Subgroups — C₃₁×#34987 #21491746

Order 7936.

2902 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2853	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2847	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2613	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2467	C₂	1	4	yes	maximal, complemented
10	C₃₁×#2463	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2460	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2456	C₂	1	4	yes	maximal, complemented
13	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₃₁×#120	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#539	—	2	8	no	—
20	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
21	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
22	C₂×C₃₁×#123	C₂²	1	2	yes	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
29	C₂×C₃₁×#120	C₂²	1	2	yes	—
30	C₂×C₃₁×#120	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	—	2	8	no	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#399	C₂²	1	2	yes	complemented
41	C₃₁×#397	C₂²	1	2	yes	complemented
42	C₃₁×#396	C₂²	1	4	yes	complemented
43	C₃₁×#394	C₂²	1	4	yes	—
44	C₃₁×#394	C₂²	1	4	yes	—
45	C₃₁×#394	C₂²	1	4	yes	complemented
46	C₃₁×#393	C₂²	1	2	yes	complemented
47	C₃₁×#392	C₂²	1	4	yes	—
48	C₃₁×#392	C₂²	1	4	yes	—
49	C₃₁×#392	C₂²	1	2	yes	complemented
50	C₃₁×#390	C₂²	1	4	yes	complemented
51	C₃₁×#388	C₂²	1	4	yes	complemented
52	C₃₁×#388	C₂²	1	4	yes	complemented
53	C₃₁×#388	C₂²	1	4	yes	complemented
54	C₃₁×#388	C₂²	1	4	yes	complemented
55	C₃₁×#387	C₂²	1	4	yes	complemented
56	C₃₁×#387	C₂²	1	4	yes	complemented
57	C₃₁×#387	C₂²	1	4	yes	complemented
58	C₃₁×#387	C₂²	1	4	yes	complemented
59	C₃₁×#386	C₂²	1	2	yes	—
60	C₃₁×#386	C₂²	1	2	yes	—
61	C₃₁×#386	C₂²	1	4	yes	complemented
62	C₃₁×#386	C₂²	1	4	yes	complemented
63	C₃₁×#386	C₂²	1	4	yes	complemented
64	C₃₁×#385	C₂²	1	2	yes	—
65	C₃₁×#385	C₂²	1	2	yes	—
66	C₃₁×#385	C₂²	1	4	yes	complemented
67	C₃₁×#385	C₂²	1	4	yes	complemented
68	C₃₁×#381	C₂²	1	2	yes	—
69	C₃₁×#380	C₂²	1	1	yes	characteristic
70	C₃₁×#380	C₂²	1	1	yes	characteristic
71	C₃₁×#380	C₂²	1	2	yes	complemented
72	C₃₁×#380	C₂²	1	2	yes	complemented
73	C₃₁×#379	C₂²	1	2	yes	—
74	C₃₁×#379	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
77	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
78	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₃₁	—	2	4	no	—
81	C₂²×D₄×C₃₁	—	2	4	no	—
82	C₂²×D₄×C₃₁	—	2	4	no	—
83	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
84	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
85	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	—	2	4	no	—
89	C₂³×C₄×C₃₁	—	2	4	no	—
90	C₂³×C₄×C₃₁	—	4	4	no	—
91	C₂³×C₄×C₃₁	—	4	4	no	—
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₃₁×#126	—	2	8	no	—
102	C₃₁×#125	—	2	8	no	—
103	C₃₁×#123	—	2	8	no	—
104	C₃₁×#123	—	2	8	no	—
105	C₃₁×C₂²⋊Q₈	—	2	4	no	—
106	C₃₁×C₂²⋊Q₈	—	2	8	no	—
107	C₃₁×C₂²⋊Q₈	—	4	4	no	—
108	C₃₁×#121	—	2	4	no	—
109	C₃₁×#121	—	4	4	no	—
110	C₃₁×#120	—	2	8	no	—
111	C₃₁×#120	—	2	8	no	—
112	C₄×D₄×C₃₁	—	2	8	no	—
113	C₄×D₄×C₃₁	—	2	16	no	—
114	C₄×D₄×C₃₁	—	2	16	no	—
115	C₄×D₄×C₃₁	—	4	8	no	—
116	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₄²×C₃₁	—	2	4	no	—
150	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
151	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	2	yes	—
155	C₃₁×#95	C₂³	1	4	yes	—
