Subgroups — C₃₁×#34881 #21491640

Order 7936.

1826 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2593	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2585	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2573	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2554	C₂	1	2	yes	maximal
5	C₃₁×#2525	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2516	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2469	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2458	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2402	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2398	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2392	C₂	1	1	yes	maximal, characteristic
13	C₄×C₃₁×#126	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2298	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2293	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#126	C₂²	1	2	yes	—
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
26	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#117	C₂²	1	2	yes	—
29	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#400	C₂²	1	2	yes	—
31	C₃₁×#400	C₂²	1	2	yes	—
32	C₃₁×#400	C₂²	1	1	yes	characteristic
33	C₃₁×#400	C₂²	1	2	yes	—
34	C₃₁×#399	C₂²	1	1	yes	characteristic
35	C₃₁×#398	C₂²	1	1	yes	characteristic
36	C₃₁×#398	C₂²	1	2	yes	—
37	C₃₁×#398	C₂²	1	2	yes	—
38	C₃₁×#398	C₂²	1	2	yes	—
39	C₃₁×#397	C₂²	1	1	yes	characteristic
40	C₃₁×#397	C₂²	1	2	yes	—
41	C₃₁×#396	C₂²	1	2	yes	—
42	C₃₁×#396	C₂²	1	2	yes	—
43	C₃₁×#395	C₂²	1	1	yes	characteristic
44	C₃₁×#394	C₂²	1	1	yes	characteristic
45	C₃₁×#394	C₂²	1	2	yes	—
46	C₃₁×#394	C₂²	1	2	yes	—
47	C₃₁×#393	C₂²	1	1	yes	characteristic
48	C₃₁×#393	C₂²	1	2	yes	—
49	C₃₁×#392	C₂²	1	1	yes	characteristic
50	C₃₁×#390	C₂²	1	2	yes	—
51	C₃₁×#390	C₂²	1	2	yes	—
52	C₃₁×#390	C₂²	1	2	yes	—
53	C₃₁×#389	C₂²	1	2	yes	—
54	C₃₁×#389	C₂²	1	2	yes	—
55	C₃₁×#389	C₂²	1	2	yes	—
56	C₃₁×#388	C₂²	1	2	yes	—
57	C₃₁×#388	C₂²	1	2	yes	—
58	C₃₁×#388	C₂²	1	2	yes	—
59	C₃₁×#388	C₂²	1	2	yes	—
60	C₃₁×#388	C₂²	1	2	yes	—
61	C₃₁×#388	C₂²	1	2	yes	—
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	—
67	C₃₁×#388	C₂²	1	2	yes	—
68	C₃₁×#388	C₂²	1	2	yes	—
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#385	C₂²	1	2	yes	—
82	C₃₁×#383	C₂²	1	2	yes	—
83	C₃₁×#381	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
85	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
86	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
88	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
89	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₃₁×#376	C₂²	1	1	yes	characteristic
103	C₃₁×#376	C₂²	1	1	yes	characteristic
104	C₄³×C₃₁	C₂²	1	1	yes	characteristic
105	C₄³×C₃₁	C₂²	1	1	yes	characteristic
106	C₄³×C₃₁	C₂²	1	2	yes	—
107	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
111	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
112	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₃₁×#126	—	2	8	no	—
114	C₃₁×#123	—	2	8	no	—
115	C₄×Q₈×C₃₁	—	2	8	no	—
116	C₄×Q₈×C₃₁	—	2	4	no	—
117	C₄×D₄×C₃₁	—	2	8	no	—
118	C₄×D₄×C₃₁	—	2	4	no	—
119	C₃₁×#117	—	2	4	no	—
120	C₃₁×#117	—	2	8	no	—
121	C₃₁×#117	—	2	4	no	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₃₁	—	2	4	no	—
