Subgroups — C₂×C₃₁×#1980 #21478010

Order 7936.

1746 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×C₃₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#104	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1980	C₂	1	8	yes	maximal, direct product factor
6	C₂²×#41×C₃₁	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
8	C₃₁×#532	—	2	2	no	—
9	C₃₁×#532	—	2	2	no	—
10	C₃₁×#532	C₄	1	4	yes	complemented
11	C₃₁×#532	C₂²	1	4	yes	—
12	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃₁×#127	C₄	1	1	yes	characteristic, complemented
14	C₂×C₃₁×#124	C₄	1	2	yes	complemented
15	C₂×C₃₁×#121	—	2	1	no	—
16	C₂×C₃₁×#121	—	2	1	no	—
17	C₂×C₄×D₄×C₃₁	—	2	1	no	—
18	C₂×C₄×D₄×C₃₁	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
20	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
21	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#104	—	2	16	no	—
23	C₂×C₃₁×#104	C₂²	1	16	yes	complemented
24	C₄×M₁₆×C₃₁	—	2	2	no	—
25	C₄×M₁₆×C₃₁	C₂²	1	4	yes	complemented
26	C₂×C₃₁×#97	—	2	1	no	—
27	C₂×C₄×C₈×C₃₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
30	C₂×C₃₁×#95	—	2	1	no	—
31	C₂×#41×C₃₁	—	2	2	no	—
32	C₂×#41×C₃₁	—	2	2	no	—
33	C₂×#41×C₃₁	—	2	8	no	—
34	C₂×#41×C₃₁	—	2	8	no	—
35	C₂×#41×C₃₁	C₂×C₄	1	4	yes	—
36	C₂×#41×C₃₁	C₂³	1	4	yes	—
37	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₃₁	—	2	2	no	—
39	C₂²×D₄×C₃₁	—	2	1	no	—
40	C₂²×D₄×C₃₁	—	2	1	no	—
41	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₃₁	—	2	2	no	—
43	C₂³×C₄×C₃₁	—	2	2	no	—
44	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₃₁	—	2	2	no	—
48	C₂×M₁₆×C₃₁	—	2	4	no	—
49	C₂×M₁₆×C₃₁	D₄	1	8	yes	complemented
50	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
51	C₂²×C₈×C₃₁	—	2	2	no	—
52	C₃₁×C₄⋊Q₈	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
54	C₃₁×#127	—	2	2	no	—
55	C₃₁×#127	C₂×C₄	1	4	yes	complemented
56	C₃₁×#124	—	2	4	no	—
57	C₃₁×#124	C₂×C₄	1	8	yes	complemented
58	C₃₁×#121	—	2	4	no	—
59	C₃₁×#121	—	2	4	no	—
60	C₃₁×#121	—	2	4	no	—
61	C₃₁×#121	—	2	4	no	—
62	C₄×D₄×C₃₁	—	2	4	no	—
63	C₄×D₄×C₃₁	—	2	4	no	—
64	C₄×D₄×C₃₁	—	2	4	no	—
65	C₄×D₄×C₃₁	—	2	4	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
72	C₂×C₄²×C₃₁	—	2	8	no	—
73	C₂×C₄²×C₃₁	—	2	2	no	—
74	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₃₁	D₄	1	2	yes	—
78	C₂×C₄²×C₃₁	D₄	1	2	yes	—
79	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
82	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
83	C₃₁×#104	—	2	32	no	—
84	C₃₁×#97	—	2	4	no	—
85	C₄×C₈×C₃₁	—	2	4	no	—
86	C₃₁×#95	—	2	4	no	—
87	C₂⁴×C₃₁	—	2	2	no	—
88	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
89	#41×C₃₁	—	2	16	no	—
90	#41×C₃₁	—	2	8	no	—
91	#41×C₃₁	—	2	8	no	—
92	#41×C₃₁	—	4	8	no	—
93	#41×C₃₁	—	4	4	no	—
94	#41×C₃₁	—	4	4	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	2	8	no	—
97	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
98	C₂×D₄×C₃₁	—	2	4	no	—
99	C₂×D₄×C₃₁	—	2	4	no	—
100	C₂×D₄×C₃₁	—	2	4	no	—
101	C₂×D₄×C₃₁	—	2	4	no	—
102	C₂×D₄×C₃₁	—	2	2	no	—
103	C₂×D₄×C₃₁	—	2	8	no	—
104	C₂×D₄×C₃₁	—	4	4	no	—
105	C₂×D₄×C₃₁	—	4	4	no	—
106	C₂×D₄×C₃₁	—	4	4	no	—
107	C₂×D₄×C₃₁	—	4	4	no	—
108	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₃₁	—	2	4	no	—
110	C₂²×C₄×C₃₁	—	2	8	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	4	no	—
115	C₂²×C₄×C₃₁	—	4	2	no	—
116	C₂²×C₄×C₃₁	—	4	4	no	—
117	C₂²×C₄×C₃₁	—	4	4	no	—
118	C₂²×C₄×C₃₁	—	4	8	no	—
119	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₁	#41	1	4	yes	—
