Subgroups — C₃₁×#35083 #21491842

Order 7936.

1850 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2854	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2654	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2650	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2512	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2511	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2509	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2508	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2488	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2481	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2452	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2449	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2448	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2447	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2419	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2332	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#126	C₂²	1	2	yes	—
26	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#123	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#400	C₂²	1	2	yes	—
41	C₃₁×#400	C₂²	1	2	yes	—
42	C₃₁×#400	C₂²	1	2	yes	—
43	C₃₁×#400	C₂²	1	2	yes	—
44	C₃₁×#400	C₂²	1	2	yes	—
45	C₃₁×#399	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#398	C₂²	1	2	yes	—
48	C₃₁×#397	C₂²	1	2	yes	—
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#397	C₂²	1	2	yes	—
51	C₃₁×#397	C₂²	1	2	yes	—
52	C₃₁×#396	C₂²	1	2	yes	—
53	C₃₁×#396	C₂²	1	2	yes	—
54	C₃₁×#395	C₂²	1	2	yes	—
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	2	yes	—
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	1	yes	characteristic
60	C₃₁×#391	C₂²	1	1	yes	characteristic
61	C₃₁×#391	C₂²	1	1	yes	characteristic
62	C₃₁×#390	C₂²	1	1	yes	characteristic
63	C₃₁×#390	C₂²	1	1	yes	characteristic
64	C₃₁×#390	C₂²	1	1	yes	characteristic
65	C₃₁×#390	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	2	yes	—
67	C₃₁×#389	C₂²	1	2	yes	—
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#389	C₂²	1	1	yes	characteristic
74	C₃₁×#389	C₂²	1	1	yes	characteristic
75	C₃₁×#389	C₂²	1	1	yes	characteristic
76	C₃₁×#388	C₂²	1	2	yes	—
77	C₃₁×#388	C₂²	1	2	yes	—
78	C₃₁×#388	C₂²	1	2	yes	—
79	C₃₁×#388	C₂²	1	2	yes	—
80	C₃₁×#388	C₂²	1	2	yes	—
81	C₃₁×#388	C₂²	1	2	yes	—
82	C₃₁×#388	C₂²	1	2	yes	—
83	C₃₁×#388	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	2	yes	—
89	C₃₁×#387	C₂²	1	2	yes	—
90	C₃₁×#387	C₂²	1	2	yes	—
91	C₃₁×#387	C₂²	1	2	yes	—
92	C₃₁×#386	C₂²	1	2	yes	—
93	C₃₁×#386	C₂²	1	2	yes	—
94	C₃₁×#386	C₂²	1	2	yes	—
95	C₃₁×#386	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#385	C₂²	1	2	yes	—
98	C₃₁×#385	C₂²	1	2	yes	—
99	C₃₁×#385	C₂²	1	2	yes	—
100	C₃₁×#384	C₂²	1	1	yes	characteristic
101	C₃₁×#382	C₂²	1	2	yes	—
102	C₃₁×#382	C₂²	1	1	yes	characteristic
103	C₃₁×#381	C₂²	1	2	yes	—
104	C₃₁×#381	C₂²	1	2	yes	—
105	C₃₁×#380	C₂²	1	1	yes	characteristic
106	C₃₁×#380	C₂²	1	1	yes	characteristic
107	C₃₁×#380	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
121	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
122	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	—	4	2	no	—
136	C₃₁×#126	—	2	8	no	—
137	C₃₁×#124	—	4	2	no	—
138	C₃₁×#123	—	4	4	no	—
