Subgroups — C₃₁×#34468 #21491227

Order 7936.

3220 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2375	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2364	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2358	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
10	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2333	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2325	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2321	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2308	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#120	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#386	C₂	1	2	yes	maximal, complemented
20	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
21	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	D₄²×C₃₁	C₄	1	16	yes	complemented
24	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#121	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	2	yes	—
27	C₂×C₃₁×#120	C₂²	1	2	yes	—
28	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
42	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#390	C₂²	1	2	yes	complemented
44	C₃₁×#390	C₂²	1	2	yes	complemented
45	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#390	C₂²	1	2	yes	complemented
47	C₃₁×#390	C₂²	1	2	yes	complemented
48	C₃₁×#388	C₂²	1	2	yes	complemented
49	C₃₁×#388	C₂²	1	2	yes	complemented
50	C₃₁×#388	C₂²	1	2	yes	complemented
51	C₃₁×#388	C₂²	1	2	yes	complemented
52	C₃₁×#388	C₂²	1	2	yes	complemented
53	C₃₁×#388	C₂²	1	2	yes	complemented
54	C₃₁×#388	C₂²	1	2	yes	complemented
55	C₃₁×#388	C₂²	1	2	yes	complemented
56	C₃₁×#387	C₂²	1	2	yes	complemented
57	C₃₁×#387	C₂²	1	2	yes	complemented
58	C₃₁×#387	C₂²	1	2	yes	complemented
59	C₃₁×#387	C₂²	1	2	yes	complemented
60	C₃₁×#386	C₂²	1	2	yes	—
61	C₃₁×#386	C₂²	1	2	yes	—
62	C₃₁×#386	C₂²	1	2	yes	—
63	C₃₁×#386	C₂²	1	2	yes	—
64	C₃₁×#386	C₂²	1	2	yes	complemented
65	C₃₁×#386	C₂²	1	2	yes	complemented
66	C₃₁×#386	C₂²	1	2	yes	complemented
67	C₃₁×#386	C₂²	1	2	yes	complemented
68	C₃₁×#386	C₂²	1	2	yes	complemented
69	C₃₁×#386	C₂²	1	2	yes	complemented
70	C₃₁×#386	C₂²	1	2	yes	complemented
71	C₃₁×#386	C₂²	1	2	yes	complemented
72	C₃₁×#386	C₂²	1	2	yes	complemented
73	C₃₁×#386	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#386	C₂²	1	2	yes	complemented
75	C₃₁×#386	C₂²	1	2	yes	complemented
76	C₃₁×#386	C₂²	1	2	yes	complemented
77	C₃₁×#386	C₂²	1	2	yes	complemented
78	C₃₁×#386	C₂²	1	2	yes	complemented
79	C₃₁×#386	C₂²	1	2	yes	complemented
80	C₃₁×#386	C₂²	1	2	yes	complemented
81	C₃₁×#386	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#386	C₂²	1	2	yes	complemented
83	C₃₁×#385	C₂²	1	2	yes	complemented
84	C₃₁×#385	C₂²	1	2	yes	complemented
85	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#385	C₂²	1	2	yes	complemented
87	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#383	C₂²	1	2	yes	complemented
89	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#381	C₂²	1	2	yes	complemented
91	C₃₁×#381	C₂²	1	2	yes	complemented
92	C₃₁×#380	C₂²	1	2	yes	complemented
93	C₃₁×#380	C₂²	1	2	yes	complemented
94	C₃₁×#379	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#379	C₂²	1	2	yes	complemented
96	C₃₁×#379	C₂²	1	2	yes	complemented
97	C₃₁×#379	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, 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	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
107	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
108	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
109	C₂⁵×C₃₁	C₂³	1	2	yes	—
110	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	—	4	4	no	—
112	C₂²×D₄×C₃₁	—	4	4	no	—
113	C₂²×D₄×C₃₁	—	4	4	no	—
114	C₂²×D₄×C₃₁	—	4	4	no	—
115	C₂²×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
116	C₂²×D₄×C₃₁	C₂×C₄	1	16	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	2	yes	—
122	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
123	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
