Subgroups — C₇₁×#19564 #31840436

Order 18176.

626 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₁×#3208	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#3208	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1702	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1686	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1682	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1666	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1545	C₂	1	1	yes	maximal, characteristic
11	C₇₁×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₇₁	C₂²	1	1	yes	characteristic
13	#533×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₇₁	C₂²	1	1	yes	characteristic
15	#492×C₇₁	—	2	1	no	—
16	#492×C₇₁	C₂²	1	2	yes	—
17	#486×C₇₁	—	2	1	no	—
18	#486×C₇₁	C₂²	1	2	yes	—
19	#475×C₇₁	—	2	1	no	—
20	#475×C₇₁	C₂²	1	2	yes	complemented
21	#470×C₇₁	—	2	2	no	—
22	#462×C₇₁	—	2	1	no	—
23	#462×C₇₁	C₂²	1	2	yes	complemented
24	#460×C₇₁	—	2	1	no	—
25	#460×C₇₁	—	2	1	no	—
26	#460×C₇₁	C₂²	1	2	yes	—
27	#460×C₇₁	C₂²	1	2	yes	—
28	#450×C₇₁	—	2	2	no	—
29	#450×C₇₁	—	2	2	no	—
30	#446×C₇₁	—	2	1	no	—
31	#446×C₇₁	C₂²	1	2	yes	complemented
32	C₈×Q₈×C₇₁	—	2	1	no	—
33	C₈×Q₈×C₇₁	C₂²	1	2	yes	complemented
34	#433×C₇₁	—	2	2	no	—
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	#423×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	1	yes	characteristic, complemented
42	#332×C₇₁	C₂²	1	1	yes	characteristic, complemented
43	#332×C₇₁	C₂²	1	1	yes	characteristic, complemented
44	#332×C₇₁	C₂²	1	1	yes	characteristic, complemented
45	#331×C₇₁	C₂²	1	2	yes	—
46	#331×C₇₁	C₂²	1	2	yes	—
47	C₂²×D₄×C₇₁	—	2	1	no	—
48	C₂²×D₄×C₇₁	—	2	1	no	—
49	C₂²×D₄×C₇₁	—	2	1	no	—
50	C₂×Q₁₆×C₇₁	—	2	2	no	—
51	C₂×SD₁₆×C₇₁	—	2	2	no	—
52	C₂×SD₁₆×C₇₁	—	2	2	no	—
53	C₂×SD₁₆×C₇₁	—	2	2	no	—
54	C₂×SD₁₆×C₇₁	—	2	2	no	—
55	C₂×M₁₆×C₇₁	—	2	1	no	—
56	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₇₁	C₂³	1	1	yes	characteristic
60	#127×C₇₁	—	2	1	no	—
61	#127×C₇₁	—	2	1	no	—
62	#127×C₇₁	—	2	1	no	—
63	#127×C₇₁	C₂³	1	2	yes	—
64	#125×C₇₁	—	2	1	no	—
65	#125×C₇₁	—	2	1	no	—
66	C₂²⋊Q₈×C₇₁	—	2	1	no	—
67	C₂²⋊Q₈×C₇₁	—	2	1	no	—
68	C₂²⋊Q₈×C₇₁	—	2	1	no	—
69	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
70	C₄×Q₈×C₇₁	—	2	1	no	—
71	C₄×Q₈×C₇₁	—	2	1	no	—
72	C₄×Q₈×C₇₁	—	2	1	no	—
73	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
74	#117×C₇₁	—	2	1	no	—
75	#117×C₇₁	—	2	1	no	—
76	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
77	#106×C₇₁	—	2	2	no	—
78	C₄⋊C₈×C₇₁	—	2	2	no	—
79	C₄⋊C₈×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	D₄	1	2	yes	—
97	#97×C₇₁	—	2	2	no	—
98	C₄×C₈×C₇₁	—	2	2	no	—
