Subgroups — C₂×C₈×D₄×D₅₃ #28247920

Order 13568.

3694 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈×D₅₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×#88322	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810688	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
7	C₂×#16810686	C₂	1	2	yes	maximal, complemented
8	C₈×D₄×D₅₃	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₄⋊C₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂²⋊C₈×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₈×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×D₄×D₅₃	C₄	1	1	yes	characteristic
14	C₂³×C₄×D₅₃	C₂²	1	2	yes	—
15	C₂³×#88322	C₂²	1	2	yes	complemented
16	C₂²×C₈×D₅₃	—	2	16	no	—
17	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
19	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
20	C₂²×C₈×D₅₃	C₂²	1	2	yes	complemented
21	C₂²×C₈×D₅₃	C₂²	1	2	yes	complemented
22	C₂²×C₈×D₅₃	C₂²	1	16	yes	complemented
23	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
24	C₂×D₄×Dic₅₃	C₄	1	1	yes	characteristic
25	C₂×#13133179	C₄	1	1	yes	characteristic
26	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
27	C₂×#13133177	C₄	1	2	yes	—
28	C₄×D₄×D₅₃	C₄	1	8	yes	—
29	C₄×D₄×D₅₃	C₂²	1	8	yes	—
30	C₂×C₄⋊C₄×D₅₃	C₄	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×D₅₃	C₄	1	2	yes	—
32	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
33	C₈×D₂₁₂	C₂²	1	8	yes	complemented
34	D₄×#88322	C₂²	1	8	yes	complemented
35	#16810688	C₂²	1	8	yes	complemented
36	C₈×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
37	#16810686	C₂²	1	16	yes	complemented
38	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133146	C₂²	1	2	yes	complemented
40	C₄⋊C₈×D₅₃	C₂²	1	8	yes	complemented
41	C₂×C₂²⋊#88322	C₂²	1	2	yes	complemented
42	C₂×#13133129	C₂²	1	2	yes	complemented
43	C₂×#13133129	C₂²	1	2	yes	complemented
44	C₂²⋊C₈×D₅₃	C₂²	1	16	yes	complemented
45	C₂×C₄×#88322	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₈×D₅₃	C₂²	1	8	yes	complemented
49	C₂³×C₈×C₅₃	C₂²	1	2	yes	complemented
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₅₃	C₂²	1	8	yes	complemented
52	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
54	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂⁴×D₅₃	C₂×C₄	1	2	yes	—
56	C₂²×D₂₁₂	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
58	C₂×D₄×D₅₃	C₈	1	16	yes	direct product factor
59	C₂×D₄×D₅₃	C₂×C₄	1	8	yes	—
60	C₂³×Dic₅₃	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₅₃	—	2	8	no	—
62	C₂²×C₄×D₅₃	—	2	8	no	—
63	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₅₃	C₂×C₄	1	2	yes	—
65	C₂²×C₄×D₅₃	C₂×C₄	1	8	yes	—
66	C₂²×C₄×D₅₃	C₂×C₄	1	2	yes	—
67	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
69	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
70	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
71	C₂²×#88322	—	2	8	no	—
