Subgroups — C₃₁×#24594 #21481353

Order 7936.

862 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#482	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2501	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2084	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2065	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1947	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1925	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1895	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1824	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#123	—	2	2	no	—
14	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#482	—	2	4	no	—
18	C₃₁×#428	—	2	4	no	—
19	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#107	C₂²	1	2	yes	—
21	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#106	C₂²	1	2	yes	—
23	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₃₁×#399	—	2	1	no	—
29	C₃₁×#399	—	2	1	no	—
30	C₃₁×#390	C₂²	1	2	yes	—
31	C₃₁×#389	C₂²	1	2	yes	—
32	C₃₁×#388	—	2	2	no	—
33	C₃₁×#384	C₂²	1	2	yes	—
34	C₃₁×#382	—	2	1	no	—
35	C₃₁×#380	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#376	—	2	1	no	—
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#340	C₂²	1	2	yes	—
41	C₃₁×#340	C₂²	1	2	yes	—
42	C₃₁×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₃₁	—	2	1	no	—
44	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₁	—	2	1	no	—
46	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₃₁	—	2	2	no	—
48	C₂×M₁₆×C₃₁	—	2	4	no	—
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
52	C₃₁×#123	—	4	8	no	—
53	C₃₁×#121	—	2	2	no	—
54	C₃₁×#121	—	2	2	no	—
55	C₃₁×#117	—	2	2	no	—
56	C₃₁×#117	D₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
74	C₂×C₄²×C₃₁	—	2	1	no	—
75	C₂×C₄²×C₃₁	—	2	2	no	—
76	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
77	C₃₁×#107	—	2	4	no	—
78	C₃₁×#107	—	2	2	no	—
79	C₃₁×#106	—	2	4	no	—
80	C₃₁×#106	—	2	2	no	—
81	C₃₁×C₄⋊C₈	—	2	4	no	—
82	C₃₁×#102	—	2	4	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×C₂²⋊C₈	—	2	2	no	—
86	C₃₁×#95	—	2	1	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₃₁×#95	—	2	2	no	—
89	C₃₁×#95	D₄	1	1	yes	characteristic
90	C₃₁×#95	D₄	1	1	yes	characteristic
91	C₂⁴×C₃₁	—	2	1	no	—
92	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₃₁	—	2	1	no	—
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	2	1	no	—
96	C₂×D₄×C₃₁	—	2	2	no	—
97	C₂×D₄×C₃₁	—	4	4	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂²×C₄×C₃₁	—	2	2	no	—
100	C₂²×C₄×C₃₁	—	2	2	no	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	2	1	no	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	1	no	—
106	C₂²×C₄×C₃₁	—	4	4	no	—
107	C₂²×C₄×C₃₁	—	4	2	no	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₃₁	#41	1	2	yes	—
113	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₃₁	—	2	8	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	1	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₂×C₈×C₃₁	#41	1	4	yes	—
122	C₄⋊C₄×C₃₁	—	2	1	no	—
123	C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	1	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	1	no	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	4	4	no	—
131	C₄⋊C₄×C₃₁	—	4	2	no	—
132	C₄⋊C₄×C₃₁	—	4	4	no	—
133	C₄⋊C₄×C₃₁	—	8	2	no	—
134	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
136	C₂²⋊C₄×C₃₁	—	2	4	no	—
137	C₂²⋊C₄×C₃₁	—	2	4	no	—
138	C₂²⋊C₄×C₃₁	—	4	4	no	—