139	C₃₁×C₂²⋊Q₈	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	—	2	8	no	—
141	C₃₁×C₂²⋊Q₈	—	4	4	no	—
142	C₃₁×#121	—	2	4	no	—
143	C₄×Q₈×C₃₁	—	4	2	no	—
144	C₄×D₄×C₃₁	—	4	2	no	—
145	C₄×D₄×C₃₁	—	4	4	no	—
146	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
147	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄²×C₃₁	—	2	4	no	—
191	C₂×C₄²×C₃₁	—	4	2	no	—
192	C₂×C₄²×C₃₁	—	4	2	no	—
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	2	yes	—
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	1	yes	characteristic
214	C₃₁×#95	C₂³	1	1	yes	characteristic
215	C₃₁×#95	C₂³	1	1	yes	characteristic
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	1	yes	characteristic
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	1	yes	characteristic
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	1	yes	characteristic
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
239	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×Q₈×C₃₁	—	4	2	no	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	4	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	4	no	—
269	C₂²×C₄×C₃₁	—	4	1	no	—
270	C₂²×C₄×C₃₁	—	4	1	no	—
271	C₂²×C₄×C₃₁	—	4	1	no	—
272	C₂²×C₄×C₃₁	—	4	1	no	—
273	C₂²×C₄×C₃₁	—	4	2	no	—
274	C₂²×C₄×C₃₁	—	4	2	no	—
275	C₂²×C₄×C₃₁	#41	1	4	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	4	no	—
306	C₄⋊C₄×C₃₁	—	2	4	no	—
307	C₄⋊C₄×C₃₁	—	2	4	no	—
308	C₄⋊C₄×C₃₁	—	2	4	no	—
309	C₄⋊C₄×C₃₁	—	2	4	no	—
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	2	no	—
312	C₄⋊C₄×C₃₁	—	2	2	no	—
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	4	2	no	—
315	C₄⋊C₄×C₃₁	—	4	2	no	—
316	C₄⋊C₄×C₃₁	—	4	2	no	—
317	C₄⋊C₄×C₃₁	—	4	2	no	—
318	C₄⋊C₄×C₃₁	—	4	2	no	—
319	C₄⋊C₄×C₃₁	—	4	2	no	—
320	C₄⋊C₄×C₃₁	—	4	2	no	—
321	C₄⋊C₄×C₃₁	—	4	2	no	—
322	C₄⋊C₄×C₃₁	#41	1	4	yes	—
323	C₄⋊C₄×C₃₁	#41	1	4	yes	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	4	no	—
329	C₂²⋊C₄×C₃₁	—	2	4	no	—
330	C₂²⋊C₄×C₃₁	—	2	4	no	—
331	C₂²⋊C₄×C₃₁	—	2	4	no	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	—	4	2	no	—
334	C₂²⋊C₄×C₃₁	—	4	2	no	—
335	C₂²⋊C₄×C₃₁	—	4	2	no	—
336	C₂²⋊C₄×C₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₃₁	—	4	2	no	—
338	C₂²⋊C₄×C₃₁	—	4	2	no	—
339	C₄²×C₃₁	—	2	2	no	—
340	C₄²×C₃₁	—	2	2	no	—
341	C₄²×C₃₁	—	2	2	no	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	2	4	no	—
344	C₄²×C₃₁	—	2	2	no	—
345	C₄²×C₃₁	—	2	2	no	—
346	C₄²×C₃₁	—	2	2	no	—
347	C₄²×C₃₁	—	2	2	no	—
348	C₄²×C₃₁	—	4	1	no	—
349	C₄²×C₃₁	—	4	1	no	—
350	C₄²×C₃₁	—	4	1	no	—
351	C₄²×C₃₁	—	4	1	no	—
352	C₄²×C₃₁	—	4	2	no	—
353	C₄²×C₃₁	—	4	2	no	—
354	#35083	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂³×C₃₁	—	2	1	no	—
356	C₂³×C₃₁	—	2	1	no	—
357	C₂³×C₃₁	—	2	1	no	—
358	C₂³×C₃₁	—	2	1	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	2	2	no	—
361	C₂³×C₃₁	—	2	2	no	—
362	C₂³×C₃₁	—	2	2	no	—
363	C₂³×C₃₁	—	2	2	no	—
364	C₂³×C₃₁	—	2	2	no	—
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	C₂×#41	1	2	yes	—
367	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
368	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
369	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
370	Q₈×C₃₁	—	4	4	no	—
371	Q₈×C₃₁	—	8	4	no	—
372	D₄×C₃₁	—	4	8	no	—
373	D₄×C₃₁	—	4	4	no	—
