Subgroups — C₃₁×#36840 #21493599

Order 7936.

1988 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2849	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2765	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2760	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2746	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2710	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2709	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2708	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2697	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2684	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2669	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2653	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2527	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2459	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2457	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2443	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2328	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2322	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₃₁×#120	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#124	C₂²	1	2	yes	—
23	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#123	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	2	yes	—
27	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#120	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₃₁	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	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#401	C₂²	1	2	yes	complemented
34	C₃₁×#401	C₂²	1	2	yes	complemented
35	C₃₁×#400	C₂²	1	2	yes	complemented
36	C₃₁×#400	C₂²	1	2	yes	complemented
37	C₃₁×#399	C₂²	1	2	yes	complemented
38	C₃₁×#398	C₂²	1	2	yes	complemented
39	C₃₁×#398	C₂²	1	2	yes	complemented
40	C₃₁×#397	C₂²	1	2	yes	—
41	C₃₁×#397	C₂²	1	2	yes	—
42	C₃₁×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	complemented
44	C₃₁×#396	C₂²	1	2	yes	—
45	C₃₁×#394	C₂²	1	2	yes	—
46	C₃₁×#394	C₂²	1	2	yes	—
47	C₃₁×#394	C₂²	1	2	yes	—
48	C₃₁×#394	C₂²	1	2	yes	—
49	C₃₁×#394	C₂²	1	2	yes	complemented
50	C₃₁×#394	C₂²	1	2	yes	complemented
51	C₃₁×#393	C₂²	1	2	yes	—
52	C₃₁×#393	C₂²	1	2	yes	—
53	C₃₁×#393	C₂²	1	2	yes	complemented
54	C₃₁×#393	C₂²	1	2	yes	complemented
55	C₃₁×#392	C₂²	1	2	yes	—
56	C₃₁×#392	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	2	yes	complemented
58	C₃₁×#391	C₂²	1	2	yes	complemented
59	C₃₁×#390	C₂²	1	1	yes	characteristic
60	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#389	C₂²	1	2	yes	complemented
62	C₃₁×#388	C₂²	1	2	yes	—
63	C₃₁×#388	C₂²	1	2	yes	—
64	C₃₁×#388	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	complemented
67	C₃₁×#388	C₂²	1	2	yes	complemented
68	C₃₁×#388	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×#387	C₂²	1	2	yes	complemented
73	C₃₁×#386	C₂²	1	1	yes	characteristic
74	C₃₁×#386	C₂²	1	2	yes	—
75	C₃₁×#386	C₂²	1	2	yes	—
76	C₃₁×#386	C₂²	1	2	yes	—
77	C₃₁×#386	C₂²	1	2	yes	—
78	C₃₁×#386	C₂²	1	2	yes	—
79	C₃₁×#386	C₂²	1	2	yes	—
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	2	yes	complemented
