Subgroups — #31963084

Order 18176.

742 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22596971	C₂	1	1	yes	maximal, characteristic
2	#22596968	C₂	1	1	yes	maximal, characteristic
3	#431×D₇₁	C₂	1	1	yes	maximal, characteristic
4	#22586641	C₂	1	1	yes	maximal, characteristic, complemented
5	#22586641	C₂	1	1	yes	maximal, characteristic, complemented
6	#22586641	C₂	1	1	yes	maximal, characteristic, complemented
7	#22586639	C₂	1	1	yes	maximal, characteristic, complemented
8	#22586637	C₂	1	1	yes	maximal, characteristic, complemented
9	#22586635	C₂	1	1	yes	maximal, characteristic, complemented
10	#22586635	C₂	1	1	yes	maximal, characteristic, complemented
11	#22586628	C₂	1	1	yes	maximal, characteristic, complemented
12	#22586626	C₂	1	1	yes	maximal, characteristic, complemented
13	#22586619	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#11765848	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄²×D₇₁	C₂²	1	1	yes	characteristic
17	#17986055	C₄	1	2	yes	—
18	#17986054	C₄	1	2	yes	—
19	#17986054	C₄	1	2	yes	—
20	#17986053	C₄	1	2	yes	—
21	#17986052	C₂²	1	1	yes	characteristic
22	#17986052	C₂²	1	1	yes	characteristic
23	#17986051	C₄	1	2	yes	—
24	#17986050	C₂²	1	1	yes	characteristic
25	#17986050	C₂²	1	1	yes	characteristic
26	#17986050	C₂²	1	1	yes	characteristic
27	#17986050	C₂²	1	1	yes	characteristic
28	#17986050	C₂²	1	1	yes	characteristic
29	#17986050	C₂²	1	1	yes	characteristic
30	#17986050	C₂²	1	1	yes	characteristic
31	#17986050	C₂²	1	1	yes	characteristic
32	#17986049	C₄	1	2	yes	—
33	#17986022	C₄	1	2	yes	—
34	#17986021	C₄	1	2	yes	—
35	C₄⋊C₈×D₇₁	C₄	1	2	yes	—
36	#17985962	C₄	1	2	yes	—
37	#17985961	C₄	1	2	yes	—
38	C₂²⋊C₈×D₇₁	C₄	1	2	yes	—
39	C₄×#11765849	C₂²	1	1	yes	characteristic
40	C₄×#11765848	C₂²	1	1	yes	characteristic
41	C₄×#11765848	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
44	#17985721	C₂²	1	1	yes	characteristic, complemented
45	#17985721	C₂²	1	1	yes	characteristic, complemented
46	#17985721	C₂²	1	1	yes	characteristic, complemented
47	#17985721	C₂²	1	1	yes	characteristic, complemented
48	#17985721	C₂²	1	1	yes	characteristic, complemented
49	#17985721	C₂²	1	1	yes	characteristic, complemented
50	#17985720	C₂²	1	1	yes	characteristic, complemented
51	#17985720	C₂²	1	1	yes	characteristic, complemented
52	#17985720	C₂²	1	1	yes	characteristic, complemented
53	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	#431×C₇₁	C₂²	1	1	yes	characteristic
57	#431×C₇₁	C₂²	1	1	yes	characteristic
58	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
59	#322×C₇₁	C₂²	1	1	yes	characteristic, complemented
60	#322×C₇₁	C₂²	1	1	yes	characteristic, complemented
61	#322×C₇₁	C₂²	1	1	yes	characteristic, complemented
