Subgroups — C₂×C₄×D₈×D₅₃ #28248090

Order 13568.

3694 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810705	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×#11719922	C₂	1	2	yes	maximal, complemented
7	C₂×#16810703	C₂	1	2	yes	maximal, complemented
8	C₄×D₈×D₅₃	C₂	1	16	yes	maximal, direct product factor
9	C₂×#107×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#102×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
14	C₂³×C₄×D₅₃	—	2	2	no	—
15	C₂²×D₄₂₄	C₂²	1	1	yes	characteristic
16	C₂²×#11719922	C₂²	1	2	yes	—
17	C₂×D₈×D₅₃	C₄	1	16	yes	direct product factor
18	C₂×D₈×D₅₃	C₂²	1	8	yes	—
19	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
20	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
22	C₂×D₄×Dic₅₃	C₂²	1	2	yes	complemented
23	C₂×#13133179	C₂²	1	2	yes	complemented
24	C₂×C₄×C₂²⋊D₅₃	—	2	2	no	—
25	C₂×#13133177	—	2	2	no	—
26	C₄×D₄×D₅₃	—	2	8	no	—
27	C₄×D₄×D₅₃	C₂²	1	16	yes	complemented
28	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₄×D₅₃	—	2	2	no	—
30	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
31	C₄×D₄₂₄	C₂²	1	8	yes	complemented
32	D₈×Dic₅₃	C₂²	1	8	yes	complemented
33	#16810705	C₂²	1	8	yes	complemented
34	C₄×#11719922	C₂²	1	16	yes	complemented
35	#16810703	C₂²	1	16	yes	complemented
36	C₂×#13133151	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13133150	C₂²	1	2	yes	complemented
38	#107×D₅₃	C₂²	1	8	yes	complemented
39	C₂×#13133139	C₂²	1	2	yes	complemented
40	C₂×#13133138	C₂²	1	2	yes	complemented
41	C₂×#13133137	C₂²	1	2	yes	complemented
42	#102×D₅₃	C₂²	1	16	yes	complemented
43	C₂×C₄×#88322	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₄×C₈×D₅₃	C₂²	1	8	yes	complemented
47	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
49	C₄×D₈×C₅₃	C₂²	1	8	yes	complemented
50	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
52	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂⁴×D₅₃	—	2	2	no	—
54	C₂²×D₂₁₂	C₂³	1	2	yes	—
55	C₂²×C₂²⋊D₅₃	—	2	2	no	—
56	C₂×D₄×D₅₃	—	2	4	no	—
57	C₂×D₄×D₅₃	—	2	8	no	—
58	C₂×D₄×D₅₃	C₂×C₄	1	16	yes	complemented
59	C₂×D₄×D₅₃	C₂³	1	8	yes	—
60	C₂³×Dic₅₃	—	2	2	no	—
61	C₂²×C₄×D₅₃	—	2	2	no	—
62	C₂²×C₄×D₅₃	—	2	2	no	—
63	C₂²×C₄×D₅₃	—	2	2	no	—
64	C₂²×C₄×D₅₃	—	2	16	no	—
65	C₂²×C₄×D₅₃	—	4	16	no	—
66	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
67	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
68	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
69	C₂×D₄₂₄	C₂×C₄	1	8	yes	complemented
70	C₂×D₄₂₄	C₂³	1	4	yes	—
71	C₂×#11719922	C₂×C₄	1	16	yes	complemented
72	C₂×#11719922	C₂³	1	8	yes	—
73	D₈×D₅₃	C₂×C₄	1	64	yes	direct product factor
74	C₂²×#88322	C₂³	1	1	yes	characteristic
