Subgroups — C₇₁×#19389 #31840261

Order 18176.

684 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1683	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1677	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1667	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1665	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1553	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×D₄×C₇₁	C₂²	1	1	yes	characteristic
15	#493×C₇₁	C₂²	1	1	yes	characteristic, complemented
16	#492×C₇₁	C₂²	1	1	yes	characteristic, complemented
17	#487×C₇₁	C₂²	1	1	yes	characteristic, complemented
18	#486×C₇₁	C₂²	1	1	yes	characteristic, complemented
19	#481×C₇₁	—	2	1	no	—
20	#480×C₇₁	—	2	1	no	—
21	#476×C₇₁	C₂²	1	2	yes	—
22	#474×C₇₁	C₂²	1	2	yes	—
23	#463×C₇₁	—	2	2	no	—
24	#459×C₇₁	C₂²	1	2	yes	—
25	#459×C₇₁	C₂²	1	2	yes	—
26	#449×C₇₁	—	2	2	no	—
27	#447×C₇₁	—	2	1	no	—
28	#447×C₇₁	—	2	1	no	—
29	#442×C₇₁	—	2	2	no	—
30	C₄×D₈×C₇₁	—	2	2	no	—
31	C₈×D₄×C₇₁	—	2	2	no	—
32	C₈×D₄×C₇₁	C₂²	1	2	yes	—
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	#431×C₇₁	C₂²	1	1	yes	characteristic
37	#431×C₇₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₇₁	—	2	2	no	—
39	#335×C₇₁	C₂²	1	2	yes	complemented
40	#334×C₇₁	C₂²	1	2	yes	complemented
41	#333×C₇₁	C₂²	1	2	yes	complemented
42	#332×C₇₁	C₂²	1	2	yes	complemented
43	#331×C₇₁	C₂²	1	2	yes	complemented
44	#331×C₇₁	C₂²	1	2	yes	complemented
45	C₂×#41×C₇₁	—	2	1	no	—
46	C₂×#41×C₇₁	—	2	1	no	—
47	C₂²×D₄×C₇₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₁	—	2	1	no	—
49	C₂×SD₁₆×C₇₁	—	2	2	no	—
50	C₂×D₈×C₇₁	—	2	2	no	—
51	C₂×D₈×C₇₁	—	2	2	no	—
52	C₂×D₈×C₇₁	—	2	2	no	—
53	C₂²×C₈×C₇₁	—	2	2	no	—
54	C₂²×C₈×C₇₁	—	2	2	no	—
55	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
57	#127×C₇₁	C₂³	1	1	yes	characteristic
58	#127×C₇₁	C₂³	1	1	yes	characteristic
59	#124×C₇₁	—	2	1	no	—
60	#124×C₇₁	—	2	1	no	—
61	#121×C₇₁	—	2	1	no	—
62	#121×C₇₁	—	2	1	no	—
63	#121×C₇₁	—	2	1	no	—
64	#121×C₇₁	—	2	1	no	—
65	C₄×D₄×C₇₁	—	2	1	no	—
66	C₄×D₄×C₇₁	—	2	1	no	—
67	C₄×D₄×C₇₁	—	2	1	no	—
68	C₄×D₄×C₇₁	—	2	1	no	—
69	C₄×D₄×C₇₁	—	2	1	no	—
70	C₄×D₄×C₇₁	—	2	1	no	—
71	C₄×D₄×C₇₁	D₄	1	2	yes	—
72	C₄×D₄×C₇₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×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	C₄⋊C₈×C₇₁	D₄	1	2	yes	—
79	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
81	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
82	#103×C₇₁	—	2	2	no	—
83	#102×C₇₁	—	2	2	no	—
84	#102×C₇₁	—	2	2	no	—
85	#102×C₇₁	—	2	2	no	—
86	#102×C₇₁	—	2	2	no	—
87	#102×C₇₁	—	2	2	no	—
88	C₂²⋊C₈×C₇₁	—	2	1	no	—
89	C₂²⋊C₈×C₇₁	—	2	1	no	—
90	C₂²⋊C₈×C₇₁	—	2	1	no	—
91	C₂²⋊C₈×C₇₁	—	2	2	no	—
92	C₂²⋊C₈×C₇₁	—	2	2	no	—
93	C₂²⋊C₈×C₇₁	D₄	1	2	yes	—
94	#97×C₇₁	—	2	1	no	—
95	C₄×C₈×C₇₁	—	2	1	no	—
96	C₄×C₈×C₇₁	—	2	1	no	—
97	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
