Subgroups — C₂×C₃₁×#2611 #21491631

Order 7936.

2638 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2611	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#399	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃₁×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#397	C₂	1	1	yes	maximal, characteristic
8	C₂×C₃₁×#389	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#388	C₂	1	2	yes	maximal
10	C₂×C₃₁×#387	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#385	C₂	1	2	yes	maximal
12	C₂×C₃₁×#376	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#125	—	2	8	no	—
15	C₂×C₃₁×#125	C₂²	1	8	yes	complemented
16	C₂×C₃₁×#117	—	2	8	no	—
17	C₂×C₃₁×#117	C₂²	1	8	yes	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
32	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#400	C₂²	1	8	yes	complemented
34	C₃₁×#399	C₂²	1	8	yes	—
35	C₃₁×#398	C₂²	1	8	yes	complemented
36	C₃₁×#397	C₂²	1	8	yes	—
37	C₃₁×#389	C₂²	1	16	yes	complemented
38	C₃₁×#388	C₂²	1	16	yes	—
39	C₃₁×#387	C₂²	1	16	yes	complemented
40	C₃₁×#385	C₂²	1	16	yes	—
41	C₃₁×#376	C₂²	1	8	yes	complemented
42	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#95	C₂²	1	2	yes	—
44	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#95	C₂²	1	2	yes	—
46	C₂×C₃₁×#95	C₂²	1	2	yes	—
47	C₂×C₃₁×#95	C₂²	1	2	yes	—
48	C₂×C₃₁×#95	C₂²	1	2	yes	—
49	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₃₁	—	2	4	no	—
51	C₂³×C₄×C₃₁	—	2	4	no	—
52	C₂³×C₄×C₃₁	—	2	4	no	—
53	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
54	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
57	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
63	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×#125	—	2	32	no	—
65	C₃₁×#117	—	2	32	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
69	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
70	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
71	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
72	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
73	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
74	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
90	C₂×C₄²×C₃₁	—	2	4	no	—
91	C₂×C₄²×C₃₁	—	2	8	no	—
92	C₂×C₄²×C₃₁	D₄	1	8	yes	—
93	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
94	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
95	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
96	C₃₁×#95	C₂³	1	4	yes	—
97	C₃₁×#95	C₂³	1	8	yes	—
98	C₃₁×#95	C₂³	1	4	yes	—
99	C₃₁×#95	C₂³	1	8	yes	—
100	C₃₁×#95	C₂³	1	8	yes	—
101	C₃₁×#95	C₂³	1	8	yes	—
102	C₃₁×#95	C₂³	1	8	yes	—
103	C₂⁴×C₃₁	—	2	2	no	—
104	C₂⁴×C₃₁	—	2	4	no	—
105	C₂⁴×C₃₁	—	2	2	no	—
106	C₂⁴×C₃₁	—	2	4	no	—
107	C₂⁴×C₃₁	#41	1	4	yes	—
108	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
109	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	—	2	32	no	—
111	C₂²×C₄×C₃₁	—	2	2	no	—
112	C₂²×C₄×C₃₁	—	2	4	no	—
113	C₂²×C₄×C₃₁	—	2	4	no	—
114	C₂²×C₄×C₃₁	—	2	8	no	—
115	C₂²×C₄×C₃₁	—	2	2	no	—
116	C₂²×C₄×C₃₁	—	2	2	no	—
117	C₂²×C₄×C₃₁	—	2	2	no	—
118	C₂²×C₄×C₃₁	—	2	4	no	—
119	C₂²×C₄×C₃₁	—	2	4	no	—
120	C₂²×C₄×C₃₁	—	2	8	no	—
121	C₂²×C₄×C₃₁	—	2	8	no	—
122	C₂²×C₄×C₃₁	—	2	2	no	—
123	C₂²×C₄×C₃₁	—	2	2	no	—
124	C₂²×C₄×C₃₁	—	2	4	no	—
125	C₂²×C₄×C₃₁	—	2	4	no	—
126	C₂²×C₄×C₃₁	—	2	4	no	—
127	C₂²×C₄×C₃₁	—	2	4	no	—
128	C₂²×C₄×C₃₁	—	2	4	no	—
129	C₂²×C₄×C₃₁	—	2	4	no	—
130	C₂²×C₄×C₃₁	—	2	4	no	—
131	C₂²×C₄×C₃₁	—	2	4	no	—