156	C₃₁×#95	C₂³	1	2	yes	—
157	C₃₁×#95	C₂³	1	4	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	4	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₂⁴×C₃₁	—	2	2	no	—
163	C₂⁴×C₃₁	—	2	2	no	—
164	C₂⁴×C₃₁	—	2	2	no	—
165	C₂⁴×C₃₁	—	2	2	no	—
166	C₂⁴×C₃₁	—	4	2	no	—
167	C₂⁴×C₃₁	—	4	2	no	—
168	C₂⁴×C₃₁	—	4	2	no	—
169	C₂⁴×C₃₁	—	4	2	no	—
170	C₂⁴×C₃₁	#41	1	4	yes	—
171	C₂⁴×C₃₁	#41	1	4	yes	—
172	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
173	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
174	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
175	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₃₁	—	2	2	no	—
177	C₂×Q₈×C₃₁	—	4	2	no	—
178	C₂×D₄×C₃₁	—	2	32	no	—
179	C₂×D₄×C₃₁	—	2	8	no	—
180	C₂×D₄×C₃₁	—	2	8	no	—
181	C₂×D₄×C₃₁	—	2	4	no	—
182	C₂×D₄×C₃₁	—	2	8	no	—
183	C₂×D₄×C₃₁	—	2	4	no	—
184	C₂×D₄×C₃₁	—	2	4	no	—
185	C₂×D₄×C₃₁	—	2	8	no	—
186	C₂×D₄×C₃₁	—	2	8	no	—
187	C₂×D₄×C₃₁	—	2	2	no	—
188	C₂×D₄×C₃₁	—	4	4	no	—
189	C₂×D₄×C₃₁	—	4	4	no	—
190	C₂×D₄×C₃₁	—	4	2	no	—
191	C₂×D₄×C₃₁	—	4	4	no	—
192	C₂×D₄×C₃₁	—	4	4	no	—
193	C₂²×C₄×C₃₁	—	2	2	no	—
194	C₂²×C₄×C₃₁	—	2	2	no	—
195	C₂²×C₄×C₃₁	—	2	2	no	—
196	C₂²×C₄×C₃₁	—	2	4	no	—
197	C₂²×C₄×C₃₁	—	2	2	no	—
198	C₂²×C₄×C₃₁	—	2	8	no	—
199	C₂²×C₄×C₃₁	—	2	4	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	2	8	no	—
202	C₂²×C₄×C₃₁	—	2	4	no	—
203	C₂²×C₄×C₃₁	—	2	4	no	—
204	C₂²×C₄×C₃₁	—	2	4	no	—
205	C₂²×C₄×C₃₁	—	4	2	no	—
206	C₂²×C₄×C₃₁	—	4	4	no	—
207	C₂²×C₄×C₃₁	—	4	2	no	—
208	C₂²×C₄×C₃₁	—	4	2	no	—
209	C₂²×C₄×C₃₁	—	4	2	no	—
210	C₂²×C₄×C₃₁	—	4	2	no	—
211	C₂²×C₄×C₃₁	—	4	4	no	—
212	C₂²×C₄×C₃₁	—	4	16	no	—
213	C₂²×C₄×C₃₁	—	4	16	no	—
214	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
228	C₄⋊C₄×C₃₁	—	2	4	no	—
229	C₄⋊C₄×C₃₁	—	2	2	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	—	2	2	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	2	8	no	—
235	C₄⋊C₄×C₃₁	—	4	4	no	—
236	C₄⋊C₄×C₃₁	—	4	2	no	—
237	C₄⋊C₄×C₃₁	—	4	2	no	—
238	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
239	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
240	C₂²⋊C₄×C₃₁	—	2	4	no	—
241	C₂²⋊C₄×C₃₁	—	2	8	no	—
242	C₂²⋊C₄×C₃₁	—	2	8	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	—	2	8	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₃₁	—	2	4	no	—
249	C₂²⋊C₄×C₃₁	—	2	4	no	—
250	C₂²⋊C₄×C₃₁	—	2	4	no	—
251	C₂²⋊C₄×C₃₁	—	2	4	no	—
252	C₂²⋊C₄×C₃₁	—	2	8	no	—
253	C₂²⋊C₄×C₃₁	—	4	4	no	—
254	C₂²⋊C₄×C₃₁	—	4	4	no	—
255	C₂²⋊C₄×C₃₁	—	4	4	no	—
256	C₂²⋊C₄×C₃₁	—	4	4	no	—
257	C₂²⋊C₄×C₃₁	—	4	4	no	—
258	C₄²×C₃₁	—	2	8	no	—
259	C₄²×C₃₁	—	2	4	no	—
260	C₄²×C₃₁	—	4	4	no	—
261	#34987	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂³×C₃₁	—	2	2	no	—
263	C₂³×C₃₁	—	2	2	no	—
264	C₂³×C₃₁	—	2	8	no	—
265	C₂³×C₃₁	—	2	8	no	—
266	C₂³×C₃₁	—	2	2	no	—
267	C₂³×C₃₁	—	2	2	no	—
268	C₂³×C₃₁	—	2	2	no	—
269	C₂³×C₃₁	—	2	2	no	—
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	4	no	—
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	—	2	2	no	—
274	C₂³×C₃₁	—	2	4	no	—
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	2	4	no	—
280	C₂³×C₃₁	—	2	4	no	—
281	C₂³×C₃₁	—	4	8	no	—
282	C₂³×C₃₁	—	4	8	no	—
283	C₂³×C₃₁	—	4	4	no	—
284	C₂³×C₃₁	—	4	4	no	—
285	C₂³×C₃₁	—	4	8	no	—
286	C₂³×C₃₁	—	4	4	no	—
287	C₂³×C₃₁	—	4	4	no	—
288	C₂³×C₃₁	—	4	8	no	—
289	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
290	C₂³×C₃₁	C₂×#41	1	4	yes	—
