Subgroups — C₃₁×#34430 #21491189

Order 7936.

1966 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#541	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2383	C₂	1	2	yes	maximal
3	C₃₁×#2382	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2373	C₂	1	2	yes	maximal
5	C₃₁×#2370	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2362	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2362	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2360	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2360	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2351	C₂	1	1	yes	maximal, characteristic, complemented
13	Q₈×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2336	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2334	C₂	1	2	yes	maximal
16	C₃₁×#2334	C₂	1	2	yes	maximal
17	C₃₁×#2330	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2317	C₂	1	1	yes	maximal, characteristic
21	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2298	C₂	1	1	yes	maximal, characteristic
24	C₃₁×#541	C₄	1	16	yes	complemented
25	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#126	C₂²	1	2	yes	—
27	C₂×C₃₁×#126	C₂²	1	2	yes	—
28	C₂×C₃₁×#125	C₂²	1	2	yes	—
29	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#125	C₂²	1	2	yes	—
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#391	C₂²	1	1	yes	characteristic
43	C₃₁×#391	C₂²	1	1	yes	characteristic
44	C₃₁×#391	C₂²	1	1	yes	characteristic
45	C₃₁×#391	C₂²	1	1	yes	characteristic
46	C₃₁×#389	C₂²	1	2	yes	—
47	C₃₁×#389	C₂²	1	2	yes	—
48	C₃₁×#389	C₂²	1	2	yes	—
49	C₃₁×#389	C₂²	1	2	yes	—
50	C₃₁×#389	C₂²	1	2	yes	—
51	C₃₁×#389	C₂²	1	1	yes	characteristic
52	C₃₁×#389	C₂²	1	1	yes	characteristic
53	C₃₁×#389	C₂²	1	2	yes	—
54	C₃₁×#389	C₂²	1	2	yes	—
55	C₃₁×#389	C₂²	1	2	yes	—
56	C₃₁×#389	C₂²	1	2	yes	—
57	C₃₁×#389	C₂²	1	2	yes	—
58	C₃₁×#389	C₂²	1	2	yes	—
59	C₃₁×#389	C₂²	1	2	yes	—
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#388	C₂²	1	1	yes	characteristic
63	C₃₁×#388	C₂²	1	1	yes	characteristic
64	C₃₁×#388	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	—
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#388	C₂²	1	1	yes	characteristic
69	C₃₁×#388	C₂²	1	1	yes	characteristic
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	1	yes	characteristic
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	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	1	yes	characteristic
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	1	yes	characteristic
88	C₃₁×#387	C₂²	1	1	yes	characteristic
89	C₃₁×#387	C₂²	1	2	yes	—
90	C₃₁×#385	C₂²	1	2	yes	—
91	C₃₁×#385	C₂²	1	2	yes	—
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#385	C₂²	1	2	yes	—
94	C₃₁×#384	C₂²	1	1	yes	characteristic
95	C₃₁×#384	C₂²	1	1	yes	characteristic
96	C₃₁×#384	C₂²	1	2	yes	—
97	C₃₁×#383	C₂²	1	2	yes	—
98	C₃₁×#382	C₂²	1	1	yes	characteristic
99	C₃₁×#382	C₂²	1	1	yes	characteristic
100	C₃₁×#382	C₂²	1	2	yes	—
101	C₃₁×#382	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#376	C₂²	1	1	yes	characteristic
122	C₃₁×#376	C₂²	1	2	yes	—
123	C₄³×C₃₁	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
129	C₃₁×#126	C₂×C₄	1	16	yes	—
130	C₃₁×#126	C₂×C₄	1	16	yes	—
131	C₃₁×#125	C₂×C₄	1	8	yes	complemented
132	C₃₁×#125	C₂×C₄	1	16	yes	complemented
133	C₃₁×#125	C₂×C₄	1	16	yes	complemented
134	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
135	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
136	C₄×Q₈×C₃₁	—	4	2	no	—
137	C₄×Q₈×C₃₁	—	4	2	no	—
138	C₄×Q₈×C₃₁	—	4	2	no	—
139	C₄×Q₈×C₃₁	—	4	2	no	—
140	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
141	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
142	C₃₁×#117	—	4	2	no	—
143	C₃₁×#117	C₂×C₄	1	8	yes	—
144	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
194	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
195	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	1	yes	characteristic
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	1	yes	characteristic
212	C₃₁×#95	C₂³	1	1	yes	characteristic
213	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	1	yes	characteristic
215	C₃₁×#95	C₂³	1	1	yes	characteristic
216	C₃₁×#95	C₂³	1	1	yes	characteristic
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	1	yes	characteristic
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	1	yes	characteristic