72	C₂²×#88322	C₂³	1	1	yes	characteristic
73	C₂²×#88322	C₂³	1	2	yes	—
74	C₂²×#88322	C₂³	1	1	yes	characteristic
75	C₂²×#88322	C₂³	1	8	yes	complemented
76	C₂×C₈×D₅₃	—	2	8	no	—
77	C₂×C₈×D₅₃	—	2	8	no	—
78	C₂×C₈×D₅₃	—	2	64	no	—
79	C₂×C₈×D₅₃	—	2	8	no	—
80	C₂×C₈×D₅₃	—	2	4	no	—
81	C₂×C₈×D₅₃	D₄	1	8	yes	direct product factor
82	C₂×C₈×D₅₃	C₂³	1	4	yes	—
83	C₂×C₈×D₅₃	C₂³	1	8	yes	—
84	C₂×C₈×D₅₃	C₂³	1	4	yes	—
85	C₂×C₈×D₅₃	C₂³	1	8	yes	complemented
86	C₂×C₈×D₅₃	C₂³	1	8	yes	complemented
87	C₄×D₂₁₂	C₂×C₄	1	4	yes	—
88	C₄×D₂₁₂	C₂³	1	4	yes	—
89	D₄×Dic₅₃	C₂×C₄	1	8	yes	—
90	#13133179	C₂×C₄	1	8	yes	—
91	C₄×C₂²⋊D₅₃	C₂×C₄	1	8	yes	—
92	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
93	#13133177	C₂×C₄	1	16	yes	—
94	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
95	C₂×#11719919	C₂×C₄	1	2	yes	—
96	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
97	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	2	yes	—
98	C₂×#11719921	C₂×C₄	1	2	yes	—
99	C₂×#11719921	C₂×C₄	1	2	yes	—
100	C₂²⋊C₄×D₅₃	C₂×C₄	1	16	yes	—
101	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
104	C₄²×D₅₃	C₂×C₄	1	4	yes	—
105	C₄²×D₅₃	C₂³	1	4	yes	—
106	C₄⋊#88322	C₂³	1	4	yes	complemented
107	#13133146	C₂³	1	8	yes	complemented
108	C₂²⋊#88322	C₂³	1	8	yes	complemented
109	#13133129	C₂³	1	8	yes	complemented
110	#13133129	C₂³	1	8	yes	complemented
111	C₄×#88322	C₂³	1	4	yes	complemented
112	C₈×Dic₅₃	C₂³	1	4	yes	complemented
113	C₈×Dic₅₃	C₂³	1	4	yes	complemented
114	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
116	C₂²×C₈×C₅₃	—	2	8	no	—
117	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₅₃	C₂³	1	8	yes	complemented
121	C₄×D₄×C₅₃	C₂×C₄	1	4	yes	—
122	C₄×D₄×C₅₃	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
125	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
127	C₂²⋊C₈×C₅₃	C₂³	1	8	yes	complemented
128	C₄×C₈×C₅₃	C₂³	1	4	yes	complemented
129	C₂⁴×C₅₃	C₂²×C₄	1	2	yes	—
130	C₂³×D₅₃	—	2	8	no	—
131	C₂³×D₅₃	—	2	8	no	—
132	C₂³×D₅₃	C₂×C₈	1	16	yes	complemented
133	C₂³×D₅₃	C₂²×C₄	1	8	yes	—
134	C₂³×D₅₃	C₂²×C₄	1	2	yes	—
135	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₄×C₅₃	C₂×C₈	1	8	yes	complemented
137	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₅₃	—	2	4	no	—
139	C₂²×C₄×C₅₃	—	2	4	no	—
140	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
146	C₂×C₂²⋊D₅₃	C₂×C₈	1	16	yes	complemented
147	C₂×C₂²⋊D₅₃	C₂²×C₄	1	8	yes	—
148	C₂²×Dic₅₃	—	2	8	no	—
149	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
151	C₂²×Dic₅₃	C₂²×C₄	1	8	yes	—
152	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
154	D₄×D₅₃	C₂×C₈	1	64	yes	direct product factor
155	C₂×D₂₁₂	C₂×C₈	1	8	yes	complemented
156	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
157	C₂×C₄×D₅₃	—	2	8	no	—
158	C₂×C₄×D₅₃	—	2	4	no	—
159	C₂×C₄×D₅₃	—	2	4	no	—
160	C₂×C₄×D₅₃	—	2	4	no	—
161	C₂×C₄×D₅₃	—	2	8	no	—
