Subgroups — C₃₁×#33040 #21489799

Order 7936.

876 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#461	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2642	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1928	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1927	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1877	C₂	1	2	yes	maximal
10	C₃₁×#1877	C₂	1	2	yes	maximal
11	C₃₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#478	—	2	4	no	—
18	C₃₁×#461	—	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	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#103	C₂²	1	2	yes	—
26	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
28	C₃₁×#400	—	2	1	no	—
29	C₃₁×#400	—	2	2	no	—
30	C₃₁×#400	—	2	1	no	—
31	C₃₁×#391	C₂²	1	2	yes	—
32	C₃₁×#391	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
36	C₄×C₂²⋊C₄×C₃₁	—	2	1	no	—
37	C₃₁×#376	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#95	—	2	1	no	—
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	2	yes	—
44	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₁	—	2	2	no	—
46	C₂³×C₄×C₃₁	—	2	1	no	—
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×C₄⋊Q₈	—	2	2	no	—
54	C₃₁×C₄⋊Q₈	—	2	2	no	—
55	C₃₁×#125	—	2	2	no	—
56	C₃₁×#125	—	2	2	no	—
57	C₄×D₄×C₃₁	—	2	4	no	—
58	C₄×D₄×C₃₁	—	2	4	no	—
59	C₄×D₄×C₃₁	—	2	2	no	—
60	C₄×D₄×C₃₁	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
71	C₂×C₄²×C₃₁	—	2	2	no	—
72	C₂×C₄²×C₃₁	—	2	1	no	—
73	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
75	C₃₁×#107	—	2	2	no	—
76	C₃₁×#106	—	2	2	no	—
77	C₃₁×C₄⋊C₈	—	2	2	no	—
78	C₃₁×C₄⋊C₈	—	2	2	no	—
79	C₃₁×#103	—	2	4	no	—
80	C₃₁×#103	—	2	4	no	—
81	C₃₁×#103	—	2	4	no	—
82	C₃₁×#102	—	2	2	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#95	—	2	2	no	—
85	C₃₁×#95	—	2	2	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	2	yes	—
92	C₃₁×#95	D₄	1	1	yes	characteristic
93	C₂⁴×C₃₁	—	2	1	no	—
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	—	2	2	no	—
98	C₂×Q₈×C₃₁	—	2	2	no	—
99	C₂×Q₈×C₃₁	—	2	2	no	—
100	C₂×D₄×C₃₁	—	2	1	no	—
101	C₂×D₄×C₃₁	—	2	2	no	—
102	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂×D₄×C₃₁	#41	1	4	yes	—
104	C₂²×C₄×C₃₁	—	2	1	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	2	8	no	—
107	C₂²×C₄×C₃₁	—	2	4	no	—
108	C₂²×C₄×C₃₁	—	2	1	no	—
109	C₂²×C₄×C₃₁	—	2	1	no	—
110	C₂²×C₄×C₃₁	—	2	2	no	—
111	C₂²×C₄×C₃₁	—	8	2	no	—
112	C₂²×C₄×C₃₁	—	8	2	no	—
113	C₂²×C₄×C₃₁	—	8	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	SD₁₆×C₃₁	—	4	8	no	—
120	C₂×C₈×C₃₁	—	2	1	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	2	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	1	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	2	1	no	—
130	C₄⋊C₄×C₃₁	—	2	1	no	—
131	C₄⋊C₄×C₃₁	—	2	1	no	—
132	C₄⋊C₄×C₃₁	—	2	1	no	—
133	C₄⋊C₄×C₃₁	—	4	2	no	—
134	C₄⋊C₄×C₃₁	—	4	2	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	—	2	8	no	—
140	C₂²⋊C₄×C₃₁	—	2	4	no	—
141	C₄²×C₃₁	—	2	2	no	—
142	C₄²×C₃₁	—	2	2	no	—
143	C₄²×C₃₁	—	8	1	no	—
144	C₄²×C₃₁	—	8	2	no	—
145	C₄²×C₃₁	C₂×D₄	1	2	yes	—
146	C₄²×C₃₁	#41	1	2	yes	—
147	#33040	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₃₁	—	2	2	no	—
