Subgroups — C₃₁×#22144 #21478903

Order 7936.

882 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2392	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
22	C₃₁×#435	—	2	4	no	—
23	C₃₁×#433	—	2	4	no	—
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#398	C₄	1	1	yes	characteristic
45	C₃₁×#397	C₄	1	1	yes	characteristic
46	C₃₁×#396	C₄	1	1	yes	characteristic
47	C₃₁×#396	C₄	1	1	yes	characteristic
48	C₃₁×#394	C₄	1	1	yes	characteristic
49	C₃₁×#394	C₄	1	1	yes	characteristic
50	C₃₁×#394	C₄	1	1	yes	characteristic
51	C₃₁×#392	C₄	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
55	C₃₁×#336	C₂²	1	1	yes	characteristic
56	C₃₁×#336	C₂²	1	1	yes	characteristic
57	C₃₁×#336	C₂²	1	1	yes	characteristic
58	C₃₁×#336	C₂²	1	1	yes	characteristic
59	C₃₁×#336	C₂²	1	1	yes	characteristic
60	C₃₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
63	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₃₁	—	2	2	no	—
68	C₂×M₁₆×C₃₁	—	4	1	no	—
69	C₂×M₁₆×C₃₁	—	4	1	no	—
70	C₂²×C₈×C₃₁	—	2	2	no	—
71	C₂²×C₈×C₃₁	—	4	1	no	—
72	C₂²×C₈×C₃₁	—	4	1	no	—
73	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₃₁	—	2	2	no	—
82	C₄×D₄×C₃₁	—	2	2	no	—
83	C₄×D₄×C₃₁	—	4	1	no	—
84	C₄×D₄×C₃₁	—	4	1	no	—
85	C₄×D₄×C₃₁	—	4	1	no	—
86	C₄×D₄×C₃₁	—	4	1	no	—
87	C₃₁×#117	—	2	2	no	—
88	C₃₁×#117	—	2	2	no	—
89	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊C₈	—	2	2	no	—
113	C₃₁×C₄⋊C₈	—	2	2	no	—
114	C₃₁×C₄⋊C₈	—	2	2	no	—
115	C₃₁×C₄⋊C₈	—	2	2	no	—
116	C₃₁×C₄⋊C₈	—	4	1	no	—
117	C₃₁×C₄⋊C₈	—	4	1	no	—
118	C₃₁×C₂²⋊C₈	—	2	2	no	—
119	C₃₁×C₂²⋊C₈	—	2	2	no	—
120	C₃₁×C₂²⋊C₈	—	2	2	no	—
121	C₃₁×C₂²⋊C₈	—	2	2	no	—
122	C₃₁×C₂²⋊C₈	—	4	1	no	—
123	C₃₁×C₂²⋊C₈	—	4	1	no	—
124	C₃₁×C₂²⋊C₈	—	4	1	no	—
125	C₃₁×C₂²⋊C₈	—	4	1	no	—
126	C₃₁×C₂²⋊C₈	—	4	1	no	—
127	C₃₁×C₂²⋊C₈	—	4	1	no	—
128	C₃₁×#97	—	4	1	no	—
129	C₃₁×#97	D₄	1	4	yes	complemented
130	C₄×C₈×C₃₁	—	2	2	no	—
131	C₄×C₈×C₃₁	—	4	1	no	—
132	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
133	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
134	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
135	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
136	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
137	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
138	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
139	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×D₄×C₃₁	—	2	2	no	—
142	C₂×D₄×C₃₁	—	2	2	no	—
143	C₂×D₄×C₃₁	—	2	2	no	—
144	C₂×D₄×C₃₁	—	2	2	no	—
145	C₂×D₄×C₃₁	—	4	1	no	—
146	C₂×D₄×C₃₁	—	4	1	no	—
147	C₂×D₄×C₃₁	—	4	1	no	—
148	C₂×D₄×C₃₁	—	4	1	no	—
149	C₂×D₄×C₃₁	—	4	1	no	—
150	C₂²×C₄×C₃₁	—	2	1	no	—
