Subgroups — C₃₁×#34457 #21491216

Order 7936.

2500 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	C₂×C₃₁×#551	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2383	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2360	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2359	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2358	C₂	1	1	yes	maximal, characteristic
8	D₄×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2322	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2317	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#120	C₂	1	1	yes	maximal, characteristic
19	C₂×C₃₁×#385	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#551	C₄	1	16	yes	complemented
22	C₂×C₃₁×#126	C₂²	1	2	yes	—
23	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₂×C₃₁×#117	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#391	C₂²	1	2	yes	complemented
42	C₃₁×#390	C₂²	1	1	yes	characteristic
43	C₃₁×#389	C₂²	1	2	yes	complemented
44	C₃₁×#389	C₂²	1	2	yes	complemented
45	C₃₁×#389	C₂²	1	2	yes	complemented
46	C₃₁×#389	C₂²	1	2	yes	complemented
47	C₃₁×#389	C₂²	1	2	yes	complemented
48	C₃₁×#389	C₂²	1	2	yes	complemented
49	C₃₁×#389	C₂²	1	2	yes	complemented
50	C₃₁×#388	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	complemented
56	C₃₁×#388	C₂²	1	2	yes	complemented
57	C₃₁×#388	C₂²	1	2	yes	complemented
58	C₃₁×#387	C₂²	1	2	yes	complemented
59	C₃₁×#387	C₂²	1	2	yes	complemented
60	C₃₁×#387	C₂²	1	2	yes	complemented
61	C₃₁×#387	C₂²	1	2	yes	complemented
62	C₃₁×#387	C₂²	1	2	yes	complemented
63	C₃₁×#387	C₂²	1	2	yes	complemented
64	C₃₁×#387	C₂²	1	2	yes	complemented
65	C₃₁×#387	C₂²	1	2	yes	complemented
66	C₃₁×#386	C₂²	1	2	yes	—
67	C₃₁×#386	C₂²	1	2	yes	—
68	C₃₁×#386	C₂²	1	1	yes	characteristic
69	C₃₁×#386	C₂²	1	1	yes	characteristic
70	C₃₁×#385	C₂²	1	2	yes	—
71	C₃₁×#385	C₂²	1	2	yes	—
72	C₃₁×#385	C₂²	1	2	yes	—
73	C₃₁×#385	C₂²	1	2	yes	—
74	C₃₁×#385	C₂²	1	2	yes	—
75	C₃₁×#385	C₂²	1	2	yes	—
76	C₃₁×#385	C₂²	1	2	yes	—
77	C₃₁×#385	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	1	yes	characteristic
83	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#385	C₂²	1	2	yes	complemented
85	C₃₁×#385	C₂²	1	2	yes	complemented
86	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#384	C₂²	1	2	yes	complemented
88	C₃₁×#383	C₂²	1	2	yes	complemented
89	C₃₁×#382	C₂²	1	2	yes	complemented
90	C₃₁×#382	C₂²	1	2	yes	complemented
91	C₃₁×#381	C₂²	1	2	yes	—
92	C₃₁×#381	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#380	C₂²	1	2	yes	—
94	C₃₁×#380	C₂²	1	2	yes	complemented
95	C₃₁×#379	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
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	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₃₁×#95	C₂²	1	2	yes	—
107	C₂×C₃₁×#95	C₂²	1	2	yes	—
108	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	—	4	2	no	—
113	C₂³×C₄×C₃₁	—	4	4	no	—
114	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
115	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₃₁×#126	C₂×C₄	1	16	yes	complemented
126	C₃₁×#124	C₂×C₄	1	8	yes	complemented
127	C₃₁×#123	C₂×C₄	1	8	yes	complemented
128	C₃₁×#123	C₂×C₄	1	16	yes	complemented
129	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
130	C₃₁×#120	C₂×C₄	1	8	yes	—
131	C₄×Q₈×C₃₁	—	4	2	no	—
132	C₄×D₄×C₃₁	—	4	2	no	—
133	C₄×D₄×C₃₁	—	4	4	no	—
134	C₄×D₄×C₃₁	—	4	4	no	—
135	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
136	C₃₁×#117	—	4	4	no	—
137	C₃₁×#117	C₂×C₄	1	16	yes	complemented
138	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
139	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
140	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
