Subgroups — C₃₁×#34562 #21491321

Order 7936.

2982 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2638	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2635	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2630	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2627	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2622	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2618	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2613	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2395	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2392	C₂	1	4	yes	maximal, complemented
14	C₃₁×#2388	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
16	C₄×C₃₁×#120	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
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
22	C₃₁×#525	—	2	8	no	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, 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	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
39	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
41	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#400	C₂²	1	2	yes	complemented
46	C₃₁×#399	C₂²	1	2	yes	complemented
47	C₃₁×#398	C₂²	1	2	yes	complemented
48	C₃₁×#398	C₂²	1	4	yes	complemented
49	C₃₁×#397	C₂²	1	2	yes	complemented
50	C₃₁×#397	C₂²	1	4	yes	complemented
51	C₃₁×#397	C₂²	1	4	yes	complemented
52	C₃₁×#396	C₂²	1	4	yes	complemented
53	C₃₁×#396	C₂²	1	4	yes	complemented
54	C₃₁×#395	C₂²	1	2	yes	complemented
55	C₃₁×#394	C₂²	1	4	yes	—
56	C₃₁×#394	C₂²	1	4	yes	—
57	C₃₁×#394	C₂²	1	4	yes	complemented
58	C₃₁×#394	C₂²	1	2	yes	complemented
59	C₃₁×#394	C₂²	1	4	yes	complemented
60	C₃₁×#394	C₂²	1	4	yes	complemented
61	C₃₁×#393	C₂²	1	2	yes	complemented
62	C₃₁×#392	C₂²	1	4	yes	—
63	C₃₁×#392	C₂²	1	4	yes	—
64	C₃₁×#392	C₂²	1	2	yes	complemented
65	C₃₁×#388	C₂²	1	4	yes	complemented
66	C₃₁×#387	C₂²	1	4	yes	complemented
67	C₃₁×#386	C₂²	1	2	yes	—
68	C₃₁×#386	C₂²	1	2	yes	—
69	C₃₁×#386	C₂²	1	4	yes	complemented
70	C₃₁×#385	C₂²	1	2	yes	—
71	C₃₁×#385	C₂²	1	2	yes	—
72	C₃₁×#385	C₂²	1	4	yes	complemented
73	C₃₁×#381	C₂²	1	2	yes	—
74	C₃₁×#381	C₂²	1	2	yes	complemented
75	C₃₁×#380	C₂²	1	1	yes	characteristic
76	C₃₁×#380	C₂²	1	1	yes	characteristic
77	C₃₁×#380	C₂²	1	2	yes	complemented
78	C₃₁×#379	C₂²	1	2	yes	—
79	C₃₁×#379	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
83	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
85	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
86	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×#41×C₃₁	—	2	4	no	—
88	C₂×#41×C₃₁	—	4	4	no	—
89	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	—	2	4	no	—
91	C₂²×D₄×C₃₁	—	2	4	no	—
92	C₂²×D₄×C₃₁	—	2	4	no	—
93	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
95	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
97	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
98	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
99	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	—	2	4	no	—
101	C₂³×C₄×C₃₁	—	4	4	no	—
102	C₂³×C₄×C₃₁	—	4	4	no	—
103	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
104	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
105	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
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	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	2	yes	—
113	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₃₁×#123	—	2	8	no	—
117	C₃₁×#123	—	2	8	no	—
118	C₃₁×C₂²⋊Q₈	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	4	no	—
120	C₃₁×#121	—	2	4	no	—
121	C₃₁×#121	—	2	4	no	—
122	C₃₁×#120	—	2	8	no	—
123	C₃₁×#120	—	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	C₄×D₄×C₃₁	—	2	8	no	—
128	C₄×D₄×C₃₁	—	2	8	no	—
129	C₄×D₄×C₃₁	—	2	8	no	—
130	C₄×D₄×C₃₁	—	4	8	no	—
131	C₃₁×#117	—	2	4	no	—
