Subgroups — C₃₁×#34983 #21491742

Order 7936.

3038 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#534	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2853	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2849	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2623	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2622	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2444	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2443	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2419	C₂	1	4	yes	maximal, complemented
10	C₃₁×#2418	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2315	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2308	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2308	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#534	—	2	8	no	—
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₃₁×#123	C₂²	1	2	yes	—
23	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
24	C₂×C₃₁×#121	C₂²	1	2	yes	—
25	C₂×C₃₁×#121	C₂²	1	2	yes	—
26	C₂×C₃₁×#120	C₂²	1	2	yes	—
27	C₂×C₃₁×#120	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₃₁	—	2	8	no	—
29	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
31	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#400	C₂²	1	4	yes	complemented
41	C₃₁×#399	C₂²	1	4	yes	complemented
42	C₃₁×#398	C₂²	1	4	yes	complemented
43	C₃₁×#397	C₂²	1	4	yes	complemented
44	C₃₁×#397	C₂²	1	4	yes	complemented
45	C₃₁×#397	C₂²	1	4	yes	complemented
46	C₃₁×#394	C₂²	1	4	yes	complemented
47	C₃₁×#394	C₂²	1	4	yes	complemented
48	C₃₁×#388	C₂²	1	4	yes	complemented
49	C₃₁×#388	C₂²	1	4	yes	complemented
50	C₃₁×#387	C₂²	1	4	yes	complemented
51	C₃₁×#387	C₂²	1	4	yes	complemented
52	C₃₁×#386	C₂²	1	2	yes	—
53	C₃₁×#386	C₂²	1	2	yes	—
54	C₃₁×#386	C₂²	1	4	yes	—
55	C₃₁×#386	C₂²	1	2	yes	—
56	C₃₁×#386	C₂²	1	2	yes	—
57	C₃₁×#386	C₂²	1	4	yes	complemented
58	C₃₁×#386	C₂²	1	4	yes	complemented
59	C₃₁×#386	C₂²	1	4	yes	complemented
60	C₃₁×#386	C₂²	1	4	yes	complemented
61	C₃₁×#385	C₂²	1	2	yes	complemented
62	C₃₁×#385	C₂²	1	2	yes	complemented
63	C₃₁×#385	C₂²	1	2	yes	complemented
64	C₃₁×#385	C₂²	1	2	yes	complemented
65	C₃₁×#385	C₂²	1	2	yes	complemented
66	C₃₁×#385	C₂²	1	4	yes	complemented
67	C₃₁×#385	C₂²	1	2	yes	complemented
68	C₃₁×#385	C₂²	1	4	yes	complemented
69	C₃₁×#381	C₂²	1	2	yes	complemented
70	C₃₁×#381	C₂²	1	2	yes	complemented
71	C₃₁×#381	C₂²	1	4	yes	complemented
72	C₃₁×#380	C₂²	1	4	yes	complemented
73	C₃₁×#379	C₂²	1	2	yes	complemented
74	C₃₁×#379	C₂²	1	2	yes	complemented
75	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
76	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
77	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
78	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
79	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₃₁	—	2	4	no	—
81	C₂²×D₄×C₃₁	—	2	4	no	—
82	C₂²×D₄×C₃₁	—	2	4	no	—
83	C₂²×D₄×C₃₁	—	2	4	no	—
84	C₂²×D₄×C₃₁	—	2	4	no	—
85	C₂²×D₄×C₃₁	D₄	1	8	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₃₁	—	2	4	no	—
93	C₂³×C₄×C₃₁	—	2	4	no	—
94	C₂³×C₄×C₃₁	—	4	4	no	—
95	C₂³×C₄×C₃₁	—	4	4	no	—
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
107	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×#123	—	2	8	no	—