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×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
162	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×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	2	yes	—
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	2	yes	—
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	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	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	C₂⁴×C₃₁	—	2	4	no	—
216	C₂⁴×C₃₁	—	2	4	no	—
217	C₂⁴×C₃₁	—	4	1	no	—
218	C₂⁴×C₃₁	—	4	1	no	—
219	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
220	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₃₁	—	4	1	no	—
224	C₂×Q₈×C₃₁	—	4	1	no	—
225	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	complemented
226	C₂×D₄×C₃₁	—	2	4	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	4	1	no	—
229	C₂×D₄×C₃₁	—	4	1	no	—
230	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
231	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
232	C₂²×C₄×C₃₁	—	2	4	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	4	no	—
235	C₂²×C₄×C₃₁	—	2	4	no	—
236	C₂²×C₄×C₃₁	—	2	4	no	—
237	C₂²×C₄×C₃₁	—	2	4	no	—
238	C₂²×C₄×C₃₁	—	2	4	no	—
239	C₂²×C₄×C₃₁	—	2	2	no	—
240	C₂²×C₄×C₃₁	—	2	2	no	—
241	C₂²×C₄×C₃₁	—	4	2	no	—
242	C₂²×C₄×C₃₁	—	4	1	no	—
243	C₂²×C₄×C₃₁	—	4	2	no	—
244	C₂²×C₄×C₃₁	—	4	2	no	—
245	C₂²×C₄×C₃₁	—	4	2	no	—
246	C₂²×C₄×C₃₁	—	4	2	no	—
247	C₂²×C₄×C₃₁	—	4	2	no	—
248	C₂²×C₄×C₃₁	—	4	1	no	—
249	C₂²×C₄×C₃₁	—	4	2	no	—
250	C₂²×C₄×C₃₁	—	4	1	no	—
251	C₂²×C₄×C₃₁	—	4	2	no	—
252	C₂²×C₄×C₃₁	—	4	2	no	—
253	C₂²×C₄×C₃₁	—	4	2	no	—
254	C₂²×C₄×C₃₁	—	4	1	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	16	no	—
259	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
260	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
261	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	complemented
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	yes	—
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	—	4	2	no	—
281	C₄⋊C₄×C₃₁	—	4	2	no	—
282	C₄⋊C₄×C₃₁	—	4	2	no	—
283	C₄⋊C₄×C₃₁	—	4	2	no	—
284	C₄⋊C₄×C₃₁	—	4	2	no	—
285	C₄⋊C₄×C₃₁	—	4	2	no	—
286	C₄⋊C₄×C₃₁	—	4	2	no	—
287	C₄⋊C₄×C₃₁	—	4	2	no	—
288	C₄⋊C₄×C₃₁	—	4	2	no	—
289	C₄⋊C₄×C₃₁	—	4	2	no	—
290	C₄⋊C₄×C₃₁	—	4	1	no	—
291	C₄⋊C₄×C₃₁	—	4	2	no	—
292	C₄⋊C₄×C₃₁	—	4	2	no	—
293	C₄⋊C₄×C₃₁	—	4	1	no	—
294	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
295	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
296	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
297	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
298	C₂²⋊C₄×C₃₁	—	2	4	no	—
299	C₂²⋊C₄×C₃₁	—	2	4	no	—
300	C₂²⋊C₄×C₃₁	—	2	4	no	—
301	C₂²⋊C₄×C₃₁	—	2	4	no	—
302	C₂²⋊C₄×C₃₁	—	4	2	no	—
303	C₂²⋊C₄×C₃₁	—	4	2	no	—
304	C₂²⋊C₄×C₃₁	—	4	1	no	—
305	C₂²⋊C₄×C₃₁	—	4	1	no	—
306	C₂²⋊C₄×C₃₁	—	4	1	no	—
307	C₂²⋊C₄×C₃₁	—	4	1	no	—
308	C₂²⋊C₄×C₃₁	—	4	2	no	—
309	C₂²⋊C₄×C₃₁	—	4	2	no	—
310	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
311	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
312	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
313	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
314	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
315	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
316	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
317	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	complemented
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	4	2	no	—
320	C₄²×C₃₁	—	4	1	no	—
321	C₄²×C₃₁	—	4	2	no	—
322	C₄²×C₃₁	—	4	2	no	—
323	C₄²×C₃₁	—	4	2	no	—
324	C₄²×C₃₁	—	4	2	no	—
325	C₄²×C₃₁	—	4	2	no	—
326	C₄²×C₃₁	C₂²×C₄	1	4	yes	complemented
