Subgroups — C₃₁×#34969 #21491728

Order 7936.

1962 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2530	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2527	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2511	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2492	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2477	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2470	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2427	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2422	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2401	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2398	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
20	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
21	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#123	C₂²	1	2	yes	—
27	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
40	C₃₁×#401	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×#400	C₂²	1	2	yes	—
46	C₃₁×#397	C₂²	1	2	yes	—
47	C₃₁×#397	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×#396	C₂²	1	2	yes	—
52	C₃₁×#394	C₂²	1	2	yes	—
53	C₃₁×#394	C₂²	1	2	yes	—
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	1	yes	characteristic
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	2	yes	—
62	C₃₁×#390	C₂²	1	1	yes	characteristic
63	C₃₁×#390	C₂²	1	1	yes	characteristic
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	2	yes	—
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	2	yes	—
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#386	C₂²	1	2	yes	—
85	C₃₁×#386	C₂²	1	2	yes	—
86	C₃₁×#385	C₂²	1	2	yes	—
87	C₃₁×#385	C₂²	1	2	yes	—
88	C₃₁×#385	C₂²	1	2	yes	—
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#384	C₂²	1	1	yes	characteristic
91	C₃₁×#382	C₂²	1	1	yes	characteristic
92	C₃₁×#381	C₂²	1	2	yes	—
93	C₃₁×#380	C₂²	1	1	yes	characteristic
94	C₃₁×#380	C₂²	1	2	yes	—
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
107	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₃₁×#376	C₂²	1	2	yes	—
119	C₃₁×#376	C₂²	1	1	yes	characteristic
120	C₃₁×#376	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	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	2	yes	—
131	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	—	2	4	no	—
134	C₃₁×#124	—	2	4	no	—
135	C₃₁×#123	—	2	8	no	—
136	C₃₁×C₂²⋊Q₈	—	2	8	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×#121	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	4	4	no	—
141	C₄×D₄×C₃₁	—	2	4	no	—
142	C₄×D₄×C₃₁	—	2	4	no	—
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	—	4	4	no	—
145	C₃₁×#117	—	2	4	no	—
146	C₃₁×#117	—	2	4	no	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
185	C₂×C₄²×C₃₁	—	2	4	no	—
186	C₂×C₄²×C₃₁	—	4	4	no	—
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₃₁×#95	C₂³	1	2	yes	—
209	C₃₁×#95	C₂³	1	1	yes	characteristic
210	C₃₁×#95	C₂³	1	1	yes	characteristic
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	1	yes	characteristic
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	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
239	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
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	—	2	4	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	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	4	2	no	—
251	C₂×D₄×C₃₁	#41	1	4	yes	—
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	4	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	4	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	4	no	—
264	C₂²×C₄×C₃₁	—	2	4	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	4	no	—
268	C₂²×C₄×C₃₁	—	4	2	no	—
269	C₂²×C₄×C₃₁	—	4	2	no	—
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	4	no	—
300	C₄⋊C₄×C₃₁	—	2	4	no	—
301	C₄⋊C₄×C₃₁	—	2	4	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	2	no	—
306	C₄⋊C₄×C₃₁	—	4	2	no	—
307	C₄⋊C₄×C₃₁	—	4	2	no	—
308	C₄⋊C₄×C₃₁	—	4	2	no	—
309	C₄⋊C₄×C₃₁	—	4	2	no	—
310	C₄⋊C₄×C₃₁	#41	1	4	yes	—
311	C₄⋊C₄×C₃₁	#41	1	4	yes	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	2	4	no	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	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	—	4	2	no	—
327	C₂²⋊C₄×C₃₁	—	4	2	no	—
328	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	—	2	4	no	—
339	C₄²×C₃₁	—	2	2	no	—
340	C₄²×C₃₁	—	2	2	no	—
341	C₄²×C₃₁	—	2	2	no	—
342	C₄²×C₃₁	—	2	4	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	—	4	2	no	—
348	C₄²×C₃₁	—	4	2	no	—
349	C₄²×C₃₁	#41	1	4	yes	—
350	#34969	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	1	no	—
358	C₂³×C₃₁	—	2	1	no	—
359	C₂³×C₃₁	—	2	1	no	—
360	C₂³×C₃₁	—	2	2	no	—
361	C₂³×C₃₁	—	2	1	no	—