151	C₂²×C₄×C₃₁	—	2	1	no	—
152	C₂²×C₄×C₃₁	—	2	1	no	—
153	C₂²×C₄×C₃₁	—	2	1	no	—
154	C₂²×C₄×C₃₁	—	2	1	no	—
155	C₂²×C₄×C₃₁	—	2	1	no	—
156	C₂²×C₄×C₃₁	—	2	1	no	—
157	C₂²×C₄×C₃₁	—	2	1	no	—
158	C₂²×C₄×C₃₁	—	2	1	no	—
159	C₂²×C₄×C₃₁	—	2	1	no	—
160	C₂²×C₄×C₃₁	—	2	1	no	—
161	C₂²×C₄×C₃₁	—	2	1	no	—
162	C₂²×C₄×C₃₁	—	2	1	no	—
163	C₂²×C₄×C₃₁	—	2	1	no	—
164	C₂²×C₄×C₃₁	—	2	1	no	—
165	C₂²×C₄×C₃₁	—	2	1	no	—
166	C₂²×C₄×C₃₁	—	2	1	no	—
167	C₂²×C₄×C₃₁	—	2	1	no	—
168	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
180	M₁₆×C₃₁	—	4	4	no	—
181	C₂×C₈×C₃₁	—	2	1	no	—
182	C₂×C₈×C₃₁	—	2	1	no	—
183	C₂×C₈×C₃₁	—	2	1	no	—
184	C₂×C₈×C₃₁	—	2	1	no	—
185	C₂×C₈×C₃₁	—	2	1	no	—
186	C₂×C₈×C₃₁	—	2	1	no	—
187	C₂×C₈×C₃₁	—	2	1	no	—
188	C₂×C₈×C₃₁	—	2	1	no	—
189	C₂×C₈×C₃₁	—	2	1	no	—
190	C₂×C₈×C₃₁	—	2	1	no	—
191	C₂×C₈×C₃₁	—	2	1	no	—
192	C₂×C₈×C₃₁	—	2	1	no	—
193	C₂×C₈×C₃₁	—	2	1	no	—
194	C₂×C₈×C₃₁	—	2	1	no	—
195	C₂×C₈×C₃₁	—	2	1	no	—
196	C₂×C₈×C₃₁	—	2	1	no	—
197	C₂×C₈×C₃₁	—	2	1	no	—
198	C₂×C₈×C₃₁	—	2	1	no	—
199	C₂×C₈×C₃₁	—	2	1	no	—
200	C₂×C₈×C₃₁	—	2	1	no	—
201	C₂×C₈×C₃₁	—	2	1	no	—
202	C₂×C₈×C₃₁	—	2	1	no	—
203	C₂×C₈×C₃₁	—	4	4	no	—
204	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
205	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₃₁	—	2	2	no	—
207	C₄⋊C₄×C₃₁	—	2	2	no	—
208	C₄⋊C₄×C₃₁	—	2	2	no	—
209	C₄⋊C₄×C₃₁	—	2	2	no	—
210	C₄⋊C₄×C₃₁	—	4	1	no	—
211	C₄⋊C₄×C₃₁	—	4	1	no	—
212	C₄⋊C₄×C₃₁	—	4	1	no	—
213	C₂²⋊C₄×C₃₁	—	2	2	no	—
214	C₂²⋊C₄×C₃₁	—	2	2	no	—
215	C₂²⋊C₄×C₃₁	—	2	2	no	—
216	C₂²⋊C₄×C₃₁	—	2	2	no	—
217	C₂²⋊C₄×C₃₁	—	2	2	no	—
218	C₂²⋊C₄×C₃₁	—	2	2	no	—
219	C₂²⋊C₄×C₃₁	—	4	1	no	—
220	C₂²⋊C₄×C₃₁	—	4	1	no	—
221	C₂²⋊C₄×C₃₁	—	4	1	no	—
222	C₂²⋊C₄×C₃₁	—	4	1	no	—
223	C₂²⋊C₄×C₃₁	—	4	1	no	—
224	C₂²⋊C₄×C₃₁	—	4	1	no	—
225	C₄²×C₃₁	—	2	1	no	—
226	C₄²×C₃₁	—	2	1	no	—
227	C₄²×C₃₁	—	2	1	no	—
228	C₄²×C₃₁	—	2	1	no	—
229	C₄²×C₃₁	—	2	1	no	—
230	C₄²×C₃₁	—	2	1	no	—
231	C₄²×C₃₁	C₂×D₄	1	2	yes	—
232	C₄²×C₃₁	#41	1	2	yes	—
233	#22144	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₃₁	—	2	1	no	—
235	C₂³×C₃₁	—	2	1	no	—
236	C₂³×C₃₁	—	2	1	no	—
237	C₂³×C₃₁	—	2	1	no	—
238	C₂³×C₃₁	—	2	1	no	—
239	C₂³×C₃₁	—	2	1	no	—
240	C₂³×C₃₁	—	2	1	no	—
241	C₂³×C₃₁	—	2	1	no	—
242	C₂³×C₃₁	—	2	1	no	—
243	C₂³×C₃₁	—	2	1	no	—
244	C₂³×C₃₁	—	2	1	no	—
245	C₂³×C₃₁	—	2	1	no	—
246	C₂³×C₃₁	—	2	1	no	—
247	C₂³×C₃₁	—	2	1	no	—
248	C₂³×C₃₁	—	2	1	no	—
249	C₂³×C₃₁	—	2	1	no	—
250	C₂³×C₃₁	—	2	1	no	—
251	C₂³×C₃₁	—	2	1	no	—
252	C₂³×C₃₁	—	2	1	no	—
253	C₂³×C₃₁	—	2	1	no	—
254	C₂³×C₃₁	#131	1	2	yes	—
255	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
256	D₄×C₃₁	—	4	4	no	—
257	D₄×C₃₁	—	4	4	no	—
258	D₄×C₃₁	—	4	4	no	—
259	C₂×C₄×C₃₁	—	2	1	no	—