62	C₈²×C₇₁	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
66	C₂×#11765849	C₂×C₄	1	2	yes	—
67	C₂×#11765848	C₂×C₄	1	2	yes	—
68	C₂×#11765848	C₂×C₄	1	2	yes	—
69	C₂×C₈×D₇₁	C₂×C₄	1	2	yes	—
70	C₂×C₈×D₇₁	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
79	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
80	C₄²×D₇₁	C₂³	1	1	yes	characteristic
81	C₄²×D₇₁	C₂³	1	1	yes	characteristic
82	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
83	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
84	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
85	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
86	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
87	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
88	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
89	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
90	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
91	Dic₇₁⋊C₈	C₂×C₄	1	2	yes	—
92	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
93	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
94	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
95	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
96	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
97	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
98	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
99	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
100	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
101	(C₂×D₇₁)⋊C₈	C₂×C₄	1	2	yes	—
102	#14556039	C₂×C₄	1	2	yes	—
103	#14556038	C₂×C₄	1	2	yes	—
104	#14556038	C₂×C₄	1	2	yes	—
105	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
106	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
107	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
109	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
111	C₈×Dic₇₁	C₂×C₄	1	2	yes	—
112	C₈×Dic₇₁	C₂×C₄	1	2	yes	—
113	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
114	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
116	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
117	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
118	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
119	#97×C₇₁	C₂×C₄	1	2	yes	—
120	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
126	C₂³×D₇₁	C₄²	1	1	yes	characteristic
127	C₂²×Dic₇₁	C₄²	1	1	yes	characteristic
128	C₂²×Dic₇₁	C₄²	1	1	yes	characteristic
129	C₂²×Dic₇₁	C₄²	1	1	yes	characteristic
130	C₂×C₄×D₇₁	—	2	4	no	—
131	C₂×C₄×D₇₁	—	4	2	no	—
132	C₂×C₄×D₇₁	—	4	2	no	—
133	C₂×C₄×D₇₁	C₄²	1	1	yes	characteristic
134	C₂×C₄×D₇₁	C₄²	1	1	yes	characteristic
135	C₂×C₄×D₇₁	C₄²	1	1	yes	characteristic
136	C₂×C₄×D₇₁	C₄²	1	1	yes	characteristic
