Subgroups — C₃₁×#36737 #21493496

Order 7936.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2847	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2717	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2709	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2708	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2688	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2686	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2673	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2671	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2668	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2617	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2498	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2430	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2412	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2410	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#535	—	2	8	no	—
25	C₃₁×#534	—	2	8	no	—
26	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×#123	C₂²	1	2	yes	—
31	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
34	C₂×C₃₁×#121	C₂²	1	2	yes	—
35	C₂×C₃₁×#121	C₂²	1	2	yes	—
36	C₂×C₃₁×#121	C₂²	1	2	yes	—
37	C₂×C₃₁×#121	C₂²	1	2	yes	—
38	C₂×C₃₁×#121	C₂²	1	2	yes	—
39	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
40	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
42	C₂×C₃₁×#120	C₂²	1	2	yes	—
43	C₂×C₃₁×#120	C₂²	1	2	yes	—
44	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
47	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
48	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
51	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#400	C₂²	1	2	yes	complemented
53	C₃₁×#399	C₂²	1	2	yes	complemented
54	C₃₁×#398	C₂²	1	2	yes	complemented
55	C₃₁×#397	C₂²	1	2	yes	complemented
56	C₃₁×#397	C₂²	1	2	yes	complemented
57	C₃₁×#397	C₂²	1	2	yes	complemented
58	C₃₁×#397	C₂²	1	2	yes	complemented
59	C₃₁×#397	C₂²	1	2	yes	complemented
60	C₃₁×#395	C₂²	1	2	yes	complemented
61	C₃₁×#394	C₂²	1	2	yes	complemented
62	C₃₁×#394	C₂²	1	2	yes	complemented
63	C₃₁×#394	C₂²	1	2	yes	complemented
64	C₃₁×#394	C₂²	1	2	yes	complemented
65	C₃₁×#394	C₂²	1	2	yes	complemented
66	C₃₁×#394	C₂²	1	2	yes	complemented
67	C₃₁×#394	C₂²	1	2	yes	complemented
68	C₃₁×#394	C₂²	1	2	yes	complemented
69	C₃₁×#394	C₂²	1	2	yes	complemented
70	C₃₁×#393	C₂²	1	2	yes	complemented
71	C₃₁×#392	C₂²	1	2	yes	complemented
72	C₃₁×#392	C₂²	1	2	yes	complemented
73	C₃₁×#392	C₂²	1	2	yes	complemented
74	C₃₁×#392	C₂²	1	2	yes	complemented
75	C₃₁×#392	C₂²	1	2	yes	complemented
76	C₃₁×#388	C₂²	1	2	yes	complemented
77	C₃₁×#388	C₂²	1	2	yes	complemented
78	C₃₁×#387	C₂²	1	2	yes	complemented
79	C₃₁×#387	C₂²	1	2	yes	complemented
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#386	C₂²	1	2	yes	—
82	C₃₁×#386	C₂²	1	2	yes	—
83	C₃₁×#386	C₂²	1	1	yes	characteristic
84	C₃₁×#386	C₂²	1	1	yes	characteristic
85	C₃₁×#386	C₂²	1	2	yes	complemented
86	C₃₁×#386	C₂²	1	2	yes	complemented
87	C₃₁×#386	C₂²	1	2	yes	complemented
88	C₃₁×#386	C₂²	1	2	yes	complemented
89	C₃₁×#386	C₂²	1	2	yes	complemented
90	C₃₁×#386	C₂²	1	2	yes	complemented
91	C₃₁×#386	C₂²	1	2	yes	complemented
92	C₃₁×#386	C₂²	1	2	yes	complemented
93	C₃₁×#386	C₂²	1	2	yes	complemented
94	C₃₁×#386	C₂²	1	2	yes	complemented
95	C₃₁×#386	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#386	C₂²	1	2	yes	complemented
97	C₃₁×#386	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#385	C₂²	1	2	yes	complemented
99	C₃₁×#385	C₂²	1	2	yes	complemented
100	C₃₁×#385	C₂²	1	2	yes	complemented
101	C₃₁×#385	C₂²	1	2	yes	complemented
102	C₃₁×#381	C₂²	1	2	yes	complemented
103	C₃₁×#380	C₂²	1	2	yes	complemented
104	C₃₁×#380	C₂²	1	2	yes	complemented
105	C₃₁×#380	C₂²	1	2	yes	complemented
106	C₃₁×#380	C₂²	1	2	yes	complemented
107	C₃₁×#379	C₂²	1	2	yes	complemented
108	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
109	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
110	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
111	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×#41×C₃₁	—	2	4	no	—
