Subgroups — #32017014

Order 18176.

810 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22588955	C₂	1	1	yes	maximal, characteristic, complemented
2	#22588948	C₂	1	1	yes	maximal, characteristic, complemented
3	#22588906	C₂	1	1	yes	maximal, characteristic, complemented
4	#22588899	C₂	1	1	yes	maximal, characteristic, complemented
5	#22588633	C₂	1	1	yes	maximal, characteristic
6	#22588633	C₂	1	1	yes	maximal, characteristic
7	#22588485	C₂	1	1	yes	maximal, characteristic, complemented
8	#22588411	C₂	1	1	yes	maximal, characteristic, complemented
9	#22588320	C₂	1	1	yes	maximal, characteristic, complemented
10	#22588118	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²⋊C₄×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#22588106	C₂	1	1	yes	maximal, characteristic, complemented
13	#22588092	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17985754	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2290	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×#14556039	C₂²	1	1	yes	characteristic
27	C₂×#14556039	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
30	#17985754	C₂²	1	1	yes	characteristic
31	#17985754	C₂²	1	1	yes	characteristic
32	#17985754	C₂²	1	1	yes	characteristic
33	#17985754	C₂²	1	1	yes	characteristic
34	#17985754	C₂²	1	1	yes	characteristic
35	#17985754	C₂²	1	1	yes	characteristic
36	#17985754	C₂²	1	1	yes	characteristic
37	#17985754	C₂²	1	1	yes	characteristic
38	#17985754	C₂²	1	1	yes	characteristic
39	#17985754	C₂²	1	1	yes	characteristic
40	#17985754	C₂²	1	1	yes	characteristic
41	#17985754	C₂²	1	1	yes	characteristic
42	#17985754	C₂²	1	1	yes	characteristic
43	#17985754	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
45	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
47	#388×C₇₁	C₄	1	1	yes	characteristic
48	#388×C₇₁	C₄	1	1	yes	characteristic
49	#387×C₇₁	C₄	1	1	yes	characteristic
50	#387×C₇₁	C₄	1	1	yes	characteristic
51	#386×C₇₁	C₄	1	1	yes	characteristic
52	#386×C₇₁	C₄	1	1	yes	characteristic
53	#385×C₇₁	C₄	1	1	yes	characteristic
54	#385×C₇₁	C₄	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
58	#376×C₇₁	C₂²	1	1	yes	characteristic
59	C₂²×C₇₁⋊C₈	—	2	2	no	—
60	C₂²×C₇₁⋊C₈	—	2	2	no	—
61	C₂²×C₇₁⋊C₈	—	2	2	no	—
62	C₂²×C₇₁⋊C₈	—	2	2	no	—
63	C₂²×C₇₁⋊C₈	—	4	1	no	—
64	C₂²×C₇₁⋊C₈	—	4	1	no	—
65	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
73	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
74	C₄⋊(C₇₁⋊C₈)	—	4	1	no	—
75	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₇₁⋊C₈)	—	4	1	no	—
80	C₂²⋊(C₇₁⋊C₈)	—	4	1	no	—
81	#14556039	—	2	2	no	—
82	#14556039	—	4	1	no	—
83	C₄×C₇₁⋊C₈	—	2	2	no	—
84	C₄×C₇₁⋊C₈	—	4	1	no	—
85	C₂²×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
87	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
