Subgroups — C₇₁×#19522 #31840394

Order 18176.

646 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3205	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1702	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1688	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1682	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1668	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1555	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1553	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×#127×C₇₁	C₂²	1	1	yes	characteristic
15	#497×C₇₁	—	2	1	no	—
16	#493×C₇₁	C₂²	1	1	yes	characteristic
17	#493×C₇₁	C₂²	1	1	yes	characteristic
18	#492×C₇₁	—	2	1	no	—
19	#489×C₇₁	—	2	1	no	—
20	#486×C₇₁	—	2	1	no	—
21	#486×C₇₁	C₂²	1	1	yes	characteristic
22	#486×C₇₁	C₂²	1	1	yes	characteristic
23	#462×C₇₁	C₂²	1	2	yes	complemented
24	#460×C₇₁	C₂²	1	2	yes	—
25	#460×C₇₁	C₂²	1	2	yes	—
26	#460×C₇₁	C₂²	1	2	yes	complemented
27	#459×C₇₁	—	2	2	no	—
28	#452×C₇₁	—	2	2	no	—
29	#450×C₇₁	—	2	2	no	—
30	#447×C₇₁	—	2	2	no	—
31	#446×C₇₁	—	2	2	no	—
32	#446×C₇₁	C₂²	1	2	yes	complemented
33	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
34	#433×C₇₁	—	2	2	no	—
35	#432×C₇₁	C₂²	1	1	yes	characteristic
36	#432×C₇₁	C₂²	1	1	yes	characteristic
37	#431×C₇₁	C₂²	1	1	yes	characteristic
38	#431×C₇₁	C₂²	1	1	yes	characteristic
39	#335×C₇₁	C₂²	1	2	yes	complemented
40	#334×C₇₁	C₂²	1	2	yes	complemented
41	#332×C₇₁	C₂²	1	2	yes	complemented
42	#331×C₇₁	C₂²	1	2	yes	—
43	#331×C₇₁	C₂²	1	2	yes	—
44	#331×C₇₁	C₂²	1	2	yes	complemented
45	C₂×#41×C₇₁	—	2	1	no	—
46	C₂²×D₄×C₇₁	—	2	1	no	—
47	C₂²×D₄×C₇₁	—	2	1	no	—
48	C₂²×D₄×C₇₁	—	2	1	no	—
49	C₂×Q₁₆×C₇₁	—	2	2	no	—
50	C₂×SD₁₆×C₇₁	—	2	2	no	—
51	C₂×SD₁₆×C₇₁	—	2	2	no	—
52	C₂×SD₁₆×C₇₁	—	2	2	no	—
53	C₂×D₈×C₇₁	—	2	2	no	—
54	C₂×D₈×C₇₁	—	2	2	no	—
55	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
58	#127×C₇₁	—	2	1	no	—
59	#127×C₇₁	—	2	1	no	—
60	#127×C₇₁	—	2	1	no	—
61	#127×C₇₁	C₂³	1	1	yes	characteristic
62	#127×C₇₁	C₂³	1	1	yes	characteristic
63	#127×C₇₁	C₂³	1	1	yes	characteristic
64	#125×C₇₁	—	2	1	no	—
65	#124×C₇₁	—	2	1	no	—
66	C₂²⋊Q₈×C₇₁	—	2	1	no	—
67	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
68	#121×C₇₁	—	2	1	no	—
69	#121×C₇₁	—	2	1	no	—
70	C₄×Q₈×C₇₁	—	2	1	no	—
71	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
72	C₄×D₄×C₇₁	—	2	1	no	—
73	C₄×D₄×C₇₁	—	2	1	no	—
74	#117×C₇₁	—	2	1	no	—
75	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₇₁	—	2	2	no	—
77	C₄⋊C₈×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	D₄	1	2	yes	—
92	#97×C₇₁	—	2	2	no	—
93	#97×C₇₁	—	2	1	no	—
94	#97×C₇₁	—	2	1	no	—
95	C₄×C₈×C₇₁	—	2	2	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	—	4	1	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	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₇₁	—	2	1	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	—	2	1	no	—
113	C₂×D₄×C₇₁	—	4	1	no	—
114	C₂×D₄×C₇₁	—	4	1	no	—
115	C₂×D₄×C₇₁	—	4	1	no	—
116	C₂×D₄×C₇₁	—	4	1	no	—
117	C₂×D₄×C₇₁	—	8	2	no	—
118	C₂×D₄×C₇₁	—	8	2	no	—
119	C₂×D₄×C₇₁	—	8	2	no	—
120	C₂²×C₄×C₇₁	—	4	1	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	Q₁₆×C₇₁	—	8	2	no	—
125	SD₁₆×C₇₁	—	8	2	no	—
126	SD₁₆×C₇₁	—	8	2	no	—
127	SD₁₆×C₇₁	—	8	2	no	—
128	D₈×C₇₁	—	8	2	no	—
129	D₈×C₇₁	—	8	2	no	—
130	C₂×C₈×C₇₁	—	2	2	no	—
131	C₂×C₈×C₇₁	—	2	2	no	—
132	C₂×C₈×C₇₁	—	2	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	2	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	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₇₁	—	2	2	no	—
