Subgroups — C₃₁×#36748 #21493507

Order 7936.

1858 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2848	C₂	1	2	yes	maximal
2	C₃₁×#2807	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2790	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2788	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2768	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2763	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2729	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2720	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2704	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2677	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#2569	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2549	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2442	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2440	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2312	C₂	1	2	yes	maximal
19	C₂×C₃₁×#385	C₂	1	1	yes	maximal, characteristic
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#400	C₂²	1	2	yes	complemented
32	C₃₁×#400	C₂²	1	2	yes	complemented
33	C₃₁×#400	C₂²	1	2	yes	complemented
34	C₃₁×#400	C₂²	1	2	yes	complemented
35	C₃₁×#399	C₂²	1	1	yes	characteristic
36	C₃₁×#399	C₂²	1	1	yes	characteristic
37	C₃₁×#399	C₂²	1	1	yes	characteristic
38	C₃₁×#399	C₂²	1	1	yes	characteristic
39	C₃₁×#398	C₂²	1	2	yes	complemented
40	C₃₁×#398	C₂²	1	2	yes	complemented
41	C₃₁×#398	C₂²	1	2	yes	complemented
42	C₃₁×#398	C₂²	1	2	yes	complemented
43	C₃₁×#398	C₂²	1	2	yes	complemented
44	C₃₁×#398	C₂²	1	2	yes	complemented
45	C₃₁×#398	C₂²	1	2	yes	complemented
46	C₃₁×#398	C₂²	1	2	yes	complemented
47	C₃₁×#396	C₂²	1	2	yes	—
48	C₃₁×#396	C₂²	1	2	yes	—
49	C₃₁×#396	C₂²	1	2	yes	—
50	C₃₁×#396	C₂²	1	2	yes	—
51	C₃₁×#395	C₂²	1	2	yes	complemented
52	C₃₁×#395	C₂²	1	2	yes	complemented
53	C₃₁×#395	C₂²	1	2	yes	complemented
54	C₃₁×#395	C₂²	1	2	yes	complemented
55	C₃₁×#393	C₂²	1	1	yes	characteristic
56	C₃₁×#393	C₂²	1	1	yes	characteristic
57	C₃₁×#393	C₂²	1	1	yes	characteristic
58	C₃₁×#393	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	2	yes	complemented
60	C₃₁×#391	C₂²	1	2	yes	complemented
61	C₃₁×#389	C₂²	1	2	yes	complemented
62	C₃₁×#389	C₂²	1	2	yes	complemented
63	C₃₁×#389	C₂²	1	2	yes	complemented
64	C₃₁×#389	C₂²	1	2	yes	complemented
65	C₃₁×#389	C₂²	1	2	yes	complemented
66	C₃₁×#389	C₂²	1	2	yes	complemented
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#388	C₂²	1	2	yes	—
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#388	C₂²	1	2	yes	—
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	complemented
76	C₃₁×#387	C₂²	1	2	yes	complemented
77	C₃₁×#387	C₂²	1	2	yes	complemented
78	C₃₁×#387	C₂²	1	2	yes	complemented
79	C₃₁×#385	C₂²	1	2	yes	—
80	C₃₁×#385	C₂²	1	2	yes	—
81	C₃₁×#385	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#385	C₂²	1	2	yes	—
84	C₃₁×#385	C₂²	1	2	yes	—
85	C₃₁×#385	C₂²	1	2	yes	—
86	C₃₁×#385	C₂²	1	2	yes	—
