Subgroups — C₇₁×#23703 #31844575

Order 18176.

932 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#433×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#2324	C₂	1	2	yes	maximal, complemented
4	C₇₁×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#2076	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#2067	C₂	1	2	yes	maximal, complemented
7	C₇₁×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#2033	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1999	C₂	1	1	yes	maximal, characteristic
10	C₄×#107×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×#121×C₇₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
15	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
16	C₄×D₈×C₇₁	—	2	4	no	—
17	#433×C₇₁	—	2	4	no	—
18	C₂×#107×C₇₁	C₂²	1	2	yes	—
19	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₇₁	C₂²	1	2	yes	—
23	C₂×#102×C₇₁	C₂²	1	2	yes	—
24	C₂×#102×C₇₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
27	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
29	#390×C₇₁	—	2	2	no	—
30	#390×C₇₁	C₂²	1	2	yes	—
31	#389×C₇₁	C₂²	1	2	yes	—
32	#388×C₇₁	—	2	2	no	—
33	#386×C₇₁	—	2	2	no	—
34	#385×C₇₁	—	2	2	no	—
35	#380×C₇₁	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
37	#340×C₇₁	C₂²	1	2	yes	—
38	#340×C₇₁	C₂²	1	2	yes	—
39	#340×C₇₁	C₂²	1	1	yes	characteristic
40	#340×C₇₁	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₇₁	—	2	2	no	—
42	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₇₁	—	2	2	no	—
44	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₇₁	—	2	4	no	—
46	C₂×D₈×C₇₁	—	2	2	no	—
47	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
51	#121×C₇₁	—	2	4	no	—
52	#121×C₇₁	—	2	4	no	—
53	C₄×D₄×C₇₁	—	2	4	no	—
54	C₄×D₄×C₇₁	—	2	4	no	—
55	#117×C₇₁	—	2	2	no	—
56	#117×C₇₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₇₁	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₇₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₇₁	—	2	2	no	—
71	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
73	#107×C₇₁	—	2	2	no	—
74	#107×C₇₁	—	2	4	no	—
75	C₄⋊C₈×C₇₁	—	2	2	no	—
76	C₄⋊C₈×C₇₁	—	2	2	no	—
77	#102×C₇₁	—	2	4	no	—
78	#102×C₇₁	—	2	4	no	—
79	#102×C₇₁	—	2	4	no	—
80	C₂²⋊C₈×C₇₁	—	2	2	no	—
81	C₂²⋊C₈×C₇₁	—	2	2	no	—
82	#97×C₇₁	—	2	2	no	—
83	C₄×C₈×C₇₁	D₄	1	4	yes	complemented
84	#95×C₇₁	—	2	2	no	—
85	#95×C₇₁	—	2	2	no	—
86	#95×C₇₁	—	2	2	no	—
87	C₂⁴×C₇₁	—	2	2	no	—
88	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₇₁	—	2	8	no	—
90	C₂×D₄×C₇₁	—	2	2	no	—
91	C₂×D₄×C₇₁	—	2	2	no	—
92	C₂×D₄×C₇₁	—	2	2	no	—
93	C₂×D₄×C₇₁	—	2	2	no	—
94	C₂×D₄×C₇₁	—	2	2	no	—
95	C₂×D₄×C₇₁	—	8	2	no	—
96	C₂×D₄×C₇₁	—	8	2	no	—
97	C₂×D₄×C₇₁	#41	1	4	yes	—