110	C₃₁×#123	—	2	8	no	—
111	C₃₁×#123	—	4	8	no	—
112	C₃₁×#121	—	2	8	no	—
113	C₃₁×#121	—	2	8	no	—
114	C₃₁×#120	—	2	8	no	—
115	C₃₁×#120	—	2	8	no	—
116	C₄×D₄×C₃₁	—	2	16	no	—
117	C₄×D₄×C₃₁	—	2	16	no	—
118	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
119	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
132	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₄²×C₃₁	—	2	4	no	—
153	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	4	yes	—
155	C₃₁×#95	C₂³	1	4	yes	—
156	C₃₁×#95	C₂³	1	4	yes	—
157	C₃₁×#95	C₂³	1	4	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	4	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₃₁×#95	C₂³	1	4	yes	—
163	C₃₁×#95	C₂³	1	4	yes	—
164	C₂⁴×C₃₁	—	2	2	no	—
165	C₂⁴×C₃₁	—	2	2	no	—
166	C₂⁴×C₃₁	—	2	2	no	—
167	C₂⁴×C₃₁	—	2	2	no	—
168	C₂⁴×C₃₁	—	2	2	no	—
169	C₂⁴×C₃₁	—	4	2	no	—
170	C₂⁴×C₃₁	—	4	2	no	—
171	C₂⁴×C₃₁	—	4	2	no	—
172	C₂⁴×C₃₁	—	4	2	no	—
173	C₂⁴×C₃₁	—	4	2	no	—
174	C₂⁴×C₃₁	—	4	2	no	—
175	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
176	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
177	C₂⁴×C₃₁	#41	1	4	yes	—
178	C₂⁴×C₃₁	#41	1	4	yes	—
179	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
180	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
181	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
184	C₂×D₄×C₃₁	—	2	32	no	—
185	C₂×D₄×C₃₁	—	2	4	no	—
186	C₂×D₄×C₃₁	—	2	4	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	4	no	—
189	C₂×D₄×C₃₁	—	2	4	no	—
190	C₂×D₄×C₃₁	—	2	4	no	—
191	C₂×D₄×C₃₁	—	2	4	no	—
192	C₂×D₄×C₃₁	—	2	4	no	—
193	C₂×D₄×C₃₁	—	2	4	no	—
194	C₂×D₄×C₃₁	—	2	4	no	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	4	no	—
197	C₂×D₄×C₃₁	—	4	4	no	—
198	C₂×D₄×C₃₁	—	4	4	no	—
199	C₂×D₄×C₃₁	—	4	16	no	—
200	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
201	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
202	C₂²×C₄×C₃₁	—	2	2	no	—
203	C₂²×C₄×C₃₁	—	2	2	no	—
204	C₂²×C₄×C₃₁	—	2	2	no	—
205	C₂²×C₄×C₃₁	—	2	4	no	—
206	C₂²×C₄×C₃₁	—	2	2	no	—
207	C₂²×C₄×C₃₁	—	2	2	no	—
208	C₂²×C₄×C₃₁	—	2	2	no	—
209	C₂²×C₄×C₃₁	—	2	8	no	—
210	C₂²×C₄×C₃₁	—	2	4	no	—
211	C₂²×C₄×C₃₁	—	2	4	no	—
212	C₂²×C₄×C₃₁	—	2	2	no	—
213	C₂²×C₄×C₃₁	—	2	4	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	2	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	8	no	—
222	C₂²×C₄×C₃₁	—	4	2	no	—
223	C₂²×C₄×C₃₁	—	4	2	no	—
224	C₂²×C₄×C₃₁	—	4	4	no	—
225	C₂²×C₄×C₃₁	—	4	2	no	—
226	C₂²×C₄×C₃₁	—	4	2	no	—
227	C₂²×C₄×C₃₁	—	4	2	no	—
228	C₂²×C₄×C₃₁	—	4	2	no	—
229	C₂²×C₄×C₃₁	—	4	2	no	—
230	C₂²×C₄×C₃₁	—	4	2	no	—
231	C₂²×C₄×C₃₁	—	4	2	no	—
232	C₂²×C₄×C₃₁	—	4	2	no	—
233	C₂²×C₄×C₃₁	—	4	2	no	—
234	C₂²×C₄×C₃₁	—	4	16	no	—
235	C₂²×C₄×C₃₁	—	4	16	no	—
236	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	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	C₄⋊C₄×C₃₁	—	2	8	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	8	no	—
251	C₄⋊C₄×C₃₁	—	4	4	no	—
252	C₄⋊C₄×C₃₁	—	4	4	no	—
253	C₄⋊C₄×C₃₁	—	4	4	no	—
254	C₂²⋊C₄×C₃₁	—	2	8	no	—
255	C₂²⋊C₄×C₃₁	—	2	4	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	no	—
259	C₂²⋊C₄×C₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	8	no	—
268	C₂²⋊C₄×C₃₁	—	4	4	no	—
269	C₂²⋊C₄×C₃₁	—	4	4	no	—
270	C₂²⋊C₄×C₃₁	—	4	4	no	—
271	C₂²⋊C₄×C₃₁	—	4	4	no	—
