Subgroups — C₃₁×#34326 #21491085

Order 7936.

2128 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2373	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2373	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2368	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2367	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2367	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2357	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2332	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	C₄×C₃₁×#126	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#2298	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#556	C₄	1	16	yes	complemented
25	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#126	C₂²	1	2	yes	—
27	C₂×C₃₁×#126	C₂²	1	2	yes	—
28	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
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	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#117	C₂²	1	2	yes	—
42	C₃₁×#391	C₂²	1	1	yes	characteristic
43	C₃₁×#391	C₂²	1	1	yes	characteristic
44	C₃₁×#391	C₂²	1	1	yes	characteristic
45	C₃₁×#391	C₂²	1	1	yes	characteristic
46	C₃₁×#391	C₂²	1	2	yes	—
47	C₃₁×#391	C₂²	1	1	yes	characteristic
48	C₃₁×#391	C₂²	1	1	yes	characteristic
49	C₃₁×#390	C₂²	1	1	yes	characteristic
50	C₃₁×#390	C₂²	1	1	yes	characteristic
51	C₃₁×#389	C₂²	1	1	yes	characteristic
52	C₃₁×#389	C₂²	1	2	yes	—
53	C₃₁×#389	C₂²	1	1	yes	characteristic
54	C₃₁×#388	C₂²	1	2	yes	—
55	C₃₁×#388	C₂²	1	2	yes	—
56	C₃₁×#388	C₂²	1	2	yes	—
57	C₃₁×#388	C₂²	1	2	yes	—
58	C₃₁×#388	C₂²	1	2	yes	—
59	C₃₁×#388	C₂²	1	2	yes	—
60	C₃₁×#388	C₂²	1	2	yes	—
61	C₃₁×#388	C₂²	1	2	yes	—
62	C₃₁×#388	C₂²	1	2	yes	—
63	C₃₁×#388	C₂²	1	2	yes	—
64	C₃₁×#387	C₂²	1	2	yes	—
65	C₃₁×#387	C₂²	1	2	yes	—
66	C₃₁×#387	C₂²	1	2	yes	—
67	C₃₁×#387	C₂²	1	2	yes	—
68	C₃₁×#387	C₂²	1	2	yes	—
69	C₃₁×#387	C₂²	1	2	yes	—
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
78	C₃₁×#387	C₂²	1	1	yes	characteristic
79	C₃₁×#387	C₂²	1	1	yes	characteristic
80	C₃₁×#385	C₂²	1	2	yes	—
81	C₃₁×#385	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#385	C₂²	1	2	yes	—
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×#382	C₂²	1	2	yes	—
88	C₃₁×#382	C₂²	1	1	yes	characteristic
89	C₃₁×#381	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	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	1	yes	characteristic
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
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×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
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	2	yes	—
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₃₁×#376	C₂²	1	1	yes	characteristic
118	C₃₁×#376	C₂²	1	1	yes	characteristic
119	C₃₁×#376	C₂²	1	2	yes	—
120	C₃₁×#376	C₂²	1	2	yes	—
121	C₂×C₃₁×#95	C₂²	1	2	yes	—
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₄³×C₃₁	C₂²	1	2	yes	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
131	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
132	C₃₁×#126	C₂×C₄	1	16	yes	complemented
133	C₃₁×#126	C₂×C₄	1	16	yes	complemented
134	C₃₁×#124	C₂×C₄	1	8	yes	—
135	C₃₁×#124	C₂×C₄	1	8	yes	—
136	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
137	C₄×Q₈×C₃₁	—	2	4	no	—
138	C₄×Q₈×C₃₁	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	2	4	no	—
141	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
142	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
143	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
144	C₄×D₄×C₃₁	—	2	4	no	—
145	C₄×D₄×C₃₁	—	2	4	no	—
146	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
147	C₃₁×#117	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊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	2	yes	—
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
187	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
213	C₃₁×#95	C₂³	1	1	yes	characteristic
214	C₃₁×#95	C₂³	1	1	yes	characteristic
215	C₃₁×#95	C₂³	1	1	yes	characteristic
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	1	yes	characteristic
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	1	yes	characteristic
221	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
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	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₃₁×#95	C₂³	1	1	yes	characteristic
