Subgroups — C₃₁×#35062 #21491821

Order 7936.

3010 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
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×#2630	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2602	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2579	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2534	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2483	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2413	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2411	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2405	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2403	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃₁×#123	—	2	8	no	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#123	C₂²	1	2	yes	—
26	C₂×C₃₁×#123	C₂²	1	2	yes	—
27	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
28	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
29	C₂×C₃₁×#120	C₂²	1	2	yes	—
30	C₂×C₃₁×#120	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	—	2	8	no	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
36	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#398	C₂²	1	4	yes	complemented
47	C₃₁×#397	C₂²	1	4	yes	complemented
48	C₃₁×#396	C₂²	1	4	yes	complemented
49	C₃₁×#396	C₂²	1	4	yes	complemented
50	C₃₁×#394	C₂²	1	4	yes	complemented
51	C₃₁×#394	C₂²	1	4	yes	complemented
52	C₃₁×#394	C₂²	1	4	yes	complemented
53	C₃₁×#392	C₂²	1	4	yes	—
54	C₃₁×#390	C₂²	1	4	yes	complemented
55	C₃₁×#389	C₂²	1	4	yes	complemented
56	C₃₁×#388	C₂²	1	4	yes	complemented
57	C₃₁×#388	C₂²	1	4	yes	complemented
58	C₃₁×#388	C₂²	1	4	yes	complemented
59	C₃₁×#388	C₂²	1	4	yes	complemented
60	C₃₁×#387	C₂²	1	4	yes	complemented
61	C₃₁×#387	C₂²	1	4	yes	complemented
62	C₃₁×#386	C₂²	1	2	yes	—
63	C₃₁×#386	C₂²	1	2	yes	—
64	C₃₁×#386	C₂²	1	2	yes	—
65	C₃₁×#386	C₂²	1	2	yes	—
66	C₃₁×#386	C₂²	1	4	yes	complemented
67	C₃₁×#386	C₂²	1	4	yes	complemented
68	C₃₁×#385	C₂²	1	2	yes	complemented
69	C₃₁×#385	C₂²	1	2	yes	complemented
70	C₃₁×#385	C₂²	1	4	yes	complemented
71	C₃₁×#385	C₂²	1	4	yes	complemented
72	C₃₁×#385	C₂²	1	2	yes	complemented
73	C₃₁×#385	C₂²	1	2	yes	complemented
74	C₃₁×#381	C₂²	1	2	yes	complemented
75	C₃₁×#381	C₂²	1	2	yes	complemented
76	C₃₁×#381	C₂²	1	2	yes	complemented
77	C₃₁×#380	C₂²	1	2	yes	complemented
78	C₃₁×#380	C₂²	1	2	yes	complemented
79	C₃₁×#379	C₂²	1	1	yes	characteristic
80	C₃₁×#379	C₂²	1	1	yes	characteristic
81	C₃₁×#379	C₂²	1	2	yes	complemented
82	C₃₁×#379	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
85	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
86	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
87	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₃₁	—	2	4	no	—
89	C₂²×D₄×C₃₁	—	2	8	no	—
90	C₂²×D₄×C₃₁	—	2	4	no	—
91	C₂²×D₄×C₃₁	—	4	4	no	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
95	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
97	C₂³×C₄×C₃₁	—	2	4	no	—
98	C₂³×C₄×C₃₁	—	4	4	no	—
99	C₂³×C₄×C₃₁	—	4	4	no	—
100	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
110	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
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	C₃₁×#123	—	2	8	no	—
116	C₃₁×#123	—	2	8	no	—
117	C₃₁×#123	—	2	8	no	—
