Subgroups — C₃₁×#22173 #21478932

Order 7936.

920 conjugacy classes of subgroups.

The subgroup lattice has 746 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×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2392	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1870	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×#1729	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
24	C₃₁×#435	—	2	4	no	—
25	C₈×D₄×C₃₁	—	2	4	no	—
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×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#398	C₄	1	1	yes	characteristic
41	C₃₁×#397	C₄	1	1	yes	characteristic
42	C₃₁×#396	C₄	1	1	yes	characteristic
43	C₃₁×#396	C₄	1	1	yes	characteristic
44	C₃₁×#394	C₄	1	1	yes	characteristic
45	C₃₁×#394	C₄	1	1	yes	characteristic
46	C₃₁×#394	C₄	1	1	yes	characteristic
47	C₃₁×#392	C₄	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#336	C₂²	1	1	yes	characteristic
52	C₃₁×#336	C₂²	1	1	yes	characteristic
53	C₃₁×#336	C₂²	1	1	yes	characteristic
54	C₃₁×#336	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	—	2	2	no	—
69	C₂×M₁₆×C₃₁	—	4	1	no	—
70	C₂×M₁₆×C₃₁	—	4	1	no	—
71	C₂×M₁₆×C₃₁	—	4	1	no	—
72	C₂×M₁₆×C₃₁	—	4	1	no	—
73	C₂²×C₈×C₃₁	—	2	2	no	—
74	C₂²×C₈×C₃₁	—	4	1	no	—
75	C₂²×C₈×C₃₁	—	4	1	no	—
76	C₂²×C₈×C₃₁	—	4	1	no	—
77	C₂²×C₈×C₃₁	—	4	1	no	—
78	C₂²×C₈×C₃₁	D₄	1	4	yes	complemented
79	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₃₁	—	2	2	no	—
88	C₄×D₄×C₃₁	—	2	2	no	—
89	C₄×D₄×C₃₁	—	2	2	no	—
90	C₄×D₄×C₃₁	—	2	2	no	—
91	C₄×D₄×C₃₁	—	4	1	no	—
92	C₄×D₄×C₃₁	—	4	1	no	—
93	C₃₁×#117	—	4	1	no	—
94	C₃₁×#117	—	4	1	no	—
95	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄⋊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×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊C₈	—	2	2	no	—
119	C₃₁×C₄⋊C₈	—	2	2	no	—
120	C₃₁×C₄⋊C₈	—	4	1	no	—
121	C₃₁×C₄⋊C₈	—	4	1	no	—
122	C₃₁×C₂²⋊C₈	—	2	2	no	—
123	C₃₁×C₂²⋊C₈	—	2	2	no	—
124	C₃₁×C₂²⋊C₈	—	2	2	no	—
125	C₃₁×C₂²⋊C₈	—	2	2	no	—
126	C₃₁×C₂²⋊C₈	—	4	1	no	—
127	C₃₁×C₂²⋊C₈	—	4	1	no	—
128	C₃₁×C₂²⋊C₈	—	4	1	no	—
129	C₃₁×C₂²⋊C₈	—	4	1	no	—
130	C₃₁×#97	—	2	2	no	—
131	C₄×C₈×C₃₁	—	2	2	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	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₃₁	#41	1	2	yes	—
179	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
180	M₁₆×C₃₁	—	4	4	no	—
181	M₁₆×C₃₁	—	4	4	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	—	2	1	no	—
204	C₂×C₈×C₃₁	—	4	4	no	—
205	C₂×C₈×C₃₁	—	4	4	no	—
206	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
207	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₃₁	—	2	2	no	—
209	C₄⋊C₄×C₃₁	—	2	2	no	—
210	C₄⋊C₄×C₃₁	—	2	2	no	—
211	C₄⋊C₄×C₃₁	—	4	1	no	—
212	C₄⋊C₄×C₃₁	—	4	1	no	—
213	C₄⋊C₄×C₃₁	—	4	1	no	—
214	C₄⋊C₄×C₃₁	—	4	1	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	—	2	2	no	—
220	C₂²⋊C₄×C₃₁	—	2	2	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	C₂²⋊C₄×C₃₁	—	4	1	no	—
226	C₂²⋊C₄×C₃₁	—	4	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	—	2	1	no	—
232	C₄²×C₃₁	—	2	1	no	—
233	C₄²×C₃₁	—	2	1	no	—
234	C₄²×C₃₁	—	2	1	no	—
235	#22173	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
