Subgroups — C₃₁×#34428 #21491187

Order 7936.

2174 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#542	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2379	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2378	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2367	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2363	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2361	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2360	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2357	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	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2335	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2317	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#542	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×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#124	C₂²	1	2	yes	—
29	C₂×C₃₁×#123	C₂²	1	2	yes	—
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
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×D₄×C₃₁	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
45	C₃₁×#391	C₂²	1	2	yes	—
46	C₃₁×#391	C₂²	1	1	yes	characteristic
47	C₃₁×#391	C₂²	1	2	yes	—
48	C₃₁×#391	C₂²	1	2	yes	—
49	C₃₁×#391	C₂²	1	1	yes	characteristic
50	C₃₁×#390	C₂²	1	1	yes	characteristic
51	C₃₁×#390	C₂²	1	2	yes	—
52	C₃₁×#390	C₂²	1	1	yes	characteristic
53	C₃₁×#389	C₂²	1	2	yes	—
54	C₃₁×#389	C₂²	1	1	yes	characteristic
55	C₃₁×#389	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	2	yes	—
62	C₃₁×#389	C₂²	1	2	yes	—
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	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	1	yes	characteristic
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	1	yes	characteristic
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
81	C₃₁×#387	C₂²	1	1	yes	characteristic
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	1	yes	characteristic
86	C₃₁×#387	C₂²	1	1	yes	characteristic
87	C₃₁×#386	C₂²	1	2	yes	—
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#385	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×#385	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#384	C₂²	1	1	yes	characteristic
98	C₃₁×#384	C₂²	1	1	yes	characteristic
99	C₃₁×#382	C₂²	1	1	yes	characteristic
100	C₃₁×#382	C₂²	1	1	yes	characteristic
101	C₃₁×#382	C₂²	1	2	yes	—
102	C₃₁×#382	C₂²	1	2	yes	—
103	C₃₁×#381	C₂²	1	2	yes	—
104	C₃₁×#380	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊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	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	2	yes	—
121	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
122	C₃₁×#376	C₂²	1	1	yes	characteristic
123	C₄³×C₃₁	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
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	C₂×C₄	1	8	yes	complemented
134	C₃₁×#126	C₂×C₄	1	16	yes	complemented
135	C₃₁×#124	C₂×C₄	1	8	yes	complemented
136	C₃₁×#124	C₂×C₄	1	16	yes	complemented
137	C₃₁×#123	C₂×C₄	1	16	yes	complemented
138	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
139	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
140	C₃₁×#121	C₂×C₄	1	8	yes	—
141	C₄×Q₈×C₃₁	—	4	4	no	—
142	C₄×Q₈×C₃₁	—	4	2	no	—
143	C₄×Q₈×C₃₁	—	4	2	no	—
144	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
145	C₄×D₄×C₃₁	—	4	2	no	—
146	C₄×D₄×C₃₁	—	4	2	no	—
147	C₄×D₄×C₃₁	—	4	4	no	—
148	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
149	C₃₁×#117	—	4	2	no	—
150	C₃₁×#117	C₂×C₄	1	8	yes	complemented
151	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
152	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
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	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
205	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
209	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
212	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	1	yes	characteristic
