Subgroups — C₃₁×#34260 #21491019

Order 7936.

2462 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2352	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2345	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2344	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2339	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2339	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2313	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
21	C₂×C₃₁×#387	C₂	1	2	yes	maximal, complemented
22	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#520	C₄	1	16	yes	complemented
26	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	2	yes	—
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#117	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
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×#391	C₂²	1	1	yes	characteristic
47	C₃₁×#389	C₂²	1	1	yes	characteristic
48	C₃₁×#389	C₂²	1	1	yes	characteristic
49	C₃₁×#389	C₂²	1	1	yes	characteristic
50	C₃₁×#389	C₂²	1	1	yes	characteristic
51	C₃₁×#388	C₂²	1	2	yes	—
52	C₃₁×#388	C₂²	1	2	yes	—
53	C₃₁×#388	C₂²	1	1	yes	characteristic
54	C₃₁×#388	C₂²	1	1	yes	characteristic
55	C₃₁×#388	C₂²	1	1	yes	characteristic
56	C₃₁×#388	C₂²	1	1	yes	characteristic
57	C₃₁×#387	C₂²	1	1	yes	characteristic
58	C₃₁×#387	C₂²	1	2	yes	—
59	C₃₁×#387	C₂²	1	2	yes	—
60	C₃₁×#387	C₂²	1	2	yes	—
61	C₃₁×#387	C₂²	1	2	yes	—
62	C₃₁×#387	C₂²	1	2	yes	—
63	C₃₁×#387	C₂²	1	2	yes	—
64	C₃₁×#387	C₂²	1	2	yes	—
65	C₃₁×#387	C₂²	1	2	yes	—
66	C₃₁×#387	C₂²	1	2	yes	—
67	C₃₁×#387	C₂²	1	1	yes	characteristic
68	C₃₁×#387	C₂²	1	1	yes	characteristic
69	C₃₁×#387	C₂²	1	2	yes	—
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	1	yes	characteristic
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#386	C₂²	1	2	yes	—
76	C₃₁×#386	C₂²	1	2	yes	—
77	C₃₁×#386	C₂²	1	2	yes	—
78	C₃₁×#386	C₂²	1	2	yes	—
79	C₃₁×#385	C₂²	1	2	yes	—
80	C₃₁×#385	C₂²	1	2	yes	—
81	C₃₁×#385	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#384	C₂²	1	1	yes	characteristic
84	C₃₁×#383	C₂²	1	2	yes	—
85	C₃₁×#383	C₂²	1	2	yes	—
86	C₃₁×#382	C₂²	1	1	yes	characteristic
87	C₃₁×#382	C₂²	1	2	yes	—
88	C₃₁×#382	C₂²	1	2	yes	—
89	C₃₁×#381	C₂²	1	2	yes	—
90	C₃₁×#381	C₂²	1	2	yes	—
91	C₃₁×#381	C₂²	1	2	yes	—
92	C₃₁×#380	C₂²	1	2	yes	—
93	C₃₁×#380	C₂²	1	2	yes	—
94	C₃₁×#380	C₂²	1	1	yes	characteristic
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₃₁×#380	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	2	yes	—
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	1	yes	characteristic
107	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₃₁×#376	C₂²	1	1	yes	characteristic
117	C₃₁×#376	C₂²	1	2	yes	—
118	C₃₁×#376	C₂²	1	2	yes	—
119	C₂×C₃₁×#95	C₂²	1	2	yes	—
120	C₂×C₃₁×#95	C₂²	1	2	yes	—
121	C₂×C₃₁×#95	C₂²	1	2	yes	—
122	C₂×C₃₁×#95	C₂²	1	2	yes	—
123	C₄³×C₃₁	C₂²	1	1	yes	characteristic
124	C₂×#41×C₃₁	—	2	4	no	—
125	C₂×#41×C₃₁	—	2	4	no	—
126	C₂×#41×C₃₁	C₂×C₄	1	8	yes	—
127	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂²×D₄×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	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
135	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
138	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
139	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
140	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
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	—	2	4	no	—
145	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
146	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
147	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
148	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
149	C₃₁×#117	—	4	4	no	—
150	C₃₁×#117	C₂×C₄	1	8	yes	complemented
151	C₃₁×#117	C₂×C₄	1	16	yes	complemented
152	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
153	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
