Subgroups — C₇₁×#19559 #31840431

Order 18176.

590 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3254	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3227	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2979	C₂	1	1	yes	maximal, characteristic
5	C₇₁×#1703	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1691	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1683	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1671	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₇₁	C₂²	1	1	yes	characteristic
13	#532×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
15	#498×C₇₁	—	2	1	no	—
16	#498×C₇₁	C₂²	1	2	yes	—
17	#487×C₇₁	C₂²	1	2	yes	—
18	#486×C₇₁	—	2	1	no	—
19	#483×C₇₁	—	2	2	no	—
20	#481×C₇₁	—	2	2	no	—
21	#477×C₇₁	—	2	1	no	—
22	#476×C₇₁	C₂²	1	2	yes	—
23	#476×C₇₁	C₂²	1	2	yes	—
24	#475×C₇₁	—	2	1	no	—
25	#475×C₇₁	—	2	1	no	—
26	#474×C₇₁	C₂²	1	2	yes	—
27	#468×C₇₁	—	2	2	no	—
28	#461×C₇₁	C₂²	1	2	yes	—
29	#460×C₇₁	—	2	1	no	—
30	#436×C₇₁	—	2	1	no	—
31	#436×C₇₁	C₂²	1	2	yes	—
32	C₈×D₄×C₇₁	—	2	1	no	—
33	C₈×D₄×C₇₁	C₂²	1	2	yes	—
34	#431×C₇₁	C₂²	1	1	yes	characteristic
35	#431×C₇₁	C₂²	1	1	yes	characteristic
36	#431×C₇₁	C₂²	1	1	yes	characteristic
37	#423×C₇₁	C₂²	1	1	yes	characteristic
38	#408×C₇₁	—	2	2	no	—
39	#335×C₇₁	C₂²	1	2	yes	—
40	#334×C₇₁	C₂²	1	2	yes	—
41	#333×C₇₁	C₂²	1	2	yes	—
42	#333×C₇₁	C₂²	1	2	yes	—
43	#332×C₇₁	C₂²	1	1	yes	characteristic
44	#332×C₇₁	C₂²	1	1	yes	characteristic
45	#332×C₇₁	C₂²	1	1	yes	characteristic
46	#332×C₇₁	C₂²	1	1	yes	characteristic
47	C₂×#41×C₇₁	—	2	1	no	—
48	C₂²×Q₈×C₇₁	—	2	1	no	—
49	C₂×SD₁₆×C₇₁	—	2	2	no	—
50	C₂×M₁₆×C₇₁	—	2	1	no	—
51	C₂×M₁₆×C₇₁	—	2	2	no	—
52	C₂²×C₈×C₇₁	—	2	2	no	—
53	C₄⋊Q₈×C₇₁	—	2	1	no	—
54	C₄⋊Q₈×C₇₁	—	2	1	no	—
55	C₄⋊Q₈×C₇₁	—	2	1	no	—
56	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
60	#127×C₇₁	D₄	1	1	yes	characteristic
61	#125×C₇₁	—	2	1	no	—
62	#124×C₇₁	—	2	1	no	—
63	C₂²⋊Q₈×C₇₁	—	2	1	no	—
64	C₂²⋊Q₈×C₇₁	—	2	1	no	—
65	#121×C₇₁	—	2	1	no	—
66	#121×C₇₁	D₄	1	2	yes	—
67	C₄×Q₈×C₇₁	—	2	1	no	—
68	C₄×Q₈×C₇₁	—	2	1	no	—
69	C₄×D₄×C₇₁	—	2	1	no	—
70	C₄×D₄×C₇₁	C₂³	1	2	yes	—
71	#117×C₇₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
74	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
75	#107×C₇₁	—	2	2	no	—
76	#106×C₇₁	—	2	2	no	—
77	#106×C₇₁	—	2	2	no	—
78	#106×C₇₁	—	2	2	no	—
79	#106×C₇₁	—	2	2	no	—
80	C₄⋊C₈×C₇₁	—	2	1	no	—
81	C₄⋊C₈×C₇₁	D₄	1	1	yes	characteristic
82	C₄⋊C₈×C₇₁	D₄	1	1	yes	characteristic
83	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
84	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
88	#103×C₇₁	—	2	2	no	—
