Subgroups — C₃₁×#36740 #21493499

Order 7936.

2262 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#538	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2700	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2698	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2689	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2687	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2681	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2680	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2674	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2672	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2659	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2639	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2564	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2417	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2412	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2412	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#388	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#543	—	2	8	no	—
21	C₃₁×#538	—	2	8	no	—
22	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃₁×#126	C₂²	1	2	yes	—
24	C₂×C₃₁×#124	C₂²	1	2	yes	—
25	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃₁×#123	C₂²	1	2	yes	—
27	C₂×C₃₁×#123	C₂²	1	2	yes	—
28	C₂×C₃₁×#123	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#121	C₂²	1	2	yes	—
40	C₂×C₃₁×#120	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#400	C₂²	1	2	yes	complemented
49	C₃₁×#400	C₂²	1	2	yes	complemented
50	C₃₁×#399	C₂²	1	2	yes	complemented
51	C₃₁×#398	C₂²	1	2	yes	complemented
52	C₃₁×#398	C₂²	1	2	yes	complemented
53	C₃₁×#398	C₂²	1	2	yes	complemented
54	C₃₁×#398	C₂²	1	2	yes	complemented
55	C₃₁×#397	C₂²	1	2	yes	—
56	C₃₁×#397	C₂²	1	2	yes	—
57	C₃₁×#397	C₂²	1	2	yes	—
58	C₃₁×#397	C₂²	1	2	yes	—
59	C₃₁×#397	C₂²	1	2	yes	complemented
60	C₃₁×#396	C₂²	1	2	yes	complemented
61	C₃₁×#396	C₂²	1	2	yes	complemented
62	C₃₁×#395	C₂²	1	2	yes	complemented
63	C₃₁×#395	C₂²	1	2	yes	complemented
64	C₃₁×#395	C₂²	1	2	yes	complemented
65	C₃₁×#394	C₂²	1	2	yes	—
66	C₃₁×#394	C₂²	1	2	yes	—
67	C₃₁×#394	C₂²	1	2	yes	—
68	C₃₁×#394	C₂²	1	2	yes	—
69	C₃₁×#394	C₂²	1	2	yes	complemented
70	C₃₁×#393	C₂²	1	2	yes	complemented
71	C₃₁×#393	C₂²	1	2	yes	complemented
72	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#391	C₂²	1	2	yes	complemented
76	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#389	C₂²	1	2	yes	complemented
78	C₃₁×#389	C₂²	1	2	yes	complemented
79	C₃₁×#389	C₂²	1	2	yes	complemented
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×#388	C₂²	1	2	yes	complemented
85	C₃₁×#388	C₂²	1	2	yes	complemented
86	C₃₁×#387	C₂²	1	2	yes	complemented
87	C₃₁×#387	C₂²	1	2	yes	complemented
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	2	yes	—
90	C₃₁×#386	C₂²	1	2	yes	—
91	C₃₁×#386	C₂²	1	2	yes	—
92	C₃₁×#386	C₂²	1	2	yes	—
93	C₃₁×#386	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	complemented
97	C₃₁×#385	C₂²	1	2	yes	complemented
98	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#381	C₂²	1	2	yes	—
101	C₃₁×#381	C₂²	1	2	yes	—
102	C₃₁×#380	C₂²	1	2	yes	—
103	C₃₁×#380	C₂²	1	2	yes	—
104	C₃₁×#380	C₂²	1	2	yes	—
105	C₃₁×#380	C₂²	1	2	yes	—
106	C₃₁×#380	C₂²	1	2	yes	complemented
107	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
