Subgroups — C₇₁×#9541 #31830413

Order 18176.

460 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#1954	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄⋊C₄×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#102×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#335×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₇₁×#1279	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×#102×C₇₁	C₄	1	1	yes	characteristic
12	C₂×#102×C₇₁	C₄	1	1	yes	characteristic
13	C₂×C₂²⋊C₈×C₇₁	—	2	1	no	—
14	C₂×C₂²⋊C₈×C₇₁	—	2	1	no	—
15	C₂×C₄×C₈×C₇₁	—	2	1	no	—
16	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
20	#340×C₇₁	C₄	1	1	yes	characteristic
21	#340×C₇₁	C₄	1	1	yes	characteristic
22	#336×C₇₁	—	2	1	no	—
23	#335×C₇₁	—	2	2	no	—
24	D₄⋊C₈×C₇₁	—	2	2	no	—
25	C₂²×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₇₁	—	2	1	no	—
27	C₂²×C₈×C₇₁	—	2	1	no	—
28	C₂²×C₈×C₇₁	—	2	1	no	—
29	C₂²×C₈×C₇₁	—	2	1	no	—
30	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
34	C₄×D₄×C₇₁	—	2	1	no	—
35	C₄×D₄×C₇₁	—	2	1	no	—
36	C₄×D₄×C₇₁	—	2	1	no	—
37	C₄×D₄×C₇₁	—	2	1	no	—
38	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
42	C₂×C₄²×C₇₁	—	2	1	no	—
43	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₇₁	—	2	1	no	—
45	C₄⋊C₈×C₇₁	—	2	1	no	—
46	C₄⋊C₈×C₇₁	—	2	1	no	—
47	C₄⋊C₈×C₇₁	D₄	1	2	yes	—
48	#102×C₇₁	—	2	2	no	—
49	#102×C₇₁	C₈	1	4	yes	complemented
50	C₂²⋊C₈×C₇₁	—	4	2	no	—
51	C₂²⋊C₈×C₇₁	—	4	2	no	—
52	C₄×C₈×C₇₁	—	2	1	no	—
53	C₄×C₈×C₇₁	—	2	1	no	—
54	C₄×C₈×C₇₁	—	2	1	no	—
55	C₄×C₈×C₇₁	—	2	1	no	—
56	C₄×C₈×C₇₁	—	2	1	no	—
57	C₄×C₈×C₇₁	—	2	1	no	—
58	C₄×C₈×C₇₁	—	4	2	no	—
59	#95×C₇₁	—	2	1	no	—
60	C₂⁴×C₇₁	—	2	1	no	—
61	C₂×D₄×C₇₁	—	2	1	no	—
62	C₂×D₄×C₇₁	—	2	1	no	—
63	C₂×D₄×C₇₁	—	2	1	no	—
64	C₂×D₄×C₇₁	—	2	1	no	—
65	C₂×D₄×C₇₁	—	2	1	no	—
66	C₂×D₄×C₇₁	C₂×C₈	1	2	yes	—
67	C₂²×C₄×C₇₁	—	2	1	no	—
68	C₂²×C₄×C₇₁	—	2	1	no	—
69	C₂²×C₄×C₇₁	—	2	1	no	—
70	C₂²×C₄×C₇₁	—	4	1	no	—
71	C₂²×C₄×C₇₁	—	4	1	no	—
72	C₂²×C₄×C₇₁	—	4	1	no	—
73	C₂²×C₄×C₇₁	—	4	1	no	—
74	C₂²×C₄×C₇₁	—	4	1	no	—
75	C₂²×C₄×C₇₁	—	4	1	no	—
76	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
79	C₂×C₈×C₇₁	—	2	1	no	—
80	C₂×C₈×C₇₁	—	2	1	no	—
81	C₂×C₈×C₇₁	—	2	1	no	—
82	C₂×C₈×C₇₁	—	2	1	no	—
83	C₂×C₈×C₇₁	—	2	2	no	—
84	C₂×C₈×C₇₁	—	2	1	no	—
85	C₂×C₈×C₇₁	—	2	2	no	—
86	C₂×C₈×C₇₁	—	2	1	no	—
87	C₂×C₈×C₇₁	—	2	1	no	—
88	C₂×C₈×C₇₁	—	2	1	no	—
89	C₂×C₈×C₇₁	—	2	1	no	—
90	C₂×C₈×C₇₁	—	2	1	no	—
91	C₂×C₈×C₇₁	—	4	1	no	—
92	C₂×C₈×C₇₁	—	4	1	no	—
93	C₂×C₈×C₇₁	—	4	1	no	—
94	C₂×C₈×C₇₁	—	4	1	no	—
95	C₂×C₈×C₇₁	—	4	1	no	—
96	C₂×C₈×C₇₁	—	4	1	no	—
97	C₂×C₈×C₇₁	—	4	1	no	—