89	#103×C₇₁	—	2	2	no	—
90	#103×C₇₁	—	2	2	no	—
91	#102×C₇₁	—	2	2	no	—
92	#102×C₇₁	—	2	2	no	—
93	#102×C₇₁	—	2	2	no	—
94	C₂²⋊C₈×C₇₁	—	2	1	no	—
95	C₂²⋊C₈×C₇₁	—	2	1	no	—
96	C₂²⋊C₈×C₇₁	—	2	2	no	—
97	C₂²⋊C₈×C₇₁	—	2	2	no	—
98	C₂²⋊C₈×C₇₁	D₄	1	2	yes	—
99	C₄×C₈×C₇₁	—	2	1	no	—
100	C₄×C₈×C₇₁	—	2	1	no	—
101	C₄×C₈×C₇₁	C₂³	1	2	yes	—
102	#41×C₇₁	—	8	1	no	—
103	#41×C₇₁	—	8	1	no	—
104	C₂×Q₈×C₇₁	—	2	1	no	—
105	C₂×Q₈×C₇₁	—	2	1	no	—
106	C₂×Q₈×C₇₁	—	2	1	no	—
107	C₂×Q₈×C₇₁	—	2	2	no	—
108	C₂×Q₈×C₇₁	—	4	1	no	—
109	C₂×Q₈×C₇₁	—	8	2	no	—
110	C₂×D₄×C₇₁	—	2	2	no	—
111	C₂×D₄×C₇₁	—	2	1	no	—
112	C₂×D₄×C₇₁	—	2	1	no	—
113	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇₁	—	2	2	no	—
115	C₂²×C₄×C₇₁	—	4	1	no	—
116	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
119	SD₁₆×C₇₁	—	8	2	no	—
120	M₁₆×C₇₁	—	8	2	no	—
121	M₁₆×C₇₁	—	8	1	no	—
122	C₂×C₈×C₇₁	—	2	1	no	—
123	C₂×C₈×C₇₁	—	2	1	no	—
124	C₂×C₈×C₇₁	—	2	1	no	—
125	C₂×C₈×C₇₁	—	2	1	no	—
126	C₂×C₈×C₇₁	—	2	2	no	—
127	C₂×C₈×C₇₁	—	8	2	no	—
128	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₇₁	—	2	1	no	—
131	C₄⋊C₄×C₇₁	—	2	2	no	—
132	C₄⋊C₄×C₇₁	—	2	1	no	—
133	C₄⋊C₄×C₇₁	—	2	2	no	—
134	C₄⋊C₄×C₇₁	—	2	1	no	—
135	C₄⋊C₄×C₇₁	—	2	1	no	—
136	C₄⋊C₄×C₇₁	—	2	1	no	—
137	C₄⋊C₄×C₇₁	—	4	1	no	—
138	C₄⋊C₄×C₇₁	—	4	1	no	—
139	C₄⋊C₄×C₇₁	—	4	1	no	—
140	C₄⋊C₄×C₇₁	—	4	1	no	—
141	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₇₁	—	2	2	no	—
143	C₂²⋊C₄×C₇₁	—	2	2	no	—
144	C₂²⋊C₄×C₇₁	—	4	1	no	—
145	C₄²×C₇₁	—	4	1	no	—
146	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₁	#41	1	1	yes	characteristic
149	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
150	C₂³×C₇₁	—	2	2	no	—
151	C₂³×C₇₁	#121	1	1	yes	characteristic
152	Q₈×C₇₁	—	4	1	no	—
153	Q₈×C₇₁	—	4	1	no	—
154	Q₈×C₇₁	—	4	1	no	—
155	Q₈×C₇₁	—	4	1	no	—
156	Q₈×C₇₁	—	8	1	no	—
157	Q₈×C₇₁	—	8	2	no	—
158	Q₈×C₇₁	—	8	2	no	—
159	D₄×C₇₁	—	2	2	no	—
160	D₄×C₇₁	—	2	2	no	—
161	D₄×C₇₁	—	4	2	no	—
162	D₄×C₇₁	—	8	1	no	—
163	D₄×C₇₁	—	8	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	2	no	—
170	C₂×C₄×C₇₁	—	4	2	no	—
171	C₂×C₄×C₇₁	—	4	2	no	—
172	C₂×C₄×C₇₁	—	4	1	no	—
173	C₂×C₄×C₇₁	—	4	1	no	—
174	C₂×C₄×C₇₁	—	4	2	no	—
175	C₂×C₄×C₇₁	—	8	2	no	—
176	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
179	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
182	C₈×C₇₁	—	2	2	no	—
183	C₈×C₇₁	—	2	2	no	—
184	C₈×C₇₁	—	4	1	no	—
185	C₈×C₇₁	—	4	1	no	—
186	C₈×C₇₁	—	4	1	no	—
187	C₈×C₇₁	—	4	2	no	—
188	C₈×C₇₁	—	4	1	no	—
189	C₂²×C₇₁	—	2	1	no	—
190	C₂²×C₇₁	—	2	1	no	—
191	C₂²×C₇₁	—	2	1	no	—
192	C₂²×C₇₁	—	4	2	no	—
193	C₂²×C₇₁	—	4	2	no	—
194	C₂²×C₇₁	—	4	2	no	—