118	C₃₁×#123	—	2	8	no	—
119	C₃₁×#123	—	2	8	no	—
120	C₃₁×#123	—	4	4	no	—
121	C₃₁×#120	—	2	8	no	—
122	C₃₁×#120	—	4	4	no	—
123	C₄×D₄×C₃₁	—	2	8	no	—
124	C₄×D₄×C₃₁	—	2	8	no	—
125	C₄×D₄×C₃₁	—	2	8	no	—
126	C₄×D₄×C₃₁	—	2	8	no	—
127	C₃₁×#117	—	4	4	no	—
128	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
129	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
130	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
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	4	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	4	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
144	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
145	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	4	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	4	yes	—
168	C₂×C₄²×C₃₁	—	2	4	no	—
169	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
172	C₃₁×#95	C₂³	1	4	yes	—
173	C₃₁×#95	C₂³	1	4	yes	—
174	C₃₁×#95	C₂³	1	4	yes	—
175	C₃₁×#95	C₂³	1	4	yes	—
176	C₃₁×#95	C₂³	1	4	yes	—
177	C₃₁×#95	C₂³	1	4	yes	—
178	C₃₁×#95	C₂³	1	4	yes	—
179	C₃₁×#95	C₂³	1	4	yes	—
180	C₂⁴×C₃₁	—	2	2	no	—
181	C₂⁴×C₃₁	—	2	4	no	—
182	C₂⁴×C₃₁	—	2	4	no	—
183	C₂⁴×C₃₁	—	2	4	no	—
184	C₂⁴×C₃₁	—	2	2	no	—
185	C₂⁴×C₃₁	—	2	4	no	—
186	C₂⁴×C₃₁	—	2	4	no	—
187	C₂⁴×C₃₁	—	4	2	no	—
188	C₂⁴×C₃₁	—	4	2	no	—
189	C₂⁴×C₃₁	—	4	2	no	—
190	C₂⁴×C₃₁	—	4	2	no	—
191	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
192	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
193	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
195	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
196	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₃₁	—	2	32	no	—
198	C₂×D₄×C₃₁	—	2	4	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	4	no	—
203	C₂×D₄×C₃₁	—	2	4	no	—
204	C₂×D₄×C₃₁	—	2	4	no	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	8	no	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	4	2	no	—
209	C₂×D₄×C₃₁	—	4	2	no	—
210	C₂×D₄×C₃₁	—	4	4	no	—
211	C₂×D₄×C₃₁	—	4	4	no	—
212	C₂×D₄×C₃₁	—	4	16	no	—
213	C₂×D₄×C₃₁	#41	1	8	yes	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	4	no	—
216	C₂²×C₄×C₃₁	—	2	4	no	—
217	C₂²×C₄×C₃₁	—	2	4	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	4	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	4	16	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	4	no	—
233	C₂²×C₄×C₃₁	—	4	4	no	—
234	C₂²×C₄×C₃₁	—	4	2	no	—
235	C₂²×C₄×C₃₁	—	4	2	no	—
236	C₂²×C₄×C₃₁	—	4	2	no	—
237	C₂²×C₄×C₃₁	—	4	16	no	—
238	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	4	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	2	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
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	8	no	—
263	C₄⋊C₄×C₃₁	—	4	4	no	—
264	C₄⋊C₄×C₃₁	—	4	4	no	—
265	C₄⋊C₄×C₃₁	—	4	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	8	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	4	no	—
281	C₂²⋊C₄×C₃₁	—	2	8	no	—
282	C₂²⋊C₄×C₃₁	—	4	2	no	—
283	C₂²⋊C₄×C₃₁	—	4	4	no	—
284	C₂²⋊C₄×C₃₁	—	4	4	no	—
285	C₂²⋊C₄×C₃₁	—	4	2	no	—
286	C₂²⋊C₄×C₃₁	—	4	4	no	—
287	C₂²⋊C₄×C₃₁	—	4	4	no	—
288	C₄²×C₃₁	—	2	4	no	—
289	C₄²×C₃₁	—	2	4	no	—
290	C₄²×C₃₁	—	4	4	no	—
291	#35062	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	2	2	no	—
