Subgroups — C₃₁×#2671 #16842604

Order 3968.

682 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#123	—	2	4	no	—
26	C₃₁×#121	—	2	4	no	—
27	C₃₁×#121	—	2	4	no	—
28	C₃₁×#121	—	2	4	no	—
29	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
49	C₃₁×#95	C₂²	1	1	yes	characteristic
50	C₃₁×#95	C₂²	1	1	yes	characteristic
51	C₃₁×#95	C₂²	1	1	yes	characteristic
52	C₃₁×#95	C₂²	1	1	yes	characteristic
53	C₃₁×#95	C₂²	1	1	yes	characteristic
54	C₃₁×#95	C₂²	1	1	yes	characteristic
55	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
56	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
57	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
58	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×D₄×C₃₁	—	2	2	no	—
60	C₂×D₄×C₃₁	—	2	2	no	—
61	C₂×D₄×C₃₁	—	2	2	no	—
62	C₂×D₄×C₃₁	—	2	2	no	—
63	C₂×D₄×C₃₁	—	2	2	no	—
64	C₂×D₄×C₃₁	—	2	2	no	—
65	C₂×D₄×C₃₁	—	2	2	no	—
66	C₂×D₄×C₃₁	—	2	2	no	—
67	C₂×D₄×C₃₁	—	2	2	no	—
68	C₂×D₄×C₃₁	—	4	1	no	—
69	C₂×D₄×C₃₁	—	4	1	no	—
70	C₂×D₄×C₃₁	—	4	1	no	—
71	C₂×D₄×C₃₁	—	4	1	no	—
72	C₂×D₄×C₃₁	—	4	1	no	—
73	C₂×D₄×C₃₁	—	4	1	no	—
74	C₂×D₄×C₃₁	—	4	1	no	—
75	C₂×D₄×C₃₁	—	4	1	no	—
76	C₂×D₄×C₃₁	D₄	1	4	yes	complemented
77	C₂²×C₄×C₃₁	—	2	2	no	—
78	C₂²×C₄×C₃₁	—	2	2	no	—
79	C₂²×C₄×C₃₁	—	2	2	no	—
80	C₂²×C₄×C₃₁	—	2	2	no	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	—	4	1	no	—
83	C₂²×C₄×C₃₁	—	4	1	no	—
84	C₂²×C₄×C₃₁	—	4	1	no	—
85	C₂²×C₄×C₃₁	—	4	1	no	—
86	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₃₁	—	2	2	no	—
98	C₄⋊C₄×C₃₁	—	2	2	no	—
99	C₄⋊C₄×C₃₁	—	2	2	no	—
100	C₄⋊C₄×C₃₁	—	2	2	no	—
101	C₄⋊C₄×C₃₁	—	2	2	no	—
102	C₄⋊C₄×C₃₁	—	4	1	no	—
103	C₄⋊C₄×C₃₁	—	4	1	no	—
104	C₂²⋊C₄×C₃₁	—	2	2	no	—
105	C₂²⋊C₄×C₃₁	—	2	2	no	—
106	C₂²⋊C₄×C₃₁	—	2	2	no	—
107	C₂²⋊C₄×C₃₁	—	2	2	no	—
108	C₂²⋊C₄×C₃₁	—	2	2	no	—
109	C₂²⋊C₄×C₃₁	—	2	2	no	—
110	C₂²⋊C₄×C₃₁	—	2	2	no	—
111	C₂²⋊C₄×C₃₁	—	2	2	no	—
112	C₂²⋊C₄×C₃₁	—	4	1	no	—
113	C₂²⋊C₄×C₃₁	—	4	1	no	—
114	C₂²⋊C₄×C₃₁	—	4	1	no	—
115	C₂²⋊C₄×C₃₁	—	4	1	no	—
116	C₂²⋊C₄×C₃₁	D₄	1	4	yes	complemented
117	C₂³×C₃₁	—	2	1	no	—
118	C₂³×C₃₁	—	2	1	no	—
119	C₂³×C₃₁	—	2	1	no	—
120	C₂³×C₃₁	—	2	1	no	—
121	C₂³×C₃₁	—	2	1	no	—
122	C₂³×C₃₁	—	2	1	no	—
123	C₂³×C₃₁	—	2	1	no	—
124	C₂³×C₃₁	—	2	1	no	—
125	C₂³×C₃₁	—	2	1	no	—
126	C₂³×C₃₁	—	2	1	no	—
127	C₂³×C₃₁	—	2	1	no	—
128	C₂³×C₃₁	—	2	1	no	—
129	C₂³×C₃₁	—	2	1	no	—
130	C₂³×C₃₁	—	2	1	no	—
131	C₂³×C₃₁	—	2	1	no	—
132	C₂³×C₃₁	—	2	1	no	—
133	C₂³×C₃₁	—	2	1	no	—
134	C₂³×C₃₁	—	2	1	no	—
135	C₂³×C₃₁	—	2	1	no	—
136	C₂³×C₃₁	—	2	1	no	—
137	C₂³×C₃₁	—	2	1	no	—
138	C₂³×C₃₁	—	2	1	no	—
139	C₂³×C₃₁	—	2	1	no	—
140	C₂³×C₃₁	—	2	1	no	—