160	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
178	C₃₁×#95	C₂³	1	2	yes	—
179	C₃₁×#95	C₂³	1	1	yes	characteristic
180	C₃₁×#95	C₂³	1	2	yes	—
181	C₃₁×#95	C₂³	1	2	yes	—
182	C₃₁×#95	C₂³	1	2	yes	—
183	C₃₁×#95	C₂³	1	1	yes	characteristic
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	1	yes	characteristic
187	C₃₁×#95	C₂³	1	1	yes	characteristic
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	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
205	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₃₁	—	2	4	no	—
207	C₂×Q₈×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	4	2	no	—
212	C₂×D₄×C₃₁	—	4	2	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	4	no	—
216	C₂²×C₄×C₃₁	—	2	4	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	4	2	no	—
221	C₂²×C₄×C₃₁	#41	1	4	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₄⋊C₄×C₃₁	—	2	4	no	—
240	C₄⋊C₄×C₃₁	—	2	2	no	—
241	C₄⋊C₄×C₃₁	—	2	2	no	—
242	C₄⋊C₄×C₃₁	—	2	4	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	2	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	2	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	4	2	no	—
254	C₄⋊C₄×C₃₁	—	4	2	no	—
255	C₄⋊C₄×C₃₁	—	4	2	no	—
256	C₄⋊C₄×C₃₁	—	4	2	no	—
257	C₄⋊C₄×C₃₁	#41	1	8	yes	—
258	C₂²⋊C₄×C₃₁	—	2	4	no	—
259	C₂²⋊C₄×C₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	4	2	no	—
273	C₂²⋊C₄×C₃₁	—	4	2	no	—
274	C₂²⋊C₄×C₃₁	—	4	2	no	—
275	C₂²⋊C₄×C₃₁	—	4	2	no	—
276	C₄²×C₃₁	—	2	2	no	—
277	C₄²×C₃₁	—	2	4	no	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	2	no	—
280	C₄²×C₃₁	—	2	2	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	—	2	4	no	—
283	C₄²×C₃₁	—	2	4	no	—
284	C₄²×C₃₁	—	2	4	no	—
285	C₄²×C₃₁	—	2	4	no	—
286	C₄²×C₃₁	—	2	4	no	—
287	C₄²×C₃₁	—	2	4	no	—
288	C₄²×C₃₁	—	4	2	no	—
289	C₄²×C₃₁	—	4	2	no	—
290	C₄²×C₃₁	—	4	2	no	—
291	C₄²×C₃₁	—	4	2	no	—
292	C₄²×C₃₁	#41	1	4	yes	—
293	C₄²×C₃₁	#41	1	4	yes	—
294	#34881	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₃₁	—	2	1	no	—
296	C₂³×C₃₁	—	2	1	no	—
297	C₂³×C₃₁	—	2	2	no	—
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	—	2	2	no	—
300	C₂³×C₃₁	—	2	2	no	—
301	C₂³×C₃₁	—	2	2	no	—
302	C₂³×C₃₁	—	2	2	no	—
303	C₂³×C₃₁	—	2	2	no	—
304	C₂³×C₃₁	—	2	2	no	—
305	C₂³×C₃₁	—	2	2	no	—
306	C₂³×C₃₁	C₂×#41	1	2	yes	—
307	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
308	Q₈×C₃₁	—	2	8	no	—
309	D₄×C₃₁	—	4	8	no	—
310	D₄×C₃₁	—	4	4	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	1	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	8	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	1	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	1	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	4	8	no	—
350	C₂×C₄×C₃₁	—	4	8	no	—
351	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
352	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
353	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
354	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
355	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
356	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
357	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
358	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
359	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
