Subgroups — C₇₁×#19558 #31840430

Order 18176.

624 conjugacy classes of subgroups.

The subgroup lattice has 452 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×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1701	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×#1671	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	#532×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	C₂²	1	2	yes	—
16	#492×C₇₁	—	2	1	no	—
17	#487×C₇₁	—	2	1	no	—
18	#486×C₇₁	C₂²	1	2	yes	—
19	#481×C₇₁	—	2	2	no	—
20	#476×C₇₁	—	2	1	no	—
21	#476×C₇₁	—	2	1	no	—
22	#476×C₇₁	—	2	1	no	—
23	#476×C₇₁	C₂²	1	2	yes	—
24	#469×C₇₁	—	2	2	no	—
25	#461×C₇₁	C₂²	1	2	yes	—
26	#461×C₇₁	C₂²	1	2	yes	—
27	#459×C₇₁	—	2	1	no	—
28	#459×C₇₁	C₂²	1	2	yes	—
29	#448×C₇₁	—	2	2	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	1	yes	characteristic
42	#333×C₇₁	C₂²	1	1	yes	characteristic
43	#332×C₇₁	C₂²	1	2	yes	—
44	#332×C₇₁	C₂²	1	2	yes	—
45	#331×C₇₁	C₂²	1	1	yes	characteristic
46	#331×C₇₁	C₂²	1	1	yes	characteristic
47	C₂×#41×C₇₁	—	2	1	no	—
48	C₂×#41×C₇₁	—	2	1	no	—
49	C₂²×Q₈×C₇₁	—	2	1	no	—
50	C₂×SD₁₆×C₇₁	—	2	2	no	—
51	C₂×SD₁₆×C₇₁	—	2	2	no	—
52	C₂×D₈×C₇₁	—	2	2	no	—
53	C₂×M₁₆×C₇₁	—	2	1	no	—
54	C₂×M₁₆×C₇₁	—	2	2	no	—
55	C₂²×C₈×C₇₁	—	2	2	no	—
56	C₄⋊Q₈×C₇₁	—	2	1	no	—
57	C₄⋊Q₈×C₇₁	—	2	1	no	—
58	C₄⋊Q₈×C₇₁	—	2	1	no	—
59	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
61	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
62	#127×C₇₁	D₄	1	1	yes	characteristic
63	#127×C₇₁	C₂³	1	1	yes	characteristic
64	#124×C₇₁	—	2	1	no	—
65	#124×C₇₁	—	2	1	no	—
66	#121×C₇₁	—	2	1	no	—
67	#121×C₇₁	—	2	1	no	—
68	#121×C₇₁	—	2	1	no	—
69	#121×C₇₁	D₄	1	2	yes	—
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	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
76	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
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	#102×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	#41×C₇₁	—	8	2	no	—
105	C₂×Q₈×C₇₁	—	2	1	no	—
106	C₂×Q₈×C₇₁	—	2	2	no	—
107	C₂×Q₈×C₇₁	—	2	1	no	—
108	C₂×Q₈×C₇₁	—	4	1	no	—
109	C₂×Q₈×C₇₁	—	8	1	no	—
110	C₂×Q₈×C₇₁	—	8	1	no	—
111	C₂×D₄×C₇₁	—	2	2	no	—
112	C₂×D₄×C₇₁	—	2	1	no	—
113	C₂×D₄×C₇₁	—	2	1	no	—
114	C₂×D₄×C₇₁	—	2	1	no	—
115	C₂×D₄×C₇₁	—	2	1	no	—
116	C₂×D₄×C₇₁	—	2	1	no	—
117	C₂×D₄×C₇₁	—	4	1	no	—
118	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇₁	—	2	2	no	—
120	C₂²×C₄×C₇₁	—	4	1	no	—
121	C₂²×C₄×C₇₁	—	4	1	no	—
122	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
125	SD₁₆×C₇₁	—	8	2	no	—
126	SD₁₆×C₇₁	—	8	2	no	—
127	D₈×C₇₁	—	8	2	no	—
128	M₁₆×C₇₁	—	8	2	no	—
129	M₁₆×C₇₁	—	8	1	no	—
130	C₂×C₈×C₇₁	—	2	1	no	—
131	C₂×C₈×C₇₁	—	2	1	no	—
132	C₂×C₈×C₇₁	—	2	1	no	—
133	C₂×C₈×C₇₁	—	2	1	no	—
134	C₂×C₈×C₇₁	—	2	2	no	—
135	C₂×C₈×C₇₁	—	8	2	no	—
136	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₇₁	—	2	1	no	—
139	C₄⋊C₄×C₇₁	—	2	2	no	—
140	C₄⋊C₄×C₇₁	—	2	1	no	—
141	C₄⋊C₄×C₇₁	—	2	1	no	—
142	C₄⋊C₄×C₇₁	—	2	2	no	—
143	C₄⋊C₄×C₇₁	—	4	1	no	—
144	C₄⋊C₄×C₇₁	—	4	1	no	—
145	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₇₁	—	2	2	no	—
147	C₂²⋊C₄×C₇₁	—	2	2	no	—
148	C₂²⋊C₄×C₇₁	—	4	1	no	—
149	C₂²⋊C₄×C₇₁	—	4	1	no	—
150	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇₁	#41	1	1	yes	characteristic
153	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
154	C₂³×C₇₁	—	2	2	no	—
155	C₂³×C₇₁	—	4	1	no	—
