Subgroups — C₇₁×#19520 #31840392

Order 18176.

612 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3237	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×#2985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1698	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1686	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1678	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1666	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
11	C₇₁×#1554	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	#501×C₇₁	—	2	1	no	—
16	#492×C₇₁	—	2	1	no	—
17	#492×C₇₁	C₂²	1	1	yes	characteristic
18	#492×C₇₁	C₂²	1	1	yes	characteristic
19	#491×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	#485×C₇₁	—	2	2	no	—
24	#477×C₇₁	C₂²	1	2	yes	complemented
25	#475×C₇₁	C₂²	1	2	yes	complemented
26	#460×C₇₁	—	2	2	no	—
27	#460×C₇₁	C₂²	1	2	yes	—
28	#460×C₇₁	C₂²	1	2	yes	—
29	#450×C₇₁	—	2	2	no	—
30	#450×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	#333×C₇₁	C₂²	1	2	yes	complemented
42	#332×C₇₁	C₂²	1	2	yes	complemented
43	#331×C₇₁	C₂²	1	2	yes	—
44	#331×C₇₁	C₂²	1	2	yes	—
45	C₂²×D₄×C₇₁	—	2	1	no	—
46	C₂²×D₄×C₇₁	—	2	1	no	—
47	C₂²×D₄×C₇₁	—	2	1	no	—
48	C₂×SD₁₆×C₇₁	—	2	2	no	—
49	C₂×SD₁₆×C₇₁	—	2	2	no	—
50	C₂×SD₁₆×C₇₁	—	2	2	no	—
51	C₂×SD₁₆×C₇₁	—	2	2	no	—
52	C₄⋊Q₈×C₇₁	D₄	1	1	yes	characteristic
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	#127×C₇₁	—	2	1	no	—
57	#127×C₇₁	—	2	1	no	—
58	#127×C₇₁	—	2	1	no	—
59	#127×C₇₁	C₂³	1	1	yes	characteristic
60	#127×C₇₁	C₂³	1	1	yes	characteristic
61	#125×C₇₁	—	2	1	no	—
62	#125×C₇₁	—	2	1	no	—
63	C₂²⋊Q₈×C₇₁	—	2	1	no	—
64	C₂²⋊Q₈×C₇₁	—	2	1	no	—
65	C₂²⋊Q₈×C₇₁	—	2	1	no	—
66	C₂²⋊Q₈×C₇₁	D₄	1	2	yes	—
67	C₄×Q₈×C₇₁	—	2	1	no	—
68	C₄×Q₈×C₇₁	—	2	1	no	—
69	C₄×Q₈×C₇₁	—	2	1	no	—
70	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
71	#117×C₇₁	—	2	1	no	—
72	#117×C₇₁	—	2	1	no	—
73	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
74	#107×C₇₁	—	2	2	no	—
75	#106×C₇₁	—	2	2	no	—
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	#103×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	C₂×Q₈×C₇₁	—	2	1	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	—	4	1	no	—
111	C₂×D₄×C₇₁	—	4	1	no	—
112	C₂×D₄×C₇₁	—	4	1	no	—
113	C₂×D₄×C₇₁	—	8	2	no	—
114	C₂×D₄×C₇₁	—	8	2	no	—
115	C₂×D₄×C₇₁	—	8	2	no	—
116	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
119	SD₁₆×C₇₁	—	8	2	no	—
120	SD₁₆×C₇₁	—	8	2	no	—
121	SD₁₆×C₇₁	—	8	2	no	—
122	SD₁₆×C₇₁	—	8	2	no	—
123	C₂×C₈×C₇₁	—	2	2	no	—
124	C₂×C₈×C₇₁	—	2	2	no	—
125	C₂×C₈×C₇₁	—	2	2	no	—
126	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₇₁	—	2	1	no	—
129	C₄⋊C₄×C₇₁	—	2	1	no	—
130	C₄⋊C₄×C₇₁	—	2	1	no	—
131	C₄⋊C₄×C₇₁	—	2	2	no	—
132	C₄⋊C₄×C₇₁	—	2	2	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	—	2	1	no	—
137	C₄⋊C₄×C₇₁	—	4	1	no	—
138	C₄⋊C₄×C₇₁	—	4	1	no	—
139	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₇₁	—	2	2	no	—
141	C₂²⋊C₄×C₇₁	—	4	1	no	—
142	C₄²×C₇₁	—	2	2	no	—
143	C₄²×C₇₁	—	4	1	no	—
144	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇₁	#41	1	1	yes	characteristic
147	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
148	C₂³×C₇₁	—	4	1	no	—
149	C₂³×C₇₁	—	4	1	no	—
150	C₂³×C₇₁	—	8	2	no	—
151	C₂³×C₇₁	—	8	2	no	—
152	C₂³×C₇₁	—	8	2	no	—