87	C₃₁×#385	C₂²	1	1	yes	characteristic
88	C₃₁×#385	C₂²	1	1	yes	characteristic
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#385	C₂²	1	2	yes	—
91	C₃₁×#385	C₂²	1	1	yes	characteristic
92	C₃₁×#385	C₂²	1	1	yes	characteristic
93	C₃₁×#384	C₂²	1	2	yes	complemented
94	C₃₁×#382	C₂²	1	2	yes	complemented
95	C₃₁×#380	C₂²	1	2	yes	—
96	C₃₁×#380	C₂²	1	2	yes	—
97	C₃₁×#380	C₂²	1	1	yes	characteristic
98	C₃₁×#380	C₂²	1	2	yes	—
99	C₃₁×#380	C₂²	1	2	yes	—
100	C₃₁×#380	C₂²	1	2	yes	—
101	C₃₁×#380	C₂²	1	1	yes	characteristic
102	C₃₁×#379	C₂²	1	2	yes	—
103	C₃₁×#379	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
106	C₂×C₃₁×#95	C₂²	1	2	yes	—
107	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
109	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₃₁	—	4	4	no	—
112	C₂³×C₄×C₃₁	—	4	2	no	—
113	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
120	C₃₁×C₄⋊Q₈	—	4	4	no	—
121	C₃₁×#125	—	4	4	no	—
122	C₃₁×C₂²⋊Q₈	—	4	4	no	—
123	C₃₁×C₂²⋊Q₈	—	4	2	no	—
124	C₃₁×C₂²⋊Q₈	—	4	2	no	—
125	C₃₁×C₂²⋊Q₈	—	4	4	no	—
126	C₃₁×C₂²⋊Q₈	—	4	4	no	—
127	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	—	4	2	no	—
156	C₂×C₂²⋊C₄×C₃₁	Q₈	1	8	yes	complemented
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
180	C₃₁×#95	C₂³	1	2	yes	—
181	C₃₁×#95	C₂³	1	2	yes	—
182	C₃₁×#95	C₂³	1	2	yes	—
183	C₃₁×#95	C₂³	1	2	yes	—
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	2	yes	—
187	C₃₁×#95	C₂³	1	2	yes	—
188	C₃₁×#95	C₂³	1	2	yes	—
189	C₃₁×#95	C₂³	1	2	yes	—
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	2	yes	—
192	C₃₁×#95	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	1	yes	characteristic
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₃₁×#95	C₂³	1	1	yes	characteristic
202	C₃₁×#95	C₂³	1	1	yes	characteristic
203	C₃₁×#95	C₂³	1	1	yes	characteristic
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	2	yes	—
206	C₂⁴×C₃₁	—	2	2	no	—
207	C₂⁴×C₃₁	—	2	2	no	—
208	C₂⁴×C₃₁	—	4	2	no	—
209	C₂⁴×C₃₁	—	4	2	no	—
210	C₂⁴×C₃₁	C₂×Q₈	1	4	yes	—
211	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
214	C₂×Q₈×C₃₁	—	2	4	no	—
215	C₂×Q₈×C₃₁	—	4	2	no	—
216	C₂×Q₈×C₃₁	—	4	2	no	—
217	C₂×Q₈×C₃₁	—	4	1	no	—
218	C₂×Q₈×C₃₁	—	4	1	no	—
219	C₂×Q₈×C₃₁	—	4	2	no	—
220	C₂×Q₈×C₃₁	—	4	2	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	—	4	2	no	—
228	C₂²×C₄×C₃₁	—	4	1	no	—
229	C₂²×C₄×C₃₁	—	4	2	no	—
230	C₂²×C₄×C₃₁	—	4	2	no	—
231	C₂²×C₄×C₃₁	—	4	2	no	—
232	C₂²×C₄×C₃₁	—	4	2	no	—
233	C₂²×C₄×C₃₁	—	4	1	no	—
234	C₂²×C₄×C₃₁	—	4	2	no	—
235	C₂²×C₄×C₃₁	—	4	2	no	—
236	C₂²×C₄×C₃₁	—	4	2	no	—
237	C₂²×C₄×C₃₁	—	4	16	no	—
238	C₂²×C₄×C₃₁	C₂×Q₈	1	8	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	4	no	—
260	C₄⋊C₄×C₃₁	—	4	2	no	—
261	C₄⋊C₄×C₃₁	—	4	2	no	—
262	C₄⋊C₄×C₃₁	—	4	2	no	—
263	C₄⋊C₄×C₃₁	—	4	2	no	—
264	C₄⋊C₄×C₃₁	—	4	2	no	—
265	C₄⋊C₄×C₃₁	—	4	2	no	—
266	C₄⋊C₄×C₃₁	—	4	2	no	—
267	C₄⋊C₄×C₃₁	—	4	2	no	—
268	C₄⋊C₄×C₃₁	—	4	2	no	—
269	C₄⋊C₄×C₃₁	—	4	2	no	—
270	C₄⋊C₄×C₃₁	—	4	2	no	—
271	C₄⋊C₄×C₃₁	—	4	1	no	—
272	C₄⋊C₄×C₃₁	—	4	2	no	—
