Subgroups — C₃₁×#33034 #21489793

Order 7936.

918 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2640	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1927	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1926	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1879	C₂	1	2	yes	maximal
10	C₃₁×#1877	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#476	—	2	4	no	—
19	C₃₁×#463	—	2	4	no	—
20	C₂×C₃₁×#106	C₂²	1	2	yes	—
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	1	yes	characteristic
25	C₂×C₃₁×#102	C₂²	1	2	yes	—
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
28	C₃₁×#397	—	2	1	no	—
29	C₃₁×#397	—	2	1	no	—
30	C₃₁×#393	—	2	2	no	—
31	C₃₁×#391	C₂²	1	2	yes	—
32	C₃₁×#390	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	1	no	—
36	C₄×C₂²⋊C₄×C₃₁	—	2	2	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	—	2	1	no	—
44	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₃₁	—	2	2	no	—
48	C₂³×C₄×C₃₁	—	2	1	no	—
49	C₂×SD₁₆×C₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₃₁	—	2	4	no	—
51	C₂×D₈×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	—	2	4	no	—
53	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₃₁×C₄⋊Q₈	—	2	2	no	—
57	C₃₁×C₄⋊Q₈	—	2	2	no	—
58	C₃₁×#124	—	2	2	no	—
59	C₃₁×#124	—	2	2	no	—
60	C₄×D₄×C₃₁	—	2	4	no	—
61	C₄×D₄×C₃₁	—	2	4	no	—
62	C₄×D₄×C₃₁	—	2	2	no	—
63	C₄×D₄×C₃₁	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
74	C₂×C₄²×C₃₁	—	2	2	no	—
75	C₂×C₄²×C₃₁	—	2	1	no	—
76	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
78	C₃₁×#106	—	2	4	no	—
79	C₃₁×C₄⋊C₈	—	2	2	no	—
80	C₃₁×C₄⋊C₈	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	2	4	no	—
83	C₃₁×#102	—	2	4	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	4	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	1	yes	characteristic
92	C₃₁×#95	D₄	1	2	yes	—
93	C₂⁴×C₃₁	—	2	1	no	—
94	C₂⁴×C₃₁	—	2	1	no	—
95	C₂×Q₈×C₃₁	—	2	1	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	—	2	1	no	—
98	C₂×Q₈×C₃₁	—	2	2	no	—
99	C₂×Q₈×C₃₁	—	4	2	no	—
100	C₂×Q₈×C₃₁	—	8	1	no	—
101	C₂×Q₈×C₃₁	—	8	1	no	—
102	C₂×D₄×C₃₁	—	2	1	no	—
103	C₂×D₄×C₃₁	—	2	1	no	—
104	C₂×D₄×C₃₁	—	2	2	no	—
105	C₂×D₄×C₃₁	—	2	2	no	—
106	C₂×D₄×C₃₁	—	2	1	no	—
107	C₂×D₄×C₃₁	—	2	2	no	—
108	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₃₁	#41	1	4	yes	—
110	C₂²×C₄×C₃₁	—	2	1	no	—
111	C₂²×C₄×C₃₁	—	2	2	no	—
112	C₂²×C₄×C₃₁	—	2	8	no	—
113	C₂²×C₄×C₃₁	—	2	4	no	—
114	C₂²×C₄×C₃₁	—	2	1	no	—
115	C₂²×C₄×C₃₁	—	2	2	no	—
116	C₂²×C₄×C₃₁	—	8	2	no	—
117	C₂²×C₄×C₃₁	—	8	2	no	—
118	C₂²×C₄×C₃₁	—	8	2	no	—
119	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
124	SD₁₆×C₃₁	—	4	4	no	—
125	D₈×C₃₁	—	4	4	no	—
126	C₂×C₈×C₃₁	—	2	2	no	—
127	C₂×C₈×C₃₁	—	2	1	no	—
