Subgroups — C₃₁×#33044 #21489803

Order 7936.

948 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1958	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1934	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1933	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1893	C₂	1	2	yes	maximal
10	C₃₁×#1892	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1835	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
13	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#488	—	2	4	no	—
19	C₂×C₃₁×#103	C₂²	1	2	yes	—
20	C₂×C₃₁×#103	C₂²	1	2	yes	—
21	C₂×C₃₁×#102	C₂²	1	2	yes	—
22	C₂×C₃₁×#102	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₃₁	—	2	4	no	—
24	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#391	C₂²	1	1	yes	characteristic
28	C₃₁×#390	C₂²	1	1	yes	characteristic
29	C₃₁×#389	C₂²	1	2	yes	—
30	C₃₁×#388	—	2	2	no	—
31	C₃₁×#387	—	2	2	no	—
32	C₃₁×#386	—	2	2	no	—
33	C₃₁×#385	—	2	2	no	—
34	C₃₁×#382	C₂²	1	1	yes	characteristic
35	C₃₁×#382	C₂²	1	1	yes	characteristic
36	C₃₁×#380	C₂²	1	2	yes	—
37	C₃₁×#340	C₂²	1	2	yes	—
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	—	2	1	no	—
43	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₁	D₄	1	2	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	—	2	4	no	—
47	C₂²×C₈×C₃₁	—	2	4	no	—
48	C₂²×C₈×C₃₁	—	2	4	no	—
49	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
51	C₃₁×#125	—	2	2	no	—
52	C₃₁×#125	—	2	2	no	—
53	C₃₁×#124	—	2	2	no	—
54	C₃₁×#124	—	2	2	no	—
55	C₃₁×C₂²⋊Q₈	—	2	4	no	—
56	C₃₁×#121	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
69	C₂×C₄²×C₃₁	—	2	2	no	—
70	C₂×C₄²×C₃₁	—	2	2	no	—
71	C₂×C₄²×C₃₁	D₄	1	2	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
74	C₃₁×#103	—	2	4	no	—
75	C₃₁×#103	—	2	4	no	—
76	C₃₁×#102	—	2	4	no	—
77	C₃₁×#102	—	2	4	no	—
78	C₄×C₈×C₃₁	—	2	4	no	—
79	C₄×C₈×C₃₁	—	2	2	no	—
80	C₄×C₈×C₃₁	D₄	1	4	yes	complemented
81	C₃₁×#95	—	2	2	no	—
82	C₃₁×#95	—	2	2	no	—
83	C₃₁×#95	—	2	2	no	—
84	C₃₁×#95	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₂⁴×C₃₁	—	2	1	no	—
87	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₃₁	—	2	1	no	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	1	no	—
92	C₂×D₄×C₃₁	—	2	1	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	2	1	no	—
96	C₂×D₄×C₃₁	—	4	2	no	—
97	C₂×D₄×C₃₁	—	4	4	no	—
98	C₂²×C₄×C₃₁	—	2	4	no	—
99	C₂²×C₄×C₃₁	—	2	4	no	—
100	C₂²×C₄×C₃₁	—	2	4	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	—	2	1	no	—
107	C₂²×C₄×C₃₁	—	2	1	no	—
108	C₂²×C₄×C₃₁	—	2	2	no	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₃₁	#41	1	4	yes	—
113	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₃₁	—	2	16	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
120	C₂×C₈×C₃₁	#41	1	4	yes	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	4	4	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	—	4	4	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	4	no	—
132	C₂²⋊C₄×C₃₁	—	4	4	no	—
133	C₂²⋊C₄×C₃₁	—	4	2	no	—
134	C₂²⋊C₄×C₃₁	—	4	4	no	—
135	C₄²×C₃₁	—	2	4	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	C₄²×C₃₁	C₂×D₄	1	2	yes	—
139	C₄²×C₃₁	#41	1	2	yes	—
140	#33044	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₃₁	—	2	1	no	—
142	C₂³×C₃₁	—	2	1	no	—
143	C₂³×C₃₁	—	2	2	no	—
144	C₂³×C₃₁	—	4	1	no	—
145	C₂³×C₃₁	—	4	1	no	—
146	C₂³×C₃₁	—	4	1	no	—
147	C₂³×C₃₁	—	4	2	no	—
148	C₂³×C₃₁	—	4	2	no	—
149	C₂³×C₃₁	#124	1	2	yes	—
150	C₂³×C₃₁	#135	1	4	yes	—
151	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₃₁	—	4	2	no	—
