Subgroups — C₃₁×#33118 #21489877

Order 7936.

930 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2619	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1982	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1949	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1926	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1925	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#481	—	2	4	no	—
19	C₃₁×#480	—	2	4	no	—
20	C₂×C₃₁×#107	C₂²	1	2	yes	—
21	C₂×C₃₁×#106	C₂²	1	2	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃₁×#102	C₂²	1	2	yes	—
24	C₂×C₃₁×#102	C₂²	1	2	yes	—
25	C₂×C₃₁×#102	C₂²	1	2	yes	—
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₃₁×#394	—	2	2	no	—
30	C₃₁×#392	—	2	2	no	—
31	C₃₁×#390	C₂²	1	1	yes	characteristic
32	C₃₁×#390	C₂²	1	1	yes	characteristic
33	C₃₁×#382	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
35	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#336	C₂²	1	2	yes	—
41	C₂²×D₄×C₃₁	—	2	1	no	—
42	C₂²×D₄×C₃₁	—	2	1	no	—
43	C₂²×D₄×C₃₁	—	2	2	no	—
44	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₁	—	2	1	no	—
47	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
50	C₃₁×#127	—	2	4	no	—
51	C₃₁×#121	—	2	2	no	—
52	C₃₁×#121	—	2	2	no	—
53	C₃₁×#121	—	2	2	no	—
54	C₃₁×#121	—	2	2	no	—
55	C₃₁×#117	—	2	4	no	—
56	C₃₁×#117	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₁	D₄	1	4	yes	complemented
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
71	C₂×C₄²×C₃₁	—	2	1	no	—
72	C₂×C₄²×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	—	2	2	no	—
74	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
76	C₃₁×#107	—	2	4	no	—
77	C₃₁×#106	—	2	4	no	—
78	C₃₁×C₄⋊C₈	—	2	4	no	—
79	C₃₁×#102	—	2	4	no	—
80	C₃₁×#102	—	2	4	no	—
81	C₃₁×#102	—	2	4	no	—
82	C₃₁×#102	—	2	4	no	—
83	C₃₁×C₂²⋊C₈	—	2	2	no	—
84	C₃₁×C₂²⋊C₈	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₃₁×#95	—	2	2	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₂⁴×C₃₁	—	2	1	no	—
89	C₂⁴×C₃₁	—	2	1	no	—
90	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×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	—	2	1	no	—
97	C₂×D₄×C₃₁	—	2	2	no	—
98	C₂×D₄×C₃₁	—	2	2	no	—
99	C₂×D₄×C₃₁	—	4	2	no	—
100	C₂×D₄×C₃₁	—	4	2	no	—
101	C₂×D₄×C₃₁	—	4	4	no	—
102	C₂×D₄×C₃₁	—	8	2	no	—
103	C₂×D₄×C₃₁	—	8	2	no	—
104	C₂×D₄×C₃₁	—	8	2	no	—
105	C₂×D₄×C₃₁	—	8	2	no	—
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	—	2	2	no	—
108	C₂²×C₄×C₃₁	—	2	2	no	—
109	C₂²×C₄×C₃₁	—	2	2	no	—
110	C₂²×C₄×C₃₁	—	2	4	no	—
111	C₂²×C₄×C₃₁	—	2	1	no	—
112	C₂²×C₄×C₃₁	—	2	1	no	—
113	C₂²×C₄×C₃₁	—	8	2	no	—
114	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₃₁	#41	1	2	yes	—
119	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₂×C₈×C₃₁	—	2	2	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	C₄⋊C₄×C₃₁	—	2	4	no	—
127	C₄⋊C₄×C₃₁	—	2	4	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	2	2	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	—	2	1	no	—
134	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
135	C₄⋊C₄×C₃₁	#41	1	4	yes	—
136	C₂²⋊C₄×C₃₁	—	2	4	no	—
137	C₂²⋊C₄×C₃₁	—	2	4	no	—
138	C₂²⋊C₄×C₃₁	—	4	2	no	—
139	C₂²⋊C₄×C₃₁	—	4	2	no	—
140	C₂²⋊C₄×C₃₁	—	8	2	no	—
141	C₂²⋊C₄×C₃₁	—	8	2	no	—
142	C₄²×C₃₁	—	2	4	no	—
143	C₄²×C₃₁	—	2	2	no	—
144	C₄²×C₃₁	—	8	2	no	—
145	C₄²×C₃₁	—	8	2	no	—
146	C₄²×C₃₁	#41	1	4	yes	—
147	#33118	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₃₁	—	2	1	no	—
149	C₂³×C₃₁	—	2	1	no	—
150	C₂³×C₃₁	—	2	2	no	—
151	C₂³×C₃₁	—	2	2	no	—
152	C₂³×C₃₁	—	4	1	no	—
153	C₂³×C₃₁	—	4	1	no	—
154	C₂³×C₃₁	—	4	1	no	—