99	C₂⁴×C₇₁	—	2	1	no	—
100	#41×C₇₁	—	8	2	no	—
101	#41×C₇₁	—	8	2	no	—
102	C₂×Q₈×C₇₁	—	2	1	no	—
103	C₂×Q₈×C₇₁	—	2	1	no	—
104	C₂×D₄×C₇₁	—	2	4	no	—
105	C₂×D₄×C₇₁	—	2	1	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	—	2	1	no	—
112	C₂×D₄×C₇₁	—	4	1	no	—
113	C₂×D₄×C₇₁	—	4	1	no	—
114	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇₁	—	2	1	no	—
116	C₂²×C₄×C₇₁	—	2	2	no	—
117	C₂²×C₄×C₇₁	—	2	2	no	—
118	C₂²×C₄×C₇₁	—	4	1	no	—
119	C₂²×C₄×C₇₁	—	4	1	no	—
120	C₂²×C₄×C₇₁	—	8	2	no	—
121	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
124	SD₁₆×C₇₁	—	8	2	no	—
125	D₈×C₇₁	—	4	4	no	—
126	D₈×C₇₁	—	4	4	no	—
127	D₈×C₇₁	—	8	2	no	—
128	C₂×C₈×C₇₁	—	2	2	no	—
129	C₂×C₈×C₇₁	—	2	2	no	—
130	C₂×C₈×C₇₁	—	2	2	no	—
131	C₂×C₈×C₇₁	—	8	2	no	—
132	C₂×C₈×C₇₁	—	8	2	no	—
133	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₇₁	—	2	1	no	—
136	C₄⋊C₄×C₇₁	—	2	1	no	—
137	C₄⋊C₄×C₇₁	—	2	1	no	—
138	C₄⋊C₄×C₇₁	—	2	1	no	—
139	C₄⋊C₄×C₇₁	—	2	1	no	—
140	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₇₁	—	2	2	no	—
142	C₂²⋊C₄×C₇₁	—	2	2	no	—
143	C₂²⋊C₄×C₇₁	—	4	1	no	—
144	C₂²⋊C₄×C₇₁	—	4	1	no	—
145	C₂²⋊C₄×C₇₁	—	4	1	no	—
146	C₂²⋊C₄×C₇₁	—	4	1	no	—
147	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇₁	#41	1	1	yes	characteristic
150	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
151	C₂³×C₇₁	—	2	4	no	—
152	C₂³×C₇₁	—	2	2	no	—
153	C₂³×C₇₁	—	4	1	no	—
154	C₂³×C₇₁	—	4	1	no	—
155	C₂³×C₇₁	—	8	1	no	—
156	C₂³×C₇₁	—	8	1	no	—
157	C₂³×C₇₁	#121	1	1	yes	characteristic
158	Q₈×C₇₁	—	4	2	no	—
159	Q₈×C₇₁	—	8	1	no	—
160	D₄×C₇₁	—	2	4	no	—
161	D₄×C₇₁	—	2	2	no	—
162	D₄×C₇₁	—	4	2	no	—
163	D₄×C₇₁	—	4	2	no	—
164	D₄×C₇₁	—	4	2	no	—
165	D₄×C₇₁	—	4	2	no	—
166	D₄×C₇₁	—	8	1	no	—
167	D₄×C₇₁	—	8	1	no	—
168	D₄×C₇₁	—	8	2	no	—
169	D₄×C₇₁	—	8	2	no	—
170	D₄×C₇₁	#135	1	4	yes	—
171	C₂×C₄×C₇₁	—	2	2	no	—
172	C₂×C₄×C₇₁	—	2	2	no	—
173	C₂×C₄×C₇₁	—	2	2	no	—
174	C₂×C₄×C₇₁	—	4	1	no	—
175	C₂×C₄×C₇₁	—	4	2	no	—
176	C₂×C₄×C₇₁	—	4	2	no	—
177	C₂×C₄×C₇₁	—	4	1	no	—
178	C₂×C₄×C₇₁	—	4	1	no	—
179	C₂×C₄×C₇₁	—	8	2	no	—
180	C₂×C₄×C₇₁	—	8	2	no	—
181	C₂×C₄×C₇₁	—	8	2	no	—
182	C₂×C₄×C₇₁	—	8	1	no	—
183	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
184	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₇₁	—	2	2	no	—
190	C₈×C₇₁	—	2	2	no	—
191	C₈×C₇₁	—	4	2	no	—
192	C₈×C₇₁	—	4	2	no	—
193	C₈×C₇₁	—	4	2	no	—
194	C₂²×C₇₁	—	2	1	no	—
195	C₂²×C₇₁	—	2	1	no	—
196	C₂²×C₇₁	—	2	4	no	—
197	C₂²×C₇₁	—	2	1	no	—
198	C₂²×C₇₁	—	4	2	no	—
199	C₂²×C₇₁	—	4	2	no	—
200	C₂²×C₇₁	—	8	4	no	—
201	C₂²×C₇₁	—	8	1	no	—
202	C₂²×C₇₁	—	8	1	no	—
203	C₂²×C₇₁	—	8	1	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	—	2	1	no	—
212	C₄×C₇₁	—	4	2	no	—
213	C₄×C₇₁	—	8	1	no	—
214	C₄×C₇₁	—	8	1	no	—
215	C₄×C₇₁	C₂×#135	1	2	yes	—
216	C₄×C₇₁	#576	1	2	yes	—
217	#19389	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂×C₇₁	—	4	1	no	—
