Subgroups — C₃₁×#8947 #21465706

Order 7936.

672 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₃₁	C₄	1	1	yes	characteristic
9	C₂³×C₈×C₃₁	—	2	1	no	—
10	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₄×D₈×C₃₁	—	2	2	no	—
13	C₄×D₈×C₃₁	—	2	2	no	—
14	C₈×D₄×C₃₁	—	2	2	no	—
15	C₈×D₄×C₃₁	—	2	2	no	—
16	C₂×C₃₁×#107	C₄	1	1	yes	characteristic
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#102	C₄	1	1	yes	characteristic
20	C₂×C₃₁×#102	C₄	1	1	yes	characteristic
21	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
22	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
23	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
24	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×D₄⋊C₈	—	2	2	no	—
28	C₃₁×D₄⋊C₈	—	2	2	no	—
29	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	—	2	1	no	—
32	C₂³×C₄×C₃₁	—	2	1	no	—
33	C₂×D₈×C₃₁	—	2	2	no	—
34	C₂×D₈×C₃₁	—	2	2	no	—
35	C₂×D₈×C₃₁	C₈	1	4	yes	complemented
36	C₂²×C₈×C₃₁	—	2	4	no	—
37	C₂²×C₈×C₃₁	—	2	1	no	—
38	C₂²×C₈×C₃₁	—	2	1	no	—
39	C₂²×C₈×C₃₁	—	2	1	no	—
40	C₂²×C₈×C₃₁	—	4	2	no	—
41	C₂²×C₈×C₃₁	—	4	2	no	—
42	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
46	C₄×D₄×C₃₁	—	2	1	no	—
47	C₄×D₄×C₃₁	—	2	1	no	—
48	C₄×D₄×C₃₁	—	2	1	no	—
49	C₄×D₄×C₃₁	—	2	1	no	—
50	C₄×D₄×C₃₁	—	2	1	no	—
51	C₄×D₄×C₃₁	—	2	1	no	—
52	C₄×D₄×C₃₁	D₄	1	2	yes	—
53	C₄×D₄×C₃₁	D₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
59	C₃₁×#107	—	2	2	no	—
60	C₃₁×C₄⋊C₈	—	2	1	no	—
61	C₃₁×C₄⋊C₈	—	2	1	no	—
62	C₃₁×C₄⋊C₈	—	2	1	no	—
63	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
64	C₃₁×#102	—	2	2	no	—
65	C₃₁×#102	—	2	2	no	—
66	C₃₁×C₂²⋊C₈	—	2	4	no	—
67	C₃₁×C₂²⋊C₈	—	4	2	no	—
68	C₃₁×C₂²⋊C₈	—	4	2	no	—
69	C₄×C₈×C₃₁	—	2	1	no	—
70	C₄×C₈×C₃₁	—	2	1	no	—
71	C₄×C₈×C₃₁	—	2	1	no	—
72	C₄×C₈×C₃₁	—	2	1	no	—
73	C₄×C₈×C₃₁	—	2	1	no	—
74	C₄×C₈×C₃₁	—	2	1	no	—
75	C₂⁴×C₃₁	—	2	1	no	—
76	C₂⁴×C₃₁	—	2	1	no	—
77	C₂×D₄×C₃₁	—	2	1	no	—
78	C₂×D₄×C₃₁	—	2	1	no	—
79	C₂×D₄×C₃₁	—	2	1	no	—
80	C₂×D₄×C₃₁	—	2	1	no	—
81	C₂×D₄×C₃₁	—	2	1	no	—
82	C₂×D₄×C₃₁	—	2	1	no	—
83	C₂×D₄×C₃₁	—	2	1	no	—
84	C₂×D₄×C₃₁	—	2	1	no	—
85	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
86	C₂×D₄×C₃₁	C₂×C₈	1	2	yes	—
87	C₂×D₄×C₃₁	C₂×C₈	1	2	yes	complemented
88	C₂×D₄×C₃₁	M₁₆	1	2	yes	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	1	no	—
93	C₂²×C₄×C₃₁	—	4	1	no	—
94	C₂²×C₄×C₃₁	—	4	1	no	—
95	C₂²×C₄×C₃₁	—	4	1	no	—
96	C₂²×C₄×C₃₁	—	4	1	no	—
97	C₂²×C₄×C₃₁	—	4	1	no	—
98	C₂²×C₄×C₃₁	—	4	1	no	—
99	C₂²×C₄×C₃₁	—	4	1	no	—
100	C₂²×C₄×C₃₁	—	4	1	no	—
101	C₂²×C₄×C₃₁	—	4	1	no	—
102	C₂²×C₄×C₃₁	—	4	1	no	—
103	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
106	D₈×C₃₁	—	2	8	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	2	1	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	2	1	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	—	2	1	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	1	no	—
119	C₂×C₈×C₃₁	—	4	8	no	—