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₃₁×#95	C₂³	1	1	yes	characteristic
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×Q₈×C₃₁	—	2	2	no	—
245	C₂×Q₈×C₃₁	—	4	1	no	—
246	C₂×Q₈×C₃₁	—	4	1	no	—
247	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
248	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
249	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
253	C₂²×C₄×C₃₁	—	2	4	no	—
254	C₂²×C₄×C₃₁	—	2	4	no	—
255	C₂²×C₄×C₃₁	—	4	2	no	—
256	C₂²×C₄×C₃₁	—	4	2	no	—
257	C₂²×C₄×C₃₁	—	4	2	no	—
258	C₂²×C₄×C₃₁	—	4	2	no	—
259	C₂²×C₄×C₃₁	—	4	2	no	—
260	C₂²×C₄×C₃₁	—	4	2	no	—
261	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	4	1	no	—
294	C₄⋊C₄×C₃₁	—	4	1	no	—
295	C₄⋊C₄×C₃₁	—	4	1	no	—
296	C₄⋊C₄×C₃₁	—	4	2	no	—
297	C₄⋊C₄×C₃₁	—	4	1	no	—
298	C₄⋊C₄×C₃₁	—	4	2	no	—
299	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
300	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
301	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
302	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
303	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
304	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
305	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
306	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
307	C₄⋊C₄×C₃₁	#41	1	4	yes	—
308	C₂²⋊C₄×C₃₁	—	2	4	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	4	2	no	—
312	C₂²⋊C₄×C₃₁	—	4	2	no	—
313	C₂²⋊C₄×C₃₁	—	4	2	no	—
314	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
315	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
316	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
317	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
318	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	2	4	no	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	4	no	—
323	C₄²×C₃₁	—	2	4	no	—
324	C₄²×C₃₁	—	2	4	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	2	no	—
327	C₄²×C₃₁	—	4	2	no	—
328	C₄²×C₃₁	—	4	2	no	—
329	C₄²×C₃₁	—	4	2	no	—
330	C₄²×C₃₁	—	4	1	no	—
331	C₄²×C₃₁	—	4	1	no	—
332	C₄²×C₃₁	—	4	1	no	—
333	C₄²×C₃₁	—	4	2	no	—
334	C₄²×C₃₁	—	4	2	no	—
335	C₄²×C₃₁	—	4	2	no	—
336	C₄²×C₃₁	—	4	2	no	—
337	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
338	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
339	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
340	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
341	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
342	C₄²×C₃₁	#41	1	4	yes	—
343	#34326	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	2	2	no	—
346	C₂³×C₃₁	—	2	2	no	—
347	C₂³×C₃₁	—	2	2	no	—
348	C₂³×C₃₁	—	2	2	no	—
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
351	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
352	Q₈×C₃₁	—	2	8	no	—
353	Q₈×C₃₁	—	2	8	no	—
354	Q₈×C₃₁	—	4	4	no	—
355	D₄×C₃₁	—	2	8	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	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	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	2	no	—
373	C₂×C₄×C₃₁	—	2	1	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	1	no	—
378	C₂×C₄×C₃₁	—	2	1	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	1	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	2	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	1	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	1	no	—
406	C₂×C₄×C₃₁	—	4	8	no	—
407	C₂×C₄×C₃₁	—	8	4	no	—
408	C₂×C₄×C₃₁	—	8	4	no	—
409	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
410	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
411	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
412	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
413	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
414	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
415	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
417	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
418	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
419	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
420	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
421	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
422	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
423	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
424	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
425	C₂×#556	C₂×C₃₁	1	1	yes	characteristic
426	#2373	C₂×C₃₁	1	2	yes	complemented