222	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
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	C₃₁×#95	C₂³	1	2	yes	—
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×Q₈×C₃₁	—	2	2	no	—
245	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
246	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	4	2	no	—
250	C₂²×C₄×C₃₁	—	4	2	no	—
251	C₂²×C₄×C₃₁	—	4	2	no	—
252	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	4	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	4	2	no	—
283	C₄⋊C₄×C₃₁	—	4	2	no	—
284	C₄⋊C₄×C₃₁	—	4	2	no	—
285	C₄⋊C₄×C₃₁	—	4	2	no	—
286	C₄⋊C₄×C₃₁	—	4	2	no	—
287	C₄⋊C₄×C₃₁	—	4	2	no	—
288	C₄⋊C₄×C₃₁	—	4	1	no	—
289	C₄⋊C₄×C₃₁	—	4	1	no	—
290	C₄⋊C₄×C₃₁	—	4	2	no	—
291	C₄⋊C₄×C₃₁	—	4	2	no	—
292	C₄⋊C₄×C₃₁	—	4	2	no	—
293	C₄⋊C₄×C₃₁	—	4	2	no	—
294	C₄⋊C₄×C₃₁	—	4	2	no	—
295	C₄⋊C₄×C₃₁	—	4	2	no	—
296	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
297	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
298	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
299	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
300	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
301	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
302	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
303	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
304	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
305	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
306	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
307	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂²⋊C₄×C₃₁	—	4	1	no	—
311	C₂²⋊C₄×C₃₁	—	4	1	no	—
312	C₂²⋊C₄×C₃₁	—	4	2	no	—
313	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
314	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
315	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
316	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
317	C₄²×C₃₁	—	2	2	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	2	4	no	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	2	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	4	2	no	—
325	C₄²×C₃₁	—	4	1	no	—
326	C₄²×C₃₁	—	4	2	no	—
327	C₄²×C₃₁	—	4	2	no	—
328	C₄²×C₃₁	—	4	1	no	—
329	C₄²×C₃₁	—	4	2	no	—
330	C₄²×C₃₁	—	4	2	no	—
331	C₄²×C₃₁	—	4	2	no	—
332	C₄²×C₃₁	—	4	2	no	—
333	C₄²×C₃₁	—	4	2	no	—
334	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
335	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
336	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
337	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
338	#34430	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂³×C₃₁	—	2	1	no	—
340	C₂³×C₃₁	—	2	1	no	—
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	—	2	1	no	—
343	C₂³×C₃₁	—	2	1	no	—
344	C₂³×C₃₁	—	2	1	no	—
345	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
346	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
347	Q₈×C₃₁	—	2	8	no	—
348	Q₈×C₃₁	—	2	8	no	—
349	C₂×C₄×C₃₁	—	2	1	no	—
350	C₂×C₄×C₃₁	—	2	1	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	1	no	—
354	C₂×C₄×C₃₁	—	2	1	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	1	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	1	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	1	no	—
371	C₂×C₄×C₃₁	—	2	8	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	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	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	1	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	2	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	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	8	4	no	—
403	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
404	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
405	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
406	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
407	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
408	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
409	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
410	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
411	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
412	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
413	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
414	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
