Subgroups — C₃₁×#2673 #16842606

Order 3968.

734 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#123	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×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#387	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#386	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	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#127	—	2	4	no	—
29	C₃₁×#123	—	2	4	no	—
30	C₃₁×#121	—	2	4	no	—
31	C₃₁×#121	—	2	4	no	—
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×C₂²⋊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×C₄²×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	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
69	C₂×D₄×C₃₁	—	2	2	no	—
70	C₂×D₄×C₃₁	—	2	2	no	—
71	C₂×D₄×C₃₁	—	2	2	no	—
72	C₂×D₄×C₃₁	—	2	2	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	—	4	1	no	—
77	C₂×D₄×C₃₁	—	4	1	no	—
78	C₂×D₄×C₃₁	—	4	1	no	—
79	C₂×D₄×C₃₁	—	4	1	no	—
80	C₂×D₄×C₃₁	—	4	1	no	—
81	C₂×D₄×C₃₁	—	4	1	no	—
82	C₂×D₄×C₃₁	—	4	1	no	—
83	C₂×D₄×C₃₁	—	4	1	no	—
84	C₂×D₄×C₃₁	—	4	1	no	—
85	C₂×D₄×C₃₁	—	4	1	no	—
86	C₂×D₄×C₃₁	—	4	1	no	—
87	C₂×D₄×C₃₁	—	4	1	no	—
88	C₂×D₄×C₃₁	—	4	1	no	—
89	C₂×D₄×C₃₁	D₄	1	4	yes	complemented
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	2	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	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	D₄	1	4	yes	complemented
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	—	2	2	no	—
113	C₂²⋊C₄×C₃₁	—	2	2	no	—
114	C₂²⋊C₄×C₃₁	—	2	2	no	—
115	C₂²⋊C₄×C₃₁	—	2	2	no	—
116	C₂²⋊C₄×C₃₁	—	2	2	no	—
117	C₂²⋊C₄×C₃₁	—	4	1	no	—
118	C₂²⋊C₄×C₃₁	—	4	1	no	—
119	C₂²⋊C₄×C₃₁	—	4	1	no	—
120	C₂²⋊C₄×C₃₁	—	4	1	no	—
121	C₂²⋊C₄×C₃₁	—	4	1	no	—
122	C₄²×C₃₁	—	2	2	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	—	2	1	no	—
143	C₂³×C₃₁	—	2	1	no	—
144	C₂³×C₃₁	—	2	1	no	—
145	C₂³×C₃₁	—	2	1	no	—
146	C₂³×C₃₁	—	2	1	no	—
147	C₂³×C₃₁	—	2	1	no	—
148	C₂³×C₃₁	—	2	1	no	—
149	C₂³×C₃₁	—	2	1	no	—
150	C₂³×C₃₁	—	2	1	no	—
151	C₂³×C₃₁	—	2	1	no	—
152	C₂³×C₃₁	—	2	1	no	—
153	C₂³×C₃₁	—	2	1	no	—
154	C₂³×C₃₁	—	2	1	no	—
155	C₂³×C₃₁	—	2	1	no	—
156	C₂³×C₃₁	C₂×D₄	1	2	yes	—
157	C₂³×C₃₁	C₂×D₄	1	2	yes	—
158	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
159	D₄×C₃₁	—	4	4	no	—
160	D₄×C₃₁	—	4	4	no	—
161	D₄×C₃₁	—	4	4	no	—
162	D₄×C₃₁	—	4	4	no	—
163	D₄×C₃₁	—	4	4	no	—
164	D₄×C₃₁	—	4	4	no	—
165	D₄×C₃₁	—	4	4	no	—
166	D₄×C₃₁	—	4	4	no	—
167	D₄×C₃₁	—	4	4	no	—
168	D₄×C₃₁	—	4	4	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	—	2	1	no	—
182	C₂×C₄×C₃₁	—	2	1	no	—
183	C₂×C₄×C₃₁	—	2	1	no	—
184	C₂×C₄×C₃₁	—	2	1	no	—
185	C₂×C₄×C₃₁	—	2	1	no	—
186	C₂×C₄×C₃₁	—	2	1	no	—
187	C₂×C₄×C₃₁	—	2	1	no	—
188	C₂×C₄×C₃₁	—	2	1	no	—
189	C₂×C₄×C₃₁	—	2	1	no	—
190	C₂×C₄×C₃₁	—	2	1	no	—
191	C₂×C₄×C₃₁	—	2	1	no	—
192	C₂×C₄×C₃₁	—	2	1	no	—
193	C₂×C₄×C₃₁	—	2	1	no	—
194	C₂×C₄×C₃₁	—	4	4	no	—
195	C₂×C₄×C₃₁	—	4	4	no	—
196	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
197	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
198	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
199	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
200	C₂×C₄×C₃₁	#41	1	2	yes	—
201	#2673	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₃₁	—	2	2	no	—
203	C₂²×C₃₁	—	2	2	no	—
204	C₂²×C₃₁	—	2	2	no	—
205	C₂²×C₃₁	—	2	2	no	—
206	C₂²×C₃₁	—	2	2	no	—
207	C₂²×C₃₁	—	2	2	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	—	4	1	no	—
