Subgroups — C₃₁×#9229 #21465988

Order 7936.

646 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#1957	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₃₁	—	2	1	no	—
9	C₂²×M₁₆×C₃₁	—	2	1	no	—
10	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#459	—	2	2	no	—
13	C₃₁×#459	C₄	1	4	yes	complemented
14	C₃₁×#436	—	2	2	no	—
15	C₃₁×#436	—	2	2	no	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#102	—	2	1	no	—
20	C₂×C₃₁×#102	—	2	1	no	—
21	C₂×C₃₁×#102	—	2	1	no	—
22	C₂×C₃₁×#102	—	2	1	no	—
23	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
24	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#384	C₂²	1	1	yes	characteristic
26	C₃₁×#340	—	2	1	no	—
27	C₃₁×#331	—	2	2	no	—
28	C₂²×D₄×C₃₁	—	2	1	no	—
29	C₂²×D₄×C₃₁	—	2	1	no	—
30	C₂²×D₄×C₃₁	—	2	1	no	—
31	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₃₁	—	2	1	no	—
33	C₂×D₈×C₃₁	—	2	4	no	—
34	C₂×D₈×C₃₁	—	4	2	no	—
35	C₂×D₈×C₃₁	—	4	2	no	—
36	C₂×M₁₆×C₃₁	—	2	4	no	—
37	C₂×M₁₆×C₃₁	—	4	2	no	—
38	C₂×M₁₆×C₃₁	—	4	2	no	—
39	C₂²×C₈×C₃₁	—	2	1	no	—
40	C₂²×C₈×C₃₁	—	2	1	no	—
41	C₂²×C₈×C₃₁	—	2	1	no	—
42	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
44	C₃₁×#127	—	2	1	no	—
45	C₃₁×#127	—	2	1	no	—
46	C₃₁×#127	—	2	1	no	—
47	C₃₁×#127	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₃₁	—	2	1	no	—
49	C₄×D₄×C₃₁	—	2	1	no	—
50	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₃₁	D₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
58	C₃₁×C₄⋊C₈	—	2	1	no	—
59	C₃₁×C₄⋊C₈	—	2	1	no	—
60	C₃₁×C₄⋊C₈	—	2	1	no	—
61	C₃₁×C₄⋊C₈	—	2	1	no	—
62	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
64	C₃₁×#102	—	2	4	no	—
65	C₃₁×#102	—	4	2	no	—
66	C₃₁×#102	—	4	2	no	—
67	C₃₁×#102	—	4	2	no	—
68	C₃₁×C₂²⋊C₈	—	2	4	no	—
69	C₄×C₈×C₃₁	—	2	1	no	—
70	C₄×C₈×C₃₁	—	2	1	no	—
71	C₂⁴×C₃₁	—	2	1	no	—
72	C₂⁴×C₃₁	—	4	1	no	—
73	C₂×D₄×C₃₁	—	2	2	no	—
74	C₂×D₄×C₃₁	—	2	2	no	—
75	C₂×D₄×C₃₁	—	2	2	no	—
76	C₂×D₄×C₃₁	—	2	1	no	—
77	C₂×D₄×C₃₁	—	2	1	no	—
78	C₂×D₄×C₃₁	—	2	1	no	—
79	C₂×D₄×C₃₁	—	2	1	no	—
80	C₂×D₄×C₃₁	—	2	1	no	—
81	C₂×D₄×C₃₁	—	4	1	no	—
82	C₂×D₄×C₃₁	—	4	1	no	—
83	C₂×D₄×C₃₁	—	4	1	no	—
84	C₂×D₄×C₃₁	—	4	1	no	—
85	C₂×D₄×C₃₁	—	4	1	no	—
86	C₂×D₄×C₃₁	—	4	1	no	—
87	C₂×D₄×C₃₁	—	4	1	no	—
88	C₂×D₄×C₃₁	—	4	1	no	—
89	C₂×D₄×C₃₁	—	4	1	no	—
90	C₂×D₄×C₃₁	—	4	1	no	—
91	C₂×D₄×C₃₁	—	4	1	no	—
92	C₂×D₄×C₃₁	—	8	1	no	—
93	C₂×D₄×C₃₁	—	8	1	no	—
94	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₃₁	—	2	1	no	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	—	2	2	no	—
98	C₂²×C₄×C₃₁	—	4	1	no	—
99	C₂²×C₄×C₃₁	—	4	1	no	—
100	C₂²×C₄×C₃₁	—	4	1	no	—
101	C₂²×C₄×C₃₁	—	4	1	no	—
102	C₂²×C₄×C₃₁	—	4	1	no	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
106	D₈×C₃₁	—	4	8	no	—
107	M₁₆×C₃₁	—	4	8	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	2	1	no	—
115	C₂×C₈×C₃₁	—	4	1	no	—
116	C₂×C₈×C₃₁	—	4	1	no	—
117	C₂×C₈×C₃₁	—	4	1	no	—