260	C₂×C₄×C₃₁	—	2	1	no	—
261	C₂×C₄×C₃₁	—	2	1	no	—
262	C₂×C₄×C₃₁	—	2	1	no	—
263	C₂×C₄×C₃₁	—	2	1	no	—
264	C₂×C₄×C₃₁	—	2	1	no	—
265	C₂×C₄×C₃₁	—	2	1	no	—
266	C₂×C₄×C₃₁	—	2	1	no	—
267	C₂×C₄×C₃₁	—	2	1	no	—
268	C₂×C₄×C₃₁	—	2	1	no	—
269	C₂×C₄×C₃₁	—	2	1	no	—
270	C₂×C₄×C₃₁	—	2	1	no	—
271	C₂×C₄×C₃₁	—	2	1	no	—
272	C₂×C₄×C₃₁	—	2	1	no	—
273	C₂×C₄×C₃₁	—	2	1	no	—
274	C₂×C₄×C₃₁	—	2	1	no	—
275	C₂×C₄×C₃₁	—	2	1	no	—
276	C₂×C₄×C₃₁	—	2	1	no	—
277	C₂×C₄×C₃₁	—	2	1	no	—
278	C₂×C₄×C₃₁	—	2	1	no	—
279	C₂×C₄×C₃₁	—	2	1	no	—
280	C₂×C₄×C₃₁	—	2	1	no	—
281	C₂×C₄×C₃₁	—	2	1	no	—
282	C₂×C₄×C₃₁	—	2	1	no	—
283	C₂×C₄×C₃₁	—	2	1	no	—
284	C₂×C₄×C₃₁	—	2	1	no	—
285	C₂×C₄×C₃₁	—	2	1	no	—
286	C₂×C₄×C₃₁	—	2	1	no	—
287	C₂×C₄×C₃₁	—	2	1	no	—
288	C₂×C₄×C₃₁	—	2	1	no	—
289	C₂×C₄×C₃₁	—	4	1	no	—
290	C₂×C₄×C₃₁	—	4	1	no	—
291	C₂×C₄×C₃₁	—	4	1	no	—
292	C₂×C₄×C₃₁	—	4	1	no	—
293	C₂×C₄×C₃₁	—	4	1	no	—
294	C₂×C₄×C₃₁	—	4	1	no	—
295	C₂×C₄×C₃₁	—	4	1	no	—
296	C₂×C₄×C₃₁	—	4	1	no	—
297	C₂×C₄×C₃₁	—	4	1	no	—
298	C₂×C₄×C₃₁	—	4	1	no	—
299	C₂×C₄×C₃₁	—	4	1	no	—
300	C₂×C₄×C₃₁	—	4	1	no	—
301	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
302	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
303	C₂×C₄×C₃₁	#131	1	2	yes	—
304	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
310	C₈×C₃₁	—	2	2	no	—
311	C₈×C₃₁	—	2	2	no	—
312	C₈×C₃₁	—	4	1	no	—
313	C₈×C₃₁	—	4	1	no	—
314	C₈×C₃₁	—	4	1	no	—
315	C₈×C₃₁	—	4	1	no	—
316	C₈×C₃₁	—	4	1	no	—
317	C₈×C₃₁	—	4	1	no	—
318	C₂×#435	C₂×C₃₁	1	1	yes	characteristic, complemented
319	C₂×#433	C₂×C₃₁	1	1	yes	characteristic, complemented
320	#2392	C₂×C₃₁	1	1	yes	characteristic
321	#1955	C₂×C₃₁	1	1	yes	characteristic, complemented
322	#1954	C₂×C₃₁	1	1	yes	characteristic, complemented
323	#1954	C₂×C₃₁	1	1	yes	characteristic, complemented
324	#1939	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#1924	C₂×C₃₁	1	1	yes	characteristic, complemented
326	#1923	C₂×C₃₁	1	1	yes	characteristic, complemented
327	#1870	C₂×C₃₁	1	1	yes	characteristic, complemented
328	#1869	C₂×C₃₁	1	1	yes	characteristic, complemented
329	#1851	C₂×C₃₁	1	1	yes	characteristic, complemented
330	#1850	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#1798	C₂×C₃₁	1	1	yes	characteristic, complemented
332	#1771	C₂×C₃₁	1	1	yes	characteristic, complemented
333	C₂²×C₃₁	—	2	2	no	—
334	C₂²×C₃₁	—	2	2	no	—
335	C₂²×C₃₁	—	2	2	no	—
336	C₂²×C₃₁	—	4	1	no	—
337	C₂²×C₃₁	—	4	1	no	—
338	C₂²×C₃₁	—	4	1	no	—
339	C₂²×C₃₁	—	4	1	no	—
340	C₂²×C₃₁	—	4	1	no	—
341	C₂²×C₃₁	—	4	1	no	—
342	C₂²×C₃₁	—	4	1	no	—
343	C₂²×C₃₁	—	4	1	no	—
344	C₂²×C₃₁	—	4	1	no	—
345	C₂²×C₃₁	—	4	1	no	—
346	C₂²×C₃₁	—	4	1	no	—