218	C₂²×C₃₁	—	4	1	no	—
219	C₂²×C₃₁	—	4	1	no	—
220	C₂²×C₃₁	—	4	1	no	—
221	C₂²×C₃₁	—	4	1	no	—
222	C₂²×C₃₁	—	4	1	no	—
223	C₂²×C₃₁	—	4	1	no	—
224	C₂²×C₃₁	—	4	1	no	—
225	C₂²×C₃₁	—	4	1	no	—
226	C₂²×C₃₁	—	4	1	no	—
227	C₂²×C₃₁	—	4	1	no	—
228	C₂²×C₃₁	—	4	1	no	—
229	C₂²×C₃₁	—	4	1	no	—
230	C₂²×C₃₁	—	4	1	no	—
231	C₂²×C₃₁	—	4	1	no	—
232	C₂²×C₃₁	—	4	1	no	—
233	C₂²×C₃₁	—	4	1	no	—
234	C₂²×C₃₁	—	4	1	no	—
235	C₂²×C₃₁	—	4	1	no	—
236	C₂²×C₃₁	—	4	1	no	—
237	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
238	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
239	C₂²×C₃₁	C₂×#41	1	1	yes	characteristic
240	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
244	C₄×C₃₁	—	2	2	no	—
245	C₄×C₃₁	—	2	2	no	—
246	C₄×C₃₁	—	2	2	no	—
247	C₄×C₃₁	—	2	2	no	—
248	C₄×C₃₁	—	2	2	no	—
249	C₄×C₃₁	—	4	1	no	—
250	C₄×C₃₁	—	4	1	no	—
251	C₄×C₃₁	—	4	1	no	—
252	C₄×C₃₁	—	4	1	no	—
253	C₄×C₃₁	—	4	1	no	—
254	C₂×#127	C₂×C₃₁	1	1	yes	characteristic, complemented
255	C₂×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
256	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
257	C₂×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
258	#394	C₂×C₃₁	1	1	yes	characteristic, complemented
259	#394	C₂×C₃₁	1	1	yes	characteristic, complemented
260	#392	C₂×C₃₁	1	1	yes	characteristic, complemented
261	#392	C₂×C₃₁	1	1	yes	characteristic, complemented
262	#392	C₂×C₃₁	1	1	yes	characteristic, complemented
263	#392	C₂×C₃₁	1	1	yes	characteristic, complemented
264	#388	C₂×C₃₁	1	1	yes	characteristic, complemented
265	#387	C₂×C₃₁	1	1	yes	characteristic, complemented
266	#386	C₂×C₃₁	1	1	yes	characteristic, complemented
267	#386	C₂×C₃₁	1	1	yes	characteristic, complemented
268	#386	C₂×C₃₁	1	1	yes	characteristic, complemented
269	C₂×C₃₁	—	4	2	no	—
270	C₂×C₃₁	—	4	2	no	—
271	C₂×C₃₁	—	8	1	no	—
272	C₂×C₃₁	—	8	1	no	—
273	C₂×C₃₁	—	8	1	no	—
274	C₂×C₃₁	#534	1	1	yes	characteristic
275	C₂×C₃₁	#535	1	1	yes	characteristic
276	C₂×C₃₁	#540	1	1	yes	characteristic
277	C₂×C₃₁	D₄²	1	1	yes	characteristic
278	C₂×C₃₁	#546	1	1	yes	characteristic
279	C₂×C₃₁	#550	1	1	yes	characteristic
280	C₂×C₃₁	#560	1	1	yes	characteristic
281	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
282	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
283	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
284	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
285	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
286	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
287	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
288	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
289	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
290	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
291	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
292	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
293	#127	—	2	4	no	—
294	#123	—	2	4	no	—
295	#121	—	2	4	no	—
296	#121	—	2	4	no	—
297	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
313	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
314	#95	C₂²×C₃₁	1	1	yes	characteristic
315	#95	C₂²×C₃₁	1	1	yes	characteristic
316	#95	C₂²×C₃₁	1	1	yes	characteristic
317	#95	C₂²×C₃₁	1	1	yes	characteristic
318	#95	C₂²×C₃₁	1	1	yes	characteristic
319	#95	C₂²×C₃₁	1	1	yes	characteristic
320	C₃₁	#2673	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
