Subgroups — D₅₃⋊#2168 #28328298

Order 13568.

754 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₅₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#20291098	C₂	1	2	yes	maximal, complemented
4	#20291097	C₂	1	2	yes	maximal, complemented
5	#20291096	C₂	1	2	yes	maximal, complemented
6	#20291095	C₂	1	2	yes	maximal, complemented
7	D₅₃⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#20290916	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133292	C₂²	1	2	yes	complemented
13	D₅₃⋊M₃₂	—	2	4	no	—
14	C₂×#13133291	C₂²	1	2	yes	complemented
15	C₂×D₅₃⋊C₁₆	—	2	4	no	—
16	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×D₅₃⋊C₁₆	C₂²	1	2	yes	complemented
21	C₂²×#11719910	C₂²	1	2	yes	complemented
22	#16811544	C₂²	1	2	yes	complemented
23	C₄⋊#11719910	C₂²	1	2	yes	complemented
24	#16811518	C₂²	1	2	yes	complemented
25	#16811518	C₂²	1	2	yes	complemented
26	C₂²⋊#11719910	C₂²	1	2	yes	complemented
27	C₂²⋊#11719910	C₂²	1	2	yes	complemented
28	#16811512	C₂²	1	2	yes	complemented
29	#16811511	C₂²	1	2	yes	complemented
30	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	C₄×D₄×D₅₃	C₄	1	1	yes	characteristic
33	C₈×D₂₁₂	C₄	1	1	yes	characteristic
34	D₄×#88322	C₂²	1	1	yes	characteristic
35	#16810688	C₂²	1	1	yes	characteristic
36	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
37	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
38	#16810686	C₂²	1	1	yes	characteristic
39	#16810686	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₅₃	C₄	1	1	yes	characteristic
41	C₂²⋊C₈×D₅₃	C₄	1	1	yes	characteristic
42	C₂²⋊C₈×D₅₃	C₄	1	1	yes	characteristic
43	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
44	C₈×D₄×C₅₃	C₄	1	1	yes	characteristic
45	#13133292	—	2	4	no	—
46	#13133291	—	2	4	no	—
47	D₅₃⋊C₁₆	—	2	2	no	—
48	D₅₃⋊C₁₆	—	2	2	no	—
49	D₅₃⋊C₁₆	—	2	2	no	—
50	D₅₃⋊C₁₆	—	2	4	no	—
51	D₅₃⋊C₁₆	D₄	1	4	yes	complemented
52	C₂×#11719910	—	2	4	no	—
53	C₂×#11719910	C₂³	1	2	yes	—
54	C₂×#11719910	C₂³	1	2	yes	—
55	C₂×#11719910	C₂³	1	2	yes	—
56	C₂×#11719910	C₂³	1	2	yes	—
57	C₂×D₄×D₅₃	C₈	1	1	yes	characteristic
58	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×#88322	C₂³	1	1	yes	characteristic
61	C₂²×#88322	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₅₃	—	2	2	no	—
63	C₂×C₈×D₅₃	—	2	2	no	—
64	C₂×C₈×D₅₃	—	2	2	no	—
65	C₂×C₈×D₅₃	—	2	2	no	—
66	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
74	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
75	D₄×Dic₅₃	C₈	1	1	yes	characteristic
76	#13133179	C₈	1	1	yes	characteristic
77	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
79	#13133177	C₈	1	1	yes	characteristic
80	#13133177	C₈	1	1	yes	characteristic
81	C₄⋊C₄×D₅₃	C₈	1	1	yes	characteristic