132	C₃₁×#117	—	4	4	no	—
133	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
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	4	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	4	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	4	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	4	yes	—
166	C₂×C₄²×C₃₁	—	2	4	no	—
167	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
171	C₃₁×#95	C₂³	1	2	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	2	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	2	no	—
182	C₂⁴×C₃₁	—	2	2	no	—
183	C₂⁴×C₃₁	—	2	2	no	—
184	C₂⁴×C₃₁	—	4	2	no	—
185	C₂⁴×C₃₁	—	4	2	no	—
186	C₂⁴×C₃₁	—	4	2	no	—
187	C₂⁴×C₃₁	—	4	2	no	—
188	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
189	C₂⁴×C₃₁	#41	1	4	yes	complemented
190	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
191	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
194	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
195	#41×C₃₁	—	4	16	no	—
196	C₂×Q₈×C₃₁	—	2	2	no	—
197	C₂×Q₈×C₃₁	—	4	2	no	—
198	C₂×D₄×C₃₁	—	2	32	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	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	4	4	no	—
213	C₂×D₄×C₃₁	—	4	4	no	—
214	C₂×D₄×C₃₁	—	4	4	no	—
215	C₂×D₄×C₃₁	—	4	2	no	—
216	C₂×D₄×C₃₁	—	4	4	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	4	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	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	2	8	no	—
228	C₂²×C₄×C₃₁	—	2	8	no	—
229	C₂²×C₄×C₃₁	—	4	16	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	4	no	—
234	C₂²×C₄×C₃₁	—	4	2	no	—
235	C₂²×C₄×C₃₁	—	4	2	no	—
236	C₂²×C₄×C₃₁	—	4	16	no	—
237	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
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	#41	1	4	yes	complemented
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	2	yes	—
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
265	C₄⋊C₄×C₃₁	—	4	2	no	—
266	C₄⋊C₄×C₃₁	—	4	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	8	no	—
280	C₂²⋊C₄×C₃₁	—	4	4	no	—
281	C₂²⋊C₄×C₃₁	—	4	4	no	—
282	C₂²⋊C₄×C₃₁	—	4	4	no	—
283	C₂²⋊C₄×C₃₁	—	4	4	no	—
284	C₂²⋊C₄×C₃₁	—	4	4	no	—
285	C₂²⋊C₄×C₃₁	—	4	4	no	—
286	C₄²×C₃₁	—	2	4	no	—
287	C₄²×C₃₁	—	2	4	no	—
288	C₄²×C₃₁	—	2	4	no	—
289	C₄²×C₃₁	—	2	8	no	—
290	#34562	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	2	8	no	—
294	C₂³×C₃₁	—	2	8	no	—
295	C₂³×C₃₁	—	2	2	no	—
296	C₂³×C₃₁	—	2	1	no	—
297	C₂³×C₃₁	—	2	1	no	—
298	C₂³×C₃₁	—	2	1	no	—
299	C₂³×C₃₁	—	2	1	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	2	no	—
308	C₂³×C₃₁	—	2	2	no	—
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	—	2	4	no	—
311	C₂³×C₃₁	—	2	4	no	—
312	C₂³×C₃₁	—	4	4	no	—
313	C₂³×C₃₁	—	4	4	no	—
314	C₂³×C₃₁	—	4	8	no	—
315	C₂³×C₃₁	—	4	4	no	—
316	C₂³×C₃₁	—	4	4	no	—
317	C₂³×C₃₁	—	4	8	no	—
318	C₂³×C₃₁	—	4	8	no	—
319	C₂³×C₃₁	—	4	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	2	yes	—
325	C₂³×C₃₁	C₂×#41	1	2	yes	—
326	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
327	Q₈×C₃₁	—	4	4	no	—
328	D₄×C₃₁	—	2	16	no	—
329	D₄×C₃₁	—	2	16	no	—
330	D₄×C₃₁	—	4	4	no	—
331	D₄×C₃₁	—	4	8	no	—
332	D₄×C₃₁	—	4	16	no	—
333	D₄×C₃₁	—	4	8	no	—
334	D₄×C₃₁	—	4	8	no	—
335	C₂×C₄×C₃₁	—	2	8	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	8	no	—
342	C₂×C₄×C₃₁	—	2	8	no	—
343	C₂×C₄×C₃₁	—	2	8	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	4	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	4	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	4	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	—	2	4	no	—
359	C₂×C₄×C₃₁	—	2	4	no	—
360	C₂×C₄×C₃₁	—	2	4	no	—
361	C₂×C₄×C₃₁	—	4	4	no	—
362	C₂×C₄×C₃₁	—	4	4	no	—
363	C₂×C₄×C₃₁	—	4	4	no	—
364	C₂×C₄×C₃₁	—	4	8	no	—
365	C₂×C₄×C₃₁	—	4	4	no	—
366	C₂×C₄×C₃₁	—	4	4	no	—
367	C₂×C₄×C₃₁	—	4	8	no	—