149	C₂³×C₃₁	—	2	4	no	—
150	C₂³×C₃₁	—	4	2	no	—
151	C₂³×C₃₁	—	4	1	no	—
152	C₂³×C₃₁	—	4	1	no	—
153	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₃₁	—	4	2	no	—
155	Q₈×C₃₁	—	4	2	no	—
156	Q₈×C₃₁	—	4	2	no	—
157	Q₈×C₃₁	—	4	2	no	—
158	D₄×C₃₁	—	2	4	no	—
159	D₄×C₃₁	—	2	2	no	—
160	D₄×C₃₁	#124	1	4	yes	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	1	no	—
164	C₂×C₄×C₃₁	—	2	2	no	—
165	C₂×C₄×C₃₁	—	2	2	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	2	no	—
171	C₂×C₄×C₃₁	—	2	2	no	—
172	C₂×C₄×C₃₁	—	4	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	4	1	no	—
176	C₂×C₄×C₃₁	—	4	1	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	2	no	—
179	C₂×C₄×C₃₁	—	4	2	no	—
180	C₂×C₄×C₃₁	—	4	2	no	—
181	C₂×C₄×C₃₁	—	4	1	no	—
182	C₂×C₄×C₃₁	—	4	1	no	—
183	C₂×C₄×C₃₁	—	8	4	no	—
184	C₂×C₄×C₃₁	—	8	8	no	—
185	C₂×C₄×C₃₁	#121	1	2	yes	—
186	C₂×C₄×C₃₁	#121	1	2	yes	—
187	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
189	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
191	C₈×C₃₁	—	4	2	no	—
192	C₈×C₃₁	—	4	1	no	—
193	C₈×C₃₁	—	4	1	no	—
194	C₂×#478	C₂×C₃₁	1	1	yes	characteristic
195	C₂×#461	C₂×C₃₁	1	1	yes	characteristic
196	#2642	C₂×C₃₁	1	1	yes	characteristic, complemented
197	#2275	C₂×C₃₁	1	1	yes	characteristic
198	#1989	C₂×C₃₁	1	1	yes	characteristic, complemented
199	#1981	C₂×C₃₁	1	1	yes	characteristic, complemented
200	#1928	C₂×C₃₁	1	2	yes	complemented
201	#1927	C₂×C₃₁	1	2	yes	complemented
202	#1877	C₂×C₃₁	1	2	yes	—
203	#1877	C₂×C₃₁	1	2	yes	—
204	#1832	C₂×C₃₁	1	1	yes	characteristic, complemented
205	C₂²×C₃₁	—	2	4	no	—
206	C₂²×C₃₁	—	4	4	no	—
207	C₂²×C₃₁	—	4	4	no	—
208	C₂²×C₃₁	—	4	2	no	—
209	C₂²×C₃₁	—	4	2	no	—
210	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
211	C₂²×C₃₁	#525	1	2	yes	—
212	C₂²×C₃₁	#577	1	2	yes	—
213	C₂²×C₃₁	#577	1	1	yes	characteristic
214	C₂²×C₃₁	#578	1	1	yes	characteristic
215	C₄×C₃₁	—	2	2	no	—
216	C₄×C₃₁	—	2	2	no	—
217	C₄×C₃₁	—	4	2	no	—
218	C₄×C₃₁	—	4	2	no	—
219	C₄×C₃₁	—	4	4	no	—
220	C₄×C₃₁	—	4	2	no	—
221	C₄×C₃₁	—	8	2	no	—
222	C₄×C₃₁	—	8	1	no	—
223	C₄×C₃₁	—	8	1	no	—
224	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
225	C₄×C₃₁	#529	1	2	yes	—
226	C₄×C₃₁	#532	1	1	yes	characteristic
227	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
231	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
232	#478	—	2	4	no	—
233	#461	—	2	4	no	—
234	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
235	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
238	C₂×#103	C₂²×C₃₁	1	2	yes	—
239	C₂×#103	C₂²×C₃₁	1	2	yes	—
240	C₂×#103	C₂²×C₃₁	1	2	yes	—
241	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
242	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
243	#400	—	2	1	no	—
244	#400	—	2	2	no	—
245	#400	—	2	1	no	—
246	#391	C₂²×C₃₁	1	2	yes	—
247	#391	C₂²×C₃₁	1	2	yes	—
248	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
249	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	—	2	2	no	—
251	C₄×C₂²⋊C₄	—	2	1	no	—
252	#376	C₂²×C₃₁	1	1	yes	characteristic
253	C₂×#95	—	2	1	no	—
254	#340	C₂²×C₃₁	1	2	yes	—
255	#340	C₂²×C₃₁	1	2	yes	—
256	#336	C₂²×C₃₁	1	2	yes	—
257	#336	C₂²×C₃₁	1	2	yes	—