141	C₂³×C₃₁	—	2	1	no	—
142	C₂³×C₃₁	C₂×D₄	1	2	yes	—
143	C₂³×C₃₁	C₂×D₄	1	2	yes	—
144	C₂³×C₃₁	C₂×D₄	1	2	yes	—
145	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
146	D₄×C₃₁	—	4	4	no	—
147	D₄×C₃₁	—	4	4	no	—
148	D₄×C₃₁	—	4	4	no	—
149	D₄×C₃₁	—	4	4	no	—
150	D₄×C₃₁	—	4	4	no	—
151	D₄×C₃₁	—	4	4	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	1	no	—
155	C₂×C₄×C₃₁	—	2	1	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	2	1	no	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	1	no	—
163	C₂×C₄×C₃₁	—	2	1	no	—
164	C₂×C₄×C₃₁	—	2	1	no	—
165	C₂×C₄×C₃₁	—	2	1	no	—
166	C₂×C₄×C₃₁	—	2	1	no	—
167	C₂×C₄×C₃₁	—	2	1	no	—
168	C₂×C₄×C₃₁	—	2	1	no	—
169	C₂×C₄×C₃₁	—	2	1	no	—
170	C₂×C₄×C₃₁	—	2	1	no	—
171	C₂×C₄×C₃₁	—	2	1	no	—
172	C₂×C₄×C₃₁	—	2	1	no	—
173	C₂×C₄×C₃₁	—	2	1	no	—
174	C₂×C₄×C₃₁	—	2	1	no	—
175	C₂×C₄×C₃₁	—	2	1	no	—
176	C₂×C₄×C₃₁	—	2	1	no	—
177	C₂×C₄×C₃₁	—	2	1	no	—
178	C₂×C₄×C₃₁	—	2	1	no	—
179	C₂×C₄×C₃₁	—	2	1	no	—
180	C₂×C₄×C₃₁	—	2	1	no	—
181	C₂×C₄×C₃₁	—	4	4	no	—
182	C₂×C₄×C₃₁	—	4	4	no	—
183	C₂×C₄×C₃₁	—	4	4	no	—
184	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
185	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
186	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
187	C₂×C₄×C₃₁	#41	1	2	yes	—
188	#2671	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₃₁	—	2	2	no	—
190	C₂²×C₃₁	—	2	2	no	—
191	C₂²×C₃₁	—	2	2	no	—
192	C₂²×C₃₁	—	2	2	no	—
193	C₂²×C₃₁	—	2	2	no	—
194	C₂²×C₃₁	—	2	2	no	—
195	C₂²×C₃₁	—	2	2	no	—
196	C₂²×C₃₁	—	2	2	no	—
197	C₂²×C₃₁	—	2	2	no	—
198	C₂²×C₃₁	—	4	1	no	—
199	C₂²×C₃₁	—	4	1	no	—
200	C₂²×C₃₁	—	4	1	no	—
201	C₂²×C₃₁	—	4	1	no	—
202	C₂²×C₃₁	—	4	1	no	—
203	C₂²×C₃₁	—	4	1	no	—
204	C₂²×C₃₁	—	4	1	no	—
205	C₂²×C₃₁	—	4	1	no	—
206	C₂²×C₃₁	—	4	1	no	—
207	C₂²×C₃₁	—	4	1	no	—
208	C₂²×C₃₁	—	4	1	no	—
209	C₂²×C₃₁	—	4	1	no	—
210	C₂²×C₃₁	—	4	1	no	—
211	C₂²×C₃₁	—	4	1	no	—
212	C₂²×C₃₁	—	4	1	no	—
213	C₂²×C₃₁	—	4	1	no	—
214	C₂²×C₃₁	—	4	1	no	—
215	C₂²×C₃₁	—	4	1	no	—
216	C₂²×C₃₁	—	4	1	no	—
217	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
218	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
219	C₂²×C₃₁	C₂×#41	1	1	yes	characteristic
220	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂²×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
224	C₄×C₃₁	—	2	2	no	—
225	C₄×C₃₁	—	2	2	no	—
226	C₄×C₃₁	—	2	2	no	—
227	C₄×C₃₁	—	2	2	no	—
228	C₄×C₃₁	—	4	1	no	—
229	C₄×C₃₁	—	4	1	no	—
230	C₄×C₃₁	—	4	1	no	—
231	C₄×C₃₁	—	4	1	no	—
232	C₄×C₃₁	—	4	1	no	—
233	C₄×C₃₁	—	4	1	no	—
234	C₄×C₃₁	—	4	1	no	—
235	C₂×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