162	C₂×C₄×D₅₃	—	2	32	no	—
163	C₂×C₄×D₅₃	—	2	16	no	—
164	C₂×C₄×D₅₃	—	2	16	no	—
165	C₂×C₄×D₅₃	C₂×C₈	1	8	yes	complemented
166	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
167	C₂×C₄×D₅₃	C₂²×C₄	1	8	yes	—
168	C₂×C₄×D₅₃	C₂²×C₄	1	8	yes	—
169	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
170	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
171	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
172	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
173	C₂×C₄×D₅₃	#41	1	4	yes	—
174	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
175	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
176	C₂×C₈×C₅₃	—	2	4	no	—
177	C₂×C₈×C₅₃	—	2	2	no	—
178	C₂×C₈×C₅₃	—	2	16	no	—
179	C₂×C₈×C₅₃	C₂×D₄	1	4	yes	complemented
180	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
181	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
182	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
183	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
184	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
185	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
186	C₄²×C₅₃	C₂⁴	1	2	yes	—
187	C₂²⋊Dic₅₃	C₂²×C₄	1	8	yes	—
188	#11719921	C₂²×C₄	1	8	yes	—
189	#11719921	C₂²×C₄	1	8	yes	—
190	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
191	#11719919	C₂²×C₄	1	8	yes	—
192	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
193	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
194	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
195	C₄×Dic₅₃	C₂⁴	1	2	yes	—
196	C₂×#88322	—	2	4	no	—
197	C₂×#88322	—	2	2	no	—
198	C₂×#88322	—	2	16	no	—
199	C₂×#88322	C₂×D₄	1	4	yes	complemented
200	C₂×#88322	C₂⁴	1	2	yes	—
201	C₂×#88322	C₂⁴	1	4	yes	—
202	C₂×#88322	C₂⁴	1	2	yes	—
203	C₈×D₅₃	—	2	16	no	—
204	C₈×D₅₃	—	2	8	no	—
205	C₈×D₅₃	—	2	16	no	—
206	C₈×D₅₃	—	2	16	no	—
207	C₈×D₅₃	C₂×D₄	1	16	yes	direct product factor
208	C₂³×C₅₃	—	2	4	no	—
209	C₂³×C₅₃	—	2	4	no	—
210	C₂³×C₅₃	C₂²×C₈	1	8	yes	complemented
211	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
212	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
213	C₂²×D₅₃	—	2	4	no	—
214	C₂²×D₅₃	—	2	4	no	—
215	C₂²×D₅₃	—	2	16	no	—
216	C₂²×D₅₃	—	2	16	no	—
217	C₂²×D₅₃	—	2	64	no	—
218	C₂²×D₅₃	C₄×D₄	1	4	yes	—
219	C₂²×D₅₃	C₂²×C₈	1	4	yes	—
220	C₂²×D₅₃	C₂²×C₈	1	32	yes	complemented
221	C₂²×D₅₃	C₂²×C₈	1	8	yes	complemented
222	C₂²×D₅₃	#131	1	4	yes	—
223	C₂²×D₅₃	C₂³×C₄	1	4	yes	—
224	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
225	D₄×C₅₃	C₂²×C₈	1	16	yes	complemented
226	C₂×C₄×C₅₃	—	2	4	no	—
227	C₂×C₄×C₅₃	—	2	2	no	—
228	C₂×C₄×C₅₃	—	2	8	no	—
229	C₂×C₄×C₅₃	—	2	4	no	—
230	C₂×C₄×C₅₃	—	2	4	no	—
231	C₂×C₄×C₅₃	C₂²×C₈	1	4	yes	complemented
232	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
233	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
236	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
