Subgroups — C₇₁×#11183 #31832055

Order 18176.

978 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#418×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#418×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#2309	C₂	1	1	yes	maximal, characteristic
4	C₂×#344×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#1740	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×H(3,ℤ/4)×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₇₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
12	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
15	#418×C₇₁	—	2	2	no	—
16	#418×C₇₁	—	2	2	no	—
17	#418×C₇₁	—	2	2	no	—
18	#418×C₇₁	—	2	2	no	—
19	C₂×#102×C₇₁	—	2	2	no	—
20	C₂×#102×C₇₁	C₄	1	4	yes	complemented
21	#390×C₇₁	—	2	2	no	—
22	#390×C₇₁	—	2	2	no	—
23	#379×C₇₁	—	2	2	no	—
24	#344×C₇₁	—	2	2	no	—
25	#342×C₇₁	—	2	2	no	—
26	#339×C₇₁	—	2	2	no	—
27	H(3,ℤ/4)×C₇₁	—	2	2	no	—
28	C₂⁵×C₇₁	—	2	1	no	—
29	C₂²×D₄×C₇₁	—	2	1	no	—
30	C₂²×D₄×C₇₁	—	2	1	no	—
31	C₂²×D₄×C₇₁	—	2	1	no	—
32	C₂²×D₄×C₇₁	—	2	1	no	—
33	C₂²×D₄×C₇₁	—	2	1	no	—
34	C₂²×D₄×C₇₁	—	2	1	no	—
35	C₂²×D₄×C₇₁	—	2	1	no	—
36	C₂²×D₄×C₇₁	—	2	1	no	—
37	C₂²×D₄×C₇₁	—	2	1	no	—
38	C₂²×D₄×C₇₁	—	2	1	no	—
39	C₂²×D₄×C₇₁	—	2	1	no	—
40	C₂²×D₄×C₇₁	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₇₁	D₄	1	2	yes	—
42	C₂²×D₄×C₇₁	D₄	1	2	yes	—
43	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₇₁	—	2	1	no	—
45	C₂×M₁₆×C₇₁	—	2	1	no	—
46	C₂×M₁₆×C₇₁	—	2	1	no	—
47	C₂×M₁₆×C₇₁	—	2	1	no	—
48	C₂×M₁₆×C₇₁	—	2	1	no	—
49	C₂×M₁₆×C₇₁	—	2	1	no	—
50	C₂×M₁₆×C₇₁	—	2	1	no	—
51	C₂×M₁₆×C₇₁	—	2	1	no	—
52	C₂×M₁₆×C₇₁	—	2	1	no	—
53	C₂×M₁₆×C₇₁	—	2	1	no	—
54	C₂×M₁₆×C₇₁	—	2	1	no	—
55	C₂×M₁₆×C₇₁	D₄	1	2	yes	—
56	C₂²×C₈×C₇₁	—	2	1	no	—
57	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
58	#117×C₇₁	—	2	1	no	—
59	#117×C₇₁	—	2	1	no	—
60	#117×C₇₁	—	2	1	no	—
61	#117×C₇₁	—	2	1	no	—
62	#117×C₇₁	—	2	1	no	—
63	#117×C₇₁	—	2	1	no	—
64	#117×C₇₁	—	2	1	no	—
65	#117×C₇₁	—	2	1	no	—
66	#117×C₇₁	—	2	1	no	—
67	#117×C₇₁	—	2	1	no	—
68	#117×C₇₁	—	2	1	no	—
69	#117×C₇₁	—	2	1	no	—
70	#117×C₇₁	—	2	1	no	—
71	#117×C₇₁	—	2	1	no	—
72	#117×C₇₁	—	2	1	no	—
73	#117×C₇₁	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₇₁	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₇₁	D₄	1	2	yes	—
83	C₂×C₄²×C₇₁	—	2	1	no	—
84	C₂×C₄²×C₇₁	—	2	1	no	—
85	C₂×C₄²×C₇₁	—	2	1	no	—
86	C₂×C₄²×C₇₁	D₄	1	2	yes	—
87	#102×C₇₁	—	2	8	no	—
88	#102×C₇₁	—	2	8	no	—
89	C₂⁴×C₇₁	—	2	2	no	—
90	C₂⁴×C₇₁	—	2	2	no	—
91	C₂⁴×C₇₁	—	2	2	no	—
92	C₂⁴×C₇₁	—	4	1	no	—
93	C₂⁴×C₇₁	—	4	1	no	—
94	C₂⁴×C₇₁	—	4	1	no	—
95	C₂⁴×C₇₁	—	4	1	no	—
96	C₂⁴×C₇₁	—	8	4	no	—
97	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₇₁	—	2	2	no	—
99	C₂×D₄×C₇₁	—	2	2	no	—
100	C₂×D₄×C₇₁	—	2	2	no	—
101	C₂×D₄×C₇₁	—	2	2	no	—
102	C₂×D₄×C₇₁	—	2	2	no	—
103	C₂×D₄×C₇₁	—	2	2	no	—
104	C₂×D₄×C₇₁	—	2	2	no	—
105	C₂×D₄×C₇₁	—	2	2	no	—
106	C₂×D₄×C₇₁	—	2	2	no	—
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	—	2	2	no	—
111	C₂×D₄×C₇₁	—	2	2	no	—
112	C₂×D₄×C₇₁	—	2	2	no	—
113	C₂×D₄×C₇₁	—	4	1	no	—
114	C₂×D₄×C₇₁	—	4	1	no	—
115	C₂×D₄×C₇₁	—	4	1	no	—
