Subgroups — C₂×C₇₁×#3174 #31881550

Order 18176.

1970 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#540×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#3174	C₂	1	16	yes	maximal, direct product factor
4	C₂×#499×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#492×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#491×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#490×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#468×C₇₁	C₂	1	2	yes	maximal, complemented
9	C₂×#465×C₇₁	C₂	1	2	yes	maximal, complemented
10	C₂×#440×C₇₁	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×SD₁₆×C₇₁	C₂	1	2	yes	maximal, complemented
12	C₂×#405×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	#541×C₇₁	—	2	4	no	—
18	#541×C₇₁	C₂²	1	8	yes	complemented
19	#540×C₇₁	—	2	4	no	—
20	#540×C₇₁	C₂²	1	8	yes	—
21	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic
23	C₂×#126×C₇₁	—	2	2	no	—
24	C₂×#125×C₇₁	—	2	2	no	—
25	C₂×#125×C₇₁	C₂²	1	1	yes	characteristic
26	C₂×#125×C₇₁	C₂²	1	1	yes	characteristic
27	C₂×#123×C₇₁	—	2	2	no	—
28	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	2	yes	—
29	C₂×#121×C₇₁	—	2	2	no	—
30	C₂×#121×C₇₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
33	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
34	#499×C₇₁	C₂²	1	8	yes	complemented
35	#492×C₇₁	C₂²	1	8	yes	complemented
36	#491×C₇₁	C₂²	1	8	yes	complemented
37	#490×C₇₁	C₂²	1	8	yes	complemented
38	#468×C₇₁	C₂²	1	16	yes	complemented
39	#465×C₇₁	C₂²	1	16	yes	complemented
40	#440×C₇₁	C₂²	1	16	yes	complemented
41	C₄×SD₁₆×C₇₁	C₂²	1	16	yes	complemented
42	C₂×#107×C₇₁	C₂²	1	2	yes	—
43	C₂×#106×C₇₁	C₂²	1	2	yes	—
44	C₂×#103×C₇₁	C₂²	1	2	yes	—
45	C₂×#103×C₇₁	C₂²	1	2	yes	—
46	C₂×#102×C₇₁	C₂²	1	2	yes	—
47	C₂×#102×C₇₁	C₂²	1	2	yes	—
48	#405×C₇₁	C₂²	1	8	yes	complemented
49	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
50	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
53	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
54	C₂²×D₄×C₇₁	—	2	2	no	—
55	C₂²×D₄×C₇₁	—	2	2	no	—
56	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
57	C₂³×C₄×C₇₁	—	2	2	no	—
58	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
59	C₂×SD₁₆×C₇₁	—	2	8	no	—
60	C₂×SD₁₆×C₇₁	—	2	8	no	—
61	C₂×SD₁₆×C₇₁	C₂³	1	8	yes	—
62	C₂×SD₁₆×C₇₁	C₂³	1	8	yes	—
63	C₂×M₁₆×C₇₁	—	2	4	no	—
64	C₂×M₁₆×C₇₁	C₂³	1	4	yes	—
65	C₂²×C₈×C₇₁	—	2	4	no	—
66	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
67	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₇₁	—	2	2	no	—
72	C₄⋊Q₈×C₇₁	C₂³	1	4	yes	—
73	#127×C₇₁	—	2	2	no	—
74	#127×C₇₁	C₂³	1	4	yes	—
75	#126×C₇₁	—	2	16	no	—
76	#125×C₇₁	—	2	16	no	—
77	#125×C₇₁	—	2	2	no	—
78	#125×C₇₁	—	2	2	no	—
79	#125×C₇₁	C₂³	1	4	yes	—
80	#125×C₇₁	C₂³	1	4	yes	—
81	#123×C₇₁	—	2	16	no	—
82	C₂²⋊Q₈×C₇₁	—	2	4	no	—
83	C₂²⋊Q₈×C₇₁	C₂³	1	8	yes	—
84	#121×C₇₁	—	2	4	no	—
85	#121×C₇₁	—	2	16	no	—
86	#121×C₇₁	C₂³	1	8	yes	—
87	C₄×Q₈×C₇₁	—	2	4	no	—
88	C₄×Q₈×C₇₁	C₂³	1	8	yes	—