415	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
416	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
417	C₂×#541	C₂×C₃₁	1	1	yes	characteristic
418	#2383	C₂×C₃₁	1	2	yes	—
419	#2382	C₂×C₃₁	1	2	yes	complemented
420	#2373	C₂×C₃₁	1	2	yes	—
421	#2370	C₂×C₃₁	1	2	yes	complemented
422	#2362	C₂×C₃₁	1	1	yes	characteristic
423	#2362	C₂×C₃₁	1	1	yes	characteristic
424	#2360	C₂×C₃₁	1	1	yes	characteristic
425	#2360	C₂×C₃₁	1	1	yes	characteristic
426	#2356	C₂×C₃₁	1	1	yes	characteristic, complemented
427	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#2351	C₂×C₃₁	1	1	yes	characteristic, complemented
429	Q₈×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
430	#2336	C₂×C₃₁	1	2	yes	complemented
431	#2334	C₂×C₃₁	1	2	yes	—
432	#2334	C₂×C₃₁	1	2	yes	—
433	#2330	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#2330	C₂×C₃₁	1	2	yes	complemented
435	#2327	C₂×C₃₁	1	1	yes	characteristic, complemented
436	#2317	C₂×C₃₁	1	1	yes	characteristic
437	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
438	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
439	#2298	C₂×C₃₁	1	1	yes	characteristic
440	C₂²×C₃₁	—	2	2	no	—
441	C₂²×C₃₁	—	2	2	no	—
442	C₂²×C₃₁	—	2	2	no	—
443	C₂²×C₃₁	—	4	1	no	—
444	C₂²×C₃₁	—	4	1	no	—
445	C₂²×C₃₁	—	4	1	no	—
446	C₂²×C₃₁	—	4	1	no	—
447	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
448	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
452	C₂²×C₃₁	#585	1	1	yes	characteristic
453	C₂²×C₃₁	#585	1	1	yes	characteristic
454	C₄×C₃₁	—	2	2	no	—
455	C₄×C₃₁	—	2	4	no	—
456	C₄×C₃₁	—	2	4	no	—
457	C₄×C₃₁	—	2	2	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	2	4	no	—
460	C₄×C₃₁	—	2	4	no	—
461	C₄×C₃₁	—	2	2	no	—
462	C₄×C₃₁	—	2	2	no	—
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	2	no	—
465	C₄×C₃₁	—	4	1	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	—	4	1	no	—
468	C₄×C₃₁	—	4	1	no	—
469	C₄×C₃₁	—	4	1	no	—
470	C₄×C₃₁	—	4	1	no	—
471	C₄×C₃₁	—	4	2	no	—
472	C₄×C₃₁	—	4	2	no	—
473	C₄×C₃₁	—	4	2	no	—
474	C₄×C₃₁	—	4	1	no	—
475	C₄×C₃₁	#520	1	4	yes	—
476	#541	C₄×C₃₁	1	16	yes	complemented
477	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
478	C₂×#126	C₂²×C₃₁	1	2	yes	—
479	C₂×#126	C₂²×C₃₁	1	2	yes	—
480	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×#125	C₂²×C₃₁	1	2	yes	—
482	C₂×#125	C₂²×C₃₁	1	2	yes	—
483	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
484	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
485	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
486	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
487	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
488	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
489	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
490	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
491	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
492	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
493	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
494	#391	C₂²×C₃₁	1	1	yes	characteristic
495	#391	C₂²×C₃₁	1	1	yes	characteristic
496	#391	C₂²×C₃₁	1	1	yes	characteristic
497	#391	C₂²×C₃₁	1	1	yes	characteristic
498	#389	C₂²×C₃₁	1	1	yes	characteristic
499	#389	C₂²×C₃₁	1	1	yes	characteristic
500	#389	C₂²×C₃₁	1	2	yes	—
501	#389	C₂²×C₃₁	1	2	yes	—
502	#389	C₂²×C₃₁	1	2	yes	—
503	#389	C₂²×C₃₁	1	2	yes	—
504	#389	C₂²×C₃₁	1	2	yes	—
505	#389	C₂²×C₃₁	1	1	yes	characteristic
506	#389	C₂²×C₃₁	1	1	yes	characteristic
507	#389	C₂²×C₃₁	1	2	yes	—
508	#389	C₂²×C₃₁	1	2	yes	—
509	#389	C₂²×C₃₁	1	2	yes	—
510	#389	C₂²×C₃₁	1	2	yes	—
511	#389	C₂²×C₃₁	1	2	yes	—
512	#389	C₂²×C₃₁	1	2	yes	—
513	#389	C₂²×C₃₁	1	2	yes	—
514	#388	C₂²×C₃₁	1	1	yes	characteristic
515	#388	C₂²×C₃₁	1	1	yes	characteristic
516	#388	C₂²×C₃₁	1	2	yes	—
517	#388	C₂²×C₃₁	1	2	yes	—
518	#388	C₂²×C₃₁	1	2	yes	—
519	#388	C₂²×C₃₁	1	2	yes	—
520	#388	C₂²×C₃₁	1	1	yes	characteristic
521	#388	C₂²×C₃₁	1	1	yes	characteristic
522	#387	C₂²×C₃₁	1	2	yes	—
523	#387	C₂²×C₃₁	1	2	yes	—
524	#387	C₂²×C₃₁	1	2	yes	—
525	#387	C₂²×C₃₁	1	2	yes	—
526	#387	C₂²×C₃₁	1	2	yes	—
527	#387	C₂²×C₃₁	1	2	yes	—
528	#387	C₂²×C₃₁	1	1	yes	characteristic
529	#387	C₂²×C₃₁	1	2	yes	—
530	#387	C₂²×C₃₁	1	2	yes	—
531	#387	C₂²×C₃₁	1	2	yes	—
532	#387	C₂²×C₃₁	1	2	yes	—
533	#387	C₂²×C₃₁	1	2	yes	—
534	#387	C₂²×C₃₁	1	2	yes	—
535	#387	C₂²×C₃₁	1	1	yes	characteristic