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	—	2	2	no	—
296	C₂³×C₃₁	—	2	8	no	—
297	C₂³×C₃₁	—	2	8	no	—
298	C₂³×C₃₁	—	2	8	no	—
299	C₂³×C₃₁	—	2	2	no	—
300	C₂³×C₃₁	—	2	2	no	—
301	C₂³×C₃₁	—	2	2	no	—
302	C₂³×C₃₁	—	2	4	no	—
303	C₂³×C₃₁	—	2	2	no	—
304	C₂³×C₃₁	—	2	2	no	—
305	C₂³×C₃₁	—	2	4	no	—
306	C₂³×C₃₁	—	2	2	no	—
307	C₂³×C₃₁	—	2	4	no	—
308	C₂³×C₃₁	—	2	2	no	—
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	—	2	4	no	—
311	C₂³×C₃₁	—	4	4	no	—
312	C₂³×C₃₁	—	4	16	no	—
313	C₂³×C₃₁	—	4	16	no	—
314	C₂³×C₃₁	—	4	4	no	—
315	C₂³×C₃₁	—	4	4	no	—
316	C₂³×C₃₁	—	4	4	no	—
317	C₂³×C₃₁	—	4	4	no	—
318	C₂³×C₃₁	—	4	4	no	—
319	C₂³×C₃₁	—	8	8	no	—
320	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
321	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
322	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
323	C₂³×C₃₁	C₂×#41	1	4	yes	—
324	C₂³×C₃₁	C₂×#41	1	4	yes	—
325	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
326	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
327	D₄×C₃₁	—	2	16	no	—
328	D₄×C₃₁	—	2	16	no	—
329	D₄×C₃₁	—	4	8	no	—
330	D₄×C₃₁	—	4	8	no	—
331	D₄×C₃₁	—	8	8	no	—
332	C₂×C₄×C₃₁	—	2	8	no	—
333	C₂×C₄×C₃₁	—	2	8	no	—
334	C₂×C₄×C₃₁	—	2	8	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	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	4	no	—
347	C₂×C₄×C₃₁	—	2	4	no	—
348	C₂×C₄×C₃₁	—	2	4	no	—
349	C₂×C₄×C₃₁	—	2	4	no	—
350	C₂×C₄×C₃₁	—	2	4	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	4	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	4	no	—
355	C₂×C₄×C₃₁	—	2	4	no	—
356	C₂×C₄×C₃₁	—	2	4	no	—
357	C₂×C₄×C₃₁	—	2	4	no	—
358	C₂×C₄×C₃₁	—	4	4	no	—
359	C₂×C₄×C₃₁	—	4	4	no	—
360	C₂×C₄×C₃₁	—	4	4	no	—
361	C₂×C₄×C₃₁	—	4	4	no	—
362	C₂×C₄×C₃₁	—	4	8	no	—
363	C₂×C₄×C₃₁	—	4	8	no	—
364	C₂×C₄×C₃₁	—	4	4	no	—
365	C₂×C₄×C₃₁	—	4	4	no	—
366	C₂×C₄×C₃₁	—	4	4	no	—
367	C₂×C₄×C₃₁	—	4	4	no	—
368	C₂×C₄×C₃₁	—	4	4	no	—
369	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
374	C₂²×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
375	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#2853	C₂×C₃₁	1	2	yes	complemented
377	#2849	C₂×C₃₁	1	2	yes	complemented
378	#2630	C₂×C₃₁	1	4	yes	complemented
379	#2602	C₂×C₃₁	1	4	yes	complemented
380	#2579	C₂×C₃₁	1	2	yes	complemented
381	#2534	C₂×C₃₁	1	2	yes	complemented
382	#2483	C₂×C₃₁	1	1	yes	characteristic, complemented
383	#2413	C₂×C₃₁	1	2	yes	complemented
384	#2411	C₂×C₃₁	1	2	yes	complemented
385	#2405	C₂×C₃₁	1	1	yes	characteristic, complemented
386	#2405	C₂×C₃₁	1	1	yes	characteristic, complemented
387	#2403	C₂×C₃₁	1	1	yes	characteristic
388	#2322	C₂×C₃₁	1	2	yes	complemented
389	#2321	C₂×C₃₁	1	2	yes	complemented
390	#2280	C₂×C₃₁	1	1	yes	characteristic, complemented
391	C₂²×C₃₁	—	2	2	no	—
392	C₂²×C₃₁	—	2	2	no	—
393	C₂²×C₃₁	—	2	2	no	—
394	C₂²×C₃₁	—	2	2	no	—
395	C₂²×C₃₁	—	2	8	no	—
396	C₂²×C₃₁	—	2	8	no	—
397	C₂²×C₃₁	—	2	2	no	—
398	C₂²×C₃₁	—	2	4	no	—
399	C₂²×C₃₁	—	2	2	no	—
400	C₂²×C₃₁	—	2	2	no	—
401	C₂²×C₃₁	—	2	8	no	—
402	C₂²×C₃₁	—	4	16	no	—
403	C₂²×C₃₁	—	4	16	no	—
404	C₂²×C₃₁	—	4	2	no	—
405	C₂²×C₃₁	—	4	2	no	—
406	C₂²×C₃₁	—	4	4	no	—
407	C₂²×C₃₁	—	4	4	no	—
408	C₂²×C₃₁	—	4	2	no	—
409	C₂²×C₃₁	—	4	2	no	—
410	C₂²×C₃₁	—	4	2	no	—
411	C₂²×C₃₁	—	4	4	no	—
412	C₂²×C₃₁	—	4	4	no	—