88	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₇₁	—	2	2	no	—
91	C₄×D₄×C₇₁	—	2	2	no	—
92	#117×C₇₁	—	4	1	no	—
93	#117×C₇₁	—	4	1	no	—
94	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₇₁	—	4	1	no	—
108	C₂×C₄²×C₇₁	—	4	1	no	—
109	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
116	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
117	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
118	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
119	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
120	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
121	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
122	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
123	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
124	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
125	#95×C₇₁	C₂×C₄	1	1	yes	characteristic
126	C₂×C₇₁⋊C₈	—	2	1	no	—
127	C₂×C₇₁⋊C₈	—	2	1	no	—
128	C₂×C₇₁⋊C₈	—	2	1	no	—
129	C₂×C₇₁⋊C₈	—	2	1	no	—
130	C₂×C₇₁⋊C₈	—	2	1	no	—
131	C₂×C₇₁⋊C₈	—	2	1	no	—
132	C₂×C₇₁⋊C₈	—	2	1	no	—
133	C₂×C₇₁⋊C₈	—	2	1	no	—
134	C₂×C₇₁⋊C₈	—	2	1	no	—
135	C₂×C₇₁⋊C₈	—	2	1	no	—
136	C₂×C₇₁⋊C₈	—	2	1	no	—
137	C₂×C₇₁⋊C₈	—	2	1	no	—
138	C₂×C₇₁⋊C₈	—	2	1	no	—
139	C₂×C₇₁⋊C₈	—	2	1	no	—
140	C₂×C₇₁⋊C₈	—	2	1	no	—
141	C₂×C₇₁⋊C₈	—	2	1	no	—
142	C₂×C₇₁⋊C₈	—	2	1	no	—
143	C₂×C₇₁⋊C₈	—	2	1	no	—
144	C₂×C₇₁⋊C₈	—	2	1	no	—
145	C₂×C₇₁⋊C₈	—	2	1	no	—
146	C₂×C₇₁⋊C₈	—	2	1	no	—
147	C₂×C₇₁⋊C₈	—	2	1	no	—
148	C₂×C₇₁⋊C₈	—	4	4	no	—
149	C₂×C₇₁⋊C₈	—	4	4	no	—
150	C₂×C₇₁⋊C₈	#41	1	2	yes	—
151	C₂×C₇₁⋊C₈	#41	1	2	yes	—
152	C₂⁴×C₇₁	C₂²×C₄	1	1	yes	characteristic
153	C₂⁴×C₇₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₄×C₇₁	—	2	2	no	—
155	C₂×D₄×C₇₁	—	2	2	no	—
156	C₂×D₄×C₇₁	—	2	2	no	—
157	C₂²×C₄×C₇₁	—	2	1	no	—
158	C₂²×C₄×C₇₁	—	2	1	no	—
159	C₂²×C₄×C₇₁	—	2	1	no	—
160	C₂²×C₄×C₇₁	—	2	1	no	—
161	C₂²×C₄×C₇₁	—	2	2	no	—
162	C₂²×C₄×C₇₁	—	2	2	no	—
163	C₂²×C₄×C₇₁	—	2	2	no	—
164	C₂²×C₄×C₇₁	—	2	1	no	—
165	C₂²×C₄×C₇₁	—	2	1	no	—
166	C₂²×C₄×C₇₁	—	2	1	no	—
167	C₂²×C₄×C₇₁	—	2	1	no	—
168	C₂²×C₄×C₇₁	—	2	1	no	—
169	C₂²×C₄×C₇₁	—	2	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	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₇₁	#41	1	2	yes	—
186	C₂²×C₄×C₇₁	#41	1	2	yes	—
187	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
188	C₄⋊C₄×C₇₁	—	2	2	no	—
189	C₄⋊C₄×C₇₁	—	2	2	no	—
190	C₄⋊C₄×C₇₁	—	4	1	no	—
191	C₄⋊C₄×C₇₁	—	4	1	no	—
192	C₄⋊C₄×C₇₁	—	4	1	no	—
193	C₂²⋊C₄×C₇₁	—	2	2	no	—
194	C₂²⋊C₄×C₇₁	—	2	2	no	—
195	C₂²⋊C₄×C₇₁	—	2	2	no	—
196	C₂²⋊C₄×C₇₁	—	2	2	no	—
197	C₂²⋊C₄×C₇₁	—	2	2	no	—
198	C₂²⋊C₄×C₇₁	—	4	1	no	—
199	C₂²⋊C₄×C₇₁	—	4	1	no	—
200	C₂²⋊C₄×C₇₁	—	4	1	no	—
201	C₄²×C₇₁	—	2	1	no	—
202	C₄²×C₇₁	—	2	1	no	—
203	C₄²×C₇₁	—	2	1	no	—
204	C₄²×C₇₁	—	2	1	no	—
205	C₄²×C₇₁	—	2	1	no	—