327	C₄²×C₃₁	C₂²×C₄	1	8	yes	complemented
328	#34457	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₃₁	—	2	2	no	—
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	2	no	—
333	C₂³×C₃₁	—	2	16	no	—
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	1	no	—
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	2	2	no	—
340	C₂³×C₃₁	—	2	1	no	—
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	—	4	4	no	—
343	C₂³×C₃₁	—	4	4	no	—
344	C₂³×C₃₁	—	4	8	no	—
345	C₂³×C₃₁	—	4	4	no	—
346	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
347	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
348	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
349	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
350	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
351	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
352	Q₈×C₃₁	—	4	4	no	—
353	D₄×C₃₁	—	2	16	no	—
354	D₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	2	16	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	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	1	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	2	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	4	8	no	—
394	C₂×C₄×C₃₁	—	4	4	no	—
395	C₂×C₄×C₃₁	—	4	8	no	—
396	C₂×C₄×C₃₁	—	4	4	no	—
397	C₂×C₄×C₃₁	—	4	8	no	—
398	C₂×C₄×C₃₁	—	4	4	no	—
399	C₂×C₄×C₃₁	—	8	2	no	—
400	C₂×C₄×C₃₁	—	8	4	no	—
401	C₂×C₄×C₃₁	—	8	4	no	—
402	C₂×C₄×C₃₁	—	8	2	no	—
403	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
405	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
406	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
407	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
408	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
409	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
410	C₂×#551	C₂×C₃₁	1	1	yes	characteristic
411	#2383	C₂×C₃₁	1	2	yes	complemented
412	#2379	C₂×C₃₁	1	1	yes	characteristic, complemented
413	#2376	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#2360	C₂×C₃₁	1	2	yes	complemented
415	#2359	C₂×C₃₁	1	2	yes	complemented
416	#2358	C₂×C₃₁	1	1	yes	characteristic
417	D₄×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
418	#2343	C₂×C₃₁	1	2	yes	complemented
419	#2342	C₂×C₃₁	1	2	yes	complemented
420	#2334	C₂×C₃₁	1	2	yes	complemented
421	#2329	C₂×C₃₁	1	2	yes	complemented
422	#2326	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#2322	C₂×C₃₁	1	2	yes	complemented
424	#2322	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#2318	C₂×C₃₁	1	2	yes	complemented
426	#2317	C₂×C₃₁	1	2	yes	complemented
427	C₄×#120	C₂×C₃₁	1	1	yes	characteristic
428	C₂×#385	C₂×C₃₁	1	2	yes	complemented
429	C₂²×C₃₁	—	2	4	no	—
430	C₂²×C₃₁	—	2	4	no	—
431	C₂²×C₃₁	—	2	4	no	—
432	C₂²×C₃₁	—	2	4	no	—
433	C₂²×C₃₁	—	2	4	no	—
434	C₂²×C₃₁	—	2	4	no	—
435	C₂²×C₃₁	—	2	4	no	—
436	C₂²×C₃₁	—	2	4	no	—
437	C₂²×C₃₁	—	2	2	no	—
438	C₂²×C₃₁	—	2	2	no	—
439	C₂²×C₃₁	—	4	16	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	—	4	1	no	—
442	C₂²×C₃₁	—	4	2	no	—
443	C₂²×C₃₁	—	4	2	no	—
444	C₂²×C₃₁	—	4	1	no	—
445	C₂²×C₃₁	—	4	1	no	—
446	C₂²×C₃₁	#520	1	8	yes	—
447	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
448	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
451	C₂²×C₃₁	#585	1	1	yes	characteristic
452	C₄×C₃₁	—	2	4	no	—
453	C₄×C₃₁	—	2	4	no	—
454	C₄×C₃₁	—	2	4	no	—
455	C₄×C₃₁	—	2	4	no	—
456	C₄×C₃₁	—	2	4	no	—
457	C₄×C₃₁	—	2	2	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	4	2	no	—
460	C₄×C₃₁	—	4	1	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	—	4	1	no	—
463	C₄×C₃₁	—	4	2	no	—
464	C₄×C₃₁	—	4	2	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	—	4	1	no	—
