Subgroups — C₃₁×#35042 #21491801

Order 7936.

1766 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2854	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2852	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2646	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2639	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2623	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2597	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2596	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2590	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2589	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2533	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2532	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2479	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2478	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2325	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#126	C₂²	1	2	yes	—
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
25	C₂×C₃₁×#117	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#400	C₂²	1	2	yes	—
32	C₃₁×#400	C₂²	1	2	yes	—
33	C₃₁×#400	C₂²	1	2	yes	—
34	C₃₁×#400	C₂²	1	2	yes	—
35	C₃₁×#400	C₂²	1	2	yes	—
36	C₃₁×#399	C₂²	1	2	yes	—
37	C₃₁×#399	C₂²	1	2	yes	—
38	C₃₁×#398	C₂²	1	2	yes	—
39	C₃₁×#398	C₂²	1	2	yes	—
40	C₃₁×#398	C₂²	1	2	yes	—
41	C₃₁×#398	C₂²	1	2	yes	—
42	C₃₁×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	—
45	C₃₁×#394	C₂²	1	2	yes	—
46	C₃₁×#393	C₂²	1	2	yes	—
47	C₃₁×#391	C₂²	1	2	yes	—
48	C₃₁×#391	C₂²	1	1	yes	characteristic
49	C₃₁×#391	C₂²	1	1	yes	characteristic
50	C₃₁×#390	C₂²	1	1	yes	characteristic
51	C₃₁×#390	C₂²	1	1	yes	characteristic
52	C₃₁×#389	C₂²	1	2	yes	—
53	C₃₁×#389	C₂²	1	2	yes	—
54	C₃₁×#389	C₂²	1	2	yes	—
55	C₃₁×#389	C₂²	1	1	yes	characteristic
56	C₃₁×#389	C₂²	1	1	yes	characteristic
57	C₃₁×#389	C₂²	1	1	yes	characteristic
58	C₃₁×#389	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	—
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#388	C₂²	1	2	yes	—
69	C₃₁×#387	C₂²	1	2	yes	—
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#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×#386	C₂²	1	2	yes	—
82	C₃₁×#386	C₂²	1	2	yes	—
83	C₃₁×#386	C₂²	1	2	yes	—
84	C₃₁×#386	C₂²	1	2	yes	—
85	C₃₁×#386	C₂²	1	2	yes	—
86	C₃₁×#385	C₂²	1	2	yes	—
87	C₃₁×#385	C₂²	1	2	yes	—
88	C₃₁×#385	C₂²	1	2	yes	—
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#385	C₂²	1	2	yes	—
91	C₃₁×#385	C₂²	1	2	yes	—
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#383	C₂²	1	2	yes	—
94	C₃₁×#381	C₂²	1	2	yes	—
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₃₁×#380	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
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	2	yes	—
102	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₃₁×#376	C₂²	1	2	yes	—
105	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