368	C₂×C₄×C₃₁	—	4	8	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	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
375	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
376	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
377	#2638	C₂×C₃₁	1	2	yes	complemented
378	#2635	C₂×C₃₁	1	2	yes	complemented
379	#2630	C₂×C₃₁	1	4	yes	complemented
380	#2627	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#2626	C₂×C₃₁	1	1	yes	characteristic, complemented
382	#2622	C₂×C₃₁	1	2	yes	complemented
383	#2618	C₂×C₃₁	1	1	yes	characteristic, complemented
384	#2617	C₂×C₃₁	1	1	yes	characteristic, complemented
385	#2613	C₂×C₃₁	1	2	yes	complemented
386	#2395	C₂×C₃₁	1	2	yes	complemented
387	#2392	C₂×C₃₁	1	4	yes	complemented
388	#2388	C₂×C₃₁	1	2	yes	complemented
389	C₄×#123	C₂×C₃₁	1	2	yes	complemented
390	C₄×#120	C₂×C₃₁	1	2	yes	complemented
391	#2280	C₂×C₃₁	1	1	yes	characteristic, complemented
392	C₂²×C₃₁	—	2	2	no	—
393	C₂²×C₃₁	—	2	2	no	—
394	C₂²×C₃₁	—	2	4	no	—
395	C₂²×C₃₁	—	2	4	no	—
396	C₂²×C₃₁	—	2	2	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	2	no	—
402	C₂²×C₃₁	—	2	2	no	—
403	C₂²×C₃₁	—	2	8	no	—
404	C₂²×C₃₁	—	4	16	no	—
405	C₂²×C₃₁	—	4	16	no	—
406	C₂²×C₃₁	—	4	2	no	—
407	C₂²×C₃₁	—	4	2	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	2	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	4	2	no	—
415	C₂²×C₃₁	—	4	2	no	—
416	C₂²×C₃₁	—	4	4	no	—
417	C₂²×C₃₁	—	4	4	no	—
418	C₂²×C₃₁	#525	1	4	yes	—
419	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
420	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
421	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
422	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂²×C₃₁	#585	1	2	yes	—
424	C₄×C₃₁	—	2	4	no	—
425	C₄×C₃₁	—	2	2	no	—
426	C₄×C₃₁	—	2	2	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	4	2	no	—
429	C₄×C₃₁	—	4	2	no	—
430	C₄×C₃₁	—	4	2	no	—
431	C₄×C₃₁	—	4	2	no	—
432	C₄×C₃₁	—	4	2	no	—
433	C₄×C₃₁	—	4	4	no	—
434	C₄×C₃₁	—	4	4	no	—
435	C₄×C₃₁	#534	1	4	yes	—
436	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
438	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
439	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
440	#525	—	2	8	no	—
441	C₂×#123	C₂²×C₃₁	1	2	yes	—
442	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
443	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
444	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
446	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
447	C₂×#120	C₂²×C₃₁	1	2	yes	—
448	C₂×#120	C₂²×C₃₁	1	2	yes	—
449	C₂×C₄×D₄	—	2	8	no	—
450	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
451	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
452	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
453	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
456	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
457	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
458	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
459	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
460	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
461	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
462	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
463	#400	C₂²×C₃₁	1	2	yes	complemented
464	#399	C₂²×C₃₁	1	2	yes	complemented
465	#398	C₂²×C₃₁	1	2	yes	complemented
466	#398	C₂²×C₃₁	1	4	yes	complemented
467	#397	C₂²×C₃₁	1	2	yes	complemented
468	#397	C₂²×C₃₁	1	4	yes	complemented
469	#397	C₂²×C₃₁	1	4	yes	complemented
470	#396	C₂²×C₃₁	1	4	yes	complemented
471	#396	C₂²×C₃₁	1	4	yes	complemented
472	#395	C₂²×C₃₁	1	2	yes	complemented
473	#394	C₂²×C₃₁	1	4	yes	—
474	#394	C₂²×C₃₁	1	4	yes	—
475	#394	C₂²×C₃₁	1	4	yes	complemented
476	#394	C₂²×C₃₁	1	2	yes	complemented
477	#394	C₂²×C₃₁	1	4	yes	complemented
478	#394	C₂²×C₃₁	1	4	yes	complemented