362	C₂³×C₃₁	—	2	2	no	—
363	C₂³×C₃₁	C₂×#41	1	4	yes	—
364	C₂³×C₃₁	C₂×#41	1	2	yes	—
365	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
366	Q₈×C₃₁	—	4	8	no	—
367	Q₈×C₃₁	—	4	4	no	—
368	D₄×C₃₁	—	2	8	no	—
369	D₄×C₃₁	—	4	8	no	—
370	C₂×C₄×C₃₁	—	2	8	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	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	2	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	2	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	1	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	1	no	—
394	C₂×C₄×C₃₁	—	2	1	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	1	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	2	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	2	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	1	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	1	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	4	8	no	—
422	C₂×C₄×C₃₁	—	4	8	no	—
423	C₂×C₄×C₃₁	—	4	4	no	—
424	C₂×C₄×C₃₁	—	4	4	no	—
425	C₂×C₄×C₃₁	—	4	8	no	—
426	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
427	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
428	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
429	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
430	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
431	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
432	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
433	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
434	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
435	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
436	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
437	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
438	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
439	#2530	C₂×C₃₁	1	2	yes	complemented
440	#2527	C₂×C₃₁	1	2	yes	complemented
441	#2511	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#2509	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#2494	C₂×C₃₁	1	1	yes	characteristic, complemented
444	#2492	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#2477	C₂×C₃₁	1	2	yes	complemented
446	#2470	C₂×C₃₁	1	2	yes	complemented
447	#2452	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#2447	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#2427	C₂×C₃₁	1	1	yes	characteristic
450	#2422	C₂×C₃₁	1	1	yes	characteristic
451	#2401	C₂×C₃₁	1	2	yes	complemented
452	#2398	C₂×C₃₁	1	2	yes	complemented
453	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
454	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
455	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
456	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
457	C₄×#123	C₂×C₃₁	1	2	yes	complemented
458	C₄×#121	C₂×C₃₁	1	1	yes	characteristic
459	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
460	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
461	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
462	C₂²×C₃₁	—	2	4	no	—
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	4	no	—
465	C₂²×C₃₁	—	2	2	no	—
466	C₂²×C₃₁	—	2	2	no	—
467	C₂²×C₃₁	—	2	4	no	—
468	C₂²×C₃₁	—	4	1	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	1	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	4	1	no	—
474	C₂²×C₃₁	—	4	2	no	—
475	C₂²×C₃₁	—	4	1	no	—
476	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
477	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
478	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
480	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
481	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	2	2	no	—
485	C₄×C₃₁	—	2	2	no	—
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	2	4	no	—
488	C₄×C₃₁	—	2	2	no	—
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	4	1	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	—	4	2	no	—
493	C₄×C₃₁	—	4	1	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	1	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	1	no	—
500	C₄×C₃₁	—	4	1	no	—
501	C₄×C₃₁	—	4	1	no	—
502	C₄×C₃₁	#529	1	4	yes	—
503	C₄×C₃₁	#542	1	4	yes	—
504	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
505	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
506	C₂×#123	C₂²×C₃₁	1	2	yes	—
507	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
508	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
509	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
510	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
511	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
513	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
516	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