153	Q₈×C₃₁	—	4	2	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	4	2	no	—
156	D₄×C₃₁	—	8	4	no	—
157	C₂×C₄×C₃₁	—	2	16	no	—
158	C₂×C₄×C₃₁	—	2	1	no	—
159	C₂×C₄×C₃₁	—	2	2	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	2	4	no	—
166	C₂×C₄×C₃₁	—	4	1	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	1	no	—
169	C₂×C₄×C₃₁	—	4	1	no	—
170	C₂×C₄×C₃₁	—	4	1	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	—	4	1	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	4	2	no	—
176	C₂×C₄×C₃₁	—	4	2	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	2	no	—
179	C₂×C₄×C₃₁	#121	1	4	yes	—
180	C₂×C₄×C₃₁	#124	1	2	yes	—
181	C₂×C₄×C₃₁	#135	1	4	yes	—
182	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
184	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
185	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
186	C₈×C₃₁	—	2	4	no	—
187	C₈×C₃₁	—	2	4	no	—
188	C₂×#488	C₂×C₃₁	1	1	yes	characteristic, complemented
189	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
190	#2851	C₂×C₃₁	1	1	yes	characteristic, complemented
191	#2850	C₂×C₃₁	1	1	yes	characteristic
192	#1991	C₂×C₃₁	1	1	yes	characteristic, complemented
193	#1958	C₂×C₃₁	1	1	yes	characteristic, complemented
194	#1934	C₂×C₃₁	1	2	yes	complemented
195	#1933	C₂×C₃₁	1	2	yes	complemented
196	#1893	C₂×C₃₁	1	2	yes	—
197	#1892	C₂×C₃₁	1	2	yes	complemented
198	#1835	C₂×C₃₁	1	1	yes	characteristic, complemented
199	C₂²×C₃₁	—	2	2	no	—
200	C₂²×C₃₁	—	2	2	no	—
201	C₂²×C₃₁	—	2	4	no	—
202	C₂²×C₃₁	—	2	4	no	—
203	C₂²×C₃₁	—	8	1	no	—
204	C₂²×C₃₁	—	8	1	no	—
205	C₂²×C₃₁	—	8	1	no	—
206	C₂²×C₃₁	—	8	2	no	—
207	C₂²×C₃₁	—	8	2	no	—
208	C₂²×C₃₁	#488	1	4	yes	complemented
209	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
210	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
211	C₂²×C₃₁	#532	1	1	yes	characteristic
212	C₂²×C₃₁	C₂×#135	1	2	yes	—
213	C₂²×C₃₁	C₂×#135	1	2	yes	—
214	C₄×C₃₁	—	2	2	no	—
215	C₄×C₃₁	—	2	4	no	—
216	C₄×C₃₁	—	2	4	no	—
217	C₄×C₃₁	—	8	1	no	—
218	C₄×C₃₁	—	8	1	no	—
219	C₄×C₃₁	—	8	1	no	—
220	C₄×C₃₁	—	8	2	no	—
221	C₄×C₃₁	—	8	2	no	—
222	C₄×C₃₁	#525	1	2	yes	—
223	C₄×C₃₁	#529	1	2	yes	—
224	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
225	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
226	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
229	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
230	#488	—	2	4	no	—
231	C₂×#103	C₂²×C₃₁	1	2	yes	—
232	C₂×#103	C₂²×C₃₁	1	2	yes	—
233	C₂×#102	C₂²×C₃₁	1	2	yes	—
234	C₂×#102	C₂²×C₃₁	1	2	yes	—
235	C₂×C₄×C₈	—	2	4	no	—
236	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
237	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
239	#391	C₂²×C₃₁	1	1	yes	characteristic
240	#390	C₂²×C₃₁	1	1	yes	characteristic
241	#389	C₂²×C₃₁	1	2	yes	—
242	#388	—	2	2	no	—
243	#387	—	2	2	no	—
244	#386	—	2	2	no	—
245	#385	—	2	2	no	—
246	#382	C₂²×C₃₁	1	1	yes	characteristic
247	#382	C₂²×C₃₁	1	1	yes	characteristic
248	#380	C₂²×C₃₁	1	2	yes	—
249	#340	C₂²×C₃₁	1	2	yes	—
250	#340	C₂²×C₃₁	1	2	yes	—
251	#340	C₂²×C₃₁	1	2	yes	—
252	#340	C₂²×C₃₁	1	2	yes	—
253	C₂×C₃₁	—	2	4	no	—
254	C₂×C₃₁	—	16	1	no	—
255	C₂×C₃₁	#2850	1	1	yes	characteristic
256	C₂×C₃₁	#3050	1	2	yes	—
257	C₂×C₃₁	C₂×#488	1	1	yes	characteristic
258	C₂×C₃₁	#3131	1	1	yes	characteristic
259	C₂×C₃₁	#3168	1	2	yes	—
260	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₃₁	1	2	yes	—
264	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
