Subgroups — C₂×C₃₁×#1876 #21477675

Order 7936.

1754 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#104	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃₁×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1876	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#135	—	2	4	no	—
12	C₂×C₃₁×#135	—	2	4	no	—
13	C₂×C₃₁×#135	C₄	1	4	yes	complemented
14	C₂×C₃₁×#135	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₃₁	C₄	1	1	yes	characteristic, complemented
16	C₂²×SD₁₆×C₃₁	C₄	1	1	yes	characteristic, complemented
17	C₂²×SD₁₆×C₃₁	C₄	1	1	yes	characteristic, complemented
18	C₂²×D₈×C₃₁	C₄	1	1	yes	characteristic, complemented
19	C₂×C₃₁×#131	—	2	4	no	—
20	C₂×C₃₁×#131	—	2	4	no	—
21	C₂×C₃₁×#131	—	2	2	no	—
22	C₂×C₃₁×#131	C₂²	1	4	yes	complemented
23	C₂²×M₁₆×C₃₁	—	2	1	no	—
24	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₃₁	—	2	1	no	—
27	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#104	—	2	4	no	—
31	C₂×C₃₁×#104	—	2	4	no	—
32	C₂×C₃₁×#104	C₂²	1	4	yes	complemented
33	C₂×C₃₁×#104	C₂²	1	4	yes	complemented
34	C₃₁×#408	—	2	2	no	—
35	C₃₁×#408	C₂²	1	4	yes	complemented
36	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
37	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
38	C₃₁×#341	C₂²	1	4	yes	complemented
39	C₃₁×#336	C₂²	1	4	yes	complemented
40	C₂×#41×C₃₁	—	2	2	no	—
41	C₂×#41×C₃₁	—	2	1	no	—
42	C₂×#41×C₃₁	—	2	1	no	—
43	C₂×#41×C₃₁	—	2	1	no	—
44	C₂×#41×C₃₁	—	2	2	no	—
45	C₂×#41×C₃₁	—	2	1	no	—
46	C₂×#41×C₃₁	—	2	2	no	—
47	C₂×#41×C₃₁	—	2	2	no	—
48	C₂×#41×C₃₁	—	2	2	no	—
49	C₂×#41×C₃₁	—	2	2	no	—
50	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×#41×C₃₁	D₄	1	4	yes	—
53	C₂×#41×C₃₁	D₄	1	4	yes	—
54	C₂×#41×C₃₁	C₂³	1	2	yes	—
55	C₂×#41×C₃₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₃₁	—	2	1	no	—
59	C₂²×D₄×C₃₁	—	2	1	no	—
60	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₃₁	—	2	1	no	—
63	C₂³×C₄×C₃₁	—	2	1	no	—
64	C₂³×C₄×C₃₁	—	2	1	no	—
65	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₃₁×#135	—	2	16	no	—
67	C₃₁×#135	—	2	8	no	—
68	C₃₁×#135	—	2	8	no	—
69	C₂×Q₁₆×C₃₁	—	2	4	no	—
70	C₂×Q₁₆×C₃₁	C₂×C₄	1	4	yes	complemented
71	C₂×SD₁₆×C₃₁	—	2	4	no	—
72	C₂×SD₁₆×C₃₁	—	2	4	no	—
73	C₂×SD₁₆×C₃₁	C₂×C₄	1	4	yes	complemented
74	C₂×SD₁₆×C₃₁	C₂×C₄	1	4	yes	complemented
75	C₂×D₈×C₃₁	—	2	4	no	—
76	C₂×D₈×C₃₁	C₂×C₄	1	4	yes	complemented
77	C₃₁×#131	—	2	16	no	—
78	C₃₁×#131	—	2	8	no	—
79	C₃₁×#131	—	2	8	no	—
80	C₂×M₁₆×C₃₁	—	2	8	no	—
81	C₂×M₁₆×C₃₁	—	2	2	no	—
82	C₂×M₁₆×C₃₁	—	2	1	no	—
83	C₂×M₁₆×C₃₁	—	2	1	no	—
84	C₂×M₁₆×C₃₁	—	2	4	no	—
85	C₂×M₁₆×C₃₁	—	2	2	no	—
86	C₂×M₁₆×C₃₁	—	2	2	no	—
87	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
88	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
