Subgroups — C₇₁×#17624 #31838496

Order 18176.

898 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×#3507	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#1521	C₂	1	2	yes	maximal, complemented
5	C₇₁×#1515	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#1514	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1512	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1509	C₂	1	2	yes	maximal, complemented
9	C₇₁×#1506	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1505	C₂	1	1	yes	maximal, characteristic
11	C₇₁×#1500	C₂	1	2	yes	maximal, complemented
12	#559×C₇₁	C₄	1	2	yes	complemented
13	#557×C₇₁	C₄	1	2	yes	complemented
14	#556×C₇₁	—	2	2	no	—
15	#556×C₇₁	C₄	1	2	yes	complemented
16	#554×C₇₁	C₄	1	2	yes	complemented
17	#552×C₇₁	—	2	2	no	—
18	#539×C₇₁	—	2	1	no	—
19	#539×C₇₁	—	2	1	no	—
20	#536×C₇₁	—	2	1	no	—
21	#533×C₇₁	C₂²	1	1	yes	characteristic
22	#532×C₇₁	C₂²	1	1	yes	characteristic
23	#529×C₇₁	C₂²	1	2	yes	—
24	#529×C₇₁	C₂²	1	2	yes	—
25	#520×C₇₁	—	2	1	no	—
26	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
27	#446×C₇₁	—	2	2	no	—
28	#446×C₇₁	—	2	2	no	—
29	#432×C₇₁	C₂²	1	1	yes	characteristic
30	#432×C₇₁	C₂²	1	1	yes	characteristic
31	#432×C₇₁	C₂²	1	2	yes	—
32	#431×C₇₁	C₂²	1	2	yes	—
33	#391×C₇₁	—	2	1	no	—
34	#387×C₇₁	—	2	1	no	—
35	#387×C₇₁	—	2	1	no	—
36	#383×C₇₁	C₂²	1	1	yes	characteristic
37	#383×C₇₁	C₂²	1	1	yes	characteristic
38	#382×C₇₁	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₇₁	—	2	1	no	—
40	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
41	#376×C₇₁	C₂²	1	1	yes	characteristic
42	#376×C₇₁	C₂²	1	1	yes	characteristic
43	#328×C₇₁	C₂²	1	2	yes	—
44	#328×C₇₁	C₂²	1	2	yes	—
45	#328×C₇₁	C₂²	1	2	yes	—
46	#328×C₇₁	C₂²	1	2	yes	—
47	#327×C₇₁	C₂²	1	2	yes	—
48	#327×C₇₁	C₂²	1	2	yes	—
49	#327×C₇₁	C₂²	1	2	yes	—
50	#327×C₇₁	C₂²	1	2	yes	—
51	C₂×#41×C₇₁	—	2	1	no	—
52	C₂²×Q₈×C₇₁	D₄	1	1	yes	characteristic
53	C₄⋊Q₈×C₇₁	—	2	2	no	—
54	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
57	#127×C₇₁	C₂×C₄	1	1	yes	characteristic
58	#126×C₇₁	—	2	2	no	—
59	#126×C₇₁	—	2	2	no	—
60	#126×C₇₁	—	2	2	no	—
61	#126×C₇₁	—	2	2	no	—
62	#125×C₇₁	—	2	2	no	—
63	#125×C₇₁	—	2	2	no	—
64	#125×C₇₁	—	2	1	no	—
65	#125×C₇₁	C₂×C₄	1	2	yes	—
66	#125×C₇₁	C₂×C₄	1	2	yes	—
67	#124×C₇₁	—	2	2	no	—
68	#124×C₇₁	—	2	1	no	—
69	#124×C₇₁	C₂×C₄	1	2	yes	—
70	#124×C₇₁	C₂×C₄	1	2	yes	—
71	#123×C₇₁	—	2	2	no	—
72	#123×C₇₁	—	2	2	no	—
73	#123×C₇₁	—	2	2	no	—
74	#123×C₇₁	—	2	2	no	—
75	C₂²⋊Q₈×C₇₁	—	2	2	no	—
76	C₂²⋊Q₈×C₇₁	—	2	2	no	—
77	C₂²⋊Q₈×C₇₁	—	2	1	no	—
78	C₂²⋊Q₈×C₇₁	—	2	2	no	—
79	C₂²⋊Q₈×C₇₁	—	2	2	no	—
