Subgroups — C₃₁×#10880 #21467639

Order 7936.

966 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#340	C₂	1	2	yes	maximal
4	C₂×C₃₁×#340	C₂	1	2	yes	maximal
5	C₃₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₃₁	—	2	4	no	—
13	C₂×C₄×C₈×C₃₁	—	2	2	no	—
14	C₃₁×#389	—	2	2	no	—
15	C₃₁×#389	C₄	1	4	yes	complemented
16	C₂×C₃₁×#95	—	2	1	no	—
17	C₂×C₃₁×#95	—	2	1	no	—
18	C₂×C₃₁×#95	—	2	1	no	—
19	C₃₁×#340	—	2	4	no	—
20	C₃₁×#340	C₄	1	8	yes	complemented
21	C₂³×C₄×C₃₁	—	2	1	no	—
22	C₂³×C₄×C₃₁	—	2	1	no	—
23	C₂³×C₄×C₃₁	—	2	2	no	—
24	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₃₁	—	2	2	no	—
28	C₂²×C₈×C₃₁	—	2	2	no	—
29	C₂²×C₈×C₃₁	—	2	2	no	—
30	C₂²×C₈×C₃₁	—	2	2	no	—
31	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₃₁	D₄	1	4	yes	—
33	C₂²×C₈×C₃₁	Q₈	1	4	yes	—
34	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
35	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
40	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
43	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
44	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
45	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
46	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
47	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
50	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₃₁	—	2	2	no	—
52	C₂×C₄²×C₃₁	—	2	2	no	—
53	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₃₁	D₄	1	2	yes	—
55	C₄×C₈×C₃₁	—	2	8	no	—
56	C₃₁×#95	—	2	4	no	—
57	C₃₁×#95	—	4	2	no	—
58	C₃₁×#95	—	4	2	no	—
59	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₃₁	—	2	2	no	—
61	C₂²×C₄×C₃₁	—	2	2	no	—
62	C₂²×C₄×C₃₁	—	2	2	no	—
63	C₂²×C₄×C₃₁	—	2	2	no	—
64	C₂²×C₄×C₃₁	—	2	2	no	—
65	C₂²×C₄×C₃₁	—	2	4	no	—
66	C₂²×C₄×C₃₁	—	2	2	no	—
67	C₂²×C₄×C₃₁	—	2	4	no	—
68	C₂²×C₄×C₃₁	—	4	1	no	—
69	C₂²×C₄×C₃₁	—	4	1	no	—
70	C₂²×C₄×C₃₁	—	4	2	no	—
71	C₂²×C₄×C₃₁	—	4	2	no	—
72	C₂²×C₄×C₃₁	—	4	2	no	—
73	C₂²×C₄×C₃₁	—	4	2	no	—
74	C₂²×C₄×C₃₁	—	4	2	no	—
75	C₂²×C₄×C₃₁	—	4	1	no	—
76	C₂²×C₄×C₃₁	—	4	2	no	—
77	C₂²×C₄×C₃₁	—	4	1	no	—
78	C₂²×C₄×C₃₁	—	4	2	no	—
79	C₂²×C₄×C₃₁	—	4	2	no	—
80	C₂²×C₄×C₃₁	—	4	2	no	—
81	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₃₁	D₈	1	2	yes	—
84	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₃₁	Q₁₆	1	2	yes	—
87	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₃₁	#41	1	2	yes	—
93	C₂²×C₄×C₃₁	#41	1	2	yes	—
94	C₂²×C₄×C₃₁	#41	1	2	yes	—
95	C₂×C₈×C₃₁	—	2	4	no	—
96	C₂×C₈×C₃₁	—	2	4	no	—
97	C₂×C₈×C₃₁	—	2	4	no	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	2	4	no	—
100	C₂×C₈×C₃₁	—	2	4	no	—
101	C₂×C₈×C₃₁	C₄⋊C₄	1	8	yes	complemented
102	C₄⋊C₄×C₃₁	—	2	2	no	—
103	C₄⋊C₄×C₃₁	—	2	4	no	—
104	C₄⋊C₄×C₃₁	—	2	4	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	4	no	—
107	C₄⋊C₄×C₃₁	—	4	8	no	—