238	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
239	C₂²⋊D₅₃	C₂²×C₈	1	32	yes	complemented
240	C₂×Dic₅₃	—	2	4	no	—
241	C₂×Dic₅₃	—	2	2	no	—
242	C₂×Dic₅₃	—	2	16	no	—
243	C₂×Dic₅₃	C₄×D₄	1	4	yes	—
244	C₂×Dic₅₃	C₂²×C₈	1	4	yes	complemented
245	C₂×Dic₅₃	C₂³×C₄	1	4	yes	—
246	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
247	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
248	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
249	D₂₁₂	C₂²×C₈	1	16	yes	complemented
250	C₄×D₅₃	—	2	16	no	—
251	C₄×D₅₃	—	2	8	no	—
252	C₄×D₅₃	—	2	8	no	—
253	C₄×D₅₃	—	2	4	no	—
254	C₄×D₅₃	—	2	4	no	—
255	C₄×D₅₃	—	2	16	no	—
256	C₄×D₅₃	C₄×D₄	1	8	yes	—
257	C₄×D₅₃	C₂²×C₈	1	16	yes	complemented
258	C₄×D₅₃	C₂²×D₄	1	4	yes	—
259	C₄×D₅₃	C₂×#41	1	4	yes	—
260	C₈×C₅₃	—	2	4	no	—
261	C₈×C₅₃	—	2	2	no	—
262	C₈×C₅₃	C₂²×D₄	1	4	yes	complemented
263	#88322	—	2	4	no	—
264	#88322	—	2	2	no	—
265	#88322	C₂²×D₄	1	4	yes	complemented
266	C₂²×C₈×D₄	—	53	1	no	maximal, Sylow
267	C₂²×C₅₃	—	2	4	no	—
268	C₂²×C₅₃	—	2	16	no	—
269	C₂²×C₅₃	—	2	4	no	—
270	C₂²×C₅₃	C₂×C₄×D₄	1	2	yes	—
271	C₂²×C₅₃	C₂³×C₈	1	2	yes	—
272	C₂²×C₅₃	C₂³×C₈	1	8	yes	complemented
273	C₂²×C₅₃	C₂×#131	1	2	yes	—
274	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
275	C₂×D₅₃	—	2	4	no	—
276	C₂×D₅₃	—	2	16	no	—
277	C₂×D₅₃	—	2	4	no	—
278	C₂×D₅₃	—	2	64	no	—
279	C₂×D₅₃	C₈×D₄	1	16	yes	direct product factor
280	C₂×D₅₃	C₂×C₄×D₄	1	4	yes	—
281	C₂×D₅₃	C₂³×C₈	1	4	yes	—
282	C₂×D₅₃	C₂³×C₈	1	8	yes	complemented
283	C₂×D₅₃	C₂×#131	1	4	yes	—
284	C₄×C₅₃	—	2	4	no	—
285	C₄×C₅₃	—	2	2	no	—
286	C₄×C₅₃	C₂×C₄×D₄	1	2	yes	—
287	C₄×C₅₃	C₂³×C₈	1	4	yes	complemented
288	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
289	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
290	Dic₅₃	—	2	4	no	—
291	Dic₅₃	—	2	2	no	—
292	Dic₅₃	C₂×C₄×D₄	1	4	yes	—
293	Dic₅₃	C₂³×C₈	1	4	yes	complemented
294	C₂⁴×C₈	—	53	2	no	—
295	C₂²×C₄×D₄	—	53	1	no	—
296	C₂×C₈×D₄	—	53	16	no	—
297	C₂×C₈×D₄	—	53	1	no	—
298	C₂×C₈×D₄	—	53	2	no	—
299	C₂×C₈×D₄	—	53	1	no	—
300	C₂×C₈×D₄	—	53	2	no	—
301	C₂×C₈×D₄	—	53	1	no	—
302	C₂×C₈×D₄	D₅₃	1	1	yes	characteristic, direct product factor
303	C₂²×C₄⋊C₈	—	53	1	no	—
304	C₂²×C₂²⋊C₈	—	53	2	no	—
305	C₂²×C₄×C₈	—	53	1	no	—
306	C₂×C₅₃	—	2	8	no	—
307	C₂×C₅₃	C₂×C₈×D₄	1	4	yes	complemented
308	C₂×C₅₃	C₂²×C₄×D₄	1	1	yes	characteristic
309	C₂×C₅₃	C₂⁴×C₈	1	1	yes	characteristic
310	C₂×C₅₃	C₂²×#131	1	1	yes	characteristic
311	D₅₃	—	2	8	no	—
312	D₅₃	C₂×C₈×D₄	1	8	yes	direct product factor
313	C₂³×D₄	—	53	1	no	—
314	C₂⁴×C₄	—	53	2	no	—
315	C₂³×C₈	—	53	1	no	—
316	C₂³×C₈	—	53	2	no	—
317	C₂³×C₈	—	53	1	no	—
318	C₂³×C₈	—	53	2	no	—
319	C₂³×C₈	—	53	2	no	—
320	C₂³×C₈	—	53	2	no	—
321	C₂³×C₈	—	53	16	no	—
322	C₂³×C₈	—	106	16	no	—
323	C₂³×C₈	C₂×D₅₃	1	2	yes	complemented
324	C₂×C₄×D₄	—	53	1	no	—
325	C₂×C₄×D₄	—	53	2	no	—
326	C₂×C₄×D₄	—	53	8	no	—
327	C₂×C₄×D₄	—	53	8	no	—