75	C₂²×#88322	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₅₃	—	2	4	no	—
77	C₂×C₈×D₅₃	C₂×C₄	1	8	yes	complemented
78	C₂×C₈×D₅₃	C₂³	1	4	yes	—
79	C₂×C₈×D₅₃	C₂³	1	4	yes	—
80	C₄×D₂₁₂	—	2	4	no	—
81	C₄×D₂₁₂	C₂³	1	8	yes	complemented
82	D₄×Dic₅₃	—	2	4	no	—
83	D₄×Dic₅₃	C₂³	1	8	yes	complemented
84	#13133179	—	2	4	no	—
85	#13133179	C₂³	1	8	yes	complemented
86	C₄×C₂²⋊D₅₃	—	2	16	no	—
87	#13133177	—	2	16	no	—
88	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
89	C₂×#11719919	—	2	2	no	—
90	C₄⋊C₄×D₅₃	—	2	4	no	—
91	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
92	C₂×C₂²⋊Dic₅₃	—	2	2	no	—
93	C₂×#11719921	—	2	2	no	—
94	C₂×#11719921	—	2	2	no	—
95	C₂²⋊C₄×D₅₃	—	2	16	no	—
96	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
97	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
98	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
99	C₄²×D₅₃	D₄	1	4	yes	—
100	C₄²×D₅₃	C₂³	1	4	yes	—
101	#13133151	C₂³	1	4	yes	complemented
102	#13133150	C₂³	1	8	yes	complemented
103	#13133139	C₂³	1	8	yes	complemented
104	#13133138	C₂³	1	8	yes	complemented
105	#13133137	C₂³	1	8	yes	complemented
106	C₄×#88322	C₂³	1	4	yes	complemented
107	C₈×Dic₅₃	C₂³	1	4	yes	complemented
108	C₈×Dic₅₃	C₂³	1	4	yes	complemented
109	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₅₃	—	2	2	no	—
111	C₂×D₈×C₅₃	C₂×C₄	1	8	yes	complemented
112	C₂×D₈×C₅₃	C₂³	1	4	yes	—
113	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₅₃	—	2	4	no	—
116	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
119	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
120	#107×C₅₃	C₂³	1	4	yes	complemented
121	#102×C₅₃	C₂³	1	8	yes	complemented
122	C₄×C₈×C₅₃	C₂³	1	4	yes	complemented
123	C₂⁴×C₅₃	—	2	2	no	—
124	C₂³×D₅₃	—	2	2	no	—
125	C₂³×D₅₃	—	2	16	no	—
126	C₂³×D₅₃	—	2	8	no	—
127	C₂³×D₅₃	—	4	8	no	—
128	C₂³×D₅₃	—	4	8	no	—
129	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₅₃	—	2	2	no	—
131	C₂×D₄×C₅₃	—	2	4	no	—
132	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	complemented
133	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₅₃	—	2	2	no	—
135	C₂²×C₄×C₅₃	—	2	8	no	—
136	C₂²×C₄×C₅₃	—	4	8	no	—
137	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
140	C₂×C₂²⋊D₅₃	—	2	16	no	—
141	C₂×C₂²⋊D₅₃	—	2	8	no	—
142	C₂²×Dic₅₃	—	2	2	no	—
143	C₂²×Dic₅₃	—	2	8	no	—
144	C₂²×Dic₅₃	—	4	8	no	—
145	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
148	D₄×D₅₃	—	2	32	no	—
149	D₄×D₅₃	—	2	16	no	—
150	D₄×D₅₃	C₂²×C₄	1	32	yes	complemented
151	C₂×D₂₁₂	—	2	2	no	—
152	C₂×D₂₁₂	—	2	4	no	—
153	C₂×D₂₁₂	C₂²×C₄	1	8	yes	complemented
154	C₂×D₂₁₂	C₂⁴	1	4	yes	—
155	C₂×C₄×D₅₃	—	2	4	no	—
156	C₂×C₄×D₅₃	—	2	8	no	—
157	C₂×C₄×D₅₃	—	2	8	no	—