374	C₂×C₄×C₃₁	—	2	8	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	8	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	1	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	1	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	1	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	4	4	no	—
430	C₂×C₄×C₃₁	—	4	4	no	—
431	C₂×C₄×C₃₁	—	4	4	no	—
432	C₂×C₄×C₃₁	—	4	4	no	—
433	C₂×C₄×C₃₁	—	4	4	no	—
434	C₂×C₄×C₃₁	—	8	4	no	—
435	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
436	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
437	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
438	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
439	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
440	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
441	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
442	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
443	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
444	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
445	#2857	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#2855	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#2854	C₂×C₃₁	1	1	yes	characteristic
448	#2850	C₂×C₃₁	1	1	yes	characteristic
449	#2654	C₂×C₃₁	1	2	yes	complemented
450	#2650	C₂×C₃₁	1	2	yes	complemented
451	#2512	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#2511	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#2509	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#2508	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#2488	C₂×C₃₁	1	2	yes	complemented
456	#2481	C₂×C₃₁	1	2	yes	complemented
457	#2452	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#2451	C₂×C₃₁	1	1	yes	characteristic, complemented
459	#2449	C₂×C₃₁	1	2	yes	complemented
460	#2448	C₂×C₃₁	1	1	yes	characteristic, complemented
461	#2447	C₂×C₃₁	1	1	yes	characteristic, complemented
462	#2419	C₂×C₃₁	1	2	yes	complemented
463	#2334	C₂×C₃₁	1	2	yes	complemented
464	#2332	C₂×C₃₁	1	2	yes	complemented
465	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
466	C₄×#121	C₂×C₃₁	1	1	yes	characteristic
467	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
468	C₂²×C₃₁	—	2	2	no	—
469	C₂²×C₃₁	—	2	2	no	—
470	C₂²×C₃₁	—	2	2	no	—
471	C₂²×C₃₁	—	2	2	no	—
472	C₂²×C₃₁	—	2	2	no	—
473	C₂²×C₃₁	—	2	2	no	—
474	C₂²×C₃₁	—	4	2	no	—
475	C₂²×C₃₁	—	4	2	no	—
476	C₂²×C₃₁	—	4	2	no	—
477	C₂²×C₃₁	—	4	2	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	#542	1	4	yes	—
482	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
483	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
484	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
485	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
488	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	2	2	no	—
491	C₄×C₃₁	—	2	2	no	—
492	C₄×C₃₁	—	2	2	no	—
493	C₄×C₃₁	—	2	2	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	2	2	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	1	no	—
499	C₄×C₃₁	—	4	1	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	1	no	—
502	C₄×C₃₁	—	4	1	no	—
503	C₄×C₃₁	—	4	2	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	—	4	1	no	—
506	C₄×C₃₁	—	4	1	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	2	no	—
509	C₄×C₃₁	#539	1	4	yes	—