120	C₂×C₈×C₃₁	—	4	1	no	—
121	C₂×C₈×C₃₁	—	4	1	no	—
122	C₂×C₈×C₃₁	—	4	1	no	—
123	C₂×C₈×C₃₁	—	4	1	no	—
124	C₂×C₈×C₃₁	—	4	1	no	—
125	C₂×C₈×C₃₁	—	4	1	no	—
126	C₂×C₈×C₃₁	—	4	1	no	—
127	C₂×C₈×C₃₁	C₂×C₈	1	2	yes	complemented
128	C₂×C₈×C₃₁	D₈	1	2	yes	complemented
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	C₂²⋊C₄	1	2	yes	—
133	C₂²⋊C₄×C₃₁	—	2	2	no	—
134	C₂²⋊C₄×C₃₁	—	2	2	no	—
135	C₂²⋊C₄×C₃₁	—	4	1	no	—
136	C₂²⋊C₄×C₃₁	—	4	1	no	—
137	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₃₁	#41	1	1	yes	characteristic
141	#8947	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	—	2	2	no	—
143	C₂³×C₃₁	—	2	2	no	—
144	C₂³×C₃₁	—	2	2	no	—
145	C₂³×C₃₁	—	2	2	no	—
146	C₂³×C₃₁	—	4	1	no	—
147	C₂³×C₃₁	—	4	1	no	—
148	C₂³×C₃₁	—	4	1	no	—
149	C₂³×C₃₁	—	4	1	no	—
150	C₂³×C₃₁	—	4	1	no	—
151	C₂³×C₃₁	—	4	1	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	C₄×D₄	1	1	yes	characteristic
157	D₄×C₃₁	—	2	2	no	—
158	D₄×C₃₁	—	2	2	no	—
159	D₄×C₃₁	—	2	2	no	—
160	D₄×C₃₁	—	2	2	no	—
161	D₄×C₃₁	—	2	2	no	—
162	D₄×C₃₁	—	4	1	no	—
163	D₄×C₃₁	—	4	1	no	—
164	D₄×C₃₁	C₂²⋊C₈	1	4	yes	complemented
165	C₂×C₄×C₃₁	—	2	1	no	—
166	C₂×C₄×C₃₁	—	2	1	no	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	4	1	no	—
169	C₂×C₄×C₃₁	—	4	1	no	—
170	C₂×C₄×C₃₁	—	4	2	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	—	4	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	1	no	—
175	C₂×C₄×C₃₁	—	4	1	no	—
176	C₂×C₄×C₃₁	—	4	1	no	—
177	C₂×C₄×C₃₁	—	8	1	no	—
178	C₂×C₄×C₃₁	—	8	1	no	—
179	C₂×C₄×C₃₁	—	8	1	no	—
180	C₂×C₄×C₃₁	—	8	1	no	—
181	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
184	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
187	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
189	C₂×C₄×C₃₁	#131	1	1	yes	characteristic
190	C₂×C₄×C₃₁	#131	1	1	yes	characteristic
191	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₃₁	#135	1	1	yes	characteristic
193	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₈×C₃₁	—	2	2	no	—
196	C₈×C₃₁	—	2	2	no	—
197	C₈×C₃₁	—	4	2	no	—
198	C₈×C₃₁	—	4	1	no	—
199	C₈×C₃₁	—	4	2	no	—
200	C₈×C₃₁	—	4	1	no	—
201	C₈×C₃₁	—	8	1	no	—
202	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic
203	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
204	#1954	C₂×C₃₁	1	1	yes	characteristic, complemented
205	C₂×D₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
206	C₂×D₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
207	#1277	C₂×C₃₁	1	1	yes	characteristic, complemented
208	#1273	C₂×C₃₁	1	1	yes	characteristic, complemented
209	C₂²×C₃₁	—	2	4	no	—
210	C₂²×C₃₁	—	4	2	no	—
211	C₂²×C₃₁	—	4	2	no	—
212	C₂²×C₃₁	—	4	2	no	—
213	C₂²×C₃₁	—	4	2	no	—
214	C₂²×C₃₁	—	4	2	no	—
215	C₂²×C₃₁	—	4	2	no	—
216	C₂²×C₃₁	—	4	2	no	—
217	C₂²×C₃₁	—	4	2	no	—
218	C₂²×C₃₁	—	4	2	no	—
219	C₂²×C₃₁	—	8	1	no	—
220	C₂²×C₃₁	—	8	1	no	—
221	C₂²×C₃₁	—	8	1	no	—
222	C₂²×C₃₁	—	8	1	no	—
223	C₂²×C₃₁	#386	1	1	yes	characteristic