106	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₃₁×#126	—	4	4	no	—
119	C₃₁×#123	—	2	8	no	—
120	C₃₁×C₂²⋊Q₈	—	2	4	no	—
121	C₃₁×#121	—	2	4	no	—
122	C₄×D₄×C₃₁	—	2	8	no	—
123	C₃₁×#117	—	4	4	no	—
124	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
125	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₃₁	—	2	4	no	—
164	C₂×C₄²×C₃₁	—	4	2	no	—
165	C₂×C₄²×C₃₁	—	4	2	no	—
166	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
177	C₃₁×#95	C₂³	1	2	yes	—
178	C₃₁×#95	C₂³	1	2	yes	—
179	C₃₁×#95	C₂³	1	2	yes	—
180	C₃₁×#95	C₂³	1	2	yes	—
181	C₃₁×#95	C₂³	1	2	yes	—
182	C₃₁×#95	C₂³	1	2	yes	—
183	C₃₁×#95	C₂³	1	2	yes	—
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	2	yes	—
187	C₃₁×#95	C₂³	1	2	yes	—
188	C₃₁×#95	C₂³	1	2	yes	—
189	C₃₁×#95	C₂³	1	2	yes	—
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	2	yes	—
192	C₃₁×#95	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	2	yes	—
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
206	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
207	C₂×Q₈×C₃₁	—	2	2	no	—
208	C₂×Q₈×C₃₁	—	4	1	no	—
209	C₂×Q₈×C₃₁	—	4	1	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	4	1	no	—
215	C₂×D₄×C₃₁	—	4	1	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	4	1	no	—
226	C₂²×C₄×C₃₁	—	4	1	no	—
227	C₂²×C₄×C₃₁	—	4	1	no	—
228	C₂²×C₄×C₃₁	—	4	1	no	—
229	C₂²×C₄×C₃₁	—	4	2	no	—
230	C₂²×C₄×C₃₁	—	4	1	no	—
231	C₂²×C₄×C₃₁	—	4	2	no	—
232	C₂²×C₄×C₃₁	—	4	1	no	—
233	C₂²×C₄×C₃₁	—	4	1	no	—
234	C₂²×C₄×C₃₁	—	4	1	no	—
235	C₂²×C₄×C₃₁	—	4	1	no	—
236	C₂²×C₄×C₃₁	—	4	1	no	—
237	C₂²×C₄×C₃₁	#41	1	4	yes	—
238	C₂²×C₄×C₃₁	#41	1	4	yes	—
239	C₂²×C₄×C₃₁	#41	1	4	yes	—
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	4	no	—
260	C₄⋊C₄×C₃₁	—	2	4	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	4	no	—
266	C₄⋊C₄×C₃₁	—	2	4	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	4	1	no	—
270	C₄⋊C₄×C₃₁	—	4	1	no	—
271	C₄⋊C₄×C₃₁	—	4	1	no	—
272	C₄⋊C₄×C₃₁	—	4	1	no	—
273	C₄⋊C₄×C₃₁	—	4	2	no	—
274	C₄⋊C₄×C₃₁	—	4	2	no	—
275	C₄⋊C₄×C₃₁	—	4	2	no	—
276	C₄⋊C₄×C₃₁	—	4	2	no	—
277	C₄⋊C₄×C₃₁	—	4	2	no	—
278	C₄⋊C₄×C₃₁	—	4	2	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	4	no	—
281	C₂²⋊C₄×C₃₁	—	2	4	no	—
282	C₂²⋊C₄×C₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	4	2	no	—
289	C₂²⋊C₄×C₃₁	—	4	2	no	—
290	C₂²⋊C₄×C₃₁	—	4	2	no	—
291	C₂²⋊C₄×C₃₁	—	4	2	no	—
292	C₂²⋊C₄×C₃₁	—	4	2	no	—
293	C₂²⋊C₄×C₃₁	—	4	2	no	—
294	C₄²×C₃₁	—	2	2	no	—
295	C₄²×C₃₁	—	2	2	no	—
296	C₄²×C₃₁	—	2	2	no	—
297	C₄²×C₃₁	—	2	2	no	—
298	C₄²×C₃₁	—	2	4	no	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	4	no	—
301	C₄²×C₃₁	—	4	2	no	—
302	C₄²×C₃₁	—	4	2	no	—
303	C₄²×C₃₁	—	4	2	no	—
304	C₄²×C₃₁	—	4	2	no	—
305	#35042	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂³×C₃₁	—	2	1	no	—
307	C₂³×C₃₁	—	2	1	no	—
308	C₂³×C₃₁	—	2	1	no	—
309	C₂³×C₃₁	—	2	1	no	—
310	C₂³×C₃₁	—	2	2	no	—
311	C₂³×C₃₁	—	2	2	no	—
312	C₂³×C₃₁	—	2	2	no	—