98	C₂²×C₄×C₇₁	—	2	2	no	—
99	C₂²×C₄×C₇₁	—	2	1	no	—
100	C₂²×C₄×C₇₁	—	2	1	no	—
101	C₂²×C₄×C₇₁	—	2	2	no	—
102	C₂²×C₄×C₇₁	—	2	2	no	—
103	C₂²×C₄×C₇₁	—	2	2	no	—
104	C₂²×C₄×C₇₁	—	2	2	no	—
105	C₂²×C₄×C₇₁	—	4	4	no	—
106	C₂²×C₄×C₇₁	—	8	2	no	—
107	C₂²×C₄×C₇₁	—	8	2	no	—
108	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
114	D₈×C₇₁	—	2	8	no	—
115	C₂×C₈×C₇₁	—	2	2	no	—
116	C₂×C₈×C₇₁	—	2	2	no	—
117	C₂×C₈×C₇₁	—	2	1	no	—
118	C₂×C₈×C₇₁	—	2	1	no	—
119	C₂×C₈×C₇₁	—	2	2	no	—
120	C₂×C₈×C₇₁	—	2	2	no	—
121	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₇₁	—	2	2	no	—
124	C₄⋊C₄×C₇₁	—	2	2	no	—
125	C₄⋊C₄×C₇₁	—	2	2	no	—
126	C₄⋊C₄×C₇₁	—	2	2	no	—
127	C₄⋊C₄×C₇₁	—	2	2	no	—
128	C₄⋊C₄×C₇₁	—	2	2	no	—
129	C₄⋊C₄×C₇₁	—	2	2	no	—
130	C₄⋊C₄×C₇₁	—	8	2	no	—
131	C₄⋊C₄×C₇₁	#41	1	4	yes	—
132	C₂²⋊C₄×C₇₁	—	2	8	no	—
133	C₂²⋊C₄×C₇₁	—	2	2	no	—
134	C₂²⋊C₄×C₇₁	—	2	2	no	—
135	C₂²⋊C₄×C₇₁	—	4	4	no	—
136	C₂²⋊C₄×C₇₁	—	8	2	no	—
137	C₂²⋊C₄×C₇₁	—	8	2	no	—
138	C₂²⋊C₄×C₇₁	—	8	2	no	—
139	C₄²×C₇₁	—	2	1	no	—
140	C₄²×C₇₁	—	2	1	no	—
141	C₄²×C₇₁	—	8	2	no	—
142	C₄²×C₇₁	C₂×D₄	1	2	yes	—
143	C₄²×C₇₁	#41	1	2	yes	—
144	C₂³×C₇₁	—	2	1	no	—
145	C₂³×C₇₁	—	2	4	no	—
146	C₂³×C₇₁	—	2	2	no	—
147	C₂³×C₇₁	—	2	2	no	—
148	C₂³×C₇₁	—	2	1	no	—
149	C₂³×C₇₁	—	2	1	no	—
150	C₂³×C₇₁	—	4	2	no	—
151	C₂³×C₇₁	—	4	2	no	—
152	C₂³×C₇₁	—	4	2	no	—
153	C₂³×C₇₁	—	4	2	no	—
154	C₂³×C₇₁	—	4	2	no	—
155	C₂³×C₇₁	—	4	2	no	—
156	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
157	D₄×C₇₁	—	2	4	no	—
158	D₄×C₇₁	—	2	4	no	—
159	D₄×C₇₁	—	4	2	no	—
160	D₄×C₇₁	—	4	2	no	—
161	D₄×C₇₁	—	8	8	no	—
162	C₂×C₄×C₇₁	—	2	1	no	—
163	C₂×C₄×C₇₁	—	2	2	no	—
164	C₂×C₄×C₇₁	—	2	1	no	—
165	C₂×C₄×C₇₁	—	2	1	no	—
166	C₂×C₄×C₇₁	—	2	1	no	—
167	C₂×C₄×C₇₁	—	2	1	no	—
168	C₂×C₄×C₇₁	—	2	2	no	—
169	C₂×C₄×C₇₁	—	2	4	no	—
170	C₂×C₄×C₇₁	—	2	1	no	—
171	C₂×C₄×C₇₁	—	2	2	no	—
172	C₂×C₄×C₇₁	—	2	1	no	—
173	C₂×C₄×C₇₁	—	4	2	no	—
174	C₂×C₄×C₇₁	—	4	2	no	—
175	C₂×C₄×C₇₁	—	4	1	no	—
176	C₂×C₄×C₇₁	—	4	2	no	—
177	C₂×C₄×C₇₁	—	4	1	no	—
178	C₂×C₄×C₇₁	—	4	2	no	—
179	C₂×C₄×C₇₁	—	4	2	no	—
180	C₂×C₄×C₇₁	—	4	2	no	—
181	C₂×C₄×C₇₁	—	4	2	no	—
182	C₂×C₄×C₇₁	—	4	2	no	—
183	C₂×C₄×C₇₁	—	4	2	no	—
184	C₂×C₄×C₇₁	—	8	8	no	—
185	C₂×C₄×C₇₁	#121	1	2	yes	—
186	C₂×C₄×C₇₁	#121	1	2	yes	—
187	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
189	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
191	C₈×C₇₁	—	2	2	no	—
192	C₈×C₇₁	—	2	2	no	—
193	C₈×C₇₁	—	4	1	no	—
194	C₈×C₇₁	—	4	1	no	—
195	C₂²×C₇₁	—	4	2	no	—
196	C₂²×C₇₁	—	4	4	no	—
197	C₂²×C₇₁	—	4	2	no	—
198	C₂²×C₇₁	—	4	4	no	—
199	C₂²×C₇₁	—	4	1	no	—
200	C₂²×C₇₁	—	4	4	no	—
201	C₂²×C₇₁	—	4	1	no	—
202	C₂²×C₇₁	—	4	1	no	—
203	C₂²×C₇₁	—	8	2	no	—
204	C₂²×C₇₁	—	8	2	no	—
205	C₂²×C₇₁	—	8	2	no	—
