Subgroups — C₃₁×#25941 #21482700

Order 7936.

1022 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×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#489	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2592	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2026	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2025	C₂	1	2	yes	maximal
7	C₃₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1880	C₂	1	2	yes	maximal
10	C₃₁×#1878	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#557	—	2	4	no	—
15	C₃₁×#557	—	2	4	no	—
16	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#125	—	2	2	no	—
19	C₂×C₃₁×#125	C₂²	1	2	yes	—
20	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
22	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#489	—	2	4	no	—
26	C₃₁×#464	—	2	4	no	—
27	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#103	C₂²	1	2	yes	—
29	C₂×C₃₁×#103	C₂²	1	2	yes	—
30	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#102	C₂²	1	2	yes	—
32	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
34	C₃₁×#397	—	2	1	no	—
35	C₃₁×#393	—	2	1	no	—
36	C₃₁×#391	C₂²	1	2	yes	—
37	C₃₁×#390	C₂²	1	2	yes	—
38	C₃₁×#388	—	2	2	no	—
39	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#340	C₂²	1	2	yes	—
41	C₃₁×#340	C₂²	1	2	yes	—
42	C₃₁×#340	C₂²	1	2	yes	—
43	C₃₁×#336	C₂²	1	2	yes	—
44	C₃₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₃₁	—	2	1	no	—
46	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₂×Q₁₆×C₃₁	—	2	2	no	—
51	C₂×Q₁₆×C₃₁	—	2	4	no	—
52	C₂×SD₁₆×C₃₁	—	2	2	no	—
53	C₂×SD₁₆×C₃₁	—	2	4	no	—
54	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×C₄⋊Q₈	—	2	8	no	—
58	C₃₁×C₄⋊Q₈	—	2	2	no	—
59	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
60	C₃₁×#125	—	2	16	no	—
61	C₃₁×#125	—	2	4	no	—
62	C₃₁×#125	—	2	4	no	—
63	C₃₁×#124	—	2	2	no	—
64	C₃₁×#124	—	2	2	no	—
65	C₄×Q₈×C₃₁	—	2	8	no	—
66	C₄×Q₈×C₃₁	—	2	4	no	—
67	C₄×Q₈×C₃₁	—	2	4	no	—
68	C₄×Q₈×C₃₁	—	2	2	no	—
69	C₄×Q₈×C₃₁	—	2	2	no	—
70	C₄×Q₈×C₃₁	—	2	2	no	—
71	C₄×Q₈×C₃₁	D₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
86	C₂×C₄²×C₃₁	—	2	2	no	—
87	C₂×C₄²×C₃₁	—	2	1	no	—
88	C₂×C₄²×C₃₁	—	2	1	no	—
89	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
91	C₃₁×C₄⋊C₈	—	2	2	no	—
92	C₃₁×#103	—	2	4	no	—
93	C₃₁×#103	—	2	2	no	—
94	C₃₁×#103	—	2	4	no	—
95	C₃₁×#102	—	2	2	no	—
96	C₃₁×#102	—	2	4	no	—
97	C₃₁×#97	—	2	2	no	—
98	C₃₁×#95	—	2	1	no	—
99	C₃₁×#95	—	2	2	no	—
100	C₃₁×#95	—	2	2	no	—
101	C₂⁴×C₃₁	—	2	1	no	—
102	C₂×Q₈×C₃₁	—	2	2	no	—
103	C₂×Q₈×C₃₁	—	2	4	no	—
104	C₂×Q₈×C₃₁	—	2	1	no	—
105	C₂×Q₈×C₃₁	—	2	2	no	—
106	C₂×Q₈×C₃₁	—	2	1	no	—
107	C₂×Q₈×C₃₁	—	2	1	no	—
108	C₂×Q₈×C₃₁	—	2	2	no	—
109	C₂×Q₈×C₃₁	—	2	2	no	—
110	C₂×Q₈×C₃₁	—	4	2	no	—
111	C₂×Q₈×C₃₁	—	4	4	no	—