272	C₂²⋊C₄×C₃₁	—	4	4	no	—
273	C₄²×C₃₁	—	2	8	no	—
274	#34983	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	2	2	no	—
280	C₂³×C₃₁	—	2	2	no	—
281	C₂³×C₃₁	—	2	8	no	—
282	C₂³×C₃₁	—	2	2	no	—
283	C₂³×C₃₁	—	2	2	no	—
284	C₂³×C₃₁	—	2	4	no	—
285	C₂³×C₃₁	—	2	4	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	4	no	—
290	C₂³×C₃₁	—	2	4	no	—
291	C₂³×C₃₁	—	4	4	no	—
292	C₂³×C₃₁	—	4	4	no	—
293	C₂³×C₃₁	—	4	4	no	—
294	C₂³×C₃₁	—	4	4	no	—
295	C₂³×C₃₁	—	4	8	no	—
296	C₂³×C₃₁	—	4	8	no	—
297	C₂³×C₃₁	—	4	8	no	—
298	C₂³×C₃₁	—	4	8	no	—
299	C₂³×C₃₁	—	4	8	no	—
300	C₂³×C₃₁	—	4	4	no	—
301	C₂³×C₃₁	—	8	2	no	—
302	C₂³×C₃₁	—	8	2	no	—
303	C₂³×C₃₁	—	8	4	no	—
304	C₂³×C₃₁	#123	1	16	yes	complemented
305	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
306	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
307	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
308	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
309	C₂³×C₃₁	C₂×#41	1	2	yes	—
310	C₂³×C₃₁	C₂×#41	1	2	yes	—
311	C₂³×C₃₁	C₂×#41	1	2	yes	—
312	C₂³×C₃₁	C₂×#41	1	2	yes	—
313	C₂³×C₃₁	C₂×#41	1	2	yes	—
314	C₂³×C₃₁	C₂×#41	1	2	yes	—
315	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
316	D₄×C₃₁	—	2	16	no	—
317	D₄×C₃₁	—	2	16	no	—
318	D₄×C₃₁	—	4	8	no	—
319	D₄×C₃₁	—	4	8	no	—
320	D₄×C₃₁	—	8	4	no	—
321	D₄×C₃₁	—	8	4	no	—
322	C₂×C₄×C₃₁	—	2	8	no	—
323	C₂×C₄×C₃₁	—	2	8	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	4	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	4	no	—
339	C₂×C₄×C₃₁	—	2	4	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	4	no	—
342	C₂×C₄×C₃₁	—	2	4	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	4	no	—
345	C₂×C₄×C₃₁	—	2	4	no	—
346	C₂×C₄×C₃₁	—	2	4	no	—
347	C₂×C₄×C₃₁	—	2	4	no	—
348	C₂×C₄×C₃₁	—	4	8	no	—
349	C₂×C₄×C₃₁	—	4	8	no	—
350	C₂×C₄×C₃₁	—	4	16	no	—
351	C₂×C₄×C₃₁	—	4	8	no	—
352	C₂×C₄×C₃₁	—	4	4	no	—
353	C₂×C₄×C₃₁	—	4	4	no	—
354	C₂×C₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	4	4	no	—
356	C₂×C₄×C₃₁	—	8	2	no	—
357	C₂×C₄×C₃₁	—	8	2	no	—
358	C₂×C₄×C₃₁	—	8	4	no	—
359	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
361	C₂×#534	C₂×C₃₁	1	1	yes	characteristic
362	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#2853	C₂×C₃₁	1	2	yes	complemented
364	#2849	C₂×C₃₁	1	2	yes	complemented
365	#2623	C₂×C₃₁	1	2	yes	complemented
366	#2622	C₂×C₃₁	1	2	yes	complemented
367	#2444	C₂×C₃₁	1	4	yes	complemented
368	#2443	C₂×C₃₁	1	4	yes	complemented
369	#2419	C₂×C₃₁	1	4	yes	complemented
370	#2418	C₂×C₃₁	1	4	yes	complemented
371	#2315	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#2308	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#2308	C₂×C₃₁	1	1	yes	characteristic, complemented
374	C₂×#386	C₂×C₃₁	1	1	yes	characteristic, complemented
375	C₂×#385	C₂×C₃₁	1	1	yes	characteristic, complemented
376	C₂²×C₃₁	—	2	4	no	—
377	C₂²×C₃₁	—	2	4	no	—
378	C₂²×C₃₁	—	2	4	no	—
379	C₂²×C₃₁	—	2	2	no	—
380	C₂²×C₃₁	—	2	2	no	—
381	C₂²×C₃₁	—	2	2	no	—
382	C₂²×C₃₁	—	2	2	no	—
383	C₂²×C₃₁	—	2	2	no	—
384	C₂²×C₃₁	—	2	2	no	—
385	C₂²×C₃₁	—	2	4	no	—
386	C₂²×C₃₁	—	2	4	no	—
387	C₂²×C₃₁	—	2	4	no	—
388	C₂²×C₃₁	—	2	4	no	—
389	C₂²×C₃₁	—	2	4	no	—
390	C₂²×C₃₁	—	2	4	no	—
391	C₂²×C₃₁	—	4	16	no	—
392	C₂²×C₃₁	—	4	16	no	—
393	C₂²×C₃₁	—	4	4	no	—
394	C₂²×C₃₁	—	4	4	no	—