291	C₂³×C₃₁	C₂×#41	1	4	yes	—
292	C₂³×C₃₁	C₂×#41	1	2	yes	—
293	C₂³×C₃₁	C₂×#41	1	2	yes	—
294	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
295	Q₈×C₃₁	—	8	2	no	—
296	D₄×C₃₁	—	2	32	no	—
297	D₄×C₃₁	—	4	16	no	—
298	D₄×C₃₁	—	4	8	no	—
299	D₄×C₃₁	—	8	2	no	—
300	D₄×C₃₁	—	8	8	no	—
301	C₂×C₄×C₃₁	—	2	8	no	—
302	C₂×C₄×C₃₁	—	2	8	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	4	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	4	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	2	4	no	—
322	C₂×C₄×C₃₁	—	2	4	no	—
323	C₂×C₄×C₃₁	—	2	4	no	—
324	C₂×C₄×C₃₁	—	2	4	no	—
325	C₂×C₄×C₃₁	—	4	4	no	—
326	C₂×C₄×C₃₁	—	4	4	no	—
327	C₂×C₄×C₃₁	—	4	16	no	—
328	C₂×C₄×C₃₁	—	4	8	no	—
329	C₂×C₄×C₃₁	—	4	8	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	8	4	no	—
332	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
337	C₂×#539	C₂×C₃₁	1	1	yes	characteristic, complemented
338	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#2853	C₂×C₃₁	1	2	yes	complemented
340	#2848	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#2847	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#2626	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#2617	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#2613	C₂×C₃₁	1	2	yes	complemented
345	#2467	C₂×C₃₁	1	4	yes	complemented
346	#2463	C₂×C₃₁	1	4	yes	complemented
347	#2460	C₂×C₃₁	1	4	yes	complemented
348	#2456	C₂×C₃₁	1	4	yes	complemented
349	#2321	C₂×C₃₁	1	2	yes	complemented
350	#2313	C₂×C₃₁	1	1	yes	characteristic, complemented
351	C₄×#120	C₂×C₃₁	1	2	yes	complemented
352	C₂²×C₃₁	—	2	4	no	—
353	C₂²×C₃₁	—	2	2	no	—
354	C₂²×C₃₁	—	2	2	no	—
355	C₂²×C₃₁	—	2	4	no	—
356	C₂²×C₃₁	—	2	4	no	—
357	C₂²×C₃₁	—	2	4	no	—
358	C₂²×C₃₁	—	2	8	no	—
359	C₂²×C₃₁	—	2	4	no	—
360	C₂²×C₃₁	—	2	4	no	—
361	C₂²×C₃₁	—	4	16	no	—
362	C₂²×C₃₁	—	4	16	no	—
363	C₂²×C₃₁	—	4	2	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	4	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	4	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	4	no	—
375	C₂²×C₃₁	#525	1	4	yes	—
376	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
377	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
378	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
379	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
380	C₂²×C₃₁	#585	1	2	yes	—
381	C₄×C₃₁	—	2	4	no	—
382	C₄×C₃₁	—	2	4	no	—
383	C₄×C₃₁	—	2	4	no	—
384	C₄×C₃₁	—	2	2	no	—
385	C₄×C₃₁	—	2	2	no	—
386	C₄×C₃₁	—	4	2	no	—
387	C₄×C₃₁	—	4	4	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	—	4	4	no	—
392	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
393	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
394	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
395	#539	—	2	8	no	—
396	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
397	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
398	C₂×#123	C₂²×C₃₁	1	2	yes	—
399	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
400	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
402	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
403	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
404	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
405	C₂×#120	C₂²×C₃₁	1	2	yes	—
406	C₂×#120	C₂²×C₃₁	1	2	yes	—
407	C₂×C₄×D₄	—	2	8	no	—
408	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