137	C₂×C₄×D₇₁	C₄²	1	1	yes	characteristic
138	C₂×C₄×D₇₁	C₄²	1	1	yes	characteristic
139	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
145	#11765849	—	4	2	no	—
146	#11765848	—	2	4	no	—
147	#11765848	—	2	4	no	—
148	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
154	C₈×D₇₁	—	4	2	no	—
155	C₈×D₇₁	—	4	2	no	—
156	C₄×Dic₇₁	C₄²	1	1	yes	characteristic
157	C₄×Dic₇₁	C₄²	1	1	yes	characteristic
158	C₄×Dic₇₁	C₄²	1	1	yes	characteristic
159	C₄×Dic₇₁	C₄²	1	1	yes	characteristic
160	C₄×Dic₇₁	C₄²	1	1	yes	characteristic
161	C₄×Dic₇₁	C₄²	1	1	yes	characteristic
162	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
171	M₁₆×C₇₁	—	4	2	no	—
172	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
178	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
182	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
183	C₂²×D₇₁	—	2	2	no	—
184	C₂²×D₇₁	—	4	1	no	—
185	C₂²×D₇₁	—	4	1	no	—
186	C₂²×D₇₁	C₂×C₄²	1	1	yes	characteristic
187	C₂²×D₇₁	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₇₁	—	2	2	no	—
189	C₂×C₄×C₇₁	—	2	2	no	—
190	C₂×C₄×C₇₁	—	2	2	no	—
191	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
192	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
194	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
197	C₂×Dic₇₁	—	2	2	no	—
198	C₂×Dic₇₁	—	4	1	no	—
199	C₂×Dic₇₁	—	4	1	no	—
200	C₂×Dic₇₁	C₂×C₄²	1	1	yes	characteristic
201	C₂×Dic₇₁	C₂×C₄²	1	1	yes	characteristic
202	C₂×Dic₇₁	C₂×C₄²	1	1	yes	characteristic
203	C₂×Dic₇₁	C₂×C₄²	1	1	yes	characteristic
204	C₂×Dic₇₁	C₂×C₄²	1	1	yes	characteristic
205	C₂×Dic₇₁	C₂×C₄²	1	1	yes	characteristic
206	C₄×D₇₁	—	2	2	no	—
207	C₄×D₇₁	—	2	2	no	—
208	C₄×D₇₁	—	2	2	no	—
209	C₄×D₇₁	—	2	2	no	—
210	C₄×D₇₁	—	2	2	no	—
211	C₄×D₇₁	—	2	2	no	—
212	C₄×D₇₁	—	2	2	no	—
213	C₄×D₇₁	—	4	1	no	—
214	C₄×D₇₁	—	4	1	no	—
215	C₄×D₇₁	—	4	1	no	—
216	C₄×D₇₁	—	4	1	no	—
217	C₄×D₇₁	#131	1	4	yes	—
218	C₈×C₇₁	—	2	2	no	—
219	C₈×C₇₁	—	2	2	no	—
220	C₈×C₇₁	—	2	2	no	—
221	C₈×C₇₁	—	2	2	no	—
222	C₈×C₇₁	—	2	2	no	—
223	C₈×C₇₁	—	2	2	no	—
224	C₇₁⋊C₈	—	2	2	no	—
225	C₇₁⋊C₈	—	2	2	no	—
226	C₇₁⋊C₈	—	2	2	no	—
227	C₇₁⋊C₈	—	2	2	no	—
228	C₇₁⋊C₈	—	2	2	no	—
229	C₇₁⋊C₈	—	2	2	no	—
230	C₂²×C₇₁	—	2	1	no	—
231	C₂²×C₇₁	—	2	1	no	—
232	C₂²×C₇₁	—	2	1	no	—
233	C₂²×C₇₁	C₂²×C₄²	1	1	yes	characteristic
234	C₂×D₇₁	—	2	1	no	—
235	C₂×D₇₁	—	2	1	no	—
236	C₂×D₇₁	—	2	1	no	—
237	C₂×D₇₁	—	2	1	no	—
238	C₂×D₇₁	—	2	1	no	—
239	C₂×D₇₁	—	4	4	no	—
240	C₂×D₇₁	#405	1	2	yes	—
241	C₄×C₇₁	—	2	1	no	—
242	C₄×C₇₁	—	2	1	no	—
243	C₄×C₇₁	—	2	1	no	—
244	C₄×C₇₁	C₂×#131	1	2	yes	—
245	C₄×C₇₁	#568	1	2	yes	—
246	C₄×C₇₁	#568	1	2	yes	—
247	Dic₇₁	—	2	1	no	—
248	Dic₇₁	—	2	1	no	—
249	Dic₇₁	—	2	1	no	—
250	Dic₇₁	—	2	1	no	—
251	Dic₇₁	—	2	1	no	—
252	Dic₇₁	#405	1	2	yes	—
253	#17324	—	71	1	no	maximal, Sylow