126	C₂³×C₄×C₃₁	—	4	2	no	—
127	C₂³×C₄×C₃₁	—	4	4	no	—
128	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
131	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
136	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
139	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
140	C₃₁×#127	C₂×C₄	1	8	yes	complemented
141	C₃₁×#121	C₂×C₄	1	16	yes	complemented
142	C₃₁×#121	C₂×C₄	1	16	yes	complemented
143	C₃₁×#120	C₂×C₄	1	8	yes	complemented
144	C₃₁×#120	C₂×C₄	1	16	yes	complemented
145	C₃₁×#120	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₃₁	—	4	2	no	—
147	C₄×D₄×C₃₁	—	4	2	no	—
148	C₄×D₄×C₃₁	—	4	4	no	—
149	C₄×D₄×C₃₁	—	4	4	no	—
150	C₄×D₄×C₃₁	—	4	4	no	—
151	C₄×D₄×C₃₁	—	4	4	no	—
152	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
161	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
162	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
163	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
164	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	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	C₂⁴×C₃₁	—	2	4	no	—
222	C₂⁴×C₃₁	—	2	4	no	—
223	C₂⁴×C₃₁	—	2	4	no	—
224	C₂⁴×C₃₁	—	2	4	no	—
225	C₂⁴×C₃₁	—	4	1	no	—
226	C₂⁴×C₃₁	—	4	1	no	—
227	C₂⁴×C₃₁	—	4	2	no	—
228	C₂⁴×C₃₁	—	4	1	no	—
229	C₂⁴×C₃₁	—	4	2	no	—
230	C₂⁴×C₃₁	—	4	2	no	—
231	C₂⁴×C₃₁	—	4	2	no	—
232	C₂⁴×C₃₁	—	4	2	no	—
233	C₂⁴×C₃₁	—	4	2	no	—
234	C₂⁴×C₃₁	—	4	1	no	—
235	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
236	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
237	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	complemented
238	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
239	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
240	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
243	C₂×D₄×C₃₁	—	2	4	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	4	no	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	4	no	—
249	C₂×D₄×C₃₁	—	4	1	no	—
250	C₂×D₄×C₃₁	—	4	1	no	—
251	C₂×D₄×C₃₁	—	4	2	no	—
252	C₂×D₄×C₃₁	—	4	2	no	—
253	C₂×D₄×C₃₁	—	4	2	no	—
254	C₂×D₄×C₃₁	—	4	2	no	—
255	C₂×D₄×C₃₁	—	4	2	no	—
256	C₂×D₄×C₃₁	—	4	2	no	—
257	C₂×D₄×C₃₁	—	4	2	no	—
258	C₂×D₄×C₃₁	—	4	2	no	—
259	C₂×D₄×C₃₁	—	4	1	no	—
260	C₂×D₄×C₃₁	—	4	1	no	—
261	C₂×D₄×C₃₁	—	4	32	no	—
262	C₂×D₄×C₃₁	—	4	32	no	—
263	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
265	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
266	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
268	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
269	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	complemented
270	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	complemented
271	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	complemented
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	—	2	4	no	—
276	C₂²×C₄×C₃₁	—	2	4	no	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	2	2	no	—
279	C₂²×C₄×C₃₁	—	4	2	no	—
280	C₂²×C₄×C₃₁	—	4	2	no	—
281	C₂²×C₄×C₃₁	—	4	1	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	2	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	1	no	—
292	C₂²×C₄×C₃₁	—	4	2	no	—
293	C₂²×C₄×C₃₁	—	4	2	no	—
294	C₂²×C₄×C₃₁	—	4	2	no	—
295	C₂²×C₄×C₃₁	—	4	2	no	—
296	C₂²×C₄×C₃₁	—	4	2	no	—
297	C₂²×C₄×C₃₁	—	4	2	no	—
298	C₂²×C₄×C₃₁	—	4	2	no	—
299	C₂²×C₄×C₃₁	—	4	2	no	—
300	C₂²×C₄×C₃₁	—	4	2	no	—
301	C₂²×C₄×C₃₁	—	4	2	no	—
302	C₂²×C₄×C₃₁	—	4	16	no	—
303	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
304	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
305	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₃₁	—	4	1	no	—
320	C₄⋊C₄×C₃₁	—	4	1	no	—
321	C₄⋊C₄×C₃₁	—	4	2	no	—
322	C₄⋊C₄×C₃₁	—	4	2	no	—
323	C₄⋊C₄×C₃₁	—	4	2	no	—
324	C₄⋊C₄×C₃₁	—	4	2	no	—
325	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	4	no	—
329	C₂²⋊C₄×C₃₁	—	2	4	no	—
330	C₂²⋊C₄×C₃₁	—	2	4	no	—
331	C₂²⋊C₄×C₃₁	—	2	4	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	2	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	—	4	1	no	—