134	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₃₁	—	2	8	no	—
136	M₁₆×C₃₁	—	2	4	no	—
137	M₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
138	C₂×C₈×C₃₁	—	2	8	no	—
139	C₂×C₈×C₃₁	—	2	4	no	—
140	C₄⋊C₄×C₃₁	—	2	16	no	—
141	C₄⋊C₄×C₃₁	—	2	4	no	—
142	C₄⋊C₄×C₃₁	—	2	4	no	—
143	C₂²⋊C₄×C₃₁	—	2	8	no	—
144	C₂²⋊C₄×C₃₁	—	2	8	no	—
145	C₄²×C₃₁	—	2	8	no	—
146	C₄²×C₃₁	—	4	4	no	—
147	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
148	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
149	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
150	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
151	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
152	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
153	C₄²×C₃₁	C₂×D₄	1	2	yes	—
154	C₄²×C₃₁	C₂×D₄	1	2	yes	—
155	C₂×#1980	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₃₁	—	2	2	no	—
157	C₂³×C₃₁	—	2	2	no	—
158	C₂³×C₃₁	—	2	4	no	—
159	C₂³×C₃₁	—	4	4	no	—
160	C₂³×C₃₁	—	4	4	no	—
161	C₂³×C₃₁	—	4	4	no	—
162	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂³×C₃₁	#124	1	2	yes	—
165	C₂³×C₃₁	#127	1	2	yes	—
166	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₃₁	—	2	8	no	—
168	Q₈×C₃₁	—	4	4	no	—
169	D₄×C₃₁	—	2	8	no	—
170	D₄×C₃₁	—	4	8	no	—
171	D₄×C₃₁	—	4	4	no	—
172	D₄×C₃₁	—	4	4	no	—
173	D₄×C₃₁	—	4	8	no	—
174	D₄×C₃₁	—	4	4	no	—
175	D₄×C₃₁	—	4	8	no	—
176	C₂×C₄×C₃₁	—	2	2	no	—
177	C₂×C₄×C₃₁	—	2	2	no	—
178	C₂×C₄×C₃₁	—	2	2	no	—
179	C₂×C₄×C₃₁	—	2	4	no	—
180	C₂×C₄×C₃₁	—	2	4	no	—
181	C₂×C₄×C₃₁	—	2	8	no	—
182	C₂×C₄×C₃₁	—	2	4	no	—
183	C₂×C₄×C₃₁	—	4	2	no	—
184	C₂×C₄×C₃₁	—	4	2	no	—
185	C₂×C₄×C₃₁	—	4	4	no	—
186	C₂×C₄×C₃₁	—	4	16	no	—
187	C₂×C₄×C₃₁	—	4	4	no	—
188	C₂×C₄×C₃₁	—	4	4	no	—
189	C₂×C₄×C₃₁	—	4	8	no	—
190	C₂×C₄×C₃₁	—	4	8	no	—
191	C₂×C₄×C₃₁	#104	1	4	yes	complemented
192	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
199	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
200	C₂×C₄×C₃₁	#121	1	4	yes	—
201	C₂×C₄×C₃₁	#121	1	4	yes	—
202	C₂×C₄×C₃₁	#124	1	2	yes	—
203	C₂×C₄×C₃₁	#127	1	2	yes	—
204	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
208	C₈×C₃₁	—	2	8	no	—
209	C₂×#532	C₂×C₃₁	1	1	yes	characteristic
210	C₂²×#104	C₂×C₃₁	1	4	yes	complemented
211	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
212	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
213	#1980	C₂×C₃₁	1	8	yes	direct product factor
214	C₂²×C₃₁	—	2	1	no	—
215	C₂²×C₃₁	—	2	1	no	—
216	C₂²×C₃₁	—	2	1	no	—
217	C₂²×C₃₁	—	2	1	no	—
218	C₂²×C₃₁	—	2	4	no	—
219	C₂²×C₃₁	—	2	4	no	—
220	C₂²×C₃₁	—	4	4	no	—
221	C₂²×C₃₁	—	4	4	no	—
222	C₂²×C₃₁	—	4	4	no	—
223	C₂²×C₃₁	—	8	8	no	—
224	C₂²×C₃₁	#390	1	2	yes	—
225	C₂²×C₃₁	#390	1	2	yes	—
226	C₂²×C₃₁	C₂×#104	1	2	yes	—
227	C₂²×C₃₁	#421	1	2	yes	—
228	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
230	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
231	C₄×C₃₁	—	2	2	no	—
232	C₄×C₃₁	—	2	2	no	—
233	C₄×C₃₁	—	2	2	no	—
234	C₄×C₃₁	—	4	8	no	—
235	C₄×C₃₁	—	4	4	no	—
236	C₄×C₃₁	#390	1	2	yes	—
237	C₄×C₃₁	#390	1	2	yes	—
238	C₄×C₃₁	C₂×#104	1	4	yes	complemented
239	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
240	C₄×C₃₁	C₂×#121	1	2	yes	—
241	C₂²×#41	C₂²×C₃₁	1	2	yes	—
242	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
243	#532	—	2	2	no	—
244	#532	—	2	2	no	—
245	#532	C₄×C₃₁	1	4	yes	complemented
246	#532	C₂²×C₃₁	1	4	yes	—
247	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic, complemented
248	C₂×#127	C₄×C₃₁	1	1	yes	characteristic, complemented
249	C₂×#124	C₄×C₃₁	1	2	yes	complemented
250	C₂×#121	—	2	1	no	—