254	C₂×C₇₁	—	4	1	no	—
255	C₂×C₇₁	C₂×#405	1	1	yes	characteristic
256	C₂×C₇₁	#2873	1	1	yes	characteristic
257	C₂×C₇₁	#2873	1	1	yes	characteristic
258	D₇₁	—	2	2	no	—
259	D₇₁	—	4	1	no	—
260	#2920	—	71	1	no	—
261	#2920	—	71	1	no	—
262	C₂×#431	—	71	1	no	—
263	#1454	—	71	1	no	—
264	#1454	—	71	1	no	—
265	#1454	—	71	1	no	—
266	#1454	—	71	1	no	—
267	#1453	—	71	1	no	—
268	#1453	—	71	1	no	—
269	#1453	—	71	1	no	—
270	#1453	D₇₁	1	1	yes	characteristic, complemented
271	#1451	—	71	1	no	—
272	#1451	—	71	1	no	—
273	C₈×M₁₆	—	71	1	no	—
274	C₈×M₁₆	—	71	1	no	—
275	C₇₁	#17324	1	1	yes	characteristic, complemented, Sylow
276	C₂²×C₄²	—	71	1	no	—
277	#432	—	71	2	no	—
278	#432	—	71	2	no	—
279	#432	—	71	2	no	—
280	#432	—	71	2	no	—
281	#431	—	71	1	no	—
282	#431	—	71	1	no	—
283	#431	—	71	2	no	—
284	#431	—	71	2	no	—
285	#431	—	71	1	no	—
286	#431	—	71	1	no	—
287	#431	—	71	1	no	—
288	#431	—	71	1	no	—
289	#431	—	71	1	no	—
290	#431	—	71	1	no	—
291	#431	—	71	1	no	—
292	#431	—	71	1	no	—
293	#431	C₂×D₇₁	1	1	yes	characteristic
294	#431	C₂×D₇₁	1	1	yes	characteristic
295	#423	—	71	2	no	—
296	#423	—	71	2	no	—
297	C₂×C₄⋊C₈	—	71	2	no	—
298	#407	—	71	2	no	—
299	#407	—	71	2	no	—
300	C₂×C₂²⋊C₈	—	71	2	no	—
301	C₄×M₁₆	—	71	1	no	—
302	C₄×M₁₆	—	71	1	no	—
303	C₄×M₁₆	—	71	1	no	—
304	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
305	C₂×C₄×C₈	—	71	1	no	—
306	C₂×C₄×C₈	—	71	1	no	—
307	#322	—	71	1	no	—
308	#322	—	71	1	no	—
309	#322	—	71	1	no	—
310	#322	—	71	1	no	—
311	#322	—	71	1	no	—
312	#322	—	71	1	no	—
313	#322	—	71	1	no	—
314	#322	—	71	1	no	—
315	#322	—	71	1	no	—
316	#322	C₂×D₇₁	1	1	yes	characteristic, complemented
317	#322	C₂×D₇₁	1	1	yes	characteristic, complemented
318	#322	C₂×D₇₁	1	1	yes	characteristic, complemented
319	C₈²	—	71	1	no	—
320	C₈²	—	71	1	no	—
321	C₈²	—	71	1	no	—
322	C₈²	C₂×D₇₁	1	1	yes	characteristic, complemented
323	C₂³×C₄	—	71	1	no	—
324	C₂³×C₄	—	71	1	no	—
325	C₂³×C₄	—	71	1	no	—
326	C₂×M₁₆	—	71	2	no	—
327	C₂×M₁₆	—	71	2	no	—
328	C₂×M₁₆	—	71	2	no	—
329	C₂×M₁₆	C₄×D₇₁	1	2	yes	—
330	C₂²×C₈	—	71	2	no	—
331	C₂²×C₈	—	71	2	no	—
332	C₂×C₄²	—	71	1	no	—
333	C₂×C₄²	—	71	1	no	—
334	C₂×C₄²	—	71	1	no	—
335	C₂×C₄²	—	71	1	no	—
336	C₂×C₄²	—	71	1	no	—
337	C₂×C₄²	—	71	1	no	—
338	C₂×C₄²	—	71	1	no	—
339	C₂×C₄²	—	71	1	no	—
340	C₂×C₄²	—	71	1	no	—
341	C₂×C₄²	—	71	1	no	—
342	C₂×C₄²	—	71	1	no	—
343	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
344	C₄⋊C₈	—	71	2	no	—
345	C₄⋊C₈	—	71	2	no	—
346	C₄⋊C₈	—	71	2	no	—
347	C₄⋊C₈	—	71	2	no	—
348	C₄⋊C₈	—	71	2	no	—
349	C₄⋊C₈	—	71	2	no	—
350	C₄⋊C₈	—	71	2	no	—
351	C₄⋊C₈	—	71	2	no	—
352	C₄⋊C₈	—	71	2	no	—
353	C₄⋊C₈	—	71	2	no	—
354	C₄⋊C₈	C₄×D₇₁	1	2	yes	—
355	C₄⋊C₈	C₄×D₇₁	1	2	yes	—
356	C₂²⋊C₈	—	71	2	no	—