536	#387	C₂²×C₃₁	1	2	yes	—
537	#387	C₂²×C₃₁	1	2	yes	—
538	#387	C₂²×C₃₁	1	2	yes	—
539	#387	C₂²×C₃₁	1	2	yes	—
540	#387	C₂²×C₃₁	1	1	yes	characteristic
541	#387	C₂²×C₃₁	1	1	yes	characteristic
542	#385	C₂²×C₃₁	1	2	yes	—
543	#385	C₂²×C₃₁	1	2	yes	—
544	#385	C₂²×C₃₁	1	2	yes	—
545	#385	C₂²×C₃₁	1	2	yes	—
546	#384	C₂²×C₃₁	1	1	yes	characteristic
547	#384	C₂²×C₃₁	1	1	yes	characteristic
548	#384	C₂²×C₃₁	1	2	yes	—
549	#383	C₂²×C₃₁	1	2	yes	—
550	#382	C₂²×C₃₁	1	1	yes	characteristic
551	#382	C₂²×C₃₁	1	1	yes	characteristic
552	#382	C₂²×C₃₁	1	2	yes	—
553	#382	C₂²×C₃₁	1	2	yes	—
554	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
555	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
558	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
559	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
565	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
566	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
569	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
571	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
572	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
573	#376	C₂²×C₃₁	1	1	yes	characteristic
574	#376	C₂²×C₃₁	1	2	yes	—
575	C₄³	C₂²×C₃₁	1	1	yes	characteristic
576	C₂×C₃₁	—	4	2	no	—
577	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
578	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
579	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
580	C₂×C₃₁	#3552	1	1	yes	characteristic
581	C₂×C₃₁	#3555	1	1	yes	characteristic
582	C₂×C₃₁	#3562	1	1	yes	characteristic
583	C₂×C₃₁	#3563	1	1	yes	characteristic
584	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
588	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
589	#126	C₂×C₄×C₃₁	1	16	yes	—
590	#126	C₂×C₄×C₃₁	1	16	yes	—
591	#125	C₂×C₄×C₃₁	1	8	yes	complemented
592	#125	C₂×C₄×C₃₁	1	16	yes	complemented
593	#125	C₂×C₄×C₃₁	1	16	yes	complemented
594	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
595	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
596	C₄×Q₈	—	4	2	no	—
597	C₄×Q₈	—	4	2	no	—
598	C₄×Q₈	—	4	2	no	—
599	C₄×Q₈	—	4	2	no	—
600	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
601	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
602	#117	—	4	2	no	—
603	#117	C₂×C₄×C₃₁	1	8	yes	—
604	C₂×C₄⋊C₄	—	4	2	no	—
605	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
654	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
659	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
662	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
664	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
667	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
668	#95	C₂³×C₃₁	1	1	yes	characteristic
669	#95	C₂³×C₃₁	1	2	yes	—
670	#95	C₂³×C₃₁	1	2	yes	—
671	#95	C₂³×C₃₁	1	1	yes	characteristic
672	#95	C₂³×C₃₁	1	1	yes	characteristic
673	#95	C₂³×C₃₁	1	2	yes	—
674	#95	C₂³×C₃₁	1	1	yes	characteristic
675	#95	C₂³×C₃₁	1	1	yes	characteristic
676	#95	C₂³×C₃₁	1	1	yes	characteristic
677	#95	C₂³×C₃₁	1	2	yes	—
678	#95	C₂³×C₃₁	1	1	yes	characteristic
679	#95	C₂³×C₃₁	1	2	yes	—
680	#95	C₂³×C₃₁	1	2	yes	—
681	#95	C₂³×C₃₁	1	1	yes	characteristic
682	#95	C₂³×C₃₁	1	1	yes	characteristic
683	#95	C₂³×C₃₁	1	1	yes	characteristic
684	#95	C₂³×C₃₁	1	2	yes	—
685	#95	C₂³×C₃₁	1	2	yes	—
686	#95	C₂³×C₃₁	1	1	yes	characteristic
687	#95	C₂³×C₃₁	1	2	yes	—
688	#95	C₂³×C₃₁	1	2	yes	—
689	#95	C₂³×C₃₁	1	2	yes	—
690	#95	C₂³×C₃₁	1	2	yes	—
691	#95	C₂³×C₃₁	1	2	yes	—
692	#95	C₂³×C₃₁	1	2	yes	—
693	#95	C₂³×C₃₁	1	1	yes	characteristic
694	#95	C₂³×C₃₁	1	2	yes	—
695	#95	C₂³×C₃₁	1	2	yes	—
696	#95	C₂³×C₃₁	1	2	yes	—
697	#95	C₂³×C₃₁	1	2	yes	—
698	#95	C₂³×C₃₁	1	2	yes	—
699	#95	C₂³×C₃₁	1	2	yes	—
700	C₃₁	#34430	1	1	yes	characteristic, direct product factor, Sylow
701	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
707	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
714	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	1	no	—
750	C₄⋊C₄	—	4	1	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
758	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
759	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
760	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
761	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
762	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