158	C₂×C₄×D₅₃	—	2	8	no	—
159	C₂×C₄×D₅₃	—	4	8	no	—
160	C₂×C₄×D₅₃	—	4	8	no	—
161	C₂×C₄×D₅₃	—	4	8	no	—
162	C₂×C₄×D₅₃	—	4	64	no	—
163	C₂×C₄×D₅₃	D₈	1	8	yes	direct product factor
164	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
165	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
166	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
167	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
168	C₂×C₄×D₅₃	#41	1	4	yes	—
169	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
170	D₈×C₅₃	C₂²×C₄	1	16	yes	complemented
171	C₂×C₈×C₅₃	—	2	2	no	—
172	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	complemented
173	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
174	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
175	C₄⋊C₄×C₅₃	—	2	2	no	—
176	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
177	C₂²⋊C₄×C₅₃	—	2	8	no	—
178	C₄²×C₅₃	C₂×D₄	1	2	yes	—
179	C₄²×C₅₃	C₂⁴	1	2	yes	—
180	C₂²⋊Dic₅₃	—	2	8	no	—
181	#11719922	C₂²×C₄	1	32	yes	complemented
182	#11719921	—	2	8	no	—
183	#11719921	—	2	8	no	—
184	C₄⋊Dic₅₃	—	2	2	no	—
185	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
186	#11719919	—	2	8	no	—
187	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
188	C₄×Dic₅₃	C₂×D₄	1	4	yes	—
189	C₄×Dic₅₃	C₂×D₄	1	4	yes	—
190	C₄×Dic₅₃	C₂⁴	1	2	yes	—
191	C₂×#88322	—	2	2	no	—
192	C₂×#88322	C₂²×C₄	1	4	yes	complemented
193	C₂×#88322	C₂⁴	1	2	yes	—
194	C₂×#88322	C₂⁴	1	2	yes	—
195	D₄₂₄	C₂²×C₄	1	16	yes	complemented
196	C₈×D₅₃	—	2	8	no	—
197	C₈×D₅₃	C₂²×C₄	1	16	yes	complemented
198	C₂³×C₅₃	—	2	8	no	—
199	C₂³×C₅₃	—	2	4	no	—
200	C₂³×C₅₃	—	4	4	no	—
201	C₂³×C₅₃	—	4	4	no	—
202	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
203	C₂²×D₅₃	—	2	8	no	—
204	C₂²×D₅₃	—	2	4	no	—
205	C₂²×D₅₃	—	2	32	no	—
206	C₂²×D₅₃	—	4	4	no	—
207	C₂²×D₅₃	—	4	4	no	—
208	C₂²×D₅₃	—	4	16	no	—
209	C₂²×D₅₃	—	4	16	no	—
210	C₂²×D₅₃	—	4	64	no	—
211	C₂²×D₅₃	C₄×D₄	1	4	yes	—
212	C₂²×D₅₃	C₂×D₈	1	4	yes	—
213	C₂²×D₅₃	#135	1	4	yes	—
214	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
215	D₄×C₅₃	—	2	8	no	—
216	D₄×C₅₃	—	2	4	no	—
217	D₄×C₅₃	C₂³×C₄	1	8	yes	complemented
218	C₂×C₄×C₅₃	—	2	2	no	—
219	C₂×C₄×C₅₃	—	2	4	no	—
220	C₂×C₄×C₅₃	—	4	4	no	—
221	C₂×C₄×C₅₃	—	4	16	no	—
222	C₂×C₄×C₅₃	C₂×D₈	1	4	yes	complemented
223	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
228	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
229	C₂²⋊D₅₃	—	2	32	no	—
230	C₂×Dic₅₃	—	2	2	no	—
231	C₂×Dic₅₃	—	2	4	no	—
232	C₂×Dic₅₃	—	4	4	no	—
233	C₂×Dic₅₃	—	4	16	no	—
234	C₂×Dic₅₃	C₄×D₄	1	4	yes	—
235	C₂×Dic₅₃	C₂×D₈	1	4	yes	complemented
236	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