265	C₂²×C₈	—	2	4	no	—
266	C₂²×C₈	—	2	4	no	—
267	C₂²×C₈	—	2	4	no	—
268	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
269	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
270	#125	—	2	2	no	—
271	#125	—	2	2	no	—
272	#124	—	2	2	no	—
273	#124	—	2	2	no	—
274	C₂²⋊Q₈	—	2	4	no	—
275	#121	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	D₄×C₃₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
293	#103	—	2	4	no	—
294	#103	—	2	4	no	—
295	#102	—	2	4	no	—
296	#102	—	2	4	no	—
297	C₄×C₈	—	2	4	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	D₄×C₃₁	1	4	yes	complemented
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	C₃₁	#33044	1	1	yes	characteristic, direct product factor, Sylow
306	C₂⁴	—	2	1	no	—
307	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
332	C₂²×C₄	#41×C₃₁	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
334	C₂×C₈	—	2	16	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
340	C₂×C₈	#41×C₃₁	1	4	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	4	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₄²	—	2	4	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	C₂×D₄×C₃₁	1	2	yes	—
359	C₄²	#41×C₃₁	1	2	yes	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	C₃₁×#124	1	2	yes	—
369	C₂³	C₃₁×#135	1	4	yes	—
370	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	4	no	—
376	C₂×C₄	—	2	16	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	C₃₁×#121	1	4	yes	—
399	C₂×C₄	C₃₁×#124	1	2	yes	—
400	C₂×C₄	C₃₁×#135	1	4	yes	—
401	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
403	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
404	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
405	C₈	—	2	4	no	—
406	C₈	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	C₃₁×#488	1	4	yes	complemented
417	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
418	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
419	C₂²	C₃₁×#532	1	1	yes	characteristic
420	C₂²	C₂×C₃₁×#135	1	2	yes	—
421	C₂²	C₂×C₃₁×#135	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₃₁×#525	1	2	yes	—
431	C₄	C₃₁×#529	1	2	yes	—
432	C₂	—	2	4	no	—
433	C₂	—	16	1	no	—
434	C₂	C₃₁×#2850	1	1	yes	characteristic
435	C₂	C₃₁×#3050	1	2	yes	—
436	C₂	C₂×C₃₁×#488	1	1	yes	characteristic
437	C₂	C₃₁×#3131	1	1	yes	characteristic
438	C₂	C₃₁×#3168	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 ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#488	C₂	semidirect
2. C₂²×C₄×C₈×C₃₁	C₂	semidirect
3. C₃₁×#2851	C₂	semidirect
5. C₃₁×#1991	C₂	semidirect
6. C₃₁×#1958	C₂	semidirect
7. C₃₁×#1934	C₂	semidirect
8. C₃₁×#1933	C₂	semidirect
10. C₃₁×#1892	C₂	semidirect
11. C₃₁×#1835	C₂	semidirect
80. C₄×C₈×C₃₁	D₄	semidirect
140. #33044	C₃₁	direct (N × H)
188. C₂×#488	C₂×C₃₁	semidirect
189. C₂²×C₄×C₈	C₂×C₃₁	semidirect
190. #2851	C₂×C₃₁	semidirect
192. #1991	C₂×C₃₁	semidirect
193. #1958	C₂×C₃₁	semidirect
194. #1934	C₂×C₃₁	semidirect
195. #1933	C₂×C₃₁	semidirect
197. #1892	C₂×C₃₁	semidirect
198. #1835	C₂×C₃₁	semidirect
208. C₂²×C₃₁	#488	semidirect
299. C₄×C₈	D₄×C₃₁	semidirect
305. C₃₁	#33044	direct (N × H)
416. C₂²	C₃₁×#488	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#488	2
C₂²×C₄×C₈×C₃₁	2
C₃₁×#2851	2
C₃₁×#2850	2
C₃₁×#1991	2
C₃₁×#1958	2
C₃₁×#1934	2
C₃₁×#1933	2
C₃₁×#1893	2
C₃₁×#1892	2
C₃₁×#1835	2
#33044	31

Subgroups — C31×#33044 #21489803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33044 #21489803