108	C₄⋊C₄×C₃₁	—	4	1	no	—
109	C₄⋊C₄×C₃₁	—	4	1	no	—
110	C₄⋊C₄×C₃₁	—	4	2	no	—
111	C₄⋊C₄×C₃₁	—	4	2	no	—
112	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
113	C₄²×C₃₁	—	2	4	no	—
114	C₄²×C₃₁	—	2	2	no	—
115	C₄²×C₃₁	—	2	2	no	—
116	#10880	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₃₁	C₄×D₄	1	2	yes	—
119	C₂³×C₃₁	#121	1	2	yes	—
120	C₂³×C₃₁	#124	1	1	yes	characteristic
121	C₂³×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
122	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
123	C₂³×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
124	C₂³×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
125	C₂³×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
126	C₂³×C₃₁	#135	1	2	yes	—
127	C₂³×C₃₁	#135	1	2	yes	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	4	no	—
133	C₂×C₄×C₃₁	—	2	4	no	—
134	C₂×C₄×C₃₁	—	2	4	no	—
135	C₂×C₄×C₃₁	—	2	4	no	—
136	C₂×C₄×C₃₁	—	2	4	no	—
137	C₂×C₄×C₃₁	—	4	2	no	—
138	C₂×C₄×C₃₁	—	4	2	no	—
139	C₂×C₄×C₃₁	—	4	4	no	—
140	C₂×C₄×C₃₁	—	4	4	no	—
141	C₂×C₄×C₃₁	—	4	2	no	—
142	C₂×C₄×C₃₁	—	4	4	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	8	2	no	—
148	C₂×C₄×C₃₁	—	8	2	no	—
149	C₂×C₄×C₃₁	—	8	2	no	—
150	C₂×C₄×C₃₁	—	8	2	no	—
151	C₂×C₄×C₃₁	—	8	2	no	—
152	C₂×C₄×C₃₁	—	8	2	no	—
153	C₂×C₄×C₃₁	#102	1	4	yes	—
154	C₂×C₄×C₃₁	#103	1	4	yes	—
155	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₃₁	#117	1	2	yes	—
158	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
163	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
164	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₃₁	#123	1	2	yes	—
168	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
169	C₂×C₄×C₃₁	#125	1	2	yes	—
170	C₂×C₄×C₃₁	#126	1	2	yes	—
171	C₈×C₃₁	—	2	8	no	—
172	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic
173	C₂×#389	C₂×C₃₁	1	1	yes	characteristic
174	C₂×#340	C₂×C₃₁	1	2	yes	—
175	C₂×#340	C₂×C₃₁	1	2	yes	—
176	C₄⋊#95	C₂×C₃₁	1	1	yes	characteristic
177	C₂²×C₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₃₁	#386	1	1	yes	characteristic
179	C₂²×C₃₁	#388	1	2	yes	—
180	C₂²×C₃₁	#389	1	2	yes	—
181	C₂²×C₃₁	#391	1	1	yes	characteristic
182	C₂²×C₃₁	C₂×#102	1	1	yes	characteristic
183	C₂²×C₃₁	C₂×#103	1	1	yes	characteristic
184	C₂²×C₃₁	#416	1	1	yes	characteristic
185	C₂²×C₃₁	#416	1	1	yes	characteristic
186	C₂²×C₃₁	C₄×D₈	1	2	yes	—
187	C₂²×C₃₁	C₄×SD₁₆	1	2	yes	—
188	C₂²×C₃₁	C₄×SD₁₆	1	2	yes	—
189	C₂²×C₃₁	C₄×Q₁₆	1	2	yes	—
190	C₂²×C₃₁	#465	1	2	yes	—
191	C₂²×C₃₁	#465	1	2	yes	—
192	C₂²×C₃₁	#466	1	2	yes	—
193	C₂²×C₃₁	#467	1	2	yes	—
194	C₂²×C₃₁	#486	1	1	yes	characteristic
195	C₂²×C₃₁	#487	1	1	yes	characteristic
196	C₂²×C₃₁	#488	1	2	yes	—
197	C₂²×C₃₁	#498	1	1	yes	characteristic
198	C₂²×C₃₁	#499	1	2	yes	—
199	C₂²×C₃₁	#500	1	1	yes	characteristic
200	C₄×C₃₁	—	2	4	no	—
