Subgroups — C₃₁×#33025 #21489784

Order 7936.

978 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2858	C₂	1	1	yes	maximal, characteristic
4	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1982	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1926	C₂	1	4	yes	maximal, complemented
8	C₃₁×#1880	C₂	1	4	yes	maximal, complemented
9	C₃₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#124	—	2	1	no	—
14	C₂×C₃₁×#124	—	2	1	no	—
15	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#475	—	2	4	no	—
18	C₃₁×#460	—	2	4	no	—
19	C₂×C₃₁×#106	C₂²	1	2	yes	—
20	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#103	C₂²	1	2	yes	—
23	C₂×C₃₁×#102	C₂²	1	4	yes	—
24	C₂×C₃₁×#102	C₂²	1	2	yes	—
25	C₃₁×#390	—	2	2	no	—
26	C₃₁×#390	C₂²	1	4	yes	—
27	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₄³×C₃₁	—	2	1	no	—
32	C₄³×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#340	C₂²	1	4	yes	—
34	C₃₁×#336	C₂²	1	4	yes	—
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
40	C₂×SD₁₆×C₃₁	—	2	4	no	—
41	C₂×SD₁₆×C₃₁	—	2	8	no	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₃₁×C₄⋊Q₈	—	2	2	no	—
45	C₃₁×C₄⋊Q₈	—	2	2	no	—
46	C₃₁×#127	—	2	2	no	—
47	C₃₁×#127	—	2	2	no	—
48	C₃₁×#124	—	4	4	no	—
49	C₃₁×#124	—	4	4	no	—
50	C₄×Q₈×C₃₁	—	2	4	no	—
51	C₄×Q₈×C₃₁	—	2	4	no	—
52	C₄×Q₈×C₃₁	—	2	2	no	—
53	C₄×Q₈×C₃₁	D₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
62	C₂×C₄²×C₃₁	—	2	2	no	—
63	C₂×C₄²×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	—	2	1	no	—
66	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₃₁	D₄	1	2	yes	—
68	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₃₁×#106	—	2	4	no	—
72	C₃₁×C₄⋊C₈	—	2	2	no	—
73	C₃₁×C₄⋊C₈	—	2	2	no	—
74	C₃₁×#103	—	2	4	no	—
75	C₃₁×#102	—	2	4	no	—
76	C₃₁×#102	—	2	8	no	—
77	C₃₁×#95	—	2	2	no	—
78	C₃₁×#95	—	2	1	no	—
79	C₂⁴×C₃₁	—	2	2	no	—
80	C₂×Q₈×C₃₁	—	2	1	no	—
81	C₂×Q₈×C₃₁	—	2	2	no	—
82	C₂×Q₈×C₃₁	—	4	2	no	—
83	C₂×Q₈×C₃₁	—	4	2	no	—
84	C₂×Q₈×C₃₁	—	4	2	no	—
85	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
86	C₂×Q₈×C₃₁	#41	1	4	yes	—
87	C₂×D₄×C₃₁	—	2	2	no	—
88	C₂×D₄×C₃₁	—	2	4	no	—
89	C₂×D₄×C₃₁	—	2	2	no	—
90	C₂×D₄×C₃₁	—	2	4	no	—
91	C₂×D₄×C₃₁	—	4	4	no	—
92	C₂×D₄×C₃₁	—	4	2	no	—
93	C₂×D₄×C₃₁	—	4	2	no	—
94	C₂×D₄×C₃₁	—	4	2	no	—
95	C₂×D₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	—	2	1	no	—
97	C₂²×C₄×C₃₁	—	2	1	no	—
98	C₂²×C₄×C₃₁	—	2	2	no	—
99	C₂²×C₄×C₃₁	—	2	2	no	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
105	SD₁₆×C₃₁	—	4	8	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	2	4	no	—
109	C₂×C₈×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	2	8	no	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	2	1	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	4	2	no	—
117	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
118	C₄⋊C₄×C₃₁	#41	1	4	yes	—
119	C₂²⋊C₄×C₃₁	—	4	8	no	—
120	C₂²⋊C₄×C₃₁	—	4	8	no	—
121	C₄²×C₃₁	—	2	8	no	—
122	C₄²×C₃₁	—	2	4	no	—
123	C₄²×C₃₁	—	2	2	no	—
124	C₄²×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	—	2	2	no	—
126	C₄²×C₃₁	—	4	2	no	—
127	C₄²×C₃₁	—	4	4	no	—
128	C₄²×C₃₁	—	4	2	no	—
129	C₄²×C₃₁	SD₁₆	1	4	yes	complemented
130	C₄²×C₃₁	C₂×D₄	1	2	yes	—
131	C₄²×C₃₁	#41	1	2	yes	—