156	C₂³×C₇₁	#121	1	1	yes	characteristic
157	Q₈×C₇₁	—	4	2	no	—
158	Q₈×C₇₁	—	4	2	no	—
159	Q₈×C₇₁	—	8	1	no	—
160	Q₈×C₇₁	—	8	1	no	—
161	Q₈×C₇₁	—	8	2	no	—
162	D₄×C₇₁	—	2	2	no	—
163	D₄×C₇₁	—	2	2	no	—
164	D₄×C₇₁	—	4	1	no	—
165	D₄×C₇₁	—	4	1	no	—
166	D₄×C₇₁	—	4	1	no	—
167	D₄×C₇₁	—	4	1	no	—
168	D₄×C₇₁	—	4	2	no	—
169	D₄×C₇₁	—	8	1	no	—
170	D₄×C₇₁	—	8	1	no	—
171	D₄×C₇₁	—	8	2	no	—
172	D₄×C₇₁	—	8	2	no	—
173	C₂×C₄×C₇₁	—	2	1	no	—
174	C₂×C₄×C₇₁	—	2	1	no	—
175	C₂×C₄×C₇₁	—	2	1	no	—
176	C₂×C₄×C₇₁	—	2	1	no	—
177	C₂×C₄×C₇₁	—	2	2	no	—
178	C₂×C₄×C₇₁	—	2	2	no	—
179	C₂×C₄×C₇₁	—	4	2	no	—
180	C₂×C₄×C₇₁	—	4	2	no	—
181	C₂×C₄×C₇₁	—	4	1	no	—
182	C₂×C₄×C₇₁	—	4	2	no	—
183	C₂×C₄×C₇₁	—	8	2	no	—
184	C₂×C₄×C₇₁	—	8	2	no	—
185	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
187	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
188	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
191	C₈×C₇₁	—	2	2	no	—
192	C₈×C₇₁	—	2	2	no	—
193	C₈×C₇₁	—	4	2	no	—
194	C₈×C₇₁	—	4	1	no	—
195	C₈×C₇₁	—	4	1	no	—
196	C₈×C₇₁	—	4	1	no	—
197	C₈×C₇₁	—	4	1	no	—
198	C₂²×C₇₁	—	2	1	no	—
199	C₂²×C₇₁	—	2	1	no	—
200	C₂²×C₇₁	—	2	1	no	—
201	C₂²×C₇₁	—	4	2	no	—
202	C₂²×C₇₁	—	4	2	no	—
203	C₂²×C₇₁	—	4	2	no	—
204	C₂²×C₇₁	—	8	1	no	—
205	C₂²×C₇₁	—	8	1	no	—
206	C₂²×C₇₁	—	8	1	no	—
207	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
208	C₄×C₇₁	—	2	1	no	—
209	C₄×C₇₁	—	2	1	no	—
210	C₄×C₇₁	—	2	1	no	—
211	C₄×C₇₁	—	4	2	no	—
212	C₄×C₇₁	—	8	2	no	—
213	C₄×C₇₁	—	8	1	no	—
214	C₄×C₇₁	#471	1	2	yes	—
215	C₄×C₇₁	#576	1	1	yes	characteristic
216	C₄×C₇₁	#577	1	1	yes	characteristic
217	C₄×C₇₁	#577	1	1	yes	characteristic
218	C₄×C₇₁	#577	1	1	yes	characteristic
219	#19558	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₇₁	—	4	1	no	—
221	C₂×C₇₁	—	8	2	no	—
222	C₂×C₇₁	—	16	1	no	—
223	C₂×C₇₁	#3042	1	1	yes	characteristic
224	C₂×C₇₁	#3062	1	1	yes	characteristic
225	C₂×C₇₁	C₂×#471	1	1	yes	characteristic
226	#3253	C₂×C₇₁	1	1	yes	characteristic
227	#3227	C₂×C₇₁	1	1	yes	characteristic, complemented
228	#3206	C₂×C₇₁	1	1	yes	characteristic, complemented
229	#2979	C₂×C₇₁	1	1	yes	characteristic, complemented
230	#1701	C₂×C₇₁	1	2	yes	complemented
231	#1691	C₂×C₇₁	1	2	yes	complemented
232	#1681	C₂×C₇₁	1	2	yes	complemented
233	#1671	C₂×C₇₁	1	2	yes	complemented
234	#1574	C₂×C₇₁	1	1	yes	characteristic, complemented
235	#1546	C₂×C₇₁	1	1	yes	characteristic, complemented
236	#1543	C₂×C₇₁	1	1	yes	characteristic, complemented
237	C₇₁	#19558	1	1	yes	characteristic, direct product factor, Sylow
238	#532	C₂²×C₇₁	1	1	yes	characteristic
239	#532	C₂²×C₇₁	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
241	#498	C₂²×C₇₁	1	2	yes	—
242	#492	—	2	1	no	—
243	#487	—	2	1	no	—
244	#486	C₂²×C₇₁	1	2	yes	—
245	#481	—	2	2	no	—
246	#476	—	2	1	no	—
247	#476	—	2	1	no	—
248	#476	—	2	1	no	—
249	#476	C₂²×C₇₁	1	2	yes	—
250	#469	—	2	2	no	—
251	#461	C₂²×C₇₁	1	2	yes	—
252	#461	C₂²×C₇₁	1	2	yes	—
253	#459	—	2	1	no	—
254	#459	C₂²×C₇₁	1	2	yes	—
255	#448	—	2	2	no	—
256	#436	—	2	1	no	—
257	#436	C₂²×C₇₁	1	2	yes	—
258	C₈×D₄	—	2	1	no	—
259	C₈×D₄	C₂²×C₇₁	1	2	yes	—
260	#431	C₂²×C₇₁	1	1	yes	characteristic
261	#431	C₂²×C₇₁	1	1	yes	characteristic
262	#431	C₂²×C₇₁	1	1	yes	characteristic
263	#423	C₂²×C₇₁	1	1	yes	characteristic
264	#408	—	2	2	no	—
265	#335	C₂²×C₇₁	1	2	yes	—
266	#334	C₂²×C₇₁	1	2	yes	—
267	#333	C₂²×C₇₁	1	1	yes	characteristic
268	#333	C₂²×C₇₁	1	1	yes	characteristic