154	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	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	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	—	4	4	no	—
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
209	C₃₁×#95	C₂³	1	1	yes	characteristic
210	C₃₁×#95	C₂³	1	1	yes	characteristic
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	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	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	1	yes	characteristic
227	C₃₁×#95	C₂³	1	1	yes	characteristic
228	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
238	C₃₁×#95	C₂³	1	1	yes	characteristic
239	C₃₁×#95	C₂³	1	1	yes	characteristic
240	C₃₁×#95	C₂³	1	2	yes	—
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	1	yes	characteristic
243	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
245	#41×C₃₁	—	2	32	no	—
246	C₂×Q₈×C₃₁	—	2	2	no	—
247	C₂×Q₈×C₃₁	—	2	2	no	—
248	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
252	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
253	C₂×D₄×C₃₁	#41	1	4	yes	—
254	C₂×D₄×C₃₁	#41	1	4	yes	—
255	C₂²×C₄×C₃₁	—	2	4	no	—
256	C₂²×C₄×C₃₁	—	2	4	no	—
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	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	4	no	—
262	C₂²×C₄×C₃₁	—	2	4	no	—
263	C₂²×C₄×C₃₁	—	2	4	no	—
264	C₂²×C₄×C₃₁	—	2	4	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	—	4	2	no	—
271	C₂²×C₄×C₃₁	—	4	2	no	—
272	C₂²×C₄×C₃₁	—	4	2	no	—
273	C₂²×C₄×C₃₁	—	4	2	no	—
274	C₂²×C₄×C₃₁	—	4	2	no	—
275	C₂²×C₄×C₃₁	—	4	2	no	—
276	C₂²×C₄×C₃₁	—	4	2	no	—
277	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
278	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
279	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
280	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
281	C₂²×C₄×C₃₁	C₂²×C₄	1	8	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	1	yes	characteristic
285	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	2	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	4	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	4	2	no	—
311	C₄⋊C₄×C₃₁	—	4	2	no	—
312	C₄⋊C₄×C₃₁	—	4	1	no	—
313	C₄⋊C₄×C₃₁	—	4	2	no	—
314	C₄⋊C₄×C₃₁	—	4	1	no	—
315	C₄⋊C₄×C₃₁	—	4	2	no	—
316	C₄⋊C₄×C₃₁	—	4	2	no	—
317	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
318	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
319	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
320	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
321	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
322	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
323	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	4	1	no	—
331	C₂²⋊C₄×C₃₁	—	4	1	no	—
332	C₂²⋊C₄×C₃₁	—	4	2	no	—
333	C₂²⋊C₄×C₃₁	—	4	2	no	—
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	4	yes	—
337	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
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	—	2	4	no	—
344	C₄²×C₃₁	—	2	2	no	—
345	C₄²×C₃₁	—	4	2	no	—
346	C₄²×C₃₁	—	4	2	no	—
347	C₄²×C₃₁	—	4	1	no	—
348	C₄²×C₃₁	—	4	2	no	—
349	C₄²×C₃₁	—	4	2	no	—
350	C₄²×C₃₁	—	4	1	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	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
356	#34260	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂³×C₃₁	—	2	2	no	—
358	C₂³×C₃₁	—	2	2	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	2	2	no	—
361	C₂³×C₃₁	—	2	1	no	—
362	C₂³×C₃₁	—	2	1	no	—
363	C₂³×C₃₁	—	2	1	no	—
364	C₂³×C₃₁	—	2	1	no	—
365	C₂³×C₃₁	—	2	1	no	—
366	C₂³×C₃₁	—	2	1	no	—
367	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
368	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
369	C₂³×C₃₁	C₂×#41	1	4	yes	—
370	C₂³×C₃₁	C₂×#41	1	4	yes	—
371	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
372	Q₈×C₃₁	—	2	8	no	—
373	D₄×C₃₁	—	2	16	no	—
374	D₄×C₃₁	#117	1	16	yes	complemented