132	#33025	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	—	4	4	no	—
135	C₂³×C₃₁	—	4	2	no	—
136	C₂³×C₃₁	—	4	2	no	—
137	C₂³×C₃₁	—	4	4	no	—
138	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₃₁	—	2	4	no	—
140	Q₈×C₃₁	—	2	2	no	—
141	Q₈×C₃₁	—	8	4	no	—
142	Q₈×C₃₁	#124	1	4	yes	complemented
143	D₄×C₃₁	—	4	2	no	—
144	D₄×C₃₁	—	4	4	no	—
145	D₄×C₃₁	—	4	2	no	—
146	D₄×C₃₁	—	8	4	no	—
147	D₄×C₃₁	—	8	4	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	4	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	#121	1	2	yes	—
165	C₂×C₄×C₃₁	#121	1	2	yes	—
166	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
167	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
168	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
171	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
173	C₈×C₃₁	—	4	2	no	—
174	C₈×C₃₁	—	4	2	no	—
175	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
176	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
177	#2858	C₂×C₃₁	1	1	yes	characteristic
178	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#1988	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#1982	C₂×C₃₁	1	1	yes	characteristic
181	#1926	C₂×C₃₁	1	4	yes	complemented
182	#1880	C₂×C₃₁	1	4	yes	complemented
183	#1831	C₂×C₃₁	1	1	yes	characteristic, complemented
184	C₂²×C₃₁	—	8	4	no	—
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	—	8	4	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
190	C₂²×C₃₁	#525	1	2	yes	—
191	C₂²×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
192	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂²×C₃₁	#575	1	2	yes	—
194	C₄×C₃₁	—	2	4	no	—
195	C₄×C₃₁	—	2	4	no	—
196	C₄×C₃₁	—	2	2	no	—
197	C₄×C₃₁	—	4	2	no	—
198	C₄×C₃₁	—	4	4	no	—
199	C₄×C₃₁	—	4	2	no	—
200	C₄×C₃₁	—	8	2	no	—
201	C₄×C₃₁	#460	1	4	yes	—
202	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
203	C₄×C₃₁	#529	1	2	yes	—
204	C₄×C₃₁	#532	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#124	—	2	1	no	—
209	C₂×#124	—	2	1	no	—
210	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
212	#475	—	2	4	no	—
213	#460	—	2	4	no	—
214	C₂×#106	C₂²×C₃₁	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×#103	C₂²×C₃₁	1	2	yes	—
218	C₂×#102	C₂²×C₃₁	1	4	yes	—
219	C₂×#102	C₂²×C₃₁	1	2	yes	—
220	#390	—	2	2	no	—
221	#390	C₂²×C₃₁	1	4	yes	—
222	C₄×C₄⋊C₄	—	2	1	no	—
223	C₄×C₄⋊C₄	—	2	2	no	—
224	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
225	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
226	C₄³	—	2	1	no	—
227	C₄³	C₂²×C₃₁	1	1	yes	characteristic
228	#340	C₂²×C₃₁	1	4	yes	—
229	#336	C₂²×C₃₁	1	4	yes	—
230	C₂×C₃₁	—	16	2	no	—
231	C₂×C₃₁	#2850	1	1	yes	characteristic
232	C₂×C₃₁	C₂×#460	1	1	yes	characteristic
233	C₂×C₃₁	#3040	1	1	yes	characteristic
234	C₂×C₃₁	#3103	1	2	yes	—
235	C₂×C₃₁	#3115	1	2	yes	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	2	8	no	—
243	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
244	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	#127	—	2	2	no	—
248	#127	—	2	2	no	—
249	#124	—	4	4	no	—
250	#124	—	4	4	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	D₄×C₃₁	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₃₁	1	2	yes	—