195	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
196	C₄×C₇₁	—	2	1	no	—
197	C₄×C₇₁	—	2	1	no	—
198	C₄×C₇₁	—	2	1	no	—
199	C₄×C₇₁	—	4	2	no	—
200	C₄×C₇₁	—	8	1	no	—
201	C₄×C₇₁	—	8	1	no	—
202	C₄×C₇₁	—	8	2	no	—
203	C₄×C₇₁	#471	1	2	yes	—
204	C₄×C₇₁	#577	1	1	yes	characteristic
205	C₄×C₇₁	#577	1	1	yes	characteristic
206	C₄×C₇₁	#577	1	1	yes	characteristic
207	C₄×C₇₁	#578	1	1	yes	characteristic
208	#19559	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂×C₇₁	—	4	1	no	—
210	C₂×C₇₁	—	8	2	no	—
211	C₂×C₇₁	#3042	1	1	yes	characteristic
212	C₂×C₇₁	#3063	1	1	yes	characteristic
213	C₂×C₇₁	C₂×#471	1	1	yes	characteristic
214	#3254	C₂×C₇₁	1	1	yes	characteristic
215	#3229	C₂×C₇₁	1	1	yes	characteristic, complemented
216	#3227	C₂×C₇₁	1	1	yes	characteristic
217	#2979	C₂×C₇₁	1	1	yes	characteristic
218	#1703	C₂×C₇₁	1	2	yes	complemented
219	#1691	C₂×C₇₁	1	2	yes	complemented
220	#1683	C₂×C₇₁	1	2	yes	complemented
221	#1671	C₂×C₇₁	1	2	yes	complemented
222	#1574	C₂×C₇₁	1	1	yes	characteristic, complemented
223	#1548	C₂×C₇₁	1	1	yes	characteristic, complemented
224	#1544	C₂×C₇₁	1	1	yes	characteristic, complemented
225	C₇₁	#19559	1	1	yes	characteristic, direct product factor, Sylow
226	#533	C₂²×C₇₁	1	1	yes	characteristic
227	#532	C₂²×C₇₁	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
229	#498	—	2	1	no	—
230	#498	C₂²×C₇₁	1	2	yes	—
231	#487	C₂²×C₇₁	1	2	yes	—
232	#486	—	2	1	no	—
233	#483	—	2	2	no	—
234	#481	—	2	2	no	—
235	#477	—	2	1	no	—
236	#476	C₂²×C₇₁	1	2	yes	—
237	#476	C₂²×C₇₁	1	2	yes	—
238	#475	—	2	1	no	—
239	#475	—	2	1	no	—
240	#474	C₂²×C₇₁	1	2	yes	—
241	#468	—	2	2	no	—
242	#461	C₂²×C₇₁	1	2	yes	—
243	#460	—	2	1	no	—
244	#436	—	2	1	no	—
245	#436	C₂²×C₇₁	1	2	yes	—
246	C₈×D₄	—	2	1	no	—
247	C₈×D₄	C₂²×C₇₁	1	2	yes	—
248	#431	C₂²×C₇₁	1	1	yes	characteristic
249	#431	C₂²×C₇₁	1	1	yes	characteristic
250	#431	C₂²×C₇₁	1	1	yes	characteristic
251	#423	C₂²×C₇₁	1	1	yes	characteristic
252	#408	—	2	2	no	—
253	#335	C₂²×C₇₁	1	2	yes	—
254	#334	C₂²×C₇₁	1	2	yes	—
255	#333	C₂²×C₇₁	1	2	yes	—
256	#333	C₂²×C₇₁	1	2	yes	—
257	#332	C₂²×C₇₁	1	1	yes	characteristic
258	#332	C₂²×C₇₁	1	1	yes	characteristic
259	#332	C₂²×C₇₁	1	1	yes	characteristic
260	#332	C₂²×C₇₁	1	1	yes	characteristic
261	C₂×#41	—	2	1	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
272	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
273	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
274	#127	D₄×C₇₁	1	1	yes	characteristic
275	#125	—	2	1	no	—
276	#124	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	D₄×C₇₁	1	2	yes	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	C₂³×C₇₁	1	2	yes	—