85	C₃₁×#386	C₂²	1	2	yes	complemented
86	C₃₁×#386	C₂²	1	2	yes	complemented
87	C₃₁×#385	C₂²	1	2	yes	—
88	C₃₁×#385	C₂²	1	2	yes	—
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#385	C₂²	1	2	yes	—
91	C₃₁×#385	C₂²	1	2	yes	—
92	C₃₁×#385	C₂²	1	1	yes	characteristic
93	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#385	C₂²	1	2	yes	complemented
95	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#381	C₂²	1	2	yes	—
97	C₃₁×#381	C₂²	1	2	yes	—
98	C₃₁×#381	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#381	C₂²	1	2	yes	complemented
100	C₃₁×#380	C₂²	1	2	yes	complemented
101	C₃₁×#379	C₂²	1	2	yes	—
102	C₃₁×#379	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₃₁	—	4	2	no	—
117	C₂³×C₄×C₃₁	—	4	4	no	—
118	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₃₁×#127	—	2	4	no	—
127	C₃₁×#124	—	4	4	no	—
128	C₃₁×#123	—	2	4	no	—
129	C₃₁×#123	—	4	4	no	—
130	C₃₁×#123	—	4	4	no	—
131	C₃₁×#121	—	4	4	no	—
132	C₃₁×#120	—	2	4	no	—
133	C₃₁×#120	—	4	4	no	—
134	C₄×D₄×C₃₁	—	4	2	no	—
135	C₄×D₄×C₃₁	—	4	2	no	—
136	C₄×D₄×C₃₁	—	4	4	no	—
137	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₄²×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
183	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	2	yes	—
187	C₃₁×#95	C₂³	1	2	yes	—
188	C₃₁×#95	C₂³	1	2	yes	—
189	C₃₁×#95	C₂³	1	2	yes	—
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	2	yes	—
192	C₃₁×#95	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	2	yes	—
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	C₂³	1	2	yes	—
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	C₂⁴×C₃₁	—	2	2	no	—
209	C₂⁴×C₃₁	—	2	4	no	—
210	C₂⁴×C₃₁	—	4	1	no	—
211	C₂⁴×C₃₁	—	4	2	no	—
212	C₂⁴×C₃₁	—	4	1	no	—
213	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
214	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₃₁	—	4	2	no	—
218	C₂×Q₈×C₃₁	—	4	2	no	—
219	C₂×Q₈×C₃₁	—	4	2	no	—
220	C₂×D₄×C₃₁	—	2	4	no	—
221	C₂×D₄×C₃₁	—	2	4	no	—
222	C₂×D₄×C₃₁	—	2	4	no	—
223	C₂×D₄×C₃₁	—	2	4	no	—
224	C₂×D₄×C₃₁	—	2	4	no	—
225	C₂×D₄×C₃₁	—	2	4	no	—
226	C₂×D₄×C₃₁	—	2	2	no	—
227	C₂×D₄×C₃₁	—	4	1	no	—
228	C₂×D₄×C₃₁	—	4	1	no	—
229	C₂×D₄×C₃₁	—	4	1	no	—
230	C₂×D₄×C₃₁	—	4	1	no	—
231	C₂×D₄×C₃₁	—	4	2	no	—
232	C₂×D₄×C₃₁	—	4	2	no	—
233	C₂×D₄×C₃₁	—	4	2	no	—
234	C₂×D₄×C₃₁	—	4	2	no	—
235	C₂×D₄×C₃₁	—	4	2	no	—
236	C₂×D₄×C₃₁	—	4	2	no	—
237	C₂×D₄×C₃₁	—	4	2	no	—
238	C₂×D₄×C₃₁	—	4	2	no	—
239	C₂×D₄×C₃₁	—	4	2	no	—
240	C₂×D₄×C₃₁	#41	1	4	yes	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	4	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	4	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	4	1	no	—
248	C₂²×C₄×C₃₁	—	4	2	no	—
249	C₂²×C₄×C₃₁	—	4	2	no	—
250	C₂²×C₄×C₃₁	—	4	2	no	—
251	C₂²×C₄×C₃₁	—	4	2	no	—
252	C₂²×C₄×C₃₁	—	4	1	no	—
253	C₂²×C₄×C₃₁	—	4	2	no	—
254	C₂²×C₄×C₃₁	—	4	1	no	—
255	C₂²×C₄×C₃₁	—	4	1	no	—
256	C₂²×C₄×C₃₁	—	4	2	no	—
257	C₂²×C₄×C₃₁	—	4	2	no	—
258	C₂²×C₄×C₃₁	—	4	2	no	—
259	C₂²×C₄×C₃₁	—	4	2	no	—
260	C₂²×C₄×C₃₁	—	4	2	no	—
261	C₂²×C₄×C₃₁	—	4	16	no	—
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₄⋊C₄×C₃₁	—	2	4	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	4	2	no	—