269	#332	C₂²×C₇₁	1	2	yes	—
270	#332	C₂²×C₇₁	1	2	yes	—
271	#331	C₂²×C₇₁	1	1	yes	characteristic
272	#331	C₂²×C₇₁	1	1	yes	characteristic
273	C₂×#41	—	2	1	no	—
274	C₂×#41	—	2	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₇₁	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
288	#127	D₄×C₇₁	1	1	yes	characteristic
289	#127	C₂³×C₇₁	1	1	yes	characteristic
290	#124	—	2	1	no	—
291	#124	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	#121	—	2	1	no	—
295	#121	D₄×C₇₁	1	2	yes	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	C₂³×C₇₁	1	2	yes	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
303	#106	—	2	2	no	—
304	#106	—	2	2	no	—
305	#106	—	2	2	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
308	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
311	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
314	#103	—	2	2	no	—
315	#103	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	D₄×C₇₁	1	2	yes	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	C₂³×C₇₁	1	2	yes	—
328	#41	—	8	1	no	—
329	#41	—	8	1	no	—
330	#41	—	8	2	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	—	8	1	no	—
336	C₂×Q₈	—	8	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
350	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
351	SD₁₆	—	8	2	no	—
352	SD₁₆	—	8	2	no	—
353	D₈	—	8	2	no	—
354	M₁₆	—	8	2	no	—
355	M₁₆	—	8	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	8	2	no	—
362	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
377	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
378	C₄²	#41×C₇₁	1	1	yes	characteristic
379	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	#121×C₇₁	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	8	1	no	—
386	Q₈	—	8	1	no	—
387	Q₈	—	8	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	8	1	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
412	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
413	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	1	no	—
440	C₄	#471×C₇₁	1	2	yes	—
441	C₄	#576×C₇₁	1	1	yes	characteristic
442	C₄	#577×C₇₁	1	1	yes	characteristic
443	C₄	#577×C₇₁	1	1	yes	characteristic
444	C₄	#577×C₇₁	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	8	2	no	—
447	C₂	—	16	1	no	—
448	C₂	C₇₁×#3042	1	1	yes	characteristic
449	C₂	C₇₁×#3062	1	1	yes	characteristic
450	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×#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×#3227	C₂	semidirect
3. C₇₁×#3206	C₂	semidirect
4. C₇₁×#2979	C₂	semidirect
5. C₇₁×#1701	C₂	semidirect
6. C₇₁×#1691	C₂	semidirect
7. C₇₁×#1681	C₂	semidirect
8. C₇₁×#1671	C₂	semidirect
9. C₇₁×#1574	C₂	semidirect
10. C₇₁×#1546	C₂	semidirect
11. C₇₁×#1543	C₂	semidirect
219. #19558	C₇₁	direct (N × H)
227. #3227	C₂×C₇₁	semidirect
228. #3206	C₂×C₇₁	semidirect
229. #2979	C₂×C₇₁	semidirect
230. #1701	C₂×C₇₁	semidirect
231. #1691	C₂×C₇₁	semidirect
232. #1681	C₂×C₇₁	semidirect
233. #1671	C₂×C₇₁	semidirect
234. #1574	C₂×C₇₁	semidirect
235. #1546	C₂×C₇₁	semidirect
236. #1543	C₂×C₇₁	semidirect
237. C₇₁	#19558	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×#3227	2
C₇₁×#3206	2
C₇₁×#2979	2
C₇₁×#1701	2
C₇₁×#1691	2
C₇₁×#1681	2
C₇₁×#1671	2
C₇₁×#1574	2
C₇₁×#1546	2
C₇₁×#1543	2
#19558	71

Subgroups — C71×#19558 #31840430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19558 #31840430