313	C₂³×C₃₁	—	2	2	no	—
314	C₂³×C₃₁	—	2	2	no	—
315	C₂³×C₃₁	—	2	2	no	—
316	C₂³×C₃₁	—	2	2	no	—
317	C₂³×C₃₁	C₂×#41	1	2	yes	—
318	C₂³×C₃₁	C₂×#41	1	2	yes	—
319	C₂³×C₃₁	C₂×#41	1	2	yes	—
320	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
321	Q₈×C₃₁	—	8	2	no	—
322	D₄×C₃₁	—	4	8	no	—
323	D₄×C₃₁	—	8	2	no	—
324	C₂×C₄×C₃₁	—	2	8	no	—
325	C₂×C₄×C₃₁	—	2	8	no	—
326	C₂×C₄×C₃₁	—	2	1	no	—
327	C₂×C₄×C₃₁	—	2	1	no	—
328	C₂×C₄×C₃₁	—	2	1	no	—
329	C₂×C₄×C₃₁	—	2	1	no	—
330	C₂×C₄×C₃₁	—	2	1	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	1	no	—
334	C₂×C₄×C₃₁	—	2	1	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	1	no	—
338	C₂×C₄×C₃₁	—	2	1	no	—
339	C₂×C₄×C₃₁	—	2	1	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	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	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	4	4	no	—
371	C₂×C₄×C₃₁	—	4	4	no	—
372	C₂×C₄×C₃₁	—	4	8	no	—
373	C₂×C₄×C₃₁	—	4	4	no	—
374	C₂×C₄×C₃₁	—	4	4	no	—
375	C₂×C₄×C₃₁	—	4	4	no	—
376	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
377	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
378	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
379	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
380	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
381	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
382	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
383	#2855	C₂×C₃₁	1	1	yes	characteristic, complemented
384	#2854	C₂×C₃₁	1	1	yes	characteristic
385	#2852	C₂×C₃₁	1	2	yes	complemented
386	#2646	C₂×C₃₁	1	1	yes	characteristic, complemented
387	#2639	C₂×C₃₁	1	1	yes	characteristic
388	#2623	C₂×C₃₁	1	2	yes	complemented
389	#2597	C₂×C₃₁	1	2	yes	complemented
390	#2596	C₂×C₃₁	1	2	yes	complemented
391	#2590	C₂×C₃₁	1	2	yes	complemented
392	#2589	C₂×C₃₁	1	2	yes	complemented
393	#2533	C₂×C₃₁	1	2	yes	complemented
394	#2532	C₂×C₃₁	1	2	yes	complemented
395	#2479	C₂×C₃₁	1	2	yes	complemented
396	#2478	C₂×C₃₁	1	2	yes	complemented
397	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
398	#2325	C₂×C₃₁	1	1	yes	characteristic
399	#2322	C₂×C₃₁	1	2	yes	complemented
400	#2290	C₂×C₃₁	1	2	yes	complemented
401	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
402	C₂²×C₃₁	—	2	2	no	—
403	C₂²×C₃₁	—	2	2	no	—
404	C₂²×C₃₁	—	2	2	no	—
405	C₂²×C₃₁	—	2	2	no	—
406	C₂²×C₃₁	—	2	2	no	—
407	C₂²×C₃₁	—	2	2	no	—
408	C₂²×C₃₁	—	4	2	no	—
409	C₂²×C₃₁	—	4	2	no	—
410	C₂²×C₃₁	—	4	2	no	—
411	C₂²×C₃₁	—	4	2	no	—
412	C₂²×C₃₁	—	4	2	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	4	2	no	—
415	C₂²×C₃₁	#529	1	4	yes	—
416	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
418	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
419	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
421	C₂²×C₃₁	#585	1	1	yes	characteristic
422	C₂²×C₃₁	#585	1	1	yes	characteristic
423	C₄×C₃₁	—	2	2	no	—
424	C₄×C₃₁	—	2	2	no	—