360	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
361	#2593	C₂×C₃₁	1	2	yes	complemented
362	#2585	C₂×C₃₁	1	2	yes	complemented
363	#2573	C₂×C₃₁	1	2	yes	complemented
364	#2554	C₂×C₃₁	1	2	yes	—
365	#2525	C₂×C₃₁	1	2	yes	complemented
366	#2516	C₂×C₃₁	1	2	yes	complemented
367	#2469	C₂×C₃₁	1	2	yes	complemented
368	#2458	C₂×C₃₁	1	2	yes	complemented
369	#2402	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#2398	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#2396	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#2392	C₂×C₃₁	1	1	yes	characteristic
373	C₄×#126	C₂×C₃₁	1	2	yes	complemented
374	C₄×#123	C₂×C₃₁	1	2	yes	complemented
375	#2298	C₂×C₃₁	1	2	yes	complemented
376	#2293	C₂×C₃₁	1	2	yes	complemented
377	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
378	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
379	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
380	C₂²×C₃₁	—	2	2	no	—
381	C₂²×C₃₁	—	2	4	no	—
382	C₂²×C₃₁	—	4	1	no	—
383	C₂²×C₃₁	—	4	1	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	—	4	2	no	—
387	C₂²×C₃₁	—	4	2	no	—
388	C₂²×C₃₁	—	4	2	no	—
389	C₂²×C₃₁	—	4	2	no	—
390	C₂²×C₃₁	—	4	2	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
393	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
394	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₃₁	C₂²×#41	1	2	yes	—
396	C₂²×C₃₁	#585	1	2	yes	—
397	C₄×C₃₁	—	2	2	no	—
398	C₄×C₃₁	—	2	4	no	—
399	C₄×C₃₁	—	2	2	no	—
400	C₄×C₃₁	—	2	2	no	—
401	C₄×C₃₁	—	2	4	no	—
402	C₄×C₃₁	—	2	4	no	—
403	C₄×C₃₁	—	2	4	no	—
404	C₄×C₃₁	—	4	2	no	—
405	C₄×C₃₁	—	4	1	no	—
406	C₄×C₃₁	—	4	1	no	—
407	C₄×C₃₁	—	4	2	no	—
408	C₄×C₃₁	—	4	2	no	—
409	C₄×C₃₁	—	4	2	no	—
410	C₄×C₃₁	—	4	2	no	—
411	C₄×C₃₁	—	4	2	no	—
412	C₄×C₃₁	—	4	2	no	—
413	C₄×C₃₁	#529	1	4	yes	—
414	C₂×#126	C₂²×C₃₁	1	2	yes	—
415	C₂×#123	C₂²×C₃₁	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
420	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
421	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×#117	C₂²×C₃₁	1	2	yes	—
423	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
424	#400	C₂²×C₃₁	1	2	yes	—
425	#400	C₂²×C₃₁	1	2	yes	—
426	#400	C₂²×C₃₁	1	1	yes	characteristic
427	#400	C₂²×C₃₁	1	2	yes	—
428	#399	C₂²×C₃₁	1	1	yes	characteristic
429	#398	C₂²×C₃₁	1	1	yes	characteristic
430	#398	C₂²×C₃₁	1	2	yes	—
431	#398	C₂²×C₃₁	1	2	yes	—
432	#398	C₂²×C₃₁	1	2	yes	—
433	#397	C₂²×C₃₁	1	1	yes	characteristic
434	#397	C₂²×C₃₁	1	2	yes	—
435	#396	C₂²×C₃₁	1	2	yes	—
436	#396	C₂²×C₃₁	1	2	yes	—
437	#395	C₂²×C₃₁	1	1	yes	characteristic
438	#394	C₂²×C₃₁	1	1	yes	characteristic
439	#394	C₂²×C₃₁	1	2	yes	—
440	#394	C₂²×C₃₁	1	2	yes	—
441	#393	C₂²×C₃₁	1	1	yes	characteristic
442	#393	C₂²×C₃₁	1	2	yes	—
443	#392	C₂²×C₃₁	1	1	yes	characteristic
444	#390	C₂²×C₃₁	1	2	yes	—
445	#390	C₂²×C₃₁	1	2	yes	—
446	#390	C₂²×C₃₁	1	2	yes	—
447	#389	C₂²×C₃₁	1	2	yes	—
448	#389	C₂²×C₃₁	1	2	yes	—
449	#389	C₂²×C₃₁	1	2	yes	—
450	#388	C₂²×C₃₁	1	2	yes	—
451	#388	C₂²×C₃₁	1	2	yes	—
452	#388	C₂²×C₃₁	1	2	yes	—
453	#388	C₂²×C₃₁	1	2	yes	—
454	#388	C₂²×C₃₁	1	2	yes	—
455	#388	C₂²×C₃₁	1	2	yes	—
456	#388	C₂²×C₃₁	1	2	yes	—
457	#388	C₂²×C₃₁	1	2	yes	—
458	#388	C₂²×C₃₁	1	2	yes	—
459	#388	C₂²×C₃₁	1	2	yes	—
