Subgroups — C₃₁×#33035 #21489794

Order 7936.

842 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2640	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2276	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1983	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1928	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1925	C₂	1	2	yes	maximal
9	C₃₁×#1880	C₂	1	2	yes	maximal
10	C₃₁×#1878	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#477	—	2	4	no	—
19	C₃₁×#464	—	2	4	no	—
20	C₂×C₃₁×#107	C₂²	1	2	yes	—
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	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
28	C₃₁×#397	—	2	1	no	—
29	C₃₁×#397	—	2	1	no	—
30	C₃₁×#393	—	2	2	no	—
31	C₃₁×#391	C₂²	1	2	yes	—
32	C₃₁×#390	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
34	C₄×C₄⋊C₄×C₃₁	—	2	2	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	—	2	1	no	—
44	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₃₁	—	2	2	no	—
48	C₂×Q₁₆×C₃₁	—	2	4	no	—
49	C₂×SD₁₆×C₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₃₁	—	2	4	no	—
51	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×C₄⋊Q₈	—	2	2	no	—
55	C₃₁×C₄⋊Q₈	—	2	2	no	—
56	C₃₁×#124	—	2	2	no	—
57	C₃₁×#124	—	2	2	no	—
58	C₄×Q₈×C₃₁	—	2	4	no	—
59	C₄×Q₈×C₃₁	—	2	4	no	—
60	C₄×Q₈×C₃₁	—	2	2	no	—
61	C₄×Q₈×C₃₁	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₄²×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	—	2	1	no	—
74	C₂×C₄²×C₃₁	—	2	2	no	—
75	C₂×C₄²×C₃₁	—	2	1	no	—
76	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
78	C₃₁×#107	—	2	4	no	—
79	C₃₁×C₄⋊C₈	—	2	2	no	—
80	C₃₁×C₄⋊C₈	—	2	2	no	—
81	C₃₁×#103	—	2	4	no	—
82	C₃₁×#103	—	2	2	no	—
83	C₃₁×#103	—	2	4	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	4	no	—
86	C₃₁×#95	—	2	2	no	—
87	C₃₁×#95	—	2	2	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	1	yes	characteristic
92	C₃₁×#95	D₄	1	2	yes	—
93	C₂⁴×C₃₁	—	2	1	no	—
94	C₂×Q₈×C₃₁	—	2	1	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	2	1	no	—
97	C₂×Q₈×C₃₁	—	2	2	no	—
98	C₂×Q₈×C₃₁	—	2	1	no	—
99	C₂×Q₈×C₃₁	—	2	2	no	—
100	C₂×Q₈×C₃₁	—	4	2	no	—
101	C₂×Q₈×C₃₁	—	8	1	no	—
102	C₂×Q₈×C₃₁	—	8	1	no	—
103	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₃₁	#41	1	4	yes	—
105	C₂×D₄×C₃₁	—	2	1	no	—
106	C₂×D₄×C₃₁	—	2	2	no	—
107	C₂×D₄×C₃₁	—	2	1	no	—
108	C₂×D₄×C₃₁	—	2	2	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	2	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	Q₁₆×C₃₁	—	4	4	no	—
120	SD₁₆×C₃₁	—	4	4	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	2	no	—
123	C₂×C₈×C₃₁	—	2	1	no	—
124	C₂×C₈×C₃₁	—	2	2	no	—
125	C₂×C₈×C₃₁	—	2	2	no	—
126	C₂×C₈×C₃₁	—	2	2	no	—
127	C₂×C₈×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	8	no	—
129	C₄⋊C₄×C₃₁	—	2	4	no	—
130	C₄⋊C₄×C₃₁	—	2	1	no	—
131	C₄⋊C₄×C₃₁	—	2	2	no	—
132	C₄⋊C₄×C₃₁	—	2	2	no	—
133	C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₄⋊C₄×C₃₁	—	4	2	no	—
135	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₃₁	#41	1	4	yes	—
137	C₂²⋊C₄×C₃₁	—	4	2	no	—
138	C₂²⋊C₄×C₃₁	—	4	2	no	—
139	C₂²⋊C₄×C₃₁	—	8	2	no	—
140	C₂²⋊C₄×C₃₁	—	8	2	no	—
141	C₄²×C₃₁	—	2	8	no	—
142	C₄²×C₃₁	—	2	4	no	—
143	C₄²×C₃₁	—	2	2	no	—
144	C₄²×C₃₁	—	2	2	no	—
145	C₄²×C₃₁	—	8	1	no	—
146	C₄²×C₃₁	—	8	2	no	—
147	C₄²×C₃₁	C₂×D₄	1	2	yes	—
148	C₄²×C₃₁	#41	1	2	yes	—
149	#33035	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₃₁	—	4	1	no	—
151	C₂³×C₃₁	—	4	2	no	—
152	C₂³×C₃₁	—	4	1	no	—