98	C₂×C₈×C₇₁	C₂×C₈	1	2	yes	—
99	C₂×C₈×C₇₁	D₈	1	2	yes	—
100	C₄⋊C₄×C₇₁	—	2	1	no	—
101	C₄⋊C₄×C₇₁	—	2	1	no	—
102	C₄⋊C₄×C₇₁	—	2	1	no	—
103	C₄⋊C₄×C₇₁	—	2	1	no	—
104	C₄⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
105	C₄⋊C₄×C₇₁	M₁₆	1	2	yes	—
106	C₂²⋊C₄×C₇₁	—	4	1	no	—
107	C₂²⋊C₄×C₇₁	—	4	1	no	—
108	C₄²×C₇₁	—	4	1	no	—
109	C₄²×C₇₁	—	4	1	no	—
110	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₇₁	#41	1	1	yes	characteristic
112	C₄²×C₇₁	#41	1	1	yes	characteristic
113	C₄²×C₇₁	#41	1	1	yes	characteristic
114	C₂³×C₇₁	—	2	2	no	—
115	C₂³×C₇₁	—	4	1	no	—
116	C₂³×C₇₁	—	4	1	no	—
117	C₂³×C₇₁	—	4	1	no	—
118	C₂³×C₇₁	—	4	1	no	—
119	C₂³×C₇₁	—	4	1	no	—
120	C₂³×C₇₁	—	4	1	no	—
121	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
122	D₄×C₇₁	—	2	2	no	—
123	D₄×C₇₁	—	2	2	no	—
124	D₄×C₇₁	—	4	1	no	—
125	D₄×C₇₁	—	4	1	no	—
126	C₂×C₄×C₇₁	—	2	1	no	—
127	C₂×C₄×C₇₁	—	2	1	no	—
128	C₂×C₄×C₇₁	—	2	2	no	—
129	C₂×C₄×C₇₁	—	2	2	no	—
130	C₂×C₄×C₇₁	—	4	1	no	—
131	C₂×C₄×C₇₁	—	4	1	no	—
132	C₂×C₄×C₇₁	—	4	1	no	—
133	C₂×C₄×C₇₁	—	4	1	no	—
134	C₂×C₄×C₇₁	—	4	1	no	—
135	C₂×C₄×C₇₁	—	4	1	no	—
136	C₂×C₄×C₇₁	—	4	1	no	—
137	C₂×C₄×C₇₁	—	8	1	no	—
138	C₂×C₄×C₇₁	—	8	1	no	—
139	C₂×C₄×C₇₁	—	8	1	no	—
140	C₂×C₄×C₇₁	—	8	1	no	—
141	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
142	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
144	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
145	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
146	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
147	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₇₁	#131	1	1	yes	characteristic
150	C₂×C₄×C₇₁	#131	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
153	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
155	C₈×C₇₁	—	2	2	no	—
156	C₈×C₇₁	—	2	2	no	—
157	C₈×C₇₁	—	4	2	no	—
158	C₈×C₇₁	—	4	1	no	—
159	C₈×C₇₁	—	4	2	no	—
160	C₈×C₇₁	—	4	1	no	—
161	C₈×C₇₁	—	8	1	no	—
162	C₂²×C₇₁	—	4	2	no	—
163	C₂²×C₇₁	—	4	2	no	—
164	C₂²×C₇₁	—	4	2	no	—
165	C₂²×C₇₁	—	8	1	no	—
166	C₂²×C₇₁	—	8	1	no	—
167	C₂²×C₇₁	—	8	1	no	—
168	C₂²×C₇₁	—	8	1	no	—
169	C₂²×C₇₁	#388	1	1	yes	characteristic
170	C₂²×C₇₁	C₈×D₄	1	1	yes	characteristic
171	C₂²×C₇₁	#435	1	1	yes	characteristic
172	C₂²×C₇₁	C₄×D₈	1	1	yes	characteristic
173	C₂²×C₇₁	#440	1	1	yes	characteristic
174	C₂²×C₇₁	#443	1	1	yes	characteristic
175	C₂²×C₇₁	#444	1	1	yes	characteristic
176	C₄×C₇₁	—	2	1	no	—
177	C₄×C₇₁	—	2	1	no	—
178	C₄×C₇₁	—	4	2	no	—
179	C₄×C₇₁	—	4	2	no	—
180	C₄×C₇₁	—	8	1	no	—
181	C₄×C₇₁	#431	1	1	yes	characteristic
182	C₄×C₇₁	#433	1	1	yes	characteristic
183	C₄×C₇₁	C₈×D₄	1	1	yes	characteristic