108	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
109	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
116	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₃₁×C₄⋊Q₈	—	4	2	no	—
128	C₃₁×#126	—	2	8	no	—
129	C₃₁×#124	—	2	8	no	—
130	C₃₁×#124	—	4	2	no	—
131	C₃₁×#123	—	2	8	no	—
132	C₃₁×#123	—	4	4	no	—
133	C₃₁×#123	—	4	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	8	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	8	no	—
139	C₃₁×C₂²⋊Q₈	—	2	8	no	—
140	C₃₁×C₂²⋊Q₈	—	2	8	no	—
141	C₃₁×C₂²⋊Q₈	—	2	8	no	—
142	C₃₁×C₂²⋊Q₈	—	4	4	no	—
143	C₃₁×#121	—	2	4	no	—
144	C₃₁×#121	—	2	8	no	—
145	C₃₁×#120	—	2	8	no	—
146	C₄×D₄×C₃₁	—	2	8	no	—
147	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₃₁	—	2	8	no	—
170	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
171	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
172	C₂×C₂²⋊C₄×C₃₁	D₄	1	8	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄²×C₃₁	—	4	2	no	—
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₃₁×#95	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	2	yes	—
206	C₃₁×#95	C₂³	1	2	yes	—
207	C₃₁×#95	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	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
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	C₂⁴×C₃₁	—	2	2	no	—
223	C₂⁴×C₃₁	—	2	2	no	—
224	C₂⁴×C₃₁	—	4	1	no	—
225	C₂⁴×C₃₁	—	4	1	no	—
226	C₂⁴×C₃₁	—	4	1	no	—
227	C₂⁴×C₃₁	—	4	1	no	—
228	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
229	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
230	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
231	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂×Q₈×C₃₁	—	2	4	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	4	2	no	—
237	C₂×Q₈×C₃₁	—	4	1	no	—
238	C₂×Q₈×C₃₁	—	4	1	no	—
239	C₂×Q₈×C₃₁	—	4	1	no	—
240	C₂×Q₈×C₃₁	—	4	2	no	—
241	C₂×Q₈×C₃₁	—	4	1	no	—
242	C₂×Q₈×C₃₁	—	4	1	no	—
243	C₂×Q₈×C₃₁	—	4	1	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	4	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	—	4	2	no	—
251	C₂×D₄×C₃₁	—	4	2	no	—
252	C₂×D₄×C₃₁	—	4	1	no	—
253	C₂×D₄×C₃₁	—	4	1	no	—
254	C₂×D₄×C₃₁	—	4	2	no	—
255	C₂×D₄×C₃₁	—	4	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	4	no	—
259	C₂²×C₄×C₃₁	—	2	4	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	4	no	—
265	C₂²×C₄×C₃₁	—	4	1	no	—
266	C₂²×C₄×C₃₁	—	4	1	no	—
267	C₂²×C₄×C₃₁	—	4	1	no	—
268	C₂²×C₄×C₃₁	—	4	1	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	1	no	—
274	C₂²×C₄×C₃₁	—	4	2	no	—
275	C₂²×C₄×C₃₁	—	4	2	no	—
276	C₂²×C₄×C₃₁	—	4	2	no	—
277	C₂²×C₄×C₃₁	—	4	2	no	—
278	C₂²×C₄×C₃₁	—	4	1	no	—
279	C₂²×C₄×C₃₁	—	4	2	no	—
280	C₂²×C₄×C₃₁	—	4	2	no	—
281	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
282	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
288	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₃₁	—	2	4	no	—
300	C₄⋊C₄×C₃₁	—	2	4	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	4	no	—
303	C₄⋊C₄×C₃₁	—	2	4	no	—
304	C₄⋊C₄×C₃₁	—	2	4	no	—
305	C₄⋊C₄×C₃₁	—	2	4	no	—
306	C₄⋊C₄×C₃₁	—	2	2	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	4	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	2	4	no	—
311	C₄⋊C₄×C₃₁	—	2	4	no	—
312	C₄⋊C₄×C₃₁	—	2	4	no	—
313	C₄⋊C₄×C₃₁	—	4	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	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