112	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₃₁	#41	1	4	yes	—
114	C₂×D₄×C₃₁	—	2	1	no	—
115	C₂×D₄×C₃₁	—	2	1	no	—
116	C₂×D₄×C₃₁	—	2	2	no	—
117	C₂×D₄×C₃₁	—	2	2	no	—
118	C₂²×C₄×C₃₁	—	2	1	no	—
119	C₂²×C₄×C₃₁	—	2	1	no	—
120	C₂²×C₄×C₃₁	—	2	2	no	—
121	C₂²×C₄×C₃₁	—	2	1	no	—
122	C₂²×C₄×C₃₁	—	2	2	no	—
123	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₃₁	—	4	4	no	—
129	SD₁₆×C₃₁	—	4	4	no	—
130	C₂×C₈×C₃₁	—	2	2	no	—
131	C₂×C₈×C₃₁	—	2	1	no	—
132	C₂×C₈×C₃₁	—	2	1	no	—
133	C₂×C₈×C₃₁	—	2	2	no	—
134	C₂×C₈×C₃₁	—	2	2	no	—
135	C₂×C₈×C₃₁	—	2	2	no	—
136	C₂×C₈×C₃₁	—	2	2	no	—
137	C₄⋊C₄×C₃₁	—	2	8	no	—
138	C₄⋊C₄×C₃₁	—	2	8	no	—
139	C₄⋊C₄×C₃₁	—	2	8	no	—
140	C₄⋊C₄×C₃₁	—	2	4	no	—
141	C₄⋊C₄×C₃₁	—	2	4	no	—
142	C₄⋊C₄×C₃₁	—	2	2	no	—
143	C₄⋊C₄×C₃₁	—	2	4	no	—
144	C₄⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	4	yes	—
149	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₃₁	—	4	4	no	—
151	C₂²⋊C₄×C₃₁	—	4	2	no	—
152	C₂²⋊C₄×C₃₁	—	4	2	no	—
153	C₂²⋊C₄×C₃₁	—	8	2	no	—
154	C₄²×C₃₁	—	2	8	no	—
155	C₄²×C₃₁	—	2	4	no	—
156	C₄²×C₃₁	—	2	2	no	—
157	C₄²×C₃₁	—	2	2	no	—
158	C₄²×C₃₁	—	8	1	no	—
159	C₄²×C₃₁	C₂×D₄	1	2	yes	—
160	C₄²×C₃₁	C₂×D₄	1	2	yes	—
161	#25941	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₃₁	—	4	1	no	—
163	C₂³×C₃₁	—	4	2	no	—
164	C₂³×C₃₁	—	4	2	no	—
165	C₂³×C₃₁	—	4	1	no	—
166	C₂³×C₃₁	—	4	1	no	—
167	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₃₁	—	2	2	no	—
169	Q₈×C₃₁	—	2	4	no	—
170	Q₈×C₃₁	—	4	4	no	—
171	Q₈×C₃₁	—	4	8	no	—
172	Q₈×C₃₁	—	4	1	no	—
173	Q₈×C₃₁	—	4	1	no	—
174	Q₈×C₃₁	—	4	2	no	—
175	Q₈×C₃₁	#124	1	4	yes	—
176	D₄×C₃₁	—	4	1	no	—
177	D₄×C₃₁	—	4	1	no	—
178	D₄×C₃₁	—	4	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	1	no	—
183	C₂×C₄×C₃₁	—	2	1	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	4	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	—	2	2	no	—
192	C₂×C₄×C₃₁	—	4	4	no	—
193	C₂×C₄×C₃₁	—	4	1	no	—
194	C₂×C₄×C₃₁	—	4	1	no	—
195	C₂×C₄×C₃₁	—	4	1	no	—
196	C₂×C₄×C₃₁	—	4	2	no	—
197	C₂×C₄×C₃₁	—	4	2	no	—
198	C₂×C₄×C₃₁	—	4	2	no	—
199	C₂×C₄×C₃₁	—	4	2	no	—
200	C₂×C₄×C₃₁	#120	1	2	yes	—
201	C₂×C₄×C₃₁	#120	1	2	yes	—
202	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
205	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
206	C₈×C₃₁	—	4	1	no	—
207	C₈×C₃₁	—	4	1	no	—
208	C₈×C₃₁	—	4	2	no	—
209	C₂×#557	C₂×C₃₁	1	1	yes	characteristic, complemented
210	C₂×#489	C₂×C₃₁	1	1	yes	characteristic
211	C₂×#464	C₂×C₃₁	1	1	yes	characteristic
212	#2592	C₂×C₃₁	1	1	yes	characteristic
213	#2026	C₂×C₃₁	1	2	yes	complemented
214	#2025	C₂×C₃₁	1	2	yes	—
215	#1987	C₂×C₃₁	1	1	yes	characteristic, complemented
216	#1985	C₂×C₃₁	1	1	yes	characteristic, complemented
217	#1880	C₂×C₃₁	1	2	yes	—
218	#1878	C₂×C₃₁	1	2	yes	complemented