280	C₄⋊C₄×C₃₁	—	4	2	no	—
281	C₄⋊C₄×C₃₁	—	4	2	no	—
282	C₄⋊C₄×C₃₁	—	4	1	no	—
283	C₄⋊C₄×C₃₁	—	4	1	no	—
284	C₄⋊C₄×C₃₁	—	4	2	no	—
285	C₄⋊C₄×C₃₁	—	4	2	no	—
286	C₄⋊C₄×C₃₁	—	4	2	no	—
287	C₄⋊C₄×C₃₁	—	4	2	no	—
288	C₄⋊C₄×C₃₁	—	4	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	2	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	4	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	4	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	1	no	—
302	C₂²⋊C₄×C₃₁	—	4	2	no	—
303	C₂²⋊C₄×C₃₁	—	4	2	no	—
304	C₂²⋊C₄×C₃₁	—	4	2	no	—
305	C₂²⋊C₄×C₃₁	—	4	1	no	—
306	C₂²⋊C₄×C₃₁	—	4	1	no	—
307	C₂²⋊C₄×C₃₁	—	4	1	no	—
308	C₂²⋊C₄×C₃₁	—	4	2	no	—
309	C₂²⋊C₄×C₃₁	—	4	2	no	—
310	C₂²⋊C₄×C₃₁	—	4	2	no	—
311	C₂²⋊C₄×C₃₁	—	4	2	no	—
312	C₂²⋊C₄×C₃₁	—	4	2	no	—
313	C₂²⋊C₄×C₃₁	—	4	2	no	—
314	C₂²⋊C₄×C₃₁	—	4	2	no	—
315	C₂²⋊C₄×C₃₁	—	4	2	no	—
316	C₂²⋊C₄×C₃₁	—	4	2	no	—
317	C₂²⋊C₄×C₃₁	—	4	2	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	4	1	no	—
321	C₄²×C₃₁	—	4	2	no	—
322	C₄²×C₃₁	—	4	2	no	—
323	#36840	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂³×C₃₁	—	2	2	no	—
325	C₂³×C₃₁	—	2	1	no	—
326	C₂³×C₃₁	—	2	1	no	—
327	C₂³×C₃₁	—	2	2	no	—
328	C₂³×C₃₁	—	2	2	no	—
329	C₂³×C₃₁	—	2	2	no	—
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	1	no	—
332	C₂³×C₃₁	—	2	2	no	—
333	C₂³×C₃₁	—	2	1	no	—
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	2	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	2	2	no	—
340	C₂³×C₃₁	—	2	2	no	—
341	C₂³×C₃₁	—	2	2	no	—
342	C₂³×C₃₁	—	2	2	no	—
343	C₂³×C₃₁	—	2	2	no	—
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	4	4	no	—
346	C₂³×C₃₁	—	4	8	no	—
347	C₂³×C₃₁	—	4	4	no	—
348	C₂³×C₃₁	—	4	8	no	—
349	C₂³×C₃₁	—	4	4	no	—
350	C₂³×C₃₁	C₂×#41	1	2	yes	—
351	C₂³×C₃₁	C₂×#41	1	2	yes	—
352	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
353	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
354	Q₈×C₃₁	—	8	4	no	—
355	D₄×C₃₁	—	4	4	no	—
356	D₄×C₃₁	—	4	4	no	—
357	D₄×C₃₁	—	4	8	no	—
358	D₄×C₃₁	—	8	4	no	—
359	D₄×C₃₁	—	8	4	no	—
360	D₄×C₃₁	—	8	4	no	—
361	D₄×C₃₁	—	8	4	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	4	8	no	—
402	C₂×C₄×C₃₁	—	4	4	no	—
403	C₂×C₄×C₃₁	—	4	4	no	—
404	C₂×C₄×C₃₁	—	4	8	no	—
405	C₂×C₄×C₃₁	—	4	4	no	—
406	C₂×C₄×C₃₁	—	8	2	no	—
407	C₂×C₄×C₃₁	—	8	2	no	—
408	C₂×C₄×C₃₁	—	8	4	no	—
409	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
410	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
411	#2849	C₂×C₃₁	1	2	yes	complemented
412	#2804	C₂×C₃₁	1	1	yes	characteristic, complemented
413	#2765	C₂×C₃₁	1	2	yes	complemented
414	#2760	C₂×C₃₁	1	2	yes	complemented
415	#2746	C₂×C₃₁	1	2	yes	complemented
416	#2710	C₂×C₃₁	1	2	yes	complemented
417	#2709	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#2708	C₂×C₃₁	1	2	yes	complemented
419	#2697	C₂×C₃₁	1	1	yes	characteristic, complemented
420	#2684	C₂×C₃₁	1	2	yes	complemented
421	#2669	C₂×C₃₁	1	1	yes	characteristic
422	#2653	C₂×C₃₁	1	2	yes	complemented
423	#2527	C₂×C₃₁	1	2	yes	complemented
424	#2459	C₂×C₃₁	1	2	yes	complemented
425	#2457	C₂×C₃₁	1	2	yes	complemented