206	C₄²×C₇₁	—	2	1	no	—
207	C₄²×C₇₁	—	2	1	no	—
208	C₄²×C₇₁	—	2	1	no	—
209	C₄²×C₇₁	—	2	1	no	—
210	C₄²×C₇₁	—	2	1	no	—
211	C₄²×C₇₁	—	4	1	no	—
212	C₄²×C₇₁	—	4	1	no	—
213	C₂³×C₇₁	—	2	1	no	—
214	C₂³×C₇₁	—	2	1	no	—
215	C₂³×C₇₁	—	2	1	no	—
216	C₂³×C₇₁	—	2	1	no	—
217	C₂³×C₇₁	—	2	1	no	—
218	C₂³×C₇₁	—	2	1	no	—
219	C₂³×C₇₁	—	2	1	no	—
220	C₂³×C₇₁	—	2	1	no	—
221	C₂³×C₇₁	—	2	1	no	—
222	C₂³×C₇₁	—	2	1	no	—
223	C₂³×C₇₁	—	2	1	no	—
224	C₂³×C₇₁	#117	1	2	yes	—
225	C₂³×C₇₁	#131	1	2	yes	—
226	C₂³×C₇₁	#131	1	2	yes	—
227	C₂³×C₇₁	C₂³×C₄	1	1	yes	characteristic
228	D₄×C₇₁	—	4	4	no	—
229	C₂×C₄×C₇₁	—	2	1	no	—
230	C₂×C₄×C₇₁	—	2	1	no	—
231	C₂×C₄×C₇₁	—	2	1	no	—
232	C₂×C₄×C₇₁	—	2	1	no	—
233	C₂×C₄×C₇₁	—	2	2	no	—
234	C₂×C₄×C₇₁	—	2	2	no	—
235	C₂×C₄×C₇₁	—	2	2	no	—
236	C₂×C₄×C₇₁	—	2	2	no	—
237	C₂×C₄×C₇₁	—	2	1	no	—
238	C₂×C₄×C₇₁	—	2	1	no	—
239	C₂×C₄×C₇₁	—	2	1	no	—
240	C₂×C₄×C₇₁	—	2	1	no	—
241	C₂×C₄×C₇₁	—	2	1	no	—
242	C₂×C₄×C₇₁	—	2	1	no	—
243	C₂×C₄×C₇₁	—	2	1	no	—
244	C₂×C₄×C₇₁	—	2	1	no	—
245	C₂×C₄×C₇₁	—	2	1	no	—
246	C₂×C₄×C₇₁	—	2	1	no	—
247	C₂×C₄×C₇₁	—	2	1	no	—
248	C₂×C₄×C₇₁	—	2	1	no	—
249	C₂×C₄×C₇₁	—	2	1	no	—
250	C₂×C₄×C₇₁	—	2	1	no	—
251	C₂×C₄×C₇₁	—	2	1	no	—
252	C₂×C₄×C₇₁	—	2	1	no	—
253	C₂×C₄×C₇₁	—	2	1	no	—
254	C₂×C₄×C₇₁	—	2	1	no	—
255	C₂×C₄×C₇₁	—	2	1	no	—
256	C₂×C₄×C₇₁	—	2	1	no	—
257	C₂×C₄×C₇₁	—	2	1	no	—
258	C₂×C₄×C₇₁	—	2	1	no	—
259	C₂×C₄×C₇₁	—	2	1	no	—
260	C₂×C₄×C₇₁	—	2	1	no	—
261	C₂×C₄×C₇₁	—	2	1	no	—
262	C₂×C₄×C₇₁	—	2	1	no	—
263	C₂×C₄×C₇₁	—	2	1	no	—
264	C₂×C₄×C₇₁	—	2	1	no	—
265	C₂×C₄×C₇₁	—	2	1	no	—
266	C₂×C₄×C₇₁	—	2	1	no	—
267	C₂×C₄×C₇₁	—	4	4	no	—
268	C₂×C₄×C₇₁	—	4	4	no	—
269	C₂×C₄×C₇₁	—	4	1	no	—
270	C₂×C₄×C₇₁	—	4	1	no	—
271	C₂×C₄×C₇₁	—	4	1	no	—
272	C₂×C₄×C₇₁	—	4	1	no	—
273	C₂×C₄×C₇₁	#117	1	2	yes	—
274	C₂×C₄×C₇₁	#131	1	2	yes	—
275	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
281	C₇₁⋊C₈	—	2	2	no	—
282	C₇₁⋊C₈	—	2	2	no	—
283	C₇₁⋊C₈	—	4	1	no	—
284	C₇₁⋊C₈	—	4	1	no	—
285	C₇₁⋊C₈	—	4	1	no	—
286	C₇₁⋊C₈	—	4	1	no	—
287	C₇₁⋊C₈	—	4	1	no	—
288	C₇₁⋊C₈	—	4	1	no	—
289	C₂²×C₇₁	—	2	2	no	—
290	C₂²×C₇₁	—	2	2	no	—
291	C₂²×C₇₁	—	2	2	no	—
292	C₂²×C₇₁	—	2	2	no	—
293	C₂²×C₇₁	—	2	2	no	—
294	C₂²×C₇₁	—	2	2	no	—
295	C₂²×C₇₁	—	4	1	no	—
296	C₂²×C₇₁	—	4	1	no	—
297	C₂²×C₇₁	—	4	1	no	—
298	C₂²×C₇₁	—	4	1	no	—
299	C₂²×C₇₁	—	4	1	no	—
300	C₂²×C₇₁	—	4	1	no	—
301	C₂²×C₇₁	—	4	1	no	—
302	C₂²×C₇₁	#433	1	4	yes	—
303	C₂²×C₇₁	C₂×#117	1	1	yes	characteristic
304	C₂²×C₇₁	C₄×#41	1	1	yes	characteristic
305	C₂²×C₇₁	#518	1	1	yes	characteristic
306	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
307	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
308	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
309	C₂²×C₇₁	#568	1	1	yes	characteristic
310	C₄×C₇₁	—	2	2	no	—
311	C₄×C₇₁	—	2	2	no	—
312	C₄×C₇₁	—	4	1	no	—
