Subgroups — C₃₁×#34408 #21491167

Order 7936.

2810 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#534	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2377	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2375	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2363	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2358	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2358	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2358	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2335	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2333	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2324	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2308	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#534	C₄	1	16	yes	complemented
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#121	C₂²	1	2	yes	—
27	C₂×C₃₁×#121	C₂²	1	2	yes	—
28	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#120	C₂²	1	2	yes	—
30	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
35	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
43	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#390	C₂²	1	2	yes	—
45	C₃₁×#390	C₂²	1	1	yes	characteristic
46	C₃₁×#390	C₂²	1	1	yes	characteristic
47	C₃₁×#390	C₂²	1	2	yes	complemented
48	C₃₁×#390	C₂²	1	2	yes	complemented
49	C₃₁×#390	C₂²	1	2	yes	complemented
50	C₃₁×#390	C₂²	1	2	yes	complemented
51	C₃₁×#390	C₂²	1	2	yes	complemented
52	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#389	C₂²	1	2	yes	complemented
55	C₃₁×#389	C₂²	1	2	yes	complemented
56	C₃₁×#388	C₂²	1	2	yes	complemented
57	C₃₁×#388	C₂²	1	2	yes	complemented
58	C₃₁×#388	C₂²	1	2	yes	complemented
59	C₃₁×#388	C₂²	1	2	yes	complemented
60	C₃₁×#388	C₂²	1	2	yes	complemented
61	C₃₁×#388	C₂²	1	2	yes	complemented
62	C₃₁×#388	C₂²	1	2	yes	complemented
63	C₃₁×#388	C₂²	1	2	yes	complemented
64	C₃₁×#388	C₂²	1	2	yes	complemented
65	C₃₁×#388	C₂²	1	2	yes	complemented
66	C₃₁×#388	C₂²	1	2	yes	complemented
67	C₃₁×#388	C₂²	1	2	yes	complemented
68	C₃₁×#387	C₂²	1	2	yes	complemented
69	C₃₁×#387	C₂²	1	2	yes	complemented
70	C₃₁×#387	C₂²	1	2	yes	complemented
71	C₃₁×#387	C₂²	1	2	yes	complemented
72	C₃₁×#386	C₂²	1	2	yes	—
73	C₃₁×#386	C₂²	1	1	yes	characteristic
74	C₃₁×#386	C₂²	1	1	yes	characteristic
75	C₃₁×#386	C₂²	1	2	yes	—
76	C₃₁×#386	C₂²	1	2	yes	—
77	C₃₁×#386	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#386	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#386	C₂²	1	2	yes	complemented
80	C₃₁×#386	C₂²	1	2	yes	complemented
81	C₃₁×#386	C₂²	1	2	yes	complemented
82	C₃₁×#386	C₂²	1	2	yes	complemented
83	C₃₁×#386	C₂²	1	2	yes	complemented
84	C₃₁×#386	C₂²	1	2	yes	complemented
85	C₃₁×#386	C₂²	1	2	yes	complemented
86	C₃₁×#385	C₂²	1	2	yes	complemented
87	C₃₁×#385	C₂²	1	2	yes	complemented
88	C₃₁×#385	C₂²	1	2	yes	complemented
89	C₃₁×#385	C₂²	1	2	yes	complemented
90	C₃₁×#385	C₂²	1	2	yes	complemented
91	C₃₁×#385	C₂²	1	2	yes	complemented
92	C₃₁×#381	C₂²	1	2	yes	complemented
93	C₃₁×#381	C₂²	1	2	yes	complemented
94	C₃₁×#380	C₂²	1	2	yes	complemented
95	C₃₁×#380	C₂²	1	2	yes	complemented
96	C₃₁×#379	C₂²	1	2	yes	—
97	C₃₁×#379	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
107	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
108	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
109	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
110	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	—	4	2	no	—
112	C₂²×D₄×C₃₁	—	4	2	no	—
113	C₂²×D₄×C₃₁	—	4	2	no	—
114	C₂²×D₄×C₃₁	—	4	2	no	—
115	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
116	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
120	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
134	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₃₁×#123	C₂×C₄	1	16	yes	complemented
136	C₃₁×#123	C₂×C₄	1	8	yes	complemented
137	C₃₁×#123	C₂×C₄	1	8	yes	complemented
138	C₃₁×#121	C₂×C₄	1	16	yes	complemented
139	C₃₁×#121	C₂×C₄	1	16	yes	complemented