425	C₄×C₃₁	—	2	4	no	—
426	C₄×C₃₁	—	2	2	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	2	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	4	2	no	—
431	C₄×C₃₁	—	4	2	no	—
432	C₄×C₃₁	—	4	2	no	—
433	C₄×C₃₁	—	4	2	no	—
434	C₄×C₃₁	—	4	2	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	2	no	—
437	C₄×C₃₁	—	4	2	no	—
438	C₄×C₃₁	—	4	2	no	—
439	C₄×C₃₁	—	4	2	no	—
440	C₂×#126	C₂²×C₃₁	1	2	yes	—
441	C₂×#123	C₂²×C₃₁	1	2	yes	—
442	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
445	C₂×#117	C₂²×C₃₁	1	2	yes	—
446	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
447	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
448	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
449	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
450	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
451	#400	C₂²×C₃₁	1	2	yes	—
452	#400	C₂²×C₃₁	1	2	yes	—
453	#400	C₂²×C₃₁	1	2	yes	—
454	#400	C₂²×C₃₁	1	2	yes	—
455	#400	C₂²×C₃₁	1	2	yes	—
456	#399	C₂²×C₃₁	1	2	yes	—
457	#399	C₂²×C₃₁	1	2	yes	—
458	#398	C₂²×C₃₁	1	2	yes	—
459	#398	C₂²×C₃₁	1	2	yes	—
460	#398	C₂²×C₃₁	1	2	yes	—
461	#398	C₂²×C₃₁	1	2	yes	—
462	#397	C₂²×C₃₁	1	2	yes	—
463	#397	C₂²×C₃₁	1	2	yes	—
464	#397	C₂²×C₃₁	1	2	yes	—
465	#394	C₂²×C₃₁	1	2	yes	—
466	#393	C₂²×C₃₁	1	2	yes	—
467	#391	C₂²×C₃₁	1	2	yes	—
468	#391	C₂²×C₃₁	1	1	yes	characteristic
469	#391	C₂²×C₃₁	1	1	yes	characteristic
470	#390	C₂²×C₃₁	1	1	yes	characteristic
471	#390	C₂²×C₃₁	1	1	yes	characteristic
472	#389	C₂²×C₃₁	1	2	yes	—
473	#389	C₂²×C₃₁	1	2	yes	—
474	#389	C₂²×C₃₁	1	2	yes	—
475	#389	C₂²×C₃₁	1	1	yes	characteristic
476	#389	C₂²×C₃₁	1	1	yes	characteristic
477	#389	C₂²×C₃₁	1	1	yes	characteristic
478	#389	C₂²×C₃₁	1	1	yes	characteristic
479	#388	C₂²×C₃₁	1	2	yes	—
480	#388	C₂²×C₃₁	1	2	yes	—
481	#388	C₂²×C₃₁	1	2	yes	—
482	#388	C₂²×C₃₁	1	2	yes	—
483	#388	C₂²×C₃₁	1	2	yes	—
484	#388	C₂²×C₃₁	1	2	yes	—
485	#388	C₂²×C₃₁	1	2	yes	—
486	#388	C₂²×C₃₁	1	2	yes	—
487	#388	C₂²×C₃₁	1	2	yes	—
488	#388	C₂²×C₃₁	1	2	yes	—
489	#387	C₂²×C₃₁	1	2	yes	—
490	#387	C₂²×C₃₁	1	2	yes	—
491	#387	C₂²×C₃₁	1	2	yes	—
492	#387	C₂²×C₃₁	1	2	yes	—
493	#387	C₂²×C₃₁	1	2	yes	—
494	#387	C₂²×C₃₁	1	2	yes	—
495	#387	C₂²×C₃₁	1	2	yes	—
496	#387	C₂²×C₃₁	1	2	yes	—
497	#387	C₂²×C₃₁	1	2	yes	—
498	#387	C₂²×C₃₁	1	2	yes	—
499	#387	C₂²×C₃₁	1	2	yes	—
500	#387	C₂²×C₃₁	1	2	yes	—
501	#386	C₂²×C₃₁	1	2	yes	—
502	#386	C₂²×C₃₁	1	2	yes	—
503	#386	C₂²×C₃₁	1	2	yes	—
504	#386	C₂²×C₃₁	1	2	yes	—
505	#386	C₂²×C₃₁	1	2	yes	—
506	#385	C₂²×C₃₁	1	2	yes	—
507	#385	C₂²×C₃₁	1	2	yes	—
508	#385	C₂²×C₃₁	1	2	yes	—
509	#385	C₂²×C₃₁	1	2	yes	—
510	#385	C₂²×C₃₁	1	2	yes	—
511	#385	C₂²×C₃₁	1	2	yes	—
512	#385	C₂²×C₃₁	1	2	yes	—
513	#383	C₂²×C₃₁	1	2	yes	—
514	#381	C₂²×C₃₁	1	2	yes	—
515	#380	C₂²×C₃₁	1	1	yes	characteristic
516	#380	C₂²×C₃₁	1	1	yes	characteristic
517	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
518	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