224	C₂²×C₃₁	C₈×D₄	1	1	yes	characteristic
225	C₂²×C₃₁	#435	1	1	yes	characteristic
226	C₂²×C₃₁	C₄×D₈	1	1	yes	characteristic
227	C₂²×C₃₁	#442	1	1	yes	characteristic
228	C₂²×C₃₁	#443	1	1	yes	characteristic
229	C₂²×C₃₁	#444	1	1	yes	characteristic
230	C₄×C₃₁	—	2	1	no	—
231	C₄×C₃₁	—	2	1	no	—
232	C₄×C₃₁	—	4	2	no	—
233	C₄×C₃₁	—	8	1	no	—
234	C₄×C₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
235	C₄×C₃₁	#408	1	1	yes	characteristic
236	C₄×C₃₁	C₈×D₄	1	1	yes	characteristic
237	C₄×C₃₁	#435	1	1	yes	characteristic
238	C₄×C₃₁	#447	1	1	yes	characteristic
239	C₄×C₃₁	#449	1	1	yes	characteristic
240	C₄×C₃₁	#459	1	1	yes	characteristic
241	C₄×C₃₁	#463	1	1	yes	characteristic
242	C₂²×D₈	C₄×C₃₁	1	1	yes	characteristic
243	C₂³×C₈	—	2	1	no	—
244	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
246	C₄×D₈	—	2	2	no	—
247	C₄×D₈	—	2	2	no	—
248	C₈×D₄	—	2	2	no	—
249	C₈×D₄	—	2	2	no	—
250	C₂×#107	C₄×C₃₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
253	C₂×#102	C₄×C₃₁	1	1	yes	characteristic
254	C₂×#102	C₄×C₃₁	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	—	2	1	no	—
256	C₂×C₂²⋊C₈	—	2	1	no	—
257	C₂×C₂²⋊C₈	—	2	1	no	—
258	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
261	D₄⋊C₈	—	2	2	no	—
262	D₄⋊C₈	—	2	2	no	—
263	C₂×C₃₁	—	4	4	no	—
264	C₂×C₃₁	—	8	2	no	—
265	C₂×C₃₁	C₈×D₈	1	1	yes	characteristic
266	C₂×C₃₁	#1580	1	1	yes	characteristic
267	C₂×C₃₁	#1581	1	1	yes	characteristic
268	C₂×C₃₁	#1586	1	1	yes	characteristic
269	C₂×C₃₁	#1869	1	1	yes	characteristic
270	C₂×C₃₁	#1876	1	1	yes	characteristic
271	C₂×C₃₁	#1879	1	1	yes	characteristic
272	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
273	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	2	1	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	C₈×C₃₁	1	4	yes	complemented
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	4	2	no	—
284	C₂²×C₈	—	4	2	no	—
285	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	D₄×C₃₁	1	2	yes	—
296	C₄×D₄	D₄×C₃₁	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	C₂²⋊C₈	—	2	4	no	—
310	C₂²⋊C₈	—	4	2	no	—
311	C₂²⋊C₈	—	4	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	—	2	1	no	—
318	C₃₁	#8947	1	1	yes	characteristic, direct product factor, Sylow
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
330	C₂×D₄	C₂×C₈×C₃₁	1	2	yes	—
331	C₂×D₄	C₂×C₈×C₃₁	1	2	yes	complemented
332	C₂×D₄	M₁₆×C₃₁	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
349	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
350	D₈	—	2	8	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	4	8	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	C₂×C₈×C₃₁	1	2	yes	complemented
372	C₂×C₈	D₈×C₃₁	1	2	yes	complemented
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
382	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
383	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
384	C₄²	#41×C₃₁	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	1	no	—
