Subgroups — C₃₁×#33182 #21489941

Order 7936.

1110 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#468	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#466	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2620	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1973	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1959	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1845	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#124	C₂²	1	2	yes	—
18	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₃₁×#121	C₂²	1	2	yes	—
20	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
21	C₃₁×#495	—	2	4	no	—
22	C₃₁×#468	—	2	8	no	—
23	C₃₁×#467	—	2	4	no	—
24	C₃₁×#466	—	2	4	no	—
25	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#107	C₂²	1	2	yes	—
28	C₂×C₃₁×#103	C₂²	1	2	yes	—
29	C₂×C₃₁×#103	C₂²	1	2	yes	—
30	C₂×C₃₁×#102	C₂²	1	2	yes	—
31	C₂×C₃₁×#102	C₂²	1	2	yes	—
32	C₃₁×#405	—	2	4	no	—
33	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#396	—	2	4	no	—
38	C₃₁×#394	—	2	4	no	—
39	C₃₁×#391	C₂²	1	2	yes	—
40	C₃₁×#390	C₂²	1	2	yes	—
41	C₃₁×#384	C₂²	1	2	yes	—
42	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₃₁	—	2	2	no	—
44	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	2	no	—
48	C₂×Q₁₆×C₃₁	—	2	2	no	—
49	C₂×SD₁₆×C₃₁	—	2	4	no	—
50	C₂×SD₁₆×C₃₁	—	2	4	no	—
51	C₂×SD₁₆×C₃₁	—	2	4	no	—
52	C₂×D₈×C₃₁	—	2	2	no	—
53	C₂×D₈×C₃₁	—	2	2	no	—
54	C₂×D₈×C₃₁	—	2	2	no	—
55	C₂×M₁₆×C₃₁	—	2	2	no	—
56	C₂×M₁₆×C₃₁	—	2	2	no	—
57	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
58	C₂²×C₈×C₃₁	—	2	2	no	—
59	C₂²×C₈×C₃₁	—	2	2	no	—
60	C₂²×C₈×C₃₁	D₄	1	4	yes	—
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
65	C₃₁×#124	—	2	4	no	—
66	C₃₁×#124	—	2	4	no	—
67	C₃₁×C₂²⋊Q₈	—	2	4	no	—
68	C₃₁×C₂²⋊Q₈	—	2	4	no	—
69	C₃₁×#121	—	2	4	no	—
70	C₃₁×#121	—	2	4	no	—
71	C₃₁×#117	—	2	2	no	—
72	C₃₁×#117	—	2	2	no	—
73	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
75	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
83	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
85	C₃₁×#107	—	2	2	no	—
86	C₃₁×#107	—	2	2	no	—
87	C₃₁×#107	—	2	4	no	—
88	C₃₁×#103	—	2	4	no	—
89	C₃₁×#103	—	2	4	no	—
90	C₃₁×#102	—	2	4	no	—
91	C₃₁×#102	—	2	4	no	—
92	C₃₁×#97	—	2	2	no	—
93	C₃₁×#97	—	2	2	no	—
94	C₄×C₈×C₃₁	—	2	2	no	—
95	C₄×C₈×C₃₁	D₄	1	4	yes	complemented
96	C₃₁×#95	—	2	4	no	—
97	C₂⁴×C₃₁	—	2	2	no	—
98	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₃₁	—	2	2	no	—
100	C₂×Q₈×C₃₁	—	2	2	no	—
101	C₂×Q₈×C₃₁	—	2	2	no	—
102	C₂×Q₈×C₃₁	—	2	2	no	—
103	C₂×Q₈×C₃₁	—	2	2	no	—
104	C₂×Q₈×C₃₁	—	2	2	no	—
105	C₂×D₄×C₃₁	—	2	2	no	—
106	C₂×D₄×C₃₁	—	2	2	no	—
107	C₂×D₄×C₃₁	—	2	2	no	—
108	C₂×D₄×C₃₁	—	2	2	no	—
109	C₂×D₄×C₃₁	—	2	2	no	—
110	C₂×D₄×C₃₁	—	2	2	no	—
111	C₂×D₄×C₃₁	—	4	4	no	—
112	C₂×D₄×C₃₁	—	8	4	no	—
113	C₂²×C₄×C₃₁	—	2	1	no	—
114	C₂²×C₄×C₃₁	—	2	1	no	—
115	C₂²×C₄×C₃₁	—	2	1	no	—
116	C₂²×C₄×C₃₁	—	2	1	no	—
117	C₂²×C₄×C₃₁	—	2	2	no	—