116	C₂×D₄×C₇₁	—	4	1	no	—
117	C₂×D₄×C₇₁	—	4	1	no	—
118	C₂×D₄×C₇₁	—	4	1	no	—
119	C₂×D₄×C₇₁	—	4	1	no	—
120	C₂×D₄×C₇₁	—	4	1	no	—
121	C₂×D₄×C₇₁	—	4	1	no	—
122	C₂×D₄×C₇₁	—	4	1	no	—
123	C₂×D₄×C₇₁	—	4	1	no	—
124	C₂×D₄×C₇₁	—	4	1	no	—
125	C₂×D₄×C₇₁	C₂²⋊C₄	1	4	yes	—
126	C₂²×C₄×C₇₁	—	2	2	no	—
127	C₂²×C₄×C₇₁	—	2	2	no	—
128	C₂²×C₄×C₇₁	—	2	2	no	—
129	C₂²×C₄×C₇₁	—	4	1	no	—
130	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
137	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
138	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
139	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
140	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
141	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
142	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
143	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
144	M₁₆×C₇₁	—	2	2	no	—
145	M₁₆×C₇₁	—	2	2	no	—
146	M₁₆×C₇₁	—	4	1	no	—
147	M₁₆×C₇₁	—	4	1	no	—
148	M₁₆×C₇₁	—	4	1	no	—
149	M₁₆×C₇₁	—	4	1	no	—
150	M₁₆×C₇₁	—	4	1	no	—
151	M₁₆×C₇₁	—	4	1	no	—
152	C₂×C₈×C₇₁	—	2	2	no	—
153	C₂×C₈×C₇₁	—	2	2	no	—
154	C₂×C₈×C₇₁	—	2	2	no	—
155	C₂×C₈×C₇₁	—	2	2	no	—
156	C₂×C₈×C₇₁	—	4	1	no	—
157	C₂×C₈×C₇₁	—	4	1	no	—
158	C₄⋊C₄×C₇₁	—	2	2	no	—
159	C₄⋊C₄×C₇₁	—	2	2	no	—
160	C₄⋊C₄×C₇₁	—	2	2	no	—
161	C₄⋊C₄×C₇₁	—	4	1	no	—
162	C₄⋊C₄×C₇₁	—	4	1	no	—
163	C₄⋊C₄×C₇₁	—	4	1	no	—
164	C₄⋊C₄×C₇₁	—	4	1	no	—
165	C₄⋊C₄×C₇₁	—	4	1	no	—
166	C₂²⋊C₄×C₇₁	—	2	2	no	—
167	C₂²⋊C₄×C₇₁	—	2	2	no	—
168	C₂²⋊C₄×C₇₁	—	2	2	no	—
169	C₂²⋊C₄×C₇₁	—	4	1	no	—
170	C₂²⋊C₄×C₇₁	—	4	1	no	—
171	C₂²⋊C₄×C₇₁	—	4	1	no	—
172	C₂²⋊C₄×C₇₁	—	4	1	no	—
173	C₂²⋊C₄×C₇₁	—	4	1	no	—
174	C₂²⋊C₄×C₇₁	—	8	8	no	—
175	C₄²×C₇₁	—	2	2	no	—
176	C₄²×C₇₁	—	2	2	no	—
177	C₄²×C₇₁	—	2	2	no	—
178	C₄²×C₇₁	—	4	1	no	—
179	C₄²×C₇₁	—	4	1	no	—
180	C₄²×C₇₁	—	4	1	no	—
181	C₄²×C₇₁	—	4	1	no	—
182	C₄²×C₇₁	—	4	1	no	—
183	C₂³×C₇₁	—	2	4	no	—
184	C₂³×C₇₁	—	4	2	no	—
185	C₂³×C₇₁	—	4	8	no	—
186	C₂³×C₇₁	—	4	2	no	—
187	C₂³×C₇₁	—	4	2	no	—
188	C₂³×C₇₁	—	4	2	no	—
189	C₂³×C₇₁	—	4	2	no	—
190	C₂³×C₇₁	—	4	2	no	—
191	C₂³×C₇₁	—	4	2	no	—
192	C₂³×C₇₁	—	8	4	no	—
193	C₂³×C₇₁	—	8	4	no	—
194	C₂³×C₇₁	—	8	4	no	—
195	C₂³×C₇₁	—	8	4	no	—
196	C₂³×C₇₁	—	8	4	no	—
197	C₂³×C₇₁	—	8	4	no	—
198	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₇₁	#120	1	1	yes	characteristic
200	C₂³×C₇₁	#121	1	1	yes	characteristic
201	C₂³×C₇₁	#121	1	1	yes	characteristic
202	C₂³×C₇₁	#121	1	1	yes	characteristic
203	C₂³×C₇₁	#123	1	1	yes	characteristic
204	C₂³×C₇₁	#124	1	1	yes	characteristic
205	D₄×C₇₁	—	2	4	no	—
206	D₄×C₇₁	—	2	4	no	—
207	D₄×C₇₁	—	4	2	no	—
208	D₄×C₇₁	—	4	2	no	—
209	D₄×C₇₁	—	4	2	no	—
210	D₄×C₇₁	—	4	2	no	—
211	D₄×C₇₁	—	4	2	no	—
212	D₄×C₇₁	—	4	2	no	—
213	C₂×C₄×C₇₁	—	4	4	no	—
214	C₂×C₄×C₇₁	—	4	4	no	—
215	C₂×C₄×C₇₁	—	4	2	no	—
216	C₂×C₄×C₇₁	—	4	2	no	—
217	C₂×C₄×C₇₁	—	4	2	no	—
218	C₂×C₄×C₇₁	—	4	2	no	—
219	C₂×C₄×C₇₁	—	8	2	no	—
220	C₂×C₄×C₇₁	—	8	2	no	—
221	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
223	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
224	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
228	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