201	C₄×C₃₁	—	2	4	no	—
202	C₄×C₃₁	—	4	4	no	—
203	C₄×C₃₁	—	8	2	no	—
204	C₄×C₃₁	—	8	4	no	—
205	C₄×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
206	C₄×C₃₁	#385	1	2	yes	—
207	C₄×C₃₁	#387	1	2	yes	—
208	C₄×C₃₁	#387	1	2	yes	—
209	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
210	C₂²×C₄⋊C₄	—	2	1	no	—
211	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
213	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×C₄×C₈	—	2	4	no	—
216	C₂×C₄×C₈	—	2	2	no	—
217	#389	—	2	2	no	—
218	#389	C₄×C₃₁	1	4	yes	complemented
219	C₂×#95	—	2	1	no	—
220	C₂×#95	—	2	1	no	—
221	C₂×#95	—	2	1	no	—
222	#340	—	2	4	no	—
223	#340	C₄×C₃₁	1	8	yes	complemented
224	C₂×C₃₁	#1436	1	1	yes	characteristic
225	C₂×C₃₁	C₄×#102	1	1	yes	characteristic
226	C₂×C₃₁	C₄×#103	1	1	yes	characteristic
227	C₂×C₃₁	#1892	1	1	yes	characteristic
228	C₂×C₃₁	#1893	1	1	yes	characteristic
229	C₂×C₃₁	#1933	1	2	yes	—
230	C₂×C₃₁	#1934	1	2	yes	—
231	C₂×C₃₁	#1941	1	2	yes	—
232	C₂×C₃₁	#1942	1	2	yes	—
233	C₂×C₃₁	#1990	1	1	yes	characteristic
234	C₂×C₃₁	#1991	1	1	yes	characteristic
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
239	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
246	C₂²×C₈	D₄×C₃₁	1	4	yes	—
247	C₂²×C₈	Q₈×C₃₁	1	4	yes	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	4	2	no	—
260	C₂×C₄⋊C₄	—	4	2	no	—
261	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
264	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
268	C₂×C₄²	D₄×C₃₁	1	2	yes	—
269	C₄×C₈	—	2	8	no	—
270	#95	—	2	4	no	—
271	#95	—	4	2	no	—
272	#95	—	4	2	no	—
273	C₃₁	#10880	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
297	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
298	C₂²×C₄	D₈×C₃₁	1	2	yes	—
299	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
300	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
301	C₂²×C₄	Q₁₆×C₃₁	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
307	C₂²×C₄	#41×C₃₁	1	2	yes	—
308	C₂²×C₄	#41×C₃₁	1	2	yes	—
309	C₂²×C₄	#41×C₃₁	1	2	yes	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	C₄⋊C₄×C₃₁	1	8	yes	complemented
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	4	8	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
328	C₄²	—	2	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
332	C₂³	C₄×D₄×C₃₁	1	2	yes	—
333	C₂³	C₃₁×#121	1	2	yes	—
334	C₂³	C₃₁×#124	1	1	yes	characteristic
335	C₂³	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
336	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
337	C₂³	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
338	C₂³	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
339	C₂³	C₂×Q₁₆×C₃₁	1	1	yes	characteristic
340	C₂³	C₃₁×#135	1	2	yes	—
341	C₂³	C₃₁×#135	1	2	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	C₃₁×#102	1	4	yes	—