140	C₃₁×#120	C₂×C₄	1	16	yes	complemented
141	C₃₁×#120	C₂×C₄	1	8	yes	complemented
142	C₃₁×#120	C₂×C₄	1	8	yes	complemented
143	C₄×D₄×C₃₁	—	4	4	no	—
144	C₄×D₄×C₃₁	—	4	4	no	—
145	C₄×D₄×C₃₁	—	4	4	no	—
146	C₄×D₄×C₃₁	—	4	4	no	—
147	C₃₁×#117	—	4	4	no	—
148	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
161	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
162	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
163	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
164	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
165	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊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	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₄²×C₃₁	—	4	2	no	—
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
205	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
206	C₃₁×#95	C₂³	1	2	yes	—
207	C₃₁×#95	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	2	yes	—
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
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	C₂⁴×C₃₁	—	2	2	no	—
223	C₂⁴×C₃₁	—	2	2	no	—
224	C₂⁴×C₃₁	—	2	2	no	—
225	C₂⁴×C₃₁	—	2	2	no	—
226	C₂⁴×C₃₁	—	4	2	no	—
227	C₂⁴×C₃₁	—	4	2	no	—
228	C₂⁴×C₃₁	—	4	2	no	—
229	C₂⁴×C₃₁	—	4	1	no	—
230	C₂⁴×C₃₁	—	4	1	no	—
231	C₂⁴×C₃₁	—	4	2	no	—
232	C₂⁴×C₃₁	—	4	2	no	—
233	C₂⁴×C₃₁	—	4	2	no	—
234	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
235	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
236	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
237	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
242	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₃₁	—	2	4	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	4	2	no	—
246	C₂×D₄×C₃₁	—	4	2	no	—
247	C₂×D₄×C₃₁	—	4	16	no	—
248	C₂×D₄×C₃₁	—	4	1	no	—
249	C₂×D₄×C₃₁	—	4	1	no	—
250	C₂×D₄×C₃₁	—	4	1	no	—
251	C₂×D₄×C₃₁	—	4	1	no	—
252	C₂×D₄×C₃₁	—	4	2	no	—
253	C₂×D₄×C₃₁	—	4	2	no	—
254	C₂×D₄×C₃₁	—	4	1	no	—
255	C₂×D₄×C₃₁	—	4	1	no	—
256	C₂×D₄×C₃₁	—	4	1	no	—
257	C₂×D₄×C₃₁	—	4	1	no	—
258	C₂×D₄×C₃₁	—	4	2	no	—
259	C₂×D₄×C₃₁	—	4	2	no	—
260	C₂×D₄×C₃₁	—	4	16	no	—
261	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
262	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
263	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
265	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
266	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
268	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	4	no	—
272	C₂²×C₄×C₃₁	—	2	4	no	—
273	C₂²×C₄×C₃₁	—	2	4	no	—
274	C₂²×C₄×C₃₁	—	2	4	no	—
275	C₂²×C₄×C₃₁	—	4	2	no	—
276	C₂²×C₄×C₃₁	—	4	2	no	—
277	C₂²×C₄×C₃₁	—	4	2	no	—
278	C₂²×C₄×C₃₁	—	4	1	no	—
279	C₂²×C₄×C₃₁	—	4	1	no	—
280	C₂²×C₄×C₃₁	—	4	1	no	—
281	C₂²×C₄×C₃₁	—	4	2	no	—
282	C₂²×C₄×C₃₁	—	4	2	no	—
283	C₂²×C₄×C₃₁	—	4	2	no	—
284	C₂²×C₄×C₃₁	—	4	2	no	—
285	C₂²×C₄×C₃₁	—	4	1	no	—
286	C₂²×C₄×C₃₁	—	4	2	no	—
287	C₂²×C₄×C₃₁	—	4	2	no	—
288	C₂²×C₄×C₃₁	—	4	2	no	—
289	C₂²×C₄×C₃₁	—	4	2	no	—
290	C₂²×C₄×C₃₁	—	4	2	no	—
291	C₂²×C₄×C₃₁	—	4	2	no	—
292	C₂²×C₄×C₃₁	—	4	2	no	—
293	C₂²×C₄×C₃₁	—	4	2	no	—
294	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
295	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
296	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₃₁	—	2	4	no	—
311	C₄⋊C₄×C₃₁	—	4	1	no	—
312	C₄⋊C₄×C₃₁	—	4	2	no	—
313	C₄⋊C₄×C₃₁	—	4	1	no	—
314	C₄⋊C₄×C₃₁	—	4	2	no	—
315	C₄⋊C₄×C₃₁	—	4	2	no	—
316	C₄⋊C₄×C₃₁	—	4	2	no	—
317	C₄⋊C₄×C₃₁	—	4	2	no	—
318	C₄⋊C₄×C₃₁	—	4	2	no	—
319	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
320	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	4	1	no	—
329	C₂²⋊C₄×C₃₁	—	4	2	no	—
330	C₂²⋊C₄×C₃₁	—	4	2	no	—
331	C₂²⋊C₄×C₃₁	—	4	2	no	—
332	C₂²⋊C₄×C₃₁	—	4	2	no	—
333	C₂²⋊C₄×C₃₁	—	4	2	no	—
334	C₂²⋊C₄×C₃₁	—	4	2	no	—
335	C₂²⋊C₄×C₃₁	—	4	1	no	—
336	C₂²⋊C₄×C₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₃₁	—	4	2	no	—
338	C₂²⋊C₄×C₃₁	—	4	2	no	—
339	C₂²⋊C₄×C₃₁	—	4	2	no	—
340	C₂²⋊C₄×C₃₁	—	4	2	no	—
