Subgroups — C₇₁×#19495 #31840367

Order 18176.

686 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3038	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1701	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1685	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1682	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1666	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1561	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₁	—	2	1	no	—
13	#533×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic
15	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
16	#492×C₇₁	C₂²	1	2	yes	—
17	#486×C₇₁	C₂²	1	2	yes	—
18	#485×C₇₁	—	2	1	no	—
19	#475×C₇₁	C₂²	1	1	yes	characteristic, complemented
20	#474×C₇₁	C₂²	1	1	yes	characteristic, complemented
21	#462×C₇₁	C₂²	1	1	yes	characteristic, complemented
22	#461×C₇₁	C₂²	1	1	yes	characteristic, complemented
23	#460×C₇₁	—	2	1	no	—
24	#460×C₇₁	—	2	1	no	—
25	#460×C₇₁	—	2	1	no	—
26	#460×C₇₁	C₂²	1	2	yes	—
27	#459×C₇₁	—	2	1	no	—
28	#459×C₇₁	C₂²	1	2	yes	—
29	#452×C₇₁	—	2	1	no	—
30	#450×C₇₁	—	2	2	no	—
31	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
32	C₄×Q₁₆×C₇₁	—	2	1	no	—
33	C₄×SD₁₆×C₇₁	—	2	1	no	—
34	#436×C₇₁	—	2	2	no	—
35	#436×C₇₁	C₂²	1	2	yes	complemented
36	#431×C₇₁	—	2	1	no	—
37	#431×C₇₁	C₂²	1	1	yes	characteristic
38	#431×C₇₁	C₂²	1	1	yes	characteristic
39	#423×C₇₁	—	2	1	no	—
40	#423×C₇₁	C₂²	1	1	yes	characteristic
41	#423×C₇₁	C₂²	1	1	yes	characteristic
42	#418×C₇₁	—	2	1	no	—
43	#335×C₇₁	C₂²	1	2	yes	complemented
44	#334×C₇₁	C₂²	1	2	yes	complemented
45	#332×C₇₁	C₂²	1	2	yes	complemented
46	#332×C₇₁	C₂²	1	2	yes	complemented
47	#331×C₇₁	C₂²	1	2	yes	—
48	#331×C₇₁	C₂²	1	2	yes	—
49	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₇₁	—	2	1	no	—
51	C₂²×D₄×C₇₁	—	2	1	no	—
52	C₂²×D₄×C₇₁	—	2	1	no	—
53	AGL(1,ℤ/8)×C₇₁	—	4	4	no	—
54	C₂×Q₁₆×C₇₁	—	2	1	no	—
55	C₂×SD₁₆×C₇₁	—	2	2	no	—
56	C₂×SD₁₆×C₇₁	—	2	1	no	—
57	C₂×SD₁₆×C₇₁	—	2	2	no	—
58	C₂×SD₁₆×C₇₁	—	2	2	no	—
59	C₂×D₈×C₇₁	—	2	2	no	—
60	C₂×M₁₆×C₇₁	—	2	1	no	—
61	C₂×M₁₆×C₇₁	—	2	1	no	—
62	C₂×M₁₆×C₇₁	—	2	2	no	—
63	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
65	#127×C₇₁	—	2	1	no	—
66	#127×C₇₁	—	2	1	no	—
67	#127×C₇₁	—	2	1	no	—
68	#127×C₇₁	C₂³	1	2	yes	—
69	#125×C₇₁	—	2	1	no	—
70	C₂²⋊Q₈×C₇₁	—	2	1	no	—
71	C₂²⋊Q₈×C₇₁	—	2	1	no	—
72	C₄×Q₈×C₇₁	—	2	1	no	—
73	C₄×Q₈×C₇₁	—	2	1	no	—
74	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₇₁	—	2	1	no	—
77	C₄×D₄×C₇₁	—	2	1	no	—
78	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
79	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
80	#117×C₇₁	—	2	1	no	—
81	#117×C₇₁	—	2	1	no	—
82	#117×C₇₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₇₁	—	2	1	no	—
84	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
85	#107×C₇₁	—	2	1	no	—
86	#106×C₇₁	—	2	1	no	—
