Subgroups — C₃₁×#33039 #21489798

Order 7936.

884 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2641	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2276	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1982	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1926	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1925	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1880	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1880	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#479	—	2	4	no	—
18	C₃₁×#460	—	2	4	no	—
19	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#102	C₂²	1	2	yes	—
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	2	yes	—
28	C₃₁×#394	—	2	1	no	—
29	C₃₁×#394	—	2	2	no	—
30	C₃₁×#394	—	2	1	no	—
31	C₃₁×#390	C₂²	1	2	yes	—
32	C₃₁×#390	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
34	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#376	—	2	1	no	—
38	C₃₁×#376	C₂²	1	1	yes	characteristic
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#340	C₂²	1	2	yes	—
41	C₃₁×#336	C₂²	1	2	yes	—
42	C₃₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₁	—	2	1	no	—
45	C₂²×D₄×C₃₁	—	2	1	no	—
46	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
47	C₂×SD₁₆×C₃₁	—	2	4	no	—
48	C₂×SD₁₆×C₃₁	—	2	4	no	—
49	C₂×SD₁₆×C₃₁	—	2	4	no	—
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
53	C₃₁×#127	—	2	2	no	—
54	C₃₁×#127	—	2	2	no	—
55	C₃₁×#125	—	2	2	no	—
56	C₃₁×#125	—	2	2	no	—
57	C₄×Q₈×C₃₁	—	2	4	no	—
58	C₄×Q₈×C₃₁	—	2	4	no	—
59	C₄×Q₈×C₃₁	—	2	2	no	—
60	C₄×Q₈×C₃₁	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	—	2	2	no	—
74	C₂×C₄²×C₃₁	—	2	1	no	—
75	C₂×C₄²×C₃₁	—	2	2	no	—
76	C₂×C₄²×C₃₁	—	2	1	no	—
77	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
78	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
79	C₃₁×#107	—	2	2	no	—
80	C₃₁×#106	—	2	2	no	—
81	C₃₁×C₄⋊C₈	—	2	2	no	—
82	C₃₁×C₄⋊C₈	—	2	2	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#102	—	2	4	no	—
86	C₃₁×#102	—	2	4	no	—
87	C₃₁×#102	—	2	4	no	—
88	C₃₁×#95	—	2	2	no	—
89	C₃₁×#95	—	2	1	no	—
90	C₃₁×#95	D₄	1	1	yes	characteristic
91	C₃₁×#95	D₄	1	2	yes	—
92	C₃₁×#95	D₄	1	1	yes	characteristic
93	C₂⁴×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	2	1	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₃₁	#41	1	4	yes	—
98	C₂×D₄×C₃₁	—	2	2	no	—
99	C₂×D₄×C₃₁	—	2	2	no	—
100	C₂×D₄×C₃₁	—	2	2	no	—
101	C₂×D₄×C₃₁	—	2	2	no	—
102	C₂×D₄×C₃₁	—	2	2	no	—
103	C₂×D₄×C₃₁	—	2	2	no	—
104	C₂×D₄×C₃₁	—	4	2	no	—
105	C₂×D₄×C₃₁	—	4	2	no	—
106	C₂×D₄×C₃₁	—	8	1	no	—
107	C₂×D₄×C₃₁	—	8	2	no	—
108	C₂×D₄×C₃₁	—	8	1	no	—
109	C₂²×C₄×C₃₁	—	2	1	no	—
110	C₂²×C₄×C₃₁	—	2	1	no	—
111	C₂²×C₄×C₃₁	—	2	2	no	—
112	C₂²×C₄×C₃₁	—	2	1	no	—
113	C₂²×C₄×C₃₁	—	2	1	no	—
114	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₃₁	—	4	8	no	—
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	1	no	—
123	C₂×C₈×C₃₁	—	2	2	no	—
124	C₂×C₈×C₃₁	—	2	2	no	—
125	C₂×C₈×C₃₁	—	2	2	no	—
126	C₂×C₈×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	8	no	—
128	C₄⋊C₄×C₃₁	—	2	4	no	—
129	C₄⋊C₄×C₃₁	—	2	1	no	—
130	C₄⋊C₄×C₃₁	—	2	2	no	—
131	C₄⋊C₄×C₃₁	—	2	1	no	—
132	C₄⋊C₄×C₃₁	—	2	1	no	—
133	C₄⋊C₄×C₃₁	—	2	1	no	—
134	C₄⋊C₄×C₃₁	—	2	1	no	—
135	C₄⋊C₄×C₃₁	—	4	2	no	—
136	C₄⋊C₄×C₃₁	—	4	2	no	—
137	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₃₁	#41	1	4	yes	—
139	C₂²⋊C₄×C₃₁	—	8	2	no	—
140	C₂²⋊C₄×C₃₁	—	8	2	no	—
141	C₂²⋊C₄×C₃₁	—	8	2	no	—
142	C₂²⋊C₄×C₃₁	—	8	2	no	—
143	C₄²×C₃₁	—	2	8	no	—
144	C₄²×C₃₁	—	2	4	no	—