517	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
518	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
519	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
520	#401	C₂²×C₃₁	1	2	yes	—
521	#400	C₂²×C₃₁	1	2	yes	—
522	#400	C₂²×C₃₁	1	2	yes	—
523	#400	C₂²×C₃₁	1	2	yes	—
524	#400	C₂²×C₃₁	1	2	yes	—
525	#400	C₂²×C₃₁	1	2	yes	—
526	#397	C₂²×C₃₁	1	2	yes	—
527	#397	C₂²×C₃₁	1	2	yes	—
528	#397	C₂²×C₃₁	1	2	yes	—
529	#397	C₂²×C₃₁	1	2	yes	—
530	#397	C₂²×C₃₁	1	2	yes	—
531	#396	C₂²×C₃₁	1	2	yes	—
532	#394	C₂²×C₃₁	1	2	yes	—
533	#394	C₂²×C₃₁	1	2	yes	—
534	#393	C₂²×C₃₁	1	2	yes	—
535	#393	C₂²×C₃₁	1	2	yes	—
536	#391	C₂²×C₃₁	1	2	yes	—
537	#391	C₂²×C₃₁	1	1	yes	characteristic
538	#391	C₂²×C₃₁	1	1	yes	characteristic
539	#391	C₂²×C₃₁	1	1	yes	characteristic
540	#391	C₂²×C₃₁	1	1	yes	characteristic
541	#391	C₂²×C₃₁	1	2	yes	—
542	#390	C₂²×C₃₁	1	1	yes	characteristic
543	#390	C₂²×C₃₁	1	1	yes	characteristic
544	#389	C₂²×C₃₁	1	1	yes	characteristic
545	#389	C₂²×C₃₁	1	1	yes	characteristic
546	#389	C₂²×C₃₁	1	2	yes	—
547	#389	C₂²×C₃₁	1	1	yes	characteristic
548	#389	C₂²×C₃₁	1	1	yes	characteristic
549	#389	C₂²×C₃₁	1	1	yes	characteristic
550	#389	C₂²×C₃₁	1	2	yes	—
551	#389	C₂²×C₃₁	1	1	yes	characteristic
552	#388	C₂²×C₃₁	1	2	yes	—
553	#388	C₂²×C₃₁	1	2	yes	—
554	#388	C₂²×C₃₁	1	2	yes	—
555	#388	C₂²×C₃₁	1	2	yes	—
556	#388	C₂²×C₃₁	1	2	yes	—
557	#387	C₂²×C₃₁	1	2	yes	—
558	#387	C₂²×C₃₁	1	2	yes	—
559	#387	C₂²×C₃₁	1	2	yes	—
560	#387	C₂²×C₃₁	1	2	yes	—
561	#387	C₂²×C₃₁	1	2	yes	—
562	#387	C₂²×C₃₁	1	2	yes	—
563	#387	C₂²×C₃₁	1	2	yes	—
564	#386	C₂²×C₃₁	1	2	yes	—
565	#386	C₂²×C₃₁	1	2	yes	—
566	#385	C₂²×C₃₁	1	2	yes	—
567	#385	C₂²×C₃₁	1	2	yes	—
568	#385	C₂²×C₃₁	1	2	yes	—
569	#385	C₂²×C₃₁	1	2	yes	—
570	#384	C₂²×C₃₁	1	1	yes	characteristic
571	#382	C₂²×C₃₁	1	1	yes	characteristic
572	#381	C₂²×C₃₁	1	2	yes	—
573	#380	C₂²×C₃₁	1	1	yes	characteristic
574	#380	C₂²×C₃₁	1	2	yes	—
575	#380	C₂²×C₃₁	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
581	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
587	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
588	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
589	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
590	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
591	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
594	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
595	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
596	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
597	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
598	#376	C₂²×C₃₁	1	2	yes	—
599	#376	C₂²×C₃₁	1	1	yes	characteristic
600	#376	C₂²×C₃₁	1	1	yes	characteristic
601	C₄³	C₂²×C₃₁	1	1	yes	characteristic
602	C₄³	C₂²×C₃₁	1	1	yes	characteristic
603	C₂×C₃₁	—	4	4	no	—
604	C₂×C₃₁	—	4	2	no	—
605	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
606	C₂×C₃₁	#3444	1	1	yes	characteristic
607	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
608	C₂×C₃₁	#3481	1	1	yes	characteristic
609	C₂×C₃₁	#3481	1	1	yes	characteristic
610	C₂×C₃₁	#3482	1	1	yes	characteristic
611	C₂×C₃₁	#3482	1	1	yes	characteristic
612	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
613	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
614	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
615	C₂²×D₄	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	1	yes	characteristic
620	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
621	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
622	C₄⋊Q₈	—	2	4	no	—
623	#124	—	2	4	no	—
624	#123	—	2	8	no	—
625	C₂²⋊Q₈	—	2	8	no	—
626	C₂²⋊Q₈	—	2	4	no	—
627	#121	—	2	4	no	—
628	C₄×Q₈	—	2	4	no	—
629	C₄×Q₈	—	4	4	no	—
630	C₄×D₄	—	2	4	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	4	4	no	—
634	#117	—	2	4	no	—
635	#117	—	2	4	no	—
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	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	1	yes	characteristic
674	C₂×C₄²	—	2	4	no	—
675	C₂×C₄²	—	4	4	no	—
676	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
681	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
686	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
692	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
695	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	#95	C₂³×C₃₁	1	1	yes	characteristic
698	#95	C₂³×C₃₁	1	1	yes	characteristic
699	#95	C₂³×C₃₁	1	1	yes	characteristic
700	#95	C₂³×C₃₁	1	1	yes	characteristic
701	#95	C₂³×C₃₁	1	1	yes	characteristic
702	#95	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	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	#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	C₃₁	#34969	1	1	yes	characteristic, direct product factor, Sylow