89	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
90	C₂²×C₈×C₃₁	—	2	8	no	—
91	C₂²×C₈×C₃₁	—	2	2	no	—
92	C₂²×C₈×C₃₁	—	2	2	no	—
93	C₂²×C₈×C₃₁	—	2	2	no	—
94	C₂²×C₈×C₃₁	—	2	2	no	—
95	C₂²×C₈×C₃₁	—	2	1	no	—
96	C₂²×C₈×C₃₁	—	2	4	no	—
97	C₂²×C₈×C₃₁	—	2	1	no	—
98	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
99	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
101	C₂²×C₈×C₃₁	D₄	1	2	yes	—
102	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
103	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
104	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂×C₄²×C₃₁	—	2	2	no	—
107	C₂×C₄²×C₃₁	—	2	2	no	—
108	C₂×C₄²×C₃₁	—	2	1	no	—
109	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
110	C₃₁×#104	—	2	8	no	—
111	C₃₁×#104	—	2	8	no	—
112	C₃₁×C₂²⋊C₈	—	2	4	no	—
113	C₃₁×C₂²⋊C₈	—	2	4	no	—
114	C₂⁴×C₃₁	—	2	1	no	—
115	C₂⁴×C₃₁	—	2	1	no	—
116	C₂⁴×C₃₁	#41	1	1	yes	characteristic
117	#41×C₃₁	—	2	4	no	—
118	#41×C₃₁	—	2	4	no	—
119	#41×C₃₁	—	2	4	no	—
120	#41×C₃₁	—	2	4	no	—
121	#41×C₃₁	—	2	4	no	—
122	#41×C₃₁	—	2	2	no	—
123	#41×C₃₁	—	2	2	no	—
124	#41×C₃₁	—	2	4	no	—
125	#41×C₃₁	—	2	4	no	—
126	#41×C₃₁	—	2	2	no	—
127	#41×C₃₁	—	2	2	no	—
128	#41×C₃₁	—	2	2	no	—
129	#41×C₃₁	—	2	2	no	—
130	#41×C₃₁	—	4	2	no	—
131	#41×C₃₁	—	4	2	no	—
132	#41×C₃₁	—	4	2	no	—
133	#41×C₃₁	—	4	2	no	—
134	#41×C₃₁	C₂²⋊C₄	1	8	yes	—
135	#41×C₃₁	C₂×D₄	1	4	yes	—
136	#41×C₃₁	C₂×D₄	1	4	yes	—
137	C₂×Q₈×C₃₁	—	2	1	no	—
138	C₂×Q₈×C₃₁	—	2	2	no	—
139	C₂×Q₈×C₃₁	—	2	1	no	—
140	C₂×Q₈×C₃₁	—	2	2	no	—
141	C₂×Q₈×C₃₁	—	2	2	no	—
142	C₂×Q₈×C₃₁	C₂²⋊C₄	1	4	yes	—
143	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
144	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₃₁	—	2	2	no	—
146	C₂×D₄×C₃₁	—	2	4	no	—
147	C₂×D₄×C₃₁	—	2	4	no	—
148	C₂×D₄×C₃₁	—	2	2	no	—
149	C₂×D₄×C₃₁	—	2	2	no	—
150	C₂×D₄×C₃₁	—	2	2	no	—
151	C₂×D₄×C₃₁	—	2	2	no	—
152	C₂×D₄×C₃₁	—	2	2	no	—
153	C₂×D₄×C₃₁	—	2	1	no	—
154	C₂×D₄×C₃₁	—	2	2	no	—
155	C₂×D₄×C₃₁	—	2	1	no	—
156	C₂×D₄×C₃₁	—	4	2	no	—
157	C₂×D₄×C₃₁	—	4	2	no	—
158	C₂×D₄×C₃₁	C₂²⋊C₄	1	4	yes	—
159	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₃₁	—	2	1	no	—
162	C₂²×C₄×C₃₁	—	2	2	no	—
163	C₂²×C₄×C₃₁	—	2	4	no	—
164	C₂²×C₄×C₃₁	—	2	4	no	—
165	C₂²×C₄×C₃₁	—	2	2	no	—
166	C₂²×C₄×C₃₁	—	2	4	no	—
167	C₂²×C₄×C₃₁	—	2	1	no	—
168	C₂²×C₄×C₃₁	—	2	2	no	—
169	C₂²×C₄×C₃₁	—	2	2	no	—
170	C₂²×C₄×C₃₁	—	2	2	no	—
171	C₂²×C₄×C₃₁	—	4	2	no	—
172	C₂²×C₄×C₃₁	—	4	2	no	—
173	C₂²×C₄×C₃₁	—	4	2	no	—
174	C₂²×C₄×C₃₁	—	4	2	no	—
175	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
183	C₂²×C₄×C₃₁	#41	1	2	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
185	Q₁₆×C₃₁	—	2	8	no	—
186	SD₁₆×C₃₁	—	2	8	no	—
187	SD₁₆×C₃₁	—	2	8	no	—
188	D₈×C₃₁	—	2	8	no	—
189	M₁₆×C₃₁	—	2	16	no	—
190	M₁₆×C₃₁	—	2	4	no	—
191	M₁₆×C₃₁	—	2	2	no	—