426	#2443	C₂×C₃₁	1	2	yes	complemented
427	#2328	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#2322	C₂×C₃₁	1	1	yes	characteristic, complemented
429	C₄×#120	C₂×C₃₁	1	1	yes	characteristic, complemented
430	C₂²×C₃₁	—	2	2	no	—
431	C₂²×C₃₁	—	2	2	no	—
432	C₂²×C₃₁	—	2	4	no	—
433	C₂²×C₃₁	—	2	4	no	—
434	C₂²×C₃₁	—	2	4	no	—
435	C₂²×C₃₁	—	2	4	no	—
436	C₂²×C₃₁	—	2	4	no	—
437	C₂²×C₃₁	—	4	16	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	4	2	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	—	4	1	no	—
442	C₂²×C₃₁	—	4	2	no	—
443	C₂²×C₃₁	—	4	2	no	—
444	C₂²×C₃₁	—	4	2	no	—
445	C₂²×C₃₁	—	4	1	no	—
446	C₂²×C₃₁	—	4	1	no	—
447	C₂²×C₃₁	—	4	2	no	—
448	C₂²×C₃₁	—	4	2	no	—
449	C₂²×C₃₁	—	4	2	no	—
450	C₂²×C₃₁	—	4	2	no	—
451	C₂²×C₃₁	—	4	2	no	—
452	C₂²×C₃₁	—	4	2	no	—
453	C₂²×C₃₁	—	4	2	no	—
454	C₂²×C₃₁	—	4	2	no	—
455	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
456	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
458	C₂²×C₃₁	#585	1	1	yes	characteristic
459	C₂²×C₃₁	#585	1	2	yes	—
460	C₄×C₃₁	—	2	2	no	—
461	C₄×C₃₁	—	2	2	no	—
462	C₄×C₃₁	—	4	2	no	—
463	C₄×C₃₁	—	4	2	no	—
464	C₄×C₃₁	—	4	2	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	—	4	1	no	—
468	C₄×C₃₁	—	4	1	no	—
469	C₄×C₃₁	—	4	2	no	—
470	C₄×C₃₁	—	4	2	no	—
471	C₄×C₃₁	—	4	2	no	—
472	C₄×C₃₁	—	4	2	no	—
473	C₄×C₃₁	—	4	2	no	—
474	C₄×C₃₁	—	4	1	no	—
475	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
476	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×#124	C₂²×C₃₁	1	2	yes	—
478	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
479	C₂×#123	C₂²×C₃₁	1	2	yes	—
480	C₂×#123	C₂²×C₃₁	1	2	yes	—
481	C₂×#121	C₂²×C₃₁	1	2	yes	—
482	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
483	C₂×#120	C₂²×C₃₁	1	2	yes	—
484	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
485	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
486	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
487	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
488	#401	C₂²×C₃₁	1	2	yes	complemented
489	#401	C₂²×C₃₁	1	2	yes	complemented
490	#400	C₂²×C₃₁	1	2	yes	complemented
491	#400	C₂²×C₃₁	1	2	yes	complemented
492	#399	C₂²×C₃₁	1	2	yes	complemented
493	#398	C₂²×C₃₁	1	2	yes	complemented
494	#398	C₂²×C₃₁	1	2	yes	complemented
495	#397	C₂²×C₃₁	1	2	yes	—
496	#397	C₂²×C₃₁	1	2	yes	—
497	#397	C₂²×C₃₁	1	2	yes	—
498	#397	C₂²×C₃₁	1	2	yes	complemented
499	#396	C₂²×C₃₁	1	2	yes	—
500	#394	C₂²×C₃₁	1	2	yes	—
501	#394	C₂²×C₃₁	1	2	yes	—
502	#394	C₂²×C₃₁	1	2	yes	—
503	#394	C₂²×C₃₁	1	2	yes	—
504	#394	C₂²×C₃₁	1	2	yes	complemented
505	#394	C₂²×C₃₁	1	2	yes	complemented
506	#393	C₂²×C₃₁	1	2	yes	—
507	#393	C₂²×C₃₁	1	2	yes	—
508	#393	C₂²×C₃₁	1	2	yes	complemented
509	#393	C₂²×C₃₁	1	2	yes	complemented
510	#392	C₂²×C₃₁	1	2	yes	—
511	#392	C₂²×C₃₁	1	2	yes	—
512	#391	C₂²×C₃₁	1	2	yes	complemented
513	#391	C₂²×C₃₁	1	2	yes	complemented
514	#390	C₂²×C₃₁	1	1	yes	characteristic
515	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
516	#389	C₂²×C₃₁	1	2	yes	complemented
517	#388	C₂²×C₃₁	1	2	yes	—
518	#388	C₂²×C₃₁	1	2	yes	—
519	#388	C₂²×C₃₁	1	2	yes	—