80	C₂²⋊Q₈×C₇₁	C₂³	1	2	yes	—
81	#121×C₇₁	—	2	1	no	—
82	#121×C₇₁	C₂³	1	2	yes	—
83	C₄×Q₈×C₇₁	—	2	2	no	—
84	C₄×Q₈×C₇₁	—	2	1	no	—
85	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
86	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
87	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
88	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
89	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
90	C₄×Q₈×C₇₁	D₄	1	2	yes	—
91	C₄×Q₈×C₇₁	D₄	1	2	yes	—
92	C₄×D₄×C₇₁	—	2	2	no	—
93	C₄×D₄×C₇₁	—	2	2	no	—
94	C₄×D₄×C₇₁	—	2	2	no	—
95	C₄×D₄×C₇₁	—	2	1	no	—
96	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
97	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
99	#117×C₇₁	—	2	1	no	—
100	#117×C₇₁	—	2	2	no	—
101	#117×C₇₁	—	2	2	no	—
102	#117×C₇₁	—	2	2	no	—
103	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
104	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₁	—	2	1	no	—
110	C₂×C₄²×C₇₁	—	2	1	no	—
111	C₂×C₄²×C₇₁	—	2	1	no	—
112	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₇₁	—	2	2	no	—
116	C₄⋊C₈×C₇₁	—	2	2	no	—
117	C₄⋊C₈×C₇₁	—	2	1	no	—
118	C₄⋊C₈×C₇₁	—	2	1	no	—
119	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
120	C₂²⋊C₈×C₇₁	C₂³	1	2	yes	—
121	#97×C₇₁	—	2	2	no	—
122	#97×C₇₁	—	2	1	no	—
123	#97×C₇₁	—	2	1	no	—
124	C₄×C₈×C₇₁	—	2	2	no	—
125	#95×C₇₁	—	2	1	no	—
126	#95×C₇₁	—	2	1	no	—
127	#95×C₇₁	—	2	1	no	—
128	#95×C₇₁	—	2	1	no	—
129	#95×C₇₁	—	2	1	no	—
130	#95×C₇₁	—	2	1	no	—
131	#95×C₇₁	—	2	1	no	—
132	#95×C₇₁	C₂³	1	1	yes	characteristic
133	#95×C₇₁	C₂³	1	1	yes	characteristic
134	#95×C₇₁	C₂³	1	1	yes	characteristic
135	#95×C₇₁	C₂³	1	1	yes	characteristic
136	#41×C₇₁	—	4	2	no	—
137	#41×C₇₁	—	4	2	no	—
138	C₂×Q₈×C₇₁	—	2	1	no	—
139	C₂×Q₈×C₇₁	—	2	1	no	—
140	C₂×Q₈×C₇₁	—	4	1	no	—
141	C₂×Q₈×C₇₁	—	4	1	no	—
142	C₂×Q₈×C₇₁	C₂²⋊C₄	1	2	yes	—
143	C₂×Q₈×C₇₁	C₂²⋊C₄	1	2	yes	—
144	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₇₁	—	2	2	no	—
146	C₂×D₄×C₇₁	—	2	1	no	—
147	C₂×D₄×C₇₁	—	2	1	no	—
148	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₇₁	—	2	1	no	—
150	C₂²×C₄×C₇₁	—	2	2	no	—
151	C₂²×C₄×C₇₁	—	2	2	no	—
152	C₂²×C₄×C₇₁	—	2	2	no	—
153	C₂²×C₄×C₇₁	—	2	1	no	—
154	C₂²×C₄×C₇₁	—	2	1	no	—
155	C₂²×C₄×C₇₁	—	2	1	no	—
156	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₇₁	—	2	2	no	—
164	C₂×C₈×C₇₁	—	2	2	no	—
165	C₄⋊C₄×C₇₁	—	2	1	no	—
166	C₄⋊C₄×C₇₁	—	2	2	no	—
167	C₄⋊C₄×C₇₁	—	2	2	no	—
168	C₄⋊C₄×C₇₁	—	2	1	no	—
169	C₄⋊C₄×C₇₁	—	2	2	no	—
170	C₄⋊C₄×C₇₁	—	2	2	no	—
171	C₄⋊C₄×C₇₁	—	2	1	no	—
172	C₄⋊C₄×C₇₁	—	2	1	no	—
173	C₄⋊C₄×C₇₁	—	2	2	no	—
174	C₄⋊C₄×C₇₁	—	2	2	no	—
175	C₄⋊C₄×C₇₁	—	2	2	no	—