82	C₂²⋊C₄×D₅₃	C₈	1	1	yes	characteristic
83	C₂²⋊C₄×D₅₃	C₈	1	1	yes	characteristic
84	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
85	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
86	#13133146	C₂×C₄	1	1	yes	characteristic
87	#13133146	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
90	#13133129	C₂×C₄	1	1	yes	characteristic
91	#13133129	C₂×C₄	1	1	yes	characteristic
92	#13133129	C₂×C₄	1	1	yes	characteristic
93	#13133129	C₂×C₄	1	1	yes	characteristic
94	C₄×#88322	C₂³	1	1	yes	characteristic
95	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
105	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
106	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
110	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
111	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
113	D₄×D₅₃	—	2	4	no	—
114	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₅₃	—	2	2	no	—
116	C₂×C₄×D₅₃	—	2	2	no	—
117	C₂×C₄×D₅₃	—	2	2	no	—
118	C₂×C₄×D₅₃	—	2	2	no	—
119	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
124	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	—	2	2	no	—
129	C₂×C₈×C₅₃	—	2	2	no	—
130	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
135	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
136	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
137	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
139	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
140	#11719921	C₂×C₈	1	1	yes	characteristic
141	#11719921	C₂×C₈	1	1	yes	characteristic
142	#11719921	C₂×C₈	1	1	yes	characteristic
143	#11719921	C₂×C₈	1	1	yes	characteristic
144	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
145	#11719919	C₂×C₈	1	1	yes	characteristic
146	#11719919	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×#88322	—	2	1	no	—
151	C₂×#88322	—	2	1	no	—
152	C₂×#88322	—	2	1	no	—
153	C₂×#88322	—	2	1	no	—
154	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
155	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
156	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
157	C₂×#88322	C₂⁴	1	1	yes	characteristic
158	C₈×D₅₃	—	2	2	no	—
159	C₈×D₅₃	—	2	2	no	—
160	C₈×D₅₃	—	2	2	no	—
161	C₈×D₅₃	—	2	2	no	—
162	C₈×D₅₃	—	2	2	no	—
163	C₈×D₅₃	—	2	1	no	—
164	C₈×D₅₃	—	2	1	no	—
165	C₈×D₅₃	—	2	1	no	—
166	C₈×D₅₃	—	2	1	no	—
167	C₈×D₅₃	C₂×D₄	1	2	yes	—
168	C₈×D₅₃	#41	1	2	yes	—
169	#11719910	—	2	2	no	—
170	#11719910	—	2	2	no	—
171	#11719910	—	2	2	no	—
172	#11719910	C₂×D₄	1	4	yes	complemented
173	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
174	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
175	C₂²×D₅₃	—	2	2	no	—
176	C₂²×D₅₃	—	2	2	no	—
