Subgroups — C₇₁×#18591 #31839463

Order 18176.

894 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3503	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#3107	C₂	1	1	yes	maximal, characteristic
5	C₇₁×#1653	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1651	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1649	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1648	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1489	C₂	1	1	yes	maximal, characteristic
11	C₇₁×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₇₁	—	2	1	no	—
13	#557×C₇₁	C₂²	1	2	yes	—
14	#554×C₇₁	—	2	1	no	—
15	#554×C₇₁	—	2	2	no	—
16	D₄×Q₈×C₇₁	—	2	2	no	—
17	D₄×Q₈×C₇₁	C₂²	1	2	yes	—
18	#544×C₇₁	—	2	2	no	—
19	#544×C₇₁	—	2	1	no	—
20	#533×C₇₁	—	2	1	no	—
21	#533×C₇₁	C₂²	1	1	yes	characteristic
22	#533×C₇₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₇₁	—	2	1	no	—
24	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
25	#520×C₇₁	—	2	1	no	—
26	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
27	#501×C₇₁	—	2	2	no	—
28	#500×C₇₁	C₂²	1	2	yes	—
29	#498×C₇₁	C₂²	1	2	yes	—
30	#485×C₇₁	—	2	1	no	—
31	#475×C₇₁	—	2	1	no	—
32	#475×C₇₁	C₂²	1	1	yes	characteristic
33	#475×C₇₁	C₂²	1	2	yes	—
34	#474×C₇₁	C₂²	1	1	yes	characteristic
35	#470×C₇₁	—	2	2	no	—
36	#462×C₇₁	—	2	1	no	—
37	#462×C₇₁	C₂²	1	1	yes	characteristic
38	#462×C₇₁	C₂²	1	2	yes	—
39	#461×C₇₁	C₂²	1	1	yes	characteristic
40	#452×C₇₁	—	2	1	no	—
41	C₄×Q₁₆×C₇₁	—	2	1	no	—
42	C₄×SD₁₆×C₇₁	—	2	1	no	—
43	#431×C₇₁	C₂²	1	1	yes	characteristic
44	#428×C₇₁	—	2	2	no	—
45	#423×C₇₁	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
47	#332×C₇₁	C₂²	1	2	yes	—
48	#332×C₇₁	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₁	C₂²	1	2	yes	—
50	Q₈⋊C₈×C₇₁	C₂²	1	2	yes	—
51	Q₈⋊C₈×C₇₁	C₂²	1	2	yes	—
52	D₄⋊C₈×C₇₁	C₂²	1	2	yes	—
53	C₂×#41×C₇₁	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₇₁	—	2	2	no	—
55	C₂²×Q₈×C₇₁	—	2	1	no	—
56	C₂×Q₁₆×C₇₁	—	2	1	no	—
57	C₂×Q₁₆×C₇₁	—	2	2	no	—
58	C₂×SD₁₆×C₇₁	—	2	1	no	—
59	C₂×M₁₆×C₇₁	—	2	1	no	—
60	C₂×M₁₆×C₇₁	—	2	1	no	—
61	C₄⋊Q₈×C₇₁	—	2	2	no	—
62	C₄⋊Q₈×C₇₁	—	2	2	no	—
63	C₄⋊Q₈×C₇₁	—	2	4	no	—
64	C₄⋊Q₈×C₇₁	—	2	2	no	—
65	C₄⋊Q₈×C₇₁	—	2	2	no	—
66	C₄⋊Q₈×C₇₁	—	2	1	no	—
67	C₄⋊Q₈×C₇₁	—	2	1	no	—
68	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₇₁	D₄	1	2	yes	—
71	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
74	#125×C₇₁	—	2	2	no	—
75	#125×C₇₁	—	2	4	no	—
76	#125×C₇₁	—	2	2	no	—
77	#125×C₇₁	—	2	1	no	—
78	#125×C₇₁	—	2	1	no	—
79	C₂²⋊Q₈×C₇₁	—	2	2	no	—
80	C₂²⋊Q₈×C₇₁	—	2	4	no	—
81	C₂²⋊Q₈×C₇₁	—	2	4	no	—
82	C₂²⋊Q₈×C₇₁	—	2	1	no	—
83	C₂²⋊Q₈×C₇₁	—	2	2	no	—
84	C₂²⋊Q₈×C₇₁	—	2	4	no	—
85	C₂²⋊Q₈×C₇₁	—	2	1	no	—
86	C₂²⋊Q₈×C₇₁	—	2	1	no	—
87	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
88	C₄×Q₈×C₇₁	—	2	2	no	—
89	C₄×Q₈×C₇₁	—	2	2	no	—
90	C₄×Q₈×C₇₁	—	2	2	no	—