479	#393	C₂²×C₃₁	1	2	yes	complemented
480	#392	C₂²×C₃₁	1	4	yes	—
481	#392	C₂²×C₃₁	1	4	yes	—
482	#392	C₂²×C₃₁	1	2	yes	complemented
483	#388	C₂²×C₃₁	1	4	yes	complemented
484	#387	C₂²×C₃₁	1	4	yes	complemented
485	#386	C₂²×C₃₁	1	2	yes	—
486	#386	C₂²×C₃₁	1	2	yes	—
487	#386	C₂²×C₃₁	1	4	yes	complemented
488	#385	C₂²×C₃₁	1	2	yes	—
489	#385	C₂²×C₃₁	1	2	yes	—
490	#385	C₂²×C₃₁	1	4	yes	complemented
491	#381	C₂²×C₃₁	1	2	yes	—
492	#381	C₂²×C₃₁	1	2	yes	complemented
493	#380	C₂²×C₃₁	1	1	yes	characteristic
494	#380	C₂²×C₃₁	1	1	yes	characteristic
495	#380	C₂²×C₃₁	1	2	yes	complemented
496	#379	C₂²×C₃₁	1	2	yes	—
497	#379	C₂²×C₃₁	1	2	yes	—
498	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
499	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
501	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
502	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
503	C₂×C₃₁	—	2	4	no	—
504	C₂×C₃₁	—	4	2	no	—
505	C₂×C₃₁	—	4	2	no	—
506	C₂×C₃₁	—	4	4	no	—
507	C₂×C₃₁	—	8	2	no	—
508	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
509	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
510	C₂×C₃₁	#3449	1	1	yes	characteristic
511	C₂×C₃₁	#3459	1	2	yes	—
512	C₂×C₃₁	#3460	1	2	yes	—
513	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
514	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
515	C₂×#41	—	2	4	no	—
516	C₂×#41	—	4	4	no	—
517	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
522	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
523	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
524	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
525	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
526	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
527	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂³×C₄	—	2	4	no	—
529	C₂³×C₄	—	4	4	no	—
530	C₂³×C₄	—	4	4	no	—
531	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
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	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
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	#123	—	2	8	no	—
545	#123	—	2	8	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	C₂²⋊Q₈	—	2	4	no	—
548	#121	—	2	4	no	—
549	#121	—	2	4	no	—
550	#120	—	2	8	no	—
551	#120	—	2	8	no	—
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	—	2	8	no	—
554	C₄×D₄	—	2	8	no	—
555	C₄×D₄	—	2	8	no	—
556	C₄×D₄	—	2	8	no	—
557	C₄×D₄	—	2	8	no	—
558	C₄×D₄	—	4	8	no	—
559	#117	—	2	4	no	—
560	#117	—	4	4	no	—
561	C₂×C₄⋊C₄	—	2	4	no	—
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	4	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	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
573	C₂×C₂²⋊C₄	—	2	4	no	—
574	C₂×C₂²⋊C₄	—	2	4	no	—
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	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	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
594	C₂×C₄²	—	2	4	no	—
595	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
596	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
597	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
598	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
599	#95	C₂³×C₃₁	1	4	yes	—
600	#95	C₂³×C₃₁	1	2	yes	—
601	#95	C₂³×C₃₁	1	2	yes	—
602	#95	C₂³×C₃₁	1	4	yes	—
603	#95	C₂³×C₃₁	1	4	yes	—
604	#95	C₂³×C₃₁	1	4	yes	—
605	#95	C₂³×C₃₁	1	4	yes	—
606	#95	C₂³×C₃₁	1	4	yes	—
607	#95	C₂³×C₃₁	1	4	yes	—
608	C₃₁	#34562	1	1	yes	characteristic, direct product factor, Sylow
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	2	no	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	4	2	no	—
614	C₂⁴	—	4	2	no	—
615	C₂⁴	—	4	2	no	—
616	C₂⁴	—	4	2	no	—
617	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
618	C₂⁴	#41×C₃₁	1	4	yes	complemented
619	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