87	C₄⋊C₈×C₇₁	—	2	2	no	—
88	C₄⋊C₈×C₇₁	—	2	1	no	—
89	C₄⋊C₈×C₇₁	—	2	1	no	—
90	C₄⋊C₈×C₇₁	D₄	1	1	yes	characteristic
91	C₄⋊C₈×C₇₁	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
93	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
94	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
96	#103×C₇₁	—	2	1	no	—
97	#103×C₇₁	—	2	1	no	—
98	#103×C₇₁	—	2	1	no	—
99	#102×C₇₁	—	2	1	no	—
100	#102×C₇₁	—	2	2	no	—
101	#102×C₇₁	—	2	2	no	—
102	#102×C₇₁	—	2	2	no	—
103	#102×C₇₁	—	2	2	no	—
104	C₂²⋊C₈×C₇₁	—	2	1	no	—
105	C₂²⋊C₈×C₇₁	—	2	2	no	—
106	C₂²⋊C₈×C₇₁	D₄	1	2	yes	—
107	C₄×C₈×C₇₁	—	2	2	no	—
108	C₄×C₈×C₇₁	—	2	1	no	—
109	C₄×C₈×C₇₁	C₂³	1	2	yes	—
110	C₂⁴×C₇₁	—	4	1	no	—
111	#41×C₇₁	—	2	2	no	—
112	#41×C₇₁	—	4	1	no	—
113	C₂×Q₈×C₇₁	—	2	1	no	—
114	C₂×Q₈×C₇₁	—	2	1	no	—
115	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₇₁	—	2	1	no	—
117	C₂×D₄×C₇₁	—	2	2	no	—
118	C₂×D₄×C₇₁	—	2	2	no	—
119	C₂×D₄×C₇₁	—	2	2	no	—
120	C₂×D₄×C₇₁	—	4	2	no	—
121	C₂×D₄×C₇₁	—	4	2	no	—
122	C₂×D₄×C₇₁	—	4	1	no	—
123	C₂×D₄×C₇₁	—	4	1	no	—
124	C₂×D₄×C₇₁	—	4	1	no	—
125	C₂×D₄×C₇₁	—	8	1	no	—
126	C₂×D₄×C₇₁	—	8	1	no	—
127	C₂×D₄×C₇₁	—	8	2	no	—
128	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₁	—	2	1	no	—
130	C₂²×C₄×C₇₁	—	2	1	no	—
131	C₂²×C₄×C₇₁	—	2	1	no	—
132	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
135	Q₁₆×C₇₁	—	4	2	no	—
136	SD₁₆×C₇₁	—	4	2	no	—
137	SD₁₆×C₇₁	—	4	4	no	—
138	SD₁₆×C₇₁	—	8	2	no	—
139	SD₁₆×C₇₁	—	8	2	no	—
140	D₈×C₇₁	—	4	4	no	—
141	M₁₆×C₇₁	—	4	2	no	—
142	M₁₆×C₇₁	—	8	2	no	—
143	M₁₆×C₇₁	—	8	1	no	—
144	C₂×C₈×C₇₁	—	2	1	no	—
145	C₂×C₈×C₇₁	—	2	1	no	—
146	C₂×C₈×C₇₁	—	2	2	no	—
147	C₂×C₈×C₇₁	—	2	2	no	—
148	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₇₁	—	2	1	no	—
151	C₄⋊C₄×C₇₁	—	2	1	no	—
152	C₄⋊C₄×C₇₁	—	2	1	no	—
153	C₄⋊C₄×C₇₁	—	2	1	no	—
154	C₄⋊C₄×C₇₁	—	2	1	no	—
155	C₄⋊C₄×C₇₁	—	2	1	no	—
156	C₄⋊C₄×C₇₁	—	4	1	no	—
157	C₄⋊C₄×C₇₁	—	4	1	no	—
158	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₇₁	—	2	1	no	—
161	C₂²⋊C₄×C₇₁	—	2	1	no	—
162	C₂²⋊C₄×C₇₁	—	2	1	no	—
163	C₂²⋊C₄×C₇₁	—	4	1	no	—
164	C₄²×C₇₁	—	2	1	no	—
165	C₄²×C₇₁	—	2	1	no	—
166	C₄²×C₇₁	—	2	1	no	—
167	C₄²×C₇₁	—	4	1	no	—
168	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇₁	#41	1	1	yes	characteristic
171	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
172	C₂³×C₇₁	—	2	1	no	—
173	C₂³×C₇₁	—	4	2	no	—
174	C₂³×C₇₁	—	8	2	no	—
175	C₂³×C₇₁	—	8	2	no	—
176	C₂³×C₇₁	—	8	2	no	—
177	C₂³×C₇₁	#121	1	1	yes	characteristic
178	Q₈×C₇₁	—	2	1	no	—
179	Q₈×C₇₁	—	4	1	no	—
180	Q₈×C₇₁	—	4	1	no	—
181	Q₈×C₇₁	—	4	1	no	—
182	Q₈×C₇₁	—	4	1	no	—
183	Q₈×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
184	D₄×C₇₁	—	2	1	no	—
185	D₄×C₇₁	—	2	1	no	—
186	D₄×C₇₁	—	4	2	no	—
187	D₄×C₇₁	—	4	2	no	—
188	D₄×C₇₁	—	4	2	no	—
189	D₄×C₇₁	—	4	2	no	—
190	D₄×C₇₁	—	4	2	no	—
191	D₄×C₇₁	—	8	2	no	—
