Subgroups — C₂×C₃₁×#1485 #21474219

Order 7936.

1074 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1485	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×Q₈⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂²×M₁₆×C₃₁	—	2	1	no	—
7	C₃₁×#533	—	2	2	no	—
8	C₃₁×#533	—	2	2	no	—
9	C₃₁×#533	C₄	1	4	yes	—
10	C₃₁×#533	C₂²	1	4	yes	—
11	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₃₁×#125	—	2	1	no	—
14	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₃₁×C₂²⋊Q₈	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
17	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
18	C₂×C₃₁×#117	—	2	1	no	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#431	—	2	2	no	—
21	C₃₁×#431	C₂²	1	4	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
24	C₄×M₁₆×C₃₁	—	2	2	no	—
25	C₄×M₁₆×C₃₁	C₂²	1	4	yes	—
26	C₂×C₃₁×#97	—	2	1	no	—
27	C₂×C₄×C₈×C₃₁	—	2	1	no	—
28	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
29	C₃₁×Q₈⋊C₈	C₂²	1	16	yes	complemented
30	C₂²×Q₈×C₃₁	—	2	1	no	—
31	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₃₁	—	2	8	no	—
36	C₂×M₁₆×C₃₁	—	2	4	no	—
37	C₂²×C₈×C₃₁	—	2	2	no	—
38	C₂²×C₈×C₃₁	—	2	2	no	—
39	C₃₁×C₄⋊Q₈	—	2	2	no	—
40	C₃₁×C₄⋊Q₈	—	2	2	no	—
41	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
42	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
43	C₃₁×#125	—	2	4	no	—
44	C₃₁×#125	—	2	4	no	—
45	C₃₁×C₂²⋊Q₈	—	2	4	no	—
46	C₃₁×C₂²⋊Q₈	—	2	4	no	—
47	C₃₁×C₂²⋊Q₈	—	2	4	no	—
48	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
49	C₄×Q₈×C₃₁	—	2	4	no	—
50	C₄×Q₈×C₃₁	—	2	4	no	—
51	C₄×Q₈×C₃₁	—	2	2	no	—
52	C₄×Q₈×C₃₁	—	2	2	no	—
53	C₄×Q₈×C₃₁	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
55	C₃₁×#117	—	2	4	no	—
56	C₃₁×#117	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	D₄	1	2	yes	—
69	C₂×C₄²×C₃₁	D₄	1	2	yes	—
70	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
73	C₃₁×C₄⋊C₈	—	2	2	no	—
74	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
75	C₃₁×C₂²⋊C₈	—	2	4	no	—
76	C₃₁×#97	—	2	4	no	—
77	C₄×C₈×C₃₁	—	2	4	no	—
78	C₄×C₈×C₃₁	—	2	2	no	—
79	C₄×C₈×C₃₁	C₂³	1	4	yes	—
80	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×Q₈×C₃₁	—	2	2	no	—
82	C₂×Q₈×C₃₁	—	2	4	no	—
83	C₂×Q₈×C₃₁	—	2	8	no	—
84	C₂×Q₈×C₃₁	—	4	4	no	—
85	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	2	4	no	—
89	C₂²×C₄×C₃₁	—	2	2	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	M₁₆×C₃₁	—	2	16	no	—
104	C₂×C₈×C₃₁	—	2	8	no	—
105	C₂×C₈×C₃₁	—	2	4	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	4	4	no	—
108	C₄⋊C₄×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	2	4	no	—
111	C₄⋊C₄×C₃₁	—	2	8	no	—
112	C₄⋊C₄×C₃₁	—	2	4	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	4	no	—
115	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
116	C₂²⋊C₄×C₃₁	—	2	8	no	—
117	C₄²×C₃₁	—	2	4	no	—
118	C₄²×C₃₁	—	2	4	no	—
119	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
124	C₄²×C₃₁	C₂×D₄	1	2	yes	—
125	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₃₁	C₂×D₄	1	2	yes	—
127	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
129	C₂×#1485	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	2	2	no	—
132	C₂³×C₃₁	—	2	2	no	—
133	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	Q₈×C₃₁	—	2	8	no	—
136	Q₈×C₃₁	—	4	4	no	—
137	Q₈×C₃₁	—	4	8	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	4	no	—
145	C₂×C₄×C₃₁	—	2	4	no	—
146	C₂×C₄×C₃₁	—	2	4	no	—
147	C₂×C₄×C₃₁	—	2	4	no	—
148	C₂×C₄×C₃₁	—	2	4	no	—
149	C₂×C₄×C₃₁	—	4	4	no	—
150	C₂×C₄×C₃₁	—	4	4	no	—
151	C₂×C₄×C₃₁	#104	1	4	yes	—
152	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₃₁	#131	1	4	yes	—
159	C₂×C₄×C₃₁	#137	1	4	yes	—
160	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₃₁	—	2	8	no	—
164	C₈×C₃₁	—	4	4	no	—
165	C₂×#533	C₂×C₃₁	1	1	yes	characteristic
166	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
167	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
168	#1485	C₂×C₃₁	1	8	yes	direct product factor
169	C₂×Q₈⋊C₈	C₂×C₃₁	1	4	yes	complemented
170	C₂²×C₃₁	—	2	2	no	—
171	C₂²×C₃₁	—	2	2	no	—
172	C₂²×C₃₁	—	2	2	no	—
173	C₂²×C₃₁	—	4	4	no	—
174	C₂²×C₃₁	#408	1	2	yes	—
175	C₂²×C₃₁	#419	1	2	yes	—
176	C₂²×C₃₁	C₂×#104	1	2	yes	—
177	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₄×C₃₁	—	2	2	no	—
179	C₄×C₃₁	—	2	2	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	4	4	no	—
183	C₄×C₃₁	—	4	4	no	—
184	C₄×C₃₁	#408	1	2	yes	—
185	C₄×C₃₁	#419	1	2	yes	—
186	C₄×C₃₁	C₂×#104	1	4	yes	—
187	C₄×C₃₁	C₂×#131	1	2	yes	—
188	C₄×C₃₁	C₂×#137	1	2	yes	—
189	C₂²×M₁₆	—	2	1	no	—