216	C₃₁×#95	C₂³	1	1	yes	characteristic
217	C₃₁×#95	C₂³	1	1	yes	characteristic
218	C₃₁×#95	C₂³	1	1	yes	characteristic
219	C₃₁×#95	C₂³	1	1	yes	characteristic
220	C₃₁×#95	C₂³	1	1	yes	characteristic
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	1	yes	characteristic
223	C₃₁×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₃₁×#95	C₂³	1	2	yes	—
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	2	yes	—
243	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₃₁	—	2	2	no	—
246	C₂×Q₈×C₃₁	—	2	2	no	—
247	C₂×Q₈×C₃₁	—	4	2	no	—
248	C₂×Q₈×C₃₁	—	4	2	no	—
249	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
250	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	4	2	no	—
254	C₂×D₄×C₃₁	—	4	2	no	—
255	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
256	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	4	no	—
260	C₂²×C₄×C₃₁	—	4	2	no	—
261	C₂²×C₄×C₃₁	—	4	2	no	—
262	C₂²×C₄×C₃₁	—	4	2	no	—
263	C₂²×C₄×C₃₁	—	4	2	no	—
264	C₂²×C₄×C₃₁	—	4	2	no	—
265	C₂²×C₄×C₃₁	—	4	2	no	—
266	C₂²×C₄×C₃₁	—	4	2	no	—
267	C₂²×C₄×C₃₁	—	4	2	no	—
268	C₂²×C₄×C₃₁	—	4	2	no	—
269	C₂²×C₄×C₃₁	—	4	2	no	—
270	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
271	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
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	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	4	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	4	2	no	—
302	C₄⋊C₄×C₃₁	—	4	2	no	—
303	C₄⋊C₄×C₃₁	—	4	2	no	—
304	C₄⋊C₄×C₃₁	—	4	2	no	—
305	C₄⋊C₄×C₃₁	—	4	1	no	—
306	C₄⋊C₄×C₃₁	—	4	2	no	—
307	C₄⋊C₄×C₃₁	—	4	1	no	—
308	C₄⋊C₄×C₃₁	—	4	2	no	—
309	C₄⋊C₄×C₃₁	—	4	2	no	—
310	C₄⋊C₄×C₃₁	—	4	2	no	—
311	C₄⋊C₄×C₃₁	—	4	2	no	—
312	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
313	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
314	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
315	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
316	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
317	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
318	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	4	1	no	—
323	C₂²⋊C₄×C₃₁	—	4	2	no	—
324	C₂²⋊C₄×C₃₁	—	4	1	no	—
325	C₂²⋊C₄×C₃₁	—	4	2	no	—
326	C₂²⋊C₄×C₃₁	—	4	2	no	—
327	C₂²⋊C₄×C₃₁	—	4	2	no	—
328	C₂²⋊C₄×C₃₁	—	4	2	no	—
329	C₂²⋊C₄×C₃₁	—	4	2	no	—
330	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
331	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
332	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
333	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
334	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
335	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
336	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	—	2	2	no	—
339	C₄²×C₃₁	—	2	2	no	—
340	C₄²×C₃₁	—	2	2	no	—
341	C₄²×C₃₁	—	2	2	no	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	4	1	no	—
344	C₄²×C₃₁	—	4	2	no	—
345	C₄²×C₃₁	—	4	1	no	—
346	C₄²×C₃₁	—	4	2	no	—
347	C₄²×C₃₁	—	4	2	no	—
348	C₄²×C₃₁	—	4	2	no	—
349	C₄²×C₃₁	—	4	2	no	—
350	C₄²×C₃₁	—	4	2	no	—
351	C₄²×C₃₁	—	4	2	no	—
352	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
353	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
354	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
355	#34428	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
356	C₂³×C₃₁	—	2	1	no	—
357	C₂³×C₃₁	—	2	1	no	—
358	C₂³×C₃₁	—	2	2	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	2	1	no	—
361	C₂³×C₃₁	—	2	2	no	—
362	C₂³×C₃₁	—	2	1	no	—
363	C₂³×C₃₁	—	2	2	no	—
364	C₂³×C₃₁	—	2	2	no	—
365	C₂³×C₃₁	—	2	1	no	—
366	C₂³×C₃₁	—	2	2	no	—
367	C₂³×C₃₁	—	2	1	no	—
368	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
369	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
370	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
371	Q₈×C₃₁	—	2	8	no	—
372	Q₈×C₃₁	—	4	8	no	—
373	D₄×C₃₁	—	2	8	no	—