145	C₄²×C₃₁	—	2	2	no	—
146	C₄²×C₃₁	—	2	2	no	—
147	C₄²×C₃₁	—	8	1	no	—
148	C₄²×C₃₁	—	8	2	no	—
149	C₄²×C₃₁	C₂×D₄	1	2	yes	—
150	C₄²×C₃₁	#41	1	2	yes	—
151	#33039	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₃₁	—	4	2	no	—
153	C₂³×C₃₁	—	4	2	no	—
154	C₂³×C₃₁	—	4	2	no	—
155	C₂³×C₃₁	—	4	2	no	—
156	C₂³×C₃₁	—	4	2	no	—
157	C₂³×C₃₁	—	4	2	no	—
158	C₂³×C₃₁	—	4	2	no	—
159	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₃₁	—	2	4	no	—
161	Q₈×C₃₁	—	2	2	no	—
162	Q₈×C₃₁	#124	1	4	yes	—
163	D₄×C₃₁	—	4	2	no	—
164	D₄×C₃₁	—	4	2	no	—
165	D₄×C₃₁	—	4	2	no	—
166	D₄×C₃₁	—	4	2	no	—
167	D₄×C₃₁	—	8	4	no	—
168	D₄×C₃₁	—	8	4	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	4	no	—
171	C₂×C₄×C₃₁	—	2	1	no	—
172	C₂×C₄×C₃₁	—	2	2	no	—
173	C₂×C₄×C₃₁	—	2	1	no	—
174	C₂×C₄×C₃₁	—	2	2	no	—
175	C₂×C₄×C₃₁	—	2	2	no	—
176	C₂×C₄×C₃₁	—	2	2	no	—
177	C₂×C₄×C₃₁	—	2	4	no	—
178	C₂×C₄×C₃₁	—	2	2	no	—
179	C₂×C₄×C₃₁	—	2	2	no	—
180	C₂×C₄×C₃₁	—	2	2	no	—
181	C₂×C₄×C₃₁	—	2	2	no	—
182	C₂×C₄×C₃₁	—	4	2	no	—
183	C₂×C₄×C₃₁	—	4	1	no	—
184	C₂×C₄×C₃₁	—	4	2	no	—
185	C₂×C₄×C₃₁	—	4	1	no	—
186	C₂×C₄×C₃₁	—	4	1	no	—
187	C₂×C₄×C₃₁	—	4	1	no	—
188	C₂×C₄×C₃₁	—	4	1	no	—
189	C₂×C₄×C₃₁	—	4	2	no	—
190	C₂×C₄×C₃₁	—	4	1	no	—
191	C₂×C₄×C₃₁	#121	1	2	yes	—
192	C₂×C₄×C₃₁	#121	1	2	yes	—
193	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
195	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
197	C₈×C₃₁	—	4	2	no	—
198	C₈×C₃₁	—	4	1	no	—
199	C₈×C₃₁	—	4	1	no	—
200	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
201	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
202	#2641	C₂×C₃₁	1	1	yes	characteristic
203	#2276	C₂×C₃₁	1	1	yes	characteristic, complemented
204	#1989	C₂×C₃₁	1	1	yes	characteristic, complemented
205	#1982	C₂×C₃₁	1	1	yes	characteristic
206	#1926	C₂×C₃₁	1	2	yes	complemented
207	#1925	C₂×C₃₁	1	2	yes	complemented
208	#1880	C₂×C₃₁	1	2	yes	complemented
209	#1880	C₂×C₃₁	1	2	yes	complemented
210	#1832	C₂×C₃₁	1	1	yes	characteristic, complemented
211	C₂²×C₃₁	—	8	2	no	—
212	C₂²×C₃₁	—	8	2	no	—
213	C₂²×C₃₁	—	8	2	no	—
214	C₂²×C₃₁	—	8	2	no	—
215	C₂²×C₃₁	—	8	2	no	—
216	C₂²×C₃₁	—	8	2	no	—
217	C₂²×C₃₁	—	8	2	no	—
218	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
219	C₂²×C₃₁	#525	1	2	yes	—
220	C₂²×C₃₁	#576	1	1	yes	characteristic
221	C₂²×C₃₁	#577	1	2	yes	—
222	C₂²×C₃₁	#577	1	1	yes	characteristic
223	C₄×C₃₁	—	2	4	no	—
224	C₄×C₃₁	—	2	2	no	—
225	C₄×C₃₁	—	2	2	no	—
226	C₄×C₃₁	—	4	2	no	—
227	C₄×C₃₁	—	4	4	no	—
228	C₄×C₃₁	—	4	2	no	—
229	C₄×C₃₁	—	4	2	no	—
230	C₄×C₃₁	—	8	1	no	—
231	C₄×C₃₁	—	8	1	no	—
232	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
233	C₄×C₃₁	#529	1	2	yes	—
234	C₄×C₃₁	#532	1	1	yes	characteristic
235	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
236	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
239	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
240	#479	—	2	4	no	—
241	#460	—	2	4	no	—
242	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
243	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
246	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
247	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
248	C₂×#102	C₂²×C₃₁	1	2	yes	—
249	C₂×#102	C₂²×C₃₁	1	2	yes	—
250	C₂×#102	C₂²×C₃₁	1	2	yes	—
251	#394	—	2	1	no	—
252	#394	—	2	2	no	—
253	#394	—	2	1	no	—
254	#390	C₂²×C₃₁	1	2	yes	—
255	#390	C₂²×C₃₁	1	2	yes	—
256	C₄×C₄⋊C₄	—	2	2	no	—
257	C₄×C₄⋊C₄	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
259	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