341	C₂²⋊C₄×C₃₁	—	4	2	no	—
342	C₂²⋊C₄×C₃₁	—	4	2	no	—
343	C₂²⋊C₄×C₃₁	—	4	2	no	—
344	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
345	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
346	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
347	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
348	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
349	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
350	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
351	C₄²×C₃₁	—	2	4	no	—
352	C₄²×C₃₁	—	4	1	no	—
353	C₄²×C₃₁	—	4	2	no	—
354	C₄²×C₃₁	—	4	1	no	—
355	C₄²×C₃₁	—	4	2	no	—
356	C₄²×C₃₁	—	4	2	no	—
357	C₄²×C₃₁	—	4	2	no	—
358	C₄²×C₃₁	—	4	2	no	—
359	C₄²×C₃₁	—	4	2	no	—
360	#34408	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂³×C₃₁	—	2	2	no	—
362	C₂³×C₃₁	—	2	2	no	—
363	C₂³×C₃₁	—	2	2	no	—
364	C₂³×C₃₁	—	2	2	no	—
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	—	2	2	no	—
367	C₂³×C₃₁	—	2	2	no	—
368	C₂³×C₃₁	—	2	1	no	—
369	C₂³×C₃₁	—	2	1	no	—
370	C₂³×C₃₁	—	2	2	no	—
371	C₂³×C₃₁	—	2	2	no	—
372	C₂³×C₃₁	—	2	2	no	—
373	C₂³×C₃₁	—	2	1	no	—
374	C₂³×C₃₁	—	2	1	no	—
375	C₂³×C₃₁	—	2	1	no	—
376	C₂³×C₃₁	—	2	1	no	—
377	C₂³×C₃₁	—	2	1	no	—
378	C₂³×C₃₁	—	2	1	no	—
379	C₂³×C₃₁	—	2	2	no	—
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	—	2	2	no	—
382	C₂³×C₃₁	—	2	2	no	—
383	C₂³×C₃₁	—	2	2	no	—
384	C₂³×C₃₁	—	2	2	no	—
385	C₂³×C₃₁	—	2	8	no	—
386	C₂³×C₃₁	—	2	8	no	—
387	C₂³×C₃₁	—	4	4	no	—
388	C₂³×C₃₁	—	4	8	no	—
389	C₂³×C₃₁	—	4	8	no	—
390	C₂³×C₃₁	—	4	8	no	—
391	C₂³×C₃₁	—	8	4	no	—
392	C₂³×C₃₁	—	8	4	no	—
393	C₂³×C₃₁	—	8	2	no	—
394	C₂³×C₃₁	—	8	2	no	—
395	C₂³×C₃₁	—	8	2	no	—
396	C₂³×C₃₁	—	8	2	no	—
397	C₂³×C₃₁	—	8	4	no	—
398	C₂³×C₃₁	—	8	2	no	—
399	C₂³×C₃₁	—	8	2	no	—
400	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
401	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
402	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
403	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
404	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
405	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
406	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
407	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
408	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
409	D₄×C₃₁	—	2	16	no	—
410	D₄×C₃₁	—	4	4	no	—
411	D₄×C₃₁	—	4	4	no	—
412	D₄×C₃₁	—	4	4	no	—
413	D₄×C₃₁	—	4	4	no	—
414	D₄×C₃₁	—	4	8	no	—
415	D₄×C₃₁	—	4	8	no	—
416	D₄×C₃₁	—	4	8	no	—
417	C₂×C₄×C₃₁	—	2	8	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	2	no	—
443	C₂×C₄×C₃₁	—	2	2	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	4	8	no	—
452	C₂×C₄×C₃₁	—	4	4	no	—
453	C₂×C₄×C₃₁	—	4	8	no	—
454	C₂×C₄×C₃₁	—	8	4	no	—
455	C₂×C₄×C₃₁	—	8	4	no	—
456	C₂×C₄×C₃₁	—	8	4	no	—
457	C₂×C₄×C₃₁	—	8	2	no	—
458	C₂×C₄×C₃₁	—	8	4	no	—
459	C₂×C₄×C₃₁	—	8	2	no	—
460	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
461	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
462	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
465	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
466	C₂×#534	C₂×C₃₁	1	1	yes	characteristic
467	#2377	C₂×C₃₁	1	2	yes	complemented
468	#2376	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#2375	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#2374	C₂×C₃₁	1	1	yes	characteristic, complemented
471	#2363	C₂×C₃₁	1	2	yes	complemented
472	#2358	C₂×C₃₁	1	2	yes	complemented
473	#2358	C₂×C₃₁	1	2	yes	complemented
474	#2358	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#2342	C₂×C₃₁	1	2	yes	complemented
476	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
477	#2335	C₂×C₃₁	1	2	yes	complemented
478	#2333	C₂×C₃₁	1	2	yes	complemented
479	#2324	C₂×C₃₁	1	2	yes	complemented
480	#2322	C₂×C₃₁	1	2	yes	complemented
481	#2321	C₂×C₃₁	1	2	yes	complemented
482	#2308	C₂×C₃₁	1	1	yes	characteristic, complemented
483	C₄×#123	C₂×C₃₁	1	2	yes	complemented
484	C₂×#390	C₂×C₃₁	1	1	yes	characteristic, complemented
485	C₂²×C₃₁	—	2	4	no	—