91	C₄×Q₈×C₇₁	—	2	1	no	—
92	C₄×Q₈×C₇₁	—	2	1	no	—
93	C₄×Q₈×C₇₁	—	2	1	no	—
94	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
97	C₄×D₄×C₇₁	—	2	4	no	—
98	C₄×D₄×C₇₁	—	2	2	no	—
99	C₄×D₄×C₇₁	—	2	1	no	—
100	C₄×D₄×C₇₁	—	2	1	no	—
101	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
102	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
103	#117×C₇₁	—	2	2	no	—
104	#117×C₇₁	—	2	1	no	—
105	#117×C₇₁	—	2	1	no	—
106	#117×C₇₁	—	2	1	no	—
107	#117×C₇₁	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
109	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
110	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₇₁	D₄	1	2	yes	—
112	C₂×C₄²×C₇₁	—	2	1	no	—
113	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
114	#107×C₇₁	—	2	4	no	—
115	#107×C₇₁	—	2	1	no	—
116	#106×C₇₁	—	2	4	no	—
117	#106×C₇₁	—	2	1	no	—
118	#106×C₇₁	—	2	2	no	—
119	C₄⋊C₈×C₇₁	—	2	1	no	—
120	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
121	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
123	#103×C₇₁	—	2	1	no	—
124	#103×C₇₁	—	2	2	no	—
125	#103×C₇₁	—	2	1	no	—
126	#103×C₇₁	—	2	1	no	—
127	#103×C₇₁	—	2	2	no	—
128	#102×C₇₁	—	2	1	no	—
129	C₂²⋊C₈×C₇₁	—	2	1	no	—
130	#97×C₇₁	—	2	1	no	—
131	C₄×C₈×C₇₁	—	2	1	no	—
132	C₄×C₈×C₇₁	C₂³	1	2	yes	—
133	#41×C₇₁	—	2	2	no	—
134	#41×C₇₁	—	2	2	no	—
135	C₂×Q₈×C₇₁	—	2	4	no	—
136	C₂×Q₈×C₇₁	—	2	1	no	—
137	C₂×Q₈×C₇₁	—	2	2	no	—
138	C₂×Q₈×C₇₁	—	2	2	no	—
139	C₂×Q₈×C₇₁	—	2	1	no	—
140	C₂×Q₈×C₇₁	—	2	1	no	—
141	C₂×Q₈×C₇₁	—	8	1	no	—
142	C₂×Q₈×C₇₁	—	8	1	no	—
143	C₂×Q₈×C₇₁	—	8	2	no	—
144	C₂×Q₈×C₇₁	—	8	2	no	—
145	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₇₁	—	2	1	no	—
148	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₁	—	2	1	no	—
150	C₂²×C₄×C₇₁	—	2	4	no	—
151	C₂²×C₄×C₇₁	—	2	2	no	—
152	C₂²×C₄×C₇₁	—	2	1	no	—
153	C₂²×C₄×C₇₁	—	2	1	no	—
154	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
157	Q₁₆×C₇₁	—	4	2	no	—
158	Q₁₆×C₇₁	—	8	2	no	—
159	SD₁₆×C₇₁	—	4	2	no	—
160	M₁₆×C₇₁	—	2	4	no	—
161	M₁₆×C₇₁	—	8	1	no	—
162	C₂×C₈×C₇₁	—	2	2	no	—
163	C₂×C₈×C₇₁	—	2	1	no	—
164	C₂×C₈×C₇₁	—	2	1	no	—
165	C₂×C₈×C₇₁	—	2	2	no	—
166	C₄⋊C₄×C₇₁	—	2	4	no	—
167	C₄⋊C₄×C₇₁	—	2	4	no	—
168	C₄⋊C₄×C₇₁	—	2	4	no	—
169	C₄⋊C₄×C₇₁	—	2	4	no	—
170	C₄⋊C₄×C₇₁	—	2	1	no	—
171	C₄⋊C₄×C₇₁	—	2	2	no	—
172	C₄⋊C₄×C₇₁	—	2	1	no	—
173	C₄⋊C₄×C₇₁	—	2	2	no	—
174	C₄⋊C₄×C₇₁	—	2	1	no	—
175	C₄⋊C₄×C₇₁	—	2	1	no	—
176	C₄⋊C₄×C₇₁	—	2	2	no	—
177	C₄⋊C₄×C₇₁	—	2	2	no	—
178	C₄⋊C₄×C₇₁	—	2	1	no	—
179	C₄⋊C₄×C₇₁	—	2	2	no	—
180	C₄⋊C₄×C₇₁	—	2	1	no	—
181	C₄⋊C₄×C₇₁	—	2	1	no	—
182	C₄⋊C₄×C₇₁	—	2	1	no	—
183	C₄⋊C₄×C₇₁	—	2	1	no	—
184	C₄⋊C₄×C₇₁	—	4	1	no	—
185	C₄⋊C₄×C₇₁	—	4	1	no	—
186	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
190	C₂²⋊C₄×C₇₁	—	2	4	no	—
191	C₂²⋊C₄×C₇₁	—	2	2	no	—
192	C₂²⋊C₄×C₇₁	—	2	1	no	—
193	C₂²⋊C₄×C₇₁	—	2	1	no	—
194	C₂²⋊C₄×C₇₁	—	2	1	no	—