468	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
469	#551	C₄×C₃₁	1	16	yes	complemented
470	C₂×#126	C₂²×C₃₁	1	2	yes	—
471	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
472	C₂×#123	C₂²×C₃₁	1	2	yes	—
473	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
474	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
475	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
478	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
480	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
481	C₂×#117	C₂²×C₃₁	1	2	yes	—
482	C₂×#117	C₂²×C₃₁	1	2	yes	—
483	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
484	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
485	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
486	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
487	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
488	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#391	C₂²×C₃₁	1	2	yes	complemented
490	#390	C₂²×C₃₁	1	1	yes	characteristic
491	#389	C₂²×C₃₁	1	2	yes	complemented
492	#389	C₂²×C₃₁	1	2	yes	complemented
493	#389	C₂²×C₃₁	1	2	yes	complemented
494	#389	C₂²×C₃₁	1	2	yes	complemented
495	#389	C₂²×C₃₁	1	2	yes	complemented
496	#389	C₂²×C₃₁	1	2	yes	complemented
497	#389	C₂²×C₃₁	1	2	yes	complemented
498	#388	C₂²×C₃₁	1	2	yes	—
499	#388	C₂²×C₃₁	1	2	yes	—
500	#388	C₂²×C₃₁	1	2	yes	—
501	#388	C₂²×C₃₁	1	2	yes	—
502	#388	C₂²×C₃₁	1	2	yes	—
503	#388	C₂²×C₃₁	1	2	yes	complemented
504	#388	C₂²×C₃₁	1	2	yes	complemented
505	#388	C₂²×C₃₁	1	2	yes	complemented
506	#387	C₂²×C₃₁	1	2	yes	complemented
507	#387	C₂²×C₃₁	1	2	yes	complemented
508	#387	C₂²×C₃₁	1	2	yes	complemented
509	#387	C₂²×C₃₁	1	2	yes	complemented
510	#387	C₂²×C₃₁	1	2	yes	complemented
511	#387	C₂²×C₃₁	1	2	yes	complemented
512	#387	C₂²×C₃₁	1	2	yes	complemented
513	#387	C₂²×C₃₁	1	2	yes	complemented
514	#386	C₂²×C₃₁	1	2	yes	—
515	#386	C₂²×C₃₁	1	2	yes	—
516	#386	C₂²×C₃₁	1	1	yes	characteristic
517	#386	C₂²×C₃₁	1	1	yes	characteristic
518	#385	C₂²×C₃₁	1	2	yes	—
519	#385	C₂²×C₃₁	1	2	yes	—
520	#385	C₂²×C₃₁	1	2	yes	—
521	#385	C₂²×C₃₁	1	2	yes	—
522	#385	C₂²×C₃₁	1	2	yes	—
523	#385	C₂²×C₃₁	1	2	yes	—
524	#385	C₂²×C₃₁	1	2	yes	—
525	#385	C₂²×C₃₁	1	2	yes	—
526	#385	C₂²×C₃₁	1	2	yes	—
527	#385	C₂²×C₃₁	1	2	yes	—
528	#385	C₂²×C₃₁	1	2	yes	—
529	#385	C₂²×C₃₁	1	2	yes	—
530	#385	C₂²×C₃₁	1	1	yes	characteristic
531	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#385	C₂²×C₃₁	1	2	yes	complemented
533	#385	C₂²×C₃₁	1	2	yes	complemented
534	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
535	#384	C₂²×C₃₁	1	2	yes	complemented
536	#383	C₂²×C₃₁	1	2	yes	complemented
537	#382	C₂²×C₃₁	1	2	yes	complemented
538	#382	C₂²×C₃₁	1	2	yes	complemented
539	#381	C₂²×C₃₁	1	2	yes	—
540	#381	C₂²×C₃₁	1	1	yes	characteristic, complemented
541	#380	C₂²×C₃₁	1	2	yes	—
542	#380	C₂²×C₃₁	1	2	yes	complemented
543	#379	C₂²×C₃₁	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
545	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
546	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
549	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
551	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
552	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
553	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	C₂×#95	C₂²×C₃₁	1	2	yes	—
555	C₂×#95	C₂²×C₃₁	1	2	yes	—
556	C₂×C₃₁	—	2	8	no	—
557	C₂×C₃₁	—	4	2	no	—
558	C₂×C₃₁	—	4	2	no	—
559	C₂×C₃₁	C₂×#520	1	2	yes	—
560	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂×C₃₁	#3532	1	1	yes	characteristic
562	C₂×C₃₁	#3535	1	2	yes	—
563	C₂×C₃₁	#3538	1	1	yes	characteristic