486	C₂²×C₃₁	—	2	4	no	—
487	C₂²×C₃₁	—	2	2	no	—
488	C₂²×C₃₁	—	2	2	no	—
489	C₂²×C₃₁	—	2	2	no	—
490	C₂²×C₃₁	—	2	4	no	—
491	C₂²×C₃₁	—	2	2	no	—
492	C₂²×C₃₁	—	2	2	no	—
493	C₂²×C₃₁	—	2	2	no	—
494	C₂²×C₃₁	—	2	4	no	—
495	C₂²×C₃₁	—	2	4	no	—
496	C₂²×C₃₁	—	2	4	no	—
497	C₂²×C₃₁	—	2	4	no	—
498	C₂²×C₃₁	—	2	4	no	—
499	C₂²×C₃₁	—	2	4	no	—
500	C₂²×C₃₁	—	4	2	no	—
501	C₂²×C₃₁	—	4	2	no	—
502	C₂²×C₃₁	—	4	2	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	4	2	no	—
505	C₂²×C₃₁	—	4	2	no	—
506	C₂²×C₃₁	—	4	1	no	—
507	C₂²×C₃₁	—	4	2	no	—
508	C₂²×C₃₁	—	4	1	no	—
509	C₂²×C₃₁	—	4	1	no	—
510	C₂²×C₃₁	—	4	1	no	—
511	C₂²×C₃₁	—	4	1	no	—
512	C₂²×C₃₁	—	4	1	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	1	no	—
515	C₂²×C₃₁	—	4	1	no	—
516	C₂²×C₃₁	—	8	8	no	—
517	C₂²×C₃₁	—	8	8	no	—
518	C₂²×C₃₁	—	8	8	no	—
519	C₂²×C₃₁	#518	1	4	yes	—
520	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
521	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
524	C₂²×C₃₁	#585	1	2	yes	—
525	C₄×C₃₁	—	2	2	no	—
526	C₄×C₃₁	—	2	2	no	—
527	C₄×C₃₁	—	2	4	no	—
528	C₄×C₃₁	—	2	4	no	—
529	C₄×C₃₁	—	2	4	no	—
530	C₄×C₃₁	—	2	4	no	—
531	C₄×C₃₁	—	4	2	no	—
532	C₄×C₃₁	—	4	2	no	—
533	C₄×C₃₁	—	4	2	no	—
534	C₄×C₃₁	—	4	2	no	—
535	C₄×C₃₁	—	4	2	no	—
536	C₄×C₃₁	—	4	2	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
539	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
540	#534	C₄×C₃₁	1	16	yes	complemented
541	C₂×#123	C₂²×C₃₁	1	2	yes	—
542	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
543	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×#121	C₂²×C₃₁	1	2	yes	—
545	C₂×#121	C₂²×C₃₁	1	2	yes	—
546	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
547	C₂×#120	C₂²×C₃₁	1	2	yes	—
548	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
549	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
550	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
551	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
552	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
553	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
554	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
555	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
556	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
557	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
558	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
560	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
561	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	#390	C₂²×C₃₁	1	2	yes	—
563	#390	C₂²×C₃₁	1	1	yes	characteristic
564	#390	C₂²×C₃₁	1	1	yes	characteristic
565	#390	C₂²×C₃₁	1	2	yes	complemented
566	#390	C₂²×C₃₁	1	2	yes	complemented
567	#390	C₂²×C₃₁	1	2	yes	complemented
568	#390	C₂²×C₃₁	1	2	yes	complemented
569	#390	C₂²×C₃₁	1	2	yes	complemented
570	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#389	C₂²×C₃₁	1	2	yes	complemented
573	#389	C₂²×C₃₁	1	2	yes	complemented
574	#388	C₂²×C₃₁	1	2	yes	complemented
575	#388	C₂²×C₃₁	1	2	yes	complemented
576	#388	C₂²×C₃₁	1	2	yes	complemented
577	#388	C₂²×C₃₁	1	2	yes	complemented
578	#388	C₂²×C₃₁	1	2	yes	complemented
579	#388	C₂²×C₃₁	1	2	yes	complemented
580	#388	C₂²×C₃₁	1	2	yes	complemented
581	#388	C₂²×C₃₁	1	2	yes	complemented
582	#388	C₂²×C₃₁	1	2	yes	complemented
583	#388	C₂²×C₃₁	1	2	yes	complemented
584	#388	C₂²×C₃₁	1	2	yes	complemented
585	#388	C₂²×C₃₁	1	2	yes	complemented
586	#387	C₂²×C₃₁	1	2	yes	complemented
587	#387	C₂²×C₃₁	1	2	yes	complemented
588	#387	C₂²×C₃₁	1	2	yes	complemented
589	#387	C₂²×C₃₁	1	2	yes	complemented
590	#386	C₂²×C₃₁	1	2	yes	—
591	#386	C₂²×C₃₁	1	1	yes	characteristic
592	#386	C₂²×C₃₁	1	1	yes	characteristic
593	#386	C₂²×C₃₁	1	2	yes	—
594	#386	C₂²×C₃₁	1	2	yes	—
595	#386	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#386	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#386	C₂²×C₃₁	1	2	yes	complemented
598	#386	C₂²×C₃₁	1	2	yes	complemented
599	#386	C₂²×C₃₁	1	2	yes	complemented