176	C₄⋊C₄×C₇₁	—	2	2	no	—
177	C₄⋊C₄×C₇₁	—	4	2	no	—
178	C₄⋊C₄×C₇₁	—	4	2	no	—
179	C₄⋊C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
180	C₄⋊C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
181	C₄⋊C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
182	C₄⋊C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
183	C₄⋊C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
184	C₄⋊C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
185	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
186	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
187	C₂²⋊C₄×C₇₁	—	2	2	no	—
188	C₂²⋊C₄×C₇₁	—	2	2	no	—
189	C₂²⋊C₄×C₇₁	—	2	2	no	—
190	C₂²⋊C₄×C₇₁	—	2	2	no	—
191	C₂²⋊C₄×C₇₁	—	2	2	no	—
192	C₂²⋊C₄×C₇₁	—	2	2	no	—
193	C₂²⋊C₄×C₇₁	—	2	2	no	—
194	C₂²⋊C₄×C₇₁	—	2	2	no	—
195	C₂²⋊C₄×C₇₁	—	2	2	no	—
196	C₄²×C₇₁	—	2	2	no	—
197	C₄²×C₇₁	—	2	2	no	—
198	C₄²×C₇₁	—	2	2	no	—
199	C₄²×C₇₁	—	4	2	no	—
200	C₄²×C₇₁	—	4	2	no	—
201	C₄²×C₇₁	—	4	2	no	—
202	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
204	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
205	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₇₁	C₂×D₄	1	2	yes	—
207	C₄²×C₇₁	C₂×D₄	1	2	yes	—
208	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
210	C₂³×C₇₁	—	2	2	no	—
211	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₇₁	—	4	2	no	—
213	Q₈×C₇₁	—	4	2	no	—
214	Q₈×C₇₁	—	4	2	no	—
215	Q₈×C₇₁	—	4	2	no	—
216	Q₈×C₇₁	—	8	1	no	—
217	D₄×C₇₁	—	4	2	no	—
218	D₄×C₇₁	—	4	2	no	—
219	D₄×C₇₁	—	4	2	no	—
220	D₄×C₇₁	—	4	2	no	—
221	D₄×C₇₁	—	8	1	no	—
222	C₂×C₄×C₇₁	—	2	1	no	—
223	C₂×C₄×C₇₁	—	2	1	no	—
224	C₂×C₄×C₇₁	—	2	1	no	—
225	C₂×C₄×C₇₁	—	2	1	no	—
226	C₂×C₄×C₇₁	—	2	1	no	—
227	C₂×C₄×C₇₁	—	2	1	no	—
228	C₂×C₄×C₇₁	—	2	2	no	—
229	C₂×C₄×C₇₁	—	2	2	no	—
230	C₂×C₄×C₇₁	—	2	2	no	—
231	C₂×C₄×C₇₁	—	2	2	no	—
232	C₂×C₄×C₇₁	—	4	1	no	—
233	C₂×C₄×C₇₁	—	4	1	no	—
234	C₂×C₄×C₇₁	—	4	1	no	—
235	C₂×C₄×C₇₁	—	4	1	no	—
236	C₂×C₄×C₇₁	—	4	4	no	—
237	C₂×C₄×C₇₁	—	4	1	no	—
238	C₂×C₄×C₇₁	—	4	1	no	—
239	C₂×C₄×C₇₁	—	4	1	no	—
240	C₂×C₄×C₇₁	—	4	1	no	—
241	C₂×C₄×C₇₁	—	4	1	no	—
242	C₂×C₄×C₇₁	—	4	1	no	—
243	C₂×C₄×C₇₁	—	4	1	no	—
244	C₂×C₄×C₇₁	—	4	1	no	—
245	C₂×C₄×C₇₁	—	4	1	no	—
246	C₂×C₄×C₇₁	—	4	1	no	—
247	C₂×C₄×C₇₁	—	4	1	no	—
248	C₂×C₄×C₇₁	—	8	2	no	—
249	C₂×C₄×C₇₁	—	8	2	no	—
250	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
253	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
260	C₈×C₇₁	—	4	2	no	—
261	C₈×C₇₁	—	4	2	no	—
262	C₂²×C₇₁	—	2	1	no	—
263	C₂²×C₇₁	—	2	1	no	—
264	C₂²×C₇₁	—	4	2	no	—
265	C₂²×C₇₁	—	4	2	no	—
266	C₂²×C₇₁	—	4	2	no	—