368	C₂×C₄	C₃₁×#103	1	4	yes	—
369	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
371	C₂×C₄	C₃₁×#117	1	2	yes	—
372	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
373	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
374	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
375	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
376	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
377	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
378	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
379	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
380	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
381	C₂×C₄	C₃₁×#123	1	2	yes	—
382	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
383	C₂×C₄	C₃₁×#125	1	2	yes	—
384	C₂×C₄	C₃₁×#126	1	2	yes	—
385	C₈	—	2	8	no	—
386	C₂²	C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
387	C₂²	C₃₁×#386	1	1	yes	characteristic
388	C₂²	C₃₁×#388	1	2	yes	—
389	C₂²	C₃₁×#389	1	2	yes	—
390	C₂²	C₃₁×#391	1	1	yes	characteristic
391	C₂²	C₂×C₃₁×#102	1	1	yes	characteristic
392	C₂²	C₂×C₃₁×#103	1	1	yes	characteristic
393	C₂²	C₃₁×#416	1	1	yes	characteristic
394	C₂²	C₃₁×#416	1	1	yes	characteristic
395	C₂²	C₄×D₈×C₃₁	1	2	yes	—
396	C₂²	C₄×SD₁₆×C₃₁	1	2	yes	—
397	C₂²	C₄×SD₁₆×C₃₁	1	2	yes	—
398	C₂²	C₄×Q₁₆×C₃₁	1	2	yes	—
399	C₂²	C₃₁×#465	1	2	yes	—
400	C₂²	C₃₁×#465	1	2	yes	—
401	C₂²	C₃₁×#466	1	2	yes	—
402	C₂²	C₃₁×#467	1	2	yes	—
403	C₂²	C₃₁×#486	1	1	yes	characteristic
404	C₂²	C₃₁×#487	1	1	yes	characteristic
405	C₂²	C₃₁×#488	1	2	yes	—
406	C₂²	C₃₁×#498	1	1	yes	characteristic
407	C₂²	C₃₁×#499	1	2	yes	—
408	C₂²	C₃₁×#500	1	1	yes	characteristic
409	C₄	—	2	4	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	4	no	—
414	C₄	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
415	C₄	C₃₁×#385	1	2	yes	—
416	C₄	C₃₁×#387	1	2	yes	—
417	C₄	C₃₁×#387	1	2	yes	—
418	C₂	C₃₁×#1436	1	1	yes	characteristic
419	C₂	C₄×C₃₁×#102	1	1	yes	characteristic
420	C₂	C₄×C₃₁×#103	1	1	yes	characteristic
421	C₂	C₃₁×#1892	1	1	yes	characteristic
422	C₂	C₃₁×#1893	1	1	yes	characteristic
423	C₂	C₃₁×#1933	1	2	yes	—
424	C₂	C₃₁×#1934	1	2	yes	—
425	C₂	C₃₁×#1941	1	2	yes	—
426	C₂	C₃₁×#1942	1	2	yes	—
427	C₂	C₃₁×#1990	1	1	yes	characteristic
428	C₂	C₃₁×#1991	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₃₁×#389	C₄	semidirect
20. C₃₁×#340	C₄	semidirect
101. C₂×C₈×C₃₁	C₄⋊C₄	semidirect
116. #10880	C₃₁	direct (N × H)
218. #389	C₄×C₃₁	semidirect
223. #340	C₄×C₃₁	semidirect
273. C₃₁	#10880	direct (N × H)
316. C₂×C₈	C₄⋊C₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₈×C₃₁	2
C₂×C₃₁×#389	2
C₂×C₃₁×#340	2
C₃₁×C₄⋊#95	2
#10880	31

Subgroups — C31×#10880 #21467639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10880 #21467639