357	C₂²⋊C₈	—	71	2	no	—
358	C₂²⋊C₈	—	71	2	no	—
359	C₂²⋊C₈	—	71	2	no	—
360	C₂²⋊C₈	—	71	2	no	—
361	C₂²⋊C₈	—	71	2	no	—
362	C₂²⋊C₈	—	71	2	no	—
363	C₂²⋊C₈	—	71	2	no	—
364	C₂²⋊C₈	—	71	2	no	—
365	C₂²⋊C₈	—	71	2	no	—
366	C₂²⋊C₈	C₄×D₇₁	1	2	yes	—
367	C₂²⋊C₈	C₄×D₇₁	1	2	yes	—
368	#97	—	71	2	no	—
369	#97	—	71	2	no	—
370	#97	—	71	2	no	—
371	#97	C₄×D₇₁	1	2	yes	—
372	C₄×C₈	—	71	2	no	—
373	C₄×C₈	—	71	2	no	—
374	C₄×C₈	—	71	1	no	—
375	C₄×C₈	—	71	1	no	—
376	C₄×C₈	—	71	1	no	—
377	C₄×C₈	—	71	1	no	—
378	C₄×C₈	—	71	1	no	—
379	C₄×C₈	—	71	1	no	—
380	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
381	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
382	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
383	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
384	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
385	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
386	C₂⁴	—	71	1	no	—
387	C₂²×C₄	—	284	2	no	—
388	C₂²×C₄	—	284	2	no	—
389	C₂²×C₄	—	71	1	no	—
390	C₂²×C₄	—	71	1	no	—
391	C₂²×C₄	—	71	1	no	—
392	C₂²×C₄	—	71	1	no	—
393	C₂²×C₄	—	71	1	no	—
394	C₂²×C₄	—	71	1	no	—
395	C₂²×C₄	—	71	1	no	—
396	C₂²×C₄	—	71	1	no	—
397	C₂²×C₄	—	71	1	no	—
398	C₂²×C₄	—	71	1	no	—
399	C₂²×C₄	—	71	1	no	—
400	C₂²×C₄	—	71	1	no	—
401	C₂²×C₄	—	71	1	no	—
402	C₂²×C₄	—	71	1	no	—
403	C₂²×C₄	—	71	1	no	—
404	C₂²×C₄	—	142	4	no	—
405	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
408	M₁₆	—	4	2	no	—
409	M₁₆	—	284	2	no	—
410	M₁₆	—	142	4	no	—
411	M₁₆	—	142	4	no	—
412	C₂×C₈	—	284	2	no	—
413	C₂×C₈	—	284	2	no	—
414	C₂×C₈	—	71	2	no	—
415	C₂×C₈	—	71	2	no	—
416	C₂×C₈	—	71	2	no	—
417	C₂×C₈	—	71	2	no	—
418	C₂×C₈	—	71	2	no	—
419	C₂×C₈	—	71	2	no	—
420	C₂×C₈	C₂×C₄×D₇₁	1	2	yes	—
421	C₂×C₈	C₂×C₄×D₇₁	1	2	yes	—
422	C₂×C₈	C₂×C₄×D₇₁	1	2	yes	—
423	C₂×C₈	C₂×C₄×D₇₁	1	2	yes	—
424	C₂×C₈	C₂×C₄×D₇₁	1	2	yes	—
425	C₂×C₈	C₂×C₄×D₇₁	1	2	yes	—
426	C₄²	—	71	1	no	—
427	C₄²	—	71	1	no	—
428	C₄²	—	71	1	no	—
429	C₄²	—	71	1	no	—
430	C₄²	—	71	1	no	—
431	C₄²	—	71	1	no	—
432	C₄²	—	71	1	no	—
433	C₄²	—	71	1	no	—
434	C₄²	—	71	1	no	—
435	C₄²	—	71	1	no	—
436	C₄²	—	71	1	no	—
437	C₄²	—	71	1	no	—
438	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
439	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
440	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
441	C₄²	C₂³×D₇₁	1	1	yes	characteristic
442	C₂³	—	284	1	no	—
443	C₂³	—	284	1	no	—
444	C₂³	—	71	1	no	—
445	C₂³	—	71	1	no	—
446	C₂³	—	142	2	no	—
447	C₂³	C₄²×D₇₁	1	1	yes	characteristic
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	284	1	no	—
452	C₂×C₄	—	284	1	no	—
453	C₂×C₄	—	284	1	no	—
454	C₂×C₄	—	284	1	no	—
455	C₂×C₄	—	284	1	no	—
456	C₂×C₄	—	284	1	no	—
457	C₂×C₄	—	71	1	no	—
458	C₂×C₄	—	71	4	no	—
459	C₂×C₄	—	71	1	no	—