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	C₂²⋊C₄×C₃₁	—	4	2	no	—
340	C₂²⋊C₄×C₃₁	—	4	2	no	—
341	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
342	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
343	C₄²×C₃₁	—	2	4	no	—
344	C₄²×C₃₁	—	2	2	no	—
345	C₄²×C₃₁	—	2	2	no	—
346	C₄²×C₃₁	—	4	1	no	—
347	C₄²×C₃₁	—	4	1	no	—
348	#36740	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂³×C₃₁	—	2	1	no	—
350	C₂³×C₃₁	—	2	1	no	—
351	C₂³×C₃₁	—	2	1	no	—
352	C₂³×C₃₁	—	2	1	no	—
353	C₂³×C₃₁	—	2	2	no	—
354	C₂³×C₃₁	—	2	2	no	—
355	C₂³×C₃₁	—	2	2	no	—
356	C₂³×C₃₁	—	2	2	no	—
357	C₂³×C₃₁	—	2	2	no	—
358	C₂³×C₃₁	—	2	2	no	—
359	C₂³×C₃₁	—	2	8	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	—	2	2	no	—
367	C₂³×C₃₁	—	4	4	no	—
368	C₂³×C₃₁	—	4	4	no	—
369	C₂³×C₃₁	—	8	2	no	—
370	C₂³×C₃₁	—	8	2	no	—
371	C₂³×C₃₁	—	8	2	no	—
372	C₂³×C₃₁	—	8	2	no	—
373	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
374	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
375	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
376	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
377	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
378	Q₈×C₃₁	—	8	4	no	—
379	Q₈×C₃₁	—	8	2	no	—
380	Q₈×C₃₁	—	8	2	no	—
381	Q₈×C₃₁	—	8	2	no	—
382	D₄×C₃₁	—	4	8	no	—
383	D₄×C₃₁	—	8	2	no	—
384	D₄×C₃₁	—	8	4	no	—
385	D₄×C₃₁	—	8	4	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	2	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	1	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	1	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	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	1	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	1	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	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	—	8	4	no	—
434	C₂×C₄×C₃₁	—	8	4	no	—
435	C₂×C₄×C₃₁	—	8	4	no	—
436	C₂×C₄×C₃₁	—	8	2	no	—
437	C₂×C₄×C₃₁	—	8	2	no	—
438	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
439	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
442	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
443	C₂×#543	C₂×C₃₁	1	1	yes	characteristic, complemented
444	C₂×#538	C₂×C₃₁	1	1	yes	characteristic
445	#2857	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#2850	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#2700	C₂×C₃₁	1	2	yes	complemented
448	#2698	C₂×C₃₁	1	2	yes	complemented
449	#2689	C₂×C₃₁	1	2	yes	complemented
450	#2687	C₂×C₃₁	1	2	yes	complemented
451	#2681	C₂×C₃₁	1	2	yes	complemented
452	#2680	C₂×C₃₁	1	2	yes	complemented
453	#2674	C₂×C₃₁	1	2	yes	complemented
454	#2672	C₂×C₃₁	1	2	yes	complemented
455	#2659	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#2639	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#2564	C₂×C₃₁	1	2	yes	complemented
458	#2417	C₂×C₃₁	1	2	yes	complemented
459	#2412	C₂×C₃₁	1	2	yes	complemented
460	#2412	C₂×C₃₁	1	2	yes	complemented
461	C₂×#388	C₂×C₃₁	1	1	yes	characteristic, complemented
462	C₂²×C₃₁	—	2	2	no	—
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	2	no	—
465	C₂²×C₃₁	—	2	2	no	—
466	C₂²×C₃₁	—	2	2	no	—
467	C₂²×C₃₁	—	2	2	no	—
468	C₂²×C₃₁	—	2	4	no	—
469	C₂²×C₃₁	—	2	4	no	—
470	C₂²×C₃₁	—	2	4	no	—
471	C₂²×C₃₁	—	4	2	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	4	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	—	4	2	no	—