155	C₂³×C₃₁	—	4	1	no	—
156	C₂³×C₃₁	—	4	1	no	—
157	C₂³×C₃₁	—	4	1	no	—
158	C₂³×C₃₁	—	4	2	no	—
159	C₂³×C₃₁	—	4	2	no	—
160	C₂³×C₃₁	—	4	2	no	—
161	C₂³×C₃₁	—	4	2	no	—
162	C₂³×C₃₁	#121	1	2	yes	—
163	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	D₄×C₃₁	—	4	2	no	—
165	D₄×C₃₁	—	4	2	no	—
166	D₄×C₃₁	—	4	2	no	—
167	D₄×C₃₁	—	4	2	no	—
168	D₄×C₃₁	—	8	8	no	—
169	D₄×C₃₁	—	8	4	no	—
170	D₄×C₃₁	—	8	4	no	—
171	C₂×C₄×C₃₁	—	2	1	no	—
172	C₂×C₄×C₃₁	—	2	1	no	—
173	C₂×C₄×C₃₁	—	2	2	no	—
174	C₂×C₄×C₃₁	—	2	2	no	—
175	C₂×C₄×C₃₁	—	2	4	no	—
176	C₂×C₄×C₃₁	—	2	4	no	—
177	C₂×C₄×C₃₁	—	2	4	no	—
178	C₂×C₄×C₃₁	—	2	2	no	—
179	C₂×C₄×C₃₁	—	2	4	no	—
180	C₂×C₄×C₃₁	—	2	2	no	—
181	C₂×C₄×C₃₁	—	2	2	no	—
182	C₂×C₄×C₃₁	—	4	2	no	—
183	C₂×C₄×C₃₁	—	4	2	no	—
184	C₂×C₄×C₃₁	—	4	2	no	—
185	C₂×C₄×C₃₁	—	4	2	no	—
186	C₂×C₄×C₃₁	—	4	1	no	—
187	C₂×C₄×C₃₁	—	4	1	no	—
188	C₂×C₄×C₃₁	—	4	2	no	—
189	C₂×C₄×C₃₁	—	4	2	no	—
190	C₂×C₄×C₃₁	—	8	4	no	—
191	C₂×C₄×C₃₁	#121	1	2	yes	—
192	C₂×C₄×C₃₁	#123	1	4	yes	—
193	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
196	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
197	C₈×C₃₁	—	4	2	no	—
198	C₈×C₃₁	—	4	2	no	—
199	C₂×#481	C₂×C₃₁	1	1	yes	characteristic, complemented
200	C₂×#480	C₂×C₃₁	1	1	yes	characteristic, complemented
201	#2619	C₂×C₃₁	1	1	yes	characteristic
202	#2274	C₂×C₃₁	1	1	yes	characteristic, complemented
203	#1982	C₂×C₃₁	1	2	yes	complemented
204	#1949	C₂×C₃₁	1	2	yes	complemented
205	#1926	C₂×C₃₁	1	2	yes	complemented
206	#1925	C₂×C₃₁	1	2	yes	complemented
207	#1875	C₂×C₃₁	1	1	yes	characteristic, complemented
208	#1875	C₂×C₃₁	1	1	yes	characteristic, complemented
209	#1798	C₂×C₃₁	1	1	yes	characteristic, complemented
210	C₂²×C₃₁	—	2	2	no	—
211	C₂²×C₃₁	—	2	2	no	—
212	C₂²×C₃₁	—	2	2	no	—
213	C₂²×C₃₁	—	4	2	no	—
214	C₂²×C₃₁	—	4	2	no	—
215	C₂²×C₃₁	—	8	2	no	—
216	C₂²×C₃₁	—	8	2	no	—
217	C₂²×C₃₁	—	8	1	no	—
218	C₂²×C₃₁	—	8	1	no	—
219	C₂²×C₃₁	—	8	2	no	—
220	C₂²×C₃₁	—	8	2	no	—
221	C₂²×C₃₁	—	8	1	no	—
222	C₂²×C₃₁	—	8	1	no	—
223	C₂²×C₃₁	—	8	1	no	—
224	C₂²×C₃₁	—	8	1	no	—
225	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
226	C₂²×C₃₁	C₂×#123	1	1	yes	characteristic
227	C₂²×C₃₁	#525	1	1	yes	characteristic
228	C₂²×C₃₁	#576	1	2	yes	—
229	C₂²×C₃₁	#577	1	2	yes	—
230	C₄×C₃₁	—	2	4	no	—
231	C₄×C₃₁	—	2	2	no	—
232	C₄×C₃₁	—	4	2	no	—
233	C₄×C₃₁	—	4	4	no	—
234	C₄×C₃₁	—	4	4	no	—
235	C₄×C₃₁	—	8	1	no	—
236	C₄×C₃₁	—	8	1	no	—
237	C₄×C₃₁	#529	1	2	yes	—
238	C₄×C₃₁	#532	1	2	yes	—
239	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
240	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
241	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
242	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
243	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
245	#481	—	2	4	no	—
246	#480	—	2	4	no	—
247	C₂×#107	C₂²×C₃₁	1	2	yes	—
248	C₂×#106	C₂²×C₃₁	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
250	C₂×#102	C₂²×C₃₁	1	2	yes	—
251	C₂×#102	C₂²×C₃₁	1	2	yes	—
252	C₂×#102	C₂²×C₃₁	1	2	yes	—
253	C₂×#102	C₂²×C₃₁	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
256	#394	—	2	2	no	—
257	#392	—	2	2	no	—
258	#390	C₂²×C₃₁	1	1	yes	characteristic
259	#390	C₂²×C₃₁	1	1	yes	characteristic
260	#382	C₂²×C₃₁	1	1	yes	characteristic
261	C₄×C₄⋊C₄	—	2	2	no	—
262	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
263	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
264	C₄×C₂²⋊C₄	—	2	2	no	—
265	#340	C₂²×C₃₁	1	2	yes	—
266	#340	C₂²×C₃₁	1	2	yes	—
267	#336	C₂²×C₃₁	1	2	yes	—
268	C₂×C₃₁	—	4	2	no	—
269	C₂×C₃₁	—	16	1	no	—
270	C₂×C₃₁	—	16	1	no	—