89	C₄×D₄×C₇₁	—	2	4	no	—
90	C₄×D₄×C₇₁	C₂³	1	8	yes	—
91	#117×C₇₁	D₄	1	4	yes	—
92	#117×C₇₁	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
94	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
95	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
96	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
97	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
98	C₂×C₄⋊C₄×C₇₁	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₇₁	D₄	1	2	yes	—
105	C₂×C₄²×C₇₁	—	2	2	no	—
106	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
108	#107×C₇₁	C₂³	1	8	yes	—
109	#106×C₇₁	C₂³	1	8	yes	—
110	#103×C₇₁	C₂³	1	8	yes	—
111	#103×C₇₁	C₂³	1	8	yes	—
112	#102×C₇₁	C₂³	1	8	yes	—
113	#102×C₇₁	C₂³	1	8	yes	—
114	#97×C₇₁	C₂³	1	4	yes	—
115	#97×C₇₁	C₂³	1	4	yes	—
116	C₄×C₈×C₇₁	C₂³	1	4	yes	—
117	C₄×C₈×C₇₁	C₂³	1	4	yes	—
118	C₂⁴×C₇₁	—	2	2	no	—
119	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₇₁	—	2	2	no	—
121	C₂×Q₈×C₇₁	—	2	4	no	—
122	C₂×Q₈×C₇₁	—	2	4	no	—
123	C₂×Q₈×C₇₁	C₂⁴	1	4	yes	—
124	C₂×D₄×C₇₁	—	2	8	no	—
125	C₂×D₄×C₇₁	—	2	2	no	—
126	C₂×D₄×C₇₁	—	2	8	no	—
127	C₂×D₄×C₇₁	—	2	4	no	—
128	C₂×D₄×C₇₁	—	2	4	no	—
129	C₂×D₄×C₇₁	—	8	4	no	—
130	C₂×D₄×C₇₁	—	8	4	no	—
131	C₂×D₄×C₇₁	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₇₁	—	2	2	no	—
133	C₂²×C₄×C₇₁	—	2	2	no	—
134	C₂²×C₄×C₇₁	—	2	2	no	—
135	C₂²×C₄×C₇₁	—	2	2	no	—
136	C₂²×C₄×C₇₁	—	2	2	no	—
137	C₂²×C₄×C₇₁	—	2	8	no	—
138	C₂²×C₄×C₇₁	—	8	4	no	—
139	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
145	SD₁₆×C₇₁	—	2	16	no	—
146	SD₁₆×C₇₁	—	2	16	no	—
147	M₁₆×C₇₁	—	2	8	no	—
148	C₂×C₈×C₇₁	—	2	2	no	—
149	C₂×C₈×C₇₁	—	2	2	no	—
150	C₂×C₈×C₇₁	—	2	8	no	—
151	C₂×C₈×C₇₁	#41	1	4	yes	—
152	C₂×C₈×C₇₁	#41	1	4	yes	—
153	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
154	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
155	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
156	C₂×C₈×C₇₁	C₂⁴	1	2	yes	—
157	C₄⋊C₄×C₇₁	—	2	8	no	—
158	C₄⋊C₄×C₇₁	—	2	8	no	—
159	C₄⋊C₄×C₇₁	—	2	8	no	—
160	C₄⋊C₄×C₇₁	—	2	8	no	—
161	C₄⋊C₄×C₇₁	—	2	8	no	—
162	C₄⋊C₄×C₇₁	—	2	2	no	—
163	C₄⋊C₄×C₇₁	—	2	2	no	—
164	C₄⋊C₄×C₇₁	C₂×D₄	1	8	yes	—
165	C₄⋊C₄×C₇₁	C₂⁴	1	4	yes	—
166	C₄⋊C₄×C₇₁	C₂⁴	1	4	yes	—
167	C₂²⋊C₄×C₇₁	—	2	8	no	—
168	C₂²⋊C₄×C₇₁	—	2	8	no	—
169	C₂²⋊C₄×C₇₁	—	2	8	no	—
170	C₂²⋊C₄×C₇₁	C₂×D₄	1	8	yes	—
171	C₄²×C₇₁	—	2	8	no	—
172	C₄²×C₇₁	C₂×D₄	1	2	yes	—
173	C₄²×C₇₁	C₂×D₄	1	2	yes	—
174	C₄²×C₇₁	C₂⁴	1	2	yes	—
175	C₄²×C₇₁	C₂⁴	1	2	yes	—
176	C₂³×C₇₁	—	2	2	no	—
177	C₂³×C₇₁	—	2	4	no	—
178	C₂³×C₇₁	—	2	4	no	—
179	C₂³×C₇₁	—	4	4	no	—
180	C₂³×C₇₁	—	4	4	no	—
181	C₂³×C₇₁	—	4	4	no	—
182	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
183	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₇₁	—	2	4	no	—
185	Q₈×C₇₁	—	2	4	no	—
186	Q₈×C₇₁	—	4	4	no	—
187	D₄×C₇₁	—	2	4	no	—
188	D₄×C₇₁	—	2	4	no	—
189	D₄×C₇₁	—	4	4	no	—
190	D₄×C₇₁	—	8	8	no	—
191	D₄×C₇₁	—	8	8	no	—
192	C₂×C₄×C₇₁	—	2	2	no	—
193	C₂×C₄×C₇₁	—	2	4	no	—
194	C₂×C₄×C₇₁	—	2	4	no	—