153	C₂³×C₃₁	—	4	1	no	—
154	C₂³×C₃₁	—	4	2	no	—
155	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₃₁	—	2	4	no	—
157	Q₈×C₃₁	—	2	2	no	—
158	Q₈×C₃₁	—	4	1	no	—
159	Q₈×C₃₁	—	4	2	no	—
160	Q₈×C₃₁	—	4	1	no	—
161	Q₈×C₃₁	—	8	4	no	—
162	Q₈×C₃₁	#124	1	4	yes	—
163	D₄×C₃₁	—	4	1	no	—
164	D₄×C₃₁	—	4	2	no	—
165	D₄×C₃₁	—	4	1	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	1	no	—
169	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
174	C₂×C₄×C₃₁	—	2	4	no	—
175	C₂×C₄×C₃₁	—	2	2	no	—
176	C₂×C₄×C₃₁	—	2	2	no	—
177	C₂×C₄×C₃₁	—	2	2	no	—
178	C₂×C₄×C₃₁	—	2	2	no	—
179	C₂×C₄×C₃₁	—	4	2	no	—
180	C₂×C₄×C₃₁	—	4	1	no	—
181	C₂×C₄×C₃₁	—	4	1	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	2	no	—
186	C₂×C₄×C₃₁	—	4	2	no	—
187	C₂×C₄×C₃₁	—	4	2	no	—
188	C₂×C₄×C₃₁	#121	1	2	yes	—
189	C₂×C₄×C₃₁	#121	1	2	yes	—
190	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
192	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
194	C₈×C₃₁	—	4	1	no	—
195	C₈×C₃₁	—	4	1	no	—
196	C₈×C₃₁	—	4	2	no	—
197	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
198	C₂×#464	C₂×C₃₁	1	1	yes	characteristic
199	#2640	C₂×C₃₁	1	1	yes	characteristic
200	#2276	C₂×C₃₁	1	1	yes	characteristic, complemented
201	#1988	C₂×C₃₁	1	1	yes	characteristic, complemented
202	#1983	C₂×C₃₁	1	1	yes	characteristic
203	#1928	C₂×C₃₁	1	2	yes	complemented
204	#1925	C₂×C₃₁	1	2	yes	—
205	#1880	C₂×C₃₁	1	2	yes	—
206	#1878	C₂×C₃₁	1	2	yes	complemented
207	#1832	C₂×C₃₁	1	1	yes	characteristic, complemented
208	C₂²×C₃₁	—	8	1	no	—
209	C₂²×C₃₁	—	8	2	no	—
210	C₂²×C₃₁	—	8	2	no	—
211	C₂²×C₃₁	—	8	1	no	—
212	C₂²×C₃₁	—	8	1	no	—
213	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
214	C₂²×C₃₁	#525	1	2	yes	—
215	C₂²×C₃₁	#576	1	1	yes	characteristic
216	C₂²×C₃₁	#577	1	1	yes	characteristic
217	C₂²×C₃₁	#578	1	2	yes	—
218	C₄×C₃₁	—	2	4	no	—
219	C₄×C₃₁	—	2	2	no	—
220	C₄×C₃₁	—	2	2	no	—
221	C₄×C₃₁	—	4	2	no	—
222	C₄×C₃₁	—	4	2	no	—
223	C₄×C₃₁	—	4	4	no	—
224	C₄×C₃₁	—	4	2	no	—
225	C₄×C₃₁	—	8	1	no	—
226	C₄×C₃₁	—	8	2	no	—
227	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
228	C₄×C₃₁	#529	1	2	yes	—
229	C₄×C₃₁	#532	1	1	yes	characteristic
230	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
231	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
233	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
235	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
236	#477	—	2	4	no	—
237	#464	—	2	4	no	—
238	C₂×#107	C₂²×C₃₁	1	2	yes	—
239	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
241	C₂×#103	C₂²×C₃₁	1	2	yes	—
242	C₂×#103	C₂²×C₃₁	1	2	yes	—
243	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×#102	C₂²×C₃₁	1	2	yes	—
245	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
246	#397	—	2	1	no	—
247	#397	—	2	1	no	—
248	#393	—	2	2	no	—
249	#391	C₂²×C₃₁	1	2	yes	—
250	#390	C₂²×C₃₁	1	2	yes	—
251	C₄×C₄⋊C₄	—	2	2	no	—
252	C₄×C₄⋊C₄	—	2	1	no	—
253	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
254	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
255	#376	—	2	1	no	—
256	#376	C₂²×C₃₁	1	1	yes	characteristic
257	#340	C₂²×C₃₁	1	2	yes	—
258	#340	C₂²×C₃₁	1	2	yes	—
259	#336	C₂²×C₃₁	1	2	yes	—
260	#336	C₂²×C₃₁	1	2	yes	—
261	C₂×C₃₁	—	16	1	no	—
262	C₂×C₃₁	#2850	1	1	yes	characteristic
263	C₂×C₃₁	#3044	1	1	yes	characteristic
264	C₂×C₃₁	#3045	1	1	yes	characteristic
265	C₂×C₃₁	#3121	1	2	yes	—
266	C₂×C₃₁	#3124	1	2	yes	—
267	C₂²×Q₈	—	2	1	no	—