273	C₄⋊C₄×C₃₁	—	4	2	no	—
274	C₄⋊C₄×C₃₁	—	4	2	no	—
275	C₄⋊C₄×C₃₁	—	4	1	no	—
276	C₄⋊C₄×C₃₁	—	4	2	no	—
277	C₄⋊C₄×C₃₁	—	4	2	no	—
278	C₄⋊C₄×C₃₁	—	4	2	no	—
279	C₄⋊C₄×C₃₁	—	4	2	no	—
280	C₄⋊C₄×C₃₁	—	4	2	no	—
281	C₄⋊C₄×C₃₁	—	4	2	no	—
282	C₂²⋊C₄×C₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	4	1	no	—
287	C₂²⋊C₄×C₃₁	—	4	1	no	—
288	C₂²⋊C₄×C₃₁	—	4	1	no	—
289	C₂²⋊C₄×C₃₁	—	4	1	no	—
290	C₂²⋊C₄×C₃₁	—	4	2	no	—
291	C₂²⋊C₄×C₃₁	—	4	2	no	—
292	C₂²⋊C₄×C₃₁	—	4	2	no	—
293	C₂²⋊C₄×C₃₁	—	4	2	no	—
294	C₂²⋊C₄×C₃₁	—	4	2	no	—
295	C₂²⋊C₄×C₃₁	—	4	2	no	—
296	C₂²⋊C₄×C₃₁	—	4	2	no	—
297	C₂²⋊C₄×C₃₁	—	4	2	no	—
298	C₂²⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
299	C₂²⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
300	C₂²⋊C₄×C₃₁	C₂×Q₈	1	8	yes	—
301	C₄²×C₃₁	—	4	2	no	—
302	C₄²×C₃₁	—	4	2	no	—
303	C₄²×C₃₁	—	4	2	no	—
304	C₄²×C₃₁	—	4	2	no	—
305	#36748	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂³×C₃₁	—	2	2	no	—
307	C₂³×C₃₁	—	2	2	no	—
308	C₂³×C₃₁	—	2	8	no	—
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	—	2	2	no	—
311	C₂³×C₃₁	—	2	1	no	—
312	C₂³×C₃₁	—	2	1	no	—
313	C₂³×C₃₁	—	2	1	no	—
314	C₂³×C₃₁	—	2	1	no	—
315	C₂³×C₃₁	—	2	2	no	—
316	C₂³×C₃₁	—	2	2	no	—
317	C₂³×C₃₁	—	4	8	no	—
318	C₂³×C₃₁	—	4	4	no	—
319	C₂³×C₃₁	—	4	4	no	—
320	C₂³×C₃₁	—	4	8	no	—
321	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
322	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
323	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
324	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
325	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
326	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
327	Q₈×C₃₁	—	8	4	no	—
328	Q₈×C₃₁	—	8	2	no	—
329	Q₈×C₃₁	—	8	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	1	no	—
345	C₂×C₄×C₃₁	—	2	1	no	—
346	C₂×C₄×C₃₁	—	2	1	no	—
347	C₂×C₄×C₃₁	—	2	1	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	4	8	no	—
372	C₂×C₄×C₃₁	—	4	4	no	—
373	C₂×C₄×C₃₁	—	4	8	no	—
374	C₂×C₄×C₃₁	—	4	8	no	—
375	C₂×C₄×C₃₁	—	4	4	no	—
376	C₂×C₄×C₃₁	—	8	2	no	—
377	C₂×C₄×C₃₁	—	8	2	no	—
378	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
379	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
380	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
381	#2848	C₂×C₃₁	1	2	yes	—
382	#2807	C₂×C₃₁	1	1	yes	characteristic, complemented
383	#2790	C₂×C₃₁	1	2	yes	complemented
384	#2788	C₂×C₃₁	1	2	yes	complemented
385	#2768	C₂×C₃₁	1	2	yes	complemented
386	#2763	C₂×C₃₁	1	1	yes	characteristic, complemented
387	#2742	C₂×C₃₁	1	1	yes	characteristic, complemented
388	#2729	C₂×C₃₁	1	2	yes	complemented
389	#2720	C₂×C₃₁	1	2	yes	complemented
390	#2704	C₂×C₃₁	1	2	yes	complemented
391	#2677	C₂×C₃₁	1	1	yes	characteristic, complemented
392	#2626	C₂×C₃₁	1	1	yes	characteristic
393	#2626	C₂×C₃₁	1	1	yes	characteristic
394	#2569	C₂×C₃₁	1	2	yes	complemented
395	#2549	C₂×C₃₁	1	2	yes	complemented
396	#2442	C₂×C₃₁	1	2	yes	complemented
397	#2440	C₂×C₃₁	1	2	yes	complemented