192	D₄×C₇₁	—	8	2	no	—
193	D₄×C₇₁	—	8	2	no	—
194	D₄×C₇₁	—	8	2	no	—
195	C₂×C₄×C₇₁	—	2	1	no	—
196	C₂×C₄×C₇₁	—	2	1	no	—
197	C₂×C₄×C₇₁	—	2	1	no	—
198	C₂×C₄×C₇₁	—	2	1	no	—
199	C₂×C₄×C₇₁	—	2	1	no	—
200	C₂×C₄×C₇₁	—	2	2	no	—
201	C₂×C₄×C₇₁	—	2	1	no	—
202	C₂×C₄×C₇₁	—	2	1	no	—
203	C₂×C₄×C₇₁	—	4	2	no	—
204	C₂×C₄×C₇₁	—	4	1	no	—
205	C₂×C₄×C₇₁	—	4	1	no	—
206	C₂×C₄×C₇₁	—	4	2	no	—
207	C₂×C₄×C₇₁	—	4	1	no	—
208	C₂×C₄×C₇₁	—	4	1	no	—
209	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
210	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
211	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
212	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
215	C₈×C₇₁	—	2	2	no	—
216	C₈×C₇₁	—	2	2	no	—
217	C₈×C₇₁	—	4	2	no	—
218	C₈×C₇₁	—	4	1	no	—
219	C₈×C₇₁	—	4	1	no	—
220	C₈×C₇₁	—	4	2	no	—
221	C₂²×C₇₁	—	2	1	no	—
222	C₂²×C₇₁	—	2	1	no	—
223	C₂²×C₇₁	—	2	1	no	—
224	C₂²×C₇₁	—	4	1	no	—
225	C₂²×C₇₁	—	4	1	no	—
226	C₂²×C₇₁	—	4	1	no	—
227	C₂²×C₇₁	—	8	2	no	—
228	C₂²×C₇₁	—	8	2	no	—
229	C₂²×C₇₁	—	8	2	no	—
230	C₂²×C₇₁	—	16	4	no	—
231	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
232	C₄×C₇₁	—	2	1	no	—
233	C₄×C₇₁	—	2	1	no	—
234	C₄×C₇₁	—	2	2	no	—
235	C₄×C₇₁	—	2	1	no	—
236	C₄×C₇₁	—	4	1	no	—
237	C₄×C₇₁	—	4	1	no	—
238	C₄×C₇₁	—	8	1	no	—
239	C₄×C₇₁	—	8	1	no	—
240	C₄×C₇₁	#471	1	2	yes	—
241	C₄×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₄×C₇₁	#575	1	1	yes	characteristic
243	C₄×C₇₁	#576	1	1	yes	characteristic
244	C₄×C₇₁	#577	1	1	yes	characteristic
245	#19495	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂×C₇₁	—	4	1	no	—
247	C₂×C₇₁	—	8	1	no	—
248	C₂×C₇₁	—	16	2	no	—
249	C₂×C₇₁	#3045	1	1	yes	characteristic
250	C₂×C₇₁	#3055	1	1	yes	characteristic
251	C₂×C₇₁	C₂×#471	1	1	yes	characteristic
252	#3208	C₂×C₇₁	1	1	yes	characteristic, complemented
253	#3107	C₂×C₇₁	1	1	yes	characteristic, complemented
254	#3038	C₂×C₇₁	1	1	yes	characteristic
255	#2991	C₂×C₇₁	1	1	yes	characteristic, complemented
256	#1701	C₂×C₇₁	1	2	yes	complemented
257	#1685	C₂×C₇₁	1	2	yes	complemented
258	#1682	C₂×C₇₁	1	2	yes	complemented
259	#1666	C₂×C₇₁	1	2	yes	complemented
260	#1574	C₂×C₇₁	1	1	yes	characteristic, complemented
261	#1561	C₂×C₇₁	1	1	yes	characteristic, complemented
262	#1545	C₂×C₇₁	1	1	yes	characteristic, complemented
263	C₇₁	#19495	1	1	yes	characteristic, direct product factor, Sylow
264	C₂×AGL(1,ℤ/8)	—	2	1	no	—
265	#533	C₂²×C₇₁	1	1	yes	characteristic
266	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
267	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
268	#492	C₂²×C₇₁	1	2	yes	—
269	#486	C₂²×C₇₁	1	2	yes	—
270	#485	—	2	1	no	—
271	#475	C₂²×C₇₁	1	1	yes	characteristic, complemented
272	#474	C₂²×C₇₁	1	1	yes	characteristic, complemented
273	#462	C₂²×C₇₁	1	1	yes	characteristic, complemented
274	#461	C₂²×C₇₁	1	1	yes	characteristic, complemented