328	C₂×C₄×D₄	—	53	1	no	—
329	C₂×C₄×D₄	—	53	2	no	—
330	C₂×C₄×D₄	—	53	1	no	—
331	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
332	C₂²×C₄⋊C₄	—	53	1	no	—
333	C₂²×C₂²⋊C₄	—	53	2	no	—
334	C₂²×C₄²	—	53	1	no	—
335	C₈×D₄	—	53	16	no	—
336	C₈×D₄	—	53	8	no	—
337	C₈×D₄	—	53	8	no	—
338	C₈×D₄	—	53	16	no	—
339	C₈×D₄	—	53	8	no	—
340	C₈×D₄	C₂×D₅₃	1	8	yes	direct product factor
341	C₂×C₄⋊C₈	—	53	2	no	—
342	C₂×C₄⋊C₈	—	53	1	no	—
343	C₂×C₄⋊C₈	—	53	8	no	—
344	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
345	C₂×C₂²⋊C₈	—	53	2	no	—
346	C₂×C₂²⋊C₈	—	53	2	no	—
347	C₂×C₂²⋊C₈	—	53	2	no	—
348	C₂×C₂²⋊C₈	—	53	16	no	—
349	C₂×C₂²⋊C₈	C₂×D₅₃	1	2	yes	complemented
350	C₂×C₄×C₈	—	53	1	no	—
351	C₂×C₄×C₈	—	53	1	no	—
352	C₂×C₄×C₈	—	53	1	no	—
353	C₂×C₄×C₈	—	53	8	no	—
354	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
355	C₅₃	C₂²×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
356	C₂⁵	—	53	2	no	—
357	C₂²×D₄	—	53	2	no	—
358	C₂²×D₄	—	53	8	no	—
359	C₂²×D₄	—	53	16	no	—
360	C₂²×D₄	—	53	1	no	—
361	C₂²×D₄	C₄×D₅₃	1	1	yes	characteristic
362	C₂³×C₄	—	53	1	no	—
363	C₂³×C₄	—	53	1	no	—
364	C₂³×C₄	—	53	2	no	—
365	C₂³×C₄	—	53	1	no	—
366	C₂³×C₄	—	53	2	no	—
367	C₂³×C₄	—	53	2	no	—
368	C₂³×C₄	—	53	8	no	—
369	C₂³×C₄	—	53	8	no	—
370	C₂³×C₄	—	53	2	no	—
371	C₂³×C₄	—	106	8	no	—
372	C₂³×C₄	—	106	8	no	—
373	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
374	C₂²×C₈	—	2	8	no	—
375	C₂²×C₈	—	53	1	no	—
376	C₂²×C₈	—	53	8	no	—
377	C₂²×C₈	—	53	4	no	—
378	C₂²×C₈	—	53	2	no	—
379	C₂²×C₈	—	53	8	no	—
380	C₂²×C₈	—	53	1	no	—
381	C₂²×C₈	—	53	8	no	—
382	C₂²×C₈	—	53	8	no	—
383	C₂²×C₈	—	53	8	no	—
384	C₂²×C₈	—	53	4	no	—
385	C₂²×C₈	—	106	8	no	—
386	C₂²×C₈	—	106	64	no	—
387	C₂²×C₈	—	106	8	no	—
388	C₂²×C₈	—	106	4	no	—
389	C₂²×C₈	—	106	8	no	—
390	C₂²×C₈	—	106	8	no	—
391	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
392	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
393	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
394	C₂²×C₈	C₂²×D₅₃	1	8	yes	complemented
395	C₄×D₄	—	53	8	no	—
396	C₄×D₄	—	53	8	no	—
397	C₄×D₄	—	53	8	no	—
398	C₄×D₄	—	53	8	no	—
399	C₄×D₄	—	53	16	no	—
400	C₄×D₄	—	53	4	no	—
401	C₄×D₄	—	53	4	no	—
402	C₄×D₄	C₄×D₅₃	1	4	yes	—
403	C₄×D₄	C₂²×D₅₃	1	4	yes	—
404	C₂×C₄⋊C₄	—	53	2	no	—
405	C₂×C₄⋊C₄	—	53	1	no	—
406	C₂×C₄⋊C₄	—	53	8	no	—
407	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	53	2	no	—
409	C₂×C₂²⋊C₄	—	53	2	no	—
410	C₂×C₂²⋊C₄	—	53	2	no	—
411	C₂×C₂²⋊C₄	—	53	16	no	—
412	C₂×C₂²⋊C₄	C₄×D₅₃	1	2	yes	—
413	C₂×C₄²	—	53	1	no	—
414	C₂×C₄²	—	53	1	no	—
415	C₂×C₄²	—	53	1	no	—
416	C₂×C₄²	—	53	4	no	—
417	C₂×C₄²	—	53	4	no	—
418	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
419	C₄⋊C₈	—	53	8	no	—
420	C₄⋊C₈	—	53	4	no	—
421	C₄⋊C₈	C₂²×D₅₃	1	4	yes	complemented
422	C₂²⋊C₈	—	53	8	no	—
423	C₂²⋊C₈	—	53	8	no	—
424	C₂²⋊C₈	—	53	8	no	—
425	C₂²⋊C₈	C₂²×D₅₃	1	8	yes	complemented