236	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
237	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
238	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
239	#399	C₂×C₃₁	1	1	yes	characteristic, complemented
240	#398	C₂×C₃₁	1	1	yes	characteristic, complemented
241	#394	C₂×C₃₁	1	1	yes	characteristic, complemented
242	#394	C₂×C₃₁	1	1	yes	characteristic, complemented
243	#394	C₂×C₃₁	1	1	yes	characteristic, complemented
244	#392	C₂×C₃₁	1	1	yes	characteristic, complemented
245	#386	C₂×C₃₁	1	1	yes	characteristic, complemented
246	#386	C₂×C₃₁	1	1	yes	characteristic, complemented
247	#385	C₂×C₃₁	1	1	yes	characteristic, complemented
248	#385	C₂×C₃₁	1	1	yes	characteristic, complemented
249	#380	C₂×C₃₁	1	1	yes	characteristic, complemented
250	C₂×C₃₁	—	4	2	no	—
251	C₂×C₃₁	—	4	2	no	—
252	C₂×C₃₁	—	4	2	no	—
253	C₂×C₃₁	—	8	1	no	—
254	C₂×C₃₁	#534	1	1	yes	characteristic
255	C₂×C₃₁	#537	1	1	yes	characteristic
256	C₂×C₃₁	#540	1	1	yes	characteristic
257	C₂×C₃₁	D₄²	1	1	yes	characteristic
258	C₂×C₃₁	#546	1	1	yes	characteristic
259	C₂×C₃₁	#547	1	1	yes	characteristic
260	C₂×C₃₁	#562	1	1	yes	characteristic
261	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
262	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
263	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
264	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
265	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
266	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
267	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
268	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
269	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
270	#123	—	2	4	no	—
271	#121	—	2	4	no	—
272	#121	—	2	4	no	—
273	#121	—	2	4	no	—
274	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
294	#95	C₂²×C₃₁	1	1	yes	characteristic
295	#95	C₂²×C₃₁	1	1	yes	characteristic
296	#95	C₂²×C₃₁	1	1	yes	characteristic
297	#95	C₂²×C₃₁	1	1	yes	characteristic
298	#95	C₂²×C₃₁	1	1	yes	characteristic
299	#95	C₂²×C₃₁	1	1	yes	characteristic
300	C₃₁	#2671	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
302	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
303	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
304	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	D₄×C₃₁	1	4	yes	complemented
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
333	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
336	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
337	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