267	C₂²×C₇₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₇₁	#575	1	1	yes	characteristic
269	C₂²×C₇₁	#575	1	1	yes	characteristic
270	C₄×C₇₁	—	2	1	no	—
271	C₄×C₇₁	—	2	1	no	—
272	C₄×C₇₁	—	2	1	no	—
273	C₄×C₇₁	—	2	1	no	—
274	C₄×C₇₁	—	2	2	no	—
275	C₄×C₇₁	—	2	2	no	—
276	C₄×C₇₁	—	2	2	no	—
277	C₄×C₇₁	—	2	2	no	—
278	C₄×C₇₁	—	2	1	no	—
279	C₄×C₇₁	—	2	1	no	—
280	C₄×C₇₁	—	4	2	no	—
281	C₄×C₇₁	—	4	2	no	—
282	C₄×C₇₁	—	4	2	no	—
283	C₄×C₇₁	—	4	2	no	—
284	C₄×C₇₁	—	8	1	no	—
285	C₄×C₇₁	—	8	1	no	—
286	C₄×C₇₁	—	8	1	no	—
287	#17624	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂×C₇₁	—	2	1	no	—
289	C₂×C₇₁	—	2	1	no	—
290	C₂×C₇₁	—	8	2	no	—
291	C₂×C₇₁	#2884	1	1	yes	characteristic
292	C₂×C₇₁	#2896	1	1	yes	characteristic
293	C₂×C₇₁	#2901	1	1	yes	characteristic
294	#3507	C₂×C₇₁	1	1	yes	characteristic
295	#2983	C₂×C₇₁	1	1	yes	characteristic, complemented
296	#2356	C₂×C₇₁	1	1	yes	characteristic, complemented
297	#1521	C₂×C₇₁	1	2	yes	complemented
298	#1515	C₂×C₇₁	1	1	yes	characteristic, complemented
299	#1514	C₂×C₇₁	1	1	yes	characteristic
300	#1512	C₂×C₇₁	1	2	yes	complemented
301	#1509	C₂×C₇₁	1	2	yes	complemented
302	#1506	C₂×C₇₁	1	1	yes	characteristic, complemented
303	#1505	C₂×C₇₁	1	1	yes	characteristic
304	#1500	C₂×C₇₁	1	2	yes	complemented
305	C₇₁	#17624	1	1	yes	characteristic, direct product factor, Sylow
306	#559	C₄×C₇₁	1	2	yes	complemented
307	#557	C₄×C₇₁	1	2	yes	complemented
308	#556	—	2	2	no	—
309	#556	C₄×C₇₁	1	2	yes	complemented
310	#554	C₄×C₇₁	1	2	yes	complemented
311	#552	—	2	2	no	—
312	#539	—	2	1	no	—
313	#539	—	2	1	no	—
314	#536	—	2	1	no	—
315	#533	C₂²×C₇₁	1	1	yes	characteristic
316	#532	C₂²×C₇₁	1	1	yes	characteristic
317	#529	C₂²×C₇₁	1	2	yes	—
318	#529	C₂²×C₇₁	1	2	yes	—
319	#520	—	2	1	no	—
320	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
321	#446	—	2	2	no	—
322	#446	—	2	2	no	—
323	#432	C₂²×C₇₁	1	1	yes	characteristic
324	#432	C₂²×C₇₁	1	1	yes	characteristic
325	#432	C₂²×C₇₁	1	2	yes	—
326	#431	C₂²×C₇₁	1	2	yes	—
327	#391	—	2	1	no	—
328	#387	—	2	1	no	—
329	#387	—	2	1	no	—
330	#383	C₂²×C₇₁	1	1	yes	characteristic
331	#383	C₂²×C₇₁	1	1	yes	characteristic
332	#382	C₂²×C₇₁	1	1	yes	characteristic
333	C₄×C₄⋊C₄	—	2	1	no	—
334	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
335	#376	C₂²×C₇₁	1	1	yes	characteristic
336	#376	C₂²×C₇₁	1	1	yes	characteristic
337	#328	C₂²×C₇₁	1	2	yes	—
338	#328	C₂²×C₇₁	1	2	yes	—
339	#328	C₂²×C₇₁	1	2	yes	—
340	#328	C₂²×C₇₁	1	2	yes	—
341	#327	C₂²×C₇₁	1	2	yes	—
342	#327	C₂²×C₇₁	1	2	yes	—
343	#327	C₂²×C₇₁	1	2	yes	—
344	#327	C₂²×C₇₁	1	2	yes	—
345	C₂×#41	—	2	1	no	—
346	C₂²×Q₈	D₄×C₇₁	1	1	yes	characteristic