345	C₂²⋊C₄×C₃₁	—	4	1	no	—
346	C₂²⋊C₄×C₃₁	—	4	1	no	—
347	C₂²⋊C₄×C₃₁	—	4	1	no	—
348	C₂²⋊C₄×C₃₁	—	4	2	no	—
349	C₂²⋊C₄×C₃₁	—	4	2	no	—
350	C₂²⋊C₄×C₃₁	—	4	2	no	—
351	C₂²⋊C₄×C₃₁	—	4	2	no	—
352	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
354	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
355	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
356	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	complemented
357	C₄²×C₃₁	—	2	2	no	—
358	C₄²×C₃₁	—	4	1	no	—
359	C₄²×C₃₁	—	4	2	no	—
360	C₄²×C₃₁	—	4	2	no	—
361	C₄²×C₃₁	—	4	2	no	—
362	C₄²×C₃₁	—	4	2	no	—
363	C₄²×C₃₁	C₂²×C₄	1	4	yes	complemented
364	#34468	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	—	2	2	no	—
367	C₂³×C₃₁	—	2	2	no	—
368	C₂³×C₃₁	—	2	2	no	—
369	C₂³×C₃₁	—	2	16	no	—
370	C₂³×C₃₁	—	2	2	no	—
371	C₂³×C₃₁	—	2	2	no	—
372	C₂³×C₃₁	—	2	2	no	—
373	C₂³×C₃₁	—	2	2	no	—
374	C₂³×C₃₁	—	2	2	no	—
375	C₂³×C₃₁	—	2	2	no	—
376	C₂³×C₃₁	—	2	1	no	—
377	C₂³×C₃₁	—	2	1	no	—
378	C₂³×C₃₁	—	2	2	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	2	no	—
386	C₂³×C₃₁	—	2	1	no	—
387	C₂³×C₃₁	—	2	1	no	—
388	C₂³×C₃₁	—	2	2	no	—
389	C₂³×C₃₁	—	2	2	no	—
390	C₂³×C₃₁	—	2	16	no	—
391	C₂³×C₃₁	—	4	4	no	—
392	C₂³×C₃₁	—	4	8	no	—
393	C₂³×C₃₁	—	4	8	no	—
394	C₂³×C₃₁	—	4	8	no	—
395	C₂³×C₃₁	—	4	4	no	—
396	C₂³×C₃₁	—	4	4	no	—
397	C₂³×C₃₁	—	4	8	no	—
398	C₂³×C₃₁	—	4	4	no	—
399	C₂³×C₃₁	—	8	4	no	—
400	C₂³×C₃₁	—	8	4	no	—
401	C₂³×C₃₁	—	8	4	no	—
402	C₂³×C₃₁	—	8	4	no	—
403	C₂³×C₃₁	—	8	2	no	—
404	C₂³×C₃₁	—	8	4	no	—
405	C₂³×C₃₁	—	8	2	no	—
406	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
407	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
408	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
409	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
410	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
411	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
412	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
413	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
414	D₄×C₃₁	—	2	16	no	—
415	D₄×C₃₁	—	2	16	no	—
416	D₄×C₃₁	—	2	16	no	—
417	D₄×C₃₁	—	4	8	no	—
418	D₄×C₃₁	—	4	8	no	—
419	D₄×C₃₁	—	4	8	no	—
420	D₄×C₃₁	—	4	8	no	—
421	D₄×C₃₁	—	4	4	no	—
422	D₄×C₃₁	—	4	4	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	—	2	2	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	1	no	—
432	C₂×C₄×C₃₁	—	2	1	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	1	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	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	1	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	4	8	no	—
457	C₂×C₄×C₃₁	—	4	8	no	—
458	C₂×C₄×C₃₁	—	4	8	no	—
459	C₂×C₄×C₃₁	—	4	4	no	—
460	C₂×C₄×C₃₁	—	4	8	no	—
461	C₂×C₄×C₃₁	—	4	4	no	—
462	C₂×C₄×C₃₁	—	8	2	no	—
463	C₂×C₄×C₃₁	—	8	4	no	—
464	C₂×C₄×C₃₁	—	8	4	no	—
465	C₂×C₄×C₃₁	—	8	4	no	—
466	C₂×C₄×C₃₁	—	8	4	no	—
467	C₂×C₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
470	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
471	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
472	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
473	C₂×D₄²	C₂×C₃₁	1	1	yes	characteristic
474	#2380	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#2377	C₂×C₃₁	1	2	yes	complemented
476	#2375	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#2364	C₂×C₃₁	1	2	yes	complemented
478	#2358	C₂×C₃₁	1	2	yes	complemented
479	#2358	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#2353	C₂×C₃₁	1	2	yes	complemented
481	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
482	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
483	#2333	C₂×C₃₁	1	2	yes	complemented
484	#2328	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#2325	C₂×C₃₁	1	2	yes	complemented
486	#2321	C₂×C₃₁	1	2	yes	complemented
487	#2321	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#2318	C₂×C₃₁	1	2	yes	complemented
489	#2308	C₂×C₃₁	1	2	yes	complemented
490	C₄×#120	C₂×C₃₁	1	1	yes	characteristic, complemented