427	#2373	C₂×C₃₁	1	2	yes	complemented
428	#2368	C₂×C₃₁	1	2	yes	complemented
429	#2367	C₂×C₃₁	1	1	yes	characteristic
430	#2367	C₂×C₃₁	1	1	yes	characteristic
431	#2365	C₂×C₃₁	1	1	yes	characteristic, complemented
432	#2357	C₂×C₃₁	1	1	yes	characteristic
433	#2356	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
435	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#2343	C₂×C₃₁	1	2	yes	complemented
437	#2334	C₂×C₃₁	1	2	yes	complemented
438	#2332	C₂×C₃₁	1	2	yes	complemented
439	#2327	C₂×C₃₁	1	1	yes	characteristic, complemented
440	#2326	C₂×C₃₁	1	1	yes	characteristic
441	C₄×#126	C₂×C₃₁	1	2	yes	complemented
442	C₄×#124	C₂×C₃₁	1	1	yes	characteristic
443	#2298	C₂×C₃₁	1	2	yes	complemented
444	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#2276	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#2275	C₂×C₃₁	1	1	yes	characteristic
447	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
448	C₂²×C₃₁	—	2	4	no	—
449	C₂²×C₃₁	—	2	4	no	—
450	C₂²×C₃₁	—	2	4	no	—
451	C₂²×C₃₁	—	4	2	no	—
452	C₂²×C₃₁	—	4	2	no	—
453	C₂²×C₃₁	—	4	2	no	—
454	C₂²×C₃₁	—	4	2	no	—
455	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
456	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
457	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
458	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
459	C₂²×C₃₁	#585	1	1	yes	characteristic
460	C₂²×C₃₁	#585	1	1	yes	characteristic
461	C₂²×C₃₁	#585	1	1	yes	characteristic
462	C₄×C₃₁	—	2	4	no	—
463	C₄×C₃₁	—	2	4	no	—
464	C₄×C₃₁	—	2	2	no	—
465	C₄×C₃₁	—	2	4	no	—
466	C₄×C₃₁	—	2	2	no	—
467	C₄×C₃₁	—	2	2	no	—
468	C₄×C₃₁	—	2	2	no	—
469	C₄×C₃₁	—	2	2	no	—
470	C₄×C₃₁	—	2	2	no	—
471	C₄×C₃₁	—	2	2	no	—
472	C₄×C₃₁	—	2	2	no	—
473	C₄×C₃₁	—	2	2	no	—
474	C₄×C₃₁	—	2	4	no	—
475	C₄×C₃₁	—	4	2	no	—
476	C₄×C₃₁	—	4	2	no	—
477	C₄×C₃₁	—	4	2	no	—
478	C₄×C₃₁	—	4	1	no	—
479	C₄×C₃₁	—	4	1	no	—
480	C₄×C₃₁	—	4	1	no	—
481	C₄×C₃₁	—	4	1	no	—
482	C₄×C₃₁	—	4	1	no	—
483	C₄×C₃₁	C₄×#41	1	4	yes	—
484	#556	C₄×C₃₁	1	16	yes	complemented
485	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
486	C₂×#126	C₂²×C₃₁	1	2	yes	—
487	C₂×#126	C₂²×C₃₁	1	2	yes	—
488	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
489	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
490	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
491	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
494	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
495	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
496	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
497	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
501	C₂×#117	C₂²×C₃₁	1	2	yes	—
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	2	yes	—
507	#391	C₂²×C₃₁	1	1	yes	characteristic
508	#391	C₂²×C₃₁	1	1	yes	characteristic
509	#390	C₂²×C₃₁	1	1	yes	characteristic
510	#390	C₂²×C₃₁	1	1	yes	characteristic
511	#389	C₂²×C₃₁	1	1	yes	characteristic
512	#389	C₂²×C₃₁	1	2	yes	—
513	#389	C₂²×C₃₁	1	1	yes	characteristic
514	#388	C₂²×C₃₁	1	2	yes	—
515	#388	C₂²×C₃₁	1	2	yes	—
516	#388	C₂²×C₃₁	1	2	yes	—
517	#388	C₂²×C₃₁	1	2	yes	—
518	#388	C₂²×C₃₁	1	2	yes	—
519	#388	C₂²×C₃₁	1	2	yes	—
520	#388	C₂²×C₃₁	1	2	yes	—
521	#388	C₂²×C₃₁	1	2	yes	—
522	#388	C₂²×C₃₁	1	2	yes	—
523	#388	C₂²×C₃₁	1	2	yes	—
524	#387	C₂²×C₃₁	1	1	yes	characteristic
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	#387	C₂²×C₃₁	1	2	yes	—
534	#387	C₂²×C₃₁	1	2	yes	—
535	#387	C₂²×C₃₁	1	1	yes	characteristic
536	#387	C₂²×C₃₁	1	2	yes	—
537	#387	C₂²×C₃₁	1	2	yes	—
538	#387	C₂²×C₃₁	1	1	yes	characteristic
539	#387	C₂²×C₃₁	1	1	yes	characteristic
540	#385	C₂²×C₃₁	1	2	yes	—
541	#385	C₂²×C₃₁	1	2	yes	—
542	#385	C₂²×C₃₁	1	2	yes	—
543	#385	C₂²×C₃₁	1	2	yes	—
544	#384	C₂²×C₃₁	1	1	yes	characteristic
545	#383	C₂²×C₃₁	1	2	yes	—
546	#382	C₂²×C₃₁	1	1	yes	characteristic
547	#382	C₂²×C₃₁	1	2	yes	—
548	#382	C₂²×C₃₁	1	1	yes	characteristic
549	#381	C₂²×C₃₁	1	2	yes	—
550	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
551	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
552	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
554	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
555	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
560	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
568	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
569	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