275	#460	—	2	1	no	—
276	#460	—	2	1	no	—
277	#460	—	2	1	no	—
278	#460	C₂²×C₇₁	1	2	yes	—
279	#459	—	2	1	no	—
280	#459	C₂²×C₇₁	1	2	yes	—
281	#452	—	2	1	no	—
282	#450	—	2	2	no	—
283	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
284	C₄×Q₁₆	—	2	1	no	—
285	C₄×SD₁₆	—	2	1	no	—
286	#436	—	2	2	no	—
287	#436	C₂²×C₇₁	1	2	yes	complemented
288	#431	—	2	1	no	—
289	#431	C₂²×C₇₁	1	1	yes	characteristic
290	#431	C₂²×C₇₁	1	1	yes	characteristic
291	#423	—	2	1	no	—
292	#423	C₂²×C₇₁	1	1	yes	characteristic
293	#423	C₂²×C₇₁	1	1	yes	characteristic
294	#418	—	2	1	no	—
295	#335	C₂²×C₇₁	1	2	yes	complemented
296	#334	C₂²×C₇₁	1	2	yes	complemented
297	#332	C₂²×C₇₁	1	2	yes	complemented
298	#332	C₂²×C₇₁	1	2	yes	complemented
299	#331	C₂²×C₇₁	1	2	yes	—
300	#331	C₂²×C₇₁	1	2	yes	—
301	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	1	no	—
305	AGL(1,ℤ/8)	—	4	4	no	—
306	C₂×Q₁₆	—	2	1	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	1	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×SD₁₆	—	2	2	no	—
311	C₂×D₈	—	2	2	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
316	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
317	#127	—	2	1	no	—
318	#127	—	2	1	no	—
319	#127	—	2	1	no	—
320	#127	C₂³×C₇₁	1	2	yes	—
321	#125	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
327	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
331	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
332	#117	—	2	1	no	—
333	#117	—	2	1	no	—
334	#117	D₄×C₇₁	1	1	yes	characteristic
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
337	#107	—	2	1	no	—
338	#106	—	2	1	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
343	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
344	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
345	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
346	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
347	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
348	#103	—	2	1	no	—
349	#103	—	2	1	no	—
350	#103	—	2	1	no	—
351	#102	—	2	1	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₂²⋊C₈	—	2	2	no	—
358	C₂²⋊C₈	D₄×C₇₁	1	2	yes	—
359	C₄×C₈	—	2	2	no	—
360	C₄×C₈	—	2	1	no	—
361	C₄×C₈	C₂³×C₇₁	1	2	yes	—
362	C₂⁴	—	4	1	no	—
363	#41	—	2	2	no	—
364	#41	—	4	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	8	1	no	—
378	C₂×D₄	—	8	1	no	—
379	C₂×D₄	—	8	2	no	—
380	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
386	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
387	Q₁₆	—	4	2	no	—
388	SD₁₆	—	4	2	no	—
389	SD₁₆	—	4	4	no	—
390	SD₁₆	—	8	2	no	—
391	SD₁₆	—	8	2	no	—
392	D₈	—	4	4	no	—
393	M₁₆	—	4	2	no	—
394	M₁₆	—	8	2	no	—
395	M₁₆	—	8	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
401	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
411	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	4	1	no	—
