Subgroups — C₇₁×#24646 #31845518

Order 18176.

864 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#461×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#440×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2357	C₂	1	1	yes	maximal, characteristic
5	C₇₁×#2055	C₂	1	2	yes	maximal
6	C₇₁×#2013	C₂	1	2	yes	maximal
7	C₇₁×#1981	C₂	1	2	yes	maximal, complemented
8	C₇₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₁×#1928	C₂	1	2	yes	maximal, complemented
11	C₇₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₇₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
18	#461×C₇₁	—	2	4	no	—
19	#440×C₇₁	—	2	4	no	—
20	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
23	C₂×#103×C₇₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₇₁	C₂²	1	2	yes	—
25	C₂×#103×C₇₁	C₂²	1	2	yes	—
26	C₂×#103×C₇₁	C₂²	1	2	yes	—
27	C₂×#103×C₇₁	C₂²	1	2	yes	—
28	C₂×#102×C₇₁	C₂²	1	1	yes	characteristic
29	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
30	#398×C₇₁	—	2	1	no	—
31	#398×C₇₁	—	2	1	no	—
32	#391×C₇₁	C₂²	1	2	yes	—
33	#390×C₇₁	C₂²	1	2	yes	—
34	#389×C₇₁	—	2	2	no	—
35	#388×C₇₁	—	2	2	no	—
36	#382×C₇₁	C₂²	1	1	yes	characteristic
37	#381×C₇₁	—	2	1	no	—
38	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₇₁	—	2	1	no	—
41	#340×C₇₁	C₂²	1	2	yes	—
42	#336×C₇₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇₁	—	2	1	no	—
47	C₂×SD₁₆×C₇₁	—	2	2	no	—
48	C₂×SD₁₆×C₇₁	—	2	2	no	—
49	C₂×SD₁₆×C₇₁	—	2	4	no	—
50	C₂×SD₁₆×C₇₁	—	2	2	no	—
51	C₂×SD₁₆×C₇₁	—	4	2	no	—
52	C₂×SD₁₆×C₇₁	—	4	2	no	—
53	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₁	—	2	4	no	—
57	C₄⋊Q₈×C₇₁	—	2	2	no	—
58	C₄⋊Q₈×C₇₁	—	2	2	no	—
59	C₄⋊Q₈×C₇₁	—	4	2	no	—
60	C₄×Q₈×C₇₁	—	2	2	no	—
61	C₄×Q₈×C₇₁	—	2	2	no	—
62	C₄×D₄×C₇₁	—	2	2	no	—
63	C₄×D₄×C₇₁	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₁	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
76	C₂×C₄²×C₇₁	—	2	1	no	—
77	C₂×C₄²×C₇₁	—	2	2	no	—
78	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
80	#107×C₇₁	—	2	2	no	—
81	C₄⋊C₈×C₇₁	—	2	2	no	—
82	C₄⋊C₈×C₇₁	—	4	2	no	—
83	#103×C₇₁	—	2	4	no	—
84	#103×C₇₁	—	2	2	no	—
85	#103×C₇₁	—	2	4	no	—
86	#103×C₇₁	—	4	2	no	—
87	#103×C₇₁	—	4	2	no	—
88	#102×C₇₁	—	2	2	no	—
89	#97×C₇₁	—	2	2	no	—
90	#95×C₇₁	—	2	1	no	—
91	#95×C₇₁	—	2	2	no	—
92	#95×C₇₁	—	2	1	no	—
93	#95×C₇₁	—	2	2	no	—
94	#95×C₇₁	—	2	2	no	—
95	#95×C₇₁	D₄	1	1	yes	characteristic
96	#95×C₇₁	D₄	1	1	yes	characteristic
97	C₂⁴×C₇₁	—	2	1	no	—
98	C₂×Q₈×C₇₁	—	2	1	no	—
99	C₂×Q₈×C₇₁	—	2	1	no	—
100	C₂×Q₈×C₇₁	—	2	2	no	—
101	C₂×Q₈×C₇₁	—	2	1	no	—
102	C₂×Q₈×C₇₁	—	2	1	no	—
103	C₂×Q₈×C₇₁	—	2	2	no	—
104	C₂×Q₈×C₇₁	—	2	2	no	—
105	C₂×Q₈×C₇₁	—	2	2	no	—
106	C₂×Q₈×C₇₁	—	2	1	no	—
107	C₂×Q₈×C₇₁	—	2	2	no	—
108	C₂×Q₈×C₇₁	—	2	2	no	—