482	C₂²×C₃₁	—	8	8	no	—
483	C₂²×C₃₁	#536	1	4	yes	—
484	C₂²×C₃₁	C₂³×D₄	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	C₂²×C₃₁	#585	1	1	yes	characteristic
490	C₂²×C₃₁	#585	1	1	yes	characteristic
491	C₄×C₃₁	—	2	4	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	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	—	4	2	no	—
503	C₄×C₃₁	—	4	1	no	—
504	C₄×C₃₁	—	4	1	no	—
505	C₄×C₃₁	—	4	2	no	—
506	C₄×C₃₁	—	4	2	no	—
507	#543	—	2	8	no	—
508	#538	—	2	8	no	—
509	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
510	C₂×#126	C₂²×C₃₁	1	2	yes	—
511	C₂×#124	C₂²×C₃₁	1	2	yes	—
512	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	C₂×#123	C₂²×C₃₁	1	2	yes	—
514	C₂×#123	C₂²×C₃₁	1	2	yes	—
515	C₂×#123	C₂²×C₃₁	1	2	yes	—
516	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
517	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
520	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
522	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
523	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
524	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
525	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×#121	C₂²×C₃₁	1	2	yes	—
527	C₂×#120	C₂²×C₃₁	1	2	yes	—
528	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
529	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
530	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
531	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
532	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
533	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
534	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
535	#400	C₂²×C₃₁	1	2	yes	complemented
536	#400	C₂²×C₃₁	1	2	yes	complemented
537	#399	C₂²×C₃₁	1	2	yes	complemented
538	#398	C₂²×C₃₁	1	2	yes	complemented
539	#398	C₂²×C₃₁	1	2	yes	complemented
540	#398	C₂²×C₃₁	1	2	yes	complemented
541	#398	C₂²×C₃₁	1	2	yes	complemented
542	#397	C₂²×C₃₁	1	2	yes	—
543	#397	C₂²×C₃₁	1	2	yes	—
544	#397	C₂²×C₃₁	1	2	yes	—
545	#397	C₂²×C₃₁	1	2	yes	—
546	#397	C₂²×C₃₁	1	2	yes	complemented
547	#396	C₂²×C₃₁	1	2	yes	complemented
548	#396	C₂²×C₃₁	1	2	yes	complemented
549	#395	C₂²×C₃₁	1	2	yes	complemented
550	#395	C₂²×C₃₁	1	2	yes	complemented
551	#395	C₂²×C₃₁	1	2	yes	complemented
552	#394	C₂²×C₃₁	1	2	yes	—
553	#394	C₂²×C₃₁	1	2	yes	—
554	#394	C₂²×C₃₁	1	2	yes	—
555	#394	C₂²×C₃₁	1	2	yes	—
556	#394	C₂²×C₃₁	1	2	yes	complemented
557	#393	C₂²×C₃₁	1	2	yes	complemented
558	#393	C₂²×C₃₁	1	2	yes	complemented
559	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	#391	C₂²×C₃₁	1	2	yes	complemented
563	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
564	#389	C₂²×C₃₁	1	2	yes	complemented
565	#389	C₂²×C₃₁	1	2	yes	complemented
566	#389	C₂²×C₃₁	1	2	yes	complemented
567	#388	C₂²×C₃₁	1	2	yes	—
568	#388	C₂²×C₃₁	1	2	yes	—
569	#388	C₂²×C₃₁	1	2	yes	—
570	#388	C₂²×C₃₁	1	2	yes	—
571	#388	C₂²×C₃₁	1	2	yes	complemented
572	#388	C₂²×C₃₁	1	2	yes	complemented
573	#387	C₂²×C₃₁	1	2	yes	complemented
574	#387	C₂²×C₃₁	1	2	yes	complemented
575	#386	C₂²×C₃₁	1	2	yes	—
576	#386	C₂²×C₃₁	1	2	yes	—
577	#386	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	#385	C₂²×C₃₁	1	2	yes	—
582	#385	C₂²×C₃₁	1	2	yes	—
583	#385	C₂²×C₃₁	1	2	yes	complemented
584	#385	C₂²×C₃₁	1	2	yes	complemented
585	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#381	C₂²×C₃₁	1	2	yes	—