113	C₂×#41×C₃₁	—	4	2	no	—
114	C₂×#41×C₃₁	—	4	2	no	—
115	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₃₁	—	2	4	no	—
117	C₂²×D₄×C₃₁	—	4	2	no	—
118	C₂²×D₄×C₃₁	—	4	2	no	—
119	C₂²×D₄×C₃₁	—	4	2	no	—
120	C₂²×D₄×C₃₁	—	4	2	no	—
121	C₂²×D₄×C₃₁	D₄	1	8	yes	complemented
122	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
123	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
130	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
131	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
132	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
134	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₃₁	—	4	4	no	—
139	C₂³×C₄×C₃₁	—	4	2	no	—
140	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₃₁×#127	—	2	4	no	—
150	C₃₁×#127	—	2	4	no	—
151	C₃₁×#124	—	2	4	no	—
152	C₃₁×#124	—	2	4	no	—
153	C₃₁×#123	—	2	4	no	—
154	C₃₁×#123	—	2	4	no	—
155	C₃₁×#123	—	2	8	no	—
156	C₃₁×#123	—	4	4	no	—
157	C₃₁×#121	—	2	8	no	—
158	C₃₁×#121	—	2	8	no	—
159	C₃₁×#121	—	2	8	no	—
160	C₃₁×#121	—	2	8	no	—
161	C₃₁×#121	—	4	4	no	—
162	C₃₁×#121	—	4	4	no	—
163	C₃₁×#121	—	4	4	no	—
164	C₃₁×#121	—	4	4	no	—
165	C₃₁×#120	—	2	8	no	—
166	C₃₁×#120	—	2	8	no	—
167	C₃₁×#120	—	2	8	no	—
168	C₃₁×#120	—	2	4	no	—
169	C₃₁×#120	—	2	4	no	—
170	C₃₁×#120	—	4	4	no	—
171	C₃₁×#117	—	2	4	no	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
182	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
183	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
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	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₂⁴×C₃₁	—	2	2	no	—
234	C₂⁴×C₃₁	—	2	2	no	—
235	C₂⁴×C₃₁	—	2	2	no	—
236	C₂⁴×C₃₁	—	2	2	no	—
237	C₂⁴×C₃₁	—	2	2	no	—
238	C₂⁴×C₃₁	—	4	2	no	—
239	C₂⁴×C₃₁	—	4	2	no	—
240	C₂⁴×C₃₁	—	4	2	no	—
241	C₂⁴×C₃₁	—	4	1	no	—
242	C₂⁴×C₃₁	—	4	1	no	—
243	C₂⁴×C₃₁	—	4	2	no	—
244	C₂⁴×C₃₁	—	4	2	no	—
245	C₂⁴×C₃₁	—	4	2	no	—
246	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
247	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
248	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
249	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
250	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
255	#41×C₃₁	—	4	16	no	—
256	C₂×Q₈×C₃₁	—	2	2	no	—
257	C₂×Q₈×C₃₁	—	4	1	no	—
258	C₂×Q₈×C₃₁	—	4	1	no	—
259	C₂×D₄×C₃₁	—	2	4	no	—
260	C₂×D₄×C₃₁	—	2	4	no	—
261	C₂×D₄×C₃₁	—	2	4	no	—
262	C₂×D₄×C₃₁	—	2	4	no	—
263	C₂×D₄×C₃₁	—	2	4	no	—
264	C₂×D₄×C₃₁	—	2	4	no	—
265	C₂×D₄×C₃₁	—	2	4	no	—
266	C₂×D₄×C₃₁	—	2	4	no	—
267	C₂×D₄×C₃₁	—	2	4	no	—
268	C₂×D₄×C₃₁	—	2	4	no	—
269	C₂×D₄×C₃₁	—	2	4	no	—
270	C₂×D₄×C₃₁	—	2	4	no	—
271	C₂×D₄×C₃₁	—	2	4	no	—
272	C₂×D₄×C₃₁	—	2	2	no	—
273	C₂×D₄×C₃₁	—	2	4	no	—
274	C₂×D₄×C₃₁	—	4	16	no	—
275	C₂×D₄×C₃₁	—	4	1	no	—
276	C₂×D₄×C₃₁	—	4	1	no	—
277	C₂×D₄×C₃₁	—	4	1	no	—
278	C₂×D₄×C₃₁	—	4	1	no	—
279	C₂×D₄×C₃₁	—	4	1	no	—
280	C₂×D₄×C₃₁	—	4	1	no	—
281	C₂×D₄×C₃₁	—	4	1	no	—
282	C₂×D₄×C₃₁	—	4	1	no	—
283	C₂×D₄×C₃₁	—	4	2	no	—
284	C₂×D₄×C₃₁	—	4	2	no	—
285	C₂×D₄×C₃₁	—	4	1	no	—
286	C₂×D₄×C₃₁	—	4	1	no	—
287	C₂×D₄×C₃₁	—	4	2	no	—
288	C₂×D₄×C₃₁	—	4	2	no	—
289	C₂×D₄×C₃₁	—	4	2	no	—
290	C₂×D₄×C₃₁	—	4	2	no	—
291	C₂×D₄×C₃₁	—	4	2	no	—
292	C₂×D₄×C₃₁	—	4	2	no	—
293	C₂×D₄×C₃₁	—	4	2	no	—
294	C₂×D₄×C₃₁	—	4	2	no	—
295	C₂×D₄×C₃₁	—	4	2	no	—
296	C₂×D₄×C₃₁	—	4	2	no	—
297	C₂×D₄×C₃₁	—	4	2	no	—
298	C₂×D₄×C₃₁	—	4	2	no	—
299	C₂×D₄×C₃₁	—	4	2	no	—
300	C₂×D₄×C₃₁	—	4	2	no	—
301	C₂×D₄×C₃₁	—	4	2	no	—
302	C₂×D₄×C₃₁	—	4	2	no	—
303	C₂×D₄×C₃₁	—	4	2	no	—
304	C₂×D₄×C₃₁	—	4	16	no	—
305	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
306	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
307	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
308	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	2	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	4	no	—
313	C₂²×C₄×C₃₁	—	2	4	no	—
314	C₂²×C₄×C₃₁	—	2	4	no	—
315	C₂²×C₄×C₃₁	—	2	4	no	—
316	C₂²×C₄×C₃₁	—	2	4	no	—
317	C₂²×C₄×C₃₁	—	2	4	no	—
318	C₂²×C₄×C₃₁	—	2	4	no	—
319	C₂²×C₄×C₃₁	—	4	1	no	—
320	C₂²×C₄×C₃₁	—	4	2	no	—
321	C₂²×C₄×C₃₁	—	4	2	no	—
322	C₂²×C₄×C₃₁	—	4	2	no	—
323	C₂²×C₄×C₃₁	—	4	2	no	—
324	C₂²×C₄×C₃₁	—	4	1	no	—