600	#386	C₂²×C₃₁	1	2	yes	complemented
601	#386	C₂²×C₃₁	1	2	yes	complemented
602	#386	C₂²×C₃₁	1	2	yes	complemented
603	#386	C₂²×C₃₁	1	2	yes	complemented
604	#385	C₂²×C₃₁	1	2	yes	complemented
605	#385	C₂²×C₃₁	1	2	yes	complemented
606	#385	C₂²×C₃₁	1	2	yes	complemented
607	#385	C₂²×C₃₁	1	2	yes	complemented
608	#385	C₂²×C₃₁	1	2	yes	complemented
609	#385	C₂²×C₃₁	1	2	yes	complemented
610	#381	C₂²×C₃₁	1	2	yes	complemented
611	#381	C₂²×C₃₁	1	2	yes	complemented
612	#380	C₂²×C₃₁	1	2	yes	complemented
613	#380	C₂²×C₃₁	1	2	yes	complemented
614	#379	C₂²×C₃₁	1	2	yes	—
615	#379	C₂²×C₃₁	1	2	yes	complemented
616	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
617	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
618	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
619	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
620	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
621	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
622	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
623	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
624	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
625	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
626	C₂×C₃₁	—	2	4	no	—
627	C₂×C₃₁	—	4	4	no	—
628	C₂×C₃₁	—	4	2	no	—
629	C₂×C₃₁	—	4	2	no	—
630	C₂×C₃₁	—	4	2	no	—
631	C₂×C₃₁	—	4	2	no	—
632	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
633	C₂×C₃₁	C₄×H(5,𝔽₂)	1	2	yes	—
634	C₂×C₃₁	#3534	1	2	yes	—
635	C₂×C₃₁	#3543	1	1	yes	characteristic
636	C₂×C₃₁	#3545	1	1	yes	characteristic
637	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
638	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
639	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
640	C₂²×D₄	—	4	2	no	—
641	C₂²×D₄	—	4	2	no	—
642	C₂²×D₄	—	4	2	no	—
643	C₂²×D₄	—	4	2	no	—
644	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
645	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
646	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
647	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
648	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
649	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
652	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
653	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
655	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
657	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
658	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
659	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
661	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
662	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
663	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
664	#123	C₂×C₄×C₃₁	1	16	yes	complemented
665	#123	C₂×C₄×C₃₁	1	8	yes	complemented
666	#123	C₂×C₄×C₃₁	1	8	yes	complemented
667	#121	C₂×C₄×C₃₁	1	16	yes	complemented
668	#121	C₂×C₄×C₃₁	1	16	yes	complemented
669	#120	C₂×C₄×C₃₁	1	16	yes	complemented
670	#120	C₂×C₄×C₃₁	1	8	yes	complemented
671	#120	C₂×C₄×C₃₁	1	8	yes	complemented
672	C₄×D₄	—	4	4	no	—
673	C₄×D₄	—	4	4	no	—
674	C₄×D₄	—	4	4	no	—
675	C₄×D₄	—	4	4	no	—
676	#117	—	4	4	no	—
677	C₂×C₄⋊C₄	—	4	2	no	—
678	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₂²⋊C₄	—	4	4	no	—
690	C₂×C₂²⋊C₄	—	4	4	no	—
691	C₂×C₂²⋊C₄	—	4	4	no	—
692	C₂×C₂²⋊C₄	—	4	2	no	—
693	C₂×C₂²⋊C₄	—	4	2	no	—
694	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
695	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
725	C₂×C₄²	—	4	2	no	—
726	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
727	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
728	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
729	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
730	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
731	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
732	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
734	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