255	C₂³×C₃₁	C₄×D₄	1	2	yes	—
256	C₂³×C₃₁	#131	1	2	yes	—
257	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
258	D₄×C₃₁	—	2	8	no	—
259	D₄×C₃₁	—	4	4	no	—
260	D₄×C₃₁	—	4	4	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	2	no	—
266	C₂×C₄×C₃₁	—	2	2	no	—
267	C₂×C₄×C₃₁	—	2	2	no	—
268	C₂×C₄×C₃₁	—	2	2	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	—	2	1	no	—
290	C₂×C₄×C₃₁	—	2	1	no	—
291	C₂×C₄×C₃₁	—	2	1	no	—
292	C₂×C₄×C₃₁	—	2	1	no	—
293	C₂×C₄×C₃₁	—	2	1	no	—
294	C₂×C₄×C₃₁	—	2	1	no	—
295	C₂×C₄×C₃₁	—	2	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	—	4	1	no	—
302	C₂×C₄×C₃₁	—	4	1	no	—
303	C₂×C₄×C₃₁	—	4	1	no	—
304	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
305	C₂×C₄×C₃₁	#131	1	2	yes	—
306	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
312	C₈×C₃₁	—	2	2	no	—
313	C₈×C₃₁	—	2	2	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	C₈×C₃₁	—	4	1	no	—
319	C₈×C₃₁	—	4	1	no	—
320	C₂×#435	C₂×C₃₁	1	1	yes	characteristic, complemented
321	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
322	#2392	C₂×C₃₁	1	1	yes	characteristic
323	#1924	C₂×C₃₁	1	1	yes	characteristic, complemented
324	#1923	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#1917	C₂×C₃₁	1	1	yes	characteristic, complemented
326	#1916	C₂×C₃₁	1	1	yes	characteristic, complemented
327	#1870	C₂×C₃₁	1	1	yes	characteristic, complemented
328	#1870	C₂×C₃₁	1	1	yes	characteristic, complemented
329	#1870	C₂×C₃₁	1	1	yes	characteristic, complemented
330	#1869	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#1851	C₂×C₃₁	1	1	yes	characteristic, complemented
332	#1850	C₂×C₃₁	1	1	yes	characteristic, complemented
333	#1798	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#1729	C₂×C₃₁	1	1	yes	characteristic, complemented
335	C₂²×C₃₁	—	2	2	no	—
336	C₂²×C₃₁	—	2	2	no	—
337	C₂²×C₃₁	—	2	2	no	—
338	C₂²×C₃₁	—	2	2	no	—
339	C₂²×C₃₁	—	2	2	no	—
340	C₂²×C₃₁	—	2	2	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	—	4	1	no	—
355	C₂²×C₃₁	—	4	1	no	—
356	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂²×C₃₁	#518	1	1	yes	characteristic
358	C₂²×C₃₁	#520	1	1	yes	characteristic
359	C₂²×C₃₁	C₂×#131	1	1	yes	characteristic
360	C₂²×C₃₁	C₂×#131	1	1	yes	characteristic
361	C₂²×C₃₁	#568	1	1	yes	characteristic
362	C₂²×C₃₁	#568	1	1	yes	characteristic
363	C₄×C₃₁	—	2	2	no	—
364	C₄×C₃₁	—	2	2	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	—	4	1	no	—
373	C₄×C₃₁	—	4	1	no	—
374	C₄×C₃₁	#534	1	1	yes	characteristic
375	C₄×C₃₁	#537	1	1	yes	characteristic
376	C₄×C₃₁	#538	1	1	yes	characteristic
377	C₄×C₃₁	#539	1	1	yes	characteristic
378	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
379	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
380	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
381	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
385	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
386	#435	—	2	4	no	—
387	C₈×D₄	—	2	4	no	—
388	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
389	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
390	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
