Subgroups — C₇₁×#19245 #31840117

Order 18176.

606 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3246	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#3141	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1702	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1700	C₂	1	2	yes	maximal, complemented
7	C₇₁×#1682	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1680	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1540	C₂	1	1	yes	maximal, characteristic
11	C₂×#332×C₇₁	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×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
15	#494×C₇₁	—	2	1	no	—
16	#489×C₇₁	—	2	2	no	—
17	#487×C₇₁	—	2	1	no	—
18	#487×C₇₁	C₂²	1	2	yes	—
19	#486×C₇₁	C₂²	1	2	yes	—
20	#476×C₇₁	—	2	1	no	—
21	#475×C₇₁	C₂²	1	2	yes	—
22	#465×C₇₁	—	2	2	no	—
23	#462×C₇₁	C₂²	1	2	yes	—
24	#462×C₇₁	C₂²	1	2	yes	—
25	#461×C₇₁	—	2	1	no	—
26	#460×C₇₁	C₂²	1	2	yes	—
27	#451×C₇₁	—	2	2	no	—
28	#446×C₇₁	—	2	2	no	—
29	#446×C₇₁	C₂²	1	2	yes	—
30	C₈×Q₈×C₇₁	C₂²	1	2	yes	—
31	#431×C₇₁	C₂²	1	1	yes	characteristic
32	#424×C₇₁	—	2	1	no	—
33	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
35	#417×C₇₁	—	2	1	no	—
36	#417×C₇₁	—	2	1	no	—
37	#405×C₇₁	—	2	1	no	—
38	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
39	#335×C₇₁	C₂²	1	2	yes	—
40	#334×C₇₁	C₂²	1	2	yes	—
41	#332×C₇₁	C₂²	1	2	yes	—
42	#332×C₇₁	C₂²	1	2	yes	—
43	#332×C₇₁	C₂²	1	1	yes	characteristic
44	#332×C₇₁	C₂²	1	1	yes	characteristic
45	#331×C₇₁	C₂²	1	1	yes	characteristic
46	#331×C₇₁	C₂²	1	1	yes	characteristic
47	C₂×#41×C₇₁	—	2	1	no	—
48	C₂²×Q₈×C₇₁	—	2	1	no	—
49	C₂×Q₁₆×C₇₁	—	2	2	no	—
50	C₂×Q₁₆×C₇₁	—	2	2	no	—
51	C₂×SD₁₆×C₇₁	—	2	2	no	—
52	C₂×M₁₆×C₇₁	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₇₁	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₇₁	—	2	1	no	—
55	C₂²×C₈×C₇₁	—	2	1	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	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₇₁	C₂³	1	2	yes	—
62	C₄⋊Q₈×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×C₄⋊C₄×C₇₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
77	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
78	#106×C₇₁	—	2	2	no	—
79	C₄⋊C₈×C₇₁	—	2	2	no	—
80	C₄⋊C₈×C₇₁	—	2	2	no	—
81	C₄⋊C₈×C₇₁	—	2	1	no	—
82	C₄⋊C₈×C₇₁	—	2	1	no	—
83	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
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	#103×C₇₁	—	2	2	no	—
91	#103×C₇₁	—	2	2	no	—
92	#103×C₇₁	—	2	2	no	—
93	#102×C₇₁	—	2	2	no	—
94	#102×C₇₁	—	2	2	no	—
95	#102×C₇₁	—	2	2	no	—
96	C₂²⋊C₈×C₇₁	—	2	1	no	—
97	#97×C₇₁	—	2	2	no	—
98	#97×C₇₁	D₄	1	2	yes	—
99	C₄×C₈×C₇₁	—	2	2	no	—
100	C₄×C₈×C₇₁	—	2	1	no	—
101	C₄×C₈×C₇₁	C₂³	1	2	yes	—
102	#41×C₇₁	—	4	2	no	—
103	#41×C₇₁	—	4	2	no	—
104	C₂×Q₈×C₇₁	—	2	1	no	—
105	C₂×Q₈×C₇₁	—	2	1	no	—
106	C₂×Q₈×C₇₁	—	2	2	no	—
107	C₂×Q₈×C₇₁	—	4	1	no	—
108	C₂×Q₈×C₇₁	—	8	1	no	—
109	C₂×Q₈×C₇₁	—	8	1	no	—
110	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₇₁	—	2	1	no	—
112	C₂×D₄×C₇₁	—	2	1	no	—
113	C₂×D₄×C₇₁	—	2	1	no	—
114	C₂×D₄×C₇₁	—	4	1	no	—
115	C₂²×C₄×C₇₁	—	4	1	no	—
116	C₂²×C₄×C₇₁	—	4	1	no	—
117	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
120	Q₁₆×C₇₁	—	8	2	no	—
121	Q₁₆×C₇₁	—	8	2	no	—
122	SD₁₆×C₇₁	—	8	2	no	—
123	M₁₆×C₇₁	—	2	2	no	—
124	M₁₆×C₇₁	—	2	2	no	—
125	C₂×C₈×C₇₁	—	2	1	no	—
126	C₂×C₈×C₇₁	—	2	1	no	—
127	C₂×C₈×C₇₁	—	2	1	no	—
128	C₂×C₈×C₇₁	—	2	1	no	—
129	C₂×C₈×C₇₁	—	2	2	no	—
130	C₂×C₈×C₇₁	—	4	2	no	—