460	C₂×C₄	—	71	1	no	—
461	C₂×C₄	—	71	1	no	—
462	C₂×C₄	—	71	1	no	—
463	C₂×C₄	—	71	1	no	—
464	C₂×C₄	—	142	2	no	—
465	C₂×C₄	—	142	2	no	—
466	C₂×C₄	—	142	2	no	—
467	C₂×C₄	—	142	2	no	—
468	C₂×C₄	—	142	2	no	—
469	C₂×C₄	—	142	2	no	—
470	C₂×C₄	—	142	2	no	—
471	C₂×C₄	—	142	2	no	—
472	C₂×C₄	C₄²×D₇₁	1	1	yes	characteristic
473	C₂×C₄	C₄²×D₇₁	1	1	yes	characteristic
474	C₂×C₄	C₄²×D₇₁	1	1	yes	characteristic
475	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	142	2	no	—
485	C₈	—	142	2	no	—
486	C₈	—	142	2	no	—
487	C₈	—	142	2	no	—
488	C₈	—	142	2	no	—
489	C₈	—	142	2	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	284	4	no	—
494	C₂²	—	71	2	no	—
495	C₂²	—	142	1	no	—
496	C₂²	—	142	1	no	—
497	C₂²	—	142	1	no	—
498	C₂²	—	142	1	no	—
499	C₂²	—	142	1	no	—
500	C₂²	C₂×C₄²×D₇₁	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	71	2	no	—
505	C₄	—	142	1	no	—
506	C₄	—	142	1	no	—
507	C₄	—	142	1	no	—
508	C₄	—	142	1	no	—
509	C₄	—	142	1	no	—
510	C₄	#131×D₇₁	1	2	yes	—
511	C₄	#17986764	1	2	yes	—
512	C₄	#17986765	1	2	yes	—
513	C₂	—	4	1	no	—
514	C₂	—	284	1	no	—
515	C₂	—	142	2	no	—
516	C₂	#405×D₇₁	1	1	yes	characteristic
517	C₂	#22596756	1	1	yes	characteristic
518	C₂	#22596757	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂²×C₄²
Fitting	C₇₁×#1453	C₂
prime radical	C₂³×D₇₁	C₄²
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1453	D₇₁
hypocenter	C₇₁	#17324
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ #1453

Complements

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

N	H ≅ G/N	type
4. #22586641	C₂	semidirect
5. #22586641	C₂	semidirect
6. #22586641	C₂	semidirect
7. #22586639	C₂	semidirect
8. #22586637	C₂	semidirect
9. #22586635	C₂	semidirect
10. #22586635	C₂	semidirect
11. #22586628	C₂	semidirect
12. #22586626	C₂	semidirect
13. #22586619	C₂	semidirect
14. C₈×#11765848	C₂	semidirect
15. C₇₁×#1453	C₂	semidirect
44. #17985721	C₂²	semidirect
45. #17985721	C₂²	semidirect
46. #17985721	C₂²	semidirect
47. #17985721	C₂²	semidirect
48. #17985721	C₂²	semidirect
49. #17985721	C₂²	semidirect
50. #17985720	C₂²	semidirect
51. #17985720	C₂²	semidirect
52. #17985720	C₂²	semidirect
53. C₈×C₇₁⋊C₈	C₂²	semidirect
54. C₈×C₇₁⋊C₈	C₂²	semidirect
55. C₈×C₇₁⋊C₈	C₂²	semidirect
59. #322×C₇₁	C₂²	semidirect
60. #322×C₇₁	C₂²	semidirect
61. #322×C₇₁	C₂²	semidirect
62. C₈²×C₇₁	C₂²	semidirect
270. #1453	D₇₁	semidirect
275. C₇₁	#17324	semidirect
316. #322	C₂×D₇₁	semidirect
317. #322	C₂×D₇₁	semidirect
318. #322	C₂×D₇₁	semidirect
322. C₈²	C₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22596971	2
#22596968	2
#431×D₇₁	2
#22586641	2
#22586639	2
#22586637	2
#22586635	2
#22586628	2
#22586626	2
#22586619	2
C₈×#11765848	2
C₇₁×#1453	2
#17324	71