347	C₂²×C₃₁	—	4	1	no	—
348	C₂²×C₃₁	—	4	1	no	—
349	C₂²×C₃₁	—	4	1	no	—
350	C₂²×C₃₁	—	4	1	no	—
351	C₂²×C₃₁	—	4	1	no	—
352	C₂²×C₃₁	—	4	1	no	—
353	C₂²×C₃₁	—	4	1	no	—
354	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂²×C₃₁	#518	1	1	yes	characteristic
356	C₂²×C₃₁	#520	1	1	yes	characteristic
357	C₂²×C₃₁	C₂×#131	1	1	yes	characteristic
358	C₂²×C₃₁	C₂×#131	1	1	yes	characteristic
359	C₂²×C₃₁	#568	1	1	yes	characteristic
360	C₂²×C₃₁	#568	1	1	yes	characteristic
361	C₄×C₃₁	—	2	2	no	—
362	C₄×C₃₁	—	2	2	no	—
363	C₄×C₃₁	—	2	2	no	—
364	C₄×C₃₁	—	4	1	no	—
365	C₄×C₃₁	—	4	1	no	—
366	C₄×C₃₁	—	4	1	no	—
367	C₄×C₃₁	—	4	1	no	—
368	C₄×C₃₁	—	4	1	no	—
369	C₄×C₃₁	—	4	1	no	—
370	C₄×C₃₁	—	4	1	no	—
371	C₄×C₃₁	—	4	1	no	—
372	C₄×C₃₁	#535	1	1	yes	characteristic
373	C₄×C₃₁	#537	1	1	yes	characteristic
374	C₄×C₃₁	#540	1	1	yes	characteristic
375	C₄×C₃₁	#542	1	1	yes	characteristic
376	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
377	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
378	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
379	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
381	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
382	#435	—	2	4	no	—
383	#433	—	2	4	no	—
384	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
385	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
386	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
387	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
388	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
389	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
393	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
398	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
399	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
400	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
403	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
404	#398	C₄×C₃₁	1	1	yes	characteristic
405	#397	C₄×C₃₁	1	1	yes	characteristic
406	#396	C₄×C₃₁	1	1	yes	characteristic
407	#396	C₄×C₃₁	1	1	yes	characteristic
408	#394	C₄×C₃₁	1	1	yes	characteristic
409	#394	C₄×C₃₁	1	1	yes	characteristic
410	#394	C₄×C₃₁	1	1	yes	characteristic
411	#392	C₄×C₃₁	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
413	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
414	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
415	#336	C₂²×C₃₁	1	1	yes	characteristic
416	#336	C₂²×C₃₁	1	1	yes	characteristic
417	#336	C₂²×C₃₁	1	1	yes	characteristic
418	#336	C₂²×C₃₁	1	1	yes	characteristic
419	#336	C₂²×C₃₁	1	1	yes	characteristic
420	#336	C₂²×C₃₁	1	1	yes	characteristic
421	C₂×C₃₁	—	4	2	no	—
422	C₂×C₃₁	—	8	1	no	—