118	C₂²×C₄×C₃₁	—	2	2	no	—
119	C₂²×C₄×C₃₁	—	2	2	no	—
120	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₃₁	—	4	4	no	—
127	SD₁₆×C₃₁	—	4	8	no	—
128	D₈×C₃₁	—	4	4	no	—
129	M₁₆×C₃₁	—	2	8	no	—
130	C₂×C₈×C₃₁	—	2	1	no	—
131	C₂×C₈×C₃₁	—	2	1	no	—
132	C₂×C₈×C₃₁	—	2	1	no	—
133	C₂×C₈×C₃₁	—	2	1	no	—
134	C₂×C₈×C₃₁	—	2	8	no	—
135	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₃₁	#41	1	2	yes	—
142	C₂×C₈×C₃₁	#41	1	2	yes	—
143	C₄⋊C₄×C₃₁	—	2	4	no	—
144	C₄⋊C₄×C₃₁	—	2	2	no	—
145	C₄⋊C₄×C₃₁	—	2	2	no	—
146	C₄⋊C₄×C₃₁	—	2	2	no	—
147	C₄⋊C₄×C₃₁	—	2	2	no	—
148	C₄⋊C₄×C₃₁	—	4	4	no	—
149	C₄⋊C₄×C₃₁	—	8	4	no	—
150	C₂²⋊C₄×C₃₁	—	2	4	no	—
151	C₂²⋊C₄×C₃₁	—	4	4	no	—
152	C₂²⋊C₄×C₃₁	—	4	8	no	—
153	C₂²⋊C₄×C₃₁	—	4	4	no	—
154	C₂²⋊C₄×C₃₁	—	8	4	no	—
155	C₄²×C₃₁	—	2	1	no	—
156	C₄²×C₃₁	—	2	1	no	—
157	C₄²×C₃₁	C₂×D₄	1	2	yes	—
158	C₄²×C₃₁	#41	1	2	yes	—
159	#33182	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₃₁	—	2	1	no	—
161	C₂³×C₃₁	—	2	1	no	—
162	C₂³×C₃₁	—	2	2	no	—
163	C₂³×C₃₁	—	2	2	no	—
164	C₂³×C₃₁	—	4	2	no	—
165	C₂³×C₃₁	—	4	2	no	—
166	C₂³×C₃₁	—	4	2	no	—
167	C₂³×C₃₁	—	4	4	no	—
168	C₂³×C₃₁	—	4	4	no	—
169	C₂³×C₃₁	#127	1	2	yes	—
170	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₃₁	—	4	2	no	—
172	Q₈×C₃₁	—	4	2	no	—
173	Q₈×C₃₁	—	4	2	no	—
174	Q₈×C₃₁	—	4	2	no	—
175	D₄×C₃₁	—	4	2	no	—
176	D₄×C₃₁	—	4	2	no	—
177	D₄×C₃₁	—	4	2	no	—
178	D₄×C₃₁	—	4	2	no	—
179	D₄×C₃₁	—	8	8	no	—
180	C₂×C₄×C₃₁	—	2	1	no	—
181	C₂×C₄×C₃₁	—	2	1	no	—
182	C₂×C₄×C₃₁	—	2	2	no	—
183	C₂×C₄×C₃₁	—	2	2	no	—
184	C₂×C₄×C₃₁	—	2	2	no	—
185	C₂×C₄×C₃₁	—	2	2	no	—
186	C₂×C₄×C₃₁	—	2	2	no	—
187	C₂×C₄×C₃₁	—	2	2	no	—
188	C₂×C₄×C₃₁	—	2	2	no	—
189	C₂×C₄×C₃₁	—	2	2	no	—
190	C₂×C₄×C₃₁	—	2	2	no	—
191	C₂×C₄×C₃₁	—	4	2	no	—
192	C₂×C₄×C₃₁	—	4	2	no	—
193	C₂×C₄×C₃₁	—	4	2	no	—
194	C₂×C₄×C₃₁	—	4	2	no	—
195	C₂×C₄×C₃₁	—	4	2	no	—
196	C₂×C₄×C₃₁	—	4	4	no	—
197	C₂×C₄×C₃₁	—	4	4	no	—
198	C₂×C₄×C₃₁	#121	1	4	yes	—
199	C₂×C₄×C₃₁	#127	1	2	yes	—
200	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
206	C₈×C₃₁	—	2	2	no	—
207	C₈×C₃₁	—	2	2	no	—
208	C₈×C₃₁	#121	1	4	yes	—
209	C₈×C₃₁	#121	1	4	yes	—
210	C₂×#495	C₂×C₃₁	1	1	yes	characteristic, complemented
211	C₂×#468	C₂×C₃₁	1	2	yes	complemented
212	C₂×#467	C₂×C₃₁	1	1	yes	characteristic, complemented
213	C₂×#466	C₂×C₃₁	1	1	yes	characteristic
214	C₂×#405	C₂×C₃₁	1	1	yes	characteristic, complemented
215	#2620	C₂×C₃₁	1	2	yes	complemented
216	#1973	C₂×C₃₁	1	2	yes	complemented
217	#1970	C₂×C₃₁	1	1	yes	characteristic, complemented
218	#1969	C₂×C₃₁	1	1	yes	characteristic, complemented
219	#1959	C₂×C₃₁	1	2	yes	complemented
220	#1845	C₂×C₃₁	1	1	yes	characteristic, complemented
221	C₂²×C₃₁	—	2	2	no	—
222	C₂²×C₃₁	—	2	2	no	—
223	C₂²×C₃₁	—	2	2	no	—
224	C₂²×C₃₁	—	4	2	no	—
225	C₂²×C₃₁	—	4	2	no	—
226	C₂²×C₃₁	—	8	2	no	—
227	C₂²×C₃₁	—	8	2	no	—
228	C₂²×C₃₁	—	8	2	no	—
229	C₂²×C₃₁	—	8	4	no	—
230	C₂²×C₃₁	—	8	4	no	—
231	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