313	C₄×C₇₁	—	4	1	no	—
314	C₄×C₇₁	—	4	1	no	—
315	C₄×C₇₁	—	4	1	no	—
316	C₄×C₇₁	—	4	1	no	—
317	C₄×C₇₁	—	4	1	no	—
318	C₄×C₇₁	—	4	1	no	—
319	C₄×C₇₁	—	4	1	no	—
320	C₄×C₇₁	—	4	1	no	—
321	C₄×C₇₁	—	4	1	no	—
322	C₄×C₇₁	#551	1	1	yes	characteristic
323	C₄×C₇₁	#551	1	1	yes	characteristic
324	C₄×C₇₁	#553	1	1	yes	characteristic
325	C₄×C₇₁	#553	1	1	yes	characteristic
326	#22791	—	71	1	no	maximal, Sylow
327	C₂×C₇₁	—	2	4	no	—
328	C₂×C₇₁	—	8	1	no	—
329	C₂×C₇₁	#2353	1	1	yes	characteristic
330	C₂×C₇₁	C₂×#433	1	1	yes	characteristic
331	C₂×C₇₁	#2925	1	1	yes	characteristic
332	C₂×C₇₁	#2966	1	1	yes	characteristic
333	C₂×C₇₁	#2968	1	1	yes	characteristic
334	C₂×C₇₁	#2976	1	1	yes	characteristic
335	C₂×C₇₁	#2977	1	1	yes	characteristic
336	#2290	D₇₁	1	1	yes	characteristic
337	#1924	—	71	1	no	—
338	#1923	—	71	1	no	—
339	#1917	—	71	1	no	—
340	#1916	—	71	1	no	—
341	#1869	—	71	1	no	—
342	#1869	—	71	1	no	—
343	#1840	—	71	1	no	—
344	#1818	—	71	1	no	—
345	#1797	—	71	1	no	—
346	#1752	—	71	1	no	—
347	C₈×C₂²⋊C₄	—	71	1	no	—
348	#1750	—	71	1	no	—
349	#1746	—	71	1	no	—
350	C₂×#336	—	71	1	no	—
351	C₇₁	#22791	1	1	yes	characteristic, complemented, Sylow
352	C₂³×C₈	—	71	1	no	—
353	C₂³×C₈	—	71	1	no	—
354	C₂×C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
355	C₂×#117	C₂×D₇₁	1	1	yes	characteristic
356	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
357	C₂×C₄⋊C₈	—	71	1	no	—
358	C₂×C₄⋊C₈	—	71	1	no	—
359	C₂×C₂²⋊C₈	—	71	1	no	—
360	C₂×C₂²⋊C₈	—	71	1	no	—
361	C₂×C₂²⋊C₈	—	71	1	no	—
362	C₂×C₂²⋊C₈	—	71	1	no	—
363	C₂×C₂²⋊C₈	—	71	1	no	—
364	C₂×C₂²⋊C₈	—	71	1	no	—
365	C₂×#97	—	71	1	no	—
366	C₂×#97	—	71	1	no	—
367	C₂×C₄×C₈	—	71	1	no	—
368	C₂×C₄×C₈	—	71	1	no	—
369	#388	Dic₇₁	1	1	yes	characteristic
370	#388	Dic₇₁	1	1	yes	characteristic
371	#387	Dic₇₁	1	1	yes	characteristic
372	#387	Dic₇₁	1	1	yes	characteristic
373	#386	Dic₇₁	1	1	yes	characteristic
374	#386	Dic₇₁	1	1	yes	characteristic
375	#385	Dic₇₁	1	1	yes	characteristic
376	#385	Dic₇₁	1	1	yes	characteristic
377	C₄×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂×D₇₁	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	C₂×D₇₁	1	1	yes	characteristic
380	#376	C₂×D₇₁	1	1	yes	characteristic
381	#336	—	71	1	no	—
382	#336	—	71	1	no	—
383	#336	—	71	1	no	—
384	#336	—	71	1	no	—
385	#336	—	71	1	no	—
386	#336	—	71	1	no	—
387	#336	—	71	1	no	—
388	#336	—	71	1	no	—
389	#336	—	71	1	no	—
390	#336	—	71	1	no	—
391	#336	—	71	1	no	—
392	#336	—	71	1	no	—
393	#336	—	71	1	no	—
394	#336	—	71	1	no	—
395	C₂²×D₄	C₂×Dic₇₁	1	1	yes	characteristic
396	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
397	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
398	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
399	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