341	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
342	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	D₄×C₃₁	1	4	yes	complemented
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₂×D₄×C₃₁	1	2	yes	—
389	C₂³	C₂×D₄×C₃₁	1	2	yes	—
390	C₂³	C₂×D₄×C₃₁	1	2	yes	—
391	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	4	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	4	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
431	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
432	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
433	C₂×C₄	#41×C₃₁	1	2	yes	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
463	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
464	C₂²	C₂×#41×C₃₁	1	1	yes	characteristic
465	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂²	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₂	—	4	2	no	—
481	C₂	—	4	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	8	1	no	—
484	C₂	C₃₁×#534	1	1	yes	characteristic
485	C₂	C₃₁×#537	1	1	yes	characteristic
486	C₂	C₃₁×#540	1	1	yes	characteristic
487	C₂	D₄²×C₃₁	1	1	yes	characteristic
488	C₂	C₃₁×#546	1	1	yes	characteristic
489	C₂	C₃₁×#547	1	1	yes	characteristic
490	C₂	C₃₁×#562	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#123	C₂	semidirect
2. C₂×C₃₁×#121	C₂	semidirect
3. C₂×C₃₁×#121	C₂	semidirect
4. C₂×C₃₁×#121	C₂	semidirect
5. C₃₁×#399	C₂	semidirect
6. C₃₁×#398	C₂	semidirect
7. C₃₁×#394	C₂	semidirect
8. C₃₁×#394	C₂	semidirect
9. C₃₁×#394	C₂	semidirect
10. C₃₁×#392	C₂	semidirect
11. C₃₁×#386	C₂	semidirect
12. C₃₁×#386	C₂	semidirect
13. C₃₁×#385	C₂	semidirect
14. C₃₁×#385	C₂	semidirect
15. C₃₁×#380	C₂	semidirect
76. C₂×D₄×C₃₁	D₄	semidirect
116. C₂²⋊C₄×C₃₁	D₄	semidirect
188. #2671	C₃₁	direct (N × H)
235. C₂×#123	C₂×C₃₁	semidirect
236. C₂×#121	C₂×C₃₁	semidirect
237. C₂×#121	C₂×C₃₁	semidirect
238. C₂×#121	C₂×C₃₁	semidirect
239. #399	C₂×C₃₁	semidirect
240. #398	C₂×C₃₁	semidirect
241. #394	C₂×C₃₁	semidirect
242. #394	C₂×C₃₁	semidirect
243. #394	C₂×C₃₁	semidirect
244. #392	C₂×C₃₁	semidirect
245. #386	C₂×C₃₁	semidirect
246. #386	C₂×C₃₁	semidirect
247. #385	C₂×C₃₁	semidirect
248. #385	C₂×C₃₁	semidirect
249. #380	C₂×C₃₁	semidirect
300. C₃₁	#2671	direct (N × H)
322. C₂×D₄	D₄×C₃₁	semidirect
362. C₂²⋊C₄	D₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#123	2
C₂×C₃₁×#121	2
C₃₁×#399	2
C₃₁×#398	2
C₃₁×#394	2
C₃₁×#392	2
C₃₁×#386	2
C₃₁×#385	2
C₃₁×#380	2
#2671	31

Subgroups — C31×#2671 #16842604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2671 #16842604