285	#117	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	#106	—	2	2	no	—
292	#106	—	2	2	no	—
293	#106	—	2	2	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
296	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
297	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	D₄×C₇₁	1	2	yes	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	C₂³×C₇₁	1	2	yes	—
316	#41	—	8	1	no	—
317	#41	—	8	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
332	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
333	SD₁₆	—	8	2	no	—
334	M₁₆	—	8	2	no	—
335	M₁₆	—	8	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	8	2	no	—
342	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
343	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₄²	—	4	1	no	—
360	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
362	C₄²	#41×C₇₁	1	1	yes	characteristic
363	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
364	C₂³	—	2	2	no	—
365	C₂³	#121×C₇₁	1	1	yes	characteristic
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	2	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
391	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
392	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
395	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	2	no	—
417	C₄	#471×C₇₁	1	2	yes	—
418	C₄	#577×C₇₁	1	1	yes	characteristic
419	C₄	#577×C₇₁	1	1	yes	characteristic
420	C₄	#577×C₇₁	1	1	yes	characteristic
421	C₄	#578×C₇₁	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	8	2	no	—
424	C₂	C₇₁×#3042	1	1	yes	characteristic
425	C₂	C₇₁×#3063	1	1	yes	characteristic
426	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	#532×C₇₁	C₂²
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×#3229	C₂	semidirect
5. C₇₁×#1703	C₂	semidirect
6. C₇₁×#1691	C₂	semidirect
7. C₇₁×#1683	C₂	semidirect
8. C₇₁×#1671	C₂	semidirect
9. C₇₁×#1574	C₂	semidirect
10. C₇₁×#1548	C₂	semidirect
11. C₇₁×#1544	C₂	semidirect
208. #19559	C₇₁	direct (N × H)
215. #3229	C₂×C₇₁	semidirect
218. #1703	C₂×C₇₁	semidirect
219. #1691	C₂×C₇₁	semidirect
220. #1683	C₂×C₇₁	semidirect
221. #1671	C₂×C₇₁	semidirect
222. #1574	C₂×C₇₁	semidirect
223. #1548	C₂×C₇₁	semidirect
224. #1544	C₂×C₇₁	semidirect
225. C₇₁	#19559	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×#3254	2
C₇₁×#3229	2
C₇₁×#3227	2
C₇₁×#2979	2
C₇₁×#1703	2
C₇₁×#1691	2
C₇₁×#1683	2
C₇₁×#1671	2
C₇₁×#1574	2
C₇₁×#1548	2
C₇₁×#1544	2
#19559	71

Subgroups — C71×#19559 #31840431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19559 #31840431