398	#2312	C₂×C₃₁	1	2	yes	—
399	C₂×#385	C₂×C₃₁	1	1	yes	characteristic
400	C₂²×C₃₁	—	2	4	no	—
401	C₂²×C₃₁	—	2	2	no	—
402	C₂²×C₃₁	—	2	2	no	—
403	C₂²×C₃₁	—	2	4	no	—
404	C₂²×C₃₁	—	2	2	no	—
405	C₂²×C₃₁	—	2	2	no	—
406	C₂²×C₃₁	—	2	4	no	—
407	C₂²×C₃₁	—	2	4	no	—
408	C₂²×C₃₁	—	4	16	no	—
409	C₂²×C₃₁	—	4	1	no	—
410	C₂²×C₃₁	—	4	1	no	—
411	C₂²×C₃₁	—	4	1	no	—
412	C₂²×C₃₁	—	4	1	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	4	2	no	—
415	C₂²×C₃₁	#544	1	4	yes	—
416	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
417	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
419	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
420	C₂²×C₃₁	#585	1	2	yes	—
421	C₄×C₃₁	—	2	4	no	—
422	C₄×C₃₁	—	2	4	no	—
423	C₄×C₃₁	—	2	4	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	—	4	1	no	—
426	C₄×C₃₁	—	4	1	no	—
427	C₄×C₃₁	—	4	2	no	—
428	C₄×C₃₁	—	4	2	no	—
429	C₄×C₃₁	—	4	2	no	—
430	C₄×C₃₁	—	4	1	no	—
431	C₄×C₃₁	—	4	1	no	—
432	C₄×C₃₁	—	4	2	no	—
433	C₄×C₃₁	—	4	2	no	—
434	C₄×C₃₁	—	4	2	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	2	no	—
437	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
439	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
440	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
442	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
443	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
444	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
445	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
447	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
448	#400	C₂²×C₃₁	1	2	yes	complemented
449	#400	C₂²×C₃₁	1	2	yes	complemented
450	#400	C₂²×C₃₁	1	2	yes	complemented
451	#400	C₂²×C₃₁	1	2	yes	complemented
452	#399	C₂²×C₃₁	1	1	yes	characteristic
453	#399	C₂²×C₃₁	1	1	yes	characteristic
454	#399	C₂²×C₃₁	1	1	yes	characteristic
455	#399	C₂²×C₃₁	1	1	yes	characteristic
456	#398	C₂²×C₃₁	1	2	yes	complemented
457	#398	C₂²×C₃₁	1	2	yes	complemented
458	#398	C₂²×C₃₁	1	2	yes	complemented
459	#398	C₂²×C₃₁	1	2	yes	complemented
460	#398	C₂²×C₃₁	1	2	yes	complemented
461	#398	C₂²×C₃₁	1	2	yes	complemented
462	#398	C₂²×C₃₁	1	2	yes	complemented
463	#398	C₂²×C₃₁	1	2	yes	complemented
464	#396	C₂²×C₃₁	1	2	yes	—
465	#396	C₂²×C₃₁	1	2	yes	—
466	#396	C₂²×C₃₁	1	2	yes	—
467	#396	C₂²×C₃₁	1	2	yes	—
468	#395	C₂²×C₃₁	1	2	yes	complemented
469	#395	C₂²×C₃₁	1	2	yes	complemented
470	#395	C₂²×C₃₁	1	2	yes	complemented
471	#395	C₂²×C₃₁	1	2	yes	complemented
472	#393	C₂²×C₃₁	1	1	yes	characteristic
473	#393	C₂²×C₃₁	1	1	yes	characteristic
474	#393	C₂²×C₃₁	1	1	yes	characteristic
475	#393	C₂²×C₃₁	1	1	yes	characteristic
476	#391	C₂²×C₃₁	1	2	yes	complemented
477	#391	C₂²×C₃₁	1	2	yes	complemented
478	#389	C₂²×C₃₁	1	2	yes	complemented
479	#389	C₂²×C₃₁	1	2	yes	complemented
480	#389	C₂²×C₃₁	1	2	yes	complemented
481	#389	C₂²×C₃₁	1	2	yes	complemented
482	#389	C₂²×C₃₁	1	2	yes	complemented
483	#389	C₂²×C₃₁	1	2	yes	complemented
484	#388	C₂²×C₃₁	1	2	yes	—