491	C₂×#386	C₂×C₃₁	1	2	yes	complemented
492	C₂²×C₃₁	—	2	4	no	—
493	C₂²×C₃₁	—	2	4	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	—	2	4	no	—
501	C₂²×C₃₁	—	2	4	no	—
502	C₂²×C₃₁	—	2	4	no	—
503	C₂²×C₃₁	—	2	4	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	4	no	—
507	C₂²×C₃₁	—	2	4	no	—
508	C₂²×C₃₁	—	4	16	no	—
509	C₂²×C₃₁	—	4	1	no	—
510	C₂²×C₃₁	—	4	1	no	—
511	C₂²×C₃₁	—	4	2	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	2	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	2	no	—
518	C₂²×C₃₁	—	4	2	no	—
519	C₂²×C₃₁	—	4	2	no	—
520	C₂²×C₃₁	—	4	1	no	—
521	C₂²×C₃₁	—	4	1	no	—
522	C₂²×C₃₁	—	4	2	no	—
523	C₂²×C₃₁	—	8	16	no	—
524	C₂²×C₃₁	—	8	8	no	—
525	C₂²×C₃₁	#518	1	8	yes	—
526	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
527	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
528	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
529	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂²×C₃₁	#585	1	1	yes	characteristic
531	C₄×C₃₁	—	2	4	no	—
532	C₄×C₃₁	—	2	4	no	—
533	C₄×C₃₁	—	2	4	no	—
534	C₄×C₃₁	—	2	2	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	4	2	no	—
537	C₄×C₃₁	—	4	1	no	—
538	C₄×C₃₁	—	4	1	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	—	4	2	no	—
541	C₄×C₃₁	—	4	2	no	—
542	C₄×C₃₁	—	4	1	no	—
543	C₄×C₃₁	—	4	2	no	—
544	C₄×C₃₁	—	4	2	no	—
545	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
546	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
547	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	D₄²	C₄×C₃₁	1	16	yes	complemented
549	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
550	C₂×#121	C₂²×C₃₁	1	2	yes	—
551	C₂×#121	C₂²×C₃₁	1	2	yes	—
552	C₂×#120	C₂²×C₃₁	1	2	yes	—
553	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
554	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
556	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
557	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
558	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
559	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
560	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
562	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
563	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
564	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
566	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
567	#390	C₂²×C₃₁	1	1	yes	characteristic, 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	2	yes	complemented
572	#390	C₂²×C₃₁	1	2	yes	complemented
573	#388	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	#387	C₂²×C₃₁	1	2	yes	complemented
582	#387	C₂²×C₃₁	1	2	yes	complemented
583	#387	C₂²×C₃₁	1	2	yes	complemented
584	#387	C₂²×C₃₁	1	2	yes	complemented
585	#386	C₂²×C₃₁	1	2	yes	—
586	#386	C₂²×C₃₁	1	2	yes	—
587	#386	C₂²×C₃₁	1	2	yes	—
588	#386	C₂²×C₃₁	1	2	yes	—
589	#386	C₂²×C₃₁	1	2	yes	complemented
590	#386	C₂²×C₃₁	1	2	yes	complemented
591	#386	C₂²×C₃₁	1	2	yes	complemented
592	#386	C₂²×C₃₁	1	2	yes	complemented
593	#386	C₂²×C₃₁	1	2	yes	complemented
594	#386	C₂²×C₃₁	1	2	yes	complemented
595	#386	C₂²×C₃₁	1	2	yes	complemented
596	#386	C₂²×C₃₁	1	2	yes	complemented
597	#386	C₂²×C₃₁	1	2	yes	complemented
598	#386	C₂²×C₃₁	1	1	yes	characteristic, 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	#386	C₂²×C₃₁	1	2	yes	complemented
605	#386	C₂²×C₃₁	1	2	yes	complemented
606	#386	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	#386	C₂²×C₃₁	1	2	yes	complemented
608	#385	C₂²×C₃₁	1	2	yes	complemented
609	#385	C₂²×C₃₁	1	2	yes	complemented
610	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#385	C₂²×C₃₁	1	2	yes	complemented
612	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#383	C₂²×C₃₁	1	2	yes	complemented
614	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#381	C₂²×C₃₁	1	2	yes	complemented
616	#381	C₂²×C₃₁	1	2	yes	complemented
617	#380	C₂²×C₃₁	1	2	yes	complemented
618	#380	C₂²×C₃₁	1	2	yes	complemented