322	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
323	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
324	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
325	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	D₄×C₃₁	1	4	yes	complemented
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
364	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
365	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
366	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
367	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
368	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
369	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
370	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
371	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	D₄×C₃₁	1	4	yes	complemented
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₄²	—	2	2	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	C₂×D₄×C₃₁	1	2	yes	—
423	C₂³	C₂×D₄×C₃₁	1	2	yes	—
424	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
425	D₄	—	4	4	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	4	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	4	no	—
433	D₄	—	4	4	no	—
434	D₄	—	4	4	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
463	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
464	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
465	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
466	C₂×C₄	#41×C₃₁	1	2	yes	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
503	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
504	C₂²	C₂×#41×C₃₁	1	1	yes	characteristic
505	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₂	—	4	2	no	—
520	C₂	—	4	2	no	—
521	C₂	—	8	1	no	—
522	C₂	—	8	1	no	—
523	C₂	—	8	1	no	—
524	C₂	C₃₁×#534	1	1	yes	characteristic
525	C₂	C₃₁×#535	1	1	yes	characteristic
526	C₂	C₃₁×#540	1	1	yes	characteristic
527	C₂	D₄²×C₃₁	1	1	yes	characteristic
528	C₂	C₃₁×#546	1	1	yes	characteristic
529	C₂	C₃₁×#550	1	1	yes	characteristic
530	C₂	C₃₁×#560	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×#127	C₂	semidirect
2. C₂×C₃₁×#123	C₂	semidirect
3. C₂×C₃₁×#121	C₂	semidirect
4. C₂×C₃₁×#121	C₂	semidirect
5. C₃₁×#394	C₂	semidirect
6. C₃₁×#394	C₂	semidirect
7. C₃₁×#392	C₂	semidirect
8. C₃₁×#392	C₂	semidirect
9. C₃₁×#392	C₂	semidirect
10. C₃₁×#392	C₂	semidirect
11. C₃₁×#388	C₂	semidirect
12. C₃₁×#387	C₂	semidirect
13. C₃₁×#386	C₂	semidirect
14. C₃₁×#386	C₂	semidirect
15. C₃₁×#386	C₂	semidirect
89. C₂×D₄×C₃₁	D₄	semidirect
108. C₄⋊C₄×C₃₁	D₄	semidirect
201. #2673	C₃₁	direct (N × H)
254. C₂×#127	C₂×C₃₁	semidirect
255. C₂×#123	C₂×C₃₁	semidirect
256. C₂×#121	C₂×C₃₁	semidirect
257. C₂×#121	C₂×C₃₁	semidirect
258. #394	C₂×C₃₁	semidirect
259. #394	C₂×C₃₁	semidirect
260. #392	C₂×C₃₁	semidirect
261. #392	C₂×C₃₁	semidirect
262. #392	C₂×C₃₁	semidirect
263. #392	C₂×C₃₁	semidirect
264. #388	C₂×C₃₁	semidirect
265. #387	C₂×C₃₁	semidirect
266. #386	C₂×C₃₁	semidirect
267. #386	C₂×C₃₁	semidirect
268. #386	C₂×C₃₁	semidirect
320. C₃₁	#2673	direct (N × H)
355. C₂×D₄	D₄×C₃₁	semidirect
374. C₄⋊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×#127	2
C₂×C₃₁×#123	2
C₂×C₃₁×#121	2
C₃₁×#394	2
C₃₁×#392	2
C₃₁×#388	2
C₃₁×#387	2
C₃₁×#386	2
#2673	31

Subgroups — C31×#2673 #16842606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2673 #16842606