128	C₂×C₈×C₃₁	—	2	1	no	—
129	C₂×C₈×C₃₁	—	2	2	no	—
130	C₂×C₈×C₃₁	—	2	2	no	—
131	C₂×C₈×C₃₁	—	2	2	no	—
132	C₂×C₈×C₃₁	—	2	2	no	—
133	C₄⋊C₄×C₃₁	—	2	1	no	—
134	C₄⋊C₄×C₃₁	—	2	2	no	—
135	C₄⋊C₄×C₃₁	—	2	2	no	—
136	C₄⋊C₄×C₃₁	—	2	2	no	—
137	C₄⋊C₄×C₃₁	—	4	2	no	—
138	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₃₁	#41	1	4	yes	—
140	C₂²⋊C₄×C₃₁	—	2	8	no	—
141	C₂²⋊C₄×C₃₁	—	2	4	no	—
142	C₂²⋊C₄×C₃₁	—	4	2	no	—
143	C₂²⋊C₄×C₃₁	—	4	2	no	—
144	C₂²⋊C₄×C₃₁	—	8	2	no	—
145	C₂²⋊C₄×C₃₁	—	8	2	no	—
146	C₄²×C₃₁	—	2	2	no	—
147	C₄²×C₃₁	—	2	2	no	—
148	C₄²×C₃₁	—	8	1	no	—
149	C₄²×C₃₁	—	8	2	no	—
150	C₄²×C₃₁	C₂×D₄	1	2	yes	—
151	C₄²×C₃₁	#41	1	2	yes	—
152	#33034	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₃₁	—	2	2	no	—
154	C₂³×C₃₁	—	2	4	no	—
155	C₂³×C₃₁	—	4	1	no	—
156	C₂³×C₃₁	—	4	2	no	—
157	C₂³×C₃₁	—	4	1	no	—
158	C₂³×C₃₁	—	4	1	no	—
159	C₂³×C₃₁	—	4	2	no	—
160	C₂³×C₃₁	—	4	1	no	—
161	C₂³×C₃₁	—	4	1	no	—
162	C₂³×C₃₁	—	4	2	no	—
163	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₃₁	—	4	1	no	—
165	Q₈×C₃₁	—	4	2	no	—
166	Q₈×C₃₁	—	4	1	no	—
167	Q₈×C₃₁	—	8	4	no	—
168	D₄×C₃₁	—	2	4	no	—
169	D₄×C₃₁	—	2	2	no	—
170	D₄×C₃₁	—	4	1	no	—
171	D₄×C₃₁	—	4	2	no	—
172	D₄×C₃₁	—	4	1	no	—
173	D₄×C₃₁	#124	1	4	yes	—
174	C₂×C₄×C₃₁	—	2	1	no	—
175	C₂×C₄×C₃₁	—	2	2	no	—
176	C₂×C₄×C₃₁	—	2	1	no	—
177	C₂×C₄×C₃₁	—	2	2	no	—
178	C₂×C₄×C₃₁	—	2	2	no	—
179	C₂×C₄×C₃₁	—	2	2	no	—
180	C₂×C₄×C₃₁	—	2	4	no	—
181	C₂×C₄×C₃₁	—	2	2	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	—	4	2	no	—
186	C₂×C₄×C₃₁	—	4	2	no	—
187	C₂×C₄×C₃₁	—	4	2	no	—
188	C₂×C₄×C₃₁	—	4	1	no	—
189	C₂×C₄×C₃₁	—	4	2	no	—
190	C₂×C₄×C₃₁	—	4	2	no	—
191	C₂×C₄×C₃₁	—	4	2	no	—
192	C₂×C₄×C₃₁	—	4	2	no	—
193	C₂×C₄×C₃₁	—	8	4	no	—
194	C₂×C₄×C₃₁	—	8	8	no	—
195	C₂×C₄×C₃₁	#121	1	2	yes	—
196	C₂×C₄×C₃₁	#121	1	2	yes	—
197	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
199	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
201	C₈×C₃₁	—	4	1	no	—
202	C₈×C₃₁	—	4	1	no	—
203	C₈×C₃₁	—	4	2	no	—
204	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
205	C₂×#463	C₂×C₃₁	1	1	yes	characteristic
206	#2640	C₂×C₃₁	1	1	yes	characteristic, complemented
207	#2275	C₂×C₃₁	1	1	yes	characteristic, complemented
208	#1988	C₂×C₃₁	1	1	yes	characteristic, complemented
209	#1983	C₂×C₃₁	1	1	yes	characteristic, complemented
210	#1927	C₂×C₃₁	1	2	yes	complemented
211	#1926	C₂×C₃₁	1	2	yes	complemented
212	#1879	C₂×C₃₁	1	2	yes	—
213	#1877	C₂×C₃₁	1	2	yes	complemented
214	#1832	C₂×C₃₁	1	1	yes	characteristic, complemented
215	C₂²×C₃₁	—	2	4	no	—
216	C₂²×C₃₁	—	4	4	no	—
217	C₂²×C₃₁	—	4	4	no	—
218	C₂²×C₃₁	—	4	2	no	—
219	C₂²×C₃₁	—	4	2	no	—
220	C₂²×C₃₁	—	8	1	no	—
221	C₂²×C₃₁	—	8	2	no	—
