Subgroups — C₇₁×#19519 #31840391

Order 18176.

602 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3253	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1697	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1691	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1681	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1675	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1559	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₇₁	C₂²	1	1	yes	characteristic
13	#532×C₇₁	C₂²	1	1	yes	characteristic
14	#532×C₇₁	C₂²	1	1	yes	characteristic
15	#500×C₇₁	C₂²	1	1	yes	characteristic
16	#498×C₇₁	C₂²	1	1	yes	characteristic
17	#486×C₇₁	C₂²	1	1	yes	characteristic
18	#486×C₇₁	C₂²	1	1	yes	characteristic
19	#482×C₇₁	—	2	2	no	—
20	#478×C₇₁	—	2	2	no	—
21	#476×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	#469×C₇₁	—	2	2	no	—
26	#465×C₇₁	—	2	2	no	—
27	#461×C₇₁	C₂²	1	2	yes	—
28	#460×C₇₁	—	2	1	no	—
29	#459×C₇₁	—	2	1	no	—
30	#459×C₇₁	C₂²	1	2	yes	—
31	#436×C₇₁	C₂²	1	2	yes	—
32	#435×C₇₁	—	2	2	no	—
33	C₈×D₄×C₇₁	C₂²	1	2	yes	—
34	#432×C₇₁	C₂²	1	1	yes	characteristic
35	#431×C₇₁	C₂²	1	1	yes	characteristic
36	#423×C₇₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
38	#408×C₇₁	—	2	2	no	—
39	#335×C₇₁	C₂²	1	2	yes	—
40	#335×C₇₁	C₂²	1	2	yes	—
41	#333×C₇₁	C₂²	1	2	yes	—
42	#333×C₇₁	C₂²	1	2	yes	—
43	#332×C₇₁	C₂²	1	2	yes	—
44	#331×C₇₁	C₂²	1	2	yes	—
45	C₂×#41×C₇₁	—	2	1	no	—
46	C₂×#41×C₇₁	—	2	1	no	—
47	C₂×SD₁₆×C₇₁	—	2	2	no	—
48	C₂×D₈×C₇₁	—	2	2	no	—
49	C₂×M₁₆×C₇₁	—	2	1	no	—
50	C₂×M₁₆×C₇₁	—	2	2	no	—
51	C₂²×C₈×C₇₁	—	2	1	no	—
52	C₂²×C₈×C₇₁	—	2	2	no	—
53	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
57	#127×C₇₁	D₄	1	1	yes	characteristic
58	#127×C₇₁	C₂³	1	1	yes	characteristic
59	#125×C₇₁	—	2	1	no	—
60	#124×C₇₁	—	2	1	no	—
61	#124×C₇₁	—	2	1	no	—
62	C₂²⋊Q₈×C₇₁	—	2	1	no	—
63	C₂²⋊Q₈×C₇₁	—	2	1	no	—
64	#121×C₇₁	—	2	1	no	—
65	#121×C₇₁	—	2	1	no	—
66	#121×C₇₁	—	2	1	no	—
67	#121×C₇₁	D₄	1	2	yes	—
68	C₄×Q₈×C₇₁	—	2	1	no	—
69	C₄×Q₈×C₇₁	—	2	1	no	—
70	C₄×D₄×C₇₁	—	2	1	no	—
71	C₄×D₄×C₇₁	—	2	1	no	—
72	C₄×D₄×C₇₁	—	2	1	no	—
73	C₄×D₄×C₇₁	C₂³	1	2	yes	—
74	#117×C₇₁	—	2	1	no	—
75	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
76	#107×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	—	2	1	no	—
82	C₄⋊C₈×C₇₁	D₄	1	2	yes	—
83	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
84	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
85	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
86	#103×C₇₁	—	2	2	no	—
87	#102×C₇₁	—	2	2	no	—
88	#102×C₇₁	—	2	2	no	—
89	#102×C₇₁	—	2	2	no	—
90	#102×C₇₁	—	2	2	no	—
91	#102×C₇₁	—	2	2	no	—
92	C₂²⋊C₈×C₇₁	—	2	1	no	—
93	C₂²⋊C₈×C₇₁	—	2	2	no	—
94	C₂²⋊C₈×C₇₁	—	2	2	no	—