374	D₄×C₃₁	—	4	8	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	2	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	2	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	2	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	8	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	1	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	—	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	1	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	1	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	1	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	2	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	1	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	4	8	no	—
427	C₂×C₄×C₃₁	—	8	4	no	—
428	C₂×C₄×C₃₁	—	8	4	no	—
429	C₂×C₄×C₃₁	—	8	4	no	—
430	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
433	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
434	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
436	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
437	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
438	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
440	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
442	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
443	C₂×#542	C₂×C₃₁	1	1	yes	characteristic
444	#2379	C₂×C₃₁	1	2	yes	complemented
445	#2378	C₂×C₃₁	1	2	yes	complemented
446	#2367	C₂×C₃₁	1	2	yes	complemented
447	#2363	C₂×C₃₁	1	1	yes	characteristic
448	#2362	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#2361	C₂×C₃₁	1	1	yes	characteristic
450	#2360	C₂×C₃₁	1	1	yes	characteristic, complemented
451	#2360	C₂×C₃₁	1	2	yes	complemented
452	#2357	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#2351	C₂×C₃₁	1	1	yes	characteristic, complemented
455	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#2335	C₂×C₃₁	1	2	yes	complemented
457	#2334	C₂×C₃₁	1	2	yes	complemented
458	#2334	C₂×C₃₁	1	2	yes	complemented
459	#2331	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#2326	C₂×C₃₁	1	1	yes	characteristic, complemented
461	#2322	C₂×C₃₁	1	2	yes	complemented
462	#2317	C₂×C₃₁	1	1	yes	characteristic, complemented
463	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
464	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#2298	C₂×C₃₁	1	1	yes	characteristic, complemented
466	C₂²×C₃₁	—	2	2	no	—
467	C₂²×C₃₁	—	2	4	no	—
468	C₂²×C₃₁	—	2	4	no	—
469	C₂²×C₃₁	—	2	2	no	—
470	C₂²×C₃₁	—	2	2	no	—
471	C₂²×C₃₁	—	2	4	no	—
472	C₂²×C₃₁	—	4	1	no	—
473	C₂²×C₃₁	—	4	2	no	—
474	C₂²×C₃₁	—	4	1	no	—
475	C₂²×C₃₁	—	4	2	no	—
476	C₂²×C₃₁	—	4	2	no	—
477	C₂²×C₃₁	—	4	1	no	—
478	C₂²×C₃₁	—	4	1	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
481	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂²×C₃₁	#585	1	1	yes	characteristic
486	C₂²×C₃₁	#585	1	1	yes	characteristic
487	C₄×C₃₁	—	2	2	no	—
488	C₄×C₃₁	—	2	4	no	—
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	2	4	no	—
491	C₄×C₃₁	—	2	4	no	—
492	C₄×C₃₁	—	2	2	no	—
493	C₄×C₃₁	—	2	2	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	2	2	no	—
496	C₄×C₃₁	—	2	2	no	—
497	C₄×C₃₁	—	4	1	no	—
498	C₄×C₃₁	—	4	1	no	—
499	C₄×C₃₁	—	4	1	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	—	4	2	no	—
503	C₄×C₃₁	—	4	1	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	—	4	1	no	—
506	C₄×C₃₁	—	4	1	no	—
507	C₄×C₃₁	#520	1	4	yes	—
508	#542	C₄×C₃₁	1	16	yes	complemented
509	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
510	C₂×#126	C₂²×C₃₁	1	2	yes	—
511	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
512	C₂×#124	C₂²×C₃₁	1	2	yes	—
513	C₂×#123	C₂²×C₃₁	1	2	yes	—
514	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
516	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
517	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
518	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
520	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
521	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