395	C₂²×C₃₁	—	4	2	no	—
396	C₂²×C₃₁	—	4	4	no	—
397	C₂²×C₃₁	—	4	2	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	—	4	4	no	—
400	C₂²×C₃₁	—	8	8	no	—
401	C₂²×C₃₁	C₂×#123	1	4	yes	—
402	C₂²×C₃₁	C₂×#123	1	4	yes	—
403	C₂²×C₃₁	C₂×#123	1	4	yes	—
404	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
405	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₃₁	#585	1	2	yes	—
409	C₄×C₃₁	—	2	4	no	—
410	C₄×C₃₁	—	2	4	no	—
411	C₄×C₃₁	—	4	2	no	—
412	C₄×C₃₁	—	4	4	no	—
413	C₄×C₃₁	—	4	2	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	2	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	2	no	—
418	C₄×C₃₁	—	4	4	no	—
419	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
420	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
421	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
422	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
423	#534	—	2	8	no	—
424	C₂×#123	C₂²×C₃₁	1	2	yes	—
425	C₂×#123	C₂²×C₃₁	1	2	yes	—
426	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
427	C₂×#121	C₂²×C₃₁	1	2	yes	—
428	C₂×#121	C₂²×C₃₁	1	2	yes	—
429	C₂×#120	C₂²×C₃₁	1	2	yes	—
430	C₂×#120	C₂²×C₃₁	1	2	yes	—
431	C₂×C₄×D₄	—	2	8	no	—
432	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
433	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
434	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
435	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
436	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
437	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
438	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
439	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
440	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
441	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
442	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
443	#400	C₂²×C₃₁	1	4	yes	complemented
444	#399	C₂²×C₃₁	1	4	yes	complemented
445	#398	C₂²×C₃₁	1	4	yes	complemented
446	#397	C₂²×C₃₁	1	4	yes	complemented
447	#397	C₂²×C₃₁	1	4	yes	complemented
448	#397	C₂²×C₃₁	1	4	yes	complemented
449	#394	C₂²×C₃₁	1	4	yes	complemented
450	#394	C₂²×C₃₁	1	4	yes	complemented
451	#388	C₂²×C₃₁	1	4	yes	complemented
452	#388	C₂²×C₃₁	1	4	yes	complemented
453	#387	C₂²×C₃₁	1	4	yes	complemented
454	#387	C₂²×C₃₁	1	4	yes	complemented
455	#386	C₂²×C₃₁	1	2	yes	—
456	#386	C₂²×C₃₁	1	2	yes	—
457	#386	C₂²×C₃₁	1	4	yes	—
458	#386	C₂²×C₃₁	1	2	yes	—
459	#386	C₂²×C₃₁	1	2	yes	—
460	#386	C₂²×C₃₁	1	4	yes	complemented
461	#386	C₂²×C₃₁	1	4	yes	complemented
462	#386	C₂²×C₃₁	1	4	yes	complemented
463	#386	C₂²×C₃₁	1	4	yes	complemented
464	#385	C₂²×C₃₁	1	2	yes	complemented
465	#385	C₂²×C₃₁	1	2	yes	complemented
466	#385	C₂²×C₃₁	1	2	yes	complemented
467	#385	C₂²×C₃₁	1	2	yes	complemented
468	#385	C₂²×C₃₁	1	2	yes	complemented
469	#385	C₂²×C₃₁	1	4	yes	complemented
470	#385	C₂²×C₃₁	1	2	yes	complemented
471	#385	C₂²×C₃₁	1	4	yes	complemented
472	#381	C₂²×C₃₁	1	2	yes	complemented
473	#381	C₂²×C₃₁	1	2	yes	complemented
474	#381	C₂²×C₃₁	1	4	yes	complemented
475	#380	C₂²×C₃₁	1	4	yes	complemented
476	#379	C₂²×C₃₁	1	2	yes	complemented
477	#379	C₂²×C₃₁	1	2	yes	complemented
478	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
479	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