410	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
411	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
412	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
415	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
416	#399	C₂²×C₃₁	1	2	yes	complemented
417	#397	C₂²×C₃₁	1	2	yes	complemented
418	#396	C₂²×C₃₁	1	4	yes	complemented
419	#394	C₂²×C₃₁	1	4	yes	—
420	#394	C₂²×C₃₁	1	4	yes	—
421	#394	C₂²×C₃₁	1	4	yes	complemented
422	#393	C₂²×C₃₁	1	2	yes	complemented
423	#392	C₂²×C₃₁	1	4	yes	—
424	#392	C₂²×C₃₁	1	4	yes	—
425	#392	C₂²×C₃₁	1	2	yes	complemented
426	#390	C₂²×C₃₁	1	4	yes	complemented
427	#388	C₂²×C₃₁	1	4	yes	complemented
428	#388	C₂²×C₃₁	1	4	yes	complemented
429	#388	C₂²×C₃₁	1	4	yes	complemented
430	#388	C₂²×C₃₁	1	4	yes	complemented
431	#387	C₂²×C₃₁	1	4	yes	complemented
432	#387	C₂²×C₃₁	1	4	yes	complemented
433	#387	C₂²×C₃₁	1	4	yes	complemented
434	#387	C₂²×C₃₁	1	4	yes	complemented
435	#386	C₂²×C₃₁	1	2	yes	—
436	#386	C₂²×C₃₁	1	2	yes	—
437	#386	C₂²×C₃₁	1	4	yes	complemented
438	#386	C₂²×C₃₁	1	4	yes	complemented
439	#386	C₂²×C₃₁	1	4	yes	complemented
440	#385	C₂²×C₃₁	1	2	yes	—
441	#385	C₂²×C₃₁	1	2	yes	—
442	#385	C₂²×C₃₁	1	4	yes	complemented
443	#385	C₂²×C₃₁	1	4	yes	complemented
444	#381	C₂²×C₃₁	1	2	yes	—
445	#380	C₂²×C₃₁	1	1	yes	characteristic
446	#380	C₂²×C₃₁	1	1	yes	characteristic
447	#380	C₂²×C₃₁	1	2	yes	complemented
448	#380	C₂²×C₃₁	1	2	yes	complemented
449	#379	C₂²×C₃₁	1	2	yes	—
450	#379	C₂²×C₃₁	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
453	C₂×C₃₁	—	2	4	no	—
454	C₂×C₃₁	—	4	4	no	—
455	C₂×C₃₁	—	4	4	no	—
456	C₂×C₃₁	—	8	2	no	—
457	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
458	C₂×C₃₁	#3459	1	2	yes	—
459	C₂×C₃₁	#3484	1	1	yes	characteristic
460	C₂×C₃₁	#3487	1	1	yes	characteristic
461	C₂×C₃₁	#3505	1	2	yes	—
462	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
463	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
464	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
465	C₂²×D₄	—	2	4	no	—
466	C₂²×D₄	—	2	4	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
469	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
470	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
471	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
472	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂³×C₄	—	2	4	no	—
474	C₂³×C₄	—	2	4	no	—
475	C₂³×C₄	—	4	4	no	—
476	C₂³×C₄	—	4	4	no	—
477	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
479	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
480	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
481	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
484	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
486	#126	—	2	8	no	—
487	#125	—	2	8	no	—
488	#123	—	2	8	no	—
489	#123	—	2	8	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	8	no	—
492	C₂²⋊Q₈	—	4	4	no	—
493	#121	—	2	4	no	—
494	#121	—	4	4	no	—
495	#120	—	2	8	no	—
496	#120	—	2	8	no	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	16	no	—
499	C₄×D₄	—	2	16	no	—
500	C₄×D₄	—	4	8	no	—
501	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
502	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	—	2	4	no	—
516	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
534	C₂×C₄²	—	2	4	no	—
535	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
536	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