375	C₂×C₄×C₃₁	—	2	16	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	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	2	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	2	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	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	1	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	8	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	1	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	1	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	2	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	1	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	1	no	—
414	C₂×C₄×C₃₁	—	2	1	no	—
415	C₂×C₄×C₃₁	—	2	2	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	2	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	4	8	no	—
428	C₂×C₄×C₃₁	—	4	8	no	—
429	C₂×C₄×C₃₁	—	4	8	no	—
430	C₂×C₄×C₃₁	—	4	8	no	—
431	C₂×C₄×C₃₁	—	4	8	no	—
432	C₂×C₄×C₃₁	—	8	4	no	—
433	C₂×C₄×C₃₁	—	8	4	no	—
434	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
436	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
437	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
438	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
440	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
441	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
443	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
444	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
445	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
446	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
447	C₂×#520	C₂×C₃₁	1	1	yes	characteristic
448	#2356	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
450	#2353	C₂×C₃₁	1	2	yes	complemented
451	#2352	C₂×C₃₁	1	2	yes	complemented
452	#2349	C₂×C₃₁	1	1	yes	characteristic, complemented
453	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#2345	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#2344	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#2343	C₂×C₃₁	1	2	yes	complemented
457	#2343	C₂×C₃₁	1	2	yes	complemented
458	#2339	C₂×C₃₁	1	1	yes	characteristic
459	#2339	C₂×C₃₁	1	1	yes	characteristic
460	#2320	C₂×C₃₁	1	1	yes	characteristic, complemented
461	#2318	C₂×C₃₁	1	2	yes	complemented
462	#2314	C₂×C₃₁	1	1	yes	characteristic, complemented
463	#2313	C₂×C₃₁	1	2	yes	complemented
464	#2298	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
466	#2290	C₂×C₃₁	1	2	yes	complemented
467	C₂×#387	C₂×C₃₁	1	2	yes	complemented
468	#2275	C₂×C₃₁	1	1	yes	characteristic, complemented
469	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
470	C₂²×C₃₁	—	2	4	no	—
471	C₂²×C₃₁	—	2	4	no	—
472	C₂²×C₃₁	—	2	4	no	—
473	C₂²×C₃₁	—	2	4	no	—
474	C₂²×C₃₁	—	2	4	no	—
475	C₂²×C₃₁	—	2	4	no	—
476	C₂²×C₃₁	—	2	2	no	—
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	2	2	no	—
479	C₂²×C₃₁	—	4	1	no	—
480	C₂²×C₃₁	—	4	1	no	—
481	C₂²×C₃₁	—	4	1	no	—
482	C₂²×C₃₁	—	4	1	no	—
483	C₂²×C₃₁	C₂×#117	1	8	yes	—
484	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
485	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
486	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
487	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
489	C₂²×C₃₁	#585	1	1	yes	characteristic
490	C₂²×C₃₁	#585	1	1	yes	characteristic
491	C₄×C₃₁	—	2	2	no	—
492	C₄×C₃₁	—	2	4	no	—
493	C₄×C₃₁	—	2	2	no	—
494	C₄×C₃₁	—	2	4	no	—
495	C₄×C₃₁	—	2	2	no	—
496	C₄×C₃₁	—	2	4	no	—
497	C₄×C₃₁	—	2	2	no	—
498	C₄×C₃₁	—	2	2	no	—
499	C₄×C₃₁	—	2	2	no	—
500	C₄×C₃₁	—	2	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	—	4	2	no	—
503	C₄×C₃₁	—	4	1	no	—
504	C₄×C₃₁	—	4	1	no	—
505	C₄×C₃₁	—	4	1	no	—
506	C₄×C₃₁	—	4	1	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	1	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	1	no	—
511	C₄×C₃₁	C₂×#117	1	4	yes	—
512	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
513	#520	C₄×C₃₁	1	16	yes	complemented
514	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
517	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
520	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
521	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