195	C₂×C₄×C₇₁	—	2	4	no	—
196	C₂×C₄×C₇₁	—	2	2	no	—
197	C₂×C₄×C₇₁	—	2	2	no	—
198	C₂×C₄×C₇₁	—	2	4	no	—
199	C₂×C₄×C₇₁	—	2	4	no	—
200	C₂×C₄×C₇₁	—	2	4	no	—
201	C₂×C₄×C₇₁	—	4	4	no	—
202	C₂×C₄×C₇₁	—	4	4	no	—
203	C₂×C₄×C₇₁	—	4	4	no	—
204	C₂×C₄×C₇₁	—	8	8	no	—
205	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
210	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
211	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
212	C₈×C₇₁	—	2	2	no	—
213	C₈×C₇₁	—	2	2	no	—
214	C₈×C₇₁	C₂×#41	1	4	yes	—
215	C₈×C₇₁	C₂×#41	1	4	yes	—
216	C₂²×C₇₁	—	2	2	no	—
217	C₂²×C₇₁	—	2	4	no	—
218	C₂²×C₇₁	—	4	4	no	—
219	C₂²×C₇₁	—	4	4	no	—
220	C₂²×C₇₁	—	4	4	no	—
221	C₂²×C₇₁	—	4	4	no	—
222	C₂²×C₇₁	—	8	8	no	—
223	C₂²×C₇₁	#532	1	2	yes	—
224	C₂²×C₇₁	#577	1	4	yes	—
225	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₇₁	—	2	2	no	—
227	C₄×C₇₁	—	2	4	no	—
228	C₄×C₇₁	—	2	4	no	—
229	C₄×C₇₁	—	4	4	no	—
230	C₄×C₇₁	—	4	4	no	—
231	C₄×C₇₁	—	4	4	no	—
232	C₄×C₇₁	#532	1	2	yes	—
233	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
234	C₄×C₇₁	C₂²×#41	1	1	yes	characteristic
235	C₂×#3174	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂×C₇₁	—	4	2	no	—
237	C₂×C₇₁	—	8	4	no	—
238	C₂×C₇₁	#3174	1	4	yes	direct product factor
239	C₂×C₇₁	C₂×#532	1	1	yes	characteristic
240	C₂×C₇₁	C₂×#577	1	2	yes	—
241	C₂×#541	C₂×C₇₁	1	1	yes	characteristic, complemented
242	C₂×#540	C₂×C₇₁	1	1	yes	characteristic
243	#3174	C₂×C₇₁	1	16	yes	direct product factor
244	C₂×#499	C₂×C₇₁	1	1	yes	characteristic, complemented
245	C₂×#492	C₂×C₇₁	1	1	yes	characteristic, complemented
246	C₂×#491	C₂×C₇₁	1	1	yes	characteristic, complemented
247	C₂×#490	C₂×C₇₁	1	1	yes	characteristic, complemented
248	C₂×#468	C₂×C₇₁	1	2	yes	complemented
249	C₂×#465	C₂×C₇₁	1	2	yes	complemented
250	C₂×#440	C₂×C₇₁	1	2	yes	complemented
251	C₂×C₄×SD₁₆	C₂×C₇₁	1	2	yes	complemented
252	C₂×#405	C₂×C₇₁	1	1	yes	characteristic, complemented
253	C₇₁	C₂×#3174	1	1	yes	characteristic, direct product factor, Sylow
254	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
255	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
256	C₂²×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₇₁	1	1	yes	characteristic
258	#541	—	2	4	no	—
259	#541	C₂²×C₇₁	1	8	yes	complemented
260	#540	—	2	4	no	—
261	#540	C₂²×C₇₁	1	8	yes	—
262	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
263	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
264	C₂×#126	—	2	2	no	—
265	C₂×#125	—	2	2	no	—
266	C₂×#125	C₂²×C₇₁	1	1	yes	characteristic
267	C₂×#125	C₂²×C₇₁	1	1	yes	characteristic
268	C₂×#123	—	2	2	no	—
269	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	2	yes	—
270	C₂×#121	—	2	2	no	—
271	C₂×#121	C₂²×C₇₁	1	2	yes	—
272	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
274	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
275	#499	C₂²×C₇₁	1	8	yes	complemented
276	#492	C₂²×C₇₁	1	8	yes	complemented
277	#491	C₂²×C₇₁	1	8	yes	complemented