192	M₁₆×C₃₁	—	2	2	no	—
193	M₁₆×C₃₁	—	2	2	no	—
194	M₁₆×C₃₁	—	4	2	no	—
195	M₁₆×C₃₁	C₂×D₄	1	4	yes	—
196	C₂×C₈×C₃₁	—	2	16	no	—
197	C₂×C₈×C₃₁	—	2	2	no	—
198	C₂×C₈×C₃₁	—	2	2	no	—
199	C₂×C₈×C₃₁	—	2	4	no	—
200	C₂×C₈×C₃₁	—	2	2	no	—
201	C₂×C₈×C₃₁	—	2	4	no	—
202	C₂×C₈×C₃₁	—	2	2	no	—
203	C₂×C₈×C₃₁	—	2	4	no	—
204	C₂×C₈×C₃₁	—	2	2	no	—
205	C₂×C₈×C₃₁	—	2	2	no	—
206	C₂×C₈×C₃₁	—	2	2	no	—
207	C₂×C₈×C₃₁	—	2	2	no	—
208	C₂×C₈×C₃₁	—	2	2	no	—
209	C₂×C₈×C₃₁	—	2	2	no	—
210	C₂×C₈×C₃₁	—	4	2	no	—
211	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
213	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
214	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
215	C₄²×C₃₁	—	2	2	no	—
216	C₄²×C₃₁	—	2	2	no	—
217	C₄²×C₃₁	—	4	2	no	—
218	C₂×#1876	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₃₁	—	2	2	no	—
220	C₂³×C₃₁	—	2	2	no	—
221	C₂³×C₃₁	—	2	2	no	—
222	C₂³×C₃₁	—	2	4	no	—
223	C₂³×C₃₁	—	2	2	no	—
224	C₂³×C₃₁	—	4	2	no	—
225	C₂³×C₃₁	—	4	2	no	—
226	C₂³×C₃₁	—	4	2	no	—
227	C₂³×C₃₁	—	4	2	no	—
228	C₂³×C₃₁	—	4	2	no	—
229	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
230	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
231	C₂³×C₃₁	#121	1	2	yes	—
232	C₂³×C₃₁	#123	1	2	yes	—
233	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
234	Q₈×C₃₁	—	2	2	no	—
235	Q₈×C₃₁	—	2	4	no	—
236	Q₈×C₃₁	—	2	2	no	—
237	Q₈×C₃₁	—	2	2	no	—
238	Q₈×C₃₁	—	4	2	no	—
239	Q₈×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
240	D₄×C₃₁	—	2	4	no	—
241	D₄×C₃₁	—	2	4	no	—
242	D₄×C₃₁	—	2	8	no	—
243	D₄×C₃₁	—	2	2	no	—
244	D₄×C₃₁	—	2	2	no	—
245	D₄×C₃₁	—	2	2	no	—
246	D₄×C₃₁	—	2	4	no	—
247	D₄×C₃₁	—	4	2	no	—
248	D₄×C₃₁	—	4	2	no	—
249	D₄×C₃₁	—	4	4	no	—
250	D₄×C₃₁	—	4	2	no	—
251	D₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
252	C₂×C₄×C₃₁	—	2	2	no	—
253	C₂×C₄×C₃₁	—	2	4	no	—
254	C₂×C₄×C₃₁	—	2	4	no	—
255	C₂×C₄×C₃₁	—	2	4	no	—
256	C₂×C₄×C₃₁	—	2	8	no	—
257	C₂×C₄×C₃₁	—	2	4	no	—
258	C₂×C₄×C₃₁	—	2	2	no	—
259	C₂×C₄×C₃₁	—	4	8	no	—
260	C₂×C₄×C₃₁	—	4	2	no	—
261	C₂×C₄×C₃₁	—	4	2	no	—
262	C₂×C₄×C₃₁	—	4	2	no	—
263	C₂×C₄×C₃₁	—	4	2	no	—
264	C₂×C₄×C₃₁	—	4	2	no	—
265	C₂×C₄×C₃₁	—	4	4	no	—
266	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
269	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
270	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₃₁	#120	1	2	yes	—
273	C₂×C₄×C₃₁	#120	1	2	yes	—
274	C₂×C₄×C₃₁	#121	1	2	yes	—
275	C₂×C₄×C₃₁	#121	1	2	yes	—
276	C₂×C₄×C₃₁	#121	1	2	yes	—
277	C₂×C₄×C₃₁	#123	1	2	yes	—
278	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
279	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
284	C₈×C₃₁	—	2	2	no	—
285	C₈×C₃₁	—	2	2	no	—
286	C₈×C₃₁	—	2	2	no	—
287	C₈×C₃₁	—	2	4	no	—
288	C₈×C₃₁	—	2	2	no	—
289	C₈×C₃₁	—	4	2	no	—
290	C₂²×#135	C₂×C₃₁	1	1	yes	characteristic