325	C₂²×C₄×C₃₁	—	4	1	no	—
326	C₂²×C₄×C₃₁	—	4	1	no	—
327	C₂²×C₄×C₃₁	—	4	2	no	—
328	C₂²×C₄×C₃₁	—	4	2	no	—
329	C₂²×C₄×C₃₁	—	4	2	no	—
330	C₂²×C₄×C₃₁	—	4	2	no	—
331	C₂²×C₄×C₃₁	—	4	2	no	—
332	C₂²×C₄×C₃₁	—	4	2	no	—
333	C₂²×C₄×C₃₁	—	4	16	no	—
334	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
335	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₃₁	—	2	4	no	—
348	C₄⋊C₄×C₃₁	—	2	4	no	—
349	C₄⋊C₄×C₃₁	—	2	4	no	—
350	C₄⋊C₄×C₃₁	—	2	4	no	—
351	C₄⋊C₄×C₃₁	—	4	2	no	—
352	C₄⋊C₄×C₃₁	—	4	2	no	—
353	C₄⋊C₄×C₃₁	—	4	2	no	—
354	C₄⋊C₄×C₃₁	—	4	2	no	—
355	C₄⋊C₄×C₃₁	—	4	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	4	no	—
359	C₂²⋊C₄×C₃₁	—	2	4	no	—
360	C₂²⋊C₄×C₃₁	—	2	4	no	—
361	C₂²⋊C₄×C₃₁	—	2	4	no	—
362	C₂²⋊C₄×C₃₁	—	2	4	no	—
363	C₂²⋊C₄×C₃₁	—	2	4	no	—
364	C₂²⋊C₄×C₃₁	—	2	4	no	—
365	C₂²⋊C₄×C₃₁	—	2	4	no	—
366	C₂²⋊C₄×C₃₁	—	2	4	no	—
367	C₂²⋊C₄×C₃₁	—	2	4	no	—
368	C₂²⋊C₄×C₃₁	—	2	4	no	—
369	C₂²⋊C₄×C₃₁	—	2	4	no	—
370	C₂²⋊C₄×C₃₁	—	2	4	no	—
371	C₂²⋊C₄×C₃₁	—	2	4	no	—
372	C₂²⋊C₄×C₃₁	—	4	2	no	—
373	C₂²⋊C₄×C₃₁	—	4	2	no	—
374	C₂²⋊C₄×C₃₁	—	4	1	no	—
375	C₂²⋊C₄×C₃₁	—	4	2	no	—
376	C₂²⋊C₄×C₃₁	—	4	1	no	—
377	C₂²⋊C₄×C₃₁	—	4	2	no	—
378	C₂²⋊C₄×C₃₁	—	4	2	no	—
379	C₂²⋊C₄×C₃₁	—	4	2	no	—
380	C₂²⋊C₄×C₃₁	—	4	2	no	—
381	C₂²⋊C₄×C₃₁	—	4	2	no	—
382	C₂²⋊C₄×C₃₁	—	4	2	no	—
383	C₂²⋊C₄×C₃₁	—	4	2	no	—
384	C₂²⋊C₄×C₃₁	—	4	2	no	—
385	C₂²⋊C₄×C₃₁	—	4	2	no	—
386	C₂²⋊C₄×C₃₁	—	4	2	no	—
387	C₄²×C₃₁	—	2	2	no	—
388	C₄²×C₃₁	—	2	2	no	—
389	#36737	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂³×C₃₁	—	2	2	no	—
391	C₂³×C₃₁	—	2	2	no	—
392	C₂³×C₃₁	—	2	8	no	—
393	C₂³×C₃₁	—	2	2	no	—
394	C₂³×C₃₁	—	2	2	no	—
395	C₂³×C₃₁	—	2	1	no	—
396	C₂³×C₃₁	—	2	1	no	—
397	C₂³×C₃₁	—	2	2	no	—
398	C₂³×C₃₁	—	2	2	no	—
399	C₂³×C₃₁	—	2	1	no	—
400	C₂³×C₃₁	—	2	1	no	—
401	C₂³×C₃₁	—	2	1	no	—
402	C₂³×C₃₁	—	2	1	no	—
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	1	no	—
405	C₂³×C₃₁	—	2	2	no	—
406	C₂³×C₃₁	—	2	2	no	—
407	C₂³×C₃₁	—	2	2	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	2	8	no	—
410	C₂³×C₃₁	—	2	2	no	—
411	C₂³×C₃₁	—	2	2	no	—
412	C₂³×C₃₁	—	2	2	no	—
413	C₂³×C₃₁	—	2	2	no	—
414	C₂³×C₃₁	—	2	2	no	—
415	C₂³×C₃₁	—	2	2	no	—
416	C₂³×C₃₁	—	2	2	no	—
417	C₂³×C₃₁	—	2	2	no	—
418	C₂³×C₃₁	—	2	2	no	—
419	C₂³×C₃₁	—	2	2	no	—
420	C₂³×C₃₁	—	2	2	no	—
421	C₂³×C₃₁	—	2	2	no	—
422	C₂³×C₃₁	—	2	2	no	—
423	C₂³×C₃₁	—	2	2	no	—
424	C₂³×C₃₁	—	4	8	no	—
425	C₂³×C₃₁	—	4	8	no	—
426	C₂³×C₃₁	—	4	4	no	—
427	C₂³×C₃₁	—	4	4	no	—
428	C₂³×C₃₁	—	4	8	no	—
429	C₂³×C₃₁	—	4	4	no	—
430	C₂³×C₃₁	—	8	2	no	—
431	C₂³×C₃₁	—	8	2	no	—
432	C₂³×C₃₁	—	8	4	no	—
433	C₂³×C₃₁	—	8	4	no	—
434	C₂³×C₃₁	—	8	2	no	—
435	C₂³×C₃₁	—	8	2	no	—
436	C₂³×C₃₁	—	8	4	no	—
437	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
438	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
439	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
440	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
441	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
442	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
443	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
444	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
445	Q₈×C₃₁	—	4	4	no	—
446	D₄×C₃₁	—	4	4	no	—
447	D₄×C₃₁	—	4	4	no	—
448	D₄×C₃₁	—	4	4	no	—
449	D₄×C₃₁	—	4	4	no	—
450	D₄×C₃₁	—	4	4	no	—
451	D₄×C₃₁	—	4	8	no	—
452	D₄×C₃₁	—	4	8	no	—
453	D₄×C₃₁	—	4	8	no	—
454	D₄×C₃₁	—	8	4	no	—
455	D₄×C₃₁	—	8	4	no	—
456	D₄×C₃₁	—	8	4	no	—
457	D₄×C₃₁	—	8	4	no	—
458	D₄×C₃₁	—	8	4	no	—
459	D₄×C₃₁	—	8	4	no	—
460	D₄×C₃₁	—	8	4	no	—
461	D₄×C₃₁	—	8	4	no	—
462	C₂×C₄×C₃₁	—	2	8	no	—
463	C₂×C₄×C₃₁	—	2	2	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	1	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	4	4	no	—
497	C₂×C₄×C₃₁	—	4	8	no	—
498	C₂×C₄×C₃₁	—	4	8	no	—
499	C₂×C₄×C₃₁	—	4	8	no	—
500	C₂×C₄×C₃₁	—	4	4	no	—
501	C₂×C₄×C₃₁	—	4	4	no	—
502	C₂×C₄×C₃₁	—	8	4	no	—
503	C₂×C₄×C₃₁	—	8	4	no	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
507	C₂×#535	C₂×C₃₁	1	1	yes	characteristic, complemented
508	C₂×#534	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#2847	C₂×C₃₁	1	2	yes	complemented