564	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
567	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
568	C₂³×C₄	—	4	2	no	—
569	C₂³×C₄	—	4	4	no	—
570	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
571	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
572	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
573	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
574	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
575	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
580	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
581	#126	C₂×C₄×C₃₁	1	16	yes	complemented
582	#124	C₂×C₄×C₃₁	1	8	yes	complemented
583	#123	C₂×C₄×C₃₁	1	8	yes	complemented
584	#123	C₂×C₄×C₃₁	1	16	yes	complemented
585	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
586	#120	C₂×C₄×C₃₁	1	8	yes	—
587	C₄×Q₈	—	4	2	no	—
588	C₄×D₄	—	4	2	no	—
589	C₄×D₄	—	4	4	no	—
590	C₄×D₄	—	4	4	no	—
591	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
592	#117	—	4	4	no	—
593	#117	C₂×C₄×C₃₁	1	16	yes	complemented
594	C₂×C₄⋊C₄	—	4	4	no	—
595	C₂×C₄⋊C₄	—	4	2	no	—
596	C₂×C₄⋊C₄	—	4	4	no	—
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	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	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	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	1	yes	characteristic
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×C₂²⋊C₄	—	4	4	no	—
618	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
619	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
638	C₂×C₂²⋊C₄	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	2	yes	—
644	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
645	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	2	yes	—
650	#95	C₂³×C₃₁	1	2	yes	—
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	2	yes	—
653	#95	C₂³×C₃₁	1	2	yes	—
654	#95	C₂³×C₃₁	1	2	yes	—
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	#34457	1	1	yes	characteristic, direct product factor, Sylow
672	C₂⁴	—	2	4	no	—
673	C₂⁴	—	2	4	no	—
674	C₂⁴	—	4	1	no	—
675	C₂⁴	—	4	1	no	—
676	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
677	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	1	no	—
682	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	complemented
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	1	no	—
687	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
688	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	16	no	—
716	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
717	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
718	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	complemented
719	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	1	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	1	no	—
751	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
752	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
753	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
754	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	1	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
768	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
769	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
770	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
771	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
772	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
773	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
774	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	complemented
775	C₄²	—	2	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	1	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	2	no	—