485	#388	C₂²×C₃₁	1	2	yes	—
486	#388	C₂²×C₃₁	1	2	yes	—
487	#388	C₂²×C₃₁	1	2	yes	—
488	#388	C₂²×C₃₁	1	2	yes	—
489	#388	C₂²×C₃₁	1	2	yes	—
490	#388	C₂²×C₃₁	1	2	yes	—
491	#388	C₂²×C₃₁	1	2	yes	—
492	#387	C₂²×C₃₁	1	2	yes	complemented
493	#387	C₂²×C₃₁	1	2	yes	complemented
494	#387	C₂²×C₃₁	1	2	yes	complemented
495	#387	C₂²×C₃₁	1	2	yes	complemented
496	#385	C₂²×C₃₁	1	2	yes	—
497	#385	C₂²×C₃₁	1	2	yes	—
498	#385	C₂²×C₃₁	1	2	yes	—
499	#385	C₂²×C₃₁	1	2	yes	—
500	#385	C₂²×C₃₁	1	2	yes	—
501	#385	C₂²×C₃₁	1	2	yes	—
502	#385	C₂²×C₃₁	1	2	yes	—
503	#385	C₂²×C₃₁	1	2	yes	—
504	#385	C₂²×C₃₁	1	1	yes	characteristic
505	#385	C₂²×C₃₁	1	1	yes	characteristic
506	#385	C₂²×C₃₁	1	2	yes	—
507	#385	C₂²×C₃₁	1	2	yes	—
508	#385	C₂²×C₃₁	1	1	yes	characteristic
509	#385	C₂²×C₃₁	1	1	yes	characteristic
510	#384	C₂²×C₃₁	1	2	yes	complemented
511	#382	C₂²×C₃₁	1	2	yes	complemented
512	#380	C₂²×C₃₁	1	2	yes	—
513	#380	C₂²×C₃₁	1	2	yes	—
514	#380	C₂²×C₃₁	1	1	yes	characteristic
515	#380	C₂²×C₃₁	1	2	yes	—
516	#380	C₂²×C₃₁	1	2	yes	—
517	#380	C₂²×C₃₁	1	2	yes	—
518	#380	C₂²×C₃₁	1	1	yes	characteristic
519	#379	C₂²×C₃₁	1	2	yes	—
520	#379	C₂²×C₃₁	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
523	C₂×#95	C₂²×C₃₁	1	2	yes	—
524	C₂×C₃₁	—	2	4	no	—
525	C₂×C₃₁	—	4	2	no	—
526	C₂×C₃₁	—	4	2	no	—
527	C₂×C₃₁	C₂×#544	1	1	yes	characteristic
528	C₂×C₃₁	#3501	1	2	yes	—
529	C₂×C₃₁	#3532	1	1	yes	characteristic
530	C₂×C₃₁	#3533	1	1	yes	characteristic
531	C₂×C₃₁	#3541	1	2	yes	—
532	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
534	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
535	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
536	C₂³×C₄	—	4	4	no	—
537	C₂³×C₄	—	4	2	no	—
538	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
539	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
543	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
545	C₄⋊Q₈	—	4	4	no	—
546	#125	—	4	4	no	—
547	C₂²⋊Q₈	—	4	4	no	—
548	C₂²⋊Q₈	—	4	2	no	—
549	C₂²⋊Q₈	—	4	2	no	—
550	C₂²⋊Q₈	—	4	4	no	—
551	C₂²⋊Q₈	—	4	4	no	—
552	C₂×C₄⋊C₄	—	4	4	no	—
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂×C₂²⋊C₄	—	4	2	no	—
581	C₂×C₂²⋊C₄	Q₈×C₃₁	1	8	yes	complemented
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	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
602	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
603	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
605	#95	C₂³×C₃₁	1	2	yes	—
606	#95	C₂³×C₃₁	1	2	yes	—
607	#95	C₂³×C₃₁	1	2	yes	—
608	#95	C₂³×C₃₁	1	2	yes	—
609	#95	C₂³×C₃₁	1	2	yes	—
610	#95	C₂³×C₃₁	1	2	yes	—
611	#95	C₂³×C₃₁	1	2	yes	—
612	#95	C₂³×C₃₁	1	2	yes	—
613	#95	C₂³×C₃₁	1	1	yes	characteristic
614	#95	C₂³×C₃₁	1	2	yes	—
615	#95	C₂³×C₃₁	1	2	yes	—
616	#95	C₂³×C₃₁	1	2	yes	—
617	#95	C₂³×C₃₁	1	2	yes	—
618	#95	C₂³×C₃₁	1	2	yes	—
619	#95	C₂³×C₃₁	1	2	yes	—
620	#95	C₂³×C₃₁	1	2	yes	—
621	#95	C₂³×C₃₁	1	2	yes	—
622	#95	C₂³×C₃₁	1	1	yes	characteristic
623	#95	C₂³×C₃₁	1	1	yes	characteristic
624	#95	C₂³×C₃₁	1	2	yes	—