519	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
521	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
524	#376	C₂²×C₃₁	1	2	yes	—
525	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
527	C₂×C₃₁	—	2	4	no	—
528	C₂×C₃₁	—	8	2	no	—
529	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
530	C₂×C₃₁	#3459	1	1	yes	characteristic
531	C₂×C₃₁	#3461	1	1	yes	characteristic
532	C₂×C₃₁	#3491	1	1	yes	characteristic
533	C₂×C₃₁	#3492	1	1	yes	characteristic
534	C₂×C₃₁	#3506	1	1	yes	characteristic
535	C₂×C₃₁	#3507	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
538	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
545	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
547	#126	—	4	4	no	—
548	#123	—	2	8	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	#121	—	2	4	no	—
551	C₄×D₄	—	2	8	no	—
552	#117	—	4	4	no	—
553	C₂×C₄⋊C₄	—	2	4	no	—
554	C₂×C₄⋊C₄	—	2	4	no	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
592	C₂×C₄²	—	2	4	no	—
593	C₂×C₄²	—	4	2	no	—
594	C₂×C₄²	—	4	2	no	—
595	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
596	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
597	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
598	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
603	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
606	#95	C₂³×C₃₁	1	2	yes	—
607	#95	C₂³×C₃₁	1	2	yes	—
608	#95	C₂³×C₃₁	1	2	yes	—
609	#95	C₂³×C₃₁	1	2	yes	—
610	#95	C₂³×C₃₁	1	2	yes	—
611	#95	C₂³×C₃₁	1	2	yes	—
612	#95	C₂³×C₃₁	1	2	yes	—
613	#95	C₂³×C₃₁	1	2	yes	—
614	#95	C₂³×C₃₁	1	2	yes	—
615	#95	C₂³×C₃₁	1	2	yes	—
616	#95	C₂³×C₃₁	1	2	yes	—
617	#95	C₂³×C₃₁	1	2	yes	—
618	#95	C₂³×C₃₁	1	2	yes	—
619	#95	C₂³×C₃₁	1	2	yes	—
620	#95	C₂³×C₃₁	1	2	yes	—
621	#95	C₂³×C₃₁	1	2	yes	—
622	#95	C₂³×C₃₁	1	2	yes	—
623	#95	C₂³×C₃₁	1	2	yes	—
624	#95	C₂³×C₃₁	1	2	yes	—
625	#95	C₂³×C₃₁	1	2	yes	—
626	#95	C₂³×C₃₁	1	2	yes	—
627	#95	C₂³×C₃₁	1	2	yes	—
628	#95	C₂³×C₃₁	1	2	yes	—
629	#95	C₂³×C₃₁	1	2	yes	—
630	#95	C₂³×C₃₁	1	2	yes	—
631	#95	C₂³×C₃₁	1	2	yes	—
632	#95	C₂³×C₃₁	1	2	yes	—
633	#95	C₂³×C₃₁	1	2	yes	—
634	C₃₁	#35042	1	1	yes	characteristic, direct product factor, Sylow
635	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
636	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	4	1	no	—
639	C₂×Q₈	—	4	1	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	4	1	no	—
645	C₂×D₄	—	4	1	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	4	1	no	—
656	C₂²×C₄	—	4	1	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	—	4	1	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	#41×C₃₁	1	4	yes	—
668	C₂²×C₄	#41×C₃₁	1	4	yes	—
669	C₂²×C₄	#41×C₃₁	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	4	no	—
730	C₄²	—	2	4	no	—
731	C₄²	—	4	2	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	C₂×#41×C₃₁	1	2	yes	—
747	C₂³	C₂×#41×C₃₁	1	2	yes	—
748	C₂³	C₂×#41×C₃₁	1	2	yes	—