232	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
233	C₂²×C₃₁	#532	1	1	yes	characteristic
234	C₂²×C₃₁	#576	1	2	yes	—
235	C₂²×C₃₁	#578	1	2	yes	—
236	C₄×C₃₁	—	2	2	no	—
237	C₄×C₃₁	—	2	4	no	—
238	C₄×C₃₁	—	4	2	no	—
239	C₄×C₃₁	—	8	2	no	—
240	C₄×C₃₁	—	8	2	no	—
241	C₄×C₃₁	—	8	2	no	—
242	C₄×C₃₁	C₂×#121	1	1	yes	characteristic
243	C₄×C₃₁	C₂×#121	1	1	yes	characteristic
244	C₄×C₃₁	#532	1	1	yes	characteristic
245	C₄×C₃₁	#532	1	1	yes	characteristic
246	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
247	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
248	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
250	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
251	C₂×#124	C₂²×C₃₁	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
253	C₂×#121	C₂²×C₃₁	1	2	yes	—
254	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
255	#495	—	2	4	no	—
256	#468	—	2	8	no	—
257	#467	—	2	4	no	—
258	#466	—	2	4	no	—
259	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
260	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
261	C₂×#107	C₂²×C₃₁	1	2	yes	—
262	C₂×#103	C₂²×C₃₁	1	2	yes	—
263	C₂×#103	C₂²×C₃₁	1	2	yes	—
264	C₂×#102	C₂²×C₃₁	1	2	yes	—
265	C₂×#102	C₂²×C₃₁	1	2	yes	—
266	#405	—	2	4	no	—
267	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
268	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
269	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
271	#396	—	2	4	no	—
272	#394	—	2	4	no	—
273	#391	C₂²×C₃₁	1	2	yes	—
274	#390	C₂²×C₃₁	1	2	yes	—
275	#384	C₂²×C₃₁	1	2	yes	—
276	C₂×C₃₁	—	4	2	no	—
277	C₂×C₃₁	—	16	2	no	—
278	C₂×C₃₁	#2856	1	1	yes	characteristic
279	C₂×C₃₁	#3061	1	2	yes	—
280	C₂×C₃₁	#3155	1	1	yes	characteristic
281	C₂×C₃₁	#3156	1	1	yes	characteristic
282	C₂×C₃₁	#3175	1	2	yes	—
283	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
286	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	—	2	2	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×D₈	—	2	2	no	—
294	C₂×D₈	—	2	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	D₄×C₃₁	1	4	yes	—
302	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
306	#124	—	2	4	no	—
307	#124	—	2	4	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	#121	—	2	4	no	—
311	#121	—	2	4	no	—
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₂²⋊C₄	—	2	4	no	—
323	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
324	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
326	#107	—	2	2	no	—
327	#107	—	2	2	no	—
328	#107	—	2	4	no	—
329	#103	—	2	4	no	—
330	#103	—	2	4	no	—
331	#102	—	2	4	no	—
332	#102	—	2	4	no	—
333	#97	—	2	2	no	—
334	#97	—	2	2	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	D₄×C₃₁	1	4	yes	complemented
337	#95	—	2	4	no	—
338	C₃₁	#33182	1	1	yes	characteristic, direct product factor, Sylow
339	C₂⁴	—	2	2	no	—
340	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	8	4	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