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	C₂×C₄×C₇₁	1	1	yes	characteristic
349	C₄⋊Q₈	C₂×C₄×C₇₁	1	1	yes	characteristic
350	C₄⋊Q₈	C₂×C₄×C₇₁	1	1	yes	characteristic
351	#127	C₂×C₄×C₇₁	1	1	yes	characteristic
352	#126	—	2	2	no	—
353	#126	—	2	2	no	—
354	#126	—	2	2	no	—
355	#126	—	2	2	no	—
356	#125	—	2	2	no	—
357	#125	—	2	2	no	—
358	#125	—	2	1	no	—
359	#125	C₂×C₄×C₇₁	1	2	yes	—
360	#125	C₂×C₄×C₇₁	1	2	yes	—
361	#124	—	2	2	no	—
362	#124	—	2	1	no	—
363	#124	C₂×C₄×C₇₁	1	2	yes	—
364	#124	C₂×C₄×C₇₁	1	2	yes	—
365	#123	—	2	2	no	—
366	#123	—	2	2	no	—
367	#123	—	2	2	no	—
368	#123	—	2	2	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	C₂³×C₇₁	1	2	yes	—
375	#121	—	2	1	no	—
376	#121	C₂³×C₇₁	1	2	yes	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	C₂×C₄×C₇₁	1	2	yes	—
380	C₄×Q₈	C₂×C₄×C₇₁	1	2	yes	—
381	C₄×Q₈	C₂×C₄×C₇₁	1	2	yes	—
382	C₄×Q₈	C₂×C₄×C₇₁	1	2	yes	—
383	C₄×Q₈	C₂×C₄×C₇₁	1	2	yes	—
384	C₄×Q₈	D₄×C₇₁	1	2	yes	—
385	C₄×Q₈	D₄×C₇₁	1	2	yes	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	C₂×C₄×C₇₁	1	2	yes	—
391	C₄×D₄	C₂×C₄×C₇₁	1	2	yes	—
392	C₄×D₄	C₂×C₄×C₇₁	1	2	yes	—
393	#117	—	2	1	no	—
394	#117	—	2	2	no	—
395	#117	—	2	2	no	—
396	#117	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
401	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
402	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
409	C₄⋊C₈	—	2	2	no	—
410	C₄⋊C₈	—	2	2	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
414	C₂²⋊C₈	C₂³×C₇₁	1	2	yes	—
415	#97	—	2	2	no	—
416	#97	—	2	1	no	—
417	#97	—	2	1	no	—
418	C₄×C₈	—	2	2	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	C₂³×C₇₁	1	1	yes	characteristic
427	#95	C₂³×C₇₁	1	1	yes	characteristic
428	#95	C₂³×C₇₁	1	1	yes	characteristic
429	#95	C₂³×C₇₁	1	1	yes	characteristic
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	4	1	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	C₂²⋊C₄×C₇₁	1	2	yes	—
437	C₂×Q₈	C₂²⋊C₄×C₇₁	1	2	yes	—
438	C₂×Q₈	C₂²×C₄×C₇₁	1	2	yes	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	C₂²×C₄×C₇₁	1	2	yes	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
474	C₄⋊C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
475	C₄⋊C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
476	C₄⋊C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
477	C₄⋊C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
478	C₄⋊C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
479	C₄⋊C₄	C₂²×C₄×C₇₁	1	2	yes	—
480	C₄⋊C₄	C₂²×C₄×C₇₁	1	2	yes	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	4	2	no	—
495	C₄²	—	4	2	no	—
496	C₄²	C₂²×C₄×C₇₁	1	1	yes	characteristic