278	#490	C₂²×C₇₁	1	8	yes	complemented
279	#468	C₂²×C₇₁	1	16	yes	complemented
280	#465	C₂²×C₇₁	1	16	yes	complemented
281	#440	C₂²×C₇₁	1	16	yes	complemented
282	C₄×SD₁₆	C₂²×C₇₁	1	16	yes	complemented
283	C₂×#107	C₂²×C₇₁	1	2	yes	—
284	C₂×#106	C₂²×C₇₁	1	2	yes	—
285	C₂×#103	C₂²×C₇₁	1	2	yes	—
286	C₂×#103	C₂²×C₇₁	1	2	yes	—
287	C₂×#102	C₂²×C₇₁	1	2	yes	—
288	C₂×#102	C₂²×C₇₁	1	2	yes	—
289	#405	C₂²×C₇₁	1	8	yes	complemented
290	C₂×#97	C₂²×C₇₁	1	1	yes	characteristic
291	C₂×#97	C₂²×C₇₁	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
300	C₂×SD₁₆	—	2	8	no	—
301	C₂×SD₁₆	—	2	8	no	—
302	C₂×SD₁₆	C₂³×C₇₁	1	8	yes	—
303	C₂×SD₁₆	C₂³×C₇₁	1	8	yes	—
304	C₂×M₁₆	—	2	4	no	—
305	C₂×M₁₆	C₂³×C₇₁	1	4	yes	—
306	C₂²×C₈	—	2	4	no	—
307	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
309	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	C₂³×C₇₁	1	4	yes	—
314	#127	—	2	2	no	—
315	#127	C₂³×C₇₁	1	4	yes	—
316	#126	—	2	16	no	—
317	#125	—	2	16	no	—
318	#125	—	2	2	no	—
319	#125	—	2	2	no	—
320	#125	C₂³×C₇₁	1	4	yes	—
321	#125	C₂³×C₇₁	1	4	yes	—
322	#123	—	2	16	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	C₂³×C₇₁	1	8	yes	—
325	#121	—	2	4	no	—
326	#121	—	2	16	no	—
327	#121	C₂³×C₇₁	1	8	yes	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	C₂³×C₇₁	1	8	yes	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	C₂³×C₇₁	1	8	yes	—
332	#117	D₄×C₇₁	1	4	yes	—
333	#117	C₂³×C₇₁	1	4	yes	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	D₄×C₇₁	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	D₄×C₇₁	1	2	yes	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
349	#107	C₂³×C₇₁	1	8	yes	—
350	#106	C₂³×C₇₁	1	8	yes	—
351	#103	C₂³×C₇₁	1	8	yes	—
352	#103	C₂³×C₇₁	1	8	yes	—
353	#102	C₂³×C₇₁	1	8	yes	—
354	#102	C₂³×C₇₁	1	8	yes	—
355	#97	C₂³×C₇₁	1	4	yes	—
356	#97	C₂³×C₇₁	1	4	yes	—
357	C₄×C₈	C₂³×C₇₁	1	4	yes	—
358	C₄×C₈	C₂³×C₇₁	1	4	yes	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	C₂⁴×C₇₁	1	4	yes	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	8	4	no	—
371	C₂×D₄	—	8	4	no	—
372	C₂×D₄	C₂⁴×C₇₁	1	4	yes	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	8	4	no	—
380	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
386	SD₁₆	—	2	16	no	—
387	SD₁₆	—	2	16	no	—
388	M₁₆	—	2	8	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	8	no	—
392	C₂×C₈	#41×C₇₁	1	4	yes	—
393	C₂×C₈	#41×C₇₁	1	4	yes	—
394	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
395	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
396	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
397	C₂×C₈	C₂⁴×C₇₁	1	2	yes	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂×D₄×C₇₁	1	8	yes	—
406	C₄⋊C₄	C₂⁴×C₇₁	1	4	yes	—
407	C₄⋊C₄	C₂⁴×C₇₁	1	4	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	C₂×D₄×C₇₁	1	8	yes	—
412	C₄²	—	2	8	no	—
413	C₄²	C₂×D₄×C₇₁	1	2	yes	—
414	C₄²	C₂×D₄×C₇₁	1	2	yes	—
415	C₄²	C₂⁴×C₇₁	1	2	yes	—
416	C₄²	C₂⁴×C₇₁	1	2	yes	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	4	no	—