251	C₂×#121	—	2	1	no	—
252	C₂×C₄×D₄	—	2	1	no	—
253	C₂×C₄×D₄	—	2	1	no	—
254	C₂²×C₄⋊C₄	—	2	1	no	—
255	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
256	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
257	C₂×#104	—	2	16	no	—
258	C₂×#104	C₂²×C₃₁	1	16	yes	complemented
259	C₄×M₁₆	—	2	2	no	—
260	C₄×M₁₆	C₂²×C₃₁	1	4	yes	complemented
261	C₂×#97	—	2	1	no	—
262	C₂×C₄×C₈	—	2	1	no	—
263	C₄×C₄⋊C₄	—	2	2	no	—
264	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
265	C₂×#95	—	2	1	no	—
266	C₂×C₃₁	—	2	1	no	—
267	C₂×C₃₁	—	2	1	no	—
268	C₂×C₃₁	—	2	2	no	—
269	C₂×C₃₁	—	8	4	no	—
270	C₂×C₃₁	#1980	1	4	yes	direct product factor
271	C₂×C₃₁	C₂×#390	1	1	yes	characteristic
272	C₂×C₃₁	C₂²×#104	1	1	yes	characteristic
273	C₂×C₃₁	C₂×#421	1	1	yes	characteristic
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	8	no	—
277	C₂×#41	—	2	8	no	—
278	C₂×#41	C₂×C₄×C₃₁	1	4	yes	—
279	C₂×#41	C₂³×C₃₁	1	4	yes	—
280	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
288	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	4	no	—
292	C₂×M₁₆	D₄×C₃₁	1	8	yes	complemented
293	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
294	C₂²×C₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
297	#127	—	2	2	no	—
298	#127	C₂×C₄×C₃₁	1	4	yes	complemented
299	#124	—	2	4	no	—
300	#124	C₂×C₄×C₃₁	1	8	yes	complemented
301	#121	—	2	4	no	—
302	#121	—	2	4	no	—
303	#121	—	2	4	no	—
304	#121	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	8	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₄²	—	2	8	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
318	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
319	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
320	C₂×C₄²	D₄×C₃₁	1	2	yes	—
321	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
322	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₃₁	1	2	yes	—
324	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
325	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
326	#104	—	2	32	no	—
327	#97	—	2	4	no	—
328	C₄×C₈	—	2	4	no	—
329	#95	—	2	4	no	—
330	C₃₁	C₂×#1980	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
333	#41	—	2	16	no	—
334	#41	—	2	8	no	—
335	#41	—	2	8	no	—
336	#41	—	4	8	no	—
337	#41	—	4	4	no	—
338	#41	—	4	4	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	4	8	no	—
363	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
364	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
365	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
367	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
368	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
377	C₂²×C₄	#41×C₃₁	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
379	M₁₆	—	2	8	no	—
380	M₁₆	—	2	4	no	—
381	M₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
382	C₂×C₈	—	2	8	no	—
383	C₂×C₈	—	2	4	no	—
384	C₄⋊C₄	—	2	16	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₄²	—	2	8	no	—
390	C₄²	—	4	4	no	—
391	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
392	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
393	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
394	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
395	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
396	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
397	C₄²	C₂×D₄×C₃₁	1	2	yes	—
398	C₄²	C₂×D₄×C₃₁	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
406	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
407	C₂³	C₃₁×#124	1	2	yes	—