291	C₂²×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
292	C₂²×#104	C₂×C₃₁	1	1	yes	characteristic, complemented
293	C₂²×#104	C₂×C₃₁	1	1	yes	characteristic, complemented
294	C₂×#408	C₂×C₃₁	1	1	yes	characteristic, complemented
295	#1876	C₂×C₃₁	1	8	yes	direct product factor
296	C₂×#341	C₂×C₃₁	1	1	yes	characteristic, complemented
297	C₂×#336	C₂×C₃₁	1	1	yes	characteristic, complemented
298	C₂²×C₃₁	—	2	4	no	—
299	C₂²×C₃₁	—	2	4	no	—
300	C₂²×C₃₁	—	2	1	no	—
301	C₂²×C₃₁	—	2	1	no	—
302	C₂²×C₃₁	—	2	1	no	—
303	C₂²×C₃₁	—	2	1	no	—
304	C₂²×C₃₁	—	2	4	no	—
305	C₂²×C₃₁	—	4	8	no	—
306	C₂²×C₃₁	—	4	2	no	—
307	C₂²×C₃₁	—	4	2	no	—
308	C₂²×C₃₁	—	4	2	no	—
309	C₂²×C₃₁	—	4	2	no	—
310	C₂²×C₃₁	—	4	2	no	—
311	C₂²×C₃₁	—	8	4	no	—
312	C₂²×C₃₁	#386	1	2	yes	—
313	C₂²×C₃₁	#386	1	2	yes	—
314	C₂²×C₃₁	#443	1	2	yes	—
315	C₂²×C₃₁	#444	1	2	yes	—
316	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
317	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
318	C₂²×C₃₁	C₂×#123	1	1	yes	characteristic
319	C₄×C₃₁	—	2	4	no	—
320	C₄×C₃₁	—	4	4	no	—
321	C₄×C₃₁	—	4	2	no	—
322	C₄×C₃₁	#386	1	2	yes	—
323	C₄×C₃₁	#386	1	2	yes	—
324	C₄×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
325	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
326	C₄×C₃₁	C₂×#120	1	1	yes	characteristic
327	C₄×C₃₁	C₂×#121	1	1	yes	characteristic
328	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
329	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
330	C₂×#135	—	2	4	no	—
331	C₂×#135	—	2	4	no	—
332	C₂×#135	C₄×C₃₁	1	4	yes	complemented
333	C₂×#135	C₂²×C₃₁	1	4	yes	—
334	C₂²×Q₁₆	C₄×C₃₁	1	1	yes	characteristic, complemented
335	C₂²×SD₁₆	C₄×C₃₁	1	1	yes	characteristic, complemented
336	C₂²×SD₁₆	C₄×C₃₁	1	1	yes	characteristic, complemented
337	C₂²×D₈	C₄×C₃₁	1	1	yes	characteristic, complemented
338	C₂×#131	—	2	4	no	—
339	C₂×#131	—	2	4	no	—
340	C₂×#131	—	2	2	no	—
341	C₂×#131	C₂²×C₃₁	1	4	yes	complemented
342	C₂²×M₁₆	—	2	1	no	—
343	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
344	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
345	C₂³×C₈	—	2	1	no	—
346	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
347	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
349	C₂×#104	—	2	4	no	—
350	C₂×#104	—	2	4	no	—
351	C₂×#104	C₂²×C₃₁	1	4	yes	complemented
352	C₂×#104	C₂²×C₃₁	1	4	yes	complemented
353	#408	—	2	2	no	—
354	#408	C₂²×C₃₁	1	4	yes	complemented
355	C₂×C₂²⋊C₈	—	2	1	no	—
356	C₂×C₂²⋊C₈	—	2	1	no	—
357	#341	C₂²×C₃₁	1	4	yes	complemented
358	#336	C₂²×C₃₁	1	4	yes	complemented
359	C₂×C₃₁	—	2	1	no	—
360	C₂×C₃₁	—	2	1	no	—
361	C₂×C₃₁	—	2	2	no	—
362	C₂×C₃₁	—	4	4	no	—
363	C₂×C₃₁	—	8	2	no	—
364	C₂×C₃₁	#1876	1	4	yes	direct product factor
365	C₂×C₃₁	C₂×#386	1	1	yes	characteristic