153	C₂³×C₇₁	#121	1	1	yes	characteristic
154	Q₈×C₇₁	—	2	2	no	—
155	Q₈×C₇₁	—	2	2	no	—
156	Q₈×C₇₁	—	4	2	no	—
157	Q₈×C₇₁	—	8	1	no	—
158	Q₈×C₇₁	—	8	1	no	—
159	D₄×C₇₁	—	4	2	no	—
160	D₄×C₇₁	—	4	2	no	—
161	D₄×C₇₁	—	4	2	no	—
162	D₄×C₇₁	—	4	2	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	D₄×C₇₁	—	8	2	no	—
168	C₂×C₄×C₇₁	—	2	2	no	—
169	C₂×C₄×C₇₁	—	2	2	no	—
170	C₂×C₄×C₇₁	—	2	2	no	—
171	C₂×C₄×C₇₁	—	2	2	no	—
172	C₂×C₄×C₇₁	—	4	1	no	—
173	C₂×C₄×C₇₁	—	4	1	no	—
174	C₂×C₄×C₇₁	—	4	1	no	—
175	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
176	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
181	C₈×C₇₁	—	2	2	no	—
182	C₈×C₇₁	—	2	2	no	—
183	C₈×C₇₁	—	4	2	no	—
184	C₈×C₇₁	—	4	2	no	—
185	C₈×C₇₁	—	4	2	no	—
186	C₂²×C₇₁	—	2	1	no	—
187	C₂²×C₇₁	—	2	1	no	—
188	C₂²×C₇₁	—	2	1	no	—
189	C₂²×C₇₁	—	8	1	no	—
190	C₂²×C₇₁	—	8	1	no	—
191	C₂²×C₇₁	—	8	1	no	—
192	C₂²×C₇₁	—	8	1	no	—
193	C₂²×C₇₁	—	8	1	no	—
194	C₂²×C₇₁	—	8	1	no	—
195	C₂²×C₇₁	—	16	4	no	—
196	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
197	C₄×C₇₁	—	2	1	no	—
198	C₄×C₇₁	—	2	1	no	—
199	C₄×C₇₁	—	2	1	no	—
200	C₄×C₇₁	—	2	1	no	—
201	C₄×C₇₁	—	4	2	no	—
202	C₄×C₇₁	—	4	2	no	—
203	C₄×C₇₁	—	8	1	no	—
204	C₄×C₇₁	—	8	1	no	—
205	C₄×C₇₁	#577	1	2	yes	—
206	C₄×C₇₁	#577	1	2	yes	—
207	#19520	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₇₁	—	4	1	no	—
209	C₂×C₇₁	—	16	1	no	—
210	C₂×C₇₁	—	16	1	no	—
211	C₂×C₇₁	#3043	1	1	yes	characteristic
212	C₂×C₇₁	#3057	1	1	yes	characteristic
213	C₂×C₇₁	#3068	1	1	yes	characteristic
214	#3237	C₂×C₇₁	1	1	yes	characteristic, complemented
215	#3208	C₂×C₇₁	1	1	yes	characteristic
216	#3208	C₂×C₇₁	1	1	yes	characteristic
217	#2985	C₂×C₇₁	1	1	yes	characteristic, complemented
218	#1698	C₂×C₇₁	1	2	yes	complemented
219	#1686	C₂×C₇₁	1	2	yes	complemented
220	#1678	C₂×C₇₁	1	2	yes	complemented
221	#1666	C₂×C₇₁	1	2	yes	complemented
222	#1572	C₂×C₇₁	1	1	yes	characteristic, complemented
223	#1555	C₂×C₇₁	1	1	yes	characteristic
224	#1554	C₂×C₇₁	1	1	yes	characteristic, complemented
225	C₇₁	#19520	1	1	yes	characteristic, direct product factor, Sylow
226	#533	C₂²×C₇₁	1	1	yes	characteristic
227	#533	C₂²×C₇₁	1	1	yes	characteristic
228	C₂×#127	C₂²×C₇₁	1	1	yes	characteristic
229	#501	—	2	1	no	—
230	#492	—	2	1	no	—
231	#492	C₂²×C₇₁	1	1	yes	characteristic
232	#492	C₂²×C₇₁	1	1	yes	characteristic
233	#491	—	2	1	no	—
234	#486	—	2	1	no	—
235	#486	C₂²×C₇₁	1	1	yes	characteristic
236	#486	C₂²×C₇₁	1	1	yes	characteristic
237	#485	—	2	2	no	—
238	#477	C₂²×C₇₁	1	2	yes	complemented
239	#475	C₂²×C₇₁	1	2	yes	complemented
240	#460	—	2	2	no	—
241	#460	C₂²×C₇₁	1	2	yes	—
242	#460	C₂²×C₇₁	1	2	yes	—
243	#450	—	2	2	no	—
244	#450	—	2	2	no	—
245	#446	—	2	2	no	—
246	#446	C₂²×C₇₁	1	2	yes	complemented
247	C₈×Q₈	C₂²×C₇₁	1	2	yes	complemented
248	#433	—	2	2	no	—
249	#432	C₂²×C₇₁	1	1	yes	characteristic
250	#432	C₂²×C₇₁	1	1	yes	characteristic
251	#431	C₂²×C₇₁	1	1	yes	characteristic
252	#431	C₂²×C₇₁	1	1	yes	characteristic
253	#335	C₂²×C₇₁	1	2	yes	complemented
254	#334	C₂²×C₇₁	1	2	yes	complemented
255	#333	C₂²×C₇₁	1	2	yes	complemented
256	#332	C₂²×C₇₁	1	2	yes	complemented
257	#331	C₂²×C₇₁	1	2	yes	—
258	#331	C₂²×C₇₁	1	2	yes	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	—	2	1	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