391	C₂×C₄⋊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×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
402	#398	C₄×C₃₁	1	1	yes	characteristic
403	#397	C₄×C₃₁	1	1	yes	characteristic
404	#396	C₄×C₃₁	1	1	yes	characteristic
405	#396	C₄×C₃₁	1	1	yes	characteristic
406	#394	C₄×C₃₁	1	1	yes	characteristic
407	#394	C₄×C₃₁	1	1	yes	characteristic
408	#394	C₄×C₃₁	1	1	yes	characteristic
409	#392	C₄×C₃₁	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
413	#336	C₂²×C₃₁	1	1	yes	characteristic
414	#336	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	#336	C₂²×C₃₁	1	1	yes	characteristic
422	#336	C₂²×C₃₁	1	1	yes	characteristic
423	C₂×C₃₁	—	4	2	no	—
424	C₂×C₃₁	—	4	2	no	—
425	C₂×C₃₁	—	8	1	no	—
426	C₂×C₃₁	#2325	1	1	yes	characteristic
427	C₂×C₃₁	#2929	1	1	yes	characteristic
428	C₂×C₃₁	#2930	1	1	yes	characteristic
429	C₂×C₃₁	#2976	1	1	yes	characteristic
430	C₂×C₃₁	#2981	1	1	yes	characteristic
431	C₂×C₃₁	#2992	1	1	yes	characteristic
432	C₂×C₃₁	#2993	1	1	yes	characteristic
433	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
434	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
435	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
439	C₂×M₁₆	—	2	2	no	—
440	C₂×M₁₆	—	2	2	no	—
441	C₂×M₁₆	—	4	1	no	—
442	C₂×M₁₆	—	4	1	no	—
443	C₂×M₁₆	—	4	1	no	—
444	C₂×M₁₆	—	4	1	no	—
445	C₂²×C₈	—	2	2	no	—
446	C₂²×C₈	—	4	1	no	—
447	C₂²×C₈	—	4	1	no	—
448	C₂²×C₈	—	4	1	no	—
449	C₂²×C₈	—	4	1	no	—
450	C₂²×C₈	D₄×C₃₁	1	4	yes	complemented
451	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	4	1	no	—
464	C₄×D₄	—	4	1	no	—
465	#117	—	4	1	no	—
466	#117	—	4	1	no	—
467	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
473	C₂×C₄⋊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×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
490	C₄⋊C₈	—	2	2	no	—
491	C₄⋊C₈	—	2	2	no	—
492	C₄⋊C₈	—	4	1	no	—
493	C₄⋊C₈	—	4	1	no	—
494	C₂²⋊C₈	—	2	2	no	—
495	C₂²⋊C₈	—	2	2	no	—
496	C₂²⋊C₈	—	2	2	no	—
497	C₂²⋊C₈	—	2	2	no	—
498	C₂²⋊C₈	—	4	1	no	—
499	C₂²⋊C₈	—	4	1	no	—
500	C₂²⋊C₈	—	4	1	no	—
501	C₂²⋊C₈	—	4	1	no	—
502	#97	—	2	2	no	—
503	C₄×C₈	—	2	2	no	—
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	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
509	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
510	C₃₁	#22173	1	1	yes	characteristic, direct product factor, Sylow
511	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
512	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
513	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	4	1	no	—
520	C₂×D₄	—	4	1	no	—
521	C₂×D₄	—	4	1	no	—
522	C₂×D₄	—	4	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	C₂×D₄×C₃₁	1	2	yes	—
551	C₂²×C₄	#41×C₃₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
553	M₁₆	—	4	4	no	—
554	M₁₆	—	4	4	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	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	4	4	no	—
578	C₂×C₈	—	4	4	no	—
579	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
580	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	4	1	no	—
585	C₄⋊C₄	—	4	1	no	—
586	C₄⋊C₄	—	4	1	no	—
587	C₄⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	4	1	no	—
595	C₂²⋊C₄	—	4	1	no	—