620	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
621	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
622	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
623	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
624	#41	—	4	16	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	4	2	no	—
627	C₂×D₄	—	2	32	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	8	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	4	4	no	—
642	C₂×D₄	—	4	4	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	8	no	—
657	C₂²×C₄	—	2	8	no	—
658	C₂²×C₄	—	4	16	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	16	no	—
666	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
667	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
668	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
669	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
670	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
671	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
672	C₂²×C₄	#41×C₃₁	1	4	yes	complemented
673	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
674	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₃₁	1	4	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	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	8	no	—
692	C₄⋊C₄	—	4	4	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	2	4	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	8	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	8	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	8	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	8	no	—
722	C₂³	—	2	8	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	2	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	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	4	no	—
739	C₂³	—	2	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	8	no	—
746	C₂³	—	4	8	no	—
747	C₂³	—	4	8	no	—
748	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
749	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
750	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
751	C₂³	C₂×#41×C₃₁	1	4	yes	—
752	C₂³	C₂×#41×C₃₁	1	2	yes	—
753	C₂³	C₂×#41×C₃₁	1	2	yes	—
754	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
755	Q₈	—	4	4	no	—
756	D₄	—	2	16	no	—
757	D₄	—	2	16	no	—
758	D₄	—	4	4	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	16	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	C₂×C₄	—	2	8	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	8	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	8	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	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
798	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
801	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
802	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	8	no	—
815	C₂²	—	4	16	no	—
816	C₂²	—	4	16	no	—
817	C₂²	—	4	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	4	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	4	4	no	—
829	C₂²	C₃₁×#525	1	4	yes	—
830	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
831	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
832	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
833	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
834	C₂²	C₃₁×#585	1	2	yes	—
835	C₄	—	2	4	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	4	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	4	no	—
845	C₄	—	4	4	no	—
846	C₄	C₃₁×#534	1	4	yes	—
847	C₂	—	2	4	no	—
848	C₂	—	4	2	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	4	no	—
851	C₂	—	8	2	no	—
852	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
853	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
854	C₂	C₃₁×#3449	1	1	yes	characteristic
855	C₂	C₃₁×#3459	1	2	yes	—
856	C₂	C₃₁×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#525	C₂	semidirect