368	Q₁₆	—	4	4	no	—
369	SD₁₆	—	4	8	no	—
370	D₈	—	4	4	no	—
371	M₁₆	—	2	8	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	8	no	—
377	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
379	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
380	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
383	C₂×C₈	#41×C₃₁	1	2	yes	—
384	C₂×C₈	#41×C₃₁	1	2	yes	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	8	4	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	8	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	8	4	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	C₂×D₄×C₃₁	1	2	yes	—
400	C₄²	#41×C₃₁	1	2	yes	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	4	4	no	—
410	C₂³	C₃₁×#127	1	2	yes	—
411	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	8	8	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	C₃₁×#121	1	4	yes	—
440	C₂×C₄	C₃₁×#127	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	2	2	no	—
449	C₈	C₃₁×#121	1	4	yes	—
450	C₈	C₃₁×#121	1	4	yes	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	4	no	—
460	C₂²	—	8	4	no	—
461	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
462	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
463	C₂²	C₃₁×#532	1	1	yes	characteristic
464	C₂²	C₃₁×#576	1	2	yes	—
465	C₂²	C₃₁×#578	1	2	yes	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	2	no	—
472	C₄	C₂×C₃₁×#121	1	1	yes	characteristic
473	C₄	C₂×C₃₁×#121	1	1	yes	characteristic
474	C₄	C₃₁×#532	1	1	yes	characteristic
475	C₄	C₃₁×#532	1	1	yes	characteristic
476	C₂	—	4	2	no	—
477	C₂	—	16	2	no	—
478	C₂	C₃₁×#2856	1	1	yes	characteristic
479	C₂	C₃₁×#3061	1	2	yes	—
480	C₂	C₃₁×#3155	1	1	yes	characteristic
481	C₂	C₃₁×#3156	1	1	yes	characteristic
482	C₂	C₃₁×#3175	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#466	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×#495	C₂	semidirect
2. C₂×C₃₁×#468	C₂	semidirect
3. C₂×C₃₁×#467	C₂	semidirect
5. C₂×C₃₁×#405	C₂	semidirect
6. C₃₁×#2620	C₂	semidirect
7. C₃₁×#1973	C₂	semidirect
8. C₃₁×#1970	C₂	semidirect
9. C₃₁×#1969	C₂	semidirect
10. C₃₁×#1959	C₂	semidirect
11. C₃₁×#1845	C₂	semidirect
95. C₄×C₈×C₃₁	D₄	semidirect
159. #33182	C₃₁	direct (N × H)
210. C₂×#495	C₂×C₃₁	semidirect
211. C₂×#468	C₂×C₃₁	semidirect
212. C₂×#467	C₂×C₃₁	semidirect
214. C₂×#405	C₂×C₃₁	semidirect
215. #2620	C₂×C₃₁	semidirect
216. #1973	C₂×C₃₁	semidirect
217. #1970	C₂×C₃₁	semidirect
218. #1969	C₂×C₃₁	semidirect
219. #1959	C₂×C₃₁	semidirect
220. #1845	C₂×C₃₁	semidirect
336. C₄×C₈	D₄×C₃₁	semidirect
338. C₃₁	#33182	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×#495	2
C₂×C₃₁×#468	2
C₂×C₃₁×#467	2
C₂×C₃₁×#466	2
C₂×C₃₁×#405	2
C₃₁×#2620	2
C₃₁×#1973	2
C₃₁×#1970	2
C₃₁×#1969	2
C₃₁×#1959	2
C₃₁×#1845	2
#33182	31

Subgroups — C31×#33182 #21489941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33182 #21489941