95	C₂²⋊C₈×C₇₁	D₄	1	2	yes	—
96	#97×C₇₁	—	2	1	no	—
97	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
99	#41×C₇₁	—	8	2	no	—
100	#41×C₇₁	—	8	2	no	—
101	C₂×Q₈×C₇₁	—	2	1	no	—
102	C₂×Q₈×C₇₁	—	2	1	no	—
103	C₂×Q₈×C₇₁	—	2	1	no	—
104	C₂×Q₈×C₇₁	—	2	1	no	—
105	C₂×D₄×C₇₁	—	2	2	no	—
106	C₂×D₄×C₇₁	—	2	1	no	—
107	C₂×D₄×C₇₁	—	2	1	no	—
108	C₂×D₄×C₇₁	—	2	1	no	—
109	C₂×D₄×C₇₁	—	2	1	no	—
110	C₂×D₄×C₇₁	—	2	1	no	—
111	C₂×D₄×C₇₁	—	4	1	no	—
112	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇₁	—	2	2	no	—
114	C₂²×C₄×C₇₁	—	4	1	no	—
115	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
118	SD₁₆×C₇₁	—	8	2	no	—
119	D₈×C₇₁	—	8	2	no	—
120	M₁₆×C₇₁	—	8	2	no	—
121	M₁₆×C₇₁	—	8	1	no	—
122	C₂×C₈×C₇₁	—	2	2	no	—
123	C₂×C₈×C₇₁	—	2	2	no	—
124	C₂×C₈×C₇₁	—	2	2	no	—
125	C₂×C₈×C₇₁	—	8	2	no	—
126	C₂×C₈×C₇₁	—	8	1	no	—
127	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₇₁	—	2	1	no	—
130	C₄⋊C₄×C₇₁	—	2	1	no	—
131	C₄⋊C₄×C₇₁	—	2	1	no	—
132	C₄⋊C₄×C₇₁	—	2	1	no	—
133	C₄⋊C₄×C₇₁	—	2	1	no	—
134	C₄⋊C₄×C₇₁	—	2	1	no	—
135	C₄⋊C₄×C₇₁	—	2	1	no	—
136	C₄⋊C₄×C₇₁	—	4	1	no	—
137	C₄⋊C₄×C₇₁	—	4	1	no	—
138	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₇₁	—	2	2	no	—
140	C₂²⋊C₄×C₇₁	—	2	2	no	—
141	C₂²⋊C₄×C₇₁	—	4	1	no	—
142	C₂²⋊C₄×C₇₁	—	4	1	no	—
143	C₂²⋊C₄×C₇₁	—	4	1	no	—
144	C₄²×C₇₁	—	4	1	no	—
145	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₇₁	#41	1	1	yes	characteristic
148	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
149	C₂³×C₇₁	—	2	2	no	—
150	C₂³×C₇₁	—	4	1	no	—
151	C₂³×C₇₁	#121	1	1	yes	characteristic
152	Q₈×C₇₁	—	4	1	no	—
153	Q₈×C₇₁	—	4	1	no	—
154	Q₈×C₇₁	—	8	1	no	—
155	Q₈×C₇₁	—	8	1	no	—
156	Q₈×C₇₁	—	8	1	no	—
157	D₄×C₇₁	—	2	2	no	—
158	D₄×C₇₁	—	2	2	no	—
159	D₄×C₇₁	—	4	1	no	—
160	D₄×C₇₁	—	4	2	no	—
161	D₄×C₇₁	—	4	1	no	—
162	D₄×C₇₁	—	8	1	no	—
163	D₄×C₇₁	—	8	1	no	—
164	D₄×C₇₁	—	8	1	no	—
165	D₄×C₇₁	—	8	2	no	—
166	D₄×C₇₁	—	8	2	no	—
167	C₂×C₄×C₇₁	—	2	1	no	—
168	C₂×C₄×C₇₁	—	2	2	no	—
169	C₂×C₄×C₇₁	—	2	1	no	—
170	C₂×C₄×C₇₁	—	2	2	no	—
171	C₂×C₄×C₇₁	—	4	1	no	—
172	C₂×C₄×C₇₁	—	4	2	no	—
173	C₂×C₄×C₇₁	—	4	2	no	—
174	C₂×C₄×C₇₁	—	4	1	no	—
175	C₂×C₄×C₇₁	—	4	1	no	—
176	C₂×C₄×C₇₁	—	4	1	no	—
177	C₂×C₄×C₇₁	—	8	2	no	—
178	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
179	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
184	C₈×C₇₁	—	2	2	no	—
185	C₈×C₇₁	—	2	2	no	—
186	C₈×C₇₁	—	4	2	no	—
187	C₈×C₇₁	—	4	2	no	—
188	C₈×C₇₁	—	4	2	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	—	8	1	no	—
196	C₂²×C₇₁	—	8	1	no	—
197	C₂²×C₇₁	—	8	1	no	—
198	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
199	C₄×C₇₁	—	2	1	no	—
200	C₄×C₇₁	—	2	1	no	—
201	C₄×C₇₁	—	2	1	no	—
202	C₄×C₇₁	—	2	1	no	—
203	C₄×C₇₁	—	4	2	no	—
204	C₄×C₇₁	—	8	1	no	—
205	C₄×C₇₁	—	8	1	no	—