99	C₄×C₈×C₇₁	—	2	1	no	—
100	C₄×C₈×C₇₁	—	2	1	no	—
101	C₄×C₈×C₇₁	C₂³	1	2	yes	—
102	C₂⁴×C₇₁	—	4	1	no	—
103	C₂×Q₈×C₇₁	—	2	1	no	—
104	C₂×Q₈×C₇₁	—	2	1	no	—
105	C₂×Q₈×C₇₁	—	2	1	no	—
106	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₇₁	—	2	2	no	—
108	C₂×D₄×C₇₁	—	2	2	no	—
109	C₂×D₄×C₇₁	—	2	2	no	—
110	C₂×D₄×C₇₁	—	4	1	no	—
111	C₂×D₄×C₇₁	—	4	1	no	—
112	C₂×D₄×C₇₁	—	4	1	no	—
113	C₂×D₄×C₇₁	—	8	1	no	—
114	C₂×D₄×C₇₁	—	8	1	no	—
115	C₂×D₄×C₇₁	—	8	1	no	—
116	C₂×D₄×C₇₁	—	8	1	no	—
117	C₂×D₄×C₇₁	—	8	2	no	—
118	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
121	Q₁₆×C₇₁	—	8	2	no	—
122	SD₁₆×C₇₁	—	8	2	no	—
123	SD₁₆×C₇₁	—	8	2	no	—
124	SD₁₆×C₇₁	—	8	2	no	—
125	SD₁₆×C₇₁	—	8	2	no	—
126	M₁₆×C₇₁	—	8	1	no	—
127	C₂×C₈×C₇₁	—	2	1	no	—
128	C₂×C₈×C₇₁	—	2	1	no	—
129	C₂×C₈×C₇₁	—	2	1	no	—
130	C₂×C₈×C₇₁	—	2	1	no	—
131	C₂×C₈×C₇₁	—	2	2	no	—
132	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
138	C₄⋊C₄×C₇₁	—	2	2	no	—
139	C₄⋊C₄×C₇₁	—	2	1	no	—
140	C₄⋊C₄×C₇₁	—	2	1	no	—
141	C₄⋊C₄×C₇₁	—	2	1	no	—
142	C₄⋊C₄×C₇₁	—	2	1	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	—	4	1	no	—
148	C₄²×C₇₁	—	2	2	no	—
149	C₄²×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	—	4	2	no	—
155	C₂³×C₇₁	—	8	2	no	—
156	C₂³×C₇₁	—	8	2	no	—
157	C₂³×C₇₁	—	8	2	no	—
158	C₂³×C₇₁	#121	1	1	yes	characteristic
159	Q₈×C₇₁	—	2	2	no	—
160	Q₈×C₇₁	—	2	2	no	—
161	Q₈×C₇₁	—	4	2	no	—
162	Q₈×C₇₁	—	4	1	no	—
163	Q₈×C₇₁	—	4	1	no	—
164	Q₈×C₇₁	—	4	1	no	—
165	Q₈×C₇₁	—	4	1	no	—
166	D₄×C₇₁	—	4	2	no	—
167	D₄×C₇₁	—	4	2	no	—
168	D₄×C₇₁	—	4	2	no	—
169	D₄×C₇₁	—	4	2	no	—
170	D₄×C₇₁	—	8	2	no	—
171	D₄×C₇₁	—	8	2	no	—
172	D₄×C₇₁	—	8	2	no	—
173	D₄×C₇₁	—	8	2	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	1	no	—
178	C₂×C₄×C₇₁	—	2	2	no	—
179	C₂×C₄×C₇₁	—	2	2	no	—
180	C₂×C₄×C₇₁	—	2	2	no	—
181	C₂×C₄×C₇₁	—	4	1	no	—
182	C₂×C₄×C₇₁	—	4	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	1	no	—
193	C₈×C₇₁	—	4	1	no	—
194	C₈×C₇₁	—	4	1	no	—
195	C₈×C₇₁	—	4	1	no	—
196	C₂²×C₇₁	—	2	1	no	—
197	C₂²×C₇₁	—	2	1	no	—
198	C₂²×C₇₁	—	2	1	no	—
199	C₂²×C₇₁	—	8	2	no	—
200	C₂²×C₇₁	—	8	2	no	—
201	C₂²×C₇₁	—	8	2	no	—
202	C₂²×C₇₁	—	16	4	no	—
203	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
204	C₄×C₇₁	—	2	1	no	—
205	C₄×C₇₁	—	2	1	no	—
206	C₄×C₇₁	—	2	1	no	—
207	C₄×C₇₁	—	4	2	no	—
208	C₄×C₇₁	—	4	2	no	—
209	C₄×C₇₁	—	8	1	no	—
210	C₄×C₇₁	—	8	1	no	—
211	C₄×C₇₁	#471	1	2	yes	—
212	C₄×C₇₁	#576	1	1	yes	characteristic
213	C₄×C₇₁	#577	1	1	yes	characteristic
214	C₄×C₇₁	#577	1	1	yes	characteristic
215	C₄×C₇₁	#577	1	1	yes	characteristic
216	#19564	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂×C₇₁	—	4	1	no	—