480	C₂×C₃₁	—	2	4	no	—
481	C₂×C₃₁	—	2	4	no	—
482	C₂×C₃₁	—	2	4	no	—
483	C₂×C₃₁	—	4	4	no	—
484	C₂×C₃₁	—	8	2	no	—
485	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
486	C₂×C₃₁	#3459	1	2	yes	—
487	C₂×C₃₁	#3484	1	1	yes	characteristic
488	C₂×C₃₁	#3485	1	1	yes	characteristic
489	C₂×C₃₁	#3505	1	2	yes	—
490	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
491	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
492	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
493	C₂²×D₄	—	2	4	no	—
494	C₂²×D₄	—	2	4	no	—
495	C₂²×D₄	—	2	4	no	—
496	C₂²×D₄	—	2	4	no	—
497	C₂²×D₄	—	2	4	no	—
498	C₂²×D₄	D₄×C₃₁	1	8	yes	—
499	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
500	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
501	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
502	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
503	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
504	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
505	C₂³×C₄	—	2	4	no	—
506	C₂³×C₄	—	2	4	no	—
507	C₂³×C₄	—	4	4	no	—
508	C₂³×C₄	—	4	4	no	—
509	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
512	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
513	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
514	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
516	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
520	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
522	#123	—	2	8	no	—
523	#123	—	2	8	no	—
524	#123	—	4	8	no	—
525	#121	—	2	8	no	—
526	#121	—	2	8	no	—
527	#120	—	2	8	no	—
528	#120	—	2	8	no	—
529	C₄×D₄	—	2	16	no	—
530	C₄×D₄	—	2	16	no	—
531	C₂×C₄⋊C₄	—	2	4	no	—
532	C₂×C₄⋊C₄	—	4	4	no	—
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₂²⋊C₄	—	2	4	no	—
545	C₂×C₂²⋊C₄	—	4	4	no	—
546	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
565	C₂×C₄²	—	2	4	no	—
566	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
567	#95	C₂³×C₃₁	1	4	yes	—
568	#95	C₂³×C₃₁	1	4	yes	—
569	#95	C₂³×C₃₁	1	4	yes	—
570	#95	C₂³×C₃₁	1	4	yes	—
571	#95	C₂³×C₃₁	1	4	yes	—
572	#95	C₂³×C₃₁	1	4	yes	—
573	#95	C₂³×C₃₁	1	4	yes	—
574	#95	C₂³×C₃₁	1	4	yes	—
575	#95	C₂³×C₃₁	1	4	yes	—
576	#95	C₂³×C₃₁	1	4	yes	—
577	C₃₁	#34983	1	1	yes	characteristic, direct product factor, Sylow
578	C₂⁴	—	2	2	no	—
579	C₂⁴	—	2	2	no	—
580	C₂⁴	—	2	2	no	—
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	—	4	2	no	—
584	C₂⁴	—	4	2	no	—
585	C₂⁴	—	4	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	4	2	no	—
588	C₂⁴	—	4	2	no	—
589	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
590	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
591	C₂⁴	#41×C₃₁	1	4	yes	—
592	C₂⁴	#41×C₃₁	1	4	yes	—
593	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
594	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
595	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
596	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
597	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
598	C₂×D₄	—	2	32	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	16	no	—
614	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
615	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	16	no	—
649	C₂²×C₄	—	4	16	no	—