497	C₄²	C₂²×C₄×C₇₁	1	2	yes	—
498	C₄²	C₂²×C₄×C₇₁	1	2	yes	—
499	C₄²	C₂²×C₄×C₇₁	1	1	yes	characteristic
500	C₄²	C₂×D₄×C₇₁	1	2	yes	—
501	C₄²	C₂×D₄×C₇₁	1	2	yes	—
502	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
504	C₂³	—	2	2	no	—
505	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	8	1	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	8	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
545	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
546	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
547	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
548	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	2	yes	—
549	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
550	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
551	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
552	C₂×C₄	C₂³×C₄×C₇₁	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
554	C₈	—	4	2	no	—
555	C₈	—	4	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₂²×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
562	C₂²	#575×C₇₁	1	1	yes	characteristic
563	C₂²	#575×C₇₁	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	8	2	no	—
584	C₂	C₇₁×#2884	1	1	yes	characteristic
585	C₂	C₇₁×#2896	1	1	yes	characteristic
586	C₂	C₇₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₇₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
prime radical	#532×C₇₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂×C₄×Q₈×C₇₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇₁×#2983	C₂	semidirect
3. C₇₁×#2356	C₂	semidirect
4. C₇₁×#1521	C₂	semidirect
5. C₇₁×#1515	C₂	semidirect
7. C₇₁×#1512	C₂	semidirect
8. C₇₁×#1509	C₂	semidirect
9. C₇₁×#1506	C₂	semidirect
11. C₇₁×#1500	C₂	semidirect
12. #559×C₇₁	C₄	semidirect
13. #557×C₇₁	C₄	semidirect
15. #556×C₇₁	C₄	semidirect
16. #554×C₇₁	C₄	semidirect
287. #17624	C₇₁	direct (N × H)
295. #2983	C₂×C₇₁	semidirect
296. #2356	C₂×C₇₁	semidirect
297. #1521	C₂×C₇₁	semidirect
298. #1515	C₂×C₇₁	semidirect
300. #1512	C₂×C₇₁	semidirect
301. #1509	C₂×C₇₁	semidirect
302. #1506	C₂×C₇₁	semidirect
304. #1500	C₂×C₇₁	semidirect
305. C₇₁	#17624	direct (N × H)
306. #559	C₄×C₇₁	semidirect
307. #557	C₄×C₇₁	semidirect
309. #556	C₄×C₇₁	semidirect
310. #554	C₄×C₇₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇₁×#3507	2
C₇₁×#2983	2
C₇₁×#2356	2
C₇₁×#1521	2
C₇₁×#1515	2
C₇₁×#1514	2
C₇₁×#1512	2
C₇₁×#1509	2
C₇₁×#1506	2
C₇₁×#1505	2
C₇₁×#1500	2
#17624	71

Subgroups — C71×#17624 #31838496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#17624 #31838496