206	C₂²×C₇₁	—	8	2	no	—
207	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
208	C₂²×C₇₁	#525	1	2	yes	—
209	C₂²×C₇₁	#576	1	1	yes	characteristic
210	C₂²×C₇₁	#576	1	2	yes	—
211	C₂²×C₇₁	#578	1	1	yes	characteristic
212	C₄×C₇₁	—	2	2	no	—
213	C₄×C₇₁	—	2	2	no	—
214	C₄×C₇₁	—	4	4	no	—
215	C₄×C₇₁	—	4	1	no	—
216	C₄×C₇₁	—	4	1	no	—
217	C₄×C₇₁	—	4	1	no	—
218	C₄×C₇₁	—	8	2	no	—
219	C₄×C₇₁	—	8	2	no	—
220	C₄×C₇₁	#525	1	1	yes	characteristic
221	C₄×C₇₁	#529	1	2	yes	—
222	C₄×C₇₁	#532	1	1	yes	characteristic
223	#23703	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₇₁	—	8	1	no	—
225	C₂×C₇₁	—	8	4	no	—
226	C₂×C₇₁	#2392	1	1	yes	characteristic
227	C₂×C₇₁	#3058	1	1	yes	characteristic
228	C₂×C₇₁	#3061	1	1	yes	characteristic
229	C₂×C₇₁	#3122	1	2	yes	—
230	C₂×C₇₁	#3124	1	2	yes	—
231	C₂×C₄×D₈	C₂×C₇₁	1	1	yes	characteristic, complemented
232	C₂×#433	C₂×C₇₁	1	1	yes	characteristic, complemented
233	#2324	C₂×C₇₁	1	2	yes	complemented
234	#2087	C₂×C₇₁	1	1	yes	characteristic, complemented
235	#2076	C₂×C₇₁	1	1	yes	characteristic, complemented
236	#2067	C₂×C₇₁	1	2	yes	complemented
237	#2054	C₂×C₇₁	1	1	yes	characteristic, complemented
238	#2033	C₂×C₇₁	1	2	yes	complemented
239	#1999	C₂×C₇₁	1	1	yes	characteristic
240	C₄×#107	C₂×C₇₁	1	1	yes	characteristic, complemented
241	#1762	C₂×C₇₁	1	2	yes	complemented
242	C₇₁	#23703	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²×D₈	C₂²×C₇₁	1	1	yes	characteristic
244	C₂×#121	C₂²×C₇₁	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
246	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
247	C₄×D₈	—	2	4	no	—
248	#433	—	2	4	no	—
249	C₂×#107	C₂²×C₇₁	1	2	yes	—
250	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
253	C₂×#102	C₂²×C₇₁	1	2	yes	—
254	C₂×#102	C₂²×C₇₁	1	2	yes	—
255	C₂×#102	C₂²×C₇₁	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
257	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
258	C₂×#97	C₂²×C₇₁	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
260	#390	—	2	2	no	—
261	#390	C₂²×C₇₁	1	2	yes	—
262	#389	C₂²×C₇₁	1	2	yes	—
263	#388	—	2	2	no	—
264	#386	—	2	2	no	—
265	#385	—	2	2	no	—
266	#380	C₂²×C₇₁	1	2	yes	—
267	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
268	#340	C₂²×C₇₁	1	1	yes	characteristic
269	#340	C₂²×C₇₁	1	2	yes	—
270	#340	C₂²×C₇₁	1	1	yes	characteristic
271	#340	C₂²×C₇₁	1	2	yes	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
276	C₂×D₈	—	2	4	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
282	#121	—	2	4	no	—
283	#121	—	2	4	no	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	—	2	4	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	D₄×C₇₁	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	D₄×C₇₁	1	1	yes	characteristic