218	C₂×C₇₁	—	16	2	no	—
219	C₂×C₇₁	#3043	1	1	yes	characteristic
220	C₂×C₇₁	#3062	1	1	yes	characteristic
221	C₂×C₇₁	C₂×#471	1	1	yes	characteristic
222	#3255	C₂×C₇₁	1	1	yes	characteristic, complemented
223	#3208	C₂×C₇₁	1	1	yes	characteristic
224	#3208	C₂×C₇₁	1	1	yes	characteristic
225	#2986	C₂×C₇₁	1	1	yes	characteristic, complemented
226	#1702	C₂×C₇₁	1	2	yes	complemented
227	#1686	C₂×C₇₁	1	2	yes	complemented
228	#1682	C₂×C₇₁	1	2	yes	complemented
229	#1666	C₂×C₇₁	1	2	yes	complemented
230	#1574	C₂×C₇₁	1	1	yes	characteristic, complemented
231	#1545	C₂×C₇₁	1	1	yes	characteristic
232	#1544	C₂×C₇₁	1	1	yes	characteristic, complemented
233	C₇₁	#19564	1	1	yes	characteristic, direct product factor, Sylow
234	#533	C₂²×C₇₁	1	1	yes	characteristic
235	#533	C₂²×C₇₁	1	1	yes	characteristic
236	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
237	#492	—	2	1	no	—
238	#492	C₂²×C₇₁	1	2	yes	—
239	#486	—	2	1	no	—
240	#486	C₂²×C₇₁	1	2	yes	—
241	#475	—	2	1	no	—
242	#475	C₂²×C₇₁	1	2	yes	complemented
243	#470	—	2	2	no	—
244	#462	—	2	1	no	—
245	#462	C₂²×C₇₁	1	2	yes	complemented
246	#460	—	2	1	no	—
247	#460	—	2	1	no	—
248	#460	C₂²×C₇₁	1	2	yes	—
249	#460	C₂²×C₇₁	1	2	yes	—
250	#450	—	2	2	no	—
251	#450	—	2	2	no	—
252	#446	—	2	1	no	—
253	#446	C₂²×C₇₁	1	2	yes	complemented
254	C₈×Q₈	—	2	1	no	—
255	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
256	#433	—	2	2	no	—
257	#431	C₂²×C₇₁	1	1	yes	characteristic
258	#431	C₂²×C₇₁	1	1	yes	characteristic
259	#431	C₂²×C₇₁	1	1	yes	characteristic
260	#423	C₂²×C₇₁	1	1	yes	characteristic
261	#335	C₂²×C₇₁	1	2	yes	complemented
262	#334	C₂²×C₇₁	1	2	yes	complemented
263	#332	C₂²×C₇₁	1	1	yes	characteristic, complemented
264	#332	C₂²×C₇₁	1	1	yes	characteristic, complemented
265	#332	C₂²×C₇₁	1	1	yes	characteristic, complemented
266	#332	C₂²×C₇₁	1	1	yes	characteristic, complemented
267	#331	C₂²×C₇₁	1	2	yes	—
268	#331	C₂²×C₇₁	1	2	yes	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
279	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×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	2	yes	—
286	#125	—	2	1	no	—
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
299	#106	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
304	C₄⋊C₈	D₄×C₇₁	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
308	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	D₄×C₇₁	1	2	yes	—
319	#97	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂³×C₇₁	1	2	yes	—
324	C₂⁴	—	4	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	8	1	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂×D₄	—	8	1	no	—