522	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
523	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
524	C₂×#117	C₂²×C₃₁	1	2	yes	—
525	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×#117	C₂²×C₃₁	1	2	yes	—
527	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
528	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
529	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
530	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
531	#391	C₂²×C₃₁	1	1	yes	characteristic
532	#391	C₂²×C₃₁	1	1	yes	characteristic
533	#391	C₂²×C₃₁	1	1	yes	characteristic
534	#391	C₂²×C₃₁	1	1	yes	characteristic
535	#389	C₂²×C₃₁	1	1	yes	characteristic
536	#389	C₂²×C₃₁	1	1	yes	characteristic
537	#389	C₂²×C₃₁	1	1	yes	characteristic
538	#389	C₂²×C₃₁	1	1	yes	characteristic
539	#388	C₂²×C₃₁	1	2	yes	—
540	#388	C₂²×C₃₁	1	2	yes	—
541	#388	C₂²×C₃₁	1	1	yes	characteristic
542	#388	C₂²×C₃₁	1	1	yes	characteristic
543	#388	C₂²×C₃₁	1	1	yes	characteristic
544	#388	C₂²×C₃₁	1	1	yes	characteristic
545	#387	C₂²×C₃₁	1	1	yes	characteristic
546	#387	C₂²×C₃₁	1	2	yes	—
547	#387	C₂²×C₃₁	1	2	yes	—
548	#387	C₂²×C₃₁	1	2	yes	—
549	#387	C₂²×C₃₁	1	2	yes	—
550	#387	C₂²×C₃₁	1	2	yes	—
551	#387	C₂²×C₃₁	1	2	yes	—
552	#387	C₂²×C₃₁	1	2	yes	—
553	#387	C₂²×C₃₁	1	2	yes	—
554	#387	C₂²×C₃₁	1	2	yes	—
555	#387	C₂²×C₃₁	1	1	yes	characteristic
556	#387	C₂²×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
562	#387	C₂²×C₃₁	1	2	yes	—
563	#386	C₂²×C₃₁	1	2	yes	—
564	#386	C₂²×C₃₁	1	2	yes	—
565	#386	C₂²×C₃₁	1	2	yes	—
566	#386	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	#385	C₂²×C₃₁	1	2	yes	—
571	#384	C₂²×C₃₁	1	1	yes	characteristic
572	#383	C₂²×C₃₁	1	2	yes	—
573	#383	C₂²×C₃₁	1	2	yes	—
574	#382	C₂²×C₃₁	1	1	yes	characteristic
575	#382	C₂²×C₃₁	1	2	yes	—
576	#382	C₂²×C₃₁	1	2	yes	—
577	#381	C₂²×C₃₁	1	2	yes	—
578	#381	C₂²×C₃₁	1	2	yes	—
579	#381	C₂²×C₃₁	1	2	yes	—
580	#380	C₂²×C₃₁	1	2	yes	—
581	#380	C₂²×C₃₁	1	2	yes	—
582	#380	C₂²×C₃₁	1	1	yes	characteristic
583	#380	C₂²×C₃₁	1	1	yes	characteristic
584	#380	C₂²×C₃₁	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
588	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
589	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
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	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	C₄×C₂²⋊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	2	yes	—
604	#376	C₂²×C₃₁	1	1	yes	characteristic
605	#376	C₂²×C₃₁	1	2	yes	—
606	#376	C₂²×C₃₁	1	2	yes	—
607	C₂×#95	C₂²×C₃₁	1	2	yes	—
608	C₂×#95	C₂²×C₃₁	1	2	yes	—
609	C₂×#95	C₂²×C₃₁	1	2	yes	—
610	C₂×#95	C₂²×C₃₁	1	2	yes	—
611	C₄³	C₂²×C₃₁	1	1	yes	characteristic
612	C₂×C₃₁	—	2	8	no	—
613	C₂×C₃₁	—	4	2	no	—
614	C₂×C₃₁	C₂²×#117	1	1	yes	characteristic
615	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
617	C₂×C₃₁	#3513	1	1	yes	characteristic
618	C₂×C₃₁	#3515	1	1	yes	characteristic
619	C₂×C₃₁	#3520	1	1	yes	characteristic
620	C₂×C₃₁	#3521	1	1	yes	characteristic
621	C₂×#41	—	2	4	no	—
622	C₂×#41	—	2	4	no	—
623	C₂×#41	C₂×C₄×C₃₁	1	8	yes	—
624	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
626	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
628	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
629	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
630	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
632	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
633	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
634	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
635	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
636	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
637	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
638	C₄×D₄	—	2	4	no	—
639	C₄×D₄	—	2	4	no	—
640	C₄×D₄	—	2	4	no	—
641	C₄×D₄	—	2	4	no	—
642	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
643	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
644	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