728	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
729	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	2	4	no	—
735	C₂×Q₈	—	4	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	#41×C₃₁	1	4	yes	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	#41×C₃₁	1	4	yes	—
801	C₄⋊C₄	#41×C₃₁	1	4	yes	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	4	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	4	no	—
833	C₄²	—	2	4	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	2	no	—
839	C₄²	#41×C₃₁	1	4	yes	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	2	no	—
852	C₂³	C₂×#41×C₃₁	1	4	yes	—
853	C₂³	C₂×#41×C₃₁	1	2	yes	—
854	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
855	Q₈	—	4	8	no	—
856	Q₈	—	4	4	no	—
857	D₄	—	2	8	no	—
858	D₄	—	4	8	no	—
859	C₂×C₄	—	2	8	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	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	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	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	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	4	8	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
916	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
917	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
918	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
919	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
920	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
921	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
922	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
923	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
924	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
925	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
926	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
927	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	1	no	—
942	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
943	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
944	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
945	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
946	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
947	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
948	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	4	1	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	C₃₁×#529	1	4	yes	—
969	C₄	C₃₁×#542	1	4	yes	—
970	C₂	—	4	4	no	—
971	C₂	—	4	2	no	—
972	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
973	C₂	C₃₁×#3444	1	1	yes	characteristic
974	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
975	C₂	C₃₁×#3481	1	1	yes	characteristic
976	C₂	C₃₁×#3481	1	1	yes	characteristic
977	C₂	C₃₁×#3482	1	1	yes	characteristic
978	C₂	C₃₁×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2530	C₂	semidirect
2. C₃₁×#2527	C₂	semidirect
3. C₃₁×#2511	C₂	semidirect
4. C₃₁×#2509	C₂	semidirect
5. C₃₁×#2494	C₂	semidirect
6. C₃₁×#2492	C₂	semidirect
7. C₃₁×#2477	C₂	semidirect
8. C₃₁×#2470	C₂	semidirect
9. C₃₁×#2452	C₂	semidirect
10. C₃₁×#2447	C₂	semidirect
13. C₃₁×#2401	C₂	semidirect
14. C₃₁×#2398	C₂	semidirect
15. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
16. C₄×C₃₁×#124	C₂	semidirect
17. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₃₁×#123	C₂	semidirect
21. C₃₁×#2295	C₂	semidirect
22. C₄²×D₄×C₃₁	C₂	semidirect
23. C₄×C₃₁×#117	C₂	semidirect
350. #34969	C₃₁	direct (N × H)
439. #2530	C₂×C₃₁	semidirect
440. #2527	C₂×C₃₁	semidirect
441. #2511	C₂×C₃₁	semidirect
442. #2509	C₂×C₃₁	semidirect
443. #2494	C₂×C₃₁	semidirect
444. #2492	C₂×C₃₁	semidirect
445. #2477	C₂×C₃₁	semidirect
446. #2470	C₂×C₃₁	semidirect
447. #2452	C₂×C₃₁	semidirect
448. #2447	C₂×C₃₁	semidirect
451. #2401	C₂×C₃₁	semidirect
452. #2398	C₂×C₃₁	semidirect
453. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
454. C₄×#124	C₂×C₃₁	semidirect
455. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
456. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
457. C₄×#123	C₂×C₃₁	semidirect
459. #2295	C₂×C₃₁	semidirect
460. C₄²×D₄	C₂×C₃₁	semidirect
461. C₄×#117	C₂×C₃₁	semidirect
727. C₃₁	#34969	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×#2530	2
C₃₁×#2527	2
C₃₁×#2511	2
C₃₁×#2509	2
C₃₁×#2494	2
C₃₁×#2492	2
C₃₁×#2477	2
C₃₁×#2470	2
C₃₁×#2452	2
C₃₁×#2447	2
C₃₁×#2427	2
C₃₁×#2422	2
C₃₁×#2401	2
C₃₁×#2398	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#124	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#123	2
C₄×C₃₁×#121	2
C₃₁×#2295	2
C₄²×D₄×C₃₁	2
C₄×C₃₁×#117	2
#34969	31

Subgroups — C31×#34969 #21491728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34969 #21491728