338	C₂×D₄	—	8	1	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
342	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
343	Q₁₆	—	8	2	no	—
344	SD₁₆	—	8	2	no	—
345	SD₁₆	—	8	2	no	—
346	SD₁₆	—	8	2	no	—
347	SD₁₆	—	8	2	no	—
348	M₁₆	—	8	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	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	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	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	—	4	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	#121×C₇₁	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	4	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	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	#121×C₇₁	1	1	yes	characteristic
406	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
407	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	16	4	no	—
425	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	#471×C₇₁	1	2	yes	—
434	C₄	#576×C₇₁	1	1	yes	characteristic
435	C₄	#577×C₇₁	1	1	yes	characteristic
436	C₄	#577×C₇₁	1	1	yes	characteristic
437	C₄	#577×C₇₁	1	1	yes	characteristic
438	C₂	—	4	1	no	—
439	C₂	—	16	2	no	—
440	C₂	C₇₁×#3043	1	1	yes	characteristic
441	C₂	C₇₁×#3062	1	1	yes	characteristic
442	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	C₂×#127×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
1. C₇₁×#3255	C₂	semidirect
4. C₇₁×#2986	C₂	semidirect
5. C₇₁×#1702	C₂	semidirect
6. C₇₁×#1686	C₂	semidirect
7. C₇₁×#1682	C₂	semidirect
8. C₇₁×#1666	C₂	semidirect
9. C₇₁×#1574	C₂	semidirect
11. C₇₁×#1544	C₂	semidirect
20. #475×C₇₁	C₂²	semidirect
23. #462×C₇₁	C₂²	semidirect
31. #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
42. #332×C₇₁	C₂²	semidirect
43. #332×C₇₁	C₂²	semidirect
44. #332×C₇₁	C₂²	semidirect
216. #19564	C₇₁	direct (N × H)
222. #3255	C₂×C₇₁	semidirect
225. #2986	C₂×C₇₁	semidirect
226. #1702	C₂×C₇₁	semidirect
227. #1686	C₂×C₇₁	semidirect
228. #1682	C₂×C₇₁	semidirect
229. #1666	C₂×C₇₁	semidirect
230. #1574	C₂×C₇₁	semidirect
232. #1544	C₂×C₇₁	semidirect
233. C₇₁	#19564	direct (N × H)
242. #475	C₂²×C₇₁	semidirect
245. #462	C₂²×C₇₁	semidirect
253. #446	C₂²×C₇₁	semidirect
255. C₈×Q₈	C₂²×C₇₁	semidirect
261. #335	C₂²×C₇₁	semidirect
262. #334	C₂²×C₇₁	semidirect
263. #332	C₂²×C₇₁	semidirect
264. #332	C₂²×C₇₁	semidirect
265. #332	C₂²×C₇₁	semidirect
266. #332	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×#3255	2
C₇₁×#3208	2
C₇₁×#2986	2
C₇₁×#1702	2
C₇₁×#1686	2
C₇₁×#1682	2
C₇₁×#1666	2
C₇₁×#1574	2
C₇₁×#1545	2
C₇₁×#1544	2
#19564	71

Subgroups — C71×#19564 #31840436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19564 #31840436