268	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×Q₁₆	—	2	4	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	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	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	#124	—	2	2	no	—
281	#124	—	2	2	no	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	D₄×C₃₁	1	4	yes	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	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×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
301	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
302	#107	—	2	4	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	2	2	no	—
305	#103	—	2	4	no	—
306	#103	—	2	2	no	—
307	#103	—	2	4	no	—
308	#102	—	2	2	no	—
309	#102	—	2	4	no	—
310	#95	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	D₄×C₃₁	1	1	yes	characteristic
315	#95	D₄×C₃₁	1	2	yes	—
316	#95	D₄×C₃₁	1	1	yes	characteristic
317	C₃₁	#33035	1	1	yes	characteristic, direct product factor, Sylow
318	C₂⁴	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	—	8	1	no	—
328	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
329	C₂×Q₈	#41×C₃₁	1	4	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
344	Q₁₆	—	4	4	no	—
345	SD₁₆	—	4	4	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
361	C₄⋊C₄	#41×C₃₁	1	4	yes	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	8	2	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₄²	—	2	8	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	8	1	no	—
371	C₄²	—	8	2	no	—
372	C₄²	C₂×D₄×C₃₁	1	2	yes	—
373	C₄²	#41×C₃₁	1	2	yes	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
380	Q₈	—	2	4	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	8	4	no	—
386	Q₈	C₃₁×#124	1	4	yes	—
387	D₄	—	4	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	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	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	C₃₁×#121	1	2	yes	—
413	C₂×C₄	C₃₁×#121	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
416	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
427	C₂²	C₃₁×#525	1	2	yes	—
428	C₂²	C₃₁×#576	1	1	yes	characteristic
429	C₂²	C₃₁×#577	1	1	yes	characteristic
430	C₂²	C₃₁×#578	1	2	yes	—
431	C₄	—	2	4	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	2	no	—
440	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
441	C₄	C₃₁×#529	1	2	yes	—
442	C₄	C₃₁×#532	1	1	yes	characteristic
443	C₂	—	16	1	no	—
444	C₂	C₃₁×#2850	1	1	yes	characteristic
445	C₂	C₃₁×#3044	1	1	yes	characteristic
446	C₂	C₃₁×#3045	1	1	yes	characteristic
447	C₂	C₃₁×#3121	1	2	yes	—
448	C₂	C₃₁×#3124	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
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×#477	C₂	semidirect
4. C₃₁×#2276	C₂	semidirect
5. C₃₁×#1988	C₂	semidirect
7. C₃₁×#1928	C₂	semidirect
10. C₃₁×#1878	C₂	semidirect
11. C₃₁×#1832	C₂	semidirect
149. #33035	C₃₁	direct (N × H)
197. C₂×#477	C₂×C₃₁	semidirect
200. #2276	C₂×C₃₁	semidirect
201. #1988	C₂×C₃₁	semidirect
203. #1928	C₂×C₃₁	semidirect
206. #1878	C₂×C₃₁	semidirect
207. #1832	C₂×C₃₁	semidirect
317. C₃₁	#33035	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×#477	2
C₂×C₃₁×#464	2
C₃₁×#2640	2
C₃₁×#2276	2
C₃₁×#1988	2
C₃₁×#1983	2
C₃₁×#1928	2
C₃₁×#1925	2
C₃₁×#1880	2
C₃₁×#1878	2
C₃₁×#1832	2
#33035	31

Subgroups — C31×#33035 #21489794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33035 #21489794