625	#95	C₂³×C₃₁	1	2	yes	—
626	#95	C₂³×C₃₁	1	1	yes	characteristic
627	#95	C₂³×C₃₁	1	2	yes	—
628	#95	C₂³×C₃₁	1	2	yes	—
629	#95	C₂³×C₃₁	1	2	yes	—
630	#95	C₂³×C₃₁	1	2	yes	—
631	C₃₁	#36748	1	1	yes	characteristic, direct product factor, Sylow
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	C₂×Q₈×C₃₁	1	4	yes	—
637	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
638	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
639	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	4	2	no	—
642	C₂×Q₈	—	4	2	no	—
643	C₂×Q₈	—	4	1	no	—
644	C₂×Q₈	—	4	1	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂×Q₈	—	4	2	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	16	no	—
664	C₂²×C₄	C₂×Q₈×C₃₁	1	8	yes	—
665	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	1	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	4	1	no	—
713	C₂²⋊C₄	—	4	1	no	—
714	C₂²⋊C₄	—	4	1	no	—
715	C₂²⋊C₄	—	4	1	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
725	C₂²⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
726	C₂²⋊C₄	C₂×Q₈×C₃₁	1	8	yes	—
727	C₄²	—	4	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	8	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	8	no	—
746	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
747	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
748	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
749	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
750	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
751	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
752	Q₈	—	8	4	no	—
753	Q₈	—	8	2	no	—
754	Q₈	—	8	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	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	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
804	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
805	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
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	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	16	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	C₃₁×#544	1	4	yes	—
822	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
823	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
825	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
826	C₂²	C₃₁×#585	1	2	yes	—
827	C₄	—	2	4	no	—
828	C₄	—	2	4	no	—
829	C₄	—	2	4	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₂	—	2	4	no	—
844	C₂	—	4	2	no	—
845	C₂	—	4	2	no	—
846	C₂	C₂×C₃₁×#544	1	1	yes	characteristic
847	C₂	C₃₁×#3501	1	2	yes	—
848	C₂	C₃₁×#3532	1	1	yes	characteristic
849	C₂	C₃₁×#3533	1	1	yes	characteristic
850	C₂	C₃₁×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2807	C₂	semidirect
3. C₃₁×#2790	C₂	semidirect
4. C₃₁×#2788	C₂	semidirect
5. C₃₁×#2768	C₂	semidirect
6. C₃₁×#2763	C₂	semidirect
7. C₃₁×#2742	C₂	semidirect
8. C₃₁×#2729	C₂	semidirect
9. C₃₁×#2720	C₂	semidirect
10. C₃₁×#2704	C₂	semidirect
11. C₃₁×#2677	C₂	semidirect