219	C₂×C₇₁	—	4	4	no	—
220	C₂×C₇₁	—	16	1	no	—
221	C₂×C₇₁	—	16	1	no	—
222	C₂×C₇₁	#3041	1	1	yes	characteristic
223	C₂×C₇₁	#3050	1	1	yes	characteristic
224	C₂×C₇₁	#3068	1	1	yes	characteristic
225	#3207	C₂×C₇₁	1	1	yes	characteristic, complemented
226	#3109	C₂×C₇₁	1	1	yes	characteristic, complemented
227	#3100	C₂×C₇₁	1	1	yes	characteristic, complemented
228	#2972	C₂×C₇₁	1	1	yes	characteristic, complemented
229	#1683	C₂×C₇₁	1	2	yes	complemented
230	#1677	C₂×C₇₁	1	2	yes	complemented
231	#1667	C₂×C₇₁	1	2	yes	complemented
232	#1665	C₂×C₇₁	1	2	yes	complemented
233	#1572	C₂×C₇₁	1	1	yes	characteristic, complemented
234	#1553	C₂×C₇₁	1	1	yes	characteristic, complemented
235	#1543	C₂×C₇₁	1	1	yes	characteristic, complemented
236	C₇₁	#19389	1	1	yes	characteristic, direct product factor, Sylow
237	#532	C₂²×C₇₁	1	1	yes	characteristic
238	#532	C₂²×C₇₁	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
240	#493	C₂²×C₇₁	1	1	yes	characteristic, complemented
241	#492	C₂²×C₇₁	1	1	yes	characteristic, complemented
242	#487	C₂²×C₇₁	1	1	yes	characteristic, complemented
243	#486	C₂²×C₇₁	1	1	yes	characteristic, complemented
244	#481	—	2	1	no	—
245	#480	—	2	1	no	—
246	#476	C₂²×C₇₁	1	2	yes	—
247	#474	C₂²×C₇₁	1	2	yes	—
248	#463	—	2	2	no	—
249	#459	C₂²×C₇₁	1	2	yes	—
250	#459	C₂²×C₇₁	1	2	yes	—
251	#449	—	2	2	no	—
252	#447	—	2	1	no	—
253	#447	—	2	1	no	—
254	#442	—	2	2	no	—
255	C₄×D₈	—	2	2	no	—
256	C₈×D₄	—	2	2	no	—
257	C₈×D₄	C₂²×C₇₁	1	2	yes	—
258	C₈×D₄	C₂²×C₇₁	1	2	yes	—
259	#432	C₂²×C₇₁	1	1	yes	characteristic
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	C₂×C₂²⋊C₈	—	2	2	no	—
264	#335	C₂²×C₇₁	1	2	yes	complemented
265	#334	C₂²×C₇₁	1	2	yes	complemented
266	#333	C₂²×C₇₁	1	2	yes	complemented
267	#332	C₂²×C₇₁	1	2	yes	complemented
268	#331	C₂²×C₇₁	1	2	yes	complemented
269	#331	C₂²×C₇₁	1	2	yes	complemented
270	C₂×#41	—	2	1	no	—
271	C₂×#41	—	2	1	no	—
272	C₂²×D₄	D₄×C₇₁	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
282	#127	C₂³×C₇₁	1	1	yes	characteristic
283	#127	C₂³×C₇₁	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#124	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	—	2	1	no	—
289	#121	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	D₄×C₇₁	1	2	yes	—
297	C₄×D₄	C₂³×C₇₁	1	2	yes	—
298	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
301	#107	—	2	2	no	—
302	#106	—	2	2	no	—
303	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
304	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
305	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
306	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
307	#103	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	D₄×C₇₁	1	2	yes	—
319	#97	—	2	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
324	C₂⁴	—	2	1	no	—
325	#41	—	8	2	no	—