520	#388	C₂²×C₃₁	1	2	yes	—
521	#388	C₂²×C₃₁	1	2	yes	complemented
522	#388	C₂²×C₃₁	1	2	yes	complemented
523	#388	C₂²×C₃₁	1	2	yes	complemented
524	#387	C₂²×C₃₁	1	2	yes	complemented
525	#387	C₂²×C₃₁	1	2	yes	complemented
526	#387	C₂²×C₃₁	1	2	yes	complemented
527	#387	C₂²×C₃₁	1	2	yes	complemented
528	#386	C₂²×C₃₁	1	1	yes	characteristic
529	#386	C₂²×C₃₁	1	2	yes	—
530	#386	C₂²×C₃₁	1	2	yes	—
531	#386	C₂²×C₃₁	1	2	yes	—
532	#386	C₂²×C₃₁	1	2	yes	—
533	#386	C₂²×C₃₁	1	2	yes	—
534	#386	C₂²×C₃₁	1	2	yes	—
535	#386	C₂²×C₃₁	1	2	yes	—
536	#386	C₂²×C₃₁	1	2	yes	—
537	#386	C₂²×C₃₁	1	2	yes	—
538	#386	C₂²×C₃₁	1	1	yes	characteristic
539	#386	C₂²×C₃₁	1	2	yes	complemented
540	#386	C₂²×C₃₁	1	2	yes	complemented
541	#386	C₂²×C₃₁	1	2	yes	complemented
542	#385	C₂²×C₃₁	1	2	yes	—
543	#385	C₂²×C₃₁	1	2	yes	—
544	#385	C₂²×C₃₁	1	2	yes	—
545	#385	C₂²×C₃₁	1	2	yes	—
546	#385	C₂²×C₃₁	1	2	yes	—
547	#385	C₂²×C₃₁	1	1	yes	characteristic
548	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
549	#385	C₂²×C₃₁	1	2	yes	complemented
550	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	#381	C₂²×C₃₁	1	2	yes	—
552	#381	C₂²×C₃₁	1	2	yes	—
553	#381	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#381	C₂²×C₃₁	1	2	yes	complemented
555	#380	C₂²×C₃₁	1	2	yes	complemented
556	#379	C₂²×C₃₁	1	2	yes	—
557	#379	C₂²×C₃₁	1	1	yes	characteristic
558	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	C₂×C₃₁	—	4	2	no	—
563	C₂×C₃₁	—	4	2	no	—
564	C₂×C₃₁	—	4	4	no	—
565	C₂×C₃₁	—	8	2	no	—
566	C₂×C₃₁	#3459	1	1	yes	characteristic
567	C₂×C₃₁	#3513	1	2	yes	—
568	C₂×C₃₁	#3532	1	1	yes	characteristic
569	C₂×C₃₁	#3533	1	2	yes	—
570	C₂×C₃₁	#3540	1	1	yes	characteristic
571	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
573	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
574	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
576	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
577	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
578	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
579	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
580	C₂³×C₄	—	4	2	no	—
581	C₂³×C₄	—	4	4	no	—
582	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
583	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
587	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
589	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
590	#127	—	2	4	no	—
591	#124	—	4	4	no	—
592	#123	—	2	4	no	—
593	#123	—	4	4	no	—
594	#123	—	4	4	no	—
595	#121	—	4	4	no	—
596	#120	—	2	4	no	—
597	#120	—	4	4	no	—
598	C₄×D₄	—	4	2	no	—
599	C₄×D₄	—	4	2	no	—
600	C₄×D₄	—	4	4	no	—
601	C₂×C₄⋊C₄	—	4	2	no	—
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	#95	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	2	yes	—
650	#95	C₂³×C₃₁	1	2	yes	—
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	2	yes	—
653	#95	C₂³×C₃₁	1	2	yes	—
654	#95	C₂³×C₃₁	1	2	yes	—
655	#95	C₂³×C₃₁	1	2	yes	—
656	#95	C₂³×C₃₁	1	2	yes	—
657	#95	C₂³×C₃₁	1	2	yes	—
658	#95	C₂³×C₃₁	1	2	yes	—
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	2	yes	—
661	#95	C₂³×C₃₁	1	2	yes	—