366	C₂×C₃₁	C₂×#443	1	1	yes	characteristic
367	C₂×C₃₁	C₂×#444	1	1	yes	characteristic
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	2	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	2	no	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
379	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
380	C₂×#41	D₄×C₃₁	1	4	yes	—
381	C₂×#41	D₄×C₃₁	1	4	yes	—
382	C₂×#41	C₂³×C₃₁	1	2	yes	—
383	C₂×#41	C₂³×C₃₁	1	2	yes	—
384	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
385	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
389	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
394	#135	—	2	16	no	—
395	#135	—	2	8	no	—
396	#135	—	2	8	no	—
397	C₂×Q₁₆	—	2	4	no	—
398	C₂×Q₁₆	C₂×C₄×C₃₁	1	4	yes	complemented
399	C₂×SD₁₆	—	2	4	no	—
400	C₂×SD₁₆	—	2	4	no	—
401	C₂×SD₁₆	C₂×C₄×C₃₁	1	4	yes	complemented
402	C₂×SD₁₆	C₂×C₄×C₃₁	1	4	yes	complemented
403	C₂×D₈	—	2	4	no	—
404	C₂×D₈	C₂×C₄×C₃₁	1	4	yes	complemented
405	#131	—	2	16	no	—
406	#131	—	2	8	no	—
407	#131	—	2	8	no	—
408	C₂×M₁₆	—	2	8	no	—
409	C₂×M₁₆	—	2	2	no	—
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	4	no	—
413	C₂×M₁₆	—	2	2	no	—
414	C₂×M₁₆	—	2	2	no	—
415	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
416	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
417	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
418	C₂²×C₈	—	2	8	no	—
419	C₂²×C₈	—	2	1	no	—
420	C₂²×C₈	—	2	2	no	—
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	—	2	2	no	—
423	C₂²×C₈	—	2	2	no	—
424	C₂²×C₈	—	2	4	no	—
425	C₂²×C₈	—	2	1	no	—
426	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
427	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
428	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
429	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
430	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
431	C₂²×C₈	D₄×C₃₁	1	2	yes	—
432	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
433	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
434	C₂×C₄²	—	2	2	no	—
435	C₂×C₄²	—	2	2	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
438	#104	—	2	8	no	—
439	#104	—	2	8	no	—
440	C₂²⋊C₈	—	2	4	no	—
441	C₂²⋊C₈	—	2	4	no	—
442	C₃₁	C₂×#1876	1	1	yes	characteristic, direct product factor, Sylow
443	C₂⁴	—	2	1	no	—
444	C₂⁴	—	2	1	no	—
445	C₂⁴	#41×C₃₁	1	1	yes	characteristic
446	#41	—	2	4	no	—
447	#41	—	2	4	no	—
448	#41	—	2	4	no	—
449	#41	—	2	4	no	—
450	#41	—	2	4	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	4	no	—
454	#41	—	2	4	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	4	2	no	—
460	#41	—	4	2	no	—
461	#41	—	4	2	no	—
462	#41	—	4	2	no	—
463	#41	C₂²⋊C₄×C₃₁	1	8	yes	—
464	#41	C₂×D₄×C₃₁	1	4	yes	—