222	C₂²×C₃₁	—	8	2	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	#525	1	2	yes	—
227	C₂²×C₃₁	#576	1	1	yes	characteristic
228	C₂²×C₃₁	#577	1	2	yes	—
229	C₂²×C₃₁	#577	1	1	yes	characteristic
230	C₄×C₃₁	—	2	2	no	—
231	C₄×C₃₁	—	2	2	no	—
232	C₄×C₃₁	—	4	2	no	—
233	C₄×C₃₁	—	4	4	no	—
234	C₄×C₃₁	—	4	2	no	—
235	C₄×C₃₁	—	4	2	no	—
236	C₄×C₃₁	—	8	1	no	—
237	C₄×C₃₁	—	8	2	no	—
238	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
239	C₄×C₃₁	#529	1	2	yes	—
240	C₄×C₃₁	#532	1	1	yes	characteristic
241	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
242	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
246	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
247	#476	—	2	4	no	—
248	#463	—	2	4	no	—
249	C₂×#106	C₂²×C₃₁	1	2	yes	—
250	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
252	C₂×#103	C₂²×C₃₁	1	2	yes	—
253	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
254	C₂×#102	C₂²×C₃₁	1	2	yes	—
255	C₂×#102	C₂²×C₃₁	1	2	yes	—
256	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
257	#397	—	2	1	no	—
258	#397	—	2	1	no	—
259	#393	—	2	2	no	—
260	#391	C₂²×C₃₁	1	2	yes	—
261	#390	C₂²×C₃₁	1	2	yes	—
262	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
263	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	—	2	2	no	—
265	C₄×C₂²⋊C₄	—	2	1	no	—
266	#376	C₂²×C₃₁	1	1	yes	characteristic
267	C₂×#95	—	2	1	no	—
268	#340	C₂²×C₃₁	1	2	yes	—
269	#340	C₂²×C₃₁	1	2	yes	—
270	#336	C₂²×C₃₁	1	2	yes	—
271	#336	C₂²×C₃₁	1	2	yes	—
272	C₂×C₃₁	—	4	4	no	—
273	C₂×C₃₁	—	16	1	no	—
274	C₂×C₃₁	#2850	1	1	yes	characteristic
275	C₂×C₃₁	#3042	1	1	yes	characteristic
276	C₂×C₃₁	#3045	1	1	yes	characteristic
277	C₂×C₃₁	#3118	1	2	yes	—
278	C₂×C₃₁	#3125	1	2	yes	—
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
281	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
282	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	—	2	1	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	4	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	2	4	no	—
289	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	#124	—	2	2	no	—
295	#124	—	2	2	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	D₄×C₃₁	1	4	yes	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
313	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
314	#106	—	2	4	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	2	no	—
317	#103	—	2	2	no	—
318	#103	—	2	4	no	—
319	#102	—	2	4	no	—
320	#102	—	2	2	no	—
321	#102	—	2	4	no	—
322	#95	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	D₄×C₃₁	1	1	yes	characteristic
327	#95	D₄×C₃₁	1	2	yes	—
328	#95	D₄×C₃₁	1	1	yes	characteristic
329	C₃₁	#33034	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	1	no	—