525	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
527	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
528	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
529	#391	C₂²×C₃₁	1	2	yes	—
530	#391	C₂²×C₃₁	1	1	yes	characteristic
531	#391	C₂²×C₃₁	1	2	yes	—
532	#391	C₂²×C₃₁	1	2	yes	—
533	#391	C₂²×C₃₁	1	1	yes	characteristic
534	#390	C₂²×C₃₁	1	1	yes	characteristic
535	#390	C₂²×C₃₁	1	2	yes	—
536	#390	C₂²×C₃₁	1	1	yes	characteristic
537	#389	C₂²×C₃₁	1	2	yes	—
538	#389	C₂²×C₃₁	1	1	yes	characteristic
539	#389	C₂²×C₃₁	1	1	yes	characteristic
540	#389	C₂²×C₃₁	1	2	yes	—
541	#389	C₂²×C₃₁	1	2	yes	—
542	#389	C₂²×C₃₁	1	2	yes	—
543	#389	C₂²×C₃₁	1	1	yes	characteristic
544	#389	C₂²×C₃₁	1	1	yes	characteristic
545	#389	C₂²×C₃₁	1	2	yes	—
546	#389	C₂²×C₃₁	1	2	yes	—
547	#388	C₂²×C₃₁	1	1	yes	characteristic
548	#388	C₂²×C₃₁	1	2	yes	—
549	#388	C₂²×C₃₁	1	2	yes	—
550	#388	C₂²×C₃₁	1	2	yes	—
551	#388	C₂²×C₃₁	1	2	yes	—
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	1	yes	characteristic
557	#388	C₂²×C₃₁	1	2	yes	—
558	#388	C₂²×C₃₁	1	1	yes	characteristic
559	#388	C₂²×C₃₁	1	2	yes	—
560	#388	C₂²×C₃₁	1	1	yes	characteristic
561	#387	C₂²×C₃₁	1	2	yes	—
562	#387	C₂²×C₃₁	1	2	yes	—
563	#387	C₂²×C₃₁	1	2	yes	—
564	#387	C₂²×C₃₁	1	1	yes	characteristic
565	#387	C₂²×C₃₁	1	1	yes	characteristic
566	#387	C₂²×C₃₁	1	2	yes	—
567	#387	C₂²×C₃₁	1	2	yes	—
568	#387	C₂²×C₃₁	1	2	yes	—
569	#387	C₂²×C₃₁	1	1	yes	characteristic
570	#387	C₂²×C₃₁	1	1	yes	characteristic
571	#386	C₂²×C₃₁	1	2	yes	—
572	#386	C₂²×C₃₁	1	2	yes	—
573	#385	C₂²×C₃₁	1	2	yes	—
574	#385	C₂²×C₃₁	1	2	yes	—
575	#385	C₂²×C₃₁	1	2	yes	—
576	#385	C₂²×C₃₁	1	2	yes	—
577	#385	C₂²×C₃₁	1	2	yes	—
578	#385	C₂²×C₃₁	1	2	yes	—
579	#385	C₂²×C₃₁	1	2	yes	—
580	#385	C₂²×C₃₁	1	2	yes	—
581	#384	C₂²×C₃₁	1	1	yes	characteristic
582	#384	C₂²×C₃₁	1	1	yes	characteristic
583	#382	C₂²×C₃₁	1	1	yes	characteristic
584	#382	C₂²×C₃₁	1	1	yes	characteristic
585	#382	C₂²×C₃₁	1	2	yes	—
586	#382	C₂²×C₃₁	1	2	yes	—
587	#381	C₂²×C₃₁	1	2	yes	—
588	#380	C₂²×C₃₁	1	2	yes	—
589	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
595	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
596	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
597	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
599	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
600	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
601	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
603	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
604	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
605	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
606	#376	C₂²×C₃₁	1	1	yes	characteristic
607	C₄³	C₂²×C₃₁	1	1	yes	characteristic
608	C₂×C₃₁	—	4	2	no	—
609	C₂×C₃₁	—	4	4	no	—
610	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
611	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
613	C₂×C₃₁	#3552	1	1	yes	characteristic
614	C₂×C₃₁	#3554	1	1	yes	characteristic
615	C₂×C₃₁	#3558	1	1	yes	characteristic
616	C₂×C₃₁	#3565	1	1	yes	characteristic
617	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
619	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
621	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
623	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
624	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
625	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
626	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
627	#126	C₂×C₄×C₃₁	1	16	yes	complemented
628	#124	C₂×C₄×C₃₁	1	8	yes	complemented
629	#124	C₂×C₄×C₃₁	1	16	yes	complemented
630	#123	C₂×C₄×C₃₁	1	16	yes	complemented
631	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
632	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
633	#121	C₂×C₄×C₃₁	1	8	yes	—
634	C₄×Q₈	—	4	4	no	—
635	C₄×Q₈	—	4	2	no	—
636	C₄×Q₈	—	4	2	no	—
637	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