267	C₄⋊Q₈	D₄×C₇₁	1	1	yes	characteristic
268	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	C₂³×C₇₁	1	1	yes	characteristic
274	#127	C₂³×C₇₁	1	1	yes	characteristic
275	#125	—	2	1	no	—
276	#125	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
285	#117	—	2	1	no	—
286	#117	—	2	1	no	—
287	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
288	#107	—	2	2	no	—
289	#106	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
293	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
294	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
295	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
296	#103	—	2	2	no	—
297	#103	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	D₄×C₇₁	1	2	yes	—
306	#97	—	2	2	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
312	C₄×C₈	C₂³×C₇₁	1	1	yes	characteristic
313	C₂⁴	—	4	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	—	8	2	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
332	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
333	SD₁₆	—	8	2	no	—
334	SD₁₆	—	8	2	no	—
335	SD₁₆	—	8	2	no	—
336	SD₁₆	—	8	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	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	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	4	1	no	—
358	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
360	C₄²	#41×C₇₁	1	1	yes	characteristic
361	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	8	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	—	8	2	no	—
367	C₂³	#121×C₇₁	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
390	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
391	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	16	4	no	—
410	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	#577×C₇₁	1	2	yes	—
420	C₄	#577×C₇₁	1	2	yes	—
421	C₂	—	4	1	no	—
422	C₂	—	16	1	no	—
423	C₂	—	16	1	no	—
424	C₂	C₇₁×#3043	1	1	yes	characteristic
425	C₂	C₇₁×#3057	1	1	yes	characteristic
426	C₂	C₇₁×#3068	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×#3237	C₂	semidirect
4. C₇₁×#2985	C₂	semidirect
5. C₇₁×#1698	C₂	semidirect
6. C₇₁×#1686	C₂	semidirect
7. C₇₁×#1678	C₂	semidirect
8. C₇₁×#1666	C₂	semidirect
9. C₇₁×#1572	C₂	semidirect
11. C₇₁×#1554	C₂	semidirect
24. #477×C₇₁	C₂²	semidirect
25. #475×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. #333×C₇₁	C₂²	semidirect
42. #332×C₇₁	C₂²	semidirect
207. #19520	C₇₁	direct (N × H)
214. #3237	C₂×C₇₁	semidirect
217. #2985	C₂×C₇₁	semidirect
218. #1698	C₂×C₇₁	semidirect
219. #1686	C₂×C₇₁	semidirect
220. #1678	C₂×C₇₁	semidirect
221. #1666	C₂×C₇₁	semidirect
222. #1572	C₂×C₇₁	semidirect
224. #1554	C₂×C₇₁	semidirect
225. C₇₁	#19520	direct (N × H)
238. #477	C₂²×C₇₁	semidirect
239. #475	C₂²×C₇₁	semidirect
246. #446	C₂²×C₇₁	semidirect
247. C₈×Q₈	C₂²×C₇₁	semidirect
253. #335	C₂²×C₇₁	semidirect
254. #334	C₂²×C₇₁	semidirect
255. #333	C₂²×C₇₁	semidirect
256. #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×#3237	2
C₇₁×#3208	2
C₇₁×#2985	2
C₇₁×#1698	2
C₇₁×#1686	2
C₇₁×#1678	2
C₇₁×#1666	2
C₇₁×#1572	2
C₇₁×#1555	2
C₇₁×#1554	2
#19520	71

Subgroups — C71×#19520 #31840392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19520 #31840392