132	C₂²×C₄×C₃₁	—	2	4	no	—
133	C₂²×C₄×C₃₁	—	2	4	no	—
134	C₂²×C₄×C₃₁	—	2	4	no	—
135	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₃₁	#41	1	8	yes	—
139	C₂²×C₄×C₃₁	#41	1	4	yes	—
140	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
150	C₄⋊C₄×C₃₁	—	2	8	no	—
151	C₄⋊C₄×C₃₁	—	2	8	no	—
152	C₄⋊C₄×C₃₁	—	2	16	no	—
153	C₄⋊C₄×C₃₁	—	2	8	no	—
154	C₄⋊C₄×C₃₁	—	2	8	no	—
155	C₄⋊C₄×C₃₁	—	2	16	no	—
156	C₄⋊C₄×C₃₁	—	2	16	no	—
157	C₄⋊C₄×C₃₁	—	2	16	no	—
158	C₂²⋊C₄×C₃₁	—	2	16	no	—
159	C₂²⋊C₄×C₃₁	—	2	8	no	—
160	C₂²⋊C₄×C₃₁	—	2	8	no	—
161	C₂²⋊C₄×C₃₁	—	2	16	no	—
162	C₄²×C₃₁	—	2	8	no	—
163	C₄²×C₃₁	—	2	16	no	—
164	C₄²×C₃₁	C₂×D₄	1	16	yes	—
165	C₂×#2611	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₃₁	—	2	8	no	—
167	C₂³×C₃₁	—	2	16	no	—
168	C₂³×C₃₁	—	2	2	no	—
169	C₂³×C₃₁	—	2	4	no	—
170	C₂³×C₃₁	—	2	2	no	—
171	C₂³×C₃₁	—	2	4	no	—
172	C₂³×C₃₁	—	4	4	no	—
173	C₂³×C₃₁	—	4	4	no	—
174	C₂³×C₃₁	—	4	8	no	—
175	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
176	C₂³×C₃₁	C₂×#41	1	4	yes	—
177	C₂³×C₃₁	C₂×#41	1	2	yes	—
178	C₂³×C₃₁	C₂×#41	1	2	yes	—
179	C₂³×C₃₁	C₂×#41	1	4	yes	—
180	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
181	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
182	C₂×C₄×C₃₁	—	2	32	no	—
183	C₂×C₄×C₃₁	—	2	8	no	—
184	C₂×C₄×C₃₁	—	2	8	no	—
185	C₂×C₄×C₃₁	—	2	8	no	—
186	C₂×C₄×C₃₁	—	2	8	no	—
187	C₂×C₄×C₃₁	—	2	16	no	—
188	C₂×C₄×C₃₁	—	2	2	no	—
189	C₂×C₄×C₃₁	—	2	4	no	—
190	C₂×C₄×C₃₁	—	2	4	no	—
191	C₂×C₄×C₃₁	—	2	2	no	—
192	C₂×C₄×C₃₁	—	2	2	no	—
193	C₂×C₄×C₃₁	—	2	2	no	—
194	C₂×C₄×C₃₁	—	2	4	no	—
195	C₂×C₄×C₃₁	—	2	4	no	—
196	C₂×C₄×C₃₁	—	2	2	no	—
197	C₂×C₄×C₃₁	—	2	2	no	—
198	C₂×C₄×C₃₁	—	2	4	no	—
199	C₂×C₄×C₃₁	—	2	4	no	—
200	C₂×C₄×C₃₁	—	2	4	no	—
201	C₂×C₄×C₃₁	—	2	4	no	—
202	C₂×C₄×C₃₁	—	2	4	no	—
203	C₂×C₄×C₃₁	—	2	4	no	—
204	C₂×C₄×C₃₁	—	2	4	no	—
205	C₂×C₄×C₃₁	—	2	4	no	—
206	C₂×C₄×C₃₁	—	2	4	no	—
207	C₂×C₄×C₃₁	—	2	4	no	—
208	C₂×C₄×C₃₁	—	2	4	no	—
209	C₂×C₄×C₃₁	—	4	8	no	—
210	C₂×C₄×C₃₁	—	4	4	no	—
211	C₂×C₄×C₃₁	—	4	8	no	—
212	C₂×C₄×C₃₁	—	4	4	no	—
213	C₂×C₄×C₃₁	—	4	8	no	—
214	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
218	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
219	C₂²×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
220	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic
221	#2611	C₂×C₃₁	1	16	yes	direct product factor
222	C₂×#400	C₂×C₃₁	1	1	yes	characteristic, complemented
223	C₂×#399	C₂×C₃₁	1	1	yes	characteristic
224	C₂×#398	C₂×C₃₁	1	1	yes	characteristic, complemented
225	C₂×#397	C₂×C₃₁	1	1	yes	characteristic
226	C₂×#389	C₂×C₃₁	1	2	yes	complemented
227	C₂×#388	C₂×C₃₁	1	2	yes	—
228	C₂×#387	C₂×C₃₁	1	2	yes	complemented
229	C₂×#385	C₂×C₃₁	1	2	yes	—
230	C₂×#376	C₂×C₃₁	1	1	yes	characteristic, complemented
231	C₂²×C₃₁	—	2	4	no	—
232	C₂²×C₃₁	—	2	8	no	—
233	C₂²×C₃₁	—	4	16	no	—
234	C₂²×C₃₁	—	4	2	no	—
235	C₂²×C₃₁	—	4	2	no	—
236	C₂²×C₃₁	—	4	4	no	—
237	C₂²×C₃₁	#525	1	4	yes	—
238	C₂²×C₃₁	#532	1	4	yes	—
239	C₂²×C₃₁	#536	1	4	yes	—
240	C₂²×C₃₁	#552	1	8	yes	—
241	C₂²×C₃₁	#552	1	8	yes	—
242	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
244	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
245	C₂²×C₃₁	C₂²×#41	1	2	yes	—
246	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
247	C₄×C₃₁	—	2	4	no	—
248	C₄×C₃₁	—	2	4	no	—
249	C₄×C₃₁	—	2	4	no	—
250	C₄×C₃₁	—	2	4	no	—
251	C₄×C₃₁	—	2	8	no	—
252	C₄×C₃₁	—	4	4	no	—
253	C₄×C₃₁	—	4	2	no	—