510	#2717	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#2709	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#2708	C₂×C₃₁	1	2	yes	complemented
513	#2688	C₂×C₃₁	1	2	yes	complemented
514	#2686	C₂×C₃₁	1	2	yes	complemented
515	#2684	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#2673	C₂×C₃₁	1	2	yes	complemented
517	#2671	C₂×C₃₁	1	2	yes	complemented
518	#2669	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#2668	C₂×C₃₁	1	2	yes	complemented
520	#2617	C₂×C₃₁	1	2	yes	complemented
521	#2498	C₂×C₃₁	1	2	yes	complemented
522	#2430	C₂×C₃₁	1	2	yes	complemented
523	#2412	C₂×C₃₁	1	2	yes	complemented
524	#2410	C₂×C₃₁	1	2	yes	complemented
525	C₂×#386	C₂×C₃₁	1	1	yes	characteristic, complemented
526	C₂²×C₃₁	—	2	4	no	—
527	C₂²×C₃₁	—	2	2	no	—
528	C₂²×C₃₁	—	2	2	no	—
529	C₂²×C₃₁	—	2	4	no	—
530	C₂²×C₃₁	—	2	2	no	—
531	C₂²×C₃₁	—	2	2	no	—
532	C₂²×C₃₁	—	2	2	no	—
533	C₂²×C₃₁	—	2	2	no	—
534	C₂²×C₃₁	—	2	4	no	—
535	C₂²×C₃₁	—	2	4	no	—
536	C₂²×C₃₁	—	2	4	no	—
537	C₂²×C₃₁	—	2	4	no	—
538	C₂²×C₃₁	—	4	16	no	—
539	C₂²×C₃₁	—	4	1	no	—
540	C₂²×C₃₁	—	4	1	no	—
541	C₂²×C₃₁	—	4	1	no	—
542	C₂²×C₃₁	—	4	1	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	2	no	—
548	C₂²×C₃₁	—	4	2	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	—	4	2	no	—
551	C₂²×C₃₁	—	4	2	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	4	2	no	—
555	C₂²×C₃₁	—	4	2	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	4	2	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	2	no	—
560	C₂²×C₃₁	—	4	2	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	4	2	no	—
564	C₂²×C₃₁	—	4	2	no	—
565	C₂²×C₃₁	—	8	8	no	—
566	C₂²×C₃₁	—	8	8	no	—
567	C₂²×C₃₁	#534	1	4	yes	—
568	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
569	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
572	C₂²×C₃₁	#585	1	2	yes	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	2	2	no	—
575	C₄×C₃₁	—	2	4	no	—
576	C₄×C₃₁	—	4	2	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	—	4	2	no	—
579	C₄×C₃₁	—	4	2	no	—
580	C₄×C₃₁	—	4	2	no	—
581	C₄×C₃₁	—	4	2	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	—	4	2	no	—
584	C₄×C₃₁	—	4	2	no	—
585	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
588	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
589	#535	—	2	8	no	—
590	#534	—	2	8	no	—
591	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
592	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
594	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	C₂×#123	C₂²×C₃₁	1	2	yes	—
596	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
597	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
598	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
599	C₂×#121	C₂²×C₃₁	1	2	yes	—
600	C₂×#121	C₂²×C₃₁	1	2	yes	—
601	C₂×#121	C₂²×C₃₁	1	2	yes	—
602	C₂×#121	C₂²×C₃₁	1	2	yes	—
603	C₂×#121	C₂²×C₃₁	1	2	yes	—
604	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
605	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
606	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
607	C₂×#120	C₂²×C₃₁	1	2	yes	—
608	C₂×#120	C₂²×C₃₁	1	2	yes	—
609	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
610	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
611	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
612	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
613	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
615	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
616	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#400	C₂²×C₃₁	1	2	yes	complemented
618	#399	C₂²×C₃₁	1	2	yes	complemented
619	#398	C₂²×C₃₁	1	2	yes	complemented
620	#397	C₂²×C₃₁	1	2	yes	complemented
621	#397	C₂²×C₃₁	1	2	yes	complemented
622	#397	C₂²×C₃₁	1	2	yes	complemented
623	#397	C₂²×C₃₁	1	2	yes	complemented
624	#397	C₂²×C₃₁	1	2	yes	complemented
625	#395	C₂²×C₃₁	1	2	yes	complemented
626	#394	C₂²×C₃₁	1	2	yes	complemented
627	#394	C₂²×C₃₁	1	2	yes	complemented
628	#394	C₂²×C₃₁	1	2	yes	complemented
629	#394	C₂²×C₃₁	1	2	yes	complemented
630	#394	C₂²×C₃₁	1	2	yes	complemented
631	#394	C₂²×C₃₁	1	2	yes	complemented
632	#394	C₂²×C₃₁	1	2	yes	complemented