460	#388	C₂²×C₃₁	1	2	yes	—
461	#388	C₂²×C₃₁	1	2	yes	—
462	#388	C₂²×C₃₁	1	2	yes	—
463	#388	C₂²×C₃₁	1	2	yes	—
464	#388	C₂²×C₃₁	1	2	yes	—
465	#387	C₂²×C₃₁	1	2	yes	—
466	#387	C₂²×C₃₁	1	2	yes	—
467	#387	C₂²×C₃₁	1	2	yes	—
468	#387	C₂²×C₃₁	1	2	yes	—
469	#387	C₂²×C₃₁	1	2	yes	—
470	#387	C₂²×C₃₁	1	2	yes	—
471	#387	C₂²×C₃₁	1	2	yes	—
472	#387	C₂²×C₃₁	1	2	yes	—
473	#387	C₂²×C₃₁	1	2	yes	—
474	#386	C₂²×C₃₁	1	2	yes	—
475	#385	C₂²×C₃₁	1	2	yes	—
476	#383	C₂²×C₃₁	1	2	yes	—
477	#381	C₂²×C₃₁	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
485	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
486	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
494	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
496	#376	C₂²×C₃₁	1	1	yes	characteristic
497	#376	C₂²×C₃₁	1	1	yes	characteristic
498	C₄³	C₂²×C₃₁	1	1	yes	characteristic
499	C₄³	C₂²×C₃₁	1	1	yes	characteristic
500	C₄³	C₂²×C₃₁	1	2	yes	—
501	C₂×C₃₁	—	4	2	no	—
502	C₂×C₃₁	—	8	2	no	—
503	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
504	C₂×C₃₁	#3444	1	1	yes	characteristic
505	C₂×C₃₁	#3455	1	1	yes	characteristic
506	C₂×C₃₁	#3475	1	2	yes	—
507	C₂×C₃₁	#3480	1	2	yes	—
508	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
510	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
512	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
513	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
514	#126	—	2	8	no	—
515	#123	—	2	8	no	—
516	C₄×Q₈	—	2	8	no	—
517	C₄×Q₈	—	2	4	no	—
518	C₄×D₄	—	2	8	no	—
519	C₄×D₄	—	2	4	no	—
520	#117	—	2	4	no	—
521	#117	—	2	8	no	—
522	#117	—	2	4	no	—
523	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₄²	—	2	4	no	—
561	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
564	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
565	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
566	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
567	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
568	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
569	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
570	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
573	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
575	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
576	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
579	#95	C₂³×C₃₁	1	2	yes	—
580	#95	C₂³×C₃₁	1	2	yes	—
581	#95	C₂³×C₃₁	1	2	yes	—
582	#95	C₂³×C₃₁	1	2	yes	—
583	#95	C₂³×C₃₁	1	2	yes	—
584	#95	C₂³×C₃₁	1	2	yes	—
585	#95	C₂³×C₃₁	1	2	yes	—
586	#95	C₂³×C₃₁	1	2	yes	—
587	#95	C₂³×C₃₁	1	2	yes	—
588	#95	C₂³×C₃₁	1	2	yes	—
589	#95	C₂³×C₃₁	1	2	yes	—
590	#95	C₂³×C₃₁	1	2	yes	—
591	#95	C₂³×C₃₁	1	2	yes	—
592	#95	C₂³×C₃₁	1	2	yes	—
593	#95	C₂³×C₃₁	1	2	yes	—
594	#95	C₂³×C₃₁	1	2	yes	—
595	#95	C₂³×C₃₁	1	1	yes	characteristic
596	#95	C₂³×C₃₁	1	1	yes	characteristic
597	#95	C₂³×C₃₁	1	2	yes	—
598	#95	C₂³×C₃₁	1	2	yes	—
599	#95	C₂³×C₃₁	1	2	yes	—
600	#95	C₂³×C₃₁	1	2	yes	—
601	#95	C₂³×C₃₁	1	2	yes	—
602	#95	C₂³×C₃₁	1	2	yes	—
603	#95	C₂³×C₃₁	1	1	yes	characteristic
604	#95	C₂³×C₃₁	1	1	yes	characteristic
605	C₃₁	#34881	1	1	yes	characteristic, direct product factor, Sylow
606	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