588	#381	C₂²×C₃₁	1	2	yes	—
589	#380	C₂²×C₃₁	1	2	yes	—
590	#380	C₂²×C₃₁	1	2	yes	—
591	#380	C₂²×C₃₁	1	2	yes	—
592	#380	C₂²×C₃₁	1	2	yes	—
593	#380	C₂²×C₃₁	1	2	yes	complemented
594	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
595	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
596	C₂×C₃₁	—	2	4	no	—
597	C₂×C₃₁	—	4	4	no	—
598	C₂×C₃₁	—	8	2	no	—
599	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
600	C₂×C₃₁	#3496	1	1	yes	characteristic
601	C₂×C₃₁	#3496	1	1	yes	characteristic
602	C₂×C₃₁	#3535	1	1	yes	characteristic
603	C₂×C₃₁	#3536	1	1	yes	characteristic
604	C₂×C₃₁	#3561	1	1	yes	characteristic
605	C₂×C₃₁	#3564	1	1	yes	characteristic
606	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
607	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
608	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
610	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
612	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
613	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
614	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
619	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
620	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
622	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₄⋊Q₈	—	4	2	no	—
625	#126	—	2	8	no	—
626	#124	—	2	8	no	—
627	#124	—	4	2	no	—
628	#123	—	2	8	no	—
629	#123	—	4	4	no	—
630	#123	—	4	4	no	—
631	C₂²⋊Q₈	—	2	4	no	—
632	C₂²⋊Q₈	—	2	8	no	—
633	C₂²⋊Q₈	—	2	4	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	C₂²⋊Q₈	—	2	8	no	—
636	C₂²⋊Q₈	—	2	8	no	—
637	C₂²⋊Q₈	—	2	8	no	—
638	C₂²⋊Q₈	—	2	8	no	—
639	C₂²⋊Q₈	—	4	4	no	—
640	#121	—	2	4	no	—
641	#121	—	2	8	no	—
642	#120	—	2	8	no	—
643	C₄×D₄	—	2	8	no	—
644	C₂×C₄⋊C₄	—	4	2	no	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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×C₂²⋊C₄	—	2	8	no	—
667	C₂×C₂²⋊C₄	—	4	2	no	—
668	C₂×C₂²⋊C₄	—	4	2	no	—
669	C₂×C₂²⋊C₄	D₄×C₃₁	1	8	yes	—
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×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
693	C₂×C₄²	—	4	2	no	—
694	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
695	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
699	#95	C₂³×C₃₁	1	2	yes	—
700	#95	C₂³×C₃₁	1	2	yes	—
701	#95	C₂³×C₃₁	1	2	yes	—
702	#95	C₂³×C₃₁	1	2	yes	—
703	#95	C₂³×C₃₁	1	2	yes	—
704	#95	C₂³×C₃₁	1	2	yes	—
705	#95	C₂³×C₃₁	1	2	yes	—
706	#95	C₂³×C₃₁	1	2	yes	—
707	#95	C₂³×C₃₁	1	2	yes	—
708	#95	C₂³×C₃₁	1	2	yes	—
709	#95	C₂³×C₃₁	1	2	yes	—
710	#95	C₂³×C₃₁	1	2	yes	—
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	C₃₁	#36740	1	1	yes	characteristic, direct product factor, Sylow
720	C₂⁴	—	2	2	no	—
721	C₂⁴	—	2	2	no	—
722	C₂⁴	—	4	1	no	—
723	C₂⁴	—	4	1	no	—
724	C₂⁴	—	4	1	no	—
725	C₂⁴	—	4	1	no	—
726	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
727	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
728	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
729	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
730	C₂×Q₈	—	2	4	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×Q₈	—	4	1	no	—
736	C₂×Q₈	—	4	1	no	—
737	C₂×Q₈	—	4	1	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	—	4	1	no	—
740	C₂×Q₈	—	4	1	no	—
741	C₂×Q₈	—	4	1	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	1	no	—