229	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
230	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
231	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
232	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
233	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
234	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
235	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
236	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
237	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
238	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
239	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
240	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
241	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
242	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
243	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
244	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
245	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
246	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
247	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
248	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
249	C₈×C₇₁	—	4	2	no	—
250	C₈×C₇₁	—	4	2	no	—
251	C₂²×C₇₁	—	2	2	no	—
252	C₂²×C₇₁	—	2	2	no	—
253	C₂²×C₇₁	—	2	2	no	—
254	C₂²×C₇₁	—	4	1	no	—
255	C₂²×C₇₁	—	4	1	no	—
256	C₂²×C₇₁	—	4	1	no	—
257	C₂²×C₇₁	—	4	1	no	—
258	C₂²×C₇₁	—	4	8	no	—
259	C₂²×C₇₁	—	4	4	no	—
260	C₂²×C₇₁	—	8	4	no	—
261	C₂²×C₇₁	—	8	4	no	—
262	C₂²×C₇₁	—	8	4	no	—
263	C₂²×C₇₁	—	8	4	no	—
264	C₂²×C₇₁	—	8	4	no	—
265	C₂²×C₇₁	—	8	4	no	—
266	C₂²×C₇₁	#386	1	1	yes	characteristic
267	C₂²×C₇₁	#388	1	1	yes	characteristic
268	C₂²×C₇₁	#388	1	1	yes	characteristic
269	C₂²×C₇₁	#394	1	1	yes	characteristic
270	C₂²×C₇₁	#394	1	1	yes	characteristic
271	C₂²×C₇₁	#394	1	1	yes	characteristic
272	C₂²×C₇₁	#397	1	1	yes	characteristic
273	C₄×C₇₁	—	8	2	no	—
274	C₄×C₇₁	—	8	2	no	—
275	C₄×C₇₁	—	8	2	no	—
276	C₄×C₇₁	—	8	2	no	—
277	C₄×C₇₁	#381	1	1	yes	characteristic
278	C₄×C₇₁	#386	1	1	yes	characteristic
279	C₄×C₇₁	#388	1	1	yes	characteristic
280	C₄×C₇₁	#388	1	1	yes	characteristic
281	C₄×C₇₁	#394	1	1	yes	characteristic
282	C₄×C₇₁	#397	1	1	yes	characteristic
283	C₄×C₇₁	#397	1	1	yes	characteristic
284	C₄×C₇₁	#397	1	1	yes	characteristic
285	#11183	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂×C₇₁	—	2	1	no	—
287	C₂×C₇₁	—	2	1	no	—
288	C₂×C₇₁	—	2	1	no	—
289	C₂×C₇₁	—	2	1	no	—
290	C₂×C₇₁	—	2	1	no	—
291	C₂×C₇₁	—	2	1	no	—
292	C₂×C₇₁	—	8	4	no	—
293	C₂×C₇₁	#1440	1	1	yes	characteristic
294	C₂×C₇₁	#1904	1	2	yes	—
295	C₂×#418	C₂×C₇₁	1	1	yes	characteristic
296	C₂×#418	C₂×C₇₁	1	1	yes	characteristic
297	#2309	C₂×C₇₁	1	1	yes	characteristic
298	C₂×#344	C₂×C₇₁	1	1	yes	characteristic, complemented
299	#1740	C₂×C₇₁	1	1	yes	characteristic, complemented
300	#1733	C₂×C₇₁	1	1	yes	characteristic, complemented
301	C₂×H(3,ℤ/4)	C₂×C₇₁	1	1	yes	characteristic, complemented
302	C₇₁	#11183	1	1	yes	characteristic, direct product factor, Sylow
303	C₂³×D₄	C₂²×C₇₁	1	1	yes	characteristic