571	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
576	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
577	#376	C₂²×C₃₁	1	1	yes	characteristic
578	#376	C₂²×C₃₁	1	1	yes	characteristic
579	#376	C₂²×C₃₁	1	2	yes	—
580	#376	C₂²×C₃₁	1	2	yes	—
581	C₂×#95	C₂²×C₃₁	1	2	yes	—
582	C₄³	C₂²×C₃₁	1	2	yes	—
583	C₄³	C₂²×C₃₁	1	1	yes	characteristic
584	C₂×C₃₁	—	4	4	no	—
585	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
586	C₂×C₃₁	#3428	1	1	yes	characteristic
587	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
588	C₂×C₃₁	#3507	1	1	yes	characteristic
589	C₂×C₃₁	#3510	1	1	yes	characteristic
590	C₂×C₃₁	#3516	1	1	yes	characteristic
591	C₂×C₃₁	#3521	1	1	yes	characteristic
592	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
597	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
598	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
599	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
600	#126	C₂×C₄×C₃₁	1	16	yes	complemented
601	#126	C₂×C₄×C₃₁	1	16	yes	complemented
602	#124	C₂×C₄×C₃₁	1	8	yes	—
603	#124	C₂×C₄×C₃₁	1	8	yes	—
604	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
605	C₄×Q₈	—	2	4	no	—
606	C₄×Q₈	—	2	4	no	—
607	C₄×Q₈	—	2	4	no	—
608	C₄×Q₈	—	2	4	no	—
609	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
610	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
611	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
615	#117	C₂×C₄×C₃₁	1	16	yes	complemented
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
660	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
664	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
667	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
668	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
669	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
670	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
671	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
675	#95	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
680	#95	C₂³×C₃₁	1	1	yes	characteristic
681	#95	C₂³×C₃₁	1	1	yes	characteristic
682	#95	C₂³×C₃₁	1	1	yes	characteristic
683	#95	C₂³×C₃₁	1	1	yes	characteristic
684	#95	C₂³×C₃₁	1	2	yes	—
685	#95	C₂³×C₃₁	1	2	yes	—
686	#95	C₂³×C₃₁	1	1	yes	characteristic
687	#95	C₂³×C₃₁	1	2	yes	—
688	#95	C₂³×C₃₁	1	1	yes	characteristic
689	#95	C₂³×C₃₁	1	1	yes	characteristic
690	#95	C₂³×C₃₁	1	2	yes	—
691	#95	C₂³×C₃₁	1	2	yes	—
692	#95	C₂³×C₃₁	1	1	yes	characteristic
693	#95	C₂³×C₃₁	1	1	yes	characteristic
694	#95	C₂³×C₃₁	1	1	yes	characteristic
695	#95	C₂³×C₃₁	1	2	yes	—
696	#95	C₂³×C₃₁	1	2	yes	—
697	#95	C₂³×C₃₁	1	2	yes	—
698	#95	C₂³×C₃₁	1	2	yes	—
699	#95	C₂³×C₃₁	1	2	yes	—
700	#95	C₂³×C₃₁	1	2	yes	—
701	#95	C₂³×C₃₁	1	2	yes	—
702	#95	C₂³×C₃₁	1	2	yes	—
703	#95	C₂³×C₃₁	1	1	yes	characteristic
704	#95	C₂³×C₃₁	1	2	yes	—
705	#95	C₂³×C₃₁	1	2	yes	—
706	#95	C₂³×C₃₁	1	1	yes	characteristic
707	#95	C₂³×C₃₁	1	2	yes	—
708	C₃₁	#34326	1	1	yes	characteristic, direct product factor, Sylow
709	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	4	1	no	—
715	C₂×Q₈	—	4	1	no	—
716	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
717	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
718	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
731	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
769	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
770	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
771	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
772	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
773	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
774	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
775	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
776	C₄⋊C₄	#41×C₃₁	1	4	yes	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
784	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
785	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
786	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
787	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	4	2	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	1	no	—
800	C₄²	—	4	1	no	—
801	C₄²	—	4	1	no	—
802	C₄²	—	4	2	no	—
803	C₄²	—	4	2	no	—
804	C₄²	—	4	2	no	—
805	C₄²	—	4	2	no	—
806	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
807	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