260	#376	—	2	1	no	—
261	#376	C₂²×C₃₁	1	1	yes	characteristic
262	#340	C₂²×C₃₁	1	2	yes	—
263	#340	C₂²×C₃₁	1	2	yes	—
264	#336	C₂²×C₃₁	1	2	yes	—
265	#336	C₂²×C₃₁	1	2	yes	—
266	C₂×C₃₁	—	16	2	no	—
267	C₂×C₃₁	#2850	1	1	yes	characteristic
268	C₂×C₃₁	#3043	1	1	yes	characteristic
269	C₂×C₃₁	#3045	1	1	yes	characteristic
270	C₂×C₃₁	#3119	1	2	yes	—
271	C₂×C₃₁	#3126	1	2	yes	—
272	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
276	C₂×SD₁₆	—	2	4	no	—
277	C₂×SD₁₆	—	2	4	no	—
278	C₂×SD₁₆	—	2	4	no	—
279	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
280	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
282	#127	—	2	2	no	—
283	#127	—	2	2	no	—
284	#125	—	2	2	no	—
285	#125	—	2	2	no	—
286	C₄×Q₈	—	2	4	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	D₄×C₃₁	1	4	yes	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
307	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
308	#107	—	2	2	no	—
309	#106	—	2	2	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	2	2	no	—
314	#102	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	D₄×C₃₁	1	1	yes	characteristic
320	#95	D₄×C₃₁	1	2	yes	—
321	#95	D₄×C₃₁	1	1	yes	characteristic
322	C₃₁	#33039	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	—	2	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
327	C₂×Q₈	#41×C₃₁	1	4	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂×D₄	—	8	2	no	—
338	C₂×D₄	—	8	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
349	SD₁₆	—	4	8	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
368	C₄⋊C₄	#41×C₃₁	1	4	yes	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₂²⋊C₄	—	8	2	no	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	8	1	no	—
378	C₄²	—	8	2	no	—
379	C₄²	C₂×D₄×C₃₁	1	2	yes	—
380	C₄²	#41×C₃₁	1	2	yes	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	2	2	no	—
391	Q₈	C₃₁×#124	1	4	yes	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	C₃₁×#121	1	2	yes	—
421	C₂×C₄	C₃₁×#121	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
424	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
426	C₈	—	4	2	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
437	C₂²	C₃₁×#525	1	2	yes	—
438	C₂²	C₃₁×#576	1	1	yes	characteristic
439	C₂²	C₃₁×#577	1	2	yes	—
440	C₂²	C₃₁×#577	1	1	yes	characteristic
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
451	C₄	C₃₁×#529	1	2	yes	—
452	C₄	C₃₁×#532	1	1	yes	characteristic
453	C₂	—	16	2	no	—
454	C₂	C₃₁×#2850	1	1	yes	characteristic
455	C₂	C₃₁×#3043	1	1	yes	characteristic
456	C₂	C₃₁×#3045	1	1	yes	characteristic
457	C₂	C₃₁×#3119	1	2	yes	—
458	C₂	C₃₁×#3126	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₃₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#479	C₂	semidirect
4. C₃₁×#2276	C₂	semidirect
5. C₃₁×#1989	C₂	semidirect
7. C₃₁×#1926	C₂	semidirect
8. C₃₁×#1925	C₂	semidirect
9. C₃₁×#1880	C₂	semidirect
10. C₃₁×#1880	C₂	semidirect
11. C₃₁×#1832	C₂	semidirect
151. #33039	C₃₁	direct (N × H)
200. C₂×#479	C₂×C₃₁	semidirect
203. #2276	C₂×C₃₁	semidirect
204. #1989	C₂×C₃₁	semidirect
206. #1926	C₂×C₃₁	semidirect
207. #1925	C₂×C₃₁	semidirect
208. #1880	C₂×C₃₁	semidirect
209. #1880	C₂×C₃₁	semidirect
210. #1832	C₂×C₃₁	semidirect
322. C₃₁	#33039	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×#479	2
C₂×C₃₁×#460	2
C₃₁×#2641	2
C₃₁×#2276	2
C₃₁×#1989	2
C₃₁×#1982	2
C₃₁×#1926	2
C₃₁×#1925	2
C₃₁×#1880	2
C₃₁×#1832	2
#33039	31

Subgroups — C31×#33039 #21489798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33039 #21489798