426	C₄×C₈	—	53	4	no	—
427	C₄×C₈	—	53	4	no	—
428	C₄×C₈	—	53	4	no	—
429	C₄×C₈	C₂²×D₅₃	1	4	yes	complemented
430	C₂⁴	—	53	1	no	—
431	C₂⁴	—	53	16	no	—
432	C₂⁴	—	53	8	no	—
433	C₂⁴	—	53	2	no	—
434	C₂⁴	—	106	8	no	—
435	C₂⁴	—	106	8	no	—
436	C₂⁴	C₂×C₄×D₅₃	1	2	yes	—
437	C₂×D₄	—	53	16	no	—
438	C₂×D₄	—	53	8	no	—
439	C₂×D₄	—	53	64	no	—
440	C₂×D₄	—	53	8	no	—
441	C₂×D₄	—	53	4	no	—
442	C₂×D₄	C₈×D₅₃	1	8	yes	direct product factor
443	C₂×D₄	C₂×C₄×D₅₃	1	4	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	53	1	no	—
447	C₂²×C₄	—	53	1	no	—
448	C₂²×C₄	—	53	8	no	—
449	C₂²×C₄	—	53	4	no	—
450	C₂²×C₄	—	53	2	no	—
451	C₂²×C₄	—	53	4	no	—
452	C₂²×C₄	—	53	4	no	—
453	C₂²×C₄	—	53	2	no	—
454	C₂²×C₄	—	53	1	no	—
455	C₂²×C₄	—	53	2	no	—
456	C₂²×C₄	—	53	8	no	—
457	C₂²×C₄	—	53	4	no	—
458	C₂²×C₄	—	53	8	no	—
459	C₂²×C₄	—	53	8	no	—
460	C₂²×C₄	—	53	4	no	—
461	C₂²×C₄	—	53	4	no	—
462	C₂²×C₄	—	106	16	no	—
463	C₂²×C₄	—	106	8	no	—
464	C₂²×C₄	—	106	32	no	—
465	C₂²×C₄	—	106	16	no	—
466	C₂²×C₄	—	106	4	no	—
467	C₂²×C₄	—	106	8	no	—
468	C₂²×C₄	—	106	8	no	—
469	C₂²×C₄	—	106	4	no	—
470	C₂²×C₄	—	106	4	no	—
471	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
473	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	—
474	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
475	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
476	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
477	C₂×C₈	—	2	4	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	16	no	—
480	C₂×C₈	—	53	4	no	—
481	C₂×C₈	—	53	2	no	—
482	C₂×C₈	—	53	16	no	—
483	C₂×C₈	—	53	2	no	—
484	C₂×C₈	—	53	4	no	—
485	C₂×C₈	—	106	16	no	—
486	C₂×C₈	—	106	16	no	—
487	C₂×C₈	—	106	8	no	—
488	C₂×C₈	—	106	16	no	—
489	C₂×C₈	—	106	4	no	—
490	C₂×C₈	—	106	2	no	—
491	C₂×C₈	—	106	16	no	—
492	C₂×C₈	D₄×D₅₃	1	4	yes	direct product factor
493	C₂×C₈	C₂³×D₅₃	1	2	yes	—
494	C₂×C₈	C₂³×D₅₃	1	4	yes	—
495	C₂×C₈	C₂³×D₅₃	1	2	yes	—
496	C₄⋊C₄	—	53	8	no	—
497	C₄⋊C₄	—	53	4	no	—
498	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
499	C₂²⋊C₄	—	53	8	no	—
500	C₂²⋊C₄	—	53	8	no	—
501	C₂²⋊C₄	—	53	8	no	—
502	C₂²⋊C₄	C₂×C₄×D₅₃	1	8	yes	—
503	C₄²	—	53	4	no	—
504	C₄²	—	53	2	no	—
505	C₄²	—	53	4	no	—
506	C₄²	—	53	2	no	—
507	C₄²	C₂×C₄×D₅₃	1	2	yes	—
508	C₄²	C₂³×D₅₃	1	2	yes	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	53	4	no	—
512	C₂³	—	53	4	no	—
513	C₂³	—	53	4	no	—
514	C₂³	—	53	2	no	—
515	C₂³	—	53	8	no	—
516	C₂³	—	53	32	no	—
517	C₂³	—	53	4	no	—
518	C₂³	—	106	16	no	—
519	C₂³	—	106	16	no	—
520	C₂³	—	106	64	no	—
521	C₂³	—	106	4	no	—
522	C₂³	—	106	4	no	—
523	C₂³	C₂×C₈×D₅₃	1	8	yes	complemented
524	C₂³	C₂²×C₄×D₅₃	1	4	yes	—
525	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
526	D₄	—	53	32	no	—
527	D₄	—	53	16	no	—
528	D₄	C₂×C₈×D₅₃	1	16	yes	direct product factor
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	53	4	no	—
535	C₂×C₄	—	53	4	no	—
536	C₂×C₄	—	53	2	no	—