808	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
809	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
810	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
811	C₄²	#41×C₃₁	1	4	yes	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
819	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
820	Q₈	—	2	8	no	—
821	Q₈	—	2	8	no	—
822	Q₈	—	4	4	no	—
823	D₄	—	2	8	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	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	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	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	4	8	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	—	8	4	no	—
877	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
878	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
879	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
880	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
881	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
882	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
883	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
884	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
887	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
888	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
889	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
890	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
891	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
892	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
901	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
902	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
903	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
904	C₂²	C₃₁×#585	1	1	yes	characteristic
905	C₂²	C₃₁×#585	1	1	yes	characteristic
906	C₂²	C₃₁×#585	1	1	yes	characteristic
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	C₄×#41×C₃₁	1	4	yes	—
929	C₂	—	4	4	no	—
930	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
931	C₂	C₃₁×#3428	1	1	yes	characteristic
932	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
933	C₂	C₃₁×#3507	1	1	yes	characteristic
934	C₂	C₃₁×#3510	1	1	yes	characteristic
935	C₂	C₃₁×#3516	1	1	yes	characteristic
936	C₂	C₃₁×#3521	1	1	yes	characteristic

	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×#2373	C₂	semidirect
3. C₃₁×#2373	C₂	semidirect
4. C₃₁×#2368	C₂	semidirect
7. C₃₁×#2365	C₂	semidirect
9. C₃₁×#2356	C₂	semidirect
10. C₃₁×#2355	C₂	semidirect
11. C₃₁×#2355	C₂	semidirect
12. C₃₁×#2343	C₂	semidirect
13. C₃₁×#2334	C₂	semidirect
14. C₃₁×#2332	C₂	semidirect
15. C₃₁×#2327	C₂	semidirect
17. C₄×C₃₁×#126	C₂	semidirect
19. C₃₁×#2298	C₂	semidirect
20. C₃₁×#2295	C₂	semidirect
21. C₃₁×#2276	C₂	semidirect
23. C₄²×Q₈×C₃₁	C₂	semidirect
24. C₃₁×#556	C₄	semidirect
131. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
132. C₃₁×#126	C₂×C₄	semidirect
133. C₃₁×#126	C₂×C₄	semidirect
136. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
141. C₄×Q₈×C₃₁	C₂×C₄	semidirect
142. C₄×Q₈×C₃₁	C₂×C₄	semidirect
143. C₄×Q₈×C₃₁	C₂×C₄	semidirect
147. C₃₁×#117	C₂×C₄	semidirect
343. #34326	C₃₁	direct (N × H)
426. #2373	C₂×C₃₁	semidirect
427. #2373	C₂×C₃₁	semidirect
428. #2368	C₂×C₃₁	semidirect
431. #2365	C₂×C₃₁	semidirect
433. #2356	C₂×C₃₁	semidirect
434. #2355	C₂×C₃₁	semidirect
435. #2355	C₂×C₃₁	semidirect
436. #2343	C₂×C₃₁	semidirect
437. #2334	C₂×C₃₁	semidirect
438. #2332	C₂×C₃₁	semidirect
439. #2327	C₂×C₃₁	semidirect
441. C₄×#126	C₂×C₃₁	semidirect
443. #2298	C₂×C₃₁	semidirect
444. #2295	C₂×C₃₁	semidirect
445. #2276	C₂×C₃₁	semidirect
447. C₄²×Q₈	C₂×C₃₁	semidirect
484. #556	C₄×C₃₁	semidirect
599. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
600. #126	C₂×C₄×C₃₁	semidirect
601. #126	C₂×C₄×C₃₁	semidirect
604. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
609. C₄×Q₈	C₂×C₄×C₃₁	semidirect
610. C₄×Q₈	C₂×C₄×C₃₁	semidirect
611. C₄×Q₈	C₂×C₄×C₃₁	semidirect
615. #117	C₂×C₄×C₃₁	semidirect
708. C₃₁	#34326	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×#556	2
C₃₁×#2373	2
C₃₁×#2368	2
C₃₁×#2367	2
C₃₁×#2365	2
C₃₁×#2357	2
C₃₁×#2356	2
C₃₁×#2355	2
C₃₁×#2343	2
C₃₁×#2334	2
C₃₁×#2332	2
C₃₁×#2327	2
C₃₁×#2326	2
C₄×C₃₁×#126	2
C₄×C₃₁×#124	2
C₃₁×#2298	2
C₃₁×#2295	2
C₃₁×#2276	2
C₃₁×#2275	2
C₄²×Q₈×C₃₁	2
#34326	31

Subgroups — C31×#34326 #21491085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34326 #21491085