206	C₄×C₇₁	—	8	1	no	—
207	C₄×C₇₁	#576	1	1	yes	characteristic
208	C₄×C₇₁	#577	1	2	yes	—
209	C₄×C₇₁	#578	1	1	yes	characteristic
210	#19519	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₇₁	—	4	1	no	—
212	C₂×C₇₁	—	8	2	no	—
213	C₂×C₇₁	—	16	1	no	—
214	C₂×C₇₁	#3042	1	1	yes	characteristic
215	C₂×C₇₁	#3061	1	1	yes	characteristic
216	C₂×C₇₁	#3068	1	1	yes	characteristic
217	#3253	C₂×C₇₁	1	1	yes	characteristic
218	#3246	C₂×C₇₁	1	1	yes	characteristic, complemented
219	#3228	C₂×C₇₁	1	1	yes	characteristic, complemented
220	#2981	C₂×C₇₁	1	1	yes	characteristic, complemented
221	#1697	C₂×C₇₁	1	2	yes	complemented
222	#1691	C₂×C₇₁	1	2	yes	complemented
223	#1681	C₂×C₇₁	1	2	yes	complemented
224	#1675	C₂×C₇₁	1	2	yes	complemented
225	#1571	C₂×C₇₁	1	1	yes	characteristic, complemented
226	#1559	C₂×C₇₁	1	1	yes	characteristic, complemented
227	#1551	C₂×C₇₁	1	1	yes	characteristic, complemented
228	C₇₁	#19519	1	1	yes	characteristic, direct product factor, Sylow
229	#533	C₂²×C₇₁	1	1	yes	characteristic
230	#532	C₂²×C₇₁	1	1	yes	characteristic
231	#532	C₂²×C₇₁	1	1	yes	characteristic
232	#500	C₂²×C₇₁	1	1	yes	characteristic
233	#498	C₂²×C₇₁	1	1	yes	characteristic
234	#486	C₂²×C₇₁	1	1	yes	characteristic
235	#486	C₂²×C₇₁	1	1	yes	characteristic
236	#482	—	2	2	no	—
237	#478	—	2	2	no	—
238	#476	—	2	1	no	—
239	#476	C₂²×C₇₁	1	2	yes	—
240	#476	C₂²×C₇₁	1	2	yes	—
241	#475	—	2	1	no	—
242	#469	—	2	2	no	—
243	#465	—	2	2	no	—
244	#461	C₂²×C₇₁	1	2	yes	—
245	#460	—	2	1	no	—
246	#459	—	2	1	no	—
247	#459	C₂²×C₇₁	1	2	yes	—
248	#436	C₂²×C₇₁	1	2	yes	—
249	#435	—	2	2	no	—
250	C₈×D₄	C₂²×C₇₁	1	2	yes	—
251	#432	C₂²×C₇₁	1	1	yes	characteristic
252	#431	C₂²×C₇₁	1	1	yes	characteristic
253	#423	C₂²×C₇₁	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
255	#408	—	2	2	no	—
256	#335	C₂²×C₇₁	1	2	yes	—
257	#335	C₂²×C₇₁	1	2	yes	—
258	#333	C₂²×C₇₁	1	2	yes	—
259	#333	C₂²×C₇₁	1	2	yes	—
260	#332	C₂²×C₇₁	1	2	yes	—
261	#331	C₂²×C₇₁	1	2	yes	—
262	C₂×#41	—	2	1	no	—
263	C₂×#41	—	2	1	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
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	#127	C₂³×C₇₁	1	1	yes	characteristic
276	#125	—	2	1	no	—
277	#124	—	2	1	no	—
278	#124	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	#121	—	2	1	no	—
284	#121	D₄×C₇₁	1	2	yes	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	C₂³×C₇₁	1	2	yes	—
291	#117	—	2	1	no	—
292	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#106	—	2	2	no	—
295	#106	—	2	2	no	—
296	#106	—	2	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
300	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
301	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