413	C₂²×C₃₁	—	8	8	no	—
414	C₂²×C₃₁	#525	1	4	yes	—
415	C₂²×C₃₁	#534	1	4	yes	—
416	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
417	C₂²×C₃₁	C₂²×#41	1	2	yes	—
418	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
419	C₂²×C₃₁	#585	1	2	yes	—
420	C₄×C₃₁	—	2	4	no	—
421	C₄×C₃₁	—	2	2	no	—
422	C₄×C₃₁	—	2	2	no	—
423	C₄×C₃₁	—	2	2	no	—
424	C₄×C₃₁	—	2	2	no	—
425	C₄×C₃₁	—	4	2	no	—
426	C₄×C₃₁	—	4	2	no	—
427	C₄×C₃₁	—	4	2	no	—
428	C₄×C₃₁	—	4	2	no	—
429	C₄×C₃₁	—	4	2	no	—
430	C₄×C₃₁	—	4	4	no	—
431	C₄×C₃₁	—	4	4	no	—
432	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
433	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
434	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
435	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
436	C₂×#123	—	2	8	no	—
437	C₂×#123	C₂²×C₃₁	1	2	yes	—
438	C₂×#123	C₂²×C₃₁	1	2	yes	—
439	C₂×#123	C₂²×C₃₁	1	2	yes	—
440	C₂×#123	C₂²×C₃₁	1	2	yes	—
441	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
442	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
443	C₂×#120	C₂²×C₃₁	1	2	yes	—
444	C₂×#120	C₂²×C₃₁	1	2	yes	—
445	C₂×C₄×D₄	—	2	8	no	—
446	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
449	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
450	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
451	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
453	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
457	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
458	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	#398	C₂²×C₃₁	1	4	yes	complemented
461	#397	C₂²×C₃₁	1	4	yes	complemented
462	#396	C₂²×C₃₁	1	4	yes	complemented
463	#396	C₂²×C₃₁	1	4	yes	complemented
464	#394	C₂²×C₃₁	1	4	yes	complemented
465	#394	C₂²×C₃₁	1	4	yes	complemented
466	#394	C₂²×C₃₁	1	4	yes	complemented
467	#392	C₂²×C₃₁	1	4	yes	—
468	#390	C₂²×C₃₁	1	4	yes	complemented
469	#389	C₂²×C₃₁	1	4	yes	complemented
470	#388	C₂²×C₃₁	1	4	yes	complemented
471	#388	C₂²×C₃₁	1	4	yes	complemented
472	#388	C₂²×C₃₁	1	4	yes	complemented
473	#388	C₂²×C₃₁	1	4	yes	complemented
474	#387	C₂²×C₃₁	1	4	yes	complemented
475	#387	C₂²×C₃₁	1	4	yes	complemented
476	#386	C₂²×C₃₁	1	2	yes	—
477	#386	C₂²×C₃₁	1	2	yes	—
478	#386	C₂²×C₃₁	1	2	yes	—
479	#386	C₂²×C₃₁	1	2	yes	—
480	#386	C₂²×C₃₁	1	4	yes	complemented
481	#386	C₂²×C₃₁	1	4	yes	complemented
482	#385	C₂²×C₃₁	1	2	yes	complemented
483	#385	C₂²×C₃₁	1	2	yes	complemented
484	#385	C₂²×C₃₁	1	4	yes	complemented
485	#385	C₂²×C₃₁	1	4	yes	complemented
486	#385	C₂²×C₃₁	1	2	yes	complemented
487	#385	C₂²×C₃₁	1	2	yes	complemented
488	#381	C₂²×C₃₁	1	2	yes	complemented
489	#381	C₂²×C₃₁	1	2	yes	complemented
490	#381	C₂²×C₃₁	1	2	yes	complemented
491	#380	C₂²×C₃₁	1	2	yes	complemented
492	#380	C₂²×C₃₁	1	2	yes	complemented
493	#379	C₂²×C₃₁	1	1	yes	characteristic
494	#379	C₂²×C₃₁	1	1	yes	characteristic
495	#379	C₂²×C₃₁	1	2	yes	complemented
496	#379	C₂²×C₃₁	1	2	yes	complemented
497	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
498	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
499	C₂×C₃₁	—	2	4	no	—
500	C₂×C₃₁	—	2	4	no	—
501	C₂×C₃₁	—	4	2	no	—
502	C₂×C₃₁	—	4	4	no	—
503	C₂×C₃₁	—	8	2	no	—
504	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