14. C₃₁×#2569	C₂	semidirect
15. C₃₁×#2549	C₂	semidirect
16. C₃₁×#2442	C₂	semidirect
17. C₃₁×#2440	C₂	semidirect
21. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₃₁×#125	C₂²	semidirect
31. C₃₁×#400	C₂²	semidirect
32. C₃₁×#400	C₂²	semidirect
33. C₃₁×#400	C₂²	semidirect
34. C₃₁×#400	C₂²	semidirect
39. C₃₁×#398	C₂²	semidirect
40. C₃₁×#398	C₂²	semidirect
41. C₃₁×#398	C₂²	semidirect
42. C₃₁×#398	C₂²	semidirect
43. C₃₁×#398	C₂²	semidirect
44. C₃₁×#398	C₂²	semidirect
45. C₃₁×#398	C₂²	semidirect
46. C₃₁×#398	C₂²	semidirect
51. C₃₁×#395	C₂²	semidirect
52. C₃₁×#395	C₂²	semidirect
53. C₃₁×#395	C₂²	semidirect
54. C₃₁×#395	C₂²	semidirect
59. C₃₁×#391	C₂²	semidirect
60. C₃₁×#391	C₂²	semidirect
61. C₃₁×#389	C₂²	semidirect
62. C₃₁×#389	C₂²	semidirect
63. C₃₁×#389	C₂²	semidirect
64. C₃₁×#389	C₂²	semidirect
65. C₃₁×#389	C₂²	semidirect
66. C₃₁×#389	C₂²	semidirect
75. C₃₁×#387	C₂²	semidirect
76. C₃₁×#387	C₂²	semidirect
77. C₃₁×#387	C₂²	semidirect
78. C₃₁×#387	C₂²	semidirect
93. C₃₁×#384	C₂²	semidirect
94. C₃₁×#382	C₂²	semidirect
156. C₂×C₂²⋊C₄×C₃₁	Q₈	semidirect
305. #36748	C₃₁	direct (N × H)
382. #2807	C₂×C₃₁	semidirect
383. #2790	C₂×C₃₁	semidirect
384. #2788	C₂×C₃₁	semidirect
385. #2768	C₂×C₃₁	semidirect
386. #2763	C₂×C₃₁	semidirect
387. #2742	C₂×C₃₁	semidirect
388. #2729	C₂×C₃₁	semidirect
389. #2720	C₂×C₃₁	semidirect
390. #2704	C₂×C₃₁	semidirect
391. #2677	C₂×C₃₁	semidirect
394. #2569	C₂×C₃₁	semidirect
395. #2549	C₂×C₃₁	semidirect
396. #2442	C₂×C₃₁	semidirect
397. #2440	C₂×C₃₁	semidirect
438. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
439. C₂×#125	C₂²×C₃₁	semidirect
448. #400	C₂²×C₃₁	semidirect
449. #400	C₂²×C₃₁	semidirect
450. #400	C₂²×C₃₁	semidirect
451. #400	C₂²×C₃₁	semidirect
456. #398	C₂²×C₃₁	semidirect
457. #398	C₂²×C₃₁	semidirect
458. #398	C₂²×C₃₁	semidirect
459. #398	C₂²×C₃₁	semidirect
460. #398	C₂²×C₃₁	semidirect
461. #398	C₂²×C₃₁	semidirect
462. #398	C₂²×C₃₁	semidirect
463. #398	C₂²×C₃₁	semidirect
468. #395	C₂²×C₃₁	semidirect
469. #395	C₂²×C₃₁	semidirect
470. #395	C₂²×C₃₁	semidirect
471. #395	C₂²×C₃₁	semidirect
476. #391	C₂²×C₃₁	semidirect
477. #391	C₂²×C₃₁	semidirect
478. #389	C₂²×C₃₁	semidirect
479. #389	C₂²×C₃₁	semidirect
480. #389	C₂²×C₃₁	semidirect
481. #389	C₂²×C₃₁	semidirect
482. #389	C₂²×C₃₁	semidirect
483. #389	C₂²×C₃₁	semidirect
492. #387	C₂²×C₃₁	semidirect
493. #387	C₂²×C₃₁	semidirect
494. #387	C₂²×C₃₁	semidirect
495. #387	C₂²×C₃₁	semidirect
510. #384	C₂²×C₃₁	semidirect
511. #382	C₂²×C₃₁	semidirect
581. C₂×C₂²⋊C₄	Q₈×C₃₁	semidirect
631. C₃₁	#36748	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×#2848	2
C₃₁×#2807	2
C₃₁×#2790	2
C₃₁×#2788	2
C₃₁×#2768	2
C₃₁×#2763	2
C₃₁×#2742	2
C₃₁×#2729	2
C₃₁×#2720	2
C₃₁×#2704	2
C₃₁×#2677	2
C₃₁×#2626	2
C₃₁×#2569	2
C₃₁×#2549	2
C₃₁×#2442	2
C₃₁×#2440	2
C₃₁×#2312	2
C₂×C₃₁×#385	2
#36748	31

Subgroups — C31×#36748 #21493507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36748 #21493507