237	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
238	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
239	D₂₁₂	—	2	8	no	—
240	D₂₁₂	—	2	4	no	—
241	D₂₁₂	C₂³×C₄	1	8	yes	complemented
242	C₄×D₅₃	—	2	8	no	—
243	C₄×D₅₃	—	4	16	no	—
244	C₄×D₅₃	—	4	16	no	—
245	C₄×D₅₃	—	4	16	no	—
246	C₄×D₅₃	C₄×D₄	1	8	yes	—
247	C₄×D₅₃	C₂×D₈	1	16	yes	direct product factor
248	C₄×D₅₃	C₂³×C₄	1	4	yes	—
249	C₄×D₅₃	C₂×#41	1	4	yes	—
250	C₈×C₅₃	—	2	2	no	—
251	C₈×C₅₃	C₂³×C₄	1	4	yes	complemented
252	#88322	—	2	2	no	—
253	#88322	C₂³×C₄	1	4	yes	complemented
254	C₂²×C₄×D₈	—	53	1	no	maximal, Sylow
255	C₂²×C₅₃	—	2	8	no	—
256	C₂²×C₅₃	—	4	16	no	—
257	C₂²×C₅₃	—	4	4	no	—
258	C₂²×C₅₃	—	4	4	no	—
259	C₂²×C₅₃	C₂×C₄×D₄	1	2	yes	—
260	C₂²×C₅₃	C₂²×D₈	1	2	yes	—
261	C₂²×C₅₃	C₂×#135	1	2	yes	—
262	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
263	C₂×D₅₃	—	2	8	no	—
264	C₂×D₅₃	—	4	16	no	—
265	C₂×D₅₃	—	4	4	no	—
266	C₂×D₅₃	—	4	4	no	—
267	C₂×D₅₃	—	4	64	no	—
268	C₂×D₅₃	C₄×D₈	1	16	yes	direct product factor
269	C₂×D₅₃	C₂×C₄×D₄	1	4	yes	—
270	C₂×D₅₃	C₂²×D₈	1	4	yes	—
271	C₂×D₅₃	C₂×#135	1	4	yes	—
272	C₄×C₅₃	—	2	2	no	—
273	C₄×C₅₃	—	4	4	no	—
274	C₄×C₅₃	C₂×C₄×D₄	1	2	yes	—
275	C₄×C₅₃	C₂²×D₈	1	4	yes	complemented
276	C₄×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
277	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
278	Dic₅₃	—	2	2	no	—
279	Dic₅₃	—	4	4	no	—
280	Dic₅₃	C₂×C₄×D₄	1	4	yes	—
281	Dic₅₃	C₂²×D₈	1	4	yes	complemented
282	C₂³×D₈	—	53	1	no	—
283	C₂²×C₄×D₄	—	53	2	no	—
284	C₂×C₄×D₈	—	53	16	no	—
285	C₂×C₄×D₈	—	53	1	no	—
286	C₂×C₄×D₈	—	53	2	no	—
287	C₂×C₄×D₈	—	53	1	no	—
288	C₂×C₄×D₈	—	53	1	no	—
289	C₂×C₄×D₈	—	53	2	no	—
290	C₂×C₄×D₈	D₅₃	1	1	yes	characteristic, direct product factor
291	C₂²×#107	—	53	1	no	—
292	C₂²×#102	—	53	2	no	—
293	C₂²×C₄×C₈	—	53	1	no	—
294	C₂×C₅₃	—	4	8	no	—
295	C₂×C₅₃	C₂×C₄×D₈	1	4	yes	complemented
296	C₂×C₅₃	C₂²×C₄×D₄	1	1	yes	characteristic
297	C₂×C₅₃	C₂³×D₈	1	1	yes	characteristic
298	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
299	D₅₃	—	4	8	no	—
300	D₅₃	C₂×C₄×D₈	1	8	yes	direct product factor
301	C₂³×D₄	—	53	2	no	—
302	C₂⁴×C₄	—	106	2	no	—
303	C₂²×D₈	—	53	2	no	—
304	C₂²×D₈	—	53	16	no	—
305	C₂²×D₈	—	53	8	no	—
306	C₂²×D₈	—	53	1	no	—
307	C₂²×D₈	C₂×D₅₃	1	1	yes	characteristic
308	C₂³×C₈	—	53	1	no	—
309	C₂³×C₈	—	53	1	no	—
310	C₂×C₄×D₄	—	53	2	no	—
311	C₂×C₄×D₄	—	53	16	no	—
312	C₂×C₄×D₄	—	53	2	no	—
313	C₂×C₄×D₄	—	53	2	no	—
314	C₂×C₄×D₄	—	106	2	no	—
315	C₂×C₄×D₄	—	106	8	no	—
316	C₂×C₄×D₄	—	106	2	no	—
317	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
318	C₂²×C₄⋊C₄	—	53	2	no	—
319	C₂²×C₂²⋊C₄	—	106	2	no	—
320	C₂²×C₄²	—	53	1	no	—
321	C₄×D₈	—	53	8	no	—
322	C₄×D₈	—	53	16	no	—
323	C₄×D₈	—	53	8	no	—