407	D₄	C₃₁×C₂²⋊C₈	1	4	yes	complemented
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	—	8	1	no	—
424	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
426	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
427	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
428	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
429	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
431	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
432	C₂×C₄	C₃₁×#131	1	1	yes	characteristic
433	C₂×C₄	C₃₁×#131	1	1	yes	characteristic
434	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
435	C₂×C₄	C₃₁×#135	1	1	yes	characteristic
436	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	2	no	—
443	C₈	—	4	1	no	—
444	C₈	—	8	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	C₃₁×#386	1	1	yes	characteristic
460	C₂²	C₈×D₄×C₃₁	1	1	yes	characteristic
461	C₂²	C₃₁×#435	1	1	yes	characteristic
462	C₂²	C₄×D₈×C₃₁	1	1	yes	characteristic
463	C₂²	C₃₁×#442	1	1	yes	characteristic
464	C₂²	C₃₁×#443	1	1	yes	characteristic
465	C₂²	C₃₁×#444	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×C₃₁×C₂²⋊C₈	1	1	yes	characteristic
471	C₄	C₃₁×#408	1	1	yes	characteristic
472	C₄	C₈×D₄×C₃₁	1	1	yes	characteristic
473	C₄	C₃₁×#435	1	1	yes	characteristic
474	C₄	C₃₁×#447	1	1	yes	characteristic
475	C₄	C₃₁×#449	1	1	yes	characteristic
476	C₄	C₃₁×#459	1	1	yes	characteristic
477	C₄	C₃₁×#463	1	1	yes	characteristic
478	C₂	—	4	4	no	—
479	C₂	—	8	2	no	—
480	C₂	C₈×D₈×C₃₁	1	1	yes	characteristic
481	C₂	C₃₁×#1580	1	1	yes	characteristic
482	C₂	C₃₁×#1581	1	1	yes	characteristic
483	C₂	C₃₁×#1586	1	1	yes	characteristic
484	C₂	C₃₁×#1869	1	1	yes	characteristic
485	C₂	C₃₁×#1876	1	1	yes	characteristic
486	C₂	C₃₁×#1879	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
socle	C₂³×C₃₁	C₄×D₄
prime radical	C₂²×D₈×C₃₁	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₄×C₃₁	C₂	semidirect
3. C₃₁×#1954	C₂	semidirect
4. C₂×C₃₁×D₄⋊C₈	C₂	semidirect
5. C₂×C₃₁×D₄⋊C₈	C₂	semidirect
6. C₃₁×#1277	C₂	semidirect
7. C₃₁×#1273	C₂	semidirect
35. C₂×D₈×C₃₁	C₈	semidirect
87. C₂×D₄×C₃₁	C₂×C₈	semidirect
127. C₂×C₈×C₃₁	C₂×C₈	semidirect
128. C₂×C₈×C₃₁	D₈	semidirect
141. #8947	C₃₁	direct (N × H)
164. D₄×C₃₁	C₂²⋊C₈	semidirect
203. C₂×C₈×D₄	C₂×C₃₁	semidirect
204. #1954	C₂×C₃₁	semidirect
205. C₂×D₄⋊C₈	C₂×C₃₁	semidirect
206. C₂×D₄⋊C₈	C₂×C₃₁	semidirect
207. #1277	C₂×C₃₁	semidirect
208. #1273	C₂×C₃₁	semidirect
278. C₂×D₈	C₈×C₃₁	semidirect
318. C₃₁	#8947	direct (N × H)
331. C₂×D₄	C₂×C₈×C₃₁	semidirect
371. C₂×C₈	C₂×C₈×C₃₁	semidirect
372. C₂×C₈	D₈×C₃₁	semidirect
407. D₄	C₃₁×C₂²⋊C₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×D₈×C₃₁	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1954	2
C₂×C₃₁×D₄⋊C₈	2
C₃₁×#1277	2
C₃₁×#1273	2
#8947	31

Subgroups — C31×#8947 #21465706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#8947 #21465706