735	#95	C₂³×C₃₁	1	2	yes	—
736	#95	C₂³×C₃₁	1	2	yes	—
737	#95	C₂³×C₃₁	1	2	yes	—
738	#95	C₂³×C₃₁	1	2	yes	—
739	#95	C₂³×C₃₁	1	2	yes	—
740	#95	C₂³×C₃₁	1	2	yes	—
741	#95	C₂³×C₃₁	1	2	yes	—
742	#95	C₂³×C₃₁	1	2	yes	—
743	#95	C₂³×C₃₁	1	2	yes	—
744	#95	C₂³×C₃₁	1	2	yes	—
745	#95	C₂³×C₃₁	1	2	yes	—
746	#95	C₂³×C₃₁	1	2	yes	—
747	#95	C₂³×C₃₁	1	2	yes	—
748	#95	C₂³×C₃₁	1	2	yes	—
749	#95	C₂³×C₃₁	1	2	yes	—
750	#95	C₂³×C₃₁	1	2	yes	—
751	C₃₁	#34408	1	1	yes	characteristic, direct product factor, Sylow
752	C₂⁴	—	2	2	no	—
753	C₂⁴	—	2	2	no	—
754	C₂⁴	—	2	2	no	—
755	C₂⁴	—	2	2	no	—
756	C₂⁴	—	4	2	no	—
757	C₂⁴	—	4	2	no	—
758	C₂⁴	—	4	2	no	—
759	C₂⁴	—	4	1	no	—
760	C₂⁴	—	4	1	no	—
761	C₂⁴	—	4	2	no	—
762	C₂⁴	—	4	2	no	—
763	C₂⁴	—	4	2	no	—
764	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
765	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
766	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
767	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
768	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
769	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
772	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	16	no	—
778	C₂×D₄	—	4	1	no	—
779	C₂×D₄	—	4	1	no	—
780	C₂×D₄	—	4	1	no	—
781	C₂×D₄	—	4	1	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	1	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	—	4	1	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	16	no	—
791	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
792	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
793	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
794	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
795	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
796	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
797	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
798	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	—	4	1	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	1	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	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	8	yes	—
826	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
827	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	4	1	no	—
842	C₄⋊C₄	—	4	2	no	—
843	C₄⋊C₄	—	4	1	no	—
844	C₄⋊C₄	—	4	2	no	—
845	C₄⋊C₄	—	4	2	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
850	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	4	1	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	1	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
875	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
876	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
877	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
881	C₄²	—	2	4	no	—
882	C₄²	—	4	1	no	—
883	C₄²	—	4	2	no	—
884	C₄²	—	4	1	no	—
885	C₄²	—	4	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	—	4	2	no	—
888	C₄²	—	4	2	no	—
889	C₄²	—	4	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	8	no	—
915	C₂³	—	2	8	no	—
916	C₂³	—	4	4	no	—
917	C₂³	—	4	8	no	—
918	C₂³	—	4	8	no	—
919	C₂³	—	4	8	no	—
920	C₂³	—	8	4	no	—
921	C₂³	—	8	4	no	—
922	C₂³	—	8	2	no	—
923	C₂³	—	8	2	no	—
924	C₂³	—	8	2	no	—
925	C₂³	—	8	2	no	—
926	C₂³	—	8	4	no	—
927	C₂³	—	8	2	no	—
928	C₂³	—	8	2	no	—
929	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
930	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
931	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
932	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
933	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
934	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
935	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
936	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
937	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
938	D₄	—	2	16	no	—
939	D₄	—	4	4	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	4	8	no	—
944	D₄	—	4	8	no	—
945	D₄	—	4	8	no	—
946	C₂×C₄	—	2	8	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	—	8	4	no	—