751	C₂×D₄	—	4	1	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	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	4	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	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	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
780	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
781	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	2	4	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	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
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	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	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	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
840	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
841	C₄²	—	2	4	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	4	1	no	—
845	C₄²	—	4	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	8	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	8	2	no	—
867	C₂³	—	8	2	no	—
868	C₂³	—	8	2	no	—
869	C₂³	—	8	2	no	—
870	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
871	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
872	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
873	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
874	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
875	Q₈	—	8	4	no	—
876	Q₈	—	8	2	no	—
877	Q₈	—	8	2	no	—
878	Q₈	—	8	2	no	—
879	D₄	—	4	8	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	4	no	—
882	D₄	—	8	4	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	8	4	no	—
931	C₂×C₄	—	8	4	no	—
932	C₂×C₄	—	8	4	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	—	8	2	no	—
935	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
936	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
938	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
939	C₂×C₄	C₃₁×H(5,𝔽₂)	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	—	2	4	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	8	8	no	—
961	C₂²	C₃₁×#536	1	4	yes	—
962	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
963	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
964	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
965	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
966	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
967	C₂²	C₃₁×#585	1	1	yes	characteristic
968	C₂²	C₃₁×#585	1	1	yes	characteristic
969	C₄	—	2	4	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₂	—	2	4	no	—
986	C₂	—	4	4	no	—
987	C₂	—	8	2	no	—
988	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
989	C₂	C₃₁×#3496	1	1	yes	characteristic
990	C₂	C₃₁×#3496	1	1	yes	characteristic
991	C₂	C₃₁×#3535	1	1	yes	characteristic
992	C₂	C₃₁×#3536	1	1	yes	characteristic
993	C₂	C₃₁×#3561	1	1	yes	characteristic
994	C₂	C₃₁×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#538	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. C₂×C₃₁×#543	C₂	semidirect
3. C₃₁×#2857	C₂	semidirect
4. C₃₁×#2850	C₂	semidirect
5. C₃₁×#2700	C₂	semidirect
6. C₃₁×#2698	C₂	semidirect
7. C₃₁×#2689	C₂	semidirect
8. C₃₁×#2687	C₂	semidirect
9. C₃₁×#2681	C₂	semidirect
10. C₃₁×#2680	C₂	semidirect
11. C₃₁×#2674	C₂	semidirect
12. C₃₁×#2672	C₂	semidirect
13. C₃₁×#2659	C₂	semidirect
14. C₃₁×#2639	C₂	semidirect
15. C₃₁×#2564	C₂	semidirect