184	C₄×C₇₁	#436	1	1	yes	characteristic
185	C₄×C₇₁	#459	1	1	yes	characteristic
186	C₄×C₇₁	#464	1	1	yes	characteristic
187	C₄×C₇₁	#480	1	1	yes	characteristic
188	C₄×C₇₁	#482	1	1	yes	characteristic
189	#9541	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₇₁	—	8	2	no	—
191	C₂×C₇₁	C₈×D₈	1	1	yes	characteristic
192	C₂×C₇₁	SD₁₆⋊C₈	1	1	yes	characteristic
193	C₂×C₇₁	#1581	1	1	yes	characteristic
194	C₂×C₇₁	#1588	1	1	yes	characteristic
195	C₂×C₇₁	#1923	1	1	yes	characteristic
196	C₂×C₇₁	#1925	1	1	yes	characteristic
197	C₂×C₇₁	#1929	1	1	yes	characteristic
198	#1954	C₂×C₇₁	1	1	yes	characteristic
199	C₈×C₄⋊C₄	C₂×C₇₁	1	1	yes	characteristic, complemented
200	C₄×#102	C₂×C₇₁	1	1	yes	characteristic
201	C₂×#335	C₂×C₇₁	1	1	yes	characteristic, complemented
202	C₂×D₄⋊C₈	C₂×C₇₁	1	1	yes	characteristic
203	#1279	C₂×C₇₁	1	1	yes	characteristic, complemented
204	#1273	C₂×C₇₁	1	1	yes	characteristic, complemented
205	C₇₁	#9541	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
209	C₂×#102	C₄×C₇₁	1	1	yes	characteristic
210	C₂×#102	C₄×C₇₁	1	1	yes	characteristic
211	C₂×C₂²⋊C₈	—	2	1	no	—
212	C₂×C₂²⋊C₈	—	2	1	no	—
213	C₂×C₄×C₈	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
218	#340	C₄×C₇₁	1	1	yes	characteristic
219	#340	C₄×C₇₁	1	1	yes	characteristic
220	#336	—	2	1	no	—
221	#335	—	2	2	no	—
222	D₄⋊C₈	—	2	2	no	—
223	C₂²×D₄	C₂×C₄×C₇₁	1	1	yes	characteristic
224	C₂³×C₄	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	C₂×C₄×C₇₁	1	1	yes	characteristic
229	C₂²×C₈	C₂×C₄×C₇₁	1	1	yes	characteristic
230	C₂²×C₈	D₄×C₇₁	1	1	yes	characteristic
231	C₂²×C₈	D₄×C₇₁	1	1	yes	characteristic
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
246	#102	—	2	2	no	—
247	#102	C₈×C₇₁	1	4	yes	complemented
248	C₂²⋊C₈	—	4	2	no	—
249	C₂²⋊C₈	—	4	2	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	4	2	no	—
257	#95	—	2	1	no	—
258	C₂⁴	—	2	1	no	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	C₂×C₈×C₇₁	1	2	yes	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
276	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	C₂×C₈×C₇₁	1	2	yes	—
297	C₂×C₈	D₈×C₇₁	1	2	yes	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	C₂×C₈×C₇₁	1	2	yes	—
303	C₄⋊C₄	M₁₆×C₇₁	1	2	yes	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
309	C₄²	#41×C₇₁	1	1	yes	characteristic
310	C₄²	#41×C₇₁	1	1	yes	characteristic
311	C₄²	#41×C₇₁	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	C₄×D₄×C₇₁	1	1	yes	characteristic
320	D₄	—	2	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	#117×C₇₁	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₇₁	1	1	yes	characteristic