195	C₂²⋊C₄×C₇₁	—	4	1	no	—
196	C₄²×C₇₁	—	2	4	no	—
197	C₄²×C₇₁	—	2	1	no	—
198	C₄²×C₇₁	—	2	1	no	—
199	C₄²×C₇₁	—	2	1	no	—
200	C₄²×C₇₁	—	2	2	no	—
201	C₄²×C₇₁	—	4	1	no	—
202	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
206	C₂³×C₇₁	—	2	1	no	—
207	C₂³×C₇₁	#120	1	1	yes	characteristic
208	Q₈×C₇₁	—	2	1	no	—
209	Q₈×C₇₁	—	2	2	no	—
210	Q₈×C₇₁	—	2	2	no	—
211	Q₈×C₇₁	—	4	2	no	—
212	Q₈×C₇₁	—	4	2	no	—
213	Q₈×C₇₁	—	4	2	no	—
214	Q₈×C₇₁	—	4	1	no	—
215	Q₈×C₇₁	—	4	1	no	—
216	Q₈×C₇₁	—	4	1	no	—
217	Q₈×C₇₁	—	4	1	no	—
218	Q₈×C₇₁	—	8	2	no	—
219	Q₈×C₇₁	—	8	4	no	—
220	Q₈×C₇₁	#137	1	2	yes	—
221	D₄×C₇₁	—	2	4	no	—
222	D₄×C₇₁	—	2	1	no	—
223	D₄×C₇₁	#137	1	2	yes	—
224	C₂×C₄×C₇₁	—	2	4	no	—
225	C₂×C₄×C₇₁	—	2	1	no	—
226	C₂×C₄×C₇₁	—	2	1	no	—
227	C₂×C₄×C₇₁	—	2	1	no	—
228	C₂×C₄×C₇₁	—	2	1	no	—
229	C₂×C₄×C₇₁	—	2	1	no	—
230	C₂×C₄×C₇₁	—	2	2	no	—
231	C₂×C₄×C₇₁	—	2	2	no	—
232	C₂×C₄×C₇₁	—	2	1	no	—
233	C₂×C₄×C₇₁	—	2	1	no	—
234	C₂×C₄×C₇₁	—	2	2	no	—
235	C₂×C₄×C₇₁	—	2	4	no	—
236	C₂×C₄×C₇₁	—	4	1	no	—
237	C₂×C₄×C₇₁	—	4	1	no	—
238	C₂×C₄×C₇₁	—	4	2	no	—
239	C₂×C₄×C₇₁	—	4	1	no	—
240	C₂×C₄×C₇₁	—	4	1	no	—
241	C₂×C₄×C₇₁	—	8	2	no	—
242	C₂×C₄×C₇₁	—	8	4	no	—
243	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
244	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
245	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
246	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
249	C₈×C₇₁	—	2	4	no	—
250	C₈×C₇₁	—	4	1	no	—
251	C₈×C₇₁	—	4	1	no	—
252	C₈×C₇₁	—	4	2	no	—
253	C₂²×C₇₁	—	2	1	no	—
254	C₂²×C₇₁	—	2	2	no	—
255	C₂²×C₇₁	—	2	1	no	—
256	C₂²×C₇₁	—	2	1	no	—
257	C₂²×C₇₁	—	4	1	no	—
258	C₂²×C₇₁	—	4	1	no	—
259	C₂²×C₇₁	C₂×#120	1	1	yes	characteristic
260	C₄×C₇₁	—	2	1	no	—
261	C₄×C₇₁	—	2	2	no	—
262	C₄×C₇₁	—	2	1	no	—
263	C₄×C₇₁	—	2	1	no	—
264	C₄×C₇₁	—	4	1	no	—
265	C₄×C₇₁	—	4	2	no	—
266	C₄×C₇₁	—	4	4	no	—
267	C₄×C₇₁	—	4	1	no	—
268	C₄×C₇₁	—	4	2	no	—
269	C₄×C₇₁	—	8	1	no	—
270	C₄×C₇₁	—	8	1	no	—
271	C₄×C₇₁	#456	1	2	yes	—
272	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
273	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
274	C₄×C₇₁	#576	1	1	yes	characteristic
275	C₄×C₇₁	#577	1	1	yes	characteristic
276	#18591	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₇₁	—	4	1	no	—
278	C₂×C₇₁	—	4	2	no	—
279	C₂×C₇₁	#3004	1	1	yes	characteristic
280	C₂×C₇₁	#3012	1	1	yes	characteristic
281	C₂×C₇₁	C₂×#456	1	1	yes	characteristic
282	#3503	C₂×C₇₁	1	1	yes	characteristic
283	#3255	C₂×C₇₁	1	1	yes	characteristic, complemented
284	#3165	C₂×C₇₁	1	1	yes	characteristic, complemented
285	#3107	C₂×C₇₁	1	1	yes	characteristic
286	#1653	C₂×C₇₁	1	2	yes	complemented
287	#1651	C₂×C₇₁	1	2	yes	complemented
288	#1649	C₂×C₇₁	1	2	yes	complemented
289	#1648	C₂×C₇₁	1	2	yes	complemented
290	#1546	C₂×C₇₁	1	1	yes	characteristic, complemented
291	#1489	C₂×C₇₁	1	1	yes	characteristic