331	C₂⁴	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	8	1	no	—
338	C₂×Q₈	—	8	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
346	C₂×D₄	#41×C₃₁	1	4	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	2	no	—
354	C₂²×C₄	—	8	2	no	—
355	C₂²×C₄	—	8	2	no	—
356	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
361	SD₁₆	—	4	4	no	—
362	D₈	—	4	4	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
376	C₄⋊C₄	#41×C₃₁	1	4	yes	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₂²⋊C₄	—	8	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	8	1	no	—
386	C₄²	—	8	2	no	—
387	C₄²	C₂×D₄×C₃₁	1	2	yes	—
388	C₄²	#41×C₃₁	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	2	no	—
399	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
400	Q₈	—	4	1	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	8	4	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	1	no	—
409	D₄	C₃₁×#124	1	4	yes	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	8	4	no	—
430	C₂×C₄	—	8	8	no	—
431	C₂×C₄	C₃₁×#121	1	2	yes	—
432	C₂×C₄	C₃₁×#121	1	2	yes	—
433	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
435	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
451	C₂²	C₃₁×#525	1	2	yes	—
452	C₂²	C₃₁×#576	1	1	yes	characteristic
453	C₂²	C₃₁×#577	1	2	yes	—
454	C₂²	C₃₁×#577	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	2	no	—
463	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
464	C₄	C₃₁×#529	1	2	yes	—
465	C₄	C₃₁×#532	1	1	yes	characteristic
466	C₂	—	4	4	no	—
467	C₂	—	16	1	no	—
468	C₂	C₃₁×#2850	1	1	yes	characteristic
469	C₂	C₃₁×#3042	1	1	yes	characteristic
470	C₂	C₃₁×#3045	1	1	yes	characteristic
471	C₂	C₃₁×#3118	1	2	yes	—
472	C₂	C₃₁×#3125	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₈×C₃₁	C₂²
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
1. C₂×C₃₁×#476	C₂	semidirect
3. C₃₁×#2640	C₂	semidirect
4. C₃₁×#2275	C₂	semidirect
5. C₃₁×#1988	C₂	semidirect
6. C₃₁×#1983	C₂	semidirect
7. C₃₁×#1927	C₂	semidirect
8. C₃₁×#1926	C₂	semidirect
10. C₃₁×#1877	C₂	semidirect
11. C₃₁×#1832	C₂	semidirect
152. #33034	C₃₁	direct (N × H)
204. C₂×#476	C₂×C₃₁	semidirect
206. #2640	C₂×C₃₁	semidirect
207. #2275	C₂×C₃₁	semidirect
208. #1988	C₂×C₃₁	semidirect
209. #1983	C₂×C₃₁	semidirect
210. #1927	C₂×C₃₁	semidirect
211. #1926	C₂×C₃₁	semidirect
213. #1877	C₂×C₃₁	semidirect
214. #1832	C₂×C₃₁	semidirect
329. C₃₁	#33034	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×#476	2
C₂×C₃₁×#463	2
C₃₁×#2640	2
C₃₁×#2275	2
C₃₁×#1988	2
C₃₁×#1983	2
C₃₁×#1927	2
C₃₁×#1926	2
C₃₁×#1879	2
C₃₁×#1877	2
C₃₁×#1832	2
#33034	31

Subgroups — C31×#33034 #21489793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33034 #21489793