131	C₂×C₈×C₇₁	—	8	1	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	2	no	—
140	C₄⋊C₄×C₇₁	—	2	1	no	—
141	C₄⋊C₄×C₇₁	—	2	2	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	C₂²⋊C₄×C₇₁	—	4	1	no	—
149	C₄²×C₇₁	—	2	2	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	1	no	—
155	C₂³×C₇₁	#121	1	1	yes	characteristic
156	Q₈×C₇₁	—	2	2	no	—
157	Q₈×C₇₁	—	2	2	no	—
158	Q₈×C₇₁	—	4	1	no	—
159	Q₈×C₇₁	—	4	1	no	—
160	Q₈×C₇₁	—	4	2	no	—
161	Q₈×C₇₁	—	4	2	no	—
162	Q₈×C₇₁	—	8	1	no	—
163	Q₈×C₇₁	—	8	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	—	8	1	no	—
169	D₄×C₇₁	—	8	2	no	—
170	C₂×C₄×C₇₁	—	2	1	no	—
171	C₂×C₄×C₇₁	—	2	1	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	1	no	—
176	C₂×C₄×C₇₁	—	4	2	no	—
177	C₂×C₄×C₇₁	—	8	2	no	—
178	C₂×C₄×C₇₁	—	8	2	no	—
179	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₇₁	#135	1	2	yes	—
183	C₂×C₄×C₇₁	#137	1	2	yes	—
184	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
187	C₈×C₇₁	—	2	2	no	—
188	C₈×C₇₁	—	2	2	no	—
189	C₈×C₇₁	—	4	1	no	—
190	C₈×C₇₁	—	4	1	no	—
191	C₈×C₇₁	—	4	2	no	—
192	C₈×C₇₁	—	4	1	no	—
193	C₈×C₇₁	—	4	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	#464	1	2	yes	—
200	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
201	C₄×C₇₁	—	2	1	no	—
202	C₄×C₇₁	—	2	1	no	—
203	C₄×C₇₁	—	2	1	no	—
204	C₄×C₇₁	—	4	2	no	—
205	C₄×C₇₁	—	4	2	no	—
206	C₄×C₇₁	—	8	1	no	—
207	C₄×C₇₁	—	8	2	no	—
208	C₄×C₇₁	#464	1	2	yes	—
209	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
210	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
211	C₄×C₇₁	#576	1	1	yes	characteristic
212	C₄×C₇₁	#577	1	1	yes	characteristic
213	#19245	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₇₁	—	2	2	no	—
215	C₂×C₇₁	—	16	1	no	—
216	C₂×C₇₁	C₂×#464	1	1	yes	characteristic
217	C₂×C₇₁	#3062	1	1	yes	characteristic
218	C₂×C₇₁	#3069	1	1	yes	characteristic
219	#3246	C₂×C₇₁	1	1	yes	characteristic
220	#3209	C₂×C₇₁	1	1	yes	characteristic, complemented
221	#3141	C₂×C₇₁	1	1	yes	characteristic
222	#2962	C₂×C₇₁	1	1	yes	characteristic, complemented
223	#1702	C₂×C₇₁	1	2	yes	complemented
224	#1700	C₂×C₇₁	1	2	yes	complemented
225	#1682	C₂×C₇₁	1	2	yes	complemented
226	#1680	C₂×C₇₁	1	2	yes	complemented
227	#1565	C₂×C₇₁	1	1	yes	characteristic, complemented
228	#1540	C₂×C₇₁	1	1	yes	characteristic
229	C₂×#332	C₂×C₇₁	1	1	yes	characteristic, complemented
230	C₇₁	#19245	1	1	yes	characteristic, direct product factor, Sylow
231	#533	C₂²×C₇₁	1	1	yes	characteristic
232	#532	C₂²×C₇₁	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
234	#494	—	2	1	no	—
235	#489	—	2	2	no	—
236	#487	—	2	1	no	—
237	#487	C₂²×C₇₁	1	2	yes	—
238	#486	C₂²×C₇₁	1	2	yes	—
239	#476	—	2	1	no	—
240	#475	C₂²×C₇₁	1	2	yes	—
241	#465	—	2	2	no	—
242	#462	C₂²×C₇₁	1	2	yes	—
243	#462	C₂²×C₇₁	1	2	yes	—
244	#461	—	2	1	no	—
245	#460	C₂²×C₇₁	1	2	yes	—
246	#451	—	2	2	no	—
247	#446	—	2	2	no	—
248	#446	C₂²×C₇₁	1	2	yes	—
249	C₈×Q₈	C₂²×C₇₁	1	2	yes	—
250	#431	C₂²×C₇₁	1	1	yes	characteristic
251	#424	—	2	1	no	—
252	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
254	#417	—	2	1	no	—
255	#417	—	2	1	no	—
256	#405	—	2	1	no	—
257	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
258	#335	C₂²×C₇₁	1	2	yes	—
259	#334	C₂²×C₇₁	1	2	yes	—
260	#332	C₂²×C₇₁	1	2	yes	—
261	#332	C₂²×C₇₁	1	2	yes	—
262	#332	C₂²×C₇₁	1	1	yes	characteristic
263	#332	C₂²×C₇₁	1	1	yes	characteristic
264	#331	C₂²×C₇₁	1	1	yes	characteristic
265	#331	C₂²×C₇₁	1	1	yes	characteristic
266	C₂×#41	—	2	1	no	—