783	C₄²	C₂²×C₄×C₃₁	1	4	yes	complemented
784	C₄²	C₂²×C₄×C₃₁	1	8	yes	complemented
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	16	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
803	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
804	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
805	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
806	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
807	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
808	Q₈	—	4	4	no	—
809	D₄	—	2	16	no	—
810	D₄	—	4	4	no	—
811	C₂×C₄	—	2	16	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	—	8	4	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	2	no	—
859	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
860	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
861	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
862	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
863	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
864	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
865	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	16	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	C₃₁×#520	1	8	yes	—
884	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
885	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
886	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
887	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
888	C₂²	C₃₁×#585	1	1	yes	characteristic
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₂	—	2	8	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	C₂×C₃₁×#520	1	2	yes	—
909	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂	C₃₁×#3532	1	1	yes	characteristic
911	C₂	C₃₁×#3535	1	2	yes	—
912	C₂	C₃₁×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#120	C₂²
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×#2379	C₂	semidirect
4. C₃₁×#2376	C₂	semidirect
5. C₃₁×#2360	C₂	semidirect
6. C₃₁×#2359	C₂	semidirect
8. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
9. C₃₁×#2343	C₂	semidirect
10. C₃₁×#2342	C₂	semidirect
11. C₃₁×#2334	C₂	semidirect
12. C₃₁×#2329	C₂	semidirect
13. C₃₁×#2326	C₂	semidirect
14. C₃₁×#2322	C₂	semidirect
15. C₃₁×#2322	C₂	semidirect
16. C₃₁×#2318	C₂	semidirect
17. C₃₁×#2317	C₂	semidirect
19. C₂×C₃₁×#385	C₂	semidirect
21. C₃₁×#551	C₄	semidirect
28. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
40. C₃₁×#391	C₂²	semidirect
41. C₃₁×#391	C₂²	semidirect
43. C₃₁×#389	C₂²	semidirect
44. C₃₁×#389	C₂²	semidirect
45. C₃₁×#389	C₂²	semidirect
46. C₃₁×#389	C₂²	semidirect
47. C₃₁×#389	C₂²	semidirect
48. C₃₁×#389	C₂²	semidirect
49. C₃₁×#389	C₂²	semidirect
55. C₃₁×#388	C₂²	semidirect
56. C₃₁×#388	C₂²	semidirect
57. C₃₁×#388	C₂²	semidirect
58. C₃₁×#387	C₂²	semidirect
59. C₃₁×#387	C₂²	semidirect
60. C₃₁×#387	C₂²	semidirect
61. C₃₁×#387	C₂²	semidirect
62. C₃₁×#387	C₂²	semidirect
63. C₃₁×#387	C₂²	semidirect
64. C₃₁×#387	C₂²	semidirect
65. C₃₁×#387	C₂²	semidirect
83. C₃₁×#385	C₂²	semidirect
84. C₃₁×#385	C₂²	semidirect
85. C₃₁×#385	C₂²	semidirect
86. C₃₁×#384	C₂²	semidirect
87. C₃₁×#384	C₂²	semidirect
88. C₃₁×#383	C₂²	semidirect
89. C₃₁×#382	C₂²	semidirect
90. C₃₁×#382	C₂²	semidirect
92. C₃₁×#381	C₂²	semidirect
94. C₃₁×#380	C₂²	semidirect
96. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
97. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
105. C₃₁×#376	C₂²	semidirect
125. C₃₁×#126	C₂×C₄	semidirect
126. C₃₁×#124	C₂×C₄	semidirect
127. C₃₁×#123	C₂×C₄	semidirect
128. C₃₁×#123	C₂×C₄	semidirect
129. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
135. C₄×D₄×C₃₁	C₂×C₄	semidirect
137. C₃₁×#117	C₂×C₄	semidirect
162. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
225. C₂×Q₈×C₃₁	C₂²×C₄	semidirect
261. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
294. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
295. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
296. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
297. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
316. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
317. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
326. C₄²×C₃₁	C₂²×C₄	semidirect
327. C₄²×C₃₁	C₂²×C₄	semidirect
328. #34457	C₃₁	direct (N × H)
411. #2383	C₂×C₃₁	semidirect
412. #2379	C₂×C₃₁	semidirect
413. #2376	C₂×C₃₁	semidirect
414. #2360	C₂×C₃₁	semidirect
415. #2359	C₂×C₃₁	semidirect
417. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
418. #2343	C₂×C₃₁	semidirect
419. #2342	C₂×C₃₁	semidirect
420. #2334	C₂×C₃₁	semidirect
421. #2329	C₂×C₃₁	semidirect
422. #2326	C₂×C₃₁	semidirect
423. #2322	C₂×C₃₁	semidirect
424. #2322	C₂×C₃₁	semidirect
425. #2318	C₂×C₃₁	semidirect
426. #2317	C₂×C₃₁	semidirect
428. C₂×#385	C₂×C₃₁	semidirect
469. #551	C₄×C₃₁	semidirect
476. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
485. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
488. #391	C₂²×C₃₁	semidirect
489. #391	C₂²×C₃₁	semidirect
491. #389	C₂²×C₃₁	semidirect
492. #389	C₂²×C₃₁	semidirect
493. #389	C₂²×C₃₁	semidirect
494. #389	C₂²×C₃₁	semidirect
495. #389	C₂²×C₃₁	semidirect
496. #389	C₂²×C₃₁	semidirect
497. #389	C₂²×C₃₁	semidirect
503. #388	C₂²×C₃₁	semidirect
504. #388	C₂²×C₃₁	semidirect
505. #388	C₂²×C₃₁	semidirect
506. #387	C₂²×C₃₁	semidirect
507. #387	C₂²×C₃₁	semidirect
508. #387	C₂²×C₃₁	semidirect
509. #387	C₂²×C₃₁	semidirect
510. #387	C₂²×C₃₁	semidirect
511. #387	C₂²×C₃₁	semidirect
512. #387	C₂²×C₃₁	semidirect
513. #387	C₂²×C₃₁	semidirect
531. #385	C₂²×C₃₁	semidirect
532. #385	C₂²×C₃₁	semidirect
533. #385	C₂²×C₃₁	semidirect
534. #384	C₂²×C₃₁	semidirect
535. #384	C₂²×C₃₁	semidirect
536. #383	C₂²×C₃₁	semidirect
537. #382	C₂²×C₃₁	semidirect
538. #382	C₂²×C₃₁	semidirect
540. #381	C₂²×C₃₁	semidirect
542. #380	C₂²×C₃₁	semidirect
544. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
545. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
552. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
553. #376	C₂²×C₃₁	semidirect
581. #126	C₂×C₄×C₃₁	semidirect
582. #124	C₂×C₄×C₃₁	semidirect
583. #123	C₂×C₄×C₃₁	semidirect
584. #123	C₂×C₄×C₃₁	semidirect
585. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
591. C₄×D₄	C₂×C₄×C₃₁	semidirect
593. #117	C₂×C₄×C₃₁	semidirect
618. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
671. C₃₁	#34457	direct (N × H)
682. C₂×Q₈	C₂²×C₄×C₃₁	semidirect
718. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
751. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
752. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
753. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
754. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
773. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
774. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
783. C₄²	C₂²×C₄×C₃₁	semidirect
784. C₄²	C₂²×C₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#551	2
C₃₁×#2383	2
C₃₁×#2379	2
C₃₁×#2376	2
C₃₁×#2360	2
C₃₁×#2359	2
C₃₁×#2358	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2343	2
C₃₁×#2342	2
C₃₁×#2334	2
C₃₁×#2329	2
C₃₁×#2326	2
C₃₁×#2322	2
C₃₁×#2318	2
C₃₁×#2317	2
C₄×C₃₁×#120	2
C₂×C₃₁×#385	2
#34457	31

Subgroups — C31×#34457 #21491216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34457 #21491216