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
304	#107	—	2	2	no	—
305	#107	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	#97	—	2	2	no	—
314	C₄×C₈	D₄×C₇₁	1	4	yes	complemented
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	8	2	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	#41×C₇₁	1	4	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
345	D₈	—	2	8	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
353	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₄⋊C₄	#41×C₇₁	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	8	2	no	—
373	C₄²	C₂×D₄×C₇₁	1	2	yes	—
374	C₄²	#41×C₇₁	1	2	yes	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	8	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	8	no	—
416	C₂×C₄	#121×C₇₁	1	2	yes	—
417	C₂×C₄	#121×C₇₁	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
420	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
422	C₈	—	2	2	no	—
423	C₈	—	2	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
439	C₂²	#525×C₇₁	1	2	yes	—
440	C₂²	#576×C₇₁	1	2	yes	—
441	C₂²	#576×C₇₁	1	1	yes	characteristic
442	C₂²	#578×C₇₁	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	#525×C₇₁	1	1	yes	characteristic
452	C₄	#529×C₇₁	1	2	yes	—
453	C₄	#532×C₇₁	1	1	yes	characteristic
454	C₂	—	8	1	no	—
455	C₂	—	8	4	no	—
456	C₂	C₇₁×#2392	1	1	yes	characteristic
457	C₂	C₇₁×#3058	1	1	yes	characteristic
458	C₂	C₇₁×#3061	1	1	yes	characteristic
459	C₂	C₇₁×#3122	1	2	yes	—
460	C₂	C₇₁×#3124	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
prime radical	C₇₁×#1999	C₂
LCS	G ▷ C₂²×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×C₄×D₈×C₇₁	C₂	semidirect
2. C₂×#433×C₇₁	C₂	semidirect
3. C₇₁×#2324	C₂	semidirect
4. C₇₁×#2087	C₂	semidirect
5. C₇₁×#2076	C₂	semidirect
6. C₇₁×#2067	C₂	semidirect
7. C₇₁×#2054	C₂	semidirect
8. C₇₁×#2033	C₂	semidirect
10. C₄×#107×C₇₁	C₂	semidirect
11. C₇₁×#1762	C₂	semidirect
83. C₄×C₈×C₇₁	D₄	semidirect
223. #23703	C₇₁	direct (N × H)
231. C₂×C₄×D₈	C₂×C₇₁	semidirect
232. C₂×#433	C₂×C₇₁	semidirect
233. #2324	C₂×C₇₁	semidirect
234. #2087	C₂×C₇₁	semidirect
235. #2076	C₂×C₇₁	semidirect
236. #2067	C₂×C₇₁	semidirect
237. #2054	C₂×C₇₁	semidirect
238. #2033	C₂×C₇₁	semidirect
240. C₄×#107	C₂×C₇₁	semidirect
241. #1762	C₂×C₇₁	semidirect
242. C₇₁	#23703	direct (N × H)
314. C₄×C₈	D₄×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₇₁	2
C₂×#433×C₇₁	2
C₇₁×#2324	2
C₇₁×#2087	2
C₇₁×#2076	2
C₇₁×#2067	2
C₇₁×#2054	2
C₇₁×#2033	2
C₇₁×#1999	2
C₄×#107×C₇₁	2
C₇₁×#1762	2
#23703	71

Subgroups — C71×#23703 #31844575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23703 #31844575