109	C₂×Q₈×C₇₁	#41	1	2	yes	—
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	—	2	1	no	—
114	C₂×D₄×C₇₁	—	2	1	no	—
115	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇₁	—	2	1	no	—
117	C₂²×C₄×C₇₁	—	2	1	no	—
118	C₂²×C₄×C₇₁	—	2	4	no	—
119	C₂²×C₄×C₇₁	—	2	1	no	—
120	C₂²×C₄×C₇₁	—	2	2	no	—
121	C₂²×C₄×C₇₁	—	2	2	no	—
122	C₂²×C₄×C₇₁	—	8	2	no	—
123	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
128	SD₁₆×C₇₁	—	2	8	no	—
129	SD₁₆×C₇₁	—	4	8	no	—
130	C₂×C₈×C₇₁	—	2	1	no	—
131	C₂×C₈×C₇₁	—	2	1	no	—
132	C₂×C₈×C₇₁	—	2	1	no	—
133	C₂×C₈×C₇₁	—	2	2	no	—
134	C₂×C₈×C₇₁	—	2	1	no	—
135	C₂×C₈×C₇₁	—	2	2	no	—
136	C₂×C₈×C₇₁	—	2	1	no	—
137	C₂×C₈×C₇₁	—	2	2	no	—
138	C₂×C₈×C₇₁	#41	1	2	yes	—
139	C₄⋊C₄×C₇₁	—	2	4	no	—
140	C₄⋊C₄×C₇₁	—	2	1	no	—
141	C₄⋊C₄×C₇₁	—	2	1	no	—
142	C₄⋊C₄×C₇₁	—	2	2	no	—
143	C₄⋊C₄×C₇₁	—	2	1	no	—
144	C₄⋊C₄×C₇₁	—	2	2	no	—
145	C₄⋊C₄×C₇₁	—	4	4	no	—
146	C₄⋊C₄×C₇₁	—	4	4	no	—
147	C₄⋊C₄×C₇₁	—	4	2	no	—
148	C₄⋊C₄×C₇₁	—	4	2	no	—
149	C₄⋊C₄×C₇₁	—	4	2	no	—
150	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₇₁	—	2	4	no	—
152	C₂²⋊C₄×C₇₁	—	4	4	no	—
153	C₂²⋊C₄×C₇₁	—	8	2	no	—
154	C₄²×C₇₁	—	2	2	no	—
155	C₄²×C₇₁	—	2	2	no	—
156	C₄²×C₇₁	—	4	2	no	—
157	C₄²×C₇₁	—	8	2	no	—
158	C₄²×C₇₁	C₂×D₄	1	2	yes	—
159	C₄²×C₇₁	#41	1	2	yes	—
160	C₂³×C₇₁	—	2	2	no	—
161	C₂³×C₇₁	—	4	1	no	—
162	C₂³×C₇₁	—	4	1	no	—
163	C₂³×C₇₁	—	4	2	no	—
164	C₂³×C₇₁	—	4	2	no	—
165	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₇₁	—	2	2	no	—
167	Q₈×C₇₁	—	2	2	no	—
168	Q₈×C₇₁	—	4	1	no	—
169	Q₈×C₇₁	—	4	1	no	—
170	Q₈×C₇₁	—	4	2	no	—
171	Q₈×C₇₁	—	4	2	no	—
172	Q₈×C₇₁	—	4	2	no	—
173	Q₈×C₇₁	—	4	2	no	—
174	D₄×C₇₁	—	2	2	no	—
175	D₄×C₇₁	—	2	2	no	—
176	D₄×C₇₁	—	4	1	no	—
177	D₄×C₇₁	—	4	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	—	2	2	no	—
182	C₂×C₄×C₇₁	—	2	2	no	—
183	C₂×C₄×C₇₁	—	2	2	no	—
184	C₂×C₄×C₇₁	—	2	2	no	—
185	C₂×C₄×C₇₁	—	2	2	no	—
186	C₂×C₄×C₇₁	—	2	2	no	—
187	C₂×C₄×C₇₁	—	4	1	no	—
188	C₂×C₄×C₇₁	—	4	1	no	—
189	C₂×C₄×C₇₁	—	4	2	no	—
190	C₂×C₄×C₇₁	—	4	1	no	—
191	C₂×C₄×C₇₁	—	4	2	no	—
192	C₂×C₄×C₇₁	—	4	2	no	—
193	C₂×C₄×C₇₁	—	4	2	no	—
194	C₂×C₄×C₇₁	—	4	2	no	—
195	C₂×C₄×C₇₁	—	4	2	no	—
196	C₂×C₄×C₇₁	—	4	2	no	—
197	C₂×C₄×C₇₁	—	4	2	no	—
198	C₂×C₄×C₇₁	—	8	4	no	—
199	C₂×C₄×C₇₁	#121	1	2	yes	—
200	C₂×C₄×C₇₁	#121	1	2	yes	—
201	C₂×C₄×C₇₁	#137	1	4	yes	—
202	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
208	C₈×C₇₁	—	2	2	no	—
209	C₈×C₇₁	—	4	1	no	—
210	C₈×C₇₁	—	4	2	no	—
211	C₂²×C₇₁	—	4	2	no	—
212	C₂²×C₇₁	—	4	2	no	—
213	C₂²×C₇₁	—	4	2	no	—
214	C₂²×C₇₁	—	8	2	no	—
215	C₂²×C₇₁	—	8	2	no	—
216	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
217	C₂²×C₇₁	#546	1	1	yes	characteristic
218	C₂²×C₇₁	#550	1	1	yes	characteristic
219	C₂²×C₇₁	C₂×#137	1	2	yes	—
220	C₂²×C₇₁	#577	1	2	yes	—