326	#41	—	8	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
348	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
349	SD₁₆	—	8	2	no	—
350	D₈	—	4	4	no	—
351	D₈	—	4	4	no	—
352	D₈	—	8	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	8	2	no	—
357	C₂×C₈	—	8	2	no	—
358	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
374	C₄²	#41×C₇₁	1	1	yes	characteristic
375	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
376	C₂³	—	2	4	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	8	1	no	—
381	C₂³	—	8	1	no	—
382	C₂³	#121×C₇₁	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	8	1	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	1	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	#135×C₇₁	1	4	yes	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
409	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
410	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	C₂×#135×C₇₁	1	2	yes	—
441	C₄	#576×C₇₁	1	2	yes	—
442	C₂	—	4	1	no	—
443	C₂	—	4	4	no	—
444	C₂	—	16	1	no	—
445	C₂	—	16	1	no	—
446	C₂	C₇₁×#3041	1	1	yes	characteristic
447	C₂	C₇₁×#3050	1	1	yes	characteristic
448	C₂	C₇₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₁
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×#3207	C₂	semidirect
2. C₇₁×#3109	C₂	semidirect
3. C₇₁×#3100	C₂	semidirect
4. C₇₁×#2972	C₂	semidirect
5. C₇₁×#1683	C₂	semidirect
6. C₇₁×#1677	C₂	semidirect
7. C₇₁×#1667	C₂	semidirect
8. C₇₁×#1665	C₂	semidirect
9. C₇₁×#1572	C₂	semidirect
10. C₇₁×#1553	C₂	semidirect
11. C₇₁×#1543	C₂	semidirect
15. #493×C₇₁	C₂²	semidirect
16. #492×C₇₁	C₂²	semidirect
17. #487×C₇₁	C₂²	semidirect
18. #486×C₇₁	C₂²	semidirect
39. #335×C₇₁	C₂²	semidirect
40. #334×C₇₁	C₂²	semidirect
41. #333×C₇₁	C₂²	semidirect
42. #332×C₇₁	C₂²	semidirect
43. #331×C₇₁	C₂²	semidirect
44. #331×C₇₁	C₂²	semidirect
217. #19389	C₇₁	direct (N × H)
225. #3207	C₂×C₇₁	semidirect
226. #3109	C₂×C₇₁	semidirect
227. #3100	C₂×C₇₁	semidirect
228. #2972	C₂×C₇₁	semidirect
229. #1683	C₂×C₇₁	semidirect
230. #1677	C₂×C₇₁	semidirect
231. #1667	C₂×C₇₁	semidirect
232. #1665	C₂×C₇₁	semidirect
233. #1572	C₂×C₇₁	semidirect
234. #1553	C₂×C₇₁	semidirect
235. #1543	C₂×C₇₁	semidirect
236. C₇₁	#19389	direct (N × H)
240. #493	C₂²×C₇₁	semidirect
241. #492	C₂²×C₇₁	semidirect
242. #487	C₂²×C₇₁	semidirect
243. #486	C₂²×C₇₁	semidirect
264. #335	C₂²×C₇₁	semidirect
265. #334	C₂²×C₇₁	semidirect
266. #333	C₂²×C₇₁	semidirect
267. #332	C₂²×C₇₁	semidirect
268. #331	C₂²×C₇₁	semidirect
269. #331	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×#3207	2
C₇₁×#3109	2
C₇₁×#3100	2
C₇₁×#2972	2
C₇₁×#1683	2
C₇₁×#1677	2
C₇₁×#1667	2
C₇₁×#1665	2
C₇₁×#1572	2
C₇₁×#1553	2
C₇₁×#1543	2
#19389	71

Subgroups — C71×#19389 #31840261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19389 #31840261