645	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
646	#117	—	4	4	no	—
647	#117	C₂×C₄×C₃₁	1	8	yes	complemented
648	#117	C₂×C₄×C₃₁	1	16	yes	complemented
649	C₂×C₄⋊C₄	—	4	4	no	—
650	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
651	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄²	—	4	4	no	—
688	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
704	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
705	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
706	#95	C₂³×C₃₁	1	1	yes	characteristic
707	#95	C₂³×C₃₁	1	1	yes	characteristic
708	#95	C₂³×C₃₁	1	1	yes	characteristic
709	#95	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
723	#95	C₂³×C₃₁	1	1	yes	characteristic
724	#95	C₂³×C₃₁	1	1	yes	characteristic
725	#95	C₂³×C₃₁	1	1	yes	characteristic
726	#95	C₂³×C₃₁	1	2	yes	—
727	#95	C₂³×C₃₁	1	2	yes	—
728	#95	C₂³×C₃₁	1	2	yes	—
729	#95	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
735	#95	C₂³×C₃₁	1	1	yes	characteristic
736	#95	C₂³×C₃₁	1	1	yes	characteristic
737	#95	C₂³×C₃₁	1	2	yes	—
738	#95	C₂³×C₃₁	1	2	yes	—
739	#95	C₂³×C₃₁	1	1	yes	characteristic
740	C₃₁	#34260	1	1	yes	characteristic, direct product factor, Sylow
741	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
742	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
743	#41	—	2	32	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
750	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
751	C₂×D₄	#41×C₃₁	1	4	yes	—
752	C₂×D₄	#41×C₃₁	1	4	yes	—
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	—	2	4	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
776	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
777	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
778	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
779	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
780	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	1	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	1	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
816	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
817	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
818	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
819	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
820	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
821	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	4	1	no	—
829	C₂²⋊C₄	—	4	1	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
833	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
834	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
835	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	4	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	—	4	2	no	—
845	C₄²	—	4	1	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	2	no	—
848	C₄²	—	4	1	no	—
849	C₄²	—	4	2	no	—
850	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
851	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
852	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
853	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
865	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
866	C₂³	C₂×#41×C₃₁	1	4	yes	—
867	C₂³	C₂×#41×C₃₁	1	4	yes	—
868	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
869	Q₈	—	2	8	no	—
870	D₄	—	2	16	no	—
871	D₄	C₃₁×#117	1	16	yes	complemented
872	C₂×C₄	—	2	16	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	2	no	—
878	C₂×C₄	—	2	2	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	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	4	8	no	—
925	C₂×C₄	—	4	8	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	4	8	no	—
929	C₂×C₄	—	8	4	no	—
930	C₂×C₄	—	8	4	no	—
931	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
932	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
933	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
934	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
935	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