292	#1485	C₂×C₇₁	1	1	yes	characteristic, complemented
293	C₇₁	#18591	1	1	yes	characteristic, direct product factor, Sylow
294	Q₈²	—	2	1	no	—
295	#557	C₂²×C₇₁	1	2	yes	—
296	#554	—	2	1	no	—
297	#554	—	2	2	no	—
298	D₄×Q₈	—	2	2	no	—
299	D₄×Q₈	C₂²×C₇₁	1	2	yes	—
300	#544	—	2	2	no	—
301	#544	—	2	1	no	—
302	#533	—	2	1	no	—
303	#533	C₂²×C₇₁	1	1	yes	characteristic
304	#533	C₂²×C₇₁	1	1	yes	characteristic
305	C₂×C₄⋊Q₈	—	2	1	no	—
306	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
307	#520	—	2	1	no	—
308	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
309	#501	—	2	2	no	—
310	#500	C₂²×C₇₁	1	2	yes	—
311	#498	C₂²×C₇₁	1	2	yes	—
312	#485	—	2	1	no	—
313	#475	—	2	1	no	—
314	#475	C₂²×C₇₁	1	1	yes	characteristic
315	#475	C₂²×C₇₁	1	2	yes	—
316	#474	C₂²×C₇₁	1	1	yes	characteristic
317	#470	—	2	2	no	—
318	#462	—	2	1	no	—
319	#462	C₂²×C₇₁	1	1	yes	characteristic
320	#462	C₂²×C₇₁	1	2	yes	—
321	#461	C₂²×C₇₁	1	1	yes	characteristic
322	#452	—	2	1	no	—
323	C₄×Q₁₆	—	2	1	no	—
324	C₄×SD₁₆	—	2	1	no	—
325	#431	C₂²×C₇₁	1	1	yes	characteristic
326	#428	—	2	2	no	—
327	#423	C₂²×C₇₁	1	1	yes	characteristic
328	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
329	#332	C₂²×C₇₁	1	2	yes	—
330	#332	C₂²×C₇₁	1	2	yes	—
331	Q₈⋊C₈	C₂²×C₇₁	1	2	yes	—
332	Q₈⋊C₈	C₂²×C₇₁	1	2	yes	—
333	Q₈⋊C₈	C₂²×C₇₁	1	2	yes	—
334	D₄⋊C₈	C₂²×C₇₁	1	2	yes	—
335	C₂×#41	D₄×C₇₁	1	1	yes	characteristic
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂×Q₁₆	—	2	1	no	—
339	C₂×Q₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	—	2	2	no	—
345	C₄⋊Q₈	—	2	4	no	—
346	C₄⋊Q₈	—	2	2	no	—
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
351	C₄⋊Q₈	D₄×C₇₁	1	2	yes	—
352	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
356	#125	—	2	2	no	—
357	#125	—	2	4	no	—
358	#125	—	2	2	no	—
359	#125	—	2	1	no	—
360	#125	—	2	1	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	—	2	4	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	2	4	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
377	C₄×Q₈	C₂³×C₇₁	1	1	yes	characteristic
378	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
379	C₄×D₄	—	2	4	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
384	C₄×D₄	C₂³×C₇₁	1	1	yes	characteristic
385	#117	—	2	2	no	—
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	D₄×C₇₁	1	1	yes	characteristic
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	2	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	D₄×C₇₁	1	2	yes	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
396	#107	—	2	4	no	—
397	#107	—	2	1	no	—
398	#106	—	2	4	no	—
399	#106	—	2	1	no	—
400	#106	—	2	2	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
403	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
405	#103	—	2	1	no	—
406	#103	—	2	2	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	2	no	—