118	C₂×C₈×C₃₁	—	4	1	no	—
119	C₂×C₈×C₃₁	—	4	1	no	—
120	C₂×C₈×C₃₁	—	4	1	no	—
121	C₂×C₈×C₃₁	—	4	1	no	—
122	C₂×C₈×C₃₁	D₈	1	2	yes	complemented
123	C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₄⋊C₄×C₃₁	—	4	1	no	—
125	C₄⋊C₄×C₃₁	—	4	1	no	—
126	C₄⋊C₄×C₃₁	—	4	1	no	—
127	C₄⋊C₄×C₃₁	—	4	1	no	—
128	C₄⋊C₄×C₃₁	—	8	1	no	—
129	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
130	C₂²⋊C₄×C₃₁	—	2	2	no	—
131	C₂²⋊C₄×C₃₁	—	2	2	no	—
132	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₃₁	#41	1	1	yes	characteristic
136	#9229	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	2	no	—
138	C₂³×C₃₁	—	4	1	no	—
139	C₂³×C₃₁	—	4	1	no	—
140	C₂³×C₃₁	—	4	1	no	—
141	C₂³×C₃₁	—	4	1	no	—
142	C₂³×C₃₁	—	4	1	no	—
143	C₂³×C₃₁	—	4	1	no	—
144	C₂³×C₃₁	—	4	2	no	—
145	C₂³×C₃₁	—	8	1	no	—
146	C₂³×C₃₁	—	8	1	no	—
147	C₂³×C₃₁	—	8	1	no	—
148	C₂³×C₃₁	—	8	1	no	—
149	C₂³×C₃₁	—	8	1	no	—
150	C₂³×C₃₁	—	8	1	no	—
151	C₂³×C₃₁	#121	1	1	yes	characteristic
152	D₄×C₃₁	—	2	2	no	—
153	D₄×C₃₁	—	2	2	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	4	2	no	—
156	D₄×C₃₁	—	4	2	no	—
157	D₄×C₃₁	—	4	2	no	—
158	D₄×C₃₁	—	4	1	no	—
159	D₄×C₃₁	—	4	1	no	—
160	D₄×C₃₁	—	8	2	no	—
161	D₄×C₃₁	—	8	2	no	—
162	D₄×C₃₁	—	8	1	no	—
163	D₄×C₃₁	—	8	1	no	—
164	D₄×C₃₁	—	8	1	no	—
165	D₄×C₃₁	—	8	1	no	—
166	C₂×C₄×C₃₁	—	2	1	no	—
167	C₂×C₄×C₃₁	—	2	1	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	4	1	no	—
170	C₂×C₄×C₃₁	—	4	1	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	—	4	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	8	1	no	—
176	C₂×C₄×C₃₁	—	8	1	no	—
177	C₂×C₄×C₃₁	—	8	1	no	—
178	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
182	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
183	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
184	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₃₁	#135	1	1	yes	characteristic
186	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×C₄×C₃₁	#137	1	1	yes	characteristic
192	C₈×C₃₁	—	2	2	no	—
193	C₈×C₃₁	—	4	2	no	—
194	C₈×C₃₁	—	4	2	no	—
195	C₈×C₃₁	—	4	1	no	—
196	C₈×C₃₁	—	8	1	no	—
197	C₂×#459	C₂×C₃₁	1	1	yes	characteristic
198	C₂×#436	C₂×C₃₁	1	1	yes	characteristic, complemented
199	#1957	C₂×C₃₁	1	1	yes	characteristic, complemented
200	#1802	C₂×C₃₁	1	1	yes	characteristic, complemented
201	C₂×#331	C₂×C₃₁	1	1	yes	characteristic, complemented
202	#1296	C₂×C₃₁	1	1	yes	characteristic, complemented
203	#1277	C₂×C₃₁	1	1	yes	characteristic, complemented
204	C₂²×C₃₁	—	4	2	no	—
205	C₂²×C₃₁	—	4	2	no	—
206	C₂²×C₃₁	—	4	2	no	—
207	C₂²×C₃₁	—	8	1	no	—
208	C₂²×C₃₁	—	8	1	no	—
209	C₂²×C₃₁	—	8	1	no	—
210	C₂²×C₃₁	—	8	1	no	—
211	C₂²×C₃₁	—	8	2	no	—
212	C₂²×C₃₁	—	8	2	no	—
213	C₂²×C₃₁	—	8	2	no	—
214	C₂²×C₃₁	—	16	1	no	—
215	C₂²×C₃₁	—	16	1	no	—
216	C₂²×C₃₁	—	16	1	no	—
217	C₂²×C₃₁	—	16	1	no	—
218	C₂²×C₃₁	#386	1	1	yes	characteristic
219	C₂²×C₃₁	#459	1	1	yes	characteristic