324	C₄×D₈	—	53	16	no	—
325	C₄×D₈	—	53	8	no	—
326	C₄×D₈	C₂×D₅₃	1	8	yes	direct product factor
327	C₂×#107	—	53	1	no	—
328	C₂×#107	—	53	2	no	—
329	C₂×#107	—	53	8	no	—
330	C₂×#107	C₂×D₅₃	1	1	yes	characteristic, complemented
331	C₂×#102	—	53	2	no	—
332	C₂×#102	—	53	2	no	—
333	C₂×#102	—	53	2	no	—
334	C₂×#102	—	53	16	no	—
335	C₂×#102	C₂×D₅₃	1	2	yes	complemented
336	C₂×C₄×C₈	—	53	1	no	—
337	C₂×C₄×C₈	—	53	1	no	—
338	C₂×C₄×C₈	—	53	1	no	—
339	C₂×C₄×C₈	—	53	8	no	—
340	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
341	C₅₃	C₂²×C₄×D₈	1	1	yes	characteristic, complemented, Sylow
342	C₂⁵	—	106	2	no	—
343	C₂²×D₄	—	53	16	no	—
344	C₂²×D₄	—	53	8	no	—
345	C₂²×D₄	—	53	2	no	—
346	C₂²×D₄	—	106	4	no	—
347	C₂²×D₄	—	106	8	no	—
348	C₂²×D₄	—	106	2	no	—
349	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
350	C₂³×C₄	—	2	2	no	—
351	C₂³×C₄	—	53	1	no	—
352	C₂³×C₄	—	53	1	no	—
353	C₂³×C₄	—	53	1	no	—
354	C₂³×C₄	—	106	2	no	—
355	C₂³×C₄	—	106	16	no	—
356	C₂³×C₄	—	106	2	no	—
357	C₂³×C₄	—	106	2	no	—
358	C₂³×C₄	—	106	2	no	—
359	C₂³×C₄	—	212	16	no	—
360	C₂×D₈	—	53	16	no	—
361	C₂×D₈	—	53	8	no	—
362	C₂×D₈	—	53	64	no	—
363	C₂×D₈	—	53	8	no	—
364	C₂×D₈	—	53	4	no	—
365	C₂×D₈	C₄×D₅₃	1	8	yes	direct product factor
366	C₂×D₈	C₂²×D₅₃	1	4	yes	—
367	C₂²×C₈	—	53	1	no	—
368	C₂²×C₈	—	53	8	no	—
369	C₂²×C₈	—	53	4	no	—
370	C₂²×C₈	—	53	1	no	—
371	C₂²×C₈	—	53	4	no	—
372	C₂²×C₈	—	106	4	no	—
373	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
374	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
375	C₄×D₄	—	2	4	no	—
376	C₄×D₄	—	53	8	no	—
377	C₄×D₄	—	53	8	no	—
378	C₄×D₄	—	53	8	no	—
379	C₄×D₄	—	106	16	no	—
380	C₄×D₄	—	106	4	no	—
381	C₄×D₄	—	106	16	no	—
382	C₄×D₄	—	106	4	no	—
383	C₄×D₄	—	106	4	no	—
384	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
385	C₂×C₄⋊C₄	—	53	2	no	—
386	C₂×C₄⋊C₄	—	53	8	no	—
387	C₂×C₄⋊C₄	—	106	4	no	—
388	C₂×C₄⋊C₄	—	106	2	no	—
389	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	106	16	no	—
392	C₂×C₂²⋊C₄	—	106	2	no	—
393	C₂×C₂²⋊C₄	—	106	2	no	—
394	C₂×C₂²⋊C₄	—	106	2	no	—
395	C₂×C₄²	—	53	1	no	—
396	C₂×C₄²	—	53	1	no	—
397	C₂×C₄²	—	53	1	no	—
398	C₂×C₄²	—	53	4	no	—
399	C₂×C₄²	—	53	4	no	—
400	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
401	#107	—	53	4	no	—
402	#107	—	53	8	no	—
403	#107	C₂²×D₅₃	1	4	yes	complemented
404	#102	—	53	8	no	—
405	#102	—	53	8	no	—
406	#102	—	53	8	no	—
407	#102	C₂²×D₅₃	1	8	yes	complemented
408	C₄×C₈	—	53	4	no	—
409	C₄×C₈	—	53	4	no	—
410	C₄×C₈	—	53	4	no	—
411	C₄×C₈	C₂²×D₅₃	1	4	yes	complemented
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	53	1	no	—
414	C₂⁴	—	106	8	no	—
415	C₂⁴	—	106	16	no	—
416	C₂⁴	—	106	2	no	—
