C₄×C₃₁	—	2	1	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	2	no	—
355	C₂×C₄×C₃₁	—	2	1	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	1	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	2	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	1	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	1	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	1	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	1	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	1	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	4	4	no	—
398	C₂×C₄×C₃₁	—	4	4	no	—
399	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
400	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
401	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
402	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
403	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
404	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
405	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
406	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
407	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
408	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
409	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
410	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
411	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
412	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
413	#2533	C₂×C₃₁	1	2	yes	complemented
414	#2528	C₂×C₃₁	1	2	yes	complemented
415	#2514	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#2506	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#2496	C₂×C₃₁	1	1	yes	characteristic
418	#2489	C₂×C₃₁	1	1	yes	characteristic
419	#2478	C₂×C₃₁	1	2	yes	—
420	#2475	C₂×C₃₁	1	2	yes	—
421	#2453	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#2446	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#2429	C₂×C₃₁	1	1	yes	characteristic
424	#2421	C₂×C₃₁	1	1	yes	characteristic
425	#2402	C₂×C₃₁	1	2	yes	complemented
426	#2401	C₂×C₃₁	1	2	yes	—
427	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
428	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
429	C₄×#125	C₂×C₃₁	1	2	yes	complemented
430	C₄×#126	C₂×C₃₁	1	2	yes	—
431	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
432	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
433	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
434	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
435	C₄×#117	C₂×C₃₁	1	1	yes	characteristic
436	C₂²×C₃₁	—	2	2	no	—
437	C₂²×C₃₁	—	2	2	no	—
438	C₂²×C₃₁	—	2	2	no	—
439	C₂²×C₃₁	—	4	1	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	—	4	1	no	—
442	C₂²×C₃₁	—	4	1	no	—
443	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
444	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
445	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
447	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
450	C₄×C₃₁	—	2	4	no	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	2	2	no	—
453	C₄×C₃₁	—	2	2	no	—
454	C₄×C₃₁	—	2	2	no	—
455	C₄×C₃₁	—	2	4	no	—
456	C₄×C₃₁	—	2	2	no	—
457	C₄×C₃₁	—	2	2	no	—
458	C₄×C₃₁	—	4	1	no	—
459	C₄×C₃₁	—	4	2	no	—
460	C₄×C₃₁	—	4	2	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	—	4	1	no	—
463	C₄×C₃₁	—	4	1	no	—
464	C₄×C₃₁	—	4	1	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	1	no	—
467	C₄×C₃₁	—	4	1	no	—
468	C₄×C₃₁	—	4	2	no	—
469	C₄×C₃₁	—	4	2	no	—
470	C₄×C₃₁	#529	1	4	yes	—
471	C₄×C₃₁	#541	1	4	yes	—
472	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
473	C₂×#126	C₂²×C₃₁	1	2	yes	—
474	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
475	C₂×#125	C₂²×C₃₁	1	2	yes	—
476	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
478	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
479	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
482	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
483	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
484	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
485	#401	C₂²×C₃₁	1	2	yes	—
486	#400	C₂²×C₃₁	1	2	yes	—
487	#400	C₂²×C₃₁	1	2	yes	—