220	C₂²×C₃₁	#463	1	1	yes	characteristic
221	C₂²×C₃₁	#468	1	1	yes	characteristic
222	C₂²×C₃₁	#469	1	1	yes	characteristic
223	C₂²×C₃₁	#471	1	1	yes	characteristic
224	C₂²×C₃₁	#472	1	1	yes	characteristic
225	C₄×C₃₁	—	2	1	no	—
226	C₄×C₃₁	—	2	1	no	—
227	C₄×C₃₁	—	4	2	no	—
228	C₄×C₃₁	—	16	1	no	—
229	C₄×C₃₁	#417	1	1	yes	characteristic
230	C₄×C₃₁	#418	1	1	yes	characteristic
231	C₄×C₃₁	C₄×D₈	1	1	yes	characteristic
232	C₄×C₃₁	#442	1	1	yes	characteristic
233	C₄×C₃₁	#447	1	1	yes	characteristic
234	C₄×C₃₁	#449	1	1	yes	characteristic
235	C₄×C₃₁	#468	1	1	yes	characteristic
236	C₄×C₃₁	#469	1	1	yes	characteristic
237	C₂²×D₈	—	2	1	no	—
238	C₂²×M₁₆	—	2	1	no	—
239	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
241	#459	—	2	2	no	—
242	#459	C₄×C₃₁	1	4	yes	complemented
243	#436	—	2	2	no	—
244	#436	—	2	2	no	—
245	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
248	C₂×#102	—	2	1	no	—
249	C₂×#102	—	2	1	no	—
250	C₂×#102	—	2	1	no	—
251	C₂×#102	—	2	1	no	—
252	C₂×C₂²⋊C₈	—	2	1	no	—
253	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
254	#384	C₂²×C₃₁	1	1	yes	characteristic
255	#340	—	2	1	no	—
256	#331	—	2	2	no	—
257	C₂×C₃₁	—	8	2	no	—
258	C₂×C₃₁	—	16	2	no	—
259	C₂×C₃₁	#1685	1	1	yes	characteristic
260	C₂×C₃₁	#1687	1	1	yes	characteristic
261	C₂×C₃₁	#1697	1	1	yes	characteristic
262	C₂×C₃₁	#1701	1	1	yes	characteristic
263	C₂×C₃₁	#1879	1	1	yes	characteristic
264	C₂×C₃₁	#1895	1	1	yes	characteristic
265	C₂×C₃₁	#1907	1	1	yes	characteristic
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂×D₈	—	2	4	no	—
272	C₂×D₈	—	4	2	no	—
273	C₂×D₈	—	4	2	no	—
274	C₂×M₁₆	—	2	4	no	—
275	C₂×M₁₆	—	4	2	no	—
276	C₂×M₁₆	—	4	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	C₂×C₄×C₃₁	1	2	yes	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
289	C₄×D₄	D₄×C₃₁	1	2	yes	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
301	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
302	#102	—	2	4	no	—
303	#102	—	4	2	no	—
304	#102	—	4	2	no	—
305	#102	—	4	2	no	—
306	C₂²⋊C₈	—	2	4	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	2	1	no	—
309	C₃₁	#9229	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	—	2	1	no	—
311	C₂⁴	—	4	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	8	1	no	—
332	C₂×D₄	—	8	1	no	—
333	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
344	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
345	D₈	—	4	8	no	—
346	M₁₆	—	4	8	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	D₈×C₃₁	1	2	yes	complemented
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	8	1	no	—
368	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
374	C₄²	#41×C₃₁	1	1	yes	characteristic
375	C₂³	—	2	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	8	1	no	—
384	C₂³	—	8	1	no	—
385	C₂³	—	8	1	no	—
386	C₂³	—	8	1	no	—
387	C₂³	—	8	1	no	—
388	C₂³	—	8	1	no	—