538	#95	C₂³×C₃₁	1	4	yes	—
539	#95	C₂³×C₃₁	1	4	yes	—
540	#95	C₂³×C₃₁	1	4	yes	—
541	#95	C₂³×C₃₁	1	2	yes	—
542	#95	C₂³×C₃₁	1	2	yes	—
543	#95	C₂³×C₃₁	1	4	yes	—
544	#95	C₂³×C₃₁	1	4	yes	—
545	#95	C₂³×C₃₁	1	4	yes	—
546	#95	C₂³×C₃₁	1	4	yes	—
547	C₃₁	#34987	1	1	yes	characteristic, direct product factor, Sylow
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	#41×C₃₁	1	4	yes	—
557	C₂⁴	#41×C₃₁	1	4	yes	—
558	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
559	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
560	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
561	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	4	2	no	—
564	C₂×D₄	—	2	32	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	2	8	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	8	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	8	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	—	4	16	no	—
599	C₂²×C₄	—	4	16	no	—
600	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
601	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
602	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
603	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
604	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	4	4	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
625	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	8	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₄²	—	2	8	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	4	4	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	8	no	—
650	C₂³	—	2	8	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	4	8	no	—
667	C₂³	—	4	8	no	—
668	C₂³	—	4	4	no	—
669	C₂³	—	4	4	no	—
670	C₂³	—	4	8	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	8	no	—
674	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
675	C₂³	C₂×#41×C₃₁	1	4	yes	—
676	C₂³	C₂×#41×C₃₁	1	4	yes	—
677	C₂³	C₂×#41×C₃₁	1	2	yes	—
678	C₂³	C₂×#41×C₃₁	1	2	yes	—
679	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
680	Q₈	—	8	2	no	—
681	D₄	—	2	32	no	—
682	D₄	—	4	16	no	—
683	D₄	—	4	8	no	—
684	D₄	—	8	2	no	—
685	D₄	—	8	8	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	16	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
718	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
719	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
721	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	8	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	4	16	no	—
732	C₂²	—	4	16	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	4	no	—
745	C₂²	C₃₁×#525	1	4	yes	—
746	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
747	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
748	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
749	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
750	C₂²	C₃₁×#585	1	2	yes	—
751	C₄	—	2	4	no	—
752	C₄	—	2	4	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	4	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	4	no	—
762	C₂	—	2	4	no	—
763	C₂	—	4	4	no	—
764	C₂	—	4	4	no	—
765	C₂	—	8	2	no	—
766	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
767	C₂	C₃₁×#3459	1	2	yes	—
768	C₂	C₃₁×#3484	1	1	yes	characteristic
769	C₂	C₃₁×#3487	1	1	yes	characteristic
770	C₂	C₃₁×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