417	C₂⁴	—	212	8	no	—
418	C₂⁴	—	212	8	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	53	32	no	—
422	C₂×D₄	—	53	8	no	—
423	C₂×D₄	—	53	4	no	—
424	C₂×D₄	—	106	32	no	—
425	C₂×D₄	—	106	16	no	—
426	C₂×D₄	—	106	8	no	—
427	C₂×D₄	—	106	16	no	—
428	C₂×D₄	—	106	2	no	—
429	C₂×D₄	—	106	4	no	—
430	C₂×D₄	C₂×C₄×D₅₃	1	8	yes	complemented
431	C₂×D₄	C₂³×D₅₃	1	4	yes	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	8	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	—	53	1	no	—
436	C₂²×C₄	—	53	1	no	—
437	C₂²×C₄	—	53	8	no	—
438	C₂²×C₄	—	53	4	no	—
439	C₂²×C₄	—	53	2	no	—
440	C₂²×C₄	—	53	4	no	—
441	C₂²×C₄	—	53	4	no	—
442	C₂²×C₄	—	53	2	no	—
443	C₂²×C₄	—	53	1	no	—
444	C₂²×C₄	—	53	4	no	—
445	C₂²×C₄	—	106	8	no	—
446	C₂²×C₄	—	106	4	no	—
447	C₂²×C₄	—	106	8	no	—
448	C₂²×C₄	—	106	8	no	—
449	C₂²×C₄	—	106	2	no	—
450	C₂²×C₄	—	106	8	no	—
451	C₂²×C₄	—	212	8	no	—
452	C₂²×C₄	—	212	64	no	—
453	C₂²×C₄	—	212	8	no	—
454	C₂²×C₄	—	212	8	no	—
455	C₂²×C₄	—	212	8	no	—
456	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
458	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
459	D₈	—	53	32	no	—
460	D₈	—	53	16	no	—
461	D₈	C₂×C₄×D₅₃	1	16	yes	direct product factor
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	53	4	no	—
464	C₂×C₈	—	53	2	no	—
465	C₂×C₈	—	53	16	no	—
466	C₂×C₈	—	53	2	no	—
467	C₂×C₈	—	106	8	no	—
468	C₂×C₈	—	106	2	no	—
469	C₂×C₈	C₂×C₄×D₅₃	1	4	yes	complemented
470	C₂×C₈	C₂³×D₅₃	1	2	yes	—
471	C₂×C₈	C₂³×D₅₃	1	2	yes	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	53	4	no	—
474	C₄⋊C₄	—	106	8	no	—
475	C₄⋊C₄	—	106	2	no	—
476	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	106	8	no	—
479	C₂²⋊C₄	—	106	8	no	—
480	C₂²⋊C₄	—	106	8	no	—
481	C₄²	—	53	4	no	—
482	C₄²	—	53	4	no	—
483	C₄²	—	53	2	no	—
484	C₄²	—	53	2	no	—
485	C₄²	D₄×D₅₃	1	2	yes	—
486	C₄²	C₂³×D₅₃	1	2	yes	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	53	4	no	—
492	C₂³	—	53	4	no	—
493	C₂³	—	53	4	no	—
494	C₂³	—	53	2	no	—
495	C₂³	—	106	32	no	—
496	C₂³	—	106	8	no	—
497	C₂³	—	106	4	no	—
498	C₂³	—	212	16	no	—
499	C₂³	—	212	64	no	—
500	C₂³	—	212	16	no	—
501	C₂³	—	212	4	no	—
502	C₂³	—	212	4	no	—
503	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
504	D₄	—	2	8	no	—
505	D₄	—	2	4	no	—
506	D₄	—	53	8	no	—
507	D₄	—	106	32	no	—
508	D₄	—	106	8	no	—
509	D₄	—	106	4	no	—
510	D₄	C₂²×C₄×D₅₃	1	8	yes	complemented
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	16	no	—
515	C₂×C₄	—	53	4	no	—
516	C₂×C₄	—	53	4	no	—
517	C₂×C₄	—	53	2	no	—
518	C₂×C₄	—	53	2	no	—
519	C₂×C₄	—	53	8	no	—
520	C₂×C₄	—	53	16	no	—
521	C₂×C₄	—	53	4	no	—
522	C₂×C₄	—	53	4	no	—
523	C₂×C₄	—	53	2	no	—
524	C₂×C₄	—	106	8	no	—
525	C₂×C₄	—	106	2	no	—