505	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
506	C₂×C₃₁	#3449	1	1	yes	characteristic
507	C₂×C₃₁	#3513	1	4	yes	—
508	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
509	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
510	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
511	C₂²×D₄	—	2	4	no	—
512	C₂²×D₄	—	2	8	no	—
513	C₂²×D₄	—	2	4	no	—
514	C₂²×D₄	—	4	4	no	—
515	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
516	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
517	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
518	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
519	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
520	C₂³×C₄	—	2	4	no	—
521	C₂³×C₄	—	4	4	no	—
522	C₂³×C₄	—	4	4	no	—
523	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
524	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
533	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
534	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
538	#123	—	2	8	no	—
539	#123	—	2	8	no	—
540	#123	—	2	8	no	—
541	#123	—	2	8	no	—
542	#123	—	2	8	no	—
543	#123	—	4	4	no	—
544	#120	—	2	8	no	—
545	#120	—	4	4	no	—
546	C₄×D₄	—	2	8	no	—
547	C₄×D₄	—	2	8	no	—
548	C₄×D₄	—	2	8	no	—
549	C₄×D₄	—	2	8	no	—
550	#117	—	4	4	no	—
551	C₂×C₄⋊C₄	—	2	4	no	—
552	C₂×C₄⋊C₄	—	2	4	no	—
553	C₂×C₄⋊C₄	—	2	4	no	—
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₂²⋊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	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	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	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
591	C₂×C₄²	—	2	4	no	—
592	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
593	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
594	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
595	#95	C₂³×C₃₁	1	4	yes	—
596	#95	C₂³×C₃₁	1	4	yes	—
597	#95	C₂³×C₃₁	1	4	yes	—
598	#95	C₂³×C₃₁	1	4	yes	—
599	#95	C₂³×C₃₁	1	4	yes	—
600	#95	C₂³×C₃₁	1	4	yes	—
601	#95	C₂³×C₃₁	1	4	yes	—
602	#95	C₂³×C₃₁	1	4	yes	—
603	C₃₁	#35062	1	1	yes	characteristic, direct product factor, Sylow
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	2	4	no	—
607	C₂⁴	—	2	4	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	4	no	—
610	C₂⁴	—	2	4	no	—
611	C₂⁴	—	4	2	no	—
612	C₂⁴	—	4	2	no	—
613	C₂⁴	—	4	2	no	—
614	C₂⁴	—	4	2	no	—
615	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
616	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
617	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
619	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
621	C₂×D₄	—	2	32	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	16	no	—
637	C₂×D₄	#41×C₃₁	1	8	yes	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	4	16	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	16	no	—
662	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
663	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
664	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
665	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
666	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
667	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