633	#394	C₂²×C₃₁	1	2	yes	complemented
634	#394	C₂²×C₃₁	1	2	yes	complemented
635	#393	C₂²×C₃₁	1	2	yes	complemented
636	#392	C₂²×C₃₁	1	2	yes	complemented
637	#392	C₂²×C₃₁	1	2	yes	complemented
638	#392	C₂²×C₃₁	1	2	yes	complemented
639	#392	C₂²×C₃₁	1	2	yes	complemented
640	#392	C₂²×C₃₁	1	2	yes	complemented
641	#388	C₂²×C₃₁	1	2	yes	complemented
642	#388	C₂²×C₃₁	1	2	yes	complemented
643	#387	C₂²×C₃₁	1	2	yes	complemented
644	#387	C₂²×C₃₁	1	2	yes	complemented
645	#386	C₂²×C₃₁	1	2	yes	—
646	#386	C₂²×C₃₁	1	2	yes	—
647	#386	C₂²×C₃₁	1	2	yes	—
648	#386	C₂²×C₃₁	1	1	yes	characteristic
649	#386	C₂²×C₃₁	1	1	yes	characteristic
650	#386	C₂²×C₃₁	1	2	yes	complemented
651	#386	C₂²×C₃₁	1	2	yes	complemented
652	#386	C₂²×C₃₁	1	2	yes	complemented
653	#386	C₂²×C₃₁	1	2	yes	complemented
654	#386	C₂²×C₃₁	1	2	yes	complemented
655	#386	C₂²×C₃₁	1	2	yes	complemented
656	#386	C₂²×C₃₁	1	2	yes	complemented
657	#386	C₂²×C₃₁	1	2	yes	complemented
658	#386	C₂²×C₃₁	1	2	yes	complemented
659	#386	C₂²×C₃₁	1	2	yes	complemented
660	#386	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#386	C₂²×C₃₁	1	2	yes	complemented
662	#386	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#385	C₂²×C₃₁	1	2	yes	complemented
664	#385	C₂²×C₃₁	1	2	yes	complemented
665	#385	C₂²×C₃₁	1	2	yes	complemented
666	#385	C₂²×C₃₁	1	2	yes	complemented
667	#381	C₂²×C₃₁	1	2	yes	complemented
668	#380	C₂²×C₃₁	1	2	yes	complemented
669	#380	C₂²×C₃₁	1	2	yes	complemented
670	#380	C₂²×C₃₁	1	2	yes	complemented
671	#380	C₂²×C₃₁	1	2	yes	complemented
672	#379	C₂²×C₃₁	1	2	yes	complemented
673	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
674	C₂×C₃₁	—	2	4	no	—
675	C₂×C₃₁	—	4	2	no	—
676	C₂×C₃₁	—	4	2	no	—
677	C₂×C₃₁	—	4	2	no	—
678	C₂×C₃₁	—	4	2	no	—
679	C₂×C₃₁	—	8	2	no	—
680	C₂×C₃₁	—	8	2	no	—
681	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
682	C₂×C₃₁	#3496	1	2	yes	—
683	C₂×C₃₁	#3532	1	1	yes	characteristic
684	C₂×C₃₁	#3533	1	1	yes	characteristic
685	C₂×C₃₁	#3542	1	2	yes	—
686	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
687	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
688	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×#41	—	2	4	no	—
690	C₂×#41	—	4	2	no	—
691	C₂×#41	—	4	2	no	—
692	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
693	C₂²×D₄	—	2	4	no	—
694	C₂²×D₄	—	4	2	no	—
695	C₂²×D₄	—	4	2	no	—
696	C₂²×D₄	—	4	2	no	—
697	C₂²×D₄	—	4	2	no	—
698	C₂²×D₄	D₄×C₃₁	1	8	yes	complemented
699	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
700	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
701	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
702	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
703	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
704	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
705	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
706	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
707	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
708	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
709	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
711	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
712	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
714	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
715	C₂³×C₄	—	4	4	no	—
716	C₂³×C₄	—	4	2	no	—
717	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
718	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
720	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
721	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
722	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
723	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
724	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
726	#127	—	2	4	no	—
727	#127	—	2	4	no	—
728	#124	—	2	4	no	—
729	#124	—	2	4	no	—
730	#123	—	2	4	no	—
731	#123	—	2	4	no	—
732	#123	—	2	8	no	—
733	#123	—	4	4	no	—
734	#121	—	2	8	no	—
735	#121	—	2	8	no	—
736	#121	—	2	8	no	—
737	#121	—	2	8	no	—
738	#121	—	4	4	no	—
739	#121	—	4	4	no	—
740	#121	—	4	4	no	—
741	#121	—	4	4	no	—
742	#120	—	2	8	no	—
743	#120	—	2	8	no	—