619	#379	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#379	C₂²×C₃₁	1	2	yes	complemented
621	#379	C₂²×C₃₁	1	2	yes	complemented
622	#379	C₂²×C₃₁	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
626	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
628	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
629	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
630	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
632	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
633	C₂×C₃₁	—	2	8	no	—
634	C₂×C₃₁	—	4	2	no	—
635	C₂×C₃₁	—	4	2	no	—
636	C₂×C₃₁	—	4	4	no	—
637	C₂×C₃₁	—	4	4	no	—
638	C₂×C₃₁	C₂×#518	1	2	yes	—
639	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₃₁	#3532	1	1	yes	characteristic
641	C₂×C₃₁	#3534	1	2	yes	—
642	C₂×C₃₁	#3537	1	1	yes	characteristic
643	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
644	C₂⁵	C₂³×C₃₁	1	2	yes	—
645	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
646	C₂²×D₄	—	4	4	no	—
647	C₂²×D₄	—	4	4	no	—
648	C₂²×D₄	—	4	4	no	—
649	C₂²×D₄	—	4	4	no	—
650	C₂²×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
651	C₂²×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
652	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
653	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
654	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
655	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
657	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
658	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
660	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
661	C₂³×C₄	—	4	2	no	—
662	C₂³×C₄	—	4	4	no	—
663	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
664	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
665	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
666	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
668	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
670	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
671	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
672	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
673	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
674	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
675	#127	C₂×C₄×C₃₁	1	8	yes	complemented
676	#121	C₂×C₄×C₃₁	1	16	yes	complemented
677	#121	C₂×C₄×C₃₁	1	16	yes	complemented
678	#120	C₂×C₄×C₃₁	1	8	yes	complemented
679	#120	C₂×C₄×C₃₁	1	16	yes	complemented
680	#120	C₂×C₄×C₃₁	1	8	yes	complemented
681	C₄×D₄	—	4	2	no	—
682	C₄×D₄	—	4	2	no	—
683	C₄×D₄	—	4	4	no	—
684	C₄×D₄	—	4	4	no	—
685	C₄×D₄	—	4	4	no	—
686	C₄×D₄	—	4	4	no	—
687	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
688	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
695	C₂×C₂²⋊C₄	—	4	2	no	—
696	C₂×C₂²⋊C₄	—	4	4	no	—
697	C₂×C₂²⋊C₄	—	4	4	no	—
698	C₂×C₂²⋊C₄	—	4	4	no	—
699	C₂×C₂²⋊C₄	—	4	4	no	—
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	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
733	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
734	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
735	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
736	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	#95	C₂³×C₃₁	1	2	yes	—
752	#95	C₂³×C₃₁	1	2	yes	—
753	#95	C₂³×C₃₁	1	2	yes	—
754	#95	C₂³×C₃₁	1	2	yes	—
755	#95	C₂³×C₃₁	1	2	yes	—
756	C₃₁	#34468	1	1	yes	characteristic, direct product factor, Sylow
757	C₂⁴	—	2	4	no	—
758	C₂⁴	—	2	4	no	—
759	C₂⁴	—	2	4	no	—
760	C₂⁴	—	2	4	no	—
761	C₂⁴	—	4	1	no	—
762	C₂⁴	—	4	1	no	—
763	C₂⁴	—	4	2	no	—
764	C₂⁴	—	4	1	no	—
765	C₂⁴	—	4	2	no	—
766	C₂⁴	—	4	2	no	—
767	C₂⁴	—	4	2	no	—
768	C₂⁴	—	4	2	no	—
769	C₂⁴	—	4	2	no	—
770	C₂⁴	—	4	1	no	—
771	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
772	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
773	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	complemented
774	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
775	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