465	#41	C₂×D₄×C₃₁	1	4	yes	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	C₂²⋊C₄×C₃₁	1	4	yes	—
472	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
473	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	C₂²⋊C₄×C₃₁	1	4	yes	—
488	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
489	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
507	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
508	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
511	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
512	C₂²×C₄	#41×C₃₁	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
514	Q₁₆	—	2	8	no	—
515	SD₁₆	—	2	8	no	—
516	SD₁₆	—	2	8	no	—
517	D₈	—	2	8	no	—
518	M₁₆	—	2	16	no	—
519	M₁₆	—	2	4	no	—
520	M₁₆	—	2	2	no	—
521	M₁₆	—	2	2	no	—
522	M₁₆	—	2	2	no	—
523	M₁₆	—	4	2	no	—
524	M₁₆	C₂×D₄×C₃₁	1	4	yes	—
525	C₂×C₈	—	2	16	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	2	4	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	—	2	4	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	2	4	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	2	2	no	—
535	C₂×C₈	—	2	2	no	—
536	C₂×C₈	—	2	2	no	—
537	C₂×C₈	—	2	2	no	—
538	C₂×C₈	—	2	2	no	—
539	C₂×C₈	—	4	2	no	—
540	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
541	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
542	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
543	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	4	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
558	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
559	C₂³	C₃₁×#121	1	2	yes	—
560	C₂³	C₃₁×#123	1	2	yes	—
561	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
562	Q₈	—	2	2	no	—
563	Q₈	—	2	4	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	2	no	—
567	Q₈	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
568	D₄	—	2	4	no	—
569	D₄	—	2	4	no	—
570	D₄	—	2	8	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	4	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	2	no	—
579	D₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
595	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
596	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
597	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
598	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
599	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
600	C₂×C₄	C₃₁×#120	1	2	yes	—
601	C₂×C₄	C₃₁×#120	1	2	yes	—
602	C₂×C₄	C₃₁×#121	1	2	yes	—
603	C₂×C₄	C₃₁×#121	1	2	yes	—
604	C₂×C₄	C₃₁×#121	1	2	yes	—
605	C₂×C₄	C₃₁×#123	1	2	yes	—
606	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	—	2	4	no	—
616	C₈	—	2	2	no	—
617	C₈	—	4	2	no	—
618	C₂²	—	2	4	no	—
619	C₂²	—	2	4	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	8	4	no	—
632	C₂²	C₃₁×#386	1	2	yes	—