488	#400	C₂²×C₃₁	1	2	yes	—
489	#400	C₂²×C₃₁	1	2	yes	—
490	#400	C₂²×C₃₁	1	2	yes	—
491	#400	C₂²×C₃₁	1	2	yes	—
492	#400	C₂²×C₃₁	1	2	yes	—
493	#398	C₂²×C₃₁	1	2	yes	—
494	#398	C₂²×C₃₁	1	2	yes	—
495	#398	C₂²×C₃₁	1	2	yes	—
496	#398	C₂²×C₃₁	1	2	yes	—
497	#397	C₂²×C₃₁	1	2	yes	—
498	#397	C₂²×C₃₁	1	2	yes	—
499	#397	C₂²×C₃₁	1	2	yes	—
500	#396	C₂²×C₃₁	1	2	yes	—
501	#391	C₂²×C₃₁	1	1	yes	characteristic
502	#391	C₂²×C₃₁	1	1	yes	characteristic
503	#391	C₂²×C₃₁	1	1	yes	characteristic
504	#391	C₂²×C₃₁	1	1	yes	characteristic
505	#391	C₂²×C₃₁	1	1	yes	characteristic
506	#391	C₂²×C₃₁	1	1	yes	characteristic
507	#389	C₂²×C₃₁	1	1	yes	characteristic
508	#389	C₂²×C₃₁	1	2	yes	—
509	#389	C₂²×C₃₁	1	1	yes	characteristic
510	#389	C₂²×C₃₁	1	2	yes	—
511	#389	C₂²×C₃₁	1	2	yes	—
512	#389	C₂²×C₃₁	1	2	yes	—
513	#389	C₂²×C₃₁	1	1	yes	characteristic
514	#389	C₂²×C₃₁	1	1	yes	characteristic
515	#389	C₂²×C₃₁	1	1	yes	characteristic
516	#389	C₂²×C₃₁	1	1	yes	characteristic
517	#388	C₂²×C₃₁	1	2	yes	—
518	#388	C₂²×C₃₁	1	2	yes	—
519	#388	C₂²×C₃₁	1	2	yes	—
520	#387	C₂²×C₃₁	1	2	yes	—
521	#387	C₂²×C₃₁	1	2	yes	—
522	#387	C₂²×C₃₁	1	2	yes	—
523	#387	C₂²×C₃₁	1	2	yes	—
524	#387	C₂²×C₃₁	1	2	yes	—
525	#387	C₂²×C₃₁	1	2	yes	—
526	#387	C₂²×C₃₁	1	2	yes	—
527	#387	C₂²×C₃₁	1	2	yes	—
528	#387	C₂²×C₃₁	1	2	yes	—
529	#387	C₂²×C₃₁	1	2	yes	—
530	#387	C₂²×C₃₁	1	2	yes	—
531	#387	C₂²×C₃₁	1	2	yes	—
532	#387	C₂²×C₃₁	1	2	yes	—
533	#385	C₂²×C₃₁	1	2	yes	—
534	#385	C₂²×C₃₁	1	2	yes	—
535	#384	C₂²×C₃₁	1	1	yes	characteristic
536	#383	C₂²×C₃₁	1	2	yes	—
537	#382	C₂²×C₃₁	1	1	yes	characteristic
538	#382	C₂²×C₃₁	1	2	yes	—
539	#380	C₂²×C₃₁	1	1	yes	characteristic
540	#380	C₂²×C₃₁	1	1	yes	characteristic
541	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
542	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
543	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
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	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
548	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
549	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
550	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
552	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
553	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
557	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
562	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
563	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
564	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
565	#376	C₂²×C₃₁	1	2	yes	—
566	#376	C₂²×C₃₁	1	1	yes	characteristic
567	#376	C₂²×C₃₁	1	1	yes	characteristic
568	C₄³	C₂²×C₃₁	1	2	yes	—
569	C₄³	C₂²×C₃₁	1	1	yes	characteristic
570	C₄³	C₂²×C₃₁	1	1	yes	characteristic
571	C₂×C₃₁	—	4	2	no	—
572	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
573	C₂×C₃₁	#3444	1	1	yes	characteristic
574	C₂×C₃₁	C₂×#541	1	1	yes	characteristic
575	C₂×C₃₁	#3482	1	1	yes	characteristic
576	C₂×C₃₁	#3482	1	1	yes	characteristic
577	C₂×C₃₁	#3482	1	1	yes	characteristic
578	C₂×C₃₁	#3482	1	1	yes	characteristic
579	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
580	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₄⋊Q₈	—	2	4	no	—
585	#126	—	2	8	no	—
586	#125	—	2	8	no	—
587	#125	—	2	4	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₄×Q₈	—	2	4	no	—
591	C₄×Q₈	—	2	4	no	—
592	C₄×Q₈	—	2	4	no	—
593	C₄×Q₈	—	2	4	no	—
594	#117	—	2	4	no	—
595	#117	—	2	4	no	—
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄²	—	2	4	no	—
633	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
645	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
650	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
654	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
657	#95	C₂³×C₃₁	1	1	yes	characteristic
658	#95	C₂³×C₃₁	1	1	yes	characteristic
659	#95	C₂³×C₃₁	1	1	yes	characteristic
660	#95	C₂³×C₃₁	1	1	yes	characteristic
661	#95	C₂³×C₃₁	1	1	yes	characteristic
662	#95	C₂³×C₃₁	1	1	yes	characteristic
663	#95	C₂³×C₃₁	1	1	yes	characteristic
664	#95	C₂³×C₃₁	1	1	yes	characteristic
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	#95	C₂³×C₃₁	1	2	yes	—