596	C₂²⋊C₄	—	4	1	no	—
597	C₂²⋊C₄	—	4	1	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	4	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	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	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	C₄×D₄×C₃₁	1	2	yes	—
628	C₂³	C₃₁×#131	1	2	yes	—
629	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
630	D₄	—	2	8	no	—
631	D₄	—	4	4	no	—
632	D₄	—	4	4	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	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	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	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
677	C₂×C₄	C₃₁×#131	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
679	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
680	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
681	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
684	C₈	—	2	2	no	—
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₈	—	4	1	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	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	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
714	C₂²	C₃₁×#518	1	1	yes	characteristic
715	C₂²	C₃₁×#520	1	1	yes	characteristic
716	C₂²	C₂×C₃₁×#131	1	1	yes	characteristic
717	C₂²	C₂×C₃₁×#131	1	1	yes	characteristic
718	C₂²	C₃₁×#568	1	1	yes	characteristic
719	C₂²	C₃₁×#568	1	1	yes	characteristic
720	C₄	—	2	2	no	—
721	C₄	—	2	2	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	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	C₃₁×#534	1	1	yes	characteristic
732	C₄	C₃₁×#537	1	1	yes	characteristic
733	C₄	C₃₁×#538	1	1	yes	characteristic
734	C₄	C₃₁×#539	1	1	yes	characteristic
735	C₂	—	4	2	no	—
736	C₂	—	4	2	no	—
737	C₂	—	8	1	no	—
738	C₂	C₃₁×#2325	1	1	yes	characteristic
739	C₂	C₃₁×#2929	1	1	yes	characteristic
740	C₂	C₃₁×#2930	1	1	yes	characteristic
741	C₂	C₃₁×#2976	1	1	yes	characteristic
742	C₂	C₃₁×#2981	1	1	yes	characteristic
743	C₂	C₃₁×#2992	1	1	yes	characteristic
744	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×C₈×D₄×C₃₁	C₂	semidirect
4. C₃₁×#1924	C₂	semidirect
5. C₃₁×#1923	C₂	semidirect
6. C₃₁×#1917	C₂	semidirect
7. C₃₁×#1916	C₂	semidirect
8. C₃₁×#1870	C₂	semidirect
9. C₃₁×#1870	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×#1729	C₂	semidirect
78. C₂²×C₈×C₃₁	D₄	semidirect
235. #22173	C₃₁	direct (N × H)
320. C₂×#435	C₂×C₃₁	semidirect
321. C₂×C₈×D₄	C₂×C₃₁	semidirect
323. #1924	C₂×C₃₁	semidirect
324. #1923	C₂×C₃₁	semidirect
325. #1917	C₂×C₃₁	semidirect
326. #1916	C₂×C₃₁	semidirect
327. #1870	C₂×C₃₁	semidirect
328. #1870	C₂×C₃₁	semidirect
329. #1870	C₂×C₃₁	semidirect
330. #1869	C₂×C₃₁	semidirect
331. #1851	C₂×C₃₁	semidirect
332. #1850	C₂×C₃₁	semidirect
333. #1798	C₂×C₃₁	semidirect
334. #1729	C₂×C₃₁	semidirect
450. C₂²×C₈	D₄×C₃₁	semidirect
510. C₃₁	#22173	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×C₈×D₄×C₃₁	2
C₃₁×#2392	2
C₃₁×#1924	2
C₃₁×#1923	2
C₃₁×#1917	2
C₃₁×#1916	2
C₃₁×#1870	2
C₃₁×#1869	2
C₃₁×#1851	2
C₃₁×#1850	2
C₃₁×#1798	2
C₃₁×#1729	2
#22173	31

Subgroups — C31×#22173 #21478932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22173 #21478932