144	C₂²⋊C₄×C₇₁	—	4	1	no	—
145	C₂²⋊C₄×C₇₁	—	4	1	no	—
146	C₄²×C₇₁	—	2	2	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	—	4	1	no	—
152	C₂³×C₇₁	—	4	1	no	—
153	C₂³×C₇₁	—	4	1	no	—
154	C₂³×C₇₁	—	8	2	no	—
155	C₂³×C₇₁	—	8	2	no	—
156	C₂³×C₇₁	—	8	2	no	—
157	C₂³×C₇₁	#121	1	1	yes	characteristic
158	Q₈×C₇₁	—	2	2	no	—
159	Q₈×C₇₁	—	2	2	no	—
160	Q₈×C₇₁	—	4	2	no	—
161	Q₈×C₇₁	—	8	1	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	—	4	2	no	—
167	D₄×C₇₁	—	4	2	no	—
168	D₄×C₇₁	—	8	1	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	D₄×C₇₁	—	8	2	no	—
174	D₄×C₇₁	—	8	2	no	—
175	C₂×C₄×C₇₁	—	2	2	no	—
176	C₂×C₄×C₇₁	—	2	2	no	—
177	C₂×C₄×C₇₁	—	2	2	no	—
178	C₂×C₄×C₇₁	—	2	2	no	—
179	C₂×C₄×C₇₁	—	4	1	no	—
180	C₂×C₄×C₇₁	—	4	1	no	—
181	C₂×C₄×C₇₁	—	8	2	no	—
182	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
183	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
184	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
188	C₈×C₇₁	—	2	2	no	—
189	C₈×C₇₁	—	2	2	no	—
190	C₈×C₇₁	—	4	2	no	—
191	C₈×C₇₁	—	4	2	no	—
192	C₈×C₇₁	—	4	2	no	—
193	C₂²×C₇₁	—	2	1	no	—
194	C₂²×C₇₁	—	2	1	no	—
195	C₂²×C₇₁	—	2	1	no	—
196	C₂²×C₇₁	—	8	1	no	—
197	C₂²×C₇₁	—	8	1	no	—
198	C₂²×C₇₁	—	8	1	no	—
199	C₂²×C₇₁	—	8	1	no	—
200	C₂²×C₇₁	—	8	1	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	—	16	4	no	—
206	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
207	C₄×C₇₁	—	2	1	no	—
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	—	4	2	no	—
213	C₄×C₇₁	—	8	1	no	—
214	C₄×C₇₁	#576	1	2	yes	—
215	C₄×C₇₁	#577	1	2	yes	—
216	#19522	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂×C₇₁	—	4	1	no	—
218	C₂×C₇₁	—	16	1	no	—
219	C₂×C₇₁	—	16	1	no	—
220	C₂×C₇₁	—	16	1	no	—
221	C₂×C₇₁	#3043	1	1	yes	characteristic
222	C₂×C₇₁	#3058	1	1	yes	characteristic
223	C₂×C₇₁	#3068	1	1	yes	characteristic
224	#3216	C₂×C₇₁	1	1	yes	characteristic, complemented
225	#3208	C₂×C₇₁	1	1	yes	characteristic, complemented
226	#3205	C₂×C₇₁	1	1	yes	characteristic
227	#2985	C₂×C₇₁	1	1	yes	characteristic, complemented
228	#1702	C₂×C₇₁	1	2	yes	complemented
229	#1688	C₂×C₇₁	1	2	yes	complemented
230	#1682	C₂×C₇₁	1	2	yes	complemented
231	#1668	C₂×C₇₁	1	2	yes	complemented
232	#1572	C₂×C₇₁	1	1	yes	characteristic, complemented
233	#1555	C₂×C₇₁	1	1	yes	characteristic, complemented
234	#1553	C₂×C₇₁	1	1	yes	characteristic, complemented
235	C₇₁	#19522	1	1	yes	characteristic, direct product factor, Sylow
236	#533	C₂²×C₇₁	1	1	yes	characteristic
237	#532	C₂²×C₇₁	1	1	yes	characteristic
238	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
239	#497	—	2	1	no	—
240	#493	C₂²×C₇₁	1	1	yes	characteristic
241	#493	C₂²×C₇₁	1	1	yes	characteristic
242	#492	—	2	1	no	—
243	#489	—	2	1	no	—
244	#486	—	2	1	no	—
245	#486	C₂²×C₇₁	1	1	yes	characteristic
246	#486	C₂²×C₇₁	1	1	yes	characteristic
247	#462	C₂²×C₇₁	1	2	yes	complemented
248	#460	C₂²×C₇₁	1	2	yes	—
249	#460	C₂²×C₇₁	1	2	yes	—
250	#460	C₂²×C₇₁	1	2	yes	complemented
251	#459	—	2	2	no	—
252	#452	—	2	2	no	—
253	#450	—	2	2	no	—
254	#447	—	2	2	no	—
255	#446	—	2	2	no	—
256	#446	C₂²×C₇₁	1	2	yes	complemented
257	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
258	#433	—	2	2	no	—
259	#432	C₂²×C₇₁	1	1	yes	characteristic
260	#432	C₂²×C₇₁	1	1	yes	characteristic
261	#431	C₂²×C₇₁	1	1	yes	characteristic
262	#431	C₂²×C₇₁	1	1	yes	characteristic
263	#335	C₂²×C₇₁	1	2	yes	complemented
264	#334	C₂²×C₇₁	1	2	yes	complemented
265	#332	C₂²×C₇₁	1	2	yes	complemented
266	#331	C₂²×C₇₁	1	2	yes	—
267	#331	C₂²×C₇₁	1	2	yes	—