672	#95	C₂³×C₃₁	1	2	yes	—
673	#95	C₂³×C₃₁	1	2	yes	—
674	#95	C₂³×C₃₁	1	2	yes	—
675	#95	C₂³×C₃₁	1	2	yes	—
676	#95	C₂³×C₃₁	1	2	yes	—
677	#95	C₂³×C₃₁	1	2	yes	—
678	#95	C₂³×C₃₁	1	2	yes	—
679	#95	C₂³×C₃₁	1	2	yes	—
680	#95	C₂³×C₃₁	1	2	yes	—
681	#95	C₂³×C₃₁	1	2	yes	—
682	#95	C₂³×C₃₁	1	2	yes	—
683	#95	C₂³×C₃₁	1	2	yes	—
684	#95	C₂³×C₃₁	1	2	yes	—
685	#95	C₂³×C₃₁	1	2	yes	—
686	#95	C₂³×C₃₁	1	2	yes	—
687	#95	C₂³×C₃₁	1	2	yes	—
688	#95	C₂³×C₃₁	1	2	yes	—
689	#95	C₂³×C₃₁	1	2	yes	—
690	#95	C₂³×C₃₁	1	2	yes	—
691	C₃₁	#34975	1	1	yes	characteristic, direct product factor, Sylow
692	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	#41×C₃₁	1	4	yes	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	#41×C₃₁	1	4	yes	—
757	C₄⋊C₄	#41×C₃₁	1	4	yes	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	4	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	4	no	—
789	C₄²	#41×C₃₁	1	4	yes	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	C₂×#41×C₃₁	1	2	yes	—
797	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
798	Q₈	—	2	8	no	—
799	Q₈	—	4	4	no	—
800	C₂×C₄	—	2	8	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	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
856	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
857	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
858	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
859	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
860	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
861	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
862	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
863	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
864	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
865	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
866	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
867	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
868	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
877	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
878	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
879	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
880	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
881	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
883	C₄	—	2	4	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	C₃₁×#529	1	4	yes	—
904	C₄	C₃₁×#541	1	4	yes	—
905	C₂	—	4	2	no	—
906	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
907	C₂	C₃₁×#3444	1	1	yes	characteristic
908	C₂	C₂×C₃₁×#541	1	1	yes	characteristic
909	C₂	C₃₁×#3482	1	1	yes	characteristic
910	C₂	C₃₁×#3482	1	1	yes	characteristic
911	C₂	C₃₁×#3482	1	1	yes	characteristic
912	C₂	C₃₁×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂⁴×C₃₁	C₂⁴
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
1. C₃₁×#2533	C₂	semidirect
2. C₃₁×#2528	C₂	semidirect
3. C₃₁×#2514	C₂	semidirect
4. C₃₁×#2506	C₂	semidirect
9. C₃₁×#2453	C₂	semidirect
10. C₃₁×#2446	C₂	semidirect
13. C₃₁×#2402	C₂	semidirect
15. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
16. C₄×C₃₁×#125	C₂	semidirect
17. C₄×C₃₁×#125	C₂	semidirect
21. C₃₁×#2295	C₂	semidirect
22. C₄²×Q₈×C₃₁	C₂	semidirect
333. #34975	C₃₁	direct (N × H)
413. #2533	C₂×C₃₁	semidirect
414. #2528	C₂×C₃₁	semidirect
415. #2514	C₂×C₃₁	semidirect
416. #2506	C₂×C₃₁	semidirect
421. #2453	C₂×C₃₁	semidirect
422. #2446	C₂×C₃₁	semidirect
425. #2402	C₂×C₃₁	semidirect
427. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
428. C₄×#125	C₂×C₃₁	semidirect
429. C₄×#125	C₂×C₃₁	semidirect
433. #2295	C₂×C₃₁	semidirect
434. C₄²×Q₈	C₂×C₃₁	semidirect
691. C₃₁	#34975	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×#2533	2
C₃₁×#2528	2
C₃₁×#2514	2
C₃₁×#2506	2
C₃₁×#2496	2
C₃₁×#2489	2
C₃₁×#2478	2
C₃₁×#2475	2
C₃₁×#2453	2
C₃₁×#2446	2
C₃₁×#2429	2
C₃₁×#2421	2
C₃₁×#2402	2
C₃₁×#2401	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#125	2
C₄×C₃₁×#126	2
C₄×C₃₁×C₂²⋊Q₈	2
C₃₁×#2295	2
C₄²×Q₈×C₃₁	2
C₄×C₃₁×#117	2
#34975	31

Subgroups — C31×#34975 #21491734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34975 #21491734