638	C₄×D₄	—	4	2	no	—
639	C₄×D₄	—	4	2	no	—
640	C₄×D₄	—	4	4	no	—
641	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
642	#117	—	4	2	no	—
643	#117	C₂×C₄×C₃₁	1	8	yes	complemented
644	C₂×C₄⋊C₄	—	4	4	no	—
645	C₂×C₄⋊C₄	—	4	2	no	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×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	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
697	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
698	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
699	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
700	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
701	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
702	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
705	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
708	#95	C₂³×C₃₁	1	1	yes	characteristic
709	#95	C₂³×C₃₁	1	1	yes	characteristic
710	#95	C₂³×C₃₁	1	1	yes	characteristic
711	#95	C₂³×C₃₁	1	1	yes	characteristic
712	#95	C₂³×C₃₁	1	1	yes	characteristic
713	#95	C₂³×C₃₁	1	1	yes	characteristic
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
723	#95	C₂³×C₃₁	1	1	yes	characteristic
724	#95	C₂³×C₃₁	1	1	yes	characteristic
725	#95	C₂³×C₃₁	1	2	yes	—
726	#95	C₂³×C₃₁	1	1	yes	characteristic
727	#95	C₂³×C₃₁	1	2	yes	—
728	#95	C₂³×C₃₁	1	2	yes	—
729	#95	C₂³×C₃₁	1	1	yes	characteristic
730	#95	C₂³×C₃₁	1	2	yes	—
731	#95	C₂³×C₃₁	1	2	yes	—
732	#95	C₂³×C₃₁	1	2	yes	—
733	#95	C₂³×C₃₁	1	2	yes	—
734	#95	C₂³×C₃₁	1	2	yes	—
735	#95	C₂³×C₃₁	1	2	yes	—
736	C₃₁	#34428	1	1	yes	characteristic, direct product factor, Sylow
737	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
738	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	4	2	no	—
742	C₂×Q₈	—	4	2	no	—
743	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
744	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
750	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
765	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
766	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
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	2	yes	—
781	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	1	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	1	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
807	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
808	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
809	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
810	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
811	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
812	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	4	1	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	1	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	4	1	no	—
838	C₄²	—	4	2	no	—
839	C₄²	—	4	1	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	—	4	2	no	—
845	C₄²	—	4	2	no	—
846	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
847	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
848	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	1	no	—
861	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
862	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
863	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
864	Q₈	—	2	8	no	—
865	Q₈	—	4	8	no	—
866	D₄	—	2	8	no	—
867	D₄	—	4	8	no	—
868	C₂×C₄	—	2	1	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	2	no	—
874	C₂×C₄	—	2	2	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	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	4	8	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	—	8	4	no	—
922	C₂×C₄	—	8	4	no	—
923	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
924	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
925	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
926	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
927	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