668	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	4	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	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	8	no	—
687	C₄⋊C₄	—	4	4	no	—
688	C₄⋊C₄	—	4	4	no	—
689	C₄⋊C₄	—	4	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	8	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	8	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	4	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₄²	—	2	4	no	—
713	C₄²	—	2	4	no	—
714	C₄²	—	4	4	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	8	no	—
720	C₂³	—	2	8	no	—
721	C₂³	—	2	8	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	4	16	no	—
737	C₂³	—	4	4	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	8	8	no	—
743	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
744	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
745	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
746	C₂³	C₂×#41×C₃₁	1	4	yes	—
747	C₂³	C₂×#41×C₃₁	1	4	yes	—
748	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
749	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
750	D₄	—	2	16	no	—
751	D₄	—	2	16	no	—
752	D₄	—	4	8	no	—
753	D₄	—	4	8	no	—
754	D₄	—	8	8	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	8	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
796	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	8	no	—
802	C₂²	—	2	8	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	8	no	—
808	C₂²	—	4	16	no	—
809	C₂²	—	4	16	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	4	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	8	8	no	—
820	C₂²	C₃₁×#525	1	4	yes	—
821	C₂²	C₃₁×#534	1	4	yes	—
822	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
823	C₂²	C₂²×#41×C₃₁	1	2	yes	—
824	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
825	C₂²	C₃₁×#585	1	2	yes	—
826	C₄	—	2	4	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	4	no	—
837	C₄	—	4	4	no	—
838	C₂	—	2	4	no	—
839	C₂	—	2	4	no	—
840	C₂	—	4	2	no	—
841	C₂	—	4	4	no	—
842	C₂	—	8	2	no	—
843	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
844	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
845	C₂	C₃₁×#3449	1	1	yes	characteristic
846	C₂	C₃₁×#3513	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2403	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
1. C₂²×C₃₁×#123	C₂	semidirect
2. C₂²×C₄×D₄×C₃₁	C₂	semidirect
3. C₃₁×#2853	C₂	semidirect
4. C₃₁×#2849	C₂	semidirect
5. C₃₁×#2630	C₂	semidirect
6. C₃₁×#2602	C₂	semidirect
7. C₃₁×#2579	C₂	semidirect
8. C₃₁×#2534	C₂	semidirect
9. C₃₁×#2483	C₂	semidirect
10. C₃₁×#2413	C₂	semidirect
11. C₃₁×#2411	C₂	semidirect
12. C₃₁×#2405	C₂	semidirect
13. C₃₁×#2405	C₂	semidirect
15. C₃₁×#2322	C₂	semidirect
16. C₃₁×#2321	C₂	semidirect
17. C₃₁×#2280	C₂	semidirect
21. C₂⁴×C₄×C₃₁	C₂²	semidirect
27. C₂×C₃₁×#123	C₂²	semidirect
28. C₂×C₃₁×#123	C₂²	semidirect
34. C₂×C₄×D₄×C₃₁	C₂²	semidirect
35. C₂×C₄×D₄×C₃₁	C₂²	semidirect
36. C₂×C₃₁×#117	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
45. C₂²×C₄²×C₃₁	C₂²	semidirect
46. C₃₁×#398	C₂²	semidirect
47. C₃₁×#397	C₂²	semidirect
48. C₃₁×#396	C₂²	semidirect
49. C₃₁×#396	C₂²	semidirect
50. C₃₁×#394	C₂²	semidirect
51. C₃₁×#394	C₂²	semidirect
52. C₃₁×#394	C₂²	semidirect
54. C₃₁×#390	C₂²	semidirect
55. C₃₁×#389	C₂²	semidirect