510	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
511	C₂×#126	C₂²×C₃₁	1	2	yes	—
512	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
513	C₂×#123	C₂²×C₃₁	1	2	yes	—
514	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
515	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
517	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
520	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
521	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
522	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
523	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
524	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
525	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
526	#400	C₂²×C₃₁	1	2	yes	—
527	#400	C₂²×C₃₁	1	2	yes	—
528	#400	C₂²×C₃₁	1	2	yes	—
529	#400	C₂²×C₃₁	1	2	yes	—
530	#400	C₂²×C₃₁	1	2	yes	—
531	#399	C₂²×C₃₁	1	2	yes	—
532	#398	C₂²×C₃₁	1	2	yes	—
533	#398	C₂²×C₃₁	1	2	yes	—
534	#397	C₂²×C₃₁	1	2	yes	—
535	#397	C₂²×C₃₁	1	2	yes	—
536	#397	C₂²×C₃₁	1	2	yes	—
537	#397	C₂²×C₃₁	1	2	yes	—
538	#396	C₂²×C₃₁	1	2	yes	—
539	#396	C₂²×C₃₁	1	2	yes	—
540	#395	C₂²×C₃₁	1	2	yes	—
541	#393	C₂²×C₃₁	1	2	yes	—
542	#391	C₂²×C₃₁	1	2	yes	—
543	#391	C₂²×C₃₁	1	2	yes	—
544	#391	C₂²×C₃₁	1	1	yes	characteristic
545	#391	C₂²×C₃₁	1	1	yes	characteristic
546	#391	C₂²×C₃₁	1	1	yes	characteristic
547	#391	C₂²×C₃₁	1	1	yes	characteristic
548	#390	C₂²×C₃₁	1	1	yes	characteristic
549	#390	C₂²×C₃₁	1	1	yes	characteristic
550	#390	C₂²×C₃₁	1	1	yes	characteristic
551	#390	C₂²×C₃₁	1	1	yes	characteristic
552	#389	C₂²×C₃₁	1	2	yes	—
553	#389	C₂²×C₃₁	1	2	yes	—
554	#389	C₂²×C₃₁	1	1	yes	characteristic
555	#389	C₂²×C₃₁	1	1	yes	characteristic
556	#389	C₂²×C₃₁	1	1	yes	characteristic
557	#389	C₂²×C₃₁	1	1	yes	characteristic
558	#389	C₂²×C₃₁	1	1	yes	characteristic
559	#389	C₂²×C₃₁	1	1	yes	characteristic
560	#389	C₂²×C₃₁	1	1	yes	characteristic
561	#389	C₂²×C₃₁	1	1	yes	characteristic
562	#388	C₂²×C₃₁	1	2	yes	—
563	#388	C₂²×C₃₁	1	2	yes	—
564	#388	C₂²×C₃₁	1	2	yes	—
565	#388	C₂²×C₃₁	1	2	yes	—
566	#388	C₂²×C₃₁	1	2	yes	—
567	#388	C₂²×C₃₁	1	2	yes	—
568	#388	C₂²×C₃₁	1	2	yes	—
569	#388	C₂²×C₃₁	1	2	yes	—
570	#387	C₂²×C₃₁	1	2	yes	—
571	#387	C₂²×C₃₁	1	2	yes	—
572	#387	C₂²×C₃₁	1	2	yes	—
573	#387	C₂²×C₃₁	1	2	yes	—
574	#387	C₂²×C₃₁	1	2	yes	—
575	#387	C₂²×C₃₁	1	2	yes	—
576	#387	C₂²×C₃₁	1	2	yes	—
577	#387	C₂²×C₃₁	1	2	yes	—
578	#386	C₂²×C₃₁	1	2	yes	—
579	#386	C₂²×C₃₁	1	2	yes	—
580	#386	C₂²×C₃₁	1	2	yes	—
581	#386	C₂²×C₃₁	1	2	yes	—
582	#385	C₂²×C₃₁	1	2	yes	—
583	#385	C₂²×C₃₁	1	2	yes	—
584	#385	C₂²×C₃₁	1	2	yes	—
585	#385	C₂²×C₃₁	1	2	yes	—
586	#384	C₂²×C₃₁	1	1	yes	characteristic
587	#382	C₂²×C₃₁	1	2	yes	—
588	#382	C₂²×C₃₁	1	1	yes	characteristic
589	#381	C₂²×C₃₁	1	2	yes	—
590	#381	C₂²×C₃₁	1	2	yes	—
591	#380	C₂²×C₃₁	1	1	yes	characteristic
592	#380	C₂²×C₃₁	1	1	yes	characteristic
593	#380	C₂²×C₃₁	1	2	yes	—
594	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
596	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
603	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
605	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
606	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
607	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
608	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