254	C₄×C₃₁	—	4	4	no	—
255	C₄×C₃₁	—	4	2	no	—
256	C₄×C₃₁	—	4	4	no	—
257	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
258	C₂×#125	—	2	8	no	—
259	C₂×#125	C₂²×C₃₁	1	8	yes	complemented
260	C₂×#117	—	2	8	no	—
261	C₂×#117	C₂²×C₃₁	1	8	yes	—
262	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
269	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
270	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
274	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
275	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
276	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
277	#400	C₂²×C₃₁	1	8	yes	complemented
278	#399	C₂²×C₃₁	1	8	yes	—
279	#398	C₂²×C₃₁	1	8	yes	complemented
280	#397	C₂²×C₃₁	1	8	yes	—
281	#389	C₂²×C₃₁	1	16	yes	complemented
282	#388	C₂²×C₃₁	1	16	yes	—
283	#387	C₂²×C₃₁	1	16	yes	complemented
284	#385	C₂²×C₃₁	1	16	yes	—
285	#376	C₂²×C₃₁	1	8	yes	complemented
286	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
287	C₂×#95	C₂²×C₃₁	1	2	yes	—
288	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
289	C₂×#95	C₂²×C₃₁	1	2	yes	—
290	C₂×#95	C₂²×C₃₁	1	2	yes	—
291	C₂×#95	C₂²×C₃₁	1	2	yes	—
292	C₂×#95	C₂²×C₃₁	1	2	yes	—
293	C₂×C₃₁	—	4	4	no	—
294	C₂×C₃₁	#2611	1	8	yes	direct product factor
295	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
296	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
297	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
298	C₂×C₃₁	C₂×#552	1	2	yes	—
299	C₂×C₃₁	C₂×#552	1	2	yes	—
300	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
301	C₂³×C₄	—	2	4	no	—
302	C₂³×C₄	—	2	4	no	—
303	C₂³×C₄	—	2	4	no	—
304	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
305	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
306	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
309	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
310	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
314	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
315	#125	—	2	32	no	—
316	#117	—	2	32	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	8	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	8	no	—
323	C₂×C₄⋊C₄	—	2	8	no	—
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
328	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
329	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
332	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	4	no	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	2	8	no	—
337	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
341	C₂×C₄²	—	2	4	no	—
342	C₂×C₄²	—	2	8	no	—
343	C₂×C₄²	D₄×C₃₁	1	8	yes	—
344	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
345	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
346	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
347	#95	C₂³×C₃₁	1	8	yes	—
348	#95	C₂³×C₃₁	1	4	yes	—
349	#95	C₂³×C₃₁	1	4	yes	—
350	#95	C₂³×C₃₁	1	8	yes	—
351	#95	C₂³×C₃₁	1	8	yes	—
352	#95	C₂³×C₃₁	1	8	yes	—
353	#95	C₂³×C₃₁	1	8	yes	—
354	C₃₁	C₂×#2611	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	—	2	2	no	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	#41×C₃₁	1	4	yes	—
360	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
361	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
362	C₂²×C₄	—	2	32	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
388	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