537	C₂×C₄	—	53	2	no	—
538	C₂×C₄	—	53	8	no	—
539	C₂×C₄	—	53	16	no	—
540	C₂×C₄	—	53	4	no	—
541	C₂×C₄	—	53	4	no	—
542	C₂×C₄	—	53	2	no	—
543	C₂×C₄	—	53	4	no	—
544	C₂×C₄	—	106	16	no	—
545	C₂×C₄	—	106	8	no	—
546	C₂×C₄	—	106	16	no	—
547	C₂×C₄	—	106	16	no	—
548	C₂×C₄	—	106	4	no	—
549	C₂×C₄	—	106	2	no	—
550	C₂×C₄	—	106	8	no	—
551	C₂×C₄	—	106	4	no	—
552	C₂×C₄	—	106	4	no	—
553	C₂×C₄	C₂×C₈×D₅₃	1	4	yes	complemented
554	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
555	C₂×C₄	C₂²×C₄×D₅₃	1	4	yes	—
556	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
557	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
558	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
559	C₂×C₄	#41×D₅₃	1	2	yes	—
560	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
561	C₈	—	2	4	no	—
562	C₈	—	2	2	no	—
563	C₈	—	53	4	no	—
564	C₈	—	106	4	no	—
565	C₈	—	106	2	no	—
566	C₈	C₂×D₄×D₅₃	1	4	yes	direct product factor
567	C₂²	—	2	4	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	2	16	no	—
570	C₂²	—	53	4	no	—
571	C₂²	—	53	4	no	—
572	C₂²	—	53	4	no	—
573	C₂²	—	53	16	no	—
574	C₂²	—	53	8	no	—
575	C₂²	—	106	64	no	—
576	C₂²	—	106	4	no	—
577	C₂²	—	106	4	no	—
578	C₂²	—	106	16	no	—
579	C₂²	C₄×D₄×D₅₃	1	2	yes	—
580	C₂²	C₂²×C₈×D₅₃	1	2	yes	—
581	C₂²	C₂²×C₈×D₅₃	1	8	yes	complemented
582	C₂²	#131×D₅₃	1	2	yes	—
583	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
584	C₄	—	2	4	no	—
585	C₄	—	2	2	no	—
586	C₄	—	53	4	no	—
587	C₄	—	53	4	no	—
588	C₄	—	106	4	no	—
589	C₄	—	106	2	no	—
590	C₄	C₄×D₄×D₅₃	1	2	yes	—
591	C₄	C₂²×C₈×D₅₃	1	4	yes	complemented
592	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
593	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
594	C₂	—	2	8	no	—
595	C₂	—	53	8	no	—
596	C₂	—	106	8	no	—
597	C₂	C₈×D₄×D₅₃	1	4	yes	direct product factor
598	C₂	C₂×C₄×D₄×D₅₃	1	1	yes	characteristic
599	C₂	C₂³×C₈×D₅₃	1	1	yes	characteristic
600	C₂	C₂×#131×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₅₃
commutator	C₂×C₅₃	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₂×C₈×D₄×C₅₃	C₂
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂²×D₄×D₅₃	C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	C₂×C₈×D₄	D₅₃
hypocenter	C₅₃	C₂²×C₈×D₄
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₈×D₅₃	C₂	semidirect
3. C₂×C₈×D₂₁₂	C₂	semidirect
4. C₂×D₄×#88322	C₂	semidirect
5. C₂×#16810688	C₂	semidirect
6. C₂×C₈×C₂²⋊D₅₃	C₂	semidirect
7. C₂×#16810686	C₂	semidirect
8. C₈×D₄×D₅₃	C₂	direct (N × H)
9. C₂×C₄⋊C₈×D₅₃	C₂	semidirect
10. C₂×C₂²⋊C₈×D₅₃	C₂	semidirect
11. C₂×C₄×C₈×D₅₃	C₂	semidirect
12. C₂×C₈×D₄×C₅₃	C₂	semidirect
15. C₂³×#88322	C₂²	semidirect
20. C₂²×C₈×D₅₃	C₂²	semidirect
21. C₂²×C₈×D₅₃	C₂²	semidirect
22. C₂²×C₈×D₅₃	C₂²	semidirect
33. C₈×D₂₁₂	C₂²	semidirect
34. D₄×#88322	C₂²	semidirect
35. #16810688	C₂²	semidirect
36. C₈×C₂²⋊D₅₃	C₂²	semidirect
37. #16810686	C₂²	semidirect