139	C₂²⋊C₄×C₃₁	—	4	2	no	—
140	C₂²⋊C₄×C₃₁	—	4	4	no	—
141	C₂²⋊C₄×C₃₁	—	8	1	no	—
142	C₄²×C₃₁	—	2	4	no	—
143	C₄²×C₃₁	—	2	2	no	—
144	C₄²×C₃₁	—	2	2	no	—
145	C₄²×C₃₁	—	4	4	no	—
146	#24594	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₃₁	—	2	2	no	—
148	C₂³×C₃₁	—	2	2	no	—
149	C₂³×C₃₁	—	2	1	no	—
150	C₂³×C₃₁	—	2	1	no	—
151	C₂³×C₃₁	—	4	1	no	—
152	C₂³×C₃₁	—	4	2	no	—
153	C₂³×C₃₁	—	4	2	no	—
154	C₂³×C₃₁	—	4	1	no	—
155	C₂³×C₃₁	—	4	1	no	—
156	C₂³×C₃₁	#121	1	2	yes	—
157	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	D₄×C₃₁	—	4	1	no	—
159	D₄×C₃₁	—	4	1	no	—
160	D₄×C₃₁	—	4	2	no	—
161	D₄×C₃₁	—	8	4	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	2	2	no	—
165	C₂×C₄×C₃₁	—	2	2	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	2	no	—
171	C₂×C₄×C₃₁	—	2	2	no	—
172	C₂×C₄×C₃₁	—	2	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	1	no	—
175	C₂×C₄×C₃₁	—	4	1	no	—
176	C₂×C₄×C₃₁	—	4	1	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	2	no	—
179	C₂×C₄×C₃₁	—	4	2	no	—
180	C₂×C₄×C₃₁	—	4	2	no	—
181	C₂×C₄×C₃₁	—	4	2	no	—
182	C₂×C₄×C₃₁	—	4	2	no	—
183	C₂×C₄×C₃₁	—	4	2	no	—
184	C₂×C₄×C₃₁	—	8	4	no	—
185	C₂×C₄×C₃₁	#121	1	2	yes	—
186	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
187	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
189	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
191	C₈×C₃₁	—	2	4	no	—
192	C₈×C₃₁	—	4	1	no	—
193	C₈×C₃₁	—	4	1	no	—
194	C₂×#482	C₂×C₃₁	1	1	yes	characteristic
195	C₂×#428	C₂×C₃₁	1	1	yes	characteristic, complemented
196	#2501	C₂×C₃₁	1	1	yes	characteristic
197	#2346	C₂×C₃₁	1	1	yes	characteristic, complemented
198	#2084	C₂×C₃₁	1	2	yes	complemented
199	#2065	C₂×C₃₁	1	2	yes	complemented
200	#1947	C₂×C₃₁	1	2	yes	complemented
201	#1925	C₂×C₃₁	1	2	yes	complemented
202	#1895	C₂×C₃₁	1	1	yes	characteristic
203	#1851	C₂×C₃₁	1	1	yes	characteristic, complemented
204	#1824	C₂×C₃₁	1	1	yes	characteristic, complemented
205	C₂²×C₃₁	—	2	2	no	—
206	C₂²×C₃₁	—	2	2	no	—
207	C₂²×C₃₁	—	2	2	no	—
208	C₂²×C₃₁	—	4	2	no	—
209	C₂²×C₃₁	—	4	2	no	—
210	C₂²×C₃₁	—	8	2	no	—
211	C₂²×C₃₁	—	8	2	no	—
212	C₂²×C₃₁	—	8	1	no	—
213	C₂²×C₃₁	—	8	1	no	—
214	C₂²×C₃₁	—	8	1	no	—
215	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
216	C₂²×C₃₁	#547	1	2	yes	—
217	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
218	C₂²×C₃₁	#577	1	1	yes	characteristic
219	C₂²×C₃₁	#578	1	1	yes	characteristic
220	C₄×C₃₁	—	2	4	no	—
221	C₄×C₃₁	—	2	2	no	—
222	C₄×C₃₁	—	4	2	no	—
223	C₄×C₃₁	—	4	2	no	—
224	C₄×C₃₁	—	4	2	no	—
225	C₄×C₃₁	—	8	2	no	—
226	C₄×C₃₁	—	8	2	no	—
227	C₄×C₃₁	—	8	1	no	—
228	C₄×C₃₁	#525	1	1	yes	characteristic
229	C₄×C₃₁	#536	1	1	yes	characteristic
230	C₄×C₃₁	#552	1	2	yes	—
231	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×#123	—	2	2	no	—
233	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
236	#482	—	2	4	no	—
237	#428	—	2	4	no	—
238	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
239	C₂×#107	C₂²×C₃₁	1	2	yes	—
240	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
241	C₂×#106	C₂²×C₃₁	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
243	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×#102	C₂²×C₃₁	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
247	#399	—	2	1	no	—
248	#399	—	2	1	no	—
249	#390	C₂²×C₃₁	1	2	yes	—
250	#389	C₂²×C₃₁	1	2	yes	—
251	#388	—	2	2	no	—
252	#384	C₂²×C₃₁	1	2	yes	—
253	#382	—	2	1	no	—
254	#380	C₂²×C₃₁	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