177	C₂²×D₅₃	—	2	2	no	—
178	C₂²×D₅₃	—	2	2	no	—
179	C₂²×D₅₃	—	2	2	no	—
180	C₂²×D₅₃	M₃₂	1	4	yes	complemented
181	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
182	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
183	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
184	D₄×C₅₃	—	2	2	no	—
185	C₂×C₄×C₅₃	—	2	1	no	—
186	C₂×C₄×C₅₃	—	2	1	no	—
187	C₂×C₄×C₅₃	—	2	1	no	—
188	C₂×C₄×C₅₃	—	2	1	no	—
189	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
190	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
191	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
192	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
194	C₂²⋊D₅₃	—	2	2	no	—
195	C₂²⋊D₅₃	—	2	2	no	—
196	C₂×Dic₅₃	—	2	2	no	—
197	C₂×Dic₅₃	—	2	2	no	—
198	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
201	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
202	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
203	D₂₁₂	—	2	2	no	—
204	C₄×D₅₃	—	2	2	no	—
205	C₄×D₅₃	—	2	2	no	—
206	C₄×D₅₃	—	2	2	no	—
207	C₄×D₅₃	—	2	2	no	—
208	C₄×D₅₃	—	2	1	no	—
209	C₄×D₅₃	—	2	1	no	—
210	C₄×D₅₃	—	2	1	no	—
211	C₄×D₅₃	—	2	1	no	—
212	C₄×D₅₃	—	2	2	no	—
213	C₄×D₅₃	—	2	2	no	—
214	C₄×D₅₃	C₄×D₄	1	2	yes	—
215	C₄×D₅₃	#131	1	2	yes	—
216	C₈×C₅₃	—	2	1	no	—
217	C₈×C₅₃	—	2	1	no	—
218	C₈×C₅₃	—	2	1	no	—
219	C₈×C₅₃	C₄×D₄	1	2	yes	—
220	#88322	—	2	1	no	—
221	#88322	—	2	1	no	—
222	#88322	—	2	1	no	—
223	#88322	C₂²×D₄	1	1	yes	characteristic
224	#88322	C₂×#41	1	1	yes	characteristic
225	C₂×#2168	—	53	1	no	maximal, Sylow
226	C₂²×C₅₃	—	2	1	no	—
227	C₂²×C₅₃	—	2	1	no	—
228	C₂²×C₅₃	—	2	1	no	—
229	C₂²×C₅₃	—	2	1	no	—
230	C₂²×C₅₃	—	2	1	no	—
231	C₂²×C₅₃	C₂×M₃₂	1	2	yes	complemented
232	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
233	C₂×D₅₃	—	2	1	no	—
234	C₂×D₅₃	—	2	1	no	—
235	C₂×D₅₃	—	2	8	no	—
236	C₂×D₅₃	—	2	1	no	—
237	C₂×D₅₃	—	2	1	no	—
238	C₂×D₅₃	—	2	1	no	—
239	C₂×D₅₃	—	4	4	no	—
240	C₂×D₅₃	C₈×D₄	1	2	yes	—
241	C₂×D₅₃	C₂×M₃₂	1	2	yes	—
242	C₂×D₅₃	C₂×M₃₂	1	2	yes	complemented
243	C₂×D₅₃	#504	1	2	yes	—
244	C₄×C₅₃	—	2	1	no	—
245	C₄×C₅₃	—	2	1	no	—
246	C₄×C₅₃	—	2	1	no	—
247	C₄×C₅₃	—	2	1	no	—
248	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
249	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
250	Dic₅₃	—	2	1	no	—
251	Dic₅₃	—	2	1	no	—
252	Dic₅₃	—	2	1	no	—
253	Dic₅₃	—	2	1	no	—
254	Dic₅₃	C₈×D₄	1	2	yes	—
255	C₂²×M₃₂	—	53	1	no	—
256	C₂³×C₁₆	—	53	1	no	—
257	C₂×C₈×D₄	—	53	1	no	—
258	#2168	—	53	2	no	—
259	#2168	—	53	2	no	—
260	#2168	—	53	2	no	—
261	#2168	—	53	2	no	—
262	C₂×C₄⋊C₁₆	—	53	1	no	—
263	C₂×C₂²⋊C₁₆	—	53	1	no	—
264	C₂×C₂²⋊C₁₆	—	53	1	no	—
265	C₂×#346	—	53	1	no	—
266	C₂×C₅₃	—	2	2	no	—
267	C₂×C₅₃	—	4	1	no	—
268	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