16. C₃₁×#2417	C₂	semidirect
17. C₃₁×#2412	C₂	semidirect
18. C₃₁×#2412	C₂	semidirect
19. C₂×C₃₁×#388	C₂	semidirect
22. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₃₁×#124	C₂²	semidirect
37. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
48. C₃₁×#400	C₂²	semidirect
49. C₃₁×#400	C₂²	semidirect
50. C₃₁×#399	C₂²	semidirect
51. C₃₁×#398	C₂²	semidirect
52. C₃₁×#398	C₂²	semidirect
53. C₃₁×#398	C₂²	semidirect
54. C₃₁×#398	C₂²	semidirect
59. C₃₁×#397	C₂²	semidirect
60. C₃₁×#396	C₂²	semidirect
61. C₃₁×#396	C₂²	semidirect
62. C₃₁×#395	C₂²	semidirect
63. C₃₁×#395	C₂²	semidirect
64. C₃₁×#395	C₂²	semidirect
69. C₃₁×#394	C₂²	semidirect
70. C₃₁×#393	C₂²	semidirect
71. C₃₁×#393	C₂²	semidirect
72. C₃₁×#391	C₂²	semidirect
73. C₃₁×#391	C₂²	semidirect
74. C₃₁×#391	C₂²	semidirect
75. C₃₁×#391	C₂²	semidirect
76. C₃₁×#390	C₂²	semidirect
77. C₃₁×#389	C₂²	semidirect
78. C₃₁×#389	C₂²	semidirect
79. C₃₁×#389	C₂²	semidirect
84. C₃₁×#388	C₂²	semidirect
85. C₃₁×#388	C₂²	semidirect
86. C₃₁×#387	C₂²	semidirect
87. C₃₁×#387	C₂²	semidirect
96. C₃₁×#385	C₂²	semidirect
97. C₃₁×#385	C₂²	semidirect
98. C₃₁×#384	C₂²	semidirect
99. C₃₁×#382	C₂²	semidirect
106. C₃₁×#380	C₂²	semidirect
348. #36740	C₃₁	direct (N × H)
443. C₂×#543	C₂×C₃₁	semidirect
445. #2857	C₂×C₃₁	semidirect
446. #2850	C₂×C₃₁	semidirect
447. #2700	C₂×C₃₁	semidirect
448. #2698	C₂×C₃₁	semidirect
449. #2689	C₂×C₃₁	semidirect
450. #2687	C₂×C₃₁	semidirect
451. #2681	C₂×C₃₁	semidirect
452. #2680	C₂×C₃₁	semidirect
453. #2674	C₂×C₃₁	semidirect
454. #2672	C₂×C₃₁	semidirect
455. #2659	C₂×C₃₁	semidirect
456. #2639	C₂×C₃₁	semidirect
457. #2564	C₂×C₃₁	semidirect
458. #2417	C₂×C₃₁	semidirect
459. #2412	C₂×C₃₁	semidirect
460. #2412	C₂×C₃₁	semidirect
461. C₂×#388	C₂×C₃₁	semidirect
509. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
512. C₂×#124	C₂²×C₃₁	semidirect
524. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
535. #400	C₂²×C₃₁	semidirect
536. #400	C₂²×C₃₁	semidirect
537. #399	C₂²×C₃₁	semidirect
538. #398	C₂²×C₃₁	semidirect
539. #398	C₂²×C₃₁	semidirect
540. #398	C₂²×C₃₁	semidirect
541. #398	C₂²×C₃₁	semidirect
546. #397	C₂²×C₃₁	semidirect
547. #396	C₂²×C₃₁	semidirect
548. #396	C₂²×C₃₁	semidirect
549. #395	C₂²×C₃₁	semidirect
550. #395	C₂²×C₃₁	semidirect
551. #395	C₂²×C₃₁	semidirect
556. #394	C₂²×C₃₁	semidirect
557. #393	C₂²×C₃₁	semidirect
558. #393	C₂²×C₃₁	semidirect
559. #391	C₂²×C₃₁	semidirect
560. #391	C₂²×C₃₁	semidirect
561. #391	C₂²×C₃₁	semidirect
562. #391	C₂²×C₃₁	semidirect
563. #390	C₂²×C₃₁	semidirect
564. #389	C₂²×C₃₁	semidirect
565. #389	C₂²×C₃₁	semidirect
566. #389	C₂²×C₃₁	semidirect
571. #388	C₂²×C₃₁	semidirect
572. #388	C₂²×C₃₁	semidirect
573. #387	C₂²×C₃₁	semidirect
574. #387	C₂²×C₃₁	semidirect
583. #385	C₂²×C₃₁	semidirect
584. #385	C₂²×C₃₁	semidirect
585. #384	C₂²×C₃₁	semidirect
586. #382	C₂²×C₃₁	semidirect
593. #380	C₂²×C₃₁	semidirect
719. C₃₁	#36740	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#543	2
C₂×C₃₁×#538	2
C₃₁×#2857	2
C₃₁×#2850	2
C₃₁×#2700	2
C₃₁×#2698	2
C₃₁×#2689	2
C₃₁×#2687	2
C₃₁×#2681	2
C₃₁×#2680	2
C₃₁×#2674	2
C₃₁×#2672	2
C₃₁×#2659	2
C₃₁×#2639	2
C₃₁×#2564	2
C₃₁×#2417	2
C₃₁×#2412	2
C₂×C₃₁×#388	2
#36740	31

Subgroups — C31×#36740 #21493499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36740 #21493499