744	#120	—	2	8	no	—
745	#120	—	2	4	no	—
746	#120	—	2	4	no	—
747	#120	—	4	4	no	—
748	#117	—	2	4	no	—
749	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
758	C₂×C₂²⋊C₄	—	2	4	no	—
759	C₂×C₂²⋊C₄	—	4	4	no	—
760	C₂×C₂²⋊C₄	—	4	2	no	—
761	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
782	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
792	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
794	#95	C₂³×C₃₁	1	2	yes	—
795	#95	C₂³×C₃₁	1	2	yes	—
796	#95	C₂³×C₃₁	1	2	yes	—
797	#95	C₂³×C₃₁	1	2	yes	—
798	#95	C₂³×C₃₁	1	2	yes	—
799	#95	C₂³×C₃₁	1	2	yes	—
800	#95	C₂³×C₃₁	1	2	yes	—
801	#95	C₂³×C₃₁	1	2	yes	—
802	#95	C₂³×C₃₁	1	2	yes	—
803	#95	C₂³×C₃₁	1	2	yes	—
804	#95	C₂³×C₃₁	1	2	yes	—
805	#95	C₂³×C₃₁	1	2	yes	—
806	#95	C₂³×C₃₁	1	2	yes	—
807	#95	C₂³×C₃₁	1	2	yes	—
808	#95	C₂³×C₃₁	1	2	yes	—
809	#95	C₂³×C₃₁	1	2	yes	—
810	C₃₁	#36737	1	1	yes	characteristic, direct product factor, Sylow
811	C₂⁴	—	2	2	no	—
812	C₂⁴	—	2	2	no	—
813	C₂⁴	—	2	2	no	—
814	C₂⁴	—	2	2	no	—
815	C₂⁴	—	2	2	no	—
816	C₂⁴	—	4	2	no	—
817	C₂⁴	—	4	2	no	—
818	C₂⁴	—	4	2	no	—
819	C₂⁴	—	4	1	no	—
820	C₂⁴	—	4	1	no	—
821	C₂⁴	—	4	2	no	—
822	C₂⁴	—	4	2	no	—
823	C₂⁴	—	4	2	no	—
824	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
825	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
826	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
827	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
828	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
830	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
831	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
832	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
833	#41	—	4	16	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	4	1	no	—
836	C₂×Q₈	—	4	1	no	—
837	C₂×D₄	—	2	4	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	2	4	no	—
841	C₂×D₄	—	2	4	no	—
842	C₂×D₄	—	2	4	no	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	4	no	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	4	no	—
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	4	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	4	no	—
852	C₂×D₄	—	4	16	no	—
853	C₂×D₄	—	4	1	no	—
854	C₂×D₄	—	4	1	no	—
855	C₂×D₄	—	4	1	no	—
856	C₂×D₄	—	4	1	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	—	4	1	no	—
859	C₂×D₄	—	4	1	no	—
860	C₂×D₄	—	4	1	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	1	no	—
864	C₂×D₄	—	4	1	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂×D₄	—	4	2	no	—
868	C₂×D₄	—	4	2	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	—	4	2	no	—
871	C₂×D₄	—	4	2	no	—
872	C₂×D₄	—	4	2	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	—	4	2	no	—
875	C₂×D₄	—	4	2	no	—
876	C₂×D₄	—	4	2	no	—
877	C₂×D₄	—	4	2	no	—
878	C₂×D₄	—	4	2	no	—
879	C₂×D₄	—	4	2	no	—
880	C₂×D₄	—	4	2	no	—
881	C₂×D₄	—	4	2	no	—
882	C₂×D₄	—	4	16	no	—
883	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
884	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
885	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
886	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	4	no	—
891	C₂²×C₄	—	2	4	no	—
892	C₂²×C₄	—	2	4	no	—
893	C₂²×C₄	—	2	4	no	—
894	C₂²×C₄	—	2	4	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	4	1	no	—
898	C₂²×C₄	—	4	2	no	—
899	C₂²×C₄	—	4	2	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	1	no	—
903	C₂²×C₄	—	4	1	no	—
904	C₂²×C₄	—	4	1	no	—
905	C₂²×C₄	—	4	2	no	—
906	C₂²×C₄	—	4	2	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	16	no	—
912	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
913	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
914	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
915	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
916	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
925	C₄⋊C₄	—	2	4	no	—
926	C₄⋊C₄	—	2	4	no	—
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	2	4	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	4	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	4	no	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	1	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	—	4	1	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	8	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	8	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	4	8	no	—