423	C₂×C₃₁	—	8	1	no	—
424	C₂×C₃₁	#2324	1	1	yes	characteristic
425	C₂×C₃₁	#2933	1	1	yes	characteristic
426	C₂×C₃₁	#2935	1	1	yes	characteristic
427	C₂×C₃₁	#2977	1	1	yes	characteristic
428	C₂×C₃₁	#2978	1	1	yes	characteristic
429	C₂×C₃₁	#2992	1	1	yes	characteristic
430	C₂×C₃₁	#2993	1	1	yes	characteristic
431	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
432	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
433	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
437	C₂×M₁₆	—	2	2	no	—
438	C₂×M₁₆	—	4	1	no	—
439	C₂×M₁₆	—	4	1	no	—
440	C₂²×C₈	—	2	2	no	—
441	C₂²×C₈	—	4	1	no	—
442	C₂²×C₈	—	4	1	no	—
443	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	4	1	no	—
454	C₄×D₄	—	4	1	no	—
455	C₄×D₄	—	4	1	no	—
456	C₄×D₄	—	4	1	no	—
457	#117	—	2	2	no	—
458	#117	—	2	2	no	—
459	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
482	C₄⋊C₈	—	2	2	no	—
483	C₄⋊C₈	—	2	2	no	—
484	C₄⋊C₈	—	2	2	no	—
485	C₄⋊C₈	—	2	2	no	—
486	C₄⋊C₈	—	4	1	no	—
487	C₄⋊C₈	—	4	1	no	—
488	C₂²⋊C₈	—	2	2	no	—
489	C₂²⋊C₈	—	2	2	no	—
490	C₂²⋊C₈	—	2	2	no	—
491	C₂²⋊C₈	—	2	2	no	—
492	C₂²⋊C₈	—	4	1	no	—
493	C₂²⋊C₈	—	4	1	no	—
494	C₂²⋊C₈	—	4	1	no	—
495	C₂²⋊C₈	—	4	1	no	—
496	C₂²⋊C₈	—	4	1	no	—
497	C₂²⋊C₈	—	4	1	no	—
498	#97	—	4	1	no	—
499	#97	D₄×C₃₁	1	4	yes	complemented
500	C₄×C₈	—	2	2	no	—
501	C₄×C₈	—	4	1	no	—
502	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
503	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
504	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
505	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
506	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
507	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
508	C₃₁	#22144	1	1	yes	characteristic, direct product factor, Sylow
509	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
510	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
511	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	4	1	no	—
520	C₂×D₄	—	4	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
551	M₁₆	—	4	4	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	4	4	no	—
575	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
576	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₄⋊C₄	—	4	1	no	—
583	C₄⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	4	1	no	—
594	C₂²⋊C₄	—	4	1	no	—
595	C₂²⋊C₄	—	4	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	C₂×D₄×C₃₁	1	2	yes	—
603	C₄²	#41×C₃₁	1	2	yes	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	C₃₁×#131	1	2	yes	—
625	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
626	D₄	—	4	4	no	—
627	D₄	—	4	4	no	—