302	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
303	#103	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	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	#97	—	2	1	no	—
314	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
315	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
316	#41	—	8	2	no	—
317	#41	—	8	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
334	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
335	SD₁₆	—	8	2	no	—
336	D₈	—	8	2	no	—
337	M₁₆	—	8	2	no	—
338	M₁₆	—	8	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	8	2	no	—
343	C₂×C₈	—	8	1	no	—
344	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
345	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	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	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
364	C₄²	#41×C₇₁	1	1	yes	characteristic
365	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	—	4	1	no	—
368	C₂³	#121×C₇₁	1	1	yes	characteristic
369	Q₈	—	4	1	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	1	no	—
373	Q₈	—	8	1	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	1	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	1	no	—
382	D₄	—	8	2	no	—
383	D₄	—	8	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
396	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
397	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	#576×C₇₁	1	1	yes	characteristic
425	C₄	#577×C₇₁	1	2	yes	—
426	C₄	#578×C₇₁	1	1	yes	characteristic
427	C₂	—	4	1	no	—
428	C₂	—	8	2	no	—
429	C₂	—	16	1	no	—
430	C₂	C₇₁×#3042	1	1	yes	characteristic
431	C₂	C₇₁×#3061	1	1	yes	characteristic
432	C₂	C₇₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₁
prime radical	C₇₁×#3253	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
2. C₇₁×#3246	C₂	semidirect
3. C₇₁×#3228	C₂	semidirect
4. C₇₁×#2981	C₂	semidirect
5. C₇₁×#1697	C₂	semidirect
6. C₇₁×#1691	C₂	semidirect
7. C₇₁×#1681	C₂	semidirect
8. C₇₁×#1675	C₂	semidirect
9. C₇₁×#1571	C₂	semidirect
10. C₇₁×#1559	C₂	semidirect
11. C₇₁×#1551	C₂	semidirect
210. #19519	C₇₁	direct (N × H)
218. #3246	C₂×C₇₁	semidirect
219. #3228	C₂×C₇₁	semidirect
220. #2981	C₂×C₇₁	semidirect
221. #1697	C₂×C₇₁	semidirect
222. #1691	C₂×C₇₁	semidirect
223. #1681	C₂×C₇₁	semidirect
224. #1675	C₂×C₇₁	semidirect
225. #1571	C₂×C₇₁	semidirect
226. #1559	C₂×C₇₁	semidirect
227. #1551	C₂×C₇₁	semidirect
228. C₇₁	#19519	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×#3253	2
C₇₁×#3246	2
C₇₁×#3228	2
C₇₁×#2981	2
C₇₁×#1697	2
C₇₁×#1691	2
C₇₁×#1681	2
C₇₁×#1675	2
C₇₁×#1571	2
C₇₁×#1559	2
C₇₁×#1551	2
#19519	71

Subgroups — C71×#19519 #31840391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19519 #31840391