304	C₂²×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
305	C₂²×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
306	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
307	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
308	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
309	C₂×#117	C₂²×C₇₁	1	1	yes	characteristic
310	#418	—	2	2	no	—
311	#418	—	2	2	no	—
312	#418	—	2	2	no	—
313	#418	—	2	2	no	—
314	C₂×#102	—	2	2	no	—
315	C₂×#102	C₄×C₇₁	1	4	yes	complemented
316	#390	—	2	2	no	—
317	#390	—	2	2	no	—
318	#379	—	2	2	no	—
319	#344	—	2	2	no	—
320	#342	—	2	2	no	—
321	#339	—	2	2	no	—
322	H(3,ℤ/4)	—	2	2	no	—
323	C₂⁵	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	C₂×C₄×C₇₁	1	2	yes	—
336	C₂²×D₄	D₄×C₇₁	1	2	yes	—
337	C₂²×D₄	D₄×C₇₁	1	2	yes	—
338	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	D₄×C₇₁	1	2	yes	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	C₂×C₄×C₇₁	1	2	yes	—
353	#117	—	2	1	no	—
354	#117	—	2	1	no	—
355	#117	—	2	1	no	—
356	#117	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	D₄×C₇₁	1	2	yes	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	8	no	—
377	C₂×C₂²⋊C₄	D₄×C₇₁	1	2	yes	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	D₄×C₇₁	1	2	yes	—
382	#102	—	2	8	no	—
383	#102	—	2	8	no	—
384	C₂⁴	—	2	2	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	4	1	no	—
388	C₂⁴	—	4	1	no	—
389	C₂⁴	—	4	1	no	—
390	C₂⁴	—	4	1	no	—
391	C₂⁴	—	8	4	no	—
392	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	C₂²⋊C₄×C₇₁	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
431	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
432	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
433	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
434	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
435	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
436	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
437	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
438	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	4	1	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	—	4	1	no	—
446	M₁₆	—	4	1	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	4	1	no	—
452	C₂×C₈	—	4	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	8	8	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	4	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	1	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	8	4	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	—	8	4	no	—
493	C₂³	C₄×D₄×C₇₁	1	1	yes	characteristic
494	C₂³	#120×C₇₁	1	1	yes	characteristic
495	C₂³	#121×C₇₁	1	1	yes	characteristic
496	C₂³	#121×C₇₁	1	1	yes	characteristic
497	C₂³	#121×C₇₁	1	1	yes	characteristic
498	C₂³	#123×C₇₁	1	1	yes	characteristic
499	C₂³	#124×C₇₁	1	1	yes	characteristic
500	D₄	—	2	4	no	—
501	D₄	—	2	4	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
517	C₂×C₄	#117×C₇₁	1	1	yes	characteristic
518	C₂×C₄	#117×C₇₁	1	1	yes	characteristic
519	C₂×C₄	C₄×D₄×C₇₁	1	1	yes	characteristic
520	C₂×C₄	C₄×D₄×C₇₁	1	1	yes	characteristic