256	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
257	#376	—	2	1	no	—
258	#340	C₂²×C₃₁	1	2	yes	—
259	#340	C₂²×C₃₁	1	2	yes	—
260	#340	C₂²×C₃₁	1	2	yes	—
261	#336	C₂²×C₃₁	1	2	yes	—
262	C₂×C₃₁	—	4	2	no	—
263	C₂×C₃₁	—	16	1	no	—
264	C₂×C₃₁	#2413	1	1	yes	characteristic
265	C₂×C₃₁	#3038	1	1	yes	characteristic
266	C₂×C₃₁	#3046	1	1	yes	characteristic
267	C₂×C₃₁	#3343	1	2	yes	—
268	C₂×C₃₁	#3354	1	2	yes	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	4	no	—
275	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
278	#123	—	4	8	no	—
279	#121	—	2	2	no	—
280	#121	—	2	2	no	—
281	#117	—	2	2	no	—
282	#117	D₄×C₃₁	1	4	yes	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
303	#107	—	2	4	no	—
304	#107	—	2	2	no	—
305	#106	—	2	4	no	—
306	#106	—	2	2	no	—
307	C₄⋊C₈	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	D₄×C₃₁	1	1	yes	characteristic
316	#95	D₄×C₃₁	1	1	yes	characteristic
317	C₃₁	#24594	1	1	yes	characteristic, direct product factor, Sylow
318	C₂⁴	—	2	1	no	—
319	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
339	C₂²×C₄	#41×C₃₁	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
341	M₁₆	—	2	8	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	#41×C₃₁	1	4	yes	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	8	2	no	—
361	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
362	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	8	1	no	—
369	C₄²	—	2	4	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	4	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	C₃₁×#121	1	2	yes	—
383	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	4	no	—
411	C₂×C₄	C₃₁×#121	1	2	yes	—
412	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
413	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
415	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
416	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
417	C₈	—	2	4	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
431	C₂²	C₃₁×#547	1	2	yes	—
432	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
433	C₂²	C₃₁×#577	1	1	yes	characteristic
434	C₂²	C₃₁×#578	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₃₁×#525	1	1	yes	characteristic
444	C₄	C₃₁×#536	1	1	yes	characteristic
445	C₄	C₃₁×#552	1	2	yes	—
446	C₂	—	4	2	no	—
447	C₂	—	16	1	no	—
448	C₂	C₃₁×#2413	1	1	yes	characteristic
449	C₂	C₃₁×#3038	1	1	yes	characteristic
450	C₂	C₃₁×#3046	1	1	yes	characteristic
451	C₂	C₃₁×#3343	1	2	yes	—
452	C₂	C₃₁×#3354	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₄×C₂²⋊C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#428	C₂	semidirect
4. C₃₁×#2346	C₂	semidirect
5. C₃₁×#2084	C₂	semidirect
6. C₃₁×#2065	C₂	semidirect
7. C₃₁×#1947	C₂	semidirect
8. C₃₁×#1925	C₂	semidirect
10. C₃₁×#1851	C₂	semidirect
11. C₃₁×#1824	C₂	semidirect
146. #24594	C₃₁	direct (N × H)
195. C₂×#428	C₂×C₃₁	semidirect
197. #2346	C₂×C₃₁	semidirect
198. #2084	C₂×C₃₁	semidirect
199. #2065	C₂×C₃₁	semidirect
200. #1947	C₂×C₃₁	semidirect
201. #1925	C₂×C₃₁	semidirect
203. #1851	C₂×C₃₁	semidirect
204. #1824	C₂×C₃₁	semidirect
317. C₃₁	#24594	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×#482	2
C₂×C₃₁×#428	2
C₃₁×#2501	2
C₃₁×#2346	2
C₃₁×#2084	2
C₃₁×#2065	2
C₃₁×#1947	2
C₃₁×#1925	2
C₃₁×#1895	2
C₃₁×#1851	2
C₃₁×#1824	2
#24594	31

Subgroups — C31×#24594 #21481353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#24594 #21481353