650	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
661	C₄⋊C₄	—	2	8	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	4	4	no	—
666	C₄⋊C₄	—	4	4	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	—	4	4	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₄²	—	2	8	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	8	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	4	no	—
698	C₂³	—	2	4	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	4	4	no	—
705	C₂³	—	4	4	no	—
706	C₂³	—	4	4	no	—
707	C₂³	—	4	4	no	—
708	C₂³	—	4	8	no	—
709	C₂³	—	4	8	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	4	8	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	8	2	no	—
715	C₂³	—	8	2	no	—
716	C₂³	—	8	4	no	—
717	C₂³	C₃₁×#123	1	16	yes	complemented
718	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
719	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
720	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
721	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
722	C₂³	C₂×#41×C₃₁	1	2	yes	—
723	C₂³	C₂×#41×C₃₁	1	2	yes	—
724	C₂³	C₂×#41×C₃₁	1	2	yes	—
725	C₂³	C₂×#41×C₃₁	1	2	yes	—
726	C₂³	C₂×#41×C₃₁	1	2	yes	—
727	C₂³	C₂×#41×C₃₁	1	2	yes	—
728	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
729	D₄	—	2	16	no	—
730	D₄	—	2	16	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	8	no	—
733	D₄	—	8	4	no	—
734	D₄	—	8	4	no	—
735	C₂×C₄	—	2	8	no	—
736	C₂×C₄	—	2	8	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	16	no	—
764	C₂×C₄	—	4	8	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	8	2	no	—
770	C₂×C₄	—	8	2	no	—
771	C₂×C₄	—	8	4	no	—
772	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
773	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	4	16	no	—
790	C₂²	—	4	16	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	8	8	no	—
799	C₂²	C₂×C₃₁×#123	1	4	yes	—
800	C₂²	C₂×C₃₁×#123	1	4	yes	—
801	C₂²	C₂×C₃₁×#123	1	4	yes	—
802	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
803	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
804	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
805	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
806	C₂²	C₃₁×#585	1	2	yes	—
807	C₄	—	2	4	no	—
808	C₄	—	2	4	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	4	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	4	no	—
817	C₂	—	2	4	no	—
818	C₂	—	2	4	no	—
819	C₂	—	2	4	no	—
820	C₂	—	4	4	no	—
821	C₂	—	8	2	no	—
822	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
823	C₂	C₃₁×#3459	1	2	yes	—
824	C₂	C₃₁×#3484	1	1	yes	characteristic
825	C₂	C₃₁×#3485	1	1	yes	characteristic
826	C₂	C₃₁×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#534	C₂
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
2. C₂²×C₄×D₄×C₃₁	C₂	semidirect
3. C₃₁×#2853	C₂	semidirect
4. C₃₁×#2849	C₂	semidirect
5. C₃₁×#2623	C₂	semidirect
6. C₃₁×#2622	C₂	semidirect
7. C₃₁×#2444	C₂	semidirect
8. C₃₁×#2443	C₂	semidirect
9. C₃₁×#2419	C₂	semidirect
10. C₃₁×#2418	C₂	semidirect
11. C₃₁×#2315	C₂	semidirect
12. C₃₁×#2308	C₂	semidirect
13. C₃₁×#2308	C₂	semidirect
14. C₂×C₃₁×#386	C₂	semidirect
15. C₂×C₃₁×#385	C₂	semidirect
19. C₂⁴×C₄×C₃₁	C₂²	semidirect
23. C₂×C₃₁×#123	C₂²	semidirect
30. C₂×C₄×D₄×C₃₁	C₂²	semidirect
31. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
39. C₂²×C₄²×C₃₁	C₂²	semidirect
40. C₃₁×#400	C₂²	semidirect
41. C₃₁×#399	C₂²	semidirect
42. C₃₁×#398	C₂²	semidirect
43. C₃₁×#397	C₂²	semidirect
44. C₃₁×#397	C₂²	semidirect
45. C₃₁×#397	C₂²	semidirect
46. C₃₁×#394	C₂²	semidirect
47. C₃₁×#394	C₂²	semidirect
48. C₃₁×#388	C₂²	semidirect
49. C₃₁×#388	C₂²	semidirect
50. C₃₁×#387	C₂²	semidirect
51. C₃₁×#387	C₂²	semidirect
57. C₃₁×#386	C₂²	semidirect
58. C₃₁×#386	C₂²	semidirect
59. C₃₁×#386	C₂²	semidirect
60. C₃₁×#386	C₂²	semidirect
61. C₃₁×#385	C₂²	semidirect
62. C₃₁×#385	C₂²	semidirect
63. C₃₁×#385	C₂²	semidirect
64. C₃₁×#385	C₂²	semidirect
65. C₃₁×#385	C₂²	semidirect
66. C₃₁×#385	C₂²	semidirect
67. C₃₁×#385	C₂²	semidirect
68. C₃₁×#385	C₂²	semidirect
69. C₃₁×#381	C₂²	semidirect
70. C₃₁×#381	C₂²	semidirect
71. C₃₁×#381	C₂²	semidirect
72. C₃₁×#380	C₂²	semidirect
73. C₃₁×#379	C₂²	semidirect
74. C₃₁×#379	C₂²	semidirect
75. C₂×C₃₁×#95	C₂²	semidirect
76. C₂×C₃₁×#95	C₂²	semidirect
274. #34983	C₃₁	direct (N × H)
304. C₂³×C₃₁	#123	semidirect
362. C₂²×C₄×D₄	C₂×C₃₁	semidirect
363. #2853	C₂×C₃₁	semidirect
364. #2849	C₂×C₃₁	semidirect
365. #2623	C₂×C₃₁	semidirect
366. #2622	C₂×C₃₁	semidirect
367. #2444	C₂×C₃₁	semidirect
368. #2443	C₂×C₃₁	semidirect
369. #2419	C₂×C₃₁	semidirect
370. #2418	C₂×C₃₁	semidirect
371. #2315	C₂×C₃₁	semidirect
372. #2308	C₂×C₃₁	semidirect
373. #2308	C₂×C₃₁	semidirect
374. C₂×#386	C₂×C₃₁	semidirect
375. C₂×#385	C₂×C₃₁	semidirect
422. C₂⁴×C₄	C₂²×C₃₁	semidirect
426. C₂×#123	C₂²×C₃₁	semidirect
433. C₂×C₄×D₄	C₂²×C₃₁	semidirect
434. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
435. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
440. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
441. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
442. C₂²×C₄²	C₂²×C₃₁	semidirect
443. #400	C₂²×C₃₁	semidirect
444. #399	C₂²×C₃₁	semidirect
445. #398	C₂²×C₃₁	semidirect
446. #397	C₂²×C₃₁	semidirect
447. #397	C₂²×C₃₁	semidirect
448. #397	C₂²×C₃₁	semidirect
449. #394	C₂²×C₃₁	semidirect
450. #394	C₂²×C₃₁	semidirect
451. #388	C₂²×C₃₁	semidirect
452. #388	C₂²×C₃₁	semidirect
453. #387	C₂²×C₃₁	semidirect
454. #387	C₂²×C₃₁	semidirect
460. #386	C₂²×C₃₁	semidirect
461. #386	C₂²×C₃₁	semidirect
462. #386	C₂²×C₃₁	semidirect
463. #386	C₂²×C₃₁	semidirect
464. #385	C₂²×C₃₁	semidirect
465. #385	C₂²×C₃₁	semidirect
466. #385	C₂²×C₃₁	semidirect
467. #385	C₂²×C₃₁	semidirect
468. #385	C₂²×C₃₁	semidirect
469. #385	C₂²×C₃₁	semidirect
470. #385	C₂²×C₃₁	semidirect
471. #385	C₂²×C₃₁	semidirect
472. #381	C₂²×C₃₁	semidirect
473. #381	C₂²×C₃₁	semidirect
474. #381	C₂²×C₃₁	semidirect
475. #380	C₂²×C₃₁	semidirect
476. #379	C₂²×C₃₁	semidirect
477. #379	C₂²×C₃₁	semidirect
478. C₂×#95	C₂²×C₃₁	semidirect
479. C₂×#95	C₂²×C₃₁	semidirect
577. C₃₁	#34983	direct (N × H)
717. C₂³	C₃₁×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#534	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2853	2
C₃₁×#2849	2
C₃₁×#2623	2
C₃₁×#2622	2
C₃₁×#2444	2
C₃₁×#2443	2
C₃₁×#2419	2
C₃₁×#2418	2
C₃₁×#2315	2
C₃₁×#2308	2
C₂×C₃₁×#386	2
C₂×C₃₁×#385	2
#34983	31

Subgroups — C31×#34983 #21491742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34983 #21491742