56. C₃₁×#388	C₂²	semidirect
57. C₃₁×#388	C₂²	semidirect
58. C₃₁×#388	C₂²	semidirect
59. C₃₁×#388	C₂²	semidirect
60. C₃₁×#387	C₂²	semidirect
61. C₃₁×#387	C₂²	semidirect
66. C₃₁×#386	C₂²	semidirect
67. C₃₁×#386	C₂²	semidirect
68. C₃₁×#385	C₂²	semidirect
69. C₃₁×#385	C₂²	semidirect
70. C₃₁×#385	C₂²	semidirect
71. C₃₁×#385	C₂²	semidirect
72. C₃₁×#385	C₂²	semidirect
73. C₃₁×#385	C₂²	semidirect
74. C₃₁×#381	C₂²	semidirect
75. C₃₁×#381	C₂²	semidirect
76. C₃₁×#381	C₂²	semidirect
77. C₃₁×#380	C₂²	semidirect
78. C₃₁×#380	C₂²	semidirect
81. C₃₁×#379	C₂²	semidirect
82. C₃₁×#379	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
100. C₂³×C₄×C₃₁	D₄	semidirect
291. #35062	C₃₁	direct (N × H)
374. C₂²×#123	C₂×C₃₁	semidirect
375. C₂²×C₄×D₄	C₂×C₃₁	semidirect
376. #2853	C₂×C₃₁	semidirect
377. #2849	C₂×C₃₁	semidirect
378. #2630	C₂×C₃₁	semidirect
379. #2602	C₂×C₃₁	semidirect
380. #2579	C₂×C₃₁	semidirect
381. #2534	C₂×C₃₁	semidirect
382. #2483	C₂×C₃₁	semidirect
383. #2413	C₂×C₃₁	semidirect
384. #2411	C₂×C₃₁	semidirect
385. #2405	C₂×C₃₁	semidirect
386. #2405	C₂×C₃₁	semidirect
388. #2322	C₂×C₃₁	semidirect
389. #2321	C₂×C₃₁	semidirect
390. #2280	C₂×C₃₁	semidirect
435. C₂⁴×C₄	C₂²×C₃₁	semidirect
441. C₂×#123	C₂²×C₃₁	semidirect
442. C₂×#123	C₂²×C₃₁	semidirect
448. C₂×C₄×D₄	C₂²×C₃₁	semidirect
449. C₂×C₄×D₄	C₂²×C₃₁	semidirect
450. C₂×#117	C₂²×C₃₁	semidirect
451. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
452. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
453. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
456. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
457. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
458. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
459. C₂²×C₄²	C₂²×C₃₁	semidirect
460. #398	C₂²×C₃₁	semidirect
461. #397	C₂²×C₃₁	semidirect
462. #396	C₂²×C₃₁	semidirect
463. #396	C₂²×C₃₁	semidirect
464. #394	C₂²×C₃₁	semidirect
465. #394	C₂²×C₃₁	semidirect
466. #394	C₂²×C₃₁	semidirect
468. #390	C₂²×C₃₁	semidirect
469. #389	C₂²×C₃₁	semidirect
470. #388	C₂²×C₃₁	semidirect
471. #388	C₂²×C₃₁	semidirect
472. #388	C₂²×C₃₁	semidirect
473. #388	C₂²×C₃₁	semidirect
474. #387	C₂²×C₃₁	semidirect
475. #387	C₂²×C₃₁	semidirect
480. #386	C₂²×C₃₁	semidirect
481. #386	C₂²×C₃₁	semidirect
482. #385	C₂²×C₃₁	semidirect
483. #385	C₂²×C₃₁	semidirect
484. #385	C₂²×C₃₁	semidirect
485. #385	C₂²×C₃₁	semidirect
486. #385	C₂²×C₃₁	semidirect
487. #385	C₂²×C₃₁	semidirect
488. #381	C₂²×C₃₁	semidirect
489. #381	C₂²×C₃₁	semidirect
490. #381	C₂²×C₃₁	semidirect
491. #380	C₂²×C₃₁	semidirect
492. #380	C₂²×C₃₁	semidirect
495. #379	C₂²×C₃₁	semidirect
496. #379	C₂²×C₃₁	semidirect
497. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
498. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
523. C₂³×C₄	D₄×C₃₁	semidirect
603. C₃₁	#35062	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#123	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2853	2
C₃₁×#2849	2
C₃₁×#2630	2
C₃₁×#2602	2
C₃₁×#2579	2
C₃₁×#2534	2
C₃₁×#2483	2
C₃₁×#2413	2
C₃₁×#2411	2
C₃₁×#2405	2
C₃₁×#2403	2
C₃₁×#2322	2
C₃₁×#2321	2
C₃₁×#2280	2
#35062	31

Subgroups — C31×#35062 #21491821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35062 #21491821