928	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
929	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
930	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
931	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
932	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
933	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
934	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
935	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
951	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
954	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
955	C₂²	C₃₁×#585	1	1	yes	characteristic
956	C₂²	C₃₁×#585	1	1	yes	characteristic
957	C₄	—	2	2	no	—
958	C₄	—	2	4	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	1	no	—
977	C₄	C₃₁×#520	1	4	yes	—
978	C₂	—	4	2	no	—
979	C₂	—	4	4	no	—
980	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
981	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
983	C₂	C₃₁×#3552	1	1	yes	characteristic
984	C₂	C₃₁×#3554	1	1	yes	characteristic
985	C₂	C₃₁×#3558	1	1	yes	characteristic
986	C₂	C₃₁×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
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
2. C₃₁×#2379	C₂	semidirect
3. C₃₁×#2378	C₂	semidirect
4. C₃₁×#2367	C₂	semidirect
6. C₃₁×#2362	C₂	semidirect
8. C₃₁×#2360	C₂	semidirect
9. C₃₁×#2360	C₂	semidirect
10. C₃₁×#2357	C₂	semidirect
11. C₃₁×#2355	C₂	semidirect
12. C₃₁×#2351	C₂	semidirect
13. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
14. C₃₁×#2335	C₂	semidirect
15. C₃₁×#2334	C₂	semidirect
16. C₃₁×#2334	C₂	semidirect
17. C₃₁×#2331	C₂	semidirect
18. C₃₁×#2326	C₂	semidirect
19. C₃₁×#2322	C₂	semidirect
20. C₃₁×#2317	C₂	semidirect
21. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
22. C₄×C₃₁×#124	C₂	semidirect
23. C₃₁×#2298	C₂	semidirect
24. C₃₁×#542	C₄	semidirect
133. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
134. C₃₁×#126	C₂×C₄	semidirect
135. C₃₁×#124	C₂×C₄	semidirect
136. C₃₁×#124	C₂×C₄	semidirect
137. C₃₁×#123	C₂×C₄	semidirect
138. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
139. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
144. C₄×Q₈×C₃₁	C₂×C₄	semidirect
148. C₄×D₄×C₃₁	C₂×C₄	semidirect
150. C₃₁×#117	C₂×C₄	semidirect
355. #34428	C₃₁	direct (N × H)
444. #2379	C₂×C₃₁	semidirect
445. #2378	C₂×C₃₁	semidirect
446. #2367	C₂×C₃₁	semidirect
448. #2362	C₂×C₃₁	semidirect
450. #2360	C₂×C₃₁	semidirect
451. #2360	C₂×C₃₁	semidirect
452. #2357	C₂×C₃₁	semidirect
453. #2355	C₂×C₃₁	semidirect
454. #2351	C₂×C₃₁	semidirect
455. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
456. #2335	C₂×C₃₁	semidirect
457. #2334	C₂×C₃₁	semidirect
458. #2334	C₂×C₃₁	semidirect
459. #2331	C₂×C₃₁	semidirect
460. #2326	C₂×C₃₁	semidirect
461. #2322	C₂×C₃₁	semidirect
462. #2317	C₂×C₃₁	semidirect
463. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
464. C₄×#124	C₂×C₃₁	semidirect
465. #2298	C₂×C₃₁	semidirect
508. #542	C₄×C₃₁	semidirect
626. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
627. #126	C₂×C₄×C₃₁	semidirect
628. #124	C₂×C₄×C₃₁	semidirect
629. #124	C₂×C₄×C₃₁	semidirect
630. #123	C₂×C₄×C₃₁	semidirect
631. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
632. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
637. C₄×Q₈	C₂×C₄×C₃₁	semidirect
641. C₄×D₄	C₂×C₄×C₃₁	semidirect
643. #117	C₂×C₄×C₃₁	semidirect
736. C₃₁	#34428	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×#542	2
C₃₁×#2379	2
C₃₁×#2378	2
C₃₁×#2367	2
C₃₁×#2363	2
C₃₁×#2362	2
C₃₁×#2361	2
C₃₁×#2360	2
C₃₁×#2357	2
C₃₁×#2355	2
C₃₁×#2351	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2335	2
C₃₁×#2334	2
C₃₁×#2331	2
C₃₁×#2326	2
C₃₁×#2322	2
C₃₁×#2317	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#124	2
C₃₁×#2298	2
#34428	31

Subgroups — C31×#34428 #21491187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34428 #21491187