526	C₂×C₄	—	106	4	no	—
527	C₂×C₄	—	212	16	no	—
528	C₂×C₄	—	212	16	no	—
529	C₂×C₄	—	212	16	no	—
530	C₂×C₄	—	212	4	no	—
531	C₂×C₄	—	212	16	no	—
532	C₂×C₄	D₈×D₅₃	1	4	yes	direct product factor
533	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
534	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
535	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
536	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
537	C₂×C₄	#41×D₅₃	1	2	yes	—
538	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
539	C₈	—	2	2	no	—
540	C₈	—	53	4	no	—
541	C₈	—	106	2	no	—
542	C₈	C₂²×C₄×D₅₃	1	4	yes	complemented
543	C₂²	—	2	8	no	—
544	C₂²	—	4	16	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	53	16	no	—
548	C₂²	—	53	4	no	—
549	C₂²	—	53	4	no	—
550	C₂²	—	53	4	no	—
551	C₂²	—	106	8	no	—
552	C₂²	—	212	64	no	—
553	C₂²	—	212	16	no	—
554	C₂²	—	212	4	no	—
555	C₂²	—	212	4	no	—
556	C₂²	C₄×D₄×D₅₃	1	2	yes	—
557	C₂²	C₂×D₈×D₅₃	1	2	yes	—
558	C₂²	#135×D₅₃	1	2	yes	—
559	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	53	4	no	—
563	C₄	—	53	4	no	—
564	C₄	—	106	2	no	—
565	C₄	—	212	4	no	—
566	C₄	C₄×D₄×D₅₃	1	2	yes	—
567	C₄	C₂×D₈×D₅₃	1	4	yes	direct product factor
568	C₄	C₂³×C₄×D₅₃	1	1	yes	characteristic
569	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
570	C₂	—	4	8	no	—
571	C₂	—	53	8	no	—
572	C₂	—	212	8	no	—
573	C₂	C₄×D₈×D₅₃	1	4	yes	direct product factor
574	C₂	C₂×C₄×D₄×D₅₃	1	1	yes	characteristic
575	C₂	C₂²×D₈×D₅₃	1	1	yes	characteristic
576	C₂	C₂×#135×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₄×C₅₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₂×C₄×D₈×C₅₃	C₂
socle	C₂³×C₅₃	C₂²×D₄
prime radical	C₂²×D₈×D₅₃	C₂
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	C₂×C₄×D₈	D₅₃
hypocenter	C₅₃	C₂²×C₄×D₈
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×D₅₃	C₂	semidirect
3. C₂×C₄×D₄₂₄	C₂	semidirect
4. C₂×D₈×Dic₅₃	C₂	semidirect
5. C₂×#16810705	C₂	semidirect
6. C₂×C₄×#11719922	C₂	semidirect
7. C₂×#16810703	C₂	semidirect
8. C₄×D₈×D₅₃	C₂	direct (N × H)
9. C₂×#107×D₅₃	C₂	semidirect
10. C₂×#102×D₅₃	C₂	semidirect
11. C₂×C₄×C₈×D₅₃	C₂	semidirect
12. C₂×C₄×D₈×C₅₃	C₂	semidirect
17. C₂×D₈×D₅₃	C₄	direct (N × H)
21. C₂×C₄×D₂₁₂	C₂²	semidirect
22. C₂×D₄×Dic₅₃	C₂²	semidirect
23. C₂×#13133179	C₂²	semidirect
27. C₄×D₄×D₅₃	C₂²	semidirect
31. C₄×D₄₂₄	C₂²	semidirect
32. D₈×Dic₅₃	C₂²	semidirect
33. #16810705	C₂²	semidirect
34. C₄×#11719922	C₂²	semidirect
35. #16810703	C₂²	semidirect
36. C₂×#13133151	C₂²	semidirect
37. C₂×#13133150	C₂²	semidirect
38. #107×D₅₃	C₂²	semidirect
39. C₂×#13133139	C₂²	semidirect
40. C₂×#13133138	C₂²	semidirect
41. C₂×#13133137	C₂²	semidirect