609	C₂×C₃₁	—	2	4	no	—
610	C₂×C₃₁	—	8	2	no	—
611	C₂×C₃₁	#3444	1	1	yes	characteristic
612	C₂×C₃₁	C₂×#539	1	1	yes	characteristic
613	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
614	C₂×C₃₁	#3519	1	1	yes	characteristic
615	C₂×C₃₁	#3520	1	1	yes	characteristic
616	C₂×C₃₁	#3522	1	1	yes	characteristic
617	C₂×C₃₁	#3523	1	1	yes	characteristic
618	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
619	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
620	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
621	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
630	C₄⋊Q₈	—	4	2	no	—
631	#126	—	2	8	no	—
632	#124	—	4	2	no	—
633	#123	—	4	4	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	C₂²⋊Q₈	—	2	8	no	—
636	C₂²⋊Q₈	—	4	4	no	—
637	#121	—	2	4	no	—
638	C₄×Q₈	—	4	2	no	—
639	C₄×D₄	—	4	2	no	—
640	C₄×D₄	—	4	4	no	—
641	C₂×C₄⋊C₄	—	2	4	no	—
642	C₂×C₄⋊C₄	—	2	4	no	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄²	—	2	4	no	—
686	C₂×C₄²	—	4	2	no	—
687	C₂×C₄²	—	4	2	no	—
688	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
692	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
698	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
699	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
703	#95	C₂³×C₃₁	1	1	yes	characteristic
704	#95	C₂³×C₃₁	1	1	yes	characteristic
705	#95	C₂³×C₃₁	1	1	yes	characteristic
706	#95	C₂³×C₃₁	1	1	yes	characteristic
707	#95	C₂³×C₃₁	1	1	yes	characteristic
708	#95	C₂³×C₃₁	1	1	yes	characteristic
709	#95	C₂³×C₃₁	1	1	yes	characteristic
710	#95	C₂³×C₃₁	1	1	yes	characteristic
711	#95	C₂³×C₃₁	1	2	yes	—
712	#95	C₂³×C₃₁	1	2	yes	—
713	#95	C₂³×C₃₁	1	2	yes	—
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	2	yes	—
716	#95	C₂³×C₃₁	1	2	yes	—
717	#95	C₂³×C₃₁	1	2	yes	—
718	#95	C₂³×C₃₁	1	2	yes	—
719	#95	C₂³×C₃₁	1	2	yes	—
720	#95	C₂³×C₃₁	1	2	yes	—
721	#95	C₂³×C₃₁	1	2	yes	—
722	#95	C₂³×C₃₁	1	2	yes	—
723	#95	C₂³×C₃₁	1	2	yes	—
724	#95	C₂³×C₃₁	1	2	yes	—
725	#95	C₂³×C₃₁	1	2	yes	—
726	#95	C₂³×C₃₁	1	2	yes	—
727	#95	C₂³×C₃₁	1	2	yes	—
728	#95	C₂³×C₃₁	1	2	yes	—
729	#95	C₂³×C₃₁	1	2	yes	—
730	#95	C₂³×C₃₁	1	2	yes	—
731	#95	C₂³×C₃₁	1	2	yes	—
732	#95	C₂³×C₃₁	1	2	yes	—
733	C₃₁	#35083	1	1	yes	characteristic, direct product factor, Sylow
734	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
735	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	4	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	4	2	no	—
741	C₂×Q₈	—	4	2	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	#41×C₃₁	1	4	yes	—
772	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	#41×C₃₁	1	4	yes	—
819	C₄⋊C₄	#41×C₃₁	1	4	yes	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	4	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	4	1	no	—
845	C₄²	—	4	1	no	—
846	C₄²	—	4	1	no	—
847	C₄²	—	4	1	no	—
848	C₄²	—	4	2	no	—
849	C₄²	—	4	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	C₂×#41×C₃₁	1	2	yes	—
862	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
863	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
864	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
865	Q₈	—	4	4	no	—
866	Q₈	—	8	4	no	—
867	D₄	—	4	8	no	—
868	D₄	—	4	4	no	—