776	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
777	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	4	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	1	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	—	4	32	no	—
798	C₂×D₄	—	4	32	no	—
799	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
800	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
801	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
802	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
803	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
804	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
805	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	complemented
806	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	complemented
807	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	complemented
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	4	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	1	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	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	16	no	—
839	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
840	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
841	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
855	C₄⋊C₄	—	4	1	no	—
856	C₄⋊C₄	—	4	1	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	—	4	2	no	—
859	C₄⋊C₄	—	4	2	no	—
860	C₄⋊C₄	—	4	2	no	—
861	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	1	no	—
881	C₂²⋊C₄	—	4	1	no	—
882	C₂²⋊C₄	—	4	1	no	—
883	C₂²⋊C₄	—	4	1	no	—
884	C₂²⋊C₄	—	4	2	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	4	2	no	—
888	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
891	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
892	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	complemented
893	C₄²	—	2	2	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	2	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	C₂²×C₄×C₃₁	1	4	yes	complemented
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	16	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	16	no	—
926	C₂³	—	4	4	no	—
927	C₂³	—	4	8	no	—
928	C₂³	—	4	8	no	—
929	C₂³	—	4	8	no	—
930	C₂³	—	4	4	no	—
931	C₂³	—	4	4	no	—
932	C₂³	—	4	8	no	—
933	C₂³	—	4	4	no	—
934	C₂³	—	8	4	no	—
935	C₂³	—	8	4	no	—
936	C₂³	—	8	4	no	—
937	C₂³	—	8	4	no	—
938	C₂³	—	8	2	no	—
939	C₂³	—	8	4	no	—
940	C₂³	—	8	2	no	—
941	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
942	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
943	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
944	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
945	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
946	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
947	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
948	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
949	D₄	—	2	16	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	4	8	no	—
953	D₄	—	4	8	no	—
954	D₄	—	4	8	no	—
955	D₄	—	4	8	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	4	no	—
958	C₂×C₄	—	2	1	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	1	no	—
967	C₂×C₄	—	2	1	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	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	—	4	8	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	—	8	4	no	—
1000	C₂×C₄	—	8	4	no	—
1001	C₂×C₄	—	8	4	no	—
1002	C₂×C₄	—	8	2	no	—
1003	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1004	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1005	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1006	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1007	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	4	no	—
1019	C₂²	—	2	4	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	4	no	—
1024	C₂²	—	4	16	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	8	16	no	—
1040	C₂²	—	8	8	no	—
1041	C₂²	C₃₁×#518	1	8	yes	—