662	#95	C₂³×C₃₁	1	2	yes	—
663	#95	C₂³×C₃₁	1	2	yes	—
664	#95	C₂³×C₃₁	1	2	yes	—
665	#95	C₂³×C₃₁	1	2	yes	—
666	#95	C₂³×C₃₁	1	2	yes	—
667	#95	C₂³×C₃₁	1	2	yes	—
668	#95	C₂³×C₃₁	1	2	yes	—
669	#95	C₂³×C₃₁	1	2	yes	—
670	#95	C₂³×C₃₁	1	2	yes	—
671	#95	C₂³×C₃₁	1	2	yes	—
672	C₃₁	#36840	1	1	yes	characteristic, direct product factor, Sylow
673	C₂⁴	—	2	2	no	—
674	C₂⁴	—	2	4	no	—
675	C₂⁴	—	4	1	no	—
676	C₂⁴	—	4	2	no	—
677	C₂⁴	—	4	1	no	—
678	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
679	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
680	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂×D₄	—	4	1	no	—
695	C₂×D₄	—	4	1	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	#41×C₃₁	1	4	yes	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	1	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	16	no	—
727	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	1	no	—
748	C₄⋊C₄	—	4	1	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	1	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	1	no	—
771	C₂²⋊C₄	—	4	1	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	4	1	no	—
786	C₄²	—	4	2	no	—
787	C₄²	—	4	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	4	4	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	4	no	—
812	C₂³	—	4	8	no	—
813	C₂³	—	4	4	no	—
814	C₂³	C₂×#41×C₃₁	1	2	yes	—
815	C₂³	C₂×#41×C₃₁	1	2	yes	—
816	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
817	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
818	Q₈	—	8	4	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	8	4	no	—
823	D₄	—	8	4	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	4	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	8	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	4	no	—
873	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
874	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	4	16	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
901	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
903	C₂²	C₃₁×#585	1	1	yes	characteristic
904	C₂²	C₃₁×#585	1	2	yes	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	2	no	—
920	C₂	—	4	2	no	—
921	C₂	—	4	4	no	—
922	C₂	—	4	2	no	—
923	C₂	—	8	2	no	—
924	C₂	C₃₁×#3459	1	1	yes	characteristic
925	C₂	C₃₁×#3513	1	2	yes	—
926	C₂	C₃₁×#3532	1	1	yes	characteristic
927	C₂	C₃₁×#3533	1	2	yes	—
928	C₂	C₃₁×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2669	C₂
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. C₃₁×#2849	C₂	semidirect
2. C₃₁×#2804	C₂	semidirect
3. C₃₁×#2765	C₂	semidirect
4. C₃₁×#2760	C₂	semidirect
5. C₃₁×#2746	C₂	semidirect
6. C₃₁×#2710	C₂	semidirect
7. C₃₁×#2709	C₂	semidirect
8. C₃₁×#2708	C₂	semidirect
9. C₃₁×#2697	C₂	semidirect
10. C₃₁×#2684	C₂	semidirect
12. C₃₁×#2653	C₂	semidirect
13. C₃₁×#2527	C₂	semidirect
14. C₃₁×#2459	C₂	semidirect
15. C₃₁×#2457	C₂	semidirect
16. C₃₁×#2443	C₂	semidirect
17. C₃₁×#2328	C₂	semidirect
18. C₃₁×#2322	C₂	semidirect
19. C₄×C₃₁×#120	C₂	semidirect
31. C₂×C₄×D₄×C₃₁	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
33. C₃₁×#401	C₂²	semidirect