607	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	#41×C₃₁	1	4	yes	—
624	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	#41×C₃₁	1	8	yes	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	4	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	#41×C₃₁	1	4	yes	—
695	C₄²	#41×C₃₁	1	4	yes	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	C₂×#41×C₃₁	1	2	yes	—
708	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
709	Q₈	—	2	8	no	—
710	D₄	—	4	8	no	—
711	D₄	—	4	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	8	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
753	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
754	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
755	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
756	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
757	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
758	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
759	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
760	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
761	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
775	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
776	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₃₁	1	2	yes	—
778	C₂²	C₃₁×#585	1	2	yes	—
779	C₄	—	2	2	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	4	no	—
784	C₄	—	2	4	no	—
785	C₄	—	2	4	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	C₃₁×#529	1	4	yes	—
796	C₂	—	4	2	no	—
797	C₂	—	8	2	no	—
798	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
799	C₂	C₃₁×#3444	1	1	yes	characteristic
800	C₂	C₃₁×#3455	1	1	yes	characteristic
801	C₂	C₃₁×#3475	1	2	yes	—
802	C₂	C₃₁×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₃₁×#392	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2593	C₂	semidirect
2. C₃₁×#2585	C₂	semidirect
3. C₃₁×#2573	C₂	semidirect
5. C₃₁×#2525	C₂	semidirect
6. C₃₁×#2516	C₂	semidirect
7. C₃₁×#2469	C₂	semidirect
8. C₃₁×#2458	C₂	semidirect
9. C₃₁×#2402	C₂	semidirect
10. C₃₁×#2398	C₂	semidirect
11. C₃₁×#2396	C₂	semidirect
13. C₄×C₃₁×#126	C₂	semidirect
14. C₄×C₃₁×#123	C₂	semidirect
15. C₃₁×#2298	C₂	semidirect
16. C₃₁×#2293	C₂	semidirect
17. C₃₁×#2293	C₂	semidirect
18. C₄²×Q₈×C₃₁	C₂	semidirect
19. C₄×C₃₁×#117	C₂	semidirect
294. #34881	C₃₁	direct (N × H)
361. #2593	C₂×C₃₁	semidirect
362. #2585	C₂×C₃₁	semidirect
363. #2573	C₂×C₃₁	semidirect
365. #2525	C₂×C₃₁	semidirect
366. #2516	C₂×C₃₁	semidirect
367. #2469	C₂×C₃₁	semidirect
368. #2458	C₂×C₃₁	semidirect
369. #2402	C₂×C₃₁	semidirect
370. #2398	C₂×C₃₁	semidirect
371. #2396	C₂×C₃₁	semidirect
373. C₄×#126	C₂×C₃₁	semidirect
374. C₄×#123	C₂×C₃₁	semidirect
375. #2298	C₂×C₃₁	semidirect
376. #2293	C₂×C₃₁	semidirect
377. #2293	C₂×C₃₁	semidirect
378. C₄²×Q₈	C₂×C₃₁	semidirect
379. C₄×#117	C₂×C₃₁	semidirect
605. C₃₁	#34881	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×#2593	2
C₃₁×#2585	2
C₃₁×#2573	2
C₃₁×#2554	2
C₃₁×#2525	2
C₃₁×#2516	2
C₃₁×#2469	2
C₃₁×#2458	2
C₃₁×#2402	2
C₃₁×#2398	2
C₃₁×#2396	2
C₃₁×#2392	2
C₄×C₃₁×#126	2
C₄×C₃₁×#123	2
C₃₁×#2298	2
C₃₁×#2293	2
C₄²×Q₈×C₃₁	2
C₄×C₃₁×#117	2
#34881	31

Subgroups — C31×#34881 #21491640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34881 #21491640