521	C₂×C₄	C₄×D₄×C₇₁	1	1	yes	characteristic
522	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
523	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
524	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
525	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
526	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
527	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
528	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
529	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
530	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
531	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
532	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
533	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
534	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
535	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
536	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
537	C₂×C₄	#124×C₇₁	1	1	yes	characteristic
538	C₂×C₄	#124×C₇₁	1	1	yes	characteristic
539	C₂×C₄	#124×C₇₁	1	1	yes	characteristic
540	C₂×C₄	#126×C₇₁	1	1	yes	characteristic
541	C₂×C₄	#126×C₇₁	1	1	yes	characteristic
542	C₂×C₄	#126×C₇₁	1	1	yes	characteristic
543	C₂×C₄	#126×C₇₁	1	1	yes	characteristic
544	C₈	—	4	2	no	—
545	C₈	—	4	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	8	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	8	4	no	—
556	C₂²	—	8	4	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	#386×C₇₁	1	1	yes	characteristic
562	C₂²	#388×C₇₁	1	1	yes	characteristic
563	C₂²	#388×C₇₁	1	1	yes	characteristic
564	C₂²	#394×C₇₁	1	1	yes	characteristic
565	C₂²	#394×C₇₁	1	1	yes	characteristic
566	C₂²	#394×C₇₁	1	1	yes	characteristic
567	C₂²	#397×C₇₁	1	1	yes	characteristic
568	C₄	—	8	2	no	—
569	C₄	—	8	2	no	—
570	C₄	—	8	2	no	—
571	C₄	—	8	2	no	—
572	C₄	#381×C₇₁	1	1	yes	characteristic
573	C₄	#386×C₇₁	1	1	yes	characteristic
574	C₄	#388×C₇₁	1	1	yes	characteristic
575	C₄	#388×C₇₁	1	1	yes	characteristic
576	C₄	#394×C₇₁	1	1	yes	characteristic
577	C₄	#397×C₇₁	1	1	yes	characteristic
578	C₄	#397×C₇₁	1	1	yes	characteristic
579	C₄	#397×C₇₁	1	1	yes	characteristic
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	8	4	no	—
587	C₂	C₇₁×#1440	1	1	yes	characteristic
588	C₂	C₇₁×#1904	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₇₁
Frattini, cosocle	C₂³×C₄	C₂³×C₇₁
prime radical	C₂³×D₄×C₇₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂³×C₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#344×C₇₁	C₂	semidirect
5. C₇₁×#1740	C₂	semidirect
6. C₇₁×#1733	C₂	semidirect
7. C₂×H(3,ℤ/4)×C₇₁	C₂	semidirect
20. C₂×#102×C₇₁	C₄	semidirect
285. #11183	C₇₁	direct (N × H)
298. C₂×#344	C₂×C₇₁	semidirect
299. #1740	C₂×C₇₁	semidirect
300. #1733	C₂×C₇₁	semidirect
301. C₂×H(3,ℤ/4)	C₂×C₇₁	semidirect
302. C₇₁	#11183	direct (N × H)
315. C₂×#102	C₄×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#418×C₇₁	2
C₇₁×#2309	2
C₂×#344×C₇₁	2
C₇₁×#1740	2
C₇₁×#1733	2
C₂×H(3,ℤ/4)×C₇₁	2
#11183	71

Subgroups — C71×#11183 #31832055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#11183 #31832055