400	C₂²×C₈	—	284	1	no	—
401	C₂²×C₈	—	284	1	no	—
402	C₂²×C₈	—	71	1	no	—
403	C₂²×C₈	—	71	1	no	—
404	C₂²×C₈	—	71	1	no	—
405	C₂²×C₈	—	71	1	no	—
406	C₂²×C₈	—	71	1	no	—
407	C₂²×C₈	—	71	1	no	—
408	C₂²×C₈	—	71	1	no	—
409	C₂²×C₈	—	71	1	no	—
410	C₂²×C₈	—	142	2	no	—
411	C₂²×C₈	—	142	2	no	—
412	C₂²×C₈	—	142	2	no	—
413	C₂²×C₈	—	142	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	#117	—	4	1	no	—
417	#117	—	4	1	no	—
418	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
431	C₂×C₄²	—	4	1	no	—
432	C₂×C₄²	—	4	1	no	—
433	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
434	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
435	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
436	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
437	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
439	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
440	C₄⋊C₈	—	284	1	no	—
441	C₄⋊C₈	—	284	1	no	—
442	C₂²⋊C₈	—	284	1	no	—
443	C₂²⋊C₈	—	284	1	no	—
444	C₂²⋊C₈	—	142	2	no	—
445	C₂²⋊C₈	—	142	2	no	—
446	C₂²⋊C₈	—	142	2	no	—
447	C₂²⋊C₈	—	142	2	no	—
448	#97	—	284	1	no	—
449	#97	—	142	2	no	—
450	C₄×C₈	—	284	1	no	—
451	C₄×C₈	—	142	2	no	—
452	#95	C₂×Dic₇₁	1	1	yes	characteristic
453	#95	C₂×Dic₇₁	1	1	yes	characteristic
454	#95	C₂×Dic₇₁	1	1	yes	characteristic
455	#95	C₂×Dic₇₁	1	1	yes	characteristic
456	#95	C₂×Dic₇₁	1	1	yes	characteristic
457	#95	C₂×Dic₇₁	1	1	yes	characteristic
458	#95	C₂×Dic₇₁	1	1	yes	characteristic
459	#95	C₂×Dic₇₁	1	1	yes	characteristic
460	#95	C₂×Dic₇₁	1	1	yes	characteristic
461	#95	C₂×Dic₇₁	1	1	yes	characteristic
462	C₂⁴	C₂²×Dic₇₁	1	1	yes	characteristic
463	C₂⁴	C₂²×Dic₇₁	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
484	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
485	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
493	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
494	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
495	C₂²×C₄	#11765865	1	2	yes	—
496	C₂²×C₄	#11765865	1	2	yes	—
497	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
498	C₂×C₈	—	284	4	no	—
499	C₂×C₈	—	284	4	no	—
500	C₂×C₈	—	71	2	no	—
501	C₂×C₈	—	71	2	no	—
502	C₂×C₈	—	142	1	no	—
503	C₂×C₈	—	142	1	no	—
504	C₂×C₈	—	142	1	no	—
505	C₂×C₈	—	142	1	no	—
506	C₂×C₈	—	142	1	no	—
507	C₂×C₈	—	142	1	no	—
508	C₂×C₈	—	142	1	no	—
509	C₂×C₈	—	142	1	no	—
510	C₂×C₈	—	142	1	no	—
511	C₂×C₈	—	142	1	no	—
512	C₂×C₈	—	142	1	no	—
513	C₂×C₈	—	142	1	no	—
514	C₂×C₈	—	142	1	no	—
515	C₂×C₈	—	142	1	no	—
516	C₂×C₈	—	142	1	no	—
517	C₂×C₈	—	142	1	no	—
518	C₂×C₈	—	142	1	no	—
519	C₂×C₈	—	142	1	no	—
520	C₂×C₈	—	142	1	no	—
521	C₂×C₈	—	142	1	no	—
522	C₂×C₈	—	142	1	no	—
523	C₂×C₈	—	142	1	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	4	1	no	—