628	D₄	—	4	4	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
672	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
673	C₂×C₄	C₃₁×#131	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
675	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
676	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
680	C₈	—	2	2	no	—
681	C₈	—	2	2	no	—
682	C₈	—	4	1	no	—
683	C₈	—	4	1	no	—
684	C₈	—	4	1	no	—
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
710	C₂²	C₃₁×#518	1	1	yes	characteristic
711	C₂²	C₃₁×#520	1	1	yes	characteristic
712	C₂²	C₂×C₃₁×#131	1	1	yes	characteristic
713	C₂²	C₂×C₃₁×#131	1	1	yes	characteristic
714	C₂²	C₃₁×#568	1	1	yes	characteristic
715	C₂²	C₃₁×#568	1	1	yes	characteristic
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	C₃₁×#535	1	1	yes	characteristic
728	C₄	C₃₁×#537	1	1	yes	characteristic
729	C₄	C₃₁×#540	1	1	yes	characteristic
730	C₄	C₃₁×#542	1	1	yes	characteristic
731	C₂	—	4	2	no	—
732	C₂	—	8	1	no	—
733	C₂	—	8	1	no	—
734	C₂	C₃₁×#2324	1	1	yes	characteristic
735	C₂	C₃₁×#2933	1	1	yes	characteristic
736	C₂	C₃₁×#2935	1	1	yes	characteristic
737	C₂	C₃₁×#2977	1	1	yes	characteristic
738	C₂	C₃₁×#2978	1	1	yes	characteristic
739	C₂	C₃₁×#2992	1	1	yes	characteristic
740	C₂	C₃₁×#2993	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂³×C₄
prime radical	C₃₁×#392	C₄
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. C₂×C₃₁×#435	C₂	semidirect
2. C₂×C₃₁×#433	C₂	semidirect
4. C₃₁×#1955	C₂	semidirect
5. C₃₁×#1954	C₂	semidirect
6. C₃₁×#1954	C₂	semidirect
7. C₃₁×#1939	C₂	semidirect
8. C₃₁×#1924	C₂	semidirect
9. C₃₁×#1923	C₂	semidirect
10. C₃₁×#1870	C₂	semidirect
11. C₃₁×#1869	C₂	semidirect
12. C₃₁×#1851	C₂	semidirect
13. C₃₁×#1850	C₂	semidirect
14. C₃₁×#1798	C₂	semidirect
15. C₃₁×#1771	C₂	semidirect
129. C₃₁×#97	D₄	semidirect
233. #22144	C₃₁	direct (N × H)
318. C₂×#435	C₂×C₃₁	semidirect
319. C₂×#433	C₂×C₃₁	semidirect
321. #1955	C₂×C₃₁	semidirect
322. #1954	C₂×C₃₁	semidirect
323. #1954	C₂×C₃₁	semidirect
324. #1939	C₂×C₃₁	semidirect
325. #1924	C₂×C₃₁	semidirect
326. #1923	C₂×C₃₁	semidirect
327. #1870	C₂×C₃₁	semidirect
328. #1869	C₂×C₃₁	semidirect
329. #1851	C₂×C₃₁	semidirect
330. #1850	C₂×C₃₁	semidirect
331. #1798	C₂×C₃₁	semidirect
332. #1771	C₂×C₃₁	semidirect
499. #97	D₄×C₃₁	semidirect
508. C₃₁	#22144	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×#435	2
C₂×C₃₁×#433	2
C₃₁×#2392	2
C₃₁×#1955	2
C₃₁×#1954	2
C₃₁×#1939	2
C₃₁×#1924	2
C₃₁×#1923	2
C₃₁×#1870	2
C₃₁×#1869	2
C₃₁×#1851	2
C₃₁×#1850	2
C₃₁×#1798	2
C₃₁×#1771	2
#22144	31

Subgroups — C31×#22144 #21478903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22144 #21478903