984	C₂×C₄	—	8	4	no	—
985	C₂×C₄	—	8	4	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	4	no	—
988	C₂×C₄	—	8	2	no	—
989	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
990	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
991	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
992	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
993	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
994	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
995	C₂²	—	2	4	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	4	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	8	8	no	—
1027	C₂²	—	8	8	no	—
1028	C₂²	—	8	8	no	—
1029	C₂²	C₃₁×#518	1	4	yes	—
1030	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1031	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1033	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1034	C₂²	C₃₁×#585	1	2	yes	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	4	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	4	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₂	—	2	4	no	—
1049	C₂	—	4	2	no	—
1050	C₂	—	4	4	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	4	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
1055	C₂	C₄×C₃₁×H(5,𝔽₂)	1	2	yes	—
1056	C₂	C₃₁×#3534	1	2	yes	—
1057	C₂	C₃₁×#3543	1	1	yes	characteristic
1058	C₂	C₃₁×#3545	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×#534	C₂
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×#2377	C₂	semidirect
3. C₃₁×#2376	C₂	semidirect
4. C₃₁×#2375	C₂	semidirect
5. C₃₁×#2374	C₂	semidirect
6. C₃₁×#2363	C₂	semidirect
7. C₃₁×#2358	C₂	semidirect
8. C₃₁×#2358	C₂	semidirect
9. C₃₁×#2358	C₂	semidirect
10. C₃₁×#2342	C₂	semidirect
11. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
12. C₃₁×#2335	C₂	semidirect
13. C₃₁×#2333	C₂	semidirect
14. C₃₁×#2324	C₂	semidirect
15. C₃₁×#2322	C₂	semidirect
16. C₃₁×#2321	C₂	semidirect
17. C₃₁×#2308	C₂	semidirect
18. C₄×C₃₁×#123	C₂	semidirect
19. C₂×C₃₁×#390	C₂	semidirect
22. C₃₁×#534	C₄	semidirect
33. C₂×C₄×D₄×C₃₁	C₂²	semidirect
34. C₂×C₄×D₄×C₃₁	C₂²	semidirect
35. C₂×C₃₁×#117	C₂²	semidirect
36. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
43. C₂²×C₄²×C₃₁	C₂²	semidirect
47. C₃₁×#390	C₂²	semidirect
48. C₃₁×#390	C₂²	semidirect
49. C₃₁×#390	C₂²	semidirect
50. C₃₁×#390	C₂²	semidirect
51. C₃₁×#390	C₂²	semidirect
52. C₃₁×#390	C₂²	semidirect
53. C₃₁×#390	C₂²	semidirect
54. C₃₁×#389	C₂²	semidirect
55. C₃₁×#389	C₂²	semidirect
56. C₃₁×#388	C₂²	semidirect
57. C₃₁×#388	C₂²	semidirect
58. C₃₁×#388	C₂²	semidirect
59. C₃₁×#388	C₂²	semidirect
60. C₃₁×#388	C₂²	semidirect
61. C₃₁×#388	C₂²	semidirect
62. C₃₁×#388	C₂²	semidirect
63. C₃₁×#388	C₂²	semidirect
64. C₃₁×#388	C₂²	semidirect
65. C₃₁×#388	C₂²	semidirect
66. C₃₁×#388	C₂²	semidirect
67. C₃₁×#388	C₂²	semidirect
68. C₃₁×#387	C₂²	semidirect
69. C₃₁×#387	C₂²	semidirect
70. C₃₁×#387	C₂²	semidirect
71. C₃₁×#387	C₂²	semidirect
77. C₃₁×#386	C₂²	semidirect
78. C₃₁×#386	C₂²	semidirect
79. C₃₁×#386	C₂²	semidirect
80. C₃₁×#386	C₂²	semidirect
81. C₃₁×#386	C₂²	semidirect
82. C₃₁×#386	C₂²	semidirect
83. C₃₁×#386	C₂²	semidirect
84. C₃₁×#386	C₂²	semidirect
85. C₃₁×#386	C₂²	semidirect
86. C₃₁×#385	C₂²	semidirect
87. C₃₁×#385	C₂²	semidirect
88. C₃₁×#385	C₂²	semidirect
89. C₃₁×#385	C₂²	semidirect
90. C₃₁×#385	C₂²	semidirect
91. C₃₁×#385	C₂²	semidirect
92. C₃₁×#381	C₂²	semidirect
93. C₃₁×#381	C₂²	semidirect
94. C₃₁×#380	C₂²	semidirect
95. C₃₁×#380	C₂²	semidirect
97. C₃₁×#379	C₂²	semidirect
98. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
99. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
107. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
115. C₂²×D₄×C₃₁	C₂×C₄	semidirect
116. C₂²×D₄×C₃₁	C₂×C₄	semidirect
135. C₃₁×#123	C₂×C₄	semidirect
136. C₃₁×#123	C₂×C₄	semidirect
137. C₃₁×#123	C₂×C₄	semidirect
138. C₃₁×#121	C₂×C₄	semidirect
139. C₃₁×#121	C₂×C₄	semidirect