34. C₃₁×#401	C₂²	semidirect
35. C₃₁×#400	C₂²	semidirect
36. C₃₁×#400	C₂²	semidirect
37. C₃₁×#399	C₂²	semidirect
38. C₃₁×#398	C₂²	semidirect
39. C₃₁×#398	C₂²	semidirect
43. C₃₁×#397	C₂²	semidirect
49. C₃₁×#394	C₂²	semidirect
50. C₃₁×#394	C₂²	semidirect
53. C₃₁×#393	C₂²	semidirect
54. C₃₁×#393	C₂²	semidirect
57. C₃₁×#391	C₂²	semidirect
58. C₃₁×#391	C₂²	semidirect
60. C₃₁×#390	C₂²	semidirect
61. C₃₁×#389	C₂²	semidirect
66. C₃₁×#388	C₂²	semidirect
67. C₃₁×#388	C₂²	semidirect
68. C₃₁×#388	C₂²	semidirect
69. C₃₁×#387	C₂²	semidirect
70. C₃₁×#387	C₂²	semidirect
71. C₃₁×#387	C₂²	semidirect
72. C₃₁×#387	C₂²	semidirect
84. C₃₁×#386	C₂²	semidirect
85. C₃₁×#386	C₂²	semidirect
86. C₃₁×#386	C₂²	semidirect
93. C₃₁×#385	C₂²	semidirect
94. C₃₁×#385	C₂²	semidirect
95. C₃₁×#382	C₂²	semidirect
98. C₃₁×#381	C₂²	semidirect
99. C₃₁×#381	C₂²	semidirect
100. C₃₁×#380	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
106. C₃₁×#376	C₂²	semidirect
323. #36840	C₃₁	direct (N × H)
411. #2849	C₂×C₃₁	semidirect
412. #2804	C₂×C₃₁	semidirect
413. #2765	C₂×C₃₁	semidirect
414. #2760	C₂×C₃₁	semidirect
415. #2746	C₂×C₃₁	semidirect
416. #2710	C₂×C₃₁	semidirect
417. #2709	C₂×C₃₁	semidirect
418. #2708	C₂×C₃₁	semidirect
419. #2697	C₂×C₃₁	semidirect
420. #2684	C₂×C₃₁	semidirect
422. #2653	C₂×C₃₁	semidirect
423. #2527	C₂×C₃₁	semidirect
424. #2459	C₂×C₃₁	semidirect
425. #2457	C₂×C₃₁	semidirect
426. #2443	C₂×C₃₁	semidirect
427. #2328	C₂×C₃₁	semidirect
428. #2322	C₂×C₃₁	semidirect
429. C₄×#120	C₂×C₃₁	semidirect
486. C₂×C₄×D₄	C₂²×C₃₁	semidirect
487. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
488. #401	C₂²×C₃₁	semidirect
489. #401	C₂²×C₃₁	semidirect
490. #400	C₂²×C₃₁	semidirect
491. #400	C₂²×C₃₁	semidirect
492. #399	C₂²×C₃₁	semidirect
493. #398	C₂²×C₃₁	semidirect
494. #398	C₂²×C₃₁	semidirect
498. #397	C₂²×C₃₁	semidirect
504. #394	C₂²×C₃₁	semidirect
505. #394	C₂²×C₃₁	semidirect
508. #393	C₂²×C₃₁	semidirect
509. #393	C₂²×C₃₁	semidirect
512. #391	C₂²×C₃₁	semidirect
513. #391	C₂²×C₃₁	semidirect
515. #390	C₂²×C₃₁	semidirect
516. #389	C₂²×C₃₁	semidirect
521. #388	C₂²×C₃₁	semidirect
522. #388	C₂²×C₃₁	semidirect
523. #388	C₂²×C₃₁	semidirect
524. #387	C₂²×C₃₁	semidirect
525. #387	C₂²×C₃₁	semidirect
526. #387	C₂²×C₃₁	semidirect
527. #387	C₂²×C₃₁	semidirect
539. #386	C₂²×C₃₁	semidirect
540. #386	C₂²×C₃₁	semidirect
541. #386	C₂²×C₃₁	semidirect
548. #385	C₂²×C₃₁	semidirect
549. #385	C₂²×C₃₁	semidirect
550. #382	C₂²×C₃₁	semidirect
553. #381	C₂²×C₃₁	semidirect
554. #381	C₂²×C₃₁	semidirect
555. #380	C₂²×C₃₁	semidirect
560. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
561. #376	C₂²×C₃₁	semidirect
672. C₃₁	#36840	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2849	2
C₃₁×#2804	2
C₃₁×#2765	2
C₃₁×#2760	2
C₃₁×#2746	2
C₃₁×#2710	2
C₃₁×#2709	2
C₃₁×#2708	2
C₃₁×#2697	2
C₃₁×#2684	2
C₃₁×#2669	2
C₃₁×#2653	2
C₃₁×#2527	2
C₃₁×#2459	2
C₃₁×#2457	2
C₃₁×#2443	2
C₃₁×#2328	2
C₃₁×#2322	2
C₄×C₃₁×#120	2
#36840	31

Subgroups — C31×#36840 #21493599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36840 #21493599