423	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
424	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	4	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	4	no	—
431	D₄	—	8	8	no	—
432	D₄	—	8	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	8	8	no	—
446	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
451	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
452	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	C₂×#41×C₇₁	1	4	yes	—
456	C₈	C₂×#41×C₇₁	1	4	yes	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	8	no	—
464	C₂²	#532×C₇₁	1	2	yes	—
465	C₂²	#577×C₇₁	1	4	yes	—
466	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	4	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	#532×C₇₁	1	2	yes	—
474	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
475	C₄	C₂²×#41×C₇₁	1	1	yes	characteristic
476	C₂	—	4	2	no	—
477	C₂	—	8	4	no	—
478	C₂	C₇₁×#3174	1	4	yes	direct product factor
479	C₂	C₂×#532×C₇₁	1	1	yes	characteristic
480	C₂	C₂×#577×C₇₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₂×#540×C₇₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂×#117×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#541×C₇₁	C₂	semidirect
3. C₇₁×#3174	C₂	direct (N × H)
4. C₂×#499×C₇₁	C₂	semidirect
5. C₂×#492×C₇₁	C₂	semidirect
6. C₂×#491×C₇₁	C₂	semidirect
7. C₂×#490×C₇₁	C₂	semidirect
8. C₂×#468×C₇₁	C₂	semidirect
9. C₂×#465×C₇₁	C₂	semidirect
10. C₂×#440×C₇₁	C₂	semidirect
11. C₂×C₄×SD₁₆×C₇₁	C₂	semidirect
12. C₂×#405×C₇₁	C₂	semidirect
18. #541×C₇₁	C₂²	semidirect
34. #499×C₇₁	C₂²	semidirect
35. #492×C₇₁	C₂²	semidirect
36. #491×C₇₁	C₂²	semidirect
37. #490×C₇₁	C₂²	semidirect
38. #468×C₇₁	C₂²	semidirect
39. #465×C₇₁	C₂²	semidirect
40. #440×C₇₁	C₂²	semidirect
41. C₄×SD₁₆×C₇₁	C₂²	semidirect
48. #405×C₇₁	C₂²	semidirect
235. C₂×#3174	C₇₁	direct (N × H)
238. C₂×C₇₁	#3174	direct (N × H)
241. C₂×#541	C₂×C₇₁	semidirect
243. #3174	C₂×C₇₁	direct (N × H)
244. C₂×#499	C₂×C₇₁	semidirect
245. C₂×#492	C₂×C₇₁	semidirect
246. C₂×#491	C₂×C₇₁	semidirect
247. C₂×#490	C₂×C₇₁	semidirect
248. C₂×#468	C₂×C₇₁	semidirect
249. C₂×#465	C₂×C₇₁	semidirect
250. C₂×#440	C₂×C₇₁	semidirect
251. C₂×C₄×SD₁₆	C₂×C₇₁	semidirect
252. C₂×#405	C₂×C₇₁	semidirect
253. C₇₁	C₂×#3174	direct (N × H)
259. #541	C₂²×C₇₁	semidirect
275. #499	C₂²×C₇₁	semidirect
276. #492	C₂²×C₇₁	semidirect
277. #491	C₂²×C₇₁	semidirect
278. #490	C₂²×C₇₁	semidirect
279. #468	C₂²×C₇₁	semidirect
280. #465	C₂²×C₇₁	semidirect
281. #440	C₂²×C₇₁	semidirect
282. C₄×SD₁₆	C₂²×C₇₁	semidirect
289. #405	C₂²×C₇₁	semidirect
478. C₂	C₇₁×#3174	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×#541×C₇₁	2
C₂×#540×C₇₁	2
C₇₁×#3174	2
C₂×#499×C₇₁	2
C₂×#492×C₇₁	2
C₂×#491×C₇₁	2
C₂×#490×C₇₁	2
C₂×#468×C₇₁	2
C₂×#465×C₇₁	2
C₂×#440×C₇₁	2
C₂×C₄×SD₁₆×C₇₁	2
C₂×#405×C₇₁	2
C₂×#3174	71

Subgroups — C2×C71×#3174 #31881550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×#3174 #31881550