936	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
937	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
938	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
939	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
940	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
941	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
942	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
943	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	C₂×C₃₁×#117	1	8	yes	—
958	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
959	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
960	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
961	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
963	C₂²	C₃₁×#585	1	1	yes	characteristic
964	C₂²	C₃₁×#585	1	1	yes	characteristic
965	C₄	—	2	2	no	—
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	4	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	4	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	C₂×C₃₁×#117	1	4	yes	—
986	C₂	—	2	8	no	—
987	C₂	—	4	2	no	—
988	C₂	C₂²×C₃₁×#117	1	1	yes	characteristic
989	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
990	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
991	C₂	C₃₁×#3513	1	1	yes	characteristic
992	C₂	C₃₁×#3515	1	1	yes	characteristic
993	C₂	C₃₁×#3520	1	1	yes	characteristic
994	C₂	C₃₁×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×#41×C₃₁	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×#2356	C₂	semidirect
3. C₃₁×#2355	C₂	semidirect
4. C₃₁×#2353	C₂	semidirect
5. C₃₁×#2352	C₂	semidirect
6. C₃₁×#2349	C₂	semidirect
7. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
8. C₃₁×#2345	C₂	semidirect
9. C₃₁×#2344	C₂	semidirect
10. C₃₁×#2343	C₂	semidirect
11. C₃₁×#2343	C₂	semidirect
14. C₃₁×#2320	C₂	semidirect
15. C₃₁×#2318	C₂	semidirect
16. C₃₁×#2314	C₂	semidirect
17. C₃₁×#2313	C₂	semidirect
18. C₃₁×#2298	C₂	semidirect
19. C₃₁×#2295	C₂	semidirect
20. C₃₁×#2290	C₂	semidirect
21. C₂×C₃₁×#387	C₂	semidirect
22. C₃₁×#2275	C₂	semidirect
23. C₄²×D₄×C₃₁	C₂	semidirect
25. C₃₁×#520	C₄	semidirect
139. C₄×Q₈×C₃₁	C₂×C₄	semidirect
140. C₄×Q₈×C₃₁	C₂×C₄	semidirect
147. C₄×D₄×C₃₁	C₂×C₄	semidirect
148. C₄×D₄×C₃₁	C₂×C₄	semidirect
150. C₃₁×#117	C₂×C₄	semidirect
151. C₃₁×#117	C₂×C₄	semidirect
153. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
154. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
356. #34260	C₃₁	direct (N × H)
374. D₄×C₃₁	#117	semidirect
448. #2356	C₂×C₃₁	semidirect
449. #2355	C₂×C₃₁	semidirect
450. #2353	C₂×C₃₁	semidirect
451. #2352	C₂×C₃₁	semidirect
452. #2349	C₂×C₃₁	semidirect
453. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
454. #2345	C₂×C₃₁	semidirect
455. #2344	C₂×C₃₁	semidirect
456. #2343	C₂×C₃₁	semidirect
457. #2343	C₂×C₃₁	semidirect
460. #2320	C₂×C₃₁	semidirect
461. #2318	C₂×C₃₁	semidirect
462. #2314	C₂×C₃₁	semidirect
463. #2313	C₂×C₃₁	semidirect
464. #2298	C₂×C₃₁	semidirect
465. #2295	C₂×C₃₁	semidirect
466. #2290	C₂×C₃₁	semidirect
467. C₂×#387	C₂×C₃₁	semidirect
468. #2275	C₂×C₃₁	semidirect
469. C₄²×D₄	C₂×C₃₁	semidirect
513. #520	C₄×C₃₁	semidirect
636. C₄×Q₈	C₂×C₄×C₃₁	semidirect
637. C₄×Q₈	C₂×C₄×C₃₁	semidirect
644. C₄×D₄	C₂×C₄×C₃₁	semidirect
645. C₄×D₄	C₂×C₄×C₃₁	semidirect
647. #117	C₂×C₄×C₃₁	semidirect
648. #117	C₂×C₄×C₃₁	semidirect
650. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
651. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
740. C₃₁	#34260	direct (N × H)
871. D₄	C₃₁×#117	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#520	2
C₃₁×#2356	2
C₃₁×#2355	2
C₃₁×#2353	2
C₃₁×#2352	2
C₃₁×#2349	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2345	2
C₃₁×#2344	2
C₃₁×#2343	2
C₃₁×#2339	2
C₃₁×#2320	2
C₃₁×#2318	2
C₃₁×#2314	2
C₃₁×#2313	2
C₃₁×#2298	2
C₃₁×#2295	2
C₃₁×#2290	2
C₂×C₃₁×#387	2
C₃₁×#2275	2
C₄²×D₄×C₃₁	2
#34260	31

Subgroups — C31×#34260 #21491019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34260 #21491019