258	C₂×C₃₁	—	4	4	no	—
259	C₂×C₃₁	#2850	1	1	yes	characteristic
260	C₂×C₃₁	#3042	1	1	yes	characteristic
261	C₂×C₃₁	#3046	1	1	yes	characteristic
262	C₂×C₃₁	#3120	1	2	yes	—
263	C₂×C₃₁	#3123	1	2	yes	—
264	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
265	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	—	2	1	no	—
268	C₂×SD₁₆	—	2	4	no	—
269	C₂×SD₁₆	—	2	4	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
272	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	#125	—	2	2	no	—
277	#125	—	2	2	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	D₄×C₃₁	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
295	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#106	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	#103	—	2	4	no	—
301	#103	—	2	4	no	—
302	#103	—	2	4	no	—
303	#102	—	2	2	no	—
304	#102	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	D₄×C₃₁	1	1	yes	characteristic
312	#95	D₄×C₃₁	1	2	yes	—
313	#95	D₄×C₃₁	1	1	yes	characteristic
314	C₃₁	#33040	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
325	C₂×D₄	#41×C₃₁	1	4	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	8	2	no	—
334	C₂²×C₄	—	8	2	no	—
335	C₂²×C₄	—	8	2	no	—
336	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
341	SD₁₆	—	4	8	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
360	C₄⋊C₄	#41×C₃₁	1	4	yes	—
361	C₂²⋊C₄	—	2	8	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	8	1	no	—
366	C₄²	—	8	2	no	—
367	C₄²	C₂×D₄×C₃₁	1	2	yes	—
368	C₄²	#41×C₃₁	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	C₃₁×#124	1	4	yes	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	8	4	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	C₃₁×#121	1	2	yes	—
407	C₂×C₄	C₃₁×#121	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
410	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
421	C₂²	C₃₁×#525	1	2	yes	—
422	C₂²	C₃₁×#577	1	2	yes	—
423	C₂²	C₃₁×#577	1	1	yes	characteristic
424	C₂²	C₃₁×#578	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	4	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	1	no	—
434	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
435	C₄	C₃₁×#529	1	2	yes	—
436	C₄	C₃₁×#532	1	1	yes	characteristic
437	C₂	—	4	4	no	—
438	C₂	C₃₁×#2850	1	1	yes	characteristic
439	C₂	C₃₁×#3042	1	1	yes	characteristic
440	C₂	C₃₁×#3046	1	1	yes	characteristic
441	C₂	C₃₁×#3120	1	2	yes	—
442	C₂	C₃₁×#3123	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
3. C₃₁×#2642	C₂	semidirect
5. C₃₁×#1989	C₂	semidirect
6. C₃₁×#1981	C₂	semidirect
7. C₃₁×#1928	C₂	semidirect
8. C₃₁×#1927	C₂	semidirect
11. C₃₁×#1832	C₂	semidirect
147. #33040	C₃₁	direct (N × H)
196. #2642	C₂×C₃₁	semidirect
198. #1989	C₂×C₃₁	semidirect
199. #1981	C₂×C₃₁	semidirect
200. #1928	C₂×C₃₁	semidirect
201. #1927	C₂×C₃₁	semidirect
204. #1832	C₂×C₃₁	semidirect
314. C₃₁	#33040	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×#478	2
C₂×C₃₁×#461	2
C₃₁×#2642	2
C₃₁×#2275	2
C₃₁×#1989	2
C₃₁×#1981	2
C₃₁×#1928	2
C₃₁×#1927	2
C₃₁×#1877	2
C₃₁×#1832	2
#33040	31

Subgroups — C31×#33040 #21489799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33040 #21489799