1042	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1043	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1044	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1045	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1046	C₂²	C₃₁×#585	1	1	yes	characteristic
1047	C₄	—	2	4	no	—
1048	C₄	—	2	4	no	—
1049	C₄	—	2	4	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₂	—	2	8	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	4	4	no	—
1064	C₂	—	4	2	no	—
1065	C₂	—	4	4	no	—
1066	C₂	C₂×C₃₁×#518	1	2	yes	—
1067	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1068	C₂	C₃₁×#3532	1	1	yes	characteristic
1069	C₂	C₃₁×#3534	1	2	yes	—
1070	C₂	C₃₁×#3537	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×D₄²×C₃₁	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×#2380	C₂	semidirect
3. C₃₁×#2377	C₂	semidirect
4. C₃₁×#2375	C₂	semidirect
5. C₃₁×#2364	C₂	semidirect
6. C₃₁×#2358	C₂	semidirect
7. C₃₁×#2358	C₂	semidirect
8. C₃₁×#2353	C₂	semidirect
9. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
10. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
11. C₃₁×#2333	C₂	semidirect
12. C₃₁×#2328	C₂	semidirect
13. C₃₁×#2325	C₂	semidirect
14. C₃₁×#2321	C₂	semidirect
15. C₃₁×#2321	C₂	semidirect
16. C₃₁×#2318	C₂	semidirect
17. C₃₁×#2308	C₂	semidirect
18. C₄×C₃₁×#120	C₂	semidirect
19. C₂×C₃₁×#386	C₂	semidirect
22. C₂⁴×C₄×C₃₁	C₂²	semidirect
23. D₄²×C₃₁	C₄	semidirect
31. C₂×C₄×D₄×C₃₁	C₂²	semidirect
32. C₂×C₄×D₄×C₃₁	C₂²	semidirect
33. C₂×C₄×D₄×C₃₁	C₂²	semidirect
34. C₂×C₄×D₄×C₃₁	C₂²	semidirect
35. C₂×C₄×D₄×C₃₁	C₂²	semidirect
36. C₂×C₄×D₄×C₃₁	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
38. C₂²×C₂²⋊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. C₃₁×#390	C₂²	semidirect
43. C₃₁×#390	C₂²	semidirect
44. C₃₁×#390	C₂²	semidirect
45. C₃₁×#390	C₂²	semidirect
46. C₃₁×#390	C₂²	semidirect
47. C₃₁×#390	C₂²	semidirect
48. C₃₁×#388	C₂²	semidirect
49. C₃₁×#388	C₂²	semidirect
50. C₃₁×#388	C₂²	semidirect
51. C₃₁×#388	C₂²	semidirect
52. C₃₁×#388	C₂²	semidirect
53. C₃₁×#388	C₂²	semidirect
54. C₃₁×#388	C₂²	semidirect
55. C₃₁×#388	C₂²	semidirect
56. C₃₁×#387	C₂²	semidirect
57. C₃₁×#387	C₂²	semidirect
58. C₃₁×#387	C₂²	semidirect
59. C₃₁×#387	C₂²	semidirect
64. C₃₁×#386	C₂²	semidirect
65. C₃₁×#386	C₂²	semidirect
66. C₃₁×#386	C₂²	semidirect
67. C₃₁×#386	C₂²	semidirect
68. C₃₁×#386	C₂²	semidirect
69. C₃₁×#386	C₂²	semidirect
70. C₃₁×#386	C₂²	semidirect
71. C₃₁×#386	C₂²	semidirect
72. C₃₁×#386	C₂²	semidirect
73. C₃₁×#386	C₂²	semidirect
74. C₃₁×#386	C₂²	semidirect
75. C₃₁×#386	C₂²	semidirect
76. C₃₁×#386	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×#385	C₂²	semidirect
84. C₃₁×#385	C₂²	semidirect
85. C₃₁×#385	C₂²	semidirect
86. C₃₁×#385	C₂²	semidirect
87. C₃₁×#385	C₂²	semidirect
88. C₃₁×#383	C₂²	semidirect
89. C₃₁×#382	C₂²	semidirect
90. C₃₁×#381	C₂²	semidirect
91. C₃₁×#381	C₂²	semidirect
92. C₃₁×#380	C₂²	semidirect
93. C₃₁×#380	C₂²	semidirect
94. C₃₁×#379	C₂²	semidirect
95. C₃₁×#379	C₂²	semidirect
96. C₃₁×#379	C₂²	semidirect
97. C₃₁×#379	C₂²	semidirect
98. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
99. C₄×C₂²⋊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. C₃₁×#376	C₂²	semidirect
106. C₂×C₃₁×#95	C₂²	semidirect
107. C₂×C₃₁×#95	C₂²	semidirect
115. C₂²×D₄×C₃₁	C₂×C₄	semidirect
116. C₂²×D₄×C₃₁	C₂×C₄	semidirect
140. C₃₁×#127	C₂×C₄	semidirect
141. C₃₁×#121	C₂×C₄	semidirect
142. C₃₁×#121	C₂×C₄	semidirect
143. C₃₁×#120	C₂×C₄	semidirect
144. C₃₁×#120	C₂×C₄	semidirect
145. C₃₁×#120	C₂×C₄	semidirect
152. C₄×D₄×C₃₁	C₂×C₄	semidirect
237. C₂⁴×C₃₁	C₂²×C₄	semidirect
269. C₂×D₄×C₃₁	C₂²×C₄	semidirect
270. C₂×D₄×C₃₁	C₂²×C₄	semidirect
271. C₂×D₄×C₃₁	C₂²×C₄	semidirect
304. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
325. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
354. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
355. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
356. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
363. C₄²×C₃₁	C₂²×C₄	semidirect
364. #34468	C₃₁	direct (N × H)
474. #2380	C₂×C₃₁	semidirect
475. #2377	C₂×C₃₁	semidirect
476. #2375	C₂×C₃₁	semidirect
477. #2364	C₂×C₃₁	semidirect
478. #2358	C₂×C₃₁	semidirect
479. #2358	C₂×C₃₁	semidirect
480. #2353	C₂×C₃₁	semidirect
481. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
482. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
483. #2333	C₂×C₃₁	semidirect
484. #2328	C₂×C₃₁	semidirect
485. #2325	C₂×C₃₁	semidirect
486. #2321	C₂×C₃₁	semidirect
487. #2321	C₂×C₃₁	semidirect
488. #2318	C₂×C₃₁	semidirect
489. #2308	C₂×C₃₁	semidirect
490. C₄×#120	C₂×C₃₁	semidirect
491. C₂×#386	C₂×C₃₁	semidirect
547. C₂⁴×C₄	C₂²×C₃₁	semidirect
548. D₄²	C₄×C₃₁	semidirect
556. C₂×C₄×D₄	C₂²×C₃₁	semidirect
557. C₂×C₄×D₄	C₂²×C₃₁	semidirect
558. C₂×C₄×D₄	C₂²×C₃₁	semidirect
559. C₂×C₄×D₄	C₂²×C₃₁	semidirect
560. C₂×C₄×D₄	C₂²×C₃₁	semidirect
561. C₂×C₄×D₄	C₂²×C₃₁	semidirect
562. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
563. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
564. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
565. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
566. C₂²×C₂²⋊C₄	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. #390	C₂²×C₃₁	semidirect
573. #388	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. #387	C₂²×C₃₁	semidirect
582. #387	C₂²×C₃₁	semidirect
583. #387	C₂²×C₃₁	semidirect
584. #387	C₂²×C₃₁	semidirect
589. #386	C₂²×C₃₁	semidirect
590. #386	C₂²×C₃₁	semidirect
591. #386	C₂²×C₃₁	semidirect
592. #386	C₂²×C₃₁	semidirect
593. #386	C₂²×C₃₁	semidirect
594. #386	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. #386	C₂²×C₃₁	semidirect
605. #386	C₂²×C₃₁	semidirect
606. #386	C₂²×C₃₁	semidirect
607. #386	C₂²×C₃₁	semidirect
608. #385	C₂²×C₃₁	semidirect
609. #385	C₂²×C₃₁	semidirect
610. #385	C₂²×C₃₁	semidirect
611. #385	C₂²×C₃₁	semidirect
612. #385	C₂²×C₃₁	semidirect
613. #383	C₂²×C₃₁	semidirect
614. #382	C₂²×C₃₁	semidirect
615. #381	C₂²×C₃₁	semidirect
616. #381	C₂²×C₃₁	semidirect
617. #380	C₂²×C₃₁	semidirect
618. #380	C₂²×C₃₁	semidirect
619. #379	C₂²×C₃₁	semidirect
620. #379	C₂²×C₃₁	semidirect
621. #379	C₂²×C₃₁	semidirect
622. #379	C₂²×C₃₁	semidirect
623. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
624. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
625. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
626. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
627. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
628. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
629. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
630. #376	C₂²×C₃₁	semidirect
631. C₂×#95	C₂²×C₃₁	semidirect
632. C₂×#95	C₂²×C₃₁	semidirect
650. C₂²×D₄	C₂×C₄×C₃₁	semidirect
651. C₂²×D₄	C₂×C₄×C₃₁	semidirect
675. #127	C₂×C₄×C₃₁	semidirect
676. #121	C₂×C₄×C₃₁	semidirect
677. #121	C₂×C₄×C₃₁	semidirect
678. #120	C₂×C₄×C₃₁	semidirect
679. #120	C₂×C₄×C₃₁	semidirect
680. #120	C₂×C₄×C₃₁	semidirect
687. C₄×D₄	C₂×C₄×C₃₁	semidirect
756. C₃₁	#34468	direct (N × H)
773. C₂⁴	C₂²×C₄×C₃₁	semidirect
805. C₂×D₄	C₂²×C₄×C₃₁	semidirect
806. C₂×D₄	C₂²×C₄×C₃₁	semidirect
807. C₂×D₄	C₂²×C₄×C₃₁	semidirect
840. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
861. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
890. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
891. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
892. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
899. C₄²	C₂²×C₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₃₁	2
C₃₁×#2380	2
C₃₁×#2377	2
C₃₁×#2375	2
C₃₁×#2364	2
C₃₁×#2358	2
C₃₁×#2353	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2333	2
C₃₁×#2328	2
C₃₁×#2325	2
C₃₁×#2321	2
C₃₁×#2318	2
C₃₁×#2308	2
C₄×C₃₁×#120	2
C₂×C₃₁×#386	2
#34468	31

Subgroups — C31×#34468 #21491227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34468 #21491227