269	C₂×C₅₃	C₂²×M₃₂	1	1	yes	characteristic
270	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
271	D₅₃	—	2	2	no	—
272	D₅₃	—	4	1	no	—
273	D₅₃	#2168	1	4	yes	complemented
274	C₂³×C₈	—	53	1	no	—
275	C₂³×C₈	—	53	1	no	—
276	C₂×C₄×D₄	—	53	1	no	—
277	C₂×M₃₂	—	53	2	no	—
278	C₂×M₃₂	—	53	2	no	—
279	C₂×M₃₂	—	106	4	no	—
280	C₂²×C₁₆	—	53	1	no	—
281	C₂²×C₁₆	—	53	1	no	—
282	C₂²×C₁₆	—	53	1	no	—
283	C₂²×C₁₆	—	53	1	no	—
284	C₂²×C₁₆	—	53	2	no	—
285	C₂²×C₁₆	—	53	2	no	—
286	C₂²×C₁₆	—	106	4	no	—
287	C₈×D₄	—	53	1	no	—
288	C₈×D₄	—	53	1	no	—
289	C₈×D₄	—	53	1	no	—
290	C₈×D₄	—	53	1	no	—
291	C₈×D₄	—	53	1	no	—
292	C₈×D₄	—	53	1	no	—
293	C₈×D₄	—	53	1	no	—
294	C₈×D₄	#6157	1	1	yes	characteristic
295	C₂×C₄⋊C₈	—	53	1	no	—
296	C₂×C₂²⋊C₈	—	53	1	no	—
297	C₂×C₂²⋊C₈	—	53	1	no	—
298	C₂×C₄×C₈	—	53	1	no	—
299	C₄⋊C₁₆	—	53	2	no	—
300	C₄⋊C₁₆	—	53	2	no	—
301	C₂²⋊C₁₆	—	53	2	no	—
302	C₂²⋊C₁₆	—	53	2	no	—
303	C₂²⋊C₁₆	—	53	2	no	—
304	C₂²⋊C₁₆	—	53	2	no	—
305	#346	—	53	2	no	—
306	#346	—	53	2	no	—
307	C₅₃	C₂×#2168	1	1	yes	characteristic, complemented, Sylow
308	C₂²×D₄	—	53	1	no	—
309	C₂³×C₄	—	53	1	no	—
310	C₂³×C₄	—	53	1	no	—
311	C₂²×C₈	—	53	1	no	—
312	C₂²×C₈	—	53	1	no	—
313	C₂²×C₈	—	53	1	no	—
314	C₂²×C₈	—	53	1	no	—
315	C₂²×C₈	—	53	1	no	—
316	C₂²×C₈	—	53	1	no	—
317	C₂²×C₈	—	53	1	no	—
318	C₂²×C₈	—	53	1	no	—
319	C₂²×C₈	—	53	1	no	—
320	C₂²×C₈	—	53	1	no	—
321	C₂²×C₈	—	106	2	no	—
322	C₂²×C₈	—	106	2	no	—
323	C₂²×C₈	—	106	2	no	—
324	C₂²×C₈	—	106	2	no	—
325	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
326	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
327	C₄×D₄	—	53	1	no	—
328	C₄×D₄	—	53	1	no	—
329	C₄×D₄	—	53	1	no	—
330	C₄×D₄	—	53	1	no	—
331	C₄×D₄	—	53	1	no	—
332	C₄×D₄	—	53	1	no	—
333	C₄×D₄	—	53	1	no	—
334	C₄×D₄	C₂×#6157	1	1	yes	characteristic
335	C₂×C₄⋊C₄	—	53	1	no	—
336	C₂×C₂²⋊C₄	—	53	1	no	—
337	C₂×C₂²⋊C₄	—	53	1	no	—
338	C₂×C₄²	—	53	1	no	—
339	M₃₂	—	106	4	no	—
340	M₃₂	—	106	4	no	—
341	C₂×C₁₆	—	53	2	no	—
342	C₂×C₁₆	—	53	4	no	—
343	C₂×C₁₆	—	53	2	no	—
344	C₂×C₁₆	—	53	2	no	—
345	C₂×C₁₆	—	53	2	no	—
346	C₂×C₁₆	—	106	4	no	—
347	C₂×C₁₆	—	106	4	no	—
348	C₂×C₁₆	—	106	2	no	—
349	C₂×C₁₆	—	106	2	no	—
350	C₂×C₁₆	—	106	2	no	—
351	C₄⋊C₈	—	53	1	no	—
352	C₄⋊C₈	—	53	1	no	—
353	C₄⋊C₈	—	53	1	no	—
354	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
355	C₂²⋊C₈	—	53	1	no	—
356	C₂²⋊C₈	—	53	1	no	—
357	C₂²⋊C₈	—	53	1	no	—
358	C₂²⋊C₈	—	53	1	no	—
359	C₂²⋊C₈	—	53	1	no	—
360	C₂²⋊C₈	—	53	1	no	—
361	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
362	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
363	C₄×C₈	—	53	1	no	—
364	C₄×C₈	—	53	1	no	—
365	C₄×C₈	—	53	1	no	—
366	C₄×C₈	C₂×#6157	1	1	yes	characteristic