763	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
764	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
765	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
766	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
767	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
768	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	4	1	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
775	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
776	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
777	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	4	2	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	1	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
796	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
797	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
798	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
806	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
807	Q₈	—	2	8	no	—
808	Q₈	—	2	8	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	8	4	no	—
863	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
864	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
865	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
866	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
867	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
868	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
869	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
870	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
871	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
872	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
873	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
874	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
875	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
876	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
885	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
887	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
888	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
889	C₂²	C₃₁×#585	1	1	yes	characteristic
890	C₂²	C₃₁×#585	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	1	no	—
912	C₄	C₃₁×#520	1	4	yes	—
913	C₂	—	4	2	no	—
914	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
915	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
916	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
917	C₂	C₃₁×#3552	1	1	yes	characteristic
918	C₂	C₃₁×#3555	1	1	yes	characteristic
919	C₂	C₃₁×#3562	1	1	yes	characteristic
920	C₂	C₃₁×#3563	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃₁×#2382	C₂	semidirect
5. C₃₁×#2370	C₂	semidirect
10. C₃₁×#2356	C₂	semidirect
11. C₃₁×#2355	C₂	semidirect
12. C₃₁×#2351	C₂	semidirect
13. Q₈×C₄⋊C₄×C₃₁	C₂	semidirect
14. C₃₁×#2336	C₂	semidirect
17. C₃₁×#2330	C₂	semidirect
18. C₃₁×#2330	C₂	semidirect
19. C₃₁×#2327	C₂	semidirect
21. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
22. C₄×C₃₁×#125	C₂	semidirect
24. C₃₁×#541	C₄	semidirect
128. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
131. C₃₁×#125	C₂×C₄	semidirect
132. C₃₁×#125	C₂×C₄	semidirect
133. C₃₁×#125	C₂×C₄	semidirect
140. C₄×Q₈×C₃₁	C₂×C₄	semidirect
141. C₄×Q₈×C₃₁	C₂×C₄	semidirect
338. #34430	C₃₁	direct (N × H)
419. #2382	C₂×C₃₁	semidirect
421. #2370	C₂×C₃₁	semidirect
426. #2356	C₂×C₃₁	semidirect
427. #2355	C₂×C₃₁	semidirect
428. #2351	C₂×C₃₁	semidirect
429. Q₈×C₄⋊C₄	C₂×C₃₁	semidirect
430. #2336	C₂×C₃₁	semidirect
433. #2330	C₂×C₃₁	semidirect
434. #2330	C₂×C₃₁	semidirect
435. #2327	C₂×C₃₁	semidirect
437. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
438. C₄×#125	C₂×C₃₁	semidirect
476. #541	C₄×C₃₁	semidirect
588. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
591. #125	C₂×C₄×C₃₁	semidirect
592. #125	C₂×C₄×C₃₁	semidirect
593. #125	C₂×C₄×C₃₁	semidirect
600. C₄×Q₈	C₂×C₄×C₃₁	semidirect
601. C₄×Q₈	C₂×C₄×C₃₁	semidirect
700. C₃₁	#34430	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×#541	2
C₃₁×#2383	2
C₃₁×#2382	2
C₃₁×#2373	2
C₃₁×#2370	2
C₃₁×#2362	2
C₃₁×#2360	2
C₃₁×#2356	2
C₃₁×#2355	2
C₃₁×#2351	2
Q₈×C₄⋊C₄×C₃₁	2
C₃₁×#2336	2
C₃₁×#2334	2
C₃₁×#2330	2
C₃₁×#2327	2
C₃₁×#2317	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#125	2
C₃₁×#2298	2
#34430	31

Subgroups — C31×#34430 #21491189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34430 #21491189