219	#1763	C₂×C₃₁	1	1	yes	characteristic, complemented
220	C₂²×C₃₁	—	8	2	no	—
221	C₂²×C₃₁	—	8	2	no	—
222	C₂²×C₃₁	—	8	1	no	—
223	C₂²×C₃₁	—	8	1	no	—
224	C₂²×C₃₁	—	8	1	no	—
225	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
226	C₂²×C₃₁	#548	1	2	yes	—
227	C₂²×C₃₁	#575	1	2	yes	—
228	C₂²×C₃₁	#577	1	1	yes	characteristic
229	C₂²×C₃₁	#578	1	1	yes	characteristic
230	C₄×C₃₁	—	2	4	no	—
231	C₄×C₃₁	—	2	2	no	—
232	C₄×C₃₁	—	2	2	no	—
233	C₄×C₃₁	—	4	2	no	—
234	C₄×C₃₁	—	4	4	no	—
235	C₄×C₃₁	—	4	2	no	—
236	C₄×C₃₁	—	4	2	no	—
237	C₄×C₃₁	—	8	2	no	—
238	C₄×C₃₁	—	8	1	no	—
239	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
240	C₄×C₃₁	#536	1	1	yes	characteristic
241	C₄×C₃₁	#548	1	2	yes	—
242	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
243	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
244	#557	—	2	4	no	—
245	#557	—	2	4	no	—
246	C₂×C₄⋊Q₈	—	2	1	no	—
247	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
248	C₂×#125	—	2	2	no	—
249	C₂×#125	C₂²×C₃₁	1	2	yes	—
250	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
251	C₂×C₄×Q₈	—	2	1	no	—
252	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
253	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
255	#489	—	2	4	no	—
256	#464	—	2	4	no	—
257	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
258	C₂×#103	C₂²×C₃₁	1	2	yes	—
259	C₂×#103	C₂²×C₃₁	1	2	yes	—
260	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
261	C₂×#102	C₂²×C₃₁	1	2	yes	—
262	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
263	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
264	#397	—	2	1	no	—
265	#393	—	2	1	no	—
266	#391	C₂²×C₃₁	1	2	yes	—
267	#390	C₂²×C₃₁	1	2	yes	—
268	#388	—	2	2	no	—
269	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
270	#340	C₂²×C₃₁	1	2	yes	—
271	#340	C₂²×C₃₁	1	2	yes	—
272	#340	C₂²×C₃₁	1	2	yes	—
273	#336	C₂²×C₃₁	1	2	yes	—
274	#336	C₂²×C₃₁	1	2	yes	—
275	C₂×C₃₁	—	16	1	no	—
276	C₂×C₃₁	#2436	1	1	yes	characteristic
277	C₂×C₃₁	#3005	1	1	yes	characteristic
278	C₂×C₃₁	#3013	1	1	yes	characteristic
279	C₂×C₃₁	#3371	1	2	yes	—
280	C₂×C₃₁	#3377	1	2	yes	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
283	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
284	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
293	C₄⋊Q₈	—	2	8	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
296	#125	—	2	16	no	—
297	#125	—	2	4	no	—
298	#125	—	2	4	no	—
299	#124	—	2	2	no	—
300	#124	—	2	2	no	—
301	C₄×Q₈	—	2	8	no	—
302	C₄×Q₈	—	2	4	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	D₄×C₃₁	1	4	yes	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
314	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
326	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
327	C₄⋊C₈	—	2	2	no	—