749	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
750	Q₈	—	8	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	8	2	no	—
753	C₂×C₄	—	2	8	no	—
754	C₂×C₄	—	2	8	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	8	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
806	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
807	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
808	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
809	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
810	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
811	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	C₃₁×#529	1	4	yes	—
826	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
827	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
828	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
829	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
831	C₂²	C₃₁×#585	1	1	yes	characteristic
832	C₂²	C₃₁×#585	1	1	yes	characteristic
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	4	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₂	—	2	4	no	—
851	C₂	—	8	2	no	—
852	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
853	C₂	C₃₁×#3459	1	1	yes	characteristic
854	C₂	C₃₁×#3461	1	1	yes	characteristic
855	C₂	C₃₁×#3491	1	1	yes	characteristic
856	C₂	C₃₁×#3492	1	1	yes	characteristic
857	C₂	C₃₁×#3506	1	1	yes	characteristic
858	C₂	C₃₁×#3507	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2855	C₂	semidirect
3. C₃₁×#2852	C₂	semidirect
4. C₃₁×#2646	C₂	semidirect
6. C₃₁×#2623	C₂	semidirect
7. C₃₁×#2597	C₂	semidirect
8. C₃₁×#2596	C₂	semidirect
9. C₃₁×#2590	C₂	semidirect
10. C₃₁×#2589	C₂	semidirect
11. C₃₁×#2533	C₂	semidirect
12. C₃₁×#2532	C₂	semidirect
13. C₃₁×#2479	C₂	semidirect
14. C₃₁×#2478	C₂	semidirect
15. C₃₁×#2329	C₂	semidirect
17. C₃₁×#2322	C₂	semidirect
18. C₃₁×#2290	C₂	semidirect
19. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
305. #35042	C₃₁	direct (N × H)
383. #2855	C₂×C₃₁	semidirect
385. #2852	C₂×C₃₁	semidirect
386. #2646	C₂×C₃₁	semidirect
388. #2623	C₂×C₃₁	semidirect
389. #2597	C₂×C₃₁	semidirect
390. #2596	C₂×C₃₁	semidirect
391. #2590	C₂×C₃₁	semidirect
392. #2589	C₂×C₃₁	semidirect
393. #2533	C₂×C₃₁	semidirect
394. #2532	C₂×C₃₁	semidirect
395. #2479	C₂×C₃₁	semidirect
396. #2478	C₂×C₃₁	semidirect
397. #2329	C₂×C₃₁	semidirect
399. #2322	C₂×C₃₁	semidirect
400. #2290	C₂×C₃₁	semidirect
401. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
634. C₃₁	#35042	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×#2855	2
C₃₁×#2854	2
C₃₁×#2852	2
C₃₁×#2646	2
C₃₁×#2639	2
C₃₁×#2623	2
C₃₁×#2597	2
C₃₁×#2596	2
C₃₁×#2590	2
C₃₁×#2589	2
C₃₁×#2533	2
C₃₁×#2532	2
C₃₁×#2479	2
C₃₁×#2478	2
C₃₁×#2329	2
C₃₁×#2325	2
C₃₁×#2322	2
C₃₁×#2290	2
C₂×C₄×C₄⋊C₄×C₃₁	2
#35042	31

Subgroups — C31×#35042 #21491801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35042 #21491801