38. C₂×C₄⋊#88322	C₂²	semidirect
39. C₂×#13133146	C₂²	semidirect
40. C₄⋊C₈×D₅₃	C₂²	semidirect
41. C₂×C₂²⋊#88322	C₂²	semidirect
42. C₂×#13133129	C₂²	semidirect
43. C₂×#13133129	C₂²	semidirect
44. C₂²⋊C₈×D₅₃	C₂²	semidirect
45. C₂×C₄×#88322	C₂²	semidirect
46. C₂×C₈×Dic₅₃	C₂²	semidirect
47. C₂×C₈×Dic₅₃	C₂²	semidirect
48. C₄×C₈×D₅₃	C₂²	semidirect
49. C₂³×C₈×C₅₃	C₂²	semidirect
51. C₈×D₄×C₅₃	C₂²	semidirect
52. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
54. C₂×C₄×C₈×C₅₃	C₂²	semidirect
58. C₂×D₄×D₅₃	C₈	direct (N × H)
75. C₂²×#88322	C₂³	semidirect
81. C₂×C₈×D₅₃	D₄	direct (N × H)
85. C₂×C₈×D₅₃	C₂³	semidirect
86. C₂×C₈×D₅₃	C₂³	semidirect
106. C₄⋊#88322	C₂³	semidirect
107. #13133146	C₂³	semidirect
108. C₂²⋊#88322	C₂³	semidirect
109. #13133129	C₂³	semidirect
110. #13133129	C₂³	semidirect
111. C₄×#88322	C₂³	semidirect
112. C₈×Dic₅₃	C₂³	semidirect
113. C₈×Dic₅₃	C₂³	semidirect
120. C₂²×C₈×C₅₃	C₂³	semidirect
126. C₄⋊C₈×C₅₃	C₂³	semidirect
127. C₂²⋊C₈×C₅₃	C₂³	semidirect
128. C₄×C₈×C₅₃	C₂³	semidirect
132. C₂³×D₅₃	C₂×C₈	semidirect
136. C₂×D₄×C₅₃	C₂×C₈	semidirect
146. C₂×C₂²⋊D₅₃	C₂×C₈	semidirect
154. D₄×D₅₃	C₂×C₈	direct (N × H)
155. C₂×D₂₁₂	C₂×C₈	semidirect
165. C₂×C₄×D₅₃	C₂×C₈	semidirect
179. C₂×C₈×C₅₃	C₂×D₄	semidirect
199. C₂×#88322	C₂×D₄	semidirect
207. C₈×D₅₃	C₂×D₄	direct (N × H)
210. C₂³×C₅₃	C₂²×C₈	semidirect
220. C₂²×D₅₃	C₂²×C₈	semidirect
221. C₂²×D₅₃	C₂²×C₈	semidirect
225. D₄×C₅₃	C₂²×C₈	semidirect
231. C₂×C₄×C₅₃	C₂²×C₈	semidirect
239. C₂²⋊D₅₃	C₂²×C₈	semidirect
244. C₂×Dic₅₃	C₂²×C₈	semidirect
249. D₂₁₂	C₂²×C₈	semidirect
257. C₄×D₅₃	C₂²×C₈	semidirect
262. C₈×C₅₃	C₂²×D₄	semidirect
265. #88322	C₂²×D₄	semidirect
272. C₂²×C₅₃	C₂³×C₈	semidirect
279. C₂×D₅₃	C₈×D₄	direct (N × H)
282. C₂×D₅₃	C₂³×C₈	semidirect
287. C₄×C₅₃	C₂³×C₈	semidirect
293. Dic₅₃	C₂³×C₈	semidirect
302. C₂×C₈×D₄	D₅₃	direct (N × H)
307. C₂×C₅₃	C₂×C₈×D₄	semidirect
312. D₅₃	C₂×C₈×D₄	direct (N × H)
323. C₂³×C₈	C₂×D₅₃	semidirect
340. C₈×D₄	C₂×D₅₃	direct (N × H)
344. C₂×C₄⋊C₈	C₂×D₅₃	semidirect
349. C₂×C₂²⋊C₈	C₂×D₅₃	semidirect
354. C₂×C₄×C₈	C₂×D₅₃	semidirect
355. C₅₃	C₂²×C₈×D₄	semidirect
394. C₂²×C₈	C₂²×D₅₃	semidirect
421. C₄⋊C₈	C₂²×D₅₃	semidirect
425. C₂²⋊C₈	C₂²×D₅₃	semidirect
429. C₄×C₈	C₂²×D₅₃	semidirect
442. C₂×D₄	C₈×D₅₃	direct (N × H)
492. C₂×C₈	D₄×D₅₃	direct (N × H)
523. C₂³	C₂×C₈×D₅₃	semidirect
528. D₄	C₂×C₈×D₅₃	direct (N × H)
553. C₂×C₄	C₂×C₈×D₅₃	semidirect
566. C₈	C₂×D₄×D₅₃	direct (N × H)
581. C₂²	C₂²×C₈×D₅₃	semidirect
591. C₄	C₂²×C₈×D₅₃	semidirect
597. C₂	C₈×D₄×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂×C₈×D₂₁₂	2
C₂×D₄×#88322	2
C₂×#16810688	2
C₂×C₈×C₂²⋊D₅₃	2
C₂×#16810686	2
C₈×D₄×D₅₃	2
C₂×C₄⋊C₈×D₅₃	2
C₂×C₂²⋊C₈×D₅₃	2
C₂×C₄×C₈×D₅₃	2
C₂×C₈×D₄×C₅₃	2
C₂²×C₈×D₄	53

Subgroups — C2×C8×D4×D53 #28247920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×D₄×D₅₃ #28247920