267	C₂²×Q₈	—	2	1	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×M₁₆	D₄×C₇₁	1	1	yes	characteristic
272	C₂×M₁₆	D₄×C₇₁	1	1	yes	characteristic
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	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	2	yes	—
281	C₄⋊Q₈	C₂³×C₇₁	1	1	yes	characteristic
282	#127	C₂³×C₇₁	1	1	yes	characteristic
283	#125	—	2	1	no	—
284	#124	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	C₂²⋊Q₈	D₄×C₇₁	1	2	yes	—
287	#121	—	2	1	no	—
288	#121	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	C₂³×C₇₁	1	2	yes	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	#117	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
297	#106	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₇₁	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₇₁	1	2	yes	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
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	C₂²⋊C₈	—	2	1	no	—
316	#97	—	2	2	no	—
317	#97	D₄×C₇₁	1	2	yes	—
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	C₂³×C₇₁	1	2	yes	—
321	#41	—	4	2	no	—
322	#41	—	4	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	8	1	no	—
328	C₂×Q₈	—	8	1	no	—
329	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
338	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
339	Q₁₆	—	8	2	no	—
340	Q₁₆	—	8	2	no	—
341	SD₁₆	—	8	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	8	1	no	—
351	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
352	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₄²	—	2	2	no	—
369	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
371	C₄²	#41×C₇₁	1	1	yes	characteristic
372	C₄²	C₂⁴×C₇₁	1	1	yes	characteristic
373	C₂³	—	4	1	no	—
374	C₂³	#121×C₇₁	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	8	1	no	—
382	Q₈	—	8	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
399	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
400	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
401	C₂×C₄	#135×C₇₁	1	2	yes	—
402	C₂×C₄	#137×C₇₁	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	#464×C₇₁	1	2	yes	—
419	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	1	no	—
427	C₄	#464×C₇₁	1	2	yes	—
428	C₄	C₂×#135×C₇₁	1	1	yes	characteristic
429	C₄	C₂×#137×C₇₁	1	1	yes	characteristic
430	C₄	#576×C₇₁	1	1	yes	characteristic
431	C₄	#577×C₇₁	1	1	yes	characteristic
432	C₂	—	2	2	no	—
433	C₂	—	16	1	no	—
434	C₂	C₂×#464×C₇₁	1	1	yes	characteristic
435	C₂	C₇₁×#3062	1	1	yes	characteristic
436	C₂	C₇₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₁
prime radical	#532×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
2. C₇₁×#3209	C₂	semidirect
4. C₇₁×#2962	C₂	semidirect
5. C₇₁×#1702	C₂	semidirect
6. C₇₁×#1700	C₂	semidirect
7. C₇₁×#1682	C₂	semidirect
8. C₇₁×#1680	C₂	semidirect
9. C₇₁×#1565	C₂	semidirect
11. C₂×#332×C₇₁	C₂	semidirect
213. #19245	C₇₁	direct (N × H)
220. #3209	C₂×C₇₁	semidirect
222. #2962	C₂×C₇₁	semidirect
223. #1702	C₂×C₇₁	semidirect
224. #1700	C₂×C₇₁	semidirect
225. #1682	C₂×C₇₁	semidirect
226. #1680	C₂×C₇₁	semidirect
227. #1565	C₂×C₇₁	semidirect
229. C₂×#332	C₂×C₇₁	semidirect
230. C₇₁	#19245	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×#3246	2
C₇₁×#3209	2
C₇₁×#3141	2
C₇₁×#2962	2
C₇₁×#1702	2
C₇₁×#1700	2
C₇₁×#1682	2
C₇₁×#1680	2
C₇₁×#1565	2
C₇₁×#1540	2
C₂×#332×C₇₁	2
#19245	71

Subgroups — C71×#19245 #31840117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#19245 #31840117