328	#103	—	2	4	no	—
329	#103	—	2	2	no	—
330	#103	—	2	4	no	—
331	#102	—	2	2	no	—
332	#102	—	2	4	no	—
333	#97	—	2	2	no	—
334	#95	—	2	1	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	C₃₁	#25941	1	1	yes	characteristic, direct product factor, Sylow
338	C₂⁴	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	—	4	4	no	—
349	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
350	C₂×Q₈	#41×C₃₁	1	4	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
365	Q₁₆	—	4	4	no	—
366	SD₁₆	—	4	4	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
386	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	8	2	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	8	1	no	—
396	C₄²	C₂×D₄×C₃₁	1	2	yes	—
397	C₄²	C₂×D₄×C₃₁	1	2	yes	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	4	no	—
406	Q₈	—	4	4	no	—
407	Q₈	—	4	8	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	4	2	no	—
411	Q₈	C₃₁×#124	1	4	yes	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	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	—	4	4	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	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	C₃₁×#120	1	2	yes	—
437	C₂×C₄	C₃₁×#120	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
441	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
442	C₈	—	4	1	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
451	C₂²	C₃₁×#548	1	2	yes	—
452	C₂²	C₃₁×#575	1	2	yes	—
453	C₂²	C₃₁×#577	1	1	yes	characteristic
454	C₂²	C₃₁×#578	1	1	yes	characteristic
455	C₄	—	2	4	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	2	no	—
463	C₄	—	8	1	no	—
464	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
465	C₄	C₃₁×#536	1	1	yes	characteristic
466	C₄	C₃₁×#548	1	2	yes	—
467	C₂	—	16	1	no	—
468	C₂	C₃₁×#2436	1	1	yes	characteristic
469	C₂	C₃₁×#3005	1	1	yes	characteristic
470	C₂	C₃₁×#3013	1	1	yes	characteristic
471	C₂	C₃₁×#3371	1	2	yes	—
472	C₂	C₃₁×#3377	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 ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#557	C₂	semidirect
5. C₃₁×#2026	C₂	semidirect
7. C₃₁×#1987	C₂	semidirect
8. C₃₁×#1985	C₂	semidirect
10. C₃₁×#1878	C₂	semidirect
11. C₃₁×#1763	C₂	semidirect
161. #25941	C₃₁	direct (N × H)
209. C₂×#557	C₂×C₃₁	semidirect
213. #2026	C₂×C₃₁	semidirect
215. #1987	C₂×C₃₁	semidirect
216. #1985	C₂×C₃₁	semidirect
218. #1878	C₂×C₃₁	semidirect
219. #1763	C₂×C₃₁	semidirect
337. C₃₁	#25941	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×#557	2
C₂×C₃₁×#489	2
C₂×C₃₁×#464	2
C₃₁×#2592	2
C₃₁×#2026	2
C₃₁×#2025	2
C₃₁×#1987	2
C₃₁×#1985	2
C₃₁×#1880	2
C₃₁×#1878	2
C₃₁×#1763	2
#25941	31

Subgroups — C31×#25941 #21482700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25941 #21482700