548	C₄²	—	4	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	#14556087	1	2	yes	—
561	C₂³	#14556135	1	2	yes	—
562	C₂³	#14556135	1	2	yes	—
563	C₂³	C₂³×Dic₇₁	1	1	yes	characteristic
564	D₄	—	4	4	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	4	4	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	#14556087	1	2	yes	—
610	C₂×C₄	#14556135	1	2	yes	—
611	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
612	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
613	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
614	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
615	C₂×C₄	#14556173	1	1	yes	characteristic
616	C₂×C₄	#14556173	1	1	yes	characteristic
617	C₈	—	284	1	no	—
618	C₈	—	284	1	no	—
619	C₈	—	284	1	no	—
620	C₈	—	284	1	no	—
621	C₈	—	284	1	no	—
622	C₈	—	284	1	no	—
623	C₈	—	142	2	no	—
624	C₈	—	142	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	#17986060	1	4	yes	—
639	C₂²	C₂×#14556087	1	1	yes	characteristic
640	C₂²	#41×Dic₇₁	1	1	yes	characteristic
641	C₂²	#17986474	1	1	yes	characteristic
642	C₂²	C₂×#14556135	1	1	yes	characteristic
643	C₂²	C₂×#14556135	1	1	yes	characteristic
644	C₂²	C₂×#14556135	1	1	yes	characteristic
645	C₂²	#17986766	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	#17986678	1	1	yes	characteristic
659	C₄	#17986678	1	1	yes	characteristic
660	C₄	#17986698	1	1	yes	characteristic
661	C₄	#17986698	1	1	yes	characteristic
662	C₂	—	2	4	no	—
663	C₂	—	8	1	no	—
664	C₂	#22591280	1	1	yes	characteristic
665	C₂	C₂×#17986060	1	1	yes	characteristic
666	C₂	#22597006	1	1	yes	characteristic
667	C₂	#22597316	1	1	yes	characteristic
668	C₂	#22597336	1	1	yes	characteristic
669	C₂	#22597388	1	1	yes	characteristic
670	C₂	#22597396	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₁
commutator, socle	C₂³×C₇₁	C₂³×C₄
Fitting	C₇₁×#2290	C₂
prime radical	C₂²×D₄×C₇₁	C₂×C₄
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	#2290	D₇₁
hypocenter	C₇₁	#22791
LCS	G ▷ C₂³×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₄ ◁ #2290

Complements

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

N	H ≅ G/N	type
1. #22588955	C₂	semidirect
2. #22588948	C₂	semidirect
3. #22588906	C₂	semidirect
4. #22588899	C₂	semidirect
7. #22588485	C₂	semidirect
8. #22588411	C₂	semidirect
9. #22588320	C₂	semidirect
10. #22588118	C₂	semidirect
11. C₂²⋊C₄×C₇₁⋊C₈	C₂	semidirect
12. #22588106	C₂	semidirect
13. #22588092	C₂	semidirect
14. C₂×#17985754	C₂	semidirect
351. C₇₁	#22791	semidirect

Maximal subgroups

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

subgroup	index
#22588955	2
#22588948	2
#22588906	2
#22588899	2
#22588633	2
#22588485	2
#22588411	2
#22588320	2
#22588118	2
C₂²⋊C₄×C₇₁⋊C₈	2
#22588106	2
#22588092	2
C₂×#17985754	2
C₇₁×#2290	2
#22791	71