221	C₄×C₇₁	—	2	2	no	—
222	C₄×C₇₁	—	2	2	no	—
223	C₄×C₇₁	—	2	4	no	—
224	C₄×C₇₁	—	4	2	no	—
225	C₄×C₇₁	—	4	2	no	—
226	C₄×C₇₁	—	4	2	no	—
227	C₄×C₇₁	—	8	2	no	—
228	C₄×C₇₁	—	8	2	no	—
229	C₄×C₇₁	—	8	1	no	—
230	C₄×C₇₁	#525	1	1	yes	characteristic
231	C₄×C₇₁	#535	1	1	yes	characteristic
232	C₄×C₇₁	#553	1	1	yes	characteristic
233	C₄×C₇₁	#555	1	1	yes	characteristic
234	#24646	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₇₁	—	8	2	no	—
236	C₂×C₇₁	#2414	1	1	yes	characteristic
237	C₂×C₇₁	#3039	1	1	yes	characteristic
238	C₂×C₇₁	#3042	1	1	yes	characteristic
239	C₂×C₇₁	#3320	1	2	yes	—
240	C₂×C₇₁	#3400	1	2	yes	—
241	C₂×#461	C₂×C₇₁	1	1	yes	characteristic
242	C₂×#440	C₂×C₇₁	1	1	yes	characteristic
243	#2546	C₂×C₇₁	1	1	yes	characteristic, complemented
244	#2357	C₂×C₇₁	1	1	yes	characteristic
245	#2055	C₂×C₇₁	1	2	yes	—
246	#2013	C₂×C₇₁	1	2	yes	—
247	#1981	C₂×C₇₁	1	2	yes	complemented
248	#1960	C₂×C₇₁	1	1	yes	characteristic, complemented
249	#1940	C₂×C₇₁	1	1	yes	characteristic, complemented
250	#1928	C₂×C₇₁	1	2	yes	complemented
251	#1805	C₂×C₇₁	1	1	yes	characteristic, complemented
252	C₇₁	#24646	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×SD₁₆	C₂²×C₇₁	1	1	yes	characteristic
254	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₇₁	1	2	yes	—
257	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
258	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
259	#461	—	2	4	no	—
260	#440	—	2	4	no	—
261	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
264	C₂×#103	C₂²×C₇₁	1	1	yes	characteristic
265	C₂×#103	C₂²×C₇₁	1	2	yes	—
266	C₂×#103	C₂²×C₇₁	1	2	yes	—
267	C₂×#103	C₂²×C₇₁	1	2	yes	—
268	C₂×#103	C₂²×C₇₁	1	2	yes	—
269	C₂×#102	C₂²×C₇₁	1	1	yes	characteristic
270	C₂×#97	C₂²×C₇₁	1	1	yes	characteristic
271	#398	—	2	1	no	—
272	#398	—	2	1	no	—
273	#391	C₂²×C₇₁	1	2	yes	—
274	#390	C₂²×C₇₁	1	2	yes	—
275	#389	—	2	2	no	—
276	#388	—	2	2	no	—
277	#382	C₂²×C₇₁	1	1	yes	characteristic
278	#381	—	2	1	no	—
279	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
280	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
281	C₄×C₂²⋊C₄	—	2	1	no	—
282	#340	C₂²×C₇₁	1	2	yes	—
283	#336	C₂²×C₇₁	1	2	yes	—
284	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
285	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
286	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
287	C₂³×C₄	—	2	1	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	4	2	no	—
293	C₂×SD₁₆	—	4	2	no	—
294	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
295	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	4	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	4	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	D₄×C₇₁	1	4	yes	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	D₄×C₇₁	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