341	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
342	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
343	C₂×C₄	#124×C₇₁	1	1	yes	characteristic
344	C₂×C₄	#126×C₇₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₈×C₇₁	1	1	yes	characteristic
346	C₂×C₄	C₂×M₁₆×C₇₁	1	1	yes	characteristic
347	C₂×C₄	#131×C₇₁	1	1	yes	characteristic
348	C₂×C₄	#131×C₇₁	1	1	yes	characteristic
349	C₂×C₄	C₂×D₈×C₇₁	1	1	yes	characteristic
350	C₂×C₄	#135×C₇₁	1	1	yes	characteristic
351	C₂×C₄	AGL(1,ℤ/8)×C₇₁	1	1	yes	characteristic
352	C₂×C₄	#137×C₇₁	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	1	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	1	no	—
359	C₈	—	8	1	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	#388×C₇₁	1	1	yes	characteristic
368	C₂²	C₈×D₄×C₇₁	1	1	yes	characteristic
369	C₂²	#435×C₇₁	1	1	yes	characteristic
370	C₂²	C₄×D₈×C₇₁	1	1	yes	characteristic
371	C₂²	#440×C₇₁	1	1	yes	characteristic
372	C₂²	#443×C₇₁	1	1	yes	characteristic
373	C₂²	#444×C₇₁	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	1	no	—
379	C₄	#431×C₇₁	1	1	yes	characteristic
380	C₄	#433×C₇₁	1	1	yes	characteristic
381	C₄	C₈×D₄×C₇₁	1	1	yes	characteristic
382	C₄	#436×C₇₁	1	1	yes	characteristic
383	C₄	#459×C₇₁	1	1	yes	characteristic
384	C₄	#464×C₇₁	1	1	yes	characteristic
385	C₄	#480×C₇₁	1	1	yes	characteristic
386	C₄	#482×C₇₁	1	1	yes	characteristic
387	C₂	—	8	2	no	—
388	C₂	C₈×D₈×C₇₁	1	1	yes	characteristic
389	C₂	C₇₁×SD₁₆⋊C₈	1	1	yes	characteristic
390	C₂	C₇₁×#1581	1	1	yes	characteristic
391	C₂	C₇₁×#1588	1	1	yes	characteristic
392	C₂	C₇₁×#1923	1	1	yes	characteristic
393	C₂	C₇₁×#1925	1	1	yes	characteristic
394	C₂	C₇₁×#1929	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₇₁
Frattini, cosocle	C₂×C₄²	C₂³×C₇₁
socle	C₂³×C₇₁	C₄×D₄
prime radical	C₂²×D₄×C₇₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₁ ◁ C₂×C₄×C₈×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₄⋊C₄×C₇₁	C₂	semidirect
4. C₂×#335×C₇₁	C₂	semidirect
6. C₇₁×#1279	C₂	semidirect
7. C₇₁×#1273	C₂	semidirect
49. #102×C₇₁	C₈	semidirect
189. #9541	C₇₁	direct (N × H)
199. C₈×C₄⋊C₄	C₂×C₇₁	semidirect
201. C₂×#335	C₂×C₇₁	semidirect
203. #1279	C₂×C₇₁	semidirect
204. #1273	C₂×C₇₁	semidirect
205. C₇₁	#9541	direct (N × H)
247. #102	C₈×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#1954	2
C₈×C₄⋊C₄×C₇₁	2
C₄×#102×C₇₁	2
C₂×#335×C₇₁	2
C₂×D₄⋊C₈×C₇₁	2
C₇₁×#1279	2
C₇₁×#1273	2
#9541	71

Subgroups — C71×#9541 #31830413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#9541 #31830413