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×#539	C₂	semidirect
2. C₂²×C₄×D₄×C₃₁	C₂	semidirect
3. C₃₁×#2853	C₂	semidirect
4. C₃₁×#2848	C₂	semidirect
5. C₃₁×#2847	C₂	semidirect
6. C₃₁×#2626	C₂	semidirect
7. C₃₁×#2617	C₂	semidirect
8. C₃₁×#2613	C₂	semidirect
9. C₃₁×#2467	C₂	semidirect
10. C₃₁×#2463	C₂	semidirect
11. C₃₁×#2460	C₂	semidirect
12. C₃₁×#2456	C₂	semidirect
13. C₃₁×#2321	C₂	semidirect
14. C₃₁×#2313	C₂	semidirect
15. C₄×C₃₁×#120	C₂	semidirect
20. C₂×C₃₁×#126	C₂²	semidirect
21. C₂×C₃₁×#125	C₂²	semidirect
23. C₂×C₃₁×#123	C₂²	semidirect
25. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₃₁×#121	C₂²	semidirect
35. C₂×C₄×D₄×C₃₁	C₂²	semidirect
40. C₃₁×#399	C₂²	semidirect
41. C₃₁×#397	C₂²	semidirect
42. C₃₁×#396	C₂²	semidirect
45. C₃₁×#394	C₂²	semidirect
46. C₃₁×#393	C₂²	semidirect
49. C₃₁×#392	C₂²	semidirect
50. C₃₁×#390	C₂²	semidirect
51. C₃₁×#388	C₂²	semidirect
52. C₃₁×#388	C₂²	semidirect
53. C₃₁×#388	C₂²	semidirect
54. C₃₁×#388	C₂²	semidirect
55. C₃₁×#387	C₂²	semidirect
56. C₃₁×#387	C₂²	semidirect
57. C₃₁×#387	C₂²	semidirect
58. C₃₁×#387	C₂²	semidirect
61. C₃₁×#386	C₂²	semidirect
62. C₃₁×#386	C₂²	semidirect
63. C₃₁×#386	C₂²	semidirect
66. C₃₁×#385	C₂²	semidirect
67. C₃₁×#385	C₂²	semidirect
71. C₃₁×#380	C₂²	semidirect
72. C₃₁×#380	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
116. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
261. #34987	C₃₁	direct (N × H)
337. C₂×#539	C₂×C₃₁	semidirect
338. C₂²×C₄×D₄	C₂×C₃₁	semidirect
339. #2853	C₂×C₃₁	semidirect
340. #2848	C₂×C₃₁	semidirect
341. #2847	C₂×C₃₁	semidirect
342. #2626	C₂×C₃₁	semidirect
343. #2617	C₂×C₃₁	semidirect
344. #2613	C₂×C₃₁	semidirect
345. #2467	C₂×C₃₁	semidirect
346. #2463	C₂×C₃₁	semidirect
347. #2460	C₂×C₃₁	semidirect
348. #2456	C₂×C₃₁	semidirect
349. #2321	C₂×C₃₁	semidirect
350. #2313	C₂×C₃₁	semidirect
351. C₄×#120	C₂×C₃₁	semidirect
396. C₂×#126	C₂²×C₃₁	semidirect
397. C₂×#125	C₂²×C₃₁	semidirect
399. C₂×#123	C₂²×C₃₁	semidirect
401. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
402. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
404. C₂×#121	C₂²×C₃₁	semidirect
411. C₂×C₄×D₄	C₂²×C₃₁	semidirect
416. #399	C₂²×C₃₁	semidirect
417. #397	C₂²×C₃₁	semidirect
418. #396	C₂²×C₃₁	semidirect
421. #394	C₂²×C₃₁	semidirect
422. #393	C₂²×C₃₁	semidirect
425. #392	C₂²×C₃₁	semidirect
426. #390	C₂²×C₃₁	semidirect
427. #388	C₂²×C₃₁	semidirect
428. #388	C₂²×C₃₁	semidirect
429. #388	C₂²×C₃₁	semidirect
430. #388	C₂²×C₃₁	semidirect
431. #387	C₂²×C₃₁	semidirect
432. #387	C₂²×C₃₁	semidirect
433. #387	C₂²×C₃₁	semidirect
434. #387	C₂²×C₃₁	semidirect
437. #386	C₂²×C₃₁	semidirect
438. #386	C₂²×C₃₁	semidirect
439. #386	C₂²×C₃₁	semidirect
442. #385	C₂²×C₃₁	semidirect
443. #385	C₂²×C₃₁	semidirect
447. #380	C₂²×C₃₁	semidirect
448. #380	C₂²×C₃₁	semidirect
452. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
501. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
547. C₃₁	#34987	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×#539	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2853	2
C₃₁×#2848	2
C₃₁×#2847	2
C₃₁×#2626	2
C₃₁×#2617	2
C₃₁×#2613	2
C₃₁×#2467	2
C₃₁×#2463	2
C₃₁×#2460	2
C₃₁×#2456	2
C₃₁×#2321	2
C₃₁×#2313	2
C₄×C₃₁×#120	2
#34987	31

Subgroups — C31×#34987 #21491746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34987 #21491746