190	#533	—	2	2	no	—
191	#533	—	2	2	no	—
192	#533	C₄×C₃₁	1	4	yes	—
193	#533	C₂²×C₃₁	1	4	yes	—
194	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
195	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
196	C₂×#125	—	2	1	no	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₂²⋊Q₈	C₄×C₃₁	1	2	yes	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
201	C₂×#117	—	2	1	no	—
202	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
203	#431	—	2	2	no	—
204	#431	C₂²×C₃₁	1	4	yes	—
205	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
206	C₂×C₂²⋊C₈	—	2	1	no	—
207	C₄×M₁₆	—	2	2	no	—
208	C₄×M₁₆	C₂²×C₃₁	1	4	yes	—
209	C₂×#97	—	2	1	no	—
210	C₂×C₄×C₈	—	2	1	no	—
211	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
212	Q₈⋊C₈	C₂²×C₃₁	1	16	yes	complemented
213	C₂×C₃₁	—	4	2	no	—
214	C₂×C₃₁	#1485	1	4	yes	direct product factor
215	C₂×C₃₁	C₂×#408	1	1	yes	characteristic
216	C₂×C₃₁	C₂×#419	1	1	yes	characteristic
217	C₂×C₃₁	C₂²×#104	1	1	yes	characteristic
218	C₂²×Q₈	—	2	1	no	—
219	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
220	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
223	C₂×M₁₆	—	2	8	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	—
230	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	—
231	#125	—	2	4	no	—
232	#125	—	2	4	no	—
233	C₂²⋊Q₈	—	2	4	no	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	2	2	no	—
240	C₄×Q₈	—	2	2	no	—
241	C₄×Q₈	C₂×C₄×C₃₁	1	4	yes	—
242	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
243	#117	—	2	4	no	—
244	#117	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
255	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₃₁	1	2	yes	—
258	C₂×C₄²	D₄×C₃₁	1	2	yes	—
259	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
263	C₂²⋊C₈	—	2	4	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	—	2	4	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	C₂³×C₃₁	1	4	yes	—
268	C₃₁	C₂×#1485	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	8	no	—
273	C₂×Q₈	—	4	4	no	—
274	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
282	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
283	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
292	M₁₆	—	2	16	no	—
293	C₂×C₈	—	2	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	4	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
305	C₂²⋊C₄	—	2	8	no	—
306	C₄²	—	2	4	no	—
307	C₄²	—	2	4	no	—
308	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
309	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
310	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
311	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
312	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
313	C₄²	C₂×D₄×C₃₁	1	2	yes	—
314	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₃₁	1	2	yes	—
316	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
322	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
323	Q₈	—	2	8	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	8	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	C₃₁×#104	1	4	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
346	C₂×C₄	C₃₁×#131	1	4	yes	—
347	C₂×C₄	C₃₁×#137	1	4	yes	—
348	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
351	C₈	—	2	8	no	—
352	C₈	—	4	4	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	4	4	no	—
357	C₂²	C₃₁×#408	1	2	yes	—
358	C₂²	C₃₁×#419	1	2	yes	—
359	C₂²	C₂×C₃₁×#104	1	2	yes	—
360	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	4	4	no	—
366	C₄	—	4	4	no	—
367	C₄	C₃₁×#408	1	2	yes	—
368	C₄	C₃₁×#419	1	2	yes	—
369	C₄	C₂×C₃₁×#104	1	4	yes	—
370	C₄	C₂×C₃₁×#131	1	2	yes	—
371	C₄	C₂×C₃₁×#137	1	2	yes	—
372	C₂	—	4	2	no	—
373	C₂	C₃₁×#1485	1	4	yes	direct product factor
374	C₂	C₂×C₃₁×#408	1	1	yes	characteristic
375	C₂	C₂×C₃₁×#419	1	1	yes	characteristic
376	C₂	C₂²×C₃₁×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃₁	C₂²⋊C₄
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
4. C₃₁×#1485	C₂	direct (N × H)
5. C₂×C₃₁×Q₈⋊C₈	C₂	semidirect
29. C₃₁×Q₈⋊C₈	C₂²	semidirect
129. C₂×#1485	C₃₁	direct (N × H)
168. #1485	C₂×C₃₁	direct (N × H)
169. C₂×Q₈⋊C₈	C₂×C₃₁	semidirect
212. Q₈⋊C₈	C₂²×C₃₁	semidirect
214. C₂×C₃₁	#1485	direct (N × H)
268. C₃₁	C₂×#1485	direct (N × H)
373. C₂	C₃₁×#1485	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×#533	2
C₂×C₃₁×#431	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#1485	2
C₂×C₃₁×Q₈⋊C₈	2
C₂×#1485	31

Subgroups — C2×C31×#1485 #21474219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1485 #21474219