420	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
422	C₄²	#41×C₇₁	1	1	yes	characteristic
423	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
424	C₂³	—	2	1	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	8	2	no	—
427	C₂³	—	8	2	no	—
428	C₂³	—	8	2	no	—
429	C₂³	#121×C₇₁	1	1	yes	characteristic
430	Q₈	—	2	1	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	AGL(1,ℤ/8)×C₇₁	1	2	yes	—
436	D₄	—	2	1	no	—
437	D₄	—	2	1	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	8	2	no	—
444	D₄	—	8	2	no	—
445	D₄	—	8	2	no	—
446	D₄	—	8	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
462	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
463	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	16	4	no	—
483	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	#471×C₇₁	1	2	yes	—
493	C₄	C₂×AGL(1,ℤ/8)×C₇₁	1	1	yes	characteristic
494	C₄	#575×C₇₁	1	1	yes	characteristic
495	C₄	#576×C₇₁	1	1	yes	characteristic
496	C₄	#577×C₇₁	1	1	yes	characteristic
497	C₂	—	4	1	no	—
498	C₂	—	8	1	no	—
499	C₂	—	16	2	no	—
500	C₂	C₇₁×#3045	1	1	yes	characteristic
501	C₂	C₇₁×#3055	1	1	yes	characteristic
502	C₂	C₂×#471×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₁
prime radical	C₇₁×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₁×#3208	C₂	semidirect
2. C₇₁×#3107	C₂	semidirect
4. C₇₁×#2991	C₂	semidirect
5. C₇₁×#1701	C₂	semidirect
6. C₇₁×#1685	C₂	semidirect
7. C₇₁×#1682	C₂	semidirect
8. C₇₁×#1666	C₂	semidirect
9. C₇₁×#1574	C₂	semidirect
10. C₇₁×#1561	C₂	semidirect
11. C₇₁×#1545	C₂	semidirect
19. #475×C₇₁	C₂²	semidirect
20. #474×C₇₁	C₂²	semidirect
21. #462×C₇₁	C₂²	semidirect
22. #461×C₇₁	C₂²	semidirect
31. C₈×Q₈×C₇₁	C₂²	semidirect
35. #436×C₇₁	C₂²	semidirect
43. #335×C₇₁	C₂²	semidirect
44. #334×C₇₁	C₂²	semidirect
45. #332×C₇₁	C₂²	semidirect
46. #332×C₇₁	C₂²	semidirect
245. #19495	C₇₁	direct (N × H)
252. #3208	C₂×C₇₁	semidirect
253. #3107	C₂×C₇₁	semidirect
255. #2991	C₂×C₇₁	semidirect
256. #1701	C₂×C₇₁	semidirect
257. #1685	C₂×C₇₁	semidirect
258. #1682	C₂×C₇₁	semidirect
259. #1666	C₂×C₇₁	semidirect
260. #1574	C₂×C₇₁	semidirect
261. #1561	C₂×C₇₁	semidirect
262. #1545	C₂×C₇₁	semidirect
263. C₇₁	#19495	direct (N × H)
271. #475	C₂²×C₇₁	semidirect
272. #474	C₂²×C₇₁	semidirect
273. #462	C₂²×C₇₁	semidirect
274. #461	C₂²×C₇₁	semidirect
283. C₈×Q₈	C₂²×C₇₁	semidirect
287. #436	C₂²×C₇₁	semidirect
295. #335	C₂²×C₇₁	semidirect
296. #334	C₂²×C₇₁	semidirect
297. #332	C₂²×C₇₁	semidirect
298. #332	C₂²×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×#3208	2
C₇₁×#3107	2
C₇₁×#3038	2
C₇₁×#2991	2
C₇₁×#1701	2
C₇₁×#1685	2
C₇₁×#1682	2
C₇₁×#1666	2
C₇₁×#1574	2
C₇₁×#1561	2
C₇₁×#1545	2
#19495	71

Subgroups — C71×#19495 #31840367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19495 #31840367