367	C₂⁴	—	53	1	no	—
368	C₂⁴	—	53	1	no	—
369	C₂×D₄	—	53	1	no	—
370	C₂×D₄	—	53	1	no	—
371	C₂×D₄	—	53	1	no	—
372	C₂×D₄	—	106	4	no	—
373	C₂×D₄	D₅₃⋊C₈	1	1	yes	characteristic
374	C₂²×C₄	—	53	1	no	—
375	C₂²×C₄	—	53	1	no	—
376	C₂²×C₄	—	53	1	no	—
377	C₂²×C₄	—	53	1	no	—
378	C₂²×C₄	—	53	1	no	—
379	C₂²×C₄	—	53	1	no	—
380	C₂²×C₄	—	53	1	no	—
381	C₂²×C₄	—	53	1	no	—
382	C₂²×C₄	—	53	1	no	—
383	C₂²×C₄	—	53	1	no	—
384	C₂²×C₄	—	53	1	no	—
385	C₂²×C₄	—	106	2	no	—
386	C₂²×C₄	—	106	2	no	—
387	C₂²×C₄	—	106	2	no	—
388	C₂²×C₄	—	106	2	no	—
389	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
390	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	53	1	no	—
394	C₂×C₈	—	53	2	no	—
395	C₂×C₈	—	53	2	no	—
396	C₂×C₈	—	53	1	no	—
397	C₂×C₈	—	53	1	no	—
398	C₂×C₈	—	53	1	no	—
399	C₂×C₈	—	106	1	no	—
400	C₂×C₈	—	106	1	no	—
401	C₂×C₈	—	106	1	no	—
402	C₂×C₈	—	106	1	no	—
403	C₂×C₈	—	106	2	no	—
404	C₂×C₈	—	106	2	no	—
405	C₂×C₈	—	106	2	no	—
406	C₂×C₈	—	106	1	no	—
407	C₂×C₈	—	106	1	no	—
408	C₂×C₈	—	106	1	no	—
409	C₂×C₈	—	106	1	no	—
410	C₂×C₈	—	106	2	no	—
411	C₂×C₈	—	106	2	no	—
412	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
413	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
414	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
415	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
416	C₄⋊C₄	—	53	1	no	—
417	C₄⋊C₄	—	53	1	no	—
418	C₄⋊C₄	—	53	1	no	—
419	C₄⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
420	C₂²⋊C₄	—	53	1	no	—
421	C₂²⋊C₄	—	53	1	no	—
422	C₂²⋊C₄	—	53	1	no	—
423	C₂²⋊C₄	—	53	1	no	—
424	C₂²⋊C₄	—	53	1	no	—
425	C₂²⋊C₄	—	53	1	no	—
426	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
427	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
428	C₄²	—	53	1	no	—
429	C₄²	—	53	1	no	—
430	C₄²	—	53	1	no	—
431	C₄²	C₂²×#6157	1	1	yes	characteristic
432	C₁₆	—	53	4	no	—
433	C₁₆	—	106	2	no	—
434	C₁₆	—	106	2	no	—
435	C₁₆	—	106	2	no	—
436	C₂³	—	53	1	no	—
437	C₂³	—	53	4	no	—
438	C₂³	—	53	1	no	—
439	C₂³	—	53	1	no	—
440	C₂³	—	106	2	no	—
441	C₂³	—	106	2	no	—
442	C₂³	—	106	2	no	—
443	C₂³	—	106	2	no	—
444	C₂³	—	106	2	no	—
445	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
446	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
447	D₄	—	2	2	no	—
448	D₄	—	106	2	no	—
449	D₄	—	106	2	no	—
450	D₄	—	106	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	53	1	no	—
456	C₂×C₄	—	53	2	no	—
457	C₂×C₄	—	53	2	no	—
458	C₂×C₄	—	53	1	no	—
459	C₂×C₄	—	53	1	no	—
460	C₂×C₄	—	53	1	no	—
461	C₂×C₄	—	53	1	no	—
462	C₂×C₄	—	106	2	no	—
463	C₂×C₄	—	106	2	no	—
464	C₂×C₄	—	106	2	no	—
465	C₂×C₄	—	106	2	no	—
466	C₂×C₄	—	106	2	no	—
467	C₂×C₄	—	106	2	no	—
468	C₂×C₄	—	106	2	no	—
469	C₂×C₄	—	106	2	no	—