389	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
390	C₂²×C₄	#41×C₃₁	1	8	yes	—
391	C₂²×C₄	#41×C₃₁	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	16	no	—
405	C₄⋊C₄	—	2	16	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	16	no	—
409	C₄⋊C₄	—	2	16	no	—
410	C₂²⋊C₄	—	2	16	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	16	no	—
414	C₄²	—	2	8	no	—
415	C₄²	—	2	16	no	—
416	C₄²	C₂×D₄×C₃₁	1	16	yes	—
417	C₂³	—	2	8	no	—
418	C₂³	—	2	16	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	4	8	no	—
426	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
427	C₂³	C₂×#41×C₃₁	1	4	yes	—
428	C₂³	C₂×#41×C₃₁	1	2	yes	—
429	C₂³	C₂×#41×C₃₁	1	2	yes	—
430	C₂³	C₂×#41×C₃₁	1	4	yes	—
431	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
432	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
433	C₂×C₄	—	2	32	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	16	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
466	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
467	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
468	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
469	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	4	16	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	C₃₁×#525	1	4	yes	—
477	C₂²	C₃₁×#532	1	4	yes	—
478	C₂²	C₃₁×#536	1	4	yes	—
479	C₂²	C₃₁×#552	1	8	yes	—
480	C₂²	C₃₁×#552	1	8	yes	—
481	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
482	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
483	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
484	C₂²	C₂²×#41×C₃₁	1	2	yes	—
485	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
486	C₄	—	2	4	no	—
487	C₄	—	2	4	no	—
488	C₄	—	2	4	no	—
489	C₄	—	2	4	no	—
490	C₄	—	2	8	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₂	—	4	4	no	—
497	C₂	C₃₁×#2611	1	8	yes	direct product factor
498	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
499	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
500	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
501	C₂	C₂×C₃₁×#552	1	2	yes	—
502	C₂	C₂×C₃₁×#552	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#125	C₂	semidirect
3. C₃₁×#2611	C₂	direct (N × H)
4. C₂×C₃₁×#400	C₂	semidirect
6. C₂×C₃₁×#398	C₂	semidirect
8. C₂×C₃₁×#389	C₂	semidirect
10. C₂×C₃₁×#387	C₂	semidirect
12. C₂×C₃₁×#376	C₂	semidirect
15. C₂×C₃₁×#125	C₂²	semidirect
33. C₃₁×#400	C₂²	semidirect
35. C₃₁×#398	C₂²	semidirect
37. C₃₁×#389	C₂²	semidirect
39. C₃₁×#387	C₂²	semidirect
41. C₃₁×#376	C₂²	semidirect
165. C₂×#2611	C₃₁	direct (N × H)
219. C₂²×#125	C₂×C₃₁	semidirect
221. #2611	C₂×C₃₁	direct (N × H)
222. C₂×#400	C₂×C₃₁	semidirect
224. C₂×#398	C₂×C₃₁	semidirect
226. C₂×#389	C₂×C₃₁	semidirect
228. C₂×#387	C₂×C₃₁	semidirect
230. C₂×#376	C₂×C₃₁	semidirect
259. C₂×#125	C₂²×C₃₁	semidirect
277. #400	C₂²×C₃₁	semidirect
279. #398	C₂²×C₃₁	semidirect
281. #389	C₂²×C₃₁	semidirect
283. #387	C₂²×C₃₁	semidirect
285. #376	C₂²×C₃₁	semidirect
294. C₂×C₃₁	#2611	direct (N × H)
354. C₃₁	C₂×#2611	direct (N × H)
497. C₂	C₃₁×#2611	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#125	2
C₂²×C₃₁×#117	2
C₃₁×#2611	2
C₂×C₃₁×#400	2
C₂×C₃₁×#399	2
C₂×C₃₁×#398	2
C₂×C₃₁×#397	2
C₂×C₃₁×#389	2
C₂×C₃₁×#388	2
C₂×C₃₁×#387	2
C₂×C₃₁×#385	2
C₂×C₃₁×#376	2
C₂×#2611	31

Subgroups — C2×C31×#2611 #21491631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2611 #21491631