271	C₂×C₃₁	#2854	1	1	yes	characteristic
272	C₂×C₃₁	#3041	1	1	yes	characteristic
273	C₂×C₃₁	#3043	1	1	yes	characteristic
274	C₂×C₃₁	#3096	1	2	yes	—
275	C₂×C₃₁	#3119	1	2	yes	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
280	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
284	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
285	#127	—	2	4	no	—
286	#121	—	2	2	no	—
287	#121	—	2	2	no	—
288	#121	—	2	2	no	—
289	#121	—	2	2	no	—
290	#117	—	2	4	no	—
291	#117	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
295	C₂×C₄⋊C₄	D₄×C₃₁	1	4	yes	complemented
296	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
311	#107	—	2	4	no	—
312	#106	—	2	4	no	—
313	C₄⋊C₈	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#102	—	2	4	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	C₃₁	#33118	1	1	yes	characteristic, direct product factor, Sylow
324	C₂⁴	—	2	1	no	—
325	C₂⁴	—	2	1	no	—
326	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	8	2	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	—	8	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	8	2	no	—
350	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
354	C₂²×C₄	#41×C₃₁	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
371	C₄⋊C₄	#41×C₃₁	1	4	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	8	2	no	—
377	C₂²⋊C₄	—	8	2	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	8	2	no	—
381	C₄²	—	8	2	no	—
382	C₄²	#41×C₃₁	1	4	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₃₁×#121	1	2	yes	—
398	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	8	8	no	—
404	D₄	—	8	4	no	—
405	D₄	—	8	4	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	4	no	—
426	C₂×C₄	C₃₁×#121	1	2	yes	—
427	C₂×C₄	C₃₁×#123	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
431	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
450	C₂²	C₂×C₃₁×#123	1	1	yes	characteristic
451	C₂²	C₃₁×#525	1	1	yes	characteristic
452	C₂²	C₃₁×#576	1	2	yes	—
453	C₂²	C₃₁×#577	1	2	yes	—
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	4	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	1	no	—
461	C₄	C₃₁×#529	1	2	yes	—
462	C₄	C₃₁×#532	1	2	yes	—
463	C₂	—	4	2	no	—
464	C₂	—	16	1	no	—
465	C₂	—	16	1	no	—
466	C₂	C₃₁×#2854	1	1	yes	characteristic
467	C₂	C₃₁×#3041	1	1	yes	characteristic
468	C₂	C₃₁×#3043	1	1	yes	characteristic
469	C₂	C₃₁×#3096	1	2	yes	—
470	C₂	C₃₁×#3119	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₃₁×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#481	C₂	semidirect
2. C₂×C₃₁×#480	C₂	semidirect
4. C₃₁×#2274	C₂	semidirect
5. C₃₁×#1982	C₂	semidirect
6. C₃₁×#1949	C₂	semidirect
7. C₃₁×#1926	C₂	semidirect
8. C₃₁×#1925	C₂	semidirect
9. C₃₁×#1875	C₂	semidirect
10. C₃₁×#1875	C₂	semidirect
11. C₃₁×#1798	C₂	semidirect
60. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
147. #33118	C₃₁	direct (N × H)
199. C₂×#481	C₂×C₃₁	semidirect
200. C₂×#480	C₂×C₃₁	semidirect
202. #2274	C₂×C₃₁	semidirect
203. #1982	C₂×C₃₁	semidirect
204. #1949	C₂×C₃₁	semidirect
205. #1926	C₂×C₃₁	semidirect
206. #1925	C₂×C₃₁	semidirect
207. #1875	C₂×C₃₁	semidirect
208. #1875	C₂×C₃₁	semidirect
209. #1798	C₂×C₃₁	semidirect
295. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
323. C₃₁	#33118	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×#481	2
C₂×C₃₁×#480	2
C₃₁×#2619	2
C₃₁×#2274	2
C₃₁×#1982	2
C₃₁×#1949	2
C₃₁×#1926	2
C₃₁×#1925	2
C₃₁×#1875	2
C₃₁×#1798	2
#33118	31

Subgroups — C31×#33118 #21489877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33118 #21489877