269	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
271	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
272	#106	—	2	4	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	#103	—	2	4	no	—
276	#102	—	2	4	no	—
277	#102	—	2	8	no	—
278	#95	—	2	2	no	—
279	#95	—	2	1	no	—
280	C₃₁	#33025	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴	—	2	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
288	C₂×Q₈	#41×C₃₁	1	4	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×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	C₂⁴×C₃₁	1	1	yes	characteristic
307	SD₁₆	—	4	8	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
320	C₄⋊C₄	#41×C₃₁	1	4	yes	—
321	C₂²⋊C₄	—	4	8	no	—
322	C₂²⋊C₄	—	4	8	no	—
323	C₄²	—	2	8	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	4	2	no	—
329	C₄²	—	4	4	no	—
330	C₄²	—	4	2	no	—
331	C₄²	SD₁₆×C₃₁	1	4	yes	complemented
332	C₄²	C₂×D₄×C₃₁	1	2	yes	—
333	C₄²	#41×C₃₁	1	2	yes	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	4	no	—
339	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
340	Q₈	—	2	4	no	—
341	Q₈	—	2	2	no	—
342	Q₈	—	8	4	no	—
343	Q₈	C₃₁×#124	1	4	yes	complemented
344	D₄	—	4	2	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	2	no	—
347	D₄	—	8	4	no	—
348	D₄	—	8	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₃₁×#121	1	2	yes	—
366	C₂×C₄	C₃₁×#121	1	2	yes	—
367	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
368	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
369	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
372	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	8	4	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
382	C₂²	C₃₁×#525	1	2	yes	—
383	C₂²	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
384	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂²	C₃₁×#575	1	2	yes	—
386	C₄	—	2	4	no	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	2	no	—
393	C₄	C₃₁×#460	1	4	yes	—
394	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
395	C₄	C₃₁×#529	1	2	yes	—
396	C₄	C₃₁×#532	1	1	yes	characteristic
397	C₂	—	16	2	no	—
398	C₂	C₃₁×#2850	1	1	yes	characteristic
399	C₂	C₂×C₃₁×#460	1	1	yes	characteristic
400	C₂	C₃₁×#3040	1	1	yes	characteristic
401	C₂	C₃₁×#3103	1	2	yes	—
402	C₂	C₃₁×#3115	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 ◁ C₄³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#475	C₂	semidirect
4. C₄²×Q₈×C₃₁	C₂	semidirect
5. C₃₁×#1988	C₂	semidirect
7. C₃₁×#1926	C₂	semidirect
8. C₃₁×#1880	C₂	semidirect
9. C₃₁×#1831	C₂	semidirect
129. C₄²×C₃₁	SD₁₆	semidirect
132. #33025	C₃₁	direct (N × H)
142. Q₈×C₃₁	#124	semidirect
175. C₂×#475	C₂×C₃₁	semidirect
178. C₄²×Q₈	C₂×C₃₁	semidirect
179. #1988	C₂×C₃₁	semidirect
181. #1926	C₂×C₃₁	semidirect
182. #1880	C₂×C₃₁	semidirect
183. #1831	C₂×C₃₁	semidirect
280. C₃₁	#33025	direct (N × H)
331. C₄²	SD₁₆×C₃₁	semidirect
343. Q₈	C₃₁×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#475	2
C₂×C₃₁×#460	2
C₃₁×#2858	2
C₄²×Q₈×C₃₁	2
C₃₁×#1988	2
C₃₁×#1982	2
C₃₁×#1926	2
C₃₁×#1880	2
C₃₁×#1831	2
#33025	31

Subgroups — C31×#33025 #21489784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33025 #21489784