140. C₃₁×#120	C₂×C₄	semidirect
141. C₃₁×#120	C₂×C₄	semidirect
142. C₃₁×#120	C₂×C₄	semidirect
165. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
360. #34408	C₃₁	direct (N × H)
467. #2377	C₂×C₃₁	semidirect
468. #2376	C₂×C₃₁	semidirect
469. #2375	C₂×C₃₁	semidirect
470. #2374	C₂×C₃₁	semidirect
471. #2363	C₂×C₃₁	semidirect
472. #2358	C₂×C₃₁	semidirect
473. #2358	C₂×C₃₁	semidirect
474. #2358	C₂×C₃₁	semidirect
475. #2342	C₂×C₃₁	semidirect
476. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
477. #2335	C₂×C₃₁	semidirect
478. #2333	C₂×C₃₁	semidirect
479. #2324	C₂×C₃₁	semidirect
480. #2322	C₂×C₃₁	semidirect
481. #2321	C₂×C₃₁	semidirect
482. #2308	C₂×C₃₁	semidirect
483. C₄×#123	C₂×C₃₁	semidirect
484. C₂×#390	C₂×C₃₁	semidirect
540. #534	C₄×C₃₁	semidirect
551. C₂×C₄×D₄	C₂²×C₃₁	semidirect
552. C₂×C₄×D₄	C₂²×C₃₁	semidirect
553. C₂×#117	C₂²×C₃₁	semidirect
554. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
557. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
558. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
559. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
560. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
561. C₂²×C₄²	C₂²×C₃₁	semidirect
565. #390	C₂²×C₃₁	semidirect
566. #390	C₂²×C₃₁	semidirect
567. #390	C₂²×C₃₁	semidirect
568. #390	C₂²×C₃₁	semidirect
569. #390	C₂²×C₃₁	semidirect
570. #390	C₂²×C₃₁	semidirect
571. #390	C₂²×C₃₁	semidirect
572. #389	C₂²×C₃₁	semidirect
573. #389	C₂²×C₃₁	semidirect
574. #388	C₂²×C₃₁	semidirect
575. #388	C₂²×C₃₁	semidirect
576. #388	C₂²×C₃₁	semidirect
577. #388	C₂²×C₃₁	semidirect
578. #388	C₂²×C₃₁	semidirect
579. #388	C₂²×C₃₁	semidirect
580. #388	C₂²×C₃₁	semidirect
581. #388	C₂²×C₃₁	semidirect
582. #388	C₂²×C₃₁	semidirect
583. #388	C₂²×C₃₁	semidirect
584. #388	C₂²×C₃₁	semidirect
585. #388	C₂²×C₃₁	semidirect
586. #387	C₂²×C₃₁	semidirect
587. #387	C₂²×C₃₁	semidirect
588. #387	C₂²×C₃₁	semidirect
589. #387	C₂²×C₃₁	semidirect
595. #386	C₂²×C₃₁	semidirect
596. #386	C₂²×C₃₁	semidirect
597. #386	C₂²×C₃₁	semidirect
598. #386	C₂²×C₃₁	semidirect
599. #386	C₂²×C₃₁	semidirect
600. #386	C₂²×C₃₁	semidirect
601. #386	C₂²×C₃₁	semidirect
602. #386	C₂²×C₃₁	semidirect
603. #386	C₂²×C₃₁	semidirect
604. #385	C₂²×C₃₁	semidirect
605. #385	C₂²×C₃₁	semidirect
606. #385	C₂²×C₃₁	semidirect
607. #385	C₂²×C₃₁	semidirect
608. #385	C₂²×C₃₁	semidirect
609. #385	C₂²×C₃₁	semidirect
610. #381	C₂²×C₃₁	semidirect
611. #381	C₂²×C₃₁	semidirect
612. #380	C₂²×C₃₁	semidirect
613. #380	C₂²×C₃₁	semidirect
615. #379	C₂²×C₃₁	semidirect
616. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
617. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
618. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
619. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
620. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
621. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
622. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
623. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
624. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
625. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
644. C₂²×D₄	C₂×C₄×C₃₁	semidirect
645. C₂²×D₄	C₂×C₄×C₃₁	semidirect
664. #123	C₂×C₄×C₃₁	semidirect
665. #123	C₂×C₄×C₃₁	semidirect
666. #123	C₂×C₄×C₃₁	semidirect
667. #121	C₂×C₄×C₃₁	semidirect
668. #121	C₂×C₄×C₃₁	semidirect
669. #120	C₂×C₄×C₃₁	semidirect
670. #120	C₂×C₄×C₃₁	semidirect
671. #120	C₂×C₄×C₃₁	semidirect
694. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
751. C₃₁	#34408	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×#534	2
C₃₁×#2377	2
C₃₁×#2376	2
C₃₁×#2375	2
C₃₁×#2374	2
C₃₁×#2363	2
C₃₁×#2358	2
C₃₁×#2342	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2335	2
C₃₁×#2333	2
C₃₁×#2324	2
C₃₁×#2322	2
C₃₁×#2321	2
C₃₁×#2308	2
C₄×C₃₁×#123	2
C₂×C₃₁×#390	2
#34408	31

Subgroups — C31×#34408 #21491167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34408 #21491167