1002	C₂³	—	4	8	no	—
1003	C₂³	—	4	4	no	—
1004	C₂³	—	4	4	no	—
1005	C₂³	—	4	8	no	—
1006	C₂³	—	4	4	no	—
1007	C₂³	—	8	2	no	—
1008	C₂³	—	8	2	no	—
1009	C₂³	—	8	4	no	—
1010	C₂³	—	8	4	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	—	8	2	no	—
1013	C₂³	—	8	4	no	—
1014	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1015	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1016	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1017	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1018	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1019	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
1020	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
1021	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1022	Q₈	—	4	4	no	—
1023	D₄	—	4	4	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	4	no	—
1027	D₄	—	4	4	no	—
1028	D₄	—	4	8	no	—
1029	D₄	—	4	8	no	—
1030	D₄	—	4	8	no	—
1031	D₄	—	8	4	no	—
1032	D₄	—	8	4	no	—
1033	D₄	—	8	4	no	—
1034	D₄	—	8	4	no	—
1035	D₄	—	8	4	no	—
1036	D₄	—	8	4	no	—
1037	D₄	—	8	4	no	—
1038	D₄	—	8	4	no	—
1039	C₂×C₄	—	2	8	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	8	no	—
1075	C₂×C₄	—	4	8	no	—
1076	C₂×C₄	—	4	8	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	4	no	—
1079	C₂×C₄	—	8	4	no	—
1080	C₂×C₄	—	8	4	no	—
1081	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1083	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	4	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	4	no	—
1093	C₂²	—	2	4	no	—
1094	C₂²	—	2	4	no	—
1095	C₂²	—	2	4	no	—
1096	C₂²	—	4	16	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	8	8	no	—
1124	C₂²	—	8	8	no	—
1125	C₂²	C₃₁×#534	1	4	yes	—
1126	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1127	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1128	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1129	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1130	C₂²	C₃₁×#585	1	2	yes	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	4	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	2	no	—
1143	C₂	—	2	4	no	—
1144	C₂	—	4	2	no	—
1145	C₂	—	4	2	no	—
1146	C₂	—	4	2	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	8	2	no	—
1149	C₂	—	8	2	no	—
1150	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
1151	C₂	C₃₁×#3496	1	2	yes	—
1152	C₂	C₃₁×#3532	1	1	yes	characteristic
1153	C₂	C₃₁×#3533	1	1	yes	characteristic
1154	C₂	C₃₁×#3542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#535	C₂	semidirect
2. C₂×C₃₁×#534	C₂	semidirect
3. C₃₁×#2847	C₂	semidirect
4. C₃₁×#2717	C₂	semidirect
5. C₃₁×#2709	C₂	semidirect
6. C₃₁×#2708	C₂	semidirect
7. C₃₁×#2688	C₂	semidirect
8. C₃₁×#2686	C₂	semidirect
9. C₃₁×#2684	C₂	semidirect
10. C₃₁×#2673	C₂	semidirect
11. C₃₁×#2671	C₂	semidirect
12. C₃₁×#2669	C₂	semidirect
13. C₃₁×#2668	C₂	semidirect
14. C₃₁×#2617	C₂	semidirect
15. C₃₁×#2498	C₂	semidirect
16. C₃₁×#2430	C₂	semidirect
17. C₃₁×#2412	C₂	semidirect
18. C₃₁×#2410	C₂	semidirect
19. C₂×C₃₁×#386	C₂	semidirect
20. C₂²×#41×C₃₁	C₂²	semidirect
23. C₂⁴×C₄×C₃₁	C₂²	semidirect
27. C₂×C₃₁×#127	C₂²	semidirect
29. C₂×C₃₁×#124	C₂²	semidirect
33. C₂×C₃₁×#123	C₂²	semidirect
39. C₂×C₃₁×#121	C₂²	semidirect
40. C₂×C₃₁×#121	C₂²	semidirect
41. C₂×C₃₁×#121	C₂²	semidirect
46. C₂×C₃₁×#120	C₂²	semidirect
47. C₂×C₃₁×#120	C₂²	semidirect
48. C₂×C₃₁×#117	C₂²	semidirect
51. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
52. C₃₁×#400	C₂²	semidirect
53. C₃₁×#399	C₂²	semidirect
54. C₃₁×#398	C₂²	semidirect
55. C₃₁×#397	C₂²	semidirect
56. C₃₁×#397	C₂²	semidirect
57. C₃₁×#397	C₂²	semidirect
58. C₃₁×#397	C₂²	semidirect
59. C₃₁×#397	C₂²	semidirect
60. C₃₁×#395	C₂²	semidirect
61. C₃₁×#394	C₂²	semidirect
62. C₃₁×#394	C₂²	semidirect
63. C₃₁×#394	C₂²	semidirect
64. C₃₁×#394	C₂²	semidirect
65. C₃₁×#394	C₂²	semidirect
66. C₃₁×#394	C₂²	semidirect
67. C₃₁×#394	C₂²	semidirect