320	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	4	2	no	—
324	#103	—	2	4	no	—
325	#103	—	2	2	no	—
326	#103	—	2	4	no	—
327	#103	—	4	2	no	—
328	#103	—	4	2	no	—
329	#102	—	2	2	no	—
330	#97	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	1	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	D₄×C₇₁	1	1	yes	characteristic
337	#95	D₄×C₇₁	1	1	yes	characteristic
338	C₂⁴	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	#41×C₇₁	1	2	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	8	2	no	—
364	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
369	SD₁₆	—	2	8	no	—
370	SD₁₆	—	4	8	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	#41×C₇₁	1	2	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	2	no	—
398	C₄²	—	8	2	no	—
399	C₄²	C₂×D₄×C₇₁	1	2	yes	—
400	C₄²	#41×C₇₁	1	2	yes	—
401	C₂³	—	2	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	#121×C₇₁	1	2	yes	—
441	C₂×C₄	#121×C₇₁	1	2	yes	—
442	C₂×C₄	#137×C₇₁	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
447	C₂×C₄	H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
448	C₂×C₄	H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	1	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
458	C₂²	#546×C₇₁	1	1	yes	characteristic
459	C₂²	#550×C₇₁	1	1	yes	characteristic
460	C₂²	C₂×#137×C₇₁	1	2	yes	—
461	C₂²	#577×C₇₁	1	2	yes	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	2	no	—
471	C₄	#525×C₇₁	1	1	yes	characteristic
472	C₄	#535×C₇₁	1	1	yes	characteristic
473	C₄	#553×C₇₁	1	1	yes	characteristic
474	C₄	#555×C₇₁	1	1	yes	characteristic
475	C₂	—	8	2	no	—
476	C₂	C₇₁×#2414	1	1	yes	characteristic
477	C₂	C₇₁×#3039	1	1	yes	characteristic
478	C₂	C₇₁×#3042	1	1	yes	characteristic
479	C₂	C₇₁×#3320	1	2	yes	—
480	C₂	C₇₁×#3400	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
prime radical	C₂²×D₄×C₇₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₄×C₄⋊C₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇₁×#2546	C₂	semidirect
7. C₇₁×#1981	C₂	semidirect
8. C₇₁×#1960	C₂	semidirect
9. C₇₁×#1940	C₂	semidirect
10. C₇₁×#1928	C₂	semidirect
11. C₇₁×#1805	C₂	semidirect
234. #24646	C₇₁	direct (N × H)
243. #2546	C₂×C₇₁	semidirect
247. #1981	C₂×C₇₁	semidirect
248. #1960	C₂×C₇₁	semidirect
249. #1940	C₂×C₇₁	semidirect
250. #1928	C₂×C₇₁	semidirect
251. #1805	C₂×C₇₁	semidirect
252. C₇₁	#24646	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#461×C₇₁	2
C₂×#440×C₇₁	2
C₇₁×#2546	2
C₇₁×#2357	2
C₇₁×#2055	2
C₇₁×#2013	2
C₇₁×#1981	2
C₇₁×#1960	2
C₇₁×#1940	2
C₇₁×#1928	2
C₇₁×#1805	2
#24646	71

Subgroups — C71×#24646 #31845518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#24646 #31845518