470	C₂×C₄	—	106	1	no	—
471	C₂×C₄	—	106	1	no	—
472	C₂×C₄	—	106	1	no	—
473	C₂×C₄	—	106	1	no	—
474	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
475	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
476	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
477	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
478	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	1	no	—
482	C₈	—	53	1	no	—
483	C₈	—	53	1	no	—
484	C₈	—	106	1	no	—
485	C₈	—	106	1	no	—
486	C₈	—	106	1	no	—
487	C₈	D₄×#6157	1	2	yes	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	53	2	no	—
494	C₂²	—	53	2	no	—
495	C₂²	—	53	2	no	—
496	C₂²	—	53	2	no	—
497	C₂²	—	106	8	no	—
498	C₂²	—	106	1	no	—
499	C₂²	—	106	1	no	—
500	C₂²	—	106	1	no	—
501	C₂²	—	106	1	no	—
502	C₂²	—	106	1	no	—
503	C₂²	—	212	4	no	—
504	C₂²	D₅₃⋊M₃₂	1	2	yes	complemented
505	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	53	2	no	—
511	C₄	—	106	1	no	—
512	C₄	—	106	1	no	—
513	C₄	—	106	1	no	—
514	C₄	—	106	1	no	—
515	C₄	C₂×D₄×#6157	1	1	yes	characteristic
516	C₄	D₅₃⋊#131	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	4	1	no	—
519	C₂	—	53	4	no	—
520	C₂	—	106	2	no	—
521	C₂	—	212	1	no	—
522	C₂	D₄×D₅₃⋊C₈	1	1	yes	characteristic
523	C₂	C₂×D₅₃⋊M₃₂	1	1	yes	characteristic
524	C₂	D₅₃⋊#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₈×D₄×C₅₃	C₄
prime radical	C₂×D₄×D₅₃	C₈
cosocle	C₂×#88322	C₂⁴
hypercenter	C₈×D₄	#6157
hypocenter	C₅₃	C₂×#2168
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₅₃⋊M₃₂	C₂	semidirect
2. C₂²×D₅₃⋊C₁₆	C₂	semidirect
3. #20291098	C₂	semidirect
4. #20291097	C₂	semidirect
5. #20291096	C₂	semidirect
6. #20291095	C₂	semidirect
7. D₅₃⋊(C₄⋊C₁₆)	C₂	semidirect
8. D₅₃⋊(C₂²⋊C₁₆)	C₂	semidirect
9. D₅₃⋊(C₂²⋊C₁₆)	C₂	semidirect
10. #20290916	C₂	semidirect
12. C₂×#13133292	C₂²	semidirect
14. C₂×#13133291	C₂²	semidirect
20. C₂×D₅₃⋊C₁₆	C₂²	semidirect
21. C₂²×#11719910	C₂²	semidirect
22. #16811544	C₂²	semidirect
23. C₄⋊#11719910	C₂²	semidirect
24. #16811518	C₂²	semidirect
25. #16811518	C₂²	semidirect
26. C₂²⋊#11719910	C₂²	semidirect
27. C₂²⋊#11719910	C₂²	semidirect
28. #16811512	C₂²	semidirect
29. #16811511	C₂²	semidirect
51. D₅₃⋊C₁₆	D₄	semidirect
172. #11719910	C₂×D₄	semidirect
180. C₂²×D₅₃	M₃₂	semidirect
231. C₂²×C₅₃	C₂×M₃₂	semidirect
242. C₂×D₅₃	C₂×M₃₂	semidirect
273. D₅₃	#2168	semidirect
307. C₅₃	C₂×#2168	semidirect
504. C₂²	D₅₃⋊M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₃⋊M₃₂	2
C₂²×D₅₃⋊C₁₆	2
#20291098	2
#20291097	2
#20291096	2
#20291095	2
D₅₃⋊(C₄⋊C₁₆)	2
D₅₃⋊(C₂²⋊C₁₆)	2
#20290916	2
C₈×D₄×D₅₃	2
C₂×#2168	53

Subgroups — D53⋊#2168 #28328298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃⋊#2168 #28328298