389	C₂³	C₃₁×#121	1	1	yes	characteristic
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	8	1	no	—
403	D₄	—	8	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	8	1	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
417	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
418	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
419	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
420	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
421	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
422	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
423	C₂×C₄	C₃₁×#135	1	1	yes	characteristic
424	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
428	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
429	C₂×C₄	C₃₁×#137	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	8	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	1	no	—
446	C₂²	—	16	1	no	—
447	C₂²	—	16	1	no	—
448	C₂²	—	16	1	no	—
449	C₂²	C₃₁×#386	1	1	yes	characteristic
450	C₂²	C₃₁×#459	1	1	yes	characteristic
451	C₂²	C₃₁×#463	1	1	yes	characteristic
452	C₂²	C₃₁×#468	1	1	yes	characteristic
453	C₂²	C₃₁×#469	1	1	yes	characteristic
454	C₂²	C₃₁×#471	1	1	yes	characteristic
455	C₂²	C₃₁×#472	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	16	1	no	—
460	C₄	C₃₁×#417	1	1	yes	characteristic
461	C₄	C₃₁×#418	1	1	yes	characteristic
462	C₄	C₄×D₈×C₃₁	1	1	yes	characteristic
463	C₄	C₃₁×#442	1	1	yes	characteristic
464	C₄	C₃₁×#447	1	1	yes	characteristic
465	C₄	C₃₁×#449	1	1	yes	characteristic
466	C₄	C₃₁×#468	1	1	yes	characteristic
467	C₄	C₃₁×#469	1	1	yes	characteristic
468	C₂	—	8	2	no	—
469	C₂	—	16	2	no	—
470	C₂	C₃₁×#1685	1	1	yes	characteristic
471	C₂	C₃₁×#1687	1	1	yes	characteristic
472	C₂	C₃₁×#1697	1	1	yes	characteristic
473	C₂	C₃₁×#1701	1	1	yes	characteristic
474	C₂	C₃₁×#1879	1	1	yes	characteristic
475	C₂	C₃₁×#1895	1	1	yes	characteristic
476	C₂	C₃₁×#1907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator	C₄²	C₂²×C₄×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂×C₃₁×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#436	C₂	semidirect
3. C₃₁×#1957	C₂	semidirect
4. C₃₁×#1802	C₂	semidirect
5. C₂×C₃₁×#331	C₂	semidirect
6. C₃₁×#1296	C₂	semidirect
7. C₃₁×#1277	C₂	semidirect
13. C₃₁×#459	C₄	semidirect
122. C₂×C₈×C₃₁	D₈	semidirect
136. #9229	C₃₁	direct (N × H)
198. C₂×#436	C₂×C₃₁	semidirect
199. #1957	C₂×C₃₁	semidirect
200. #1802	C₂×C₃₁	semidirect
201. C₂×#331	C₂×C₃₁	semidirect
202. #1296	C₂×C₃₁	semidirect
203. #1277	C₂×C₃₁	semidirect
242. #459	C₄×C₃₁	semidirect
309. C₃₁	#9229	direct (N × H)
361. C₂×C₈	D₈×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#459	2
C₂×C₃₁×#436	2
C₃₁×#1957	2
C₃₁×#1802	2
C₂×C₃₁×#331	2
C₃₁×#1296	2
C₃₁×#1277	2
#9229	31

Subgroups — C31×#9229 #21465988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#9229 #21465988