2. C₂²×C₄×D₄×C₃₁	C₂	semidirect
3. C₃₁×#2638	C₂	semidirect
4. C₃₁×#2635	C₂	semidirect
5. C₃₁×#2630	C₂	semidirect
6. C₃₁×#2627	C₂	semidirect
7. C₃₁×#2626	C₂	semidirect
8. C₃₁×#2622	C₂	semidirect
9. C₃₁×#2618	C₂	semidirect
10. C₃₁×#2617	C₂	semidirect
11. C₃₁×#2613	C₂	semidirect
12. C₃₁×#2395	C₂	semidirect
13. C₃₁×#2392	C₂	semidirect
14. C₃₁×#2388	C₂	semidirect
15. C₄×C₃₁×#123	C₂	semidirect
16. C₄×C₃₁×#120	C₂	semidirect
17. C₃₁×#2280	C₂	semidirect
18. C₂²×#41×C₃₁	C₂²	semidirect
24. C₂×C₃₁×#123	C₂²	semidirect
26. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₃₁×#121	C₂²	semidirect
37. C₂×C₄×D₄×C₃₁	C₂²	semidirect
38. C₂×C₄×D₄×C₃₁	C₂²	semidirect
39. C₂×C₃₁×#117	C₂²	semidirect
40. C₂×C₃₁×#117	C₂²	semidirect
45. C₃₁×#400	C₂²	semidirect
46. C₃₁×#399	C₂²	semidirect
47. C₃₁×#398	C₂²	semidirect
48. C₃₁×#398	C₂²	semidirect
49. C₃₁×#397	C₂²	semidirect
50. C₃₁×#397	C₂²	semidirect
51. C₃₁×#397	C₂²	semidirect
52. C₃₁×#396	C₂²	semidirect
53. C₃₁×#396	C₂²	semidirect
54. C₃₁×#395	C₂²	semidirect
57. C₃₁×#394	C₂²	semidirect
58. C₃₁×#394	C₂²	semidirect
59. C₃₁×#394	C₂²	semidirect
60. C₃₁×#394	C₂²	semidirect
61. C₃₁×#393	C₂²	semidirect
64. C₃₁×#392	C₂²	semidirect
65. C₃₁×#388	C₂²	semidirect
66. C₃₁×#387	C₂²	semidirect
69. C₃₁×#386	C₂²	semidirect
72. C₃₁×#385	C₂²	semidirect
74. C₃₁×#381	C₂²	semidirect
77. C₃₁×#380	C₂²	semidirect
80. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
103. C₂³×C₄×C₃₁	D₄	semidirect
189. C₂⁴×C₃₁	#41	semidirect
243. C₂²×C₄×C₃₁	#41	semidirect
290. #34562	C₃₁	direct (N × H)
375. C₂×#525	C₂×C₃₁	semidirect
376. C₂²×C₄×D₄	C₂×C₃₁	semidirect
377. #2638	C₂×C₃₁	semidirect
378. #2635	C₂×C₃₁	semidirect
379. #2630	C₂×C₃₁	semidirect
380. #2627	C₂×C₃₁	semidirect
381. #2626	C₂×C₃₁	semidirect
382. #2622	C₂×C₃₁	semidirect
383. #2618	C₂×C₃₁	semidirect
384. #2617	C₂×C₃₁	semidirect
385. #2613	C₂×C₃₁	semidirect
386. #2395	C₂×C₃₁	semidirect
387. #2392	C₂×C₃₁	semidirect
388. #2388	C₂×C₃₁	semidirect
389. C₄×#123	C₂×C₃₁	semidirect
390. C₄×#120	C₂×C₃₁	semidirect
391. #2280	C₂×C₃₁	semidirect
436. C₂²×#41	C₂²×C₃₁	semidirect
442. C₂×#123	C₂²×C₃₁	semidirect
444. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
446. C₂×#121	C₂²×C₃₁	semidirect
455. C₂×C₄×D₄	C₂²×C₃₁	semidirect
456. C₂×C₄×D₄	C₂²×C₃₁	semidirect
457. C₂×#117	C₂²×C₃₁	semidirect
458. C₂×#117	C₂²×C₃₁	semidirect
463. #400	C₂²×C₃₁	semidirect
464. #399	C₂²×C₃₁	semidirect
465. #398	C₂²×C₃₁	semidirect
466. #398	C₂²×C₃₁	semidirect
467. #397	C₂²×C₃₁	semidirect
468. #397	C₂²×C₃₁	semidirect
469. #397	C₂²×C₃₁	semidirect
470. #396	C₂²×C₃₁	semidirect
471. #396	C₂²×C₃₁	semidirect
472. #395	C₂²×C₃₁	semidirect
475. #394	C₂²×C₃₁	semidirect
476. #394	C₂²×C₃₁	semidirect
477. #394	C₂²×C₃₁	semidirect
478. #394	C₂²×C₃₁	semidirect
479. #393	C₂²×C₃₁	semidirect
482. #392	C₂²×C₃₁	semidirect
483. #388	C₂²×C₃₁	semidirect
484. #387	C₂²×C₃₁	semidirect
487. #386	C₂²×C₃₁	semidirect
490. #385	C₂²×C₃₁	semidirect
492. #381	C₂²×C₃₁	semidirect
495. #380	C₂²×C₃₁	semidirect
498. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
500. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
501. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
502. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
531. C₂³×C₄	D₄×C₃₁	semidirect
608. C₃₁	#34562	direct (N × H)
618. C₂⁴	#41×C₃₁	semidirect
672. C₂²×C₄	#41×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×#525	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2638	2
C₃₁×#2635	2
C₃₁×#2630	2
C₃₁×#2627	2
C₃₁×#2626	2
C₃₁×#2622	2
C₃₁×#2618	2
C₃₁×#2617	2
C₃₁×#2613	2
C₃₁×#2395	2
C₃₁×#2392	2
C₃₁×#2388	2
C₄×C₃₁×#123	2
C₄×C₃₁×#120	2
C₃₁×#2280	2
#34562	31

Subgroups — C31×#34562 #21491321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34562 #21491321