633	C₂²	C₃₁×#386	1	2	yes	—
634	C₂²	C₃₁×#443	1	2	yes	—
635	C₂²	C₃₁×#444	1	2	yes	—
636	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
637	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
638	C₂²	C₂×C₃₁×#123	1	1	yes	characteristic
639	C₄	—	2	4	no	—
640	C₄	—	4	4	no	—
641	C₄	—	4	2	no	—
642	C₄	C₃₁×#386	1	2	yes	—
643	C₄	C₃₁×#386	1	2	yes	—
644	C₄	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
645	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
646	C₄	C₂×C₃₁×#120	1	1	yes	characteristic
647	C₄	C₂×C₃₁×#121	1	1	yes	characteristic
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	2	2	no	—
651	C₂	—	4	4	no	—
652	C₂	—	8	2	no	—
653	C₂	C₃₁×#1876	1	4	yes	direct product factor
654	C₂	C₂×C₃₁×#386	1	1	yes	characteristic
655	C₂	C₂×C₃₁×#443	1	1	yes	characteristic
656	C₂	C₂×C₃₁×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₄×D₄
prime radical	C₂²×C₃₁×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₁×#131	C₂	semidirect
3. C₂²×C₃₁×#104	C₂	semidirect
4. C₂²×C₃₁×#104	C₂	semidirect
5. C₂×C₃₁×#408	C₂	semidirect
6. C₃₁×#1876	C₂	direct (N × H)
7. C₂×C₃₁×#341	C₂	semidirect
8. C₂×C₃₁×#336	C₂	semidirect
13. C₂×C₃₁×#135	C₄	semidirect
15. C₂²×Q₁₆×C₃₁	C₄	semidirect
16. C₂²×SD₁₆×C₃₁	C₄	semidirect
17. C₂²×SD₁₆×C₃₁	C₄	semidirect
18. C₂²×D₈×C₃₁	C₄	semidirect
22. C₂×C₃₁×#131	C₂²	semidirect
32. C₂×C₃₁×#104	C₂²	semidirect
33. C₂×C₃₁×#104	C₂²	semidirect
35. C₃₁×#408	C₂²	semidirect
38. C₃₁×#341	C₂²	semidirect
39. C₃₁×#336	C₂²	semidirect
70. C₂×Q₁₆×C₃₁	C₂×C₄	semidirect
73. C₂×SD₁₆×C₃₁	C₂×C₄	semidirect
74. C₂×SD₁₆×C₃₁	C₂×C₄	semidirect
76. C₂×D₈×C₃₁	C₂×C₄	semidirect
218. C₂×#1876	C₃₁	direct (N × H)
291. C₂²×#131	C₂×C₃₁	semidirect
292. C₂²×#104	C₂×C₃₁	semidirect
293. C₂²×#104	C₂×C₃₁	semidirect
294. C₂×#408	C₂×C₃₁	semidirect
295. #1876	C₂×C₃₁	direct (N × H)
296. C₂×#341	C₂×C₃₁	semidirect
297. C₂×#336	C₂×C₃₁	semidirect
332. C₂×#135	C₄×C₃₁	semidirect
334. C₂²×Q₁₆	C₄×C₃₁	semidirect
335. C₂²×SD₁₆	C₄×C₃₁	semidirect
336. C₂²×SD₁₆	C₄×C₃₁	semidirect
337. C₂²×D₈	C₄×C₃₁	semidirect
341. C₂×#131	C₂²×C₃₁	semidirect
351. C₂×#104	C₂²×C₃₁	semidirect
352. C₂×#104	C₂²×C₃₁	semidirect
354. #408	C₂²×C₃₁	semidirect
357. #341	C₂²×C₃₁	semidirect
358. #336	C₂²×C₃₁	semidirect
364. C₂×C₃₁	#1876	direct (N × H)
398. C₂×Q₁₆	C₂×C₄×C₃₁	semidirect
401. C₂×SD₁₆	C₂×C₄×C₃₁	semidirect
402. C₂×SD₁₆	C₂×C₄×C₃₁	semidirect
404. C₂×D₈	C₂×C₄×C₃₁	semidirect
442. C₃₁	C₂×#1876	direct (N × H)
653. C₂	C₃₁×#1876	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×#135	2
C₂²×C₃₁×#131	2
C₂²×C₃₁×#104	2
C₂×C₃₁×#408	2
C₃₁×#1876	2
C₂×C₃₁×#341	2
C₂×C₃₁×#336	2
C₂×#1876	31

Subgroups — C2×C31×#1876 #21477675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1876 #21477675