408	C₂³	C₃₁×#127	1	2	yes	—
409	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
410	Q₈	—	2	8	no	—
411	Q₈	—	4	4	no	—
412	D₄	—	2	8	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	4	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	16	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	C₃₁×#104	1	4	yes	complemented
435	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
439	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
440	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
441	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
442	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
443	C₂×C₄	C₃₁×#121	1	4	yes	—
444	C₂×C₄	C₃₁×#121	1	4	yes	—
445	C₂×C₄	C₃₁×#124	1	2	yes	—
446	C₂×C₄	C₃₁×#127	1	2	yes	—
447	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
451	C₈	—	2	8	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	C₃₁×#390	1	2	yes	—
463	C₂²	C₃₁×#390	1	2	yes	—
464	C₂²	C₂×C₃₁×#104	1	2	yes	—
465	C₂²	C₃₁×#421	1	2	yes	—
466	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
467	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
468	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	8	no	—
473	C₄	—	4	4	no	—
474	C₄	C₃₁×#390	1	2	yes	—
475	C₄	C₃₁×#390	1	2	yes	—
476	C₄	C₂×C₃₁×#104	1	4	yes	complemented
477	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
478	C₄	C₂×C₃₁×#121	1	2	yes	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	2	2	no	—
482	C₂	—	8	4	no	—
483	C₂	C₃₁×#1980	1	4	yes	direct product factor
484	C₂	C₂×C₃₁×#390	1	1	yes	characteristic
485	C₂	C₂²×C₃₁×#104	1	1	yes	characteristic
486	C₂	C₂×C₃₁×#421	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	C₂×C₂²⋊C₄
prime radical	C₂×C₃₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₁×#104	C₂	semidirect
3. C₂×C₄×M₁₆×C₃₁	C₂	semidirect
4. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
5. C₃₁×#1980	C₂	direct (N × H)
10. C₃₁×#532	C₄	semidirect
12. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
13. C₂×C₃₁×#127	C₄	semidirect
14. C₂×C₃₁×#124	C₄	semidirect
23. C₂×C₃₁×#104	C₂²	semidirect
25. C₄×M₁₆×C₃₁	C₂²	semidirect
29. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
49. C₂×M₁₆×C₃₁	D₄	semidirect
53. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
55. C₃₁×#127	C₂×C₄	semidirect
57. C₃₁×#124	C₂×C₄	semidirect
137. M₁₆×C₃₁	C₂×D₄	semidirect
155. C₂×#1980	C₃₁	direct (N × H)
191. C₂×C₄×C₃₁	#104	semidirect
210. C₂²×#104	C₂×C₃₁	semidirect
211. C₂×C₄×M₁₆	C₂×C₃₁	semidirect
212. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
213. #1980	C₂×C₃₁	direct (N × H)
238. C₄×C₃₁	C₂×#104	semidirect
245. #532	C₄×C₃₁	semidirect
247. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
248. C₂×#127	C₄×C₃₁	semidirect
249. C₂×#124	C₄×C₃₁	semidirect
258. C₂×#104	C₂²×C₃₁	semidirect
260. C₄×M₁₆	C₂²×C₃₁	semidirect
264. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
270. C₂×C₃₁	#1980	direct (N × H)
292. C₂×M₁₆	D₄×C₃₁	semidirect
296. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
298. #127	C₂×C₄×C₃₁	semidirect
300. #124	C₂×C₄×C₃₁	semidirect
330. C₃₁	C₂×#1980	direct (N × H)
381. M₁₆	C₂×D₄×C₃₁	semidirect
434. C₂×C₄	C₃₁×#104	semidirect
476. C₄	C₂×C₃₁×#104	semidirect
483. C₂	C₃₁×#1980	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#532	2
C₂²×C₃₁×#104	2
C₂×C₄×M₁₆×C₃₁	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₃₁×#1980	2
C₂×#1980	31

Subgroups — C2×C31×#1980 #21478010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1980 #21478010