410	#102	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	#97	—	2	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	C₂³×C₇₁	1	2	yes	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	8	1	no	—
424	C₂×Q₈	—	8	1	no	—
425	C₂×Q₈	—	8	2	no	—
426	C₂×Q₈	—	8	2	no	—
427	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
428	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
439	Q₁₆	—	4	2	no	—
440	Q₁₆	—	8	2	no	—
441	SD₁₆	—	4	2	no	—
442	M₁₆	—	2	4	no	—
443	M₁₆	—	8	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	2	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
470	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
471	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	4	1	no	—
484	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
485	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
487	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	#120×C₇₁	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	4	2	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	8	2	no	—
501	Q₈	—	8	4	no	—
502	Q₈	#137×C₇₁	1	2	yes	—
503	D₄	—	2	4	no	—
504	D₄	—	2	1	no	—
505	D₄	#137×C₇₁	1	2	yes	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	—	8	4	no	—
525	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
526	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
527	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
531	C₈	—	2	4	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	C₂×#120×C₇₁	1	1	yes	characteristic
542	C₄	—	2	1	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	#456×C₇₁	1	2	yes	—
554	C₄	C₂×#137×C₇₁	1	1	yes	characteristic
555	C₄	C₂×#137×C₇₁	1	1	yes	characteristic
556	C₄	#576×C₇₁	1	1	yes	characteristic
557	C₄	#577×C₇₁	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	C₇₁×#3004	1	1	yes	characteristic
561	C₂	C₇₁×#3012	1	1	yes	characteristic
562	C₂	C₂×#456×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₁
prime radical	C₂×#41×C₇₁	D₄
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
2. C₇₁×#3255	C₂	semidirect
3. C₇₁×#3165	C₂	semidirect
5. C₇₁×#1653	C₂	semidirect
6. C₇₁×#1651	C₂	semidirect
7. C₇₁×#1649	C₂	semidirect
8. C₇₁×#1648	C₂	semidirect
9. C₇₁×#1546	C₂	semidirect
11. C₇₁×#1485	C₂	semidirect
276. #18591	C₇₁	direct (N × H)
283. #3255	C₂×C₇₁	semidirect
284. #3165	C₂×C₇₁	semidirect
286. #1653	C₂×C₇₁	semidirect
287. #1651	C₂×C₇₁	semidirect
288. #1649	C₂×C₇₁	semidirect
289. #1648	C₂×C₇₁	semidirect
290. #1546	C₂×C₇₁	semidirect
292. #1485	C₂×C₇₁	semidirect
293. C₇₁	#18591	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₁×#3503	2
C₇₁×#3255	2
C₇₁×#3165	2
C₇₁×#3107	2
C₇₁×#1653	2
C₇₁×#1651	2
C₇₁×#1649	2
C₇₁×#1648	2
C₇₁×#1546	2
C₇₁×#1489	2
C₇₁×#1485	2
#18591	71

Subgroups — C71×#18591 #31839463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#18591 #31839463