869	C₂×C₄	—	2	8	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	8	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	8	4	no	—
930	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
931	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
932	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
933	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
934	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
935	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
936	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
937	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
938	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
939	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	C₃₁×#542	1	4	yes	—
954	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
955	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
956	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
957	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
958	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
959	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
960	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	C₃₁×#539	1	4	yes	—
982	C₂	—	2	4	no	—
983	C₂	—	8	2	no	—
984	C₂	C₃₁×#3444	1	1	yes	characteristic
985	C₂	C₂×C₃₁×#539	1	1	yes	characteristic
986	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
987	C₂	C₃₁×#3519	1	1	yes	characteristic
988	C₂	C₃₁×#3520	1	1	yes	characteristic
989	C₂	C₃₁×#3522	1	1	yes	characteristic
990	C₂	C₃₁×#3523	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×#2857	C₂	semidirect
2. C₃₁×#2855	C₂	semidirect
5. C₃₁×#2654	C₂	semidirect
6. C₃₁×#2650	C₂	semidirect
7. C₃₁×#2512	C₂	semidirect
8. C₃₁×#2511	C₂	semidirect
9. C₃₁×#2509	C₂	semidirect
10. C₃₁×#2508	C₂	semidirect
11. C₃₁×#2488	C₂	semidirect
12. C₃₁×#2481	C₂	semidirect
13. C₃₁×#2452	C₂	semidirect
14. C₃₁×#2451	C₂	semidirect
15. C₃₁×#2449	C₂	semidirect
16. C₃₁×#2448	C₂	semidirect
17. C₃₁×#2447	C₂	semidirect
18. C₃₁×#2419	C₂	semidirect
19. C₃₁×#2334	C₂	semidirect
20. C₃₁×#2332	C₂	semidirect
21. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
354. #35083	C₃₁	direct (N × H)
445. #2857	C₂×C₃₁	semidirect
446. #2855	C₂×C₃₁	semidirect
449. #2654	C₂×C₃₁	semidirect
450. #2650	C₂×C₃₁	semidirect
451. #2512	C₂×C₃₁	semidirect
452. #2511	C₂×C₃₁	semidirect
453. #2509	C₂×C₃₁	semidirect
454. #2508	C₂×C₃₁	semidirect
455. #2488	C₂×C₃₁	semidirect
456. #2481	C₂×C₃₁	semidirect
457. #2452	C₂×C₃₁	semidirect
458. #2451	C₂×C₃₁	semidirect
459. #2449	C₂×C₃₁	semidirect
460. #2448	C₂×C₃₁	semidirect
461. #2447	C₂×C₃₁	semidirect
462. #2419	C₂×C₃₁	semidirect
463. #2334	C₂×C₃₁	semidirect
464. #2332	C₂×C₃₁	semidirect
465. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
467. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
733. C₃₁	#35083	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×#2857	2
C₃₁×#2855	2
C₃₁×#2854	2
C₃₁×#2850	2
C₃₁×#2654	2
C₃₁×#2650	2
C₃₁×#2512	2
C₃₁×#2511	2
C₃₁×#2509	2
C₃₁×#2508	2
C₃₁×#2488	2
C₃₁×#2481	2
C₃₁×#2452	2
C₃₁×#2451	2
C₃₁×#2449	2
C₃₁×#2448	2
C₃₁×#2447	2
C₃₁×#2419	2
C₃₁×#2334	2
C₃₁×#2332	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#121	2
C₂×C₄×C₄⋊C₄×C₃₁	2
#35083	31

Subgroups — C31×#35083 #21491842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35083 #21491842