268	#331	C₂²×C₇₁	1	2	yes	complemented
269	C₂×#41	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
280	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	C₂³×C₇₁	1	1	yes	characteristic
286	#127	C₂³×C₇₁	1	1	yes	characteristic
287	#127	C₂³×C₇₁	1	1	yes	characteristic
288	#125	—	2	1	no	—
289	#124	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	#117	—	2	1	no	—
299	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
303	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
304	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
305	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
306	#103	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	D₄×C₇₁	1	2	yes	—
316	#97	—	2	2	no	—
317	#97	—	2	1	no	—
318	#97	—	2	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
323	C₂⁴	—	4	1	no	—
324	#41	—	8	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	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	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	8	2	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
347	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
348	Q₁₆	—	8	2	no	—
349	SD₁₆	—	8	2	no	—
350	SD₁₆	—	8	2	no	—
351	SD₁₆	—	8	2	no	—
352	D₈	—	8	2	no	—
353	D₈	—	8	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
358	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
373	C₄²	#41×C₇₁	1	1	yes	characteristic
374	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	#121×C₇₁	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	8	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
407	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
408	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	16	4	no	—
430	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	1	no	—
438	C₄	#576×C₇₁	1	2	yes	—
439	C₄	#577×C₇₁	1	2	yes	—
440	C₂	—	4	1	no	—
441	C₂	—	16	1	no	—
442	C₂	—	16	1	no	—
443	C₂	—	16	1	no	—
444	C₂	C₇₁×#3043	1	1	yes	characteristic
445	C₂	C₇₁×#3058	1	1	yes	characteristic
446	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×#3205	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
1. C₇₁×#3216	C₂	semidirect
2. C₇₁×#3208	C₂	semidirect
4. C₇₁×#2985	C₂	semidirect
5. C₇₁×#1702	C₂	semidirect
6. C₇₁×#1688	C₂	semidirect
7. C₇₁×#1682	C₂	semidirect
8. C₇₁×#1668	C₂	semidirect
9. C₇₁×#1572	C₂	semidirect
10. C₇₁×#1555	C₂	semidirect
11. C₇₁×#1553	C₂	semidirect
23. #462×C₇₁	C₂²	semidirect
26. #460×C₇₁	C₂²	semidirect
32. #446×C₇₁	C₂²	semidirect
33. C₈×Q₈×C₇₁	C₂²	semidirect
39. #335×C₇₁	C₂²	semidirect
40. #334×C₇₁	C₂²	semidirect
41. #332×C₇₁	C₂²	semidirect
44. #331×C₇₁	C₂²	semidirect
216. #19522	C₇₁	direct (N × H)
224. #3216	C₂×C₇₁	semidirect
225. #3208	C₂×C₇₁	semidirect
227. #2985	C₂×C₇₁	semidirect
228. #1702	C₂×C₇₁	semidirect
229. #1688	C₂×C₇₁	semidirect
230. #1682	C₂×C₇₁	semidirect
231. #1668	C₂×C₇₁	semidirect
232. #1572	C₂×C₇₁	semidirect
233. #1555	C₂×C₇₁	semidirect
234. #1553	C₂×C₇₁	semidirect
235. C₇₁	#19522	direct (N × H)
247. #462	C₂²×C₇₁	semidirect
250. #460	C₂²×C₇₁	semidirect
256. #446	C₂²×C₇₁	semidirect
257. C₈×Q₈	C₂²×C₇₁	semidirect
263. #335	C₂²×C₇₁	semidirect
264. #334	C₂²×C₇₁	semidirect
265. #332	C₂²×C₇₁	semidirect
268. #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×#3216	2
C₇₁×#3208	2
C₇₁×#3205	2
C₇₁×#2985	2
C₇₁×#1702	2
C₇₁×#1688	2
C₇₁×#1682	2
C₇₁×#1668	2
C₇₁×#1572	2
C₇₁×#1555	2
C₇₁×#1553	2
#19522	71

Subgroups — C71×#19522 #31840394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19522 #31840394