42. #102×D₅₃	C₂²	semidirect
43. C₂×C₄×#88322	C₂²	semidirect
44. C₂×C₈×Dic₅₃	C₂²	semidirect
45. C₂×C₈×Dic₅₃	C₂²	semidirect
46. C₄×C₈×D₅₃	C₂²	semidirect
48. C₂×C₄×D₄×C₅₃	C₂²	semidirect
49. C₄×D₈×C₅₃	C₂²	semidirect
50. C₂×#107×C₅₃	C₂²	semidirect
51. C₂×#102×C₅₃	C₂²	semidirect
52. C₂×C₄×C₈×C₅₃	C₂²	semidirect
58. C₂×D₄×D₅₃	C₂×C₄	semidirect
69. C₂×D₄₂₄	C₂×C₄	semidirect
71. C₂×#11719922	C₂×C₄	semidirect
73. D₈×D₅₃	C₂×C₄	direct (N × H)
77. C₂×C₈×D₅₃	C₂×C₄	semidirect
81. C₄×D₂₁₂	C₂³	semidirect
83. D₄×Dic₅₃	C₂³	semidirect
85. #13133179	C₂³	semidirect
101. #13133151	C₂³	semidirect
102. #13133150	C₂³	semidirect
103. #13133139	C₂³	semidirect
104. #13133138	C₂³	semidirect
105. #13133137	C₂³	semidirect
106. C₄×#88322	C₂³	semidirect
107. C₈×Dic₅₃	C₂³	semidirect
108. C₈×Dic₅₃	C₂³	semidirect
111. C₂×D₈×C₅₃	C₂×C₄	semidirect
116. C₄×D₄×C₅₃	C₂³	semidirect
120. #107×C₅₃	C₂³	semidirect
121. #102×C₅₃	C₂³	semidirect
122. C₄×C₈×C₅₃	C₂³	semidirect
132. C₂×D₄×C₅₃	C₂²×C₄	semidirect
150. D₄×D₅₃	C₂²×C₄	semidirect
153. C₂×D₂₁₂	C₂²×C₄	semidirect
163. C₂×C₄×D₅₃	D₈	direct (N × H)
170. D₈×C₅₃	C₂²×C₄	semidirect
172. C₂×C₈×C₅₃	C₂²×C₄	semidirect
181. #11719922	C₂²×C₄	semidirect
192. C₂×#88322	C₂²×C₄	semidirect
195. D₄₂₄	C₂²×C₄	semidirect
197. C₈×D₅₃	C₂²×C₄	semidirect
217. D₄×C₅₃	C₂³×C₄	semidirect
222. C₂×C₄×C₅₃	C₂×D₈	semidirect
235. C₂×Dic₅₃	C₂×D₈	semidirect
241. D₂₁₂	C₂³×C₄	semidirect
247. C₄×D₅₃	C₂×D₈	direct (N × H)
251. C₈×C₅₃	C₂³×C₄	semidirect
253. #88322	C₂³×C₄	semidirect
268. C₂×D₅₃	C₄×D₈	direct (N × H)
275. C₄×C₅₃	C₂²×D₈	semidirect
281. Dic₅₃	C₂²×D₈	semidirect
290. C₂×C₄×D₈	D₅₃	direct (N × H)
295. C₂×C₅₃	C₂×C₄×D₈	semidirect
300. D₅₃	C₂×C₄×D₈	direct (N × H)
317. C₂×C₄×D₄	C₂×D₅₃	semidirect
326. C₄×D₈	C₂×D₅₃	direct (N × H)
330. C₂×#107	C₂×D₅₃	semidirect
335. C₂×#102	C₂×D₅₃	semidirect
340. C₂×C₄×C₈	C₂×D₅₃	semidirect
341. C₅₃	C₂²×C₄×D₈	semidirect
365. C₂×D₈	C₄×D₅₃	direct (N × H)
384. C₄×D₄	C₂²×D₅₃	semidirect
403. #107	C₂²×D₅₃	semidirect
407. #102	C₂²×D₅₃	semidirect
411. C₄×C₈	C₂²×D₅₃	semidirect
430. C₂×D₄	C₂×C₄×D₅₃	semidirect
461. D₈	C₂×C₄×D₅₃	direct (N × H)
469. C₂×C₈	C₂×C₄×D₅₃	semidirect
510. D₄	C₂²×C₄×D₅₃	semidirect
532. C₂×C₄	D₈×D₅₃	direct (N × H)
542. C₈	C₂²×C₄×D₅₃	semidirect
567. C₄	C₂×D₈×D₅₃	direct (N × H)
573. C₂	C₄×D₈×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
C₂²×D₈×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₂×C₄×D₄₂₄	2
C₂×D₈×Dic₅₃	2
C₂×#16810705	2
C₂×C₄×#11719922	2
C₂×#16810703	2
C₄×D₈×D₅₃	2
C₂×#107×D₅₃	2
C₂×#102×D₅₃	2
C₂×C₄×C₈×D₅₃	2
C₂×C₄×D₈×C₅₃	2
C₂²×C₄×D₈	53

Subgroups — C2×C4×D8×D53 #28248090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₈×D₅₃ #28248090