68. C₃₁×#394	C₂²	semidirect
69. C₃₁×#394	C₂²	semidirect
70. C₃₁×#393	C₂²	semidirect
71. C₃₁×#392	C₂²	semidirect
72. C₃₁×#392	C₂²	semidirect
73. C₃₁×#392	C₂²	semidirect
74. C₃₁×#392	C₂²	semidirect
75. C₃₁×#392	C₂²	semidirect
76. C₃₁×#388	C₂²	semidirect
77. C₃₁×#388	C₂²	semidirect
78. C₃₁×#387	C₂²	semidirect
79. C₃₁×#387	C₂²	semidirect
85. C₃₁×#386	C₂²	semidirect
86. C₃₁×#386	C₂²	semidirect
87. C₃₁×#386	C₂²	semidirect
88. C₃₁×#386	C₂²	semidirect
89. C₃₁×#386	C₂²	semidirect
90. C₃₁×#386	C₂²	semidirect
91. C₃₁×#386	C₂²	semidirect
92. C₃₁×#386	C₂²	semidirect
93. C₃₁×#386	C₂²	semidirect
94. C₃₁×#386	C₂²	semidirect
95. C₃₁×#386	C₂²	semidirect
96. C₃₁×#386	C₂²	semidirect
97. C₃₁×#386	C₂²	semidirect
98. C₃₁×#385	C₂²	semidirect
99. C₃₁×#385	C₂²	semidirect
100. C₃₁×#385	C₂²	semidirect
101. C₃₁×#385	C₂²	semidirect
102. C₃₁×#381	C₂²	semidirect
103. C₃₁×#380	C₂²	semidirect
104. C₃₁×#380	C₂²	semidirect
105. C₃₁×#380	C₂²	semidirect
106. C₃₁×#380	C₂²	semidirect
107. C₃₁×#379	C₂²	semidirect
108. C₂×C₃₁×#95	C₂²	semidirect
121. C₂²×D₄×C₃₁	D₄	semidirect
389. #36737	C₃₁	direct (N × H)
507. C₂×#535	C₂×C₃₁	semidirect
508. C₂×#534	C₂×C₃₁	semidirect
509. #2847	C₂×C₃₁	semidirect
510. #2717	C₂×C₃₁	semidirect
511. #2709	C₂×C₃₁	semidirect
512. #2708	C₂×C₃₁	semidirect
513. #2688	C₂×C₃₁	semidirect
514. #2686	C₂×C₃₁	semidirect
515. #2684	C₂×C₃₁	semidirect
516. #2673	C₂×C₃₁	semidirect
517. #2671	C₂×C₃₁	semidirect
518. #2669	C₂×C₃₁	semidirect
519. #2668	C₂×C₃₁	semidirect
520. #2617	C₂×C₃₁	semidirect
521. #2498	C₂×C₃₁	semidirect
522. #2430	C₂×C₃₁	semidirect
523. #2412	C₂×C₃₁	semidirect
524. #2410	C₂×C₃₁	semidirect
525. C₂×#386	C₂×C₃₁	semidirect
585. C₂²×#41	C₂²×C₃₁	semidirect
588. C₂⁴×C₄	C₂²×C₃₁	semidirect
592. C₂×#127	C₂²×C₃₁	semidirect
594. C₂×#124	C₂²×C₃₁	semidirect
598. C₂×#123	C₂²×C₃₁	semidirect
604. C₂×#121	C₂²×C₃₁	semidirect
605. C₂×#121	C₂²×C₃₁	semidirect
606. C₂×#121	C₂²×C₃₁	semidirect
611. C₂×#120	C₂²×C₃₁	semidirect
612. C₂×#120	C₂²×C₃₁	semidirect
613. C₂×#117	C₂²×C₃₁	semidirect
616. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
617. #400	C₂²×C₃₁	semidirect
618. #399	C₂²×C₃₁	semidirect
619. #398	C₂²×C₃₁	semidirect
620. #397	C₂²×C₃₁	semidirect
621. #397	C₂²×C₃₁	semidirect
622. #397	C₂²×C₃₁	semidirect
623. #397	C₂²×C₃₁	semidirect
624. #397	C₂²×C₃₁	semidirect
625. #395	C₂²×C₃₁	semidirect
626. #394	C₂²×C₃₁	semidirect
627. #394	C₂²×C₃₁	semidirect
628. #394	C₂²×C₃₁	semidirect
629. #394	C₂²×C₃₁	semidirect
630. #394	C₂²×C₃₁	semidirect
631. #394	C₂²×C₃₁	semidirect
632. #394	C₂²×C₃₁	semidirect
633. #394	C₂²×C₃₁	semidirect
634. #394	C₂²×C₃₁	semidirect
635. #393	C₂²×C₃₁	semidirect
636. #392	C₂²×C₃₁	semidirect
637. #392	C₂²×C₃₁	semidirect
638. #392	C₂²×C₃₁	semidirect
639. #392	C₂²×C₃₁	semidirect
640. #392	C₂²×C₃₁	semidirect
641. #388	C₂²×C₃₁	semidirect
642. #388	C₂²×C₃₁	semidirect
643. #387	C₂²×C₃₁	semidirect
644. #387	C₂²×C₃₁	semidirect
650. #386	C₂²×C₃₁	semidirect
651. #386	C₂²×C₃₁	semidirect
652. #386	C₂²×C₃₁	semidirect
653. #386	C₂²×C₃₁	semidirect
654. #386	C₂²×C₃₁	semidirect
655. #386	C₂²×C₃₁	semidirect
656. #386	C₂²×C₃₁	semidirect
657. #386	C₂²×C₃₁	semidirect
658. #386	C₂²×C₃₁	semidirect
659. #386	C₂²×C₃₁	semidirect
660. #386	C₂²×C₃₁	semidirect
661. #386	C₂²×C₃₁	semidirect
662. #386	C₂²×C₃₁	semidirect
663. #385	C₂²×C₃₁	semidirect
664. #385	C₂²×C₃₁	semidirect
665. #385	C₂²×C₃₁	semidirect
666. #385	C₂²×C₃₁	semidirect
667. #381	C₂²×C₃₁	semidirect
668. #380	C₂²×C₃₁	semidirect
669. #380	C₂²×C₃₁	semidirect
670. #380	C₂²×C₃₁	semidirect
671. #380	C₂²×C₃₁	semidirect
672. #379	C₂²×C₃₁	semidirect
673. C₂×#95	C₂²×C₃₁	semidirect
698. C₂²×D₄	D₄×C₃₁	semidirect
810. C₃₁	#36737	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×#535	2
C₂×C₃₁×#534	2
C₃₁×#2847	2
C₃₁×#2717	2
C₃₁×#2709	2
C₃₁×#2708	2
C₃₁×#2688	2
C₃₁×#2686	2
C₃₁×#2684	2
C₃₁×#2673	2
C₃₁×#2671	2
C₃₁×#2669	2
C₃₁×#2668	2
C₃₁×#2617	2
C₃₁×#2498	2
C₃₁×#2430	2
C₃₁×#2412	2
C₃₁×#2410	2
C₂×C₃₁×#386	2
#36737	31

Subgroups — C31×#36737 #21493496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36737 #21493496