Subgroups — D₅₃×#2207 #27538332

Order 13568.

806 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₅₃	C₂	1	2	yes	maximal, complemented
2	#493×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276756	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276755	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276754	C₂	1	2	yes	maximal, complemented
7	#20276753	C₂	1	2	yes	maximal, complemented
8	#20276752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#357×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic
13	C₂×D₈×D₅₃	—	2	1	no	—
14	C₂×D₈×D₅₃	C₂²	1	2	yes	—
15	#127×D₅₃	—	2	1	no	—
16	C₄×Q₈×D₅₃	—	2	1	no	—
17	C₂×#13133162	C₂²	1	2	yes	complemented
18	C₂×#13133161	C₂²	1	2	yes	complemented
19	C₂×#13133160	C₂²	1	2	yes	complemented
20	SD₃₂×D₅₃	—	2	8	no	—
21	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
22	#16811000	C₂²	1	1	yes	characteristic
23	#16810999	—	2	1	no	—
24	#16810998	—	2	1	no	—
25	#16810998	C₂²	1	2	yes	—
26	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic, complemented
27	Q₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
28	#16810717	C₂²	1	1	yes	characteristic, complemented
29	C₄×#11719925	—	2	1	no	—
30	#16810715	—	2	1	no	—
31	#107×D₅₃	C₂²	1	1	yes	characteristic
32	#103×D₅₃	—	2	1	no	—
33	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
34	C₄⋊#11719908	C₂²	1	1	yes	characteristic, complemented
35	#16810441	C₂²	1	2	yes	complemented
36	#16810425	C₂²	1	2	yes	complemented
37	#16810424	C₂²	1	2	yes	complemented
38	#16810423	C₂²	1	2	yes	complemented
39	C₂×SD₃₂×C₅₃	C₂²	1	2	yes	complemented
40	C₅₃×#493	C₂²	1	1	yes	characteristic
41	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#357	C₂²	1	2	yes	complemented
44	C₂×Q₈×D₅₃	—	2	1	no	—
45	C₂×D₄×D₅₃	—	2	2	no	—
46	C₂×D₄×D₅₃	—	4	1	no	—
47	C₂×D₄×D₅₃	—	4	1	no	—
48	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic
49	C₂×#11719925	—	2	1	no	—
50	Q₁₆×D₅₃	—	2	2	no	—
51	Q₁₆×D₅₃	D₄	1	4	yes	complemented
52	C₂×D₄₂₄	—	2	1	no	—
53	C₂×D₄₂₄	C₂³	1	2	yes	—
54	C₂×#11719922	—	2	2	no	—
55	C₂×#11719922	—	2	2	no	—
56	D₈×D₅₃	—	2	4	no	—
57	D₈×D₅₃	—	2	4	no	—
58	D₈×D₅₃	—	4	4	no	—
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
61	#13133214	—	2	1	no	—
62	#13133213	—	2	2	no	—
63	#13133213	—	4	1	no	—
64	#13133213	—	4	1	no	—
65	Q₈×Dic₅₃	—	2	1	no	—
66	C₄×Dic₁₀₆	—	2	1	no	—
67	C₄×Dic₁₀₆	—	4	1	no	—
68	#13133182	—	2	1	no	—
69	#13133182	—	4	1	no	—
70	C₄⋊C₄×D₅₃	—	2	1	no	—
71	C₄⋊C₄×D₅₃	—	4	1	no	—
72	C₄²×D₅₃	—	4	1	no	—
73	C₄²×D₅₃	D₄	1	1	yes	characteristic
74	#13133162	—	2	4	no	—
75	#13133161	—	2	4	no	—
76	#13133160	—	2	4	no	—
77	C₂×#11719908	C₂³	1	2	yes	—
78	C₁₆×D₅₃	—	2	4	no	—
79	#13133151	C₂³	1	1	yes	characteristic
80	#13133150	—	2	1	no	—
81	#13133142	—	2	1	no	—
82	#13133141	—	2	1	no	—
83	#13133140	—	2	1	no	—
84	C₄×#88322	D₄	1	1	yes	characteristic
85	C₈×Dic₅₃	D₄	1	1	yes	characteristic
86	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
88	C₂×D₈×C₅₃	—	2	1	no	—
89	C₂×D₈×C₅₃	C₂³	1	2	yes	—
90	#127×C₅₃	—	2	1	no	—
91	C₄×Q₈×C₅₃	—	2	1	no	—
92	SD₃₂×C₅₃	—	2	4	no	—
93	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
94	#107×C₅₃	C₂³	1	1	yes	characteristic
95	#103×C₅₃	—	2	1	no	—
96	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₂³×D₅₃	—	4	2	no	—
98	C₂×Q₈×C₅₃	—	2	1	no	—
99	C₂×D₄×C₅₃	—	2	2	no	—
100	C₂×D₄×C₅₃	—	4	1	no	—
101	C₂×D₄×C₅₃	—	4	1	no	—
102	C₂×C₂²⋊D₅₃	—	4	2	no	—
103	C₂×C₂²⋊D₅₃	—	4	2	no	—
104	C₂×C₂²⋊D₅₃	—	4	2	no	—
105	Q₈×D₅₃	—	2	4	no	—
106	Q₈×D₅₃	—	4	2	no	—
107	D₄×D₅₃	—	4	4	no	—
108	D₄×D₅₃	—	4	4	no	—
109	D₄×D₅₃	—	8	4	no	—
110	D₄×D₅₃	—	8	4	no	—
111	C₂×D₂₁₂	—	2	2	no	—
112	C₂×D₂₁₂	—	4	1	no	—
113	C₂×D₂₁₂	—	4	1	no	—
114	C₂×C₄×D₅₃	—	4	1	no	—
115	C₂×C₄×D₅₃	—	4	1	no	—
116	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
117	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Dic₁₀₆	—	2	1	no	—
120	C₂×Dic₁₀₆	—	4	1	no	—
121	Q₁₆×C₅₃	—	2	1	no	—
122	Q₁₆×C₅₃	C₂×D₄	1	2	yes	complemented
123	D₈×C₅₃	—	2	2	no	—
124	D₈×C₅₃	—	2	2	no	—
125	D₈×C₅₃	—	4	2	no	—
126	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₅₃	—	2	1	no	—
129	C₄⋊C₄×C₅₃	—	4	1	no	—
130	C₄²×C₅₃	—	4	1	no	—
131	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
132	#11719925	—	2	4	no	—
133	#11719922	—	4	4	no	—
134	#11719922	—	4	4	no	—
135	C₄⋊Dic₅₃	—	2	1	no	—
136	C₄⋊Dic₅₃	—	4	1	no	—
137	#11719919	—	4	1	no	—
138	#11719919	—	4	1	no	—
139	#11719919	—	4	1	no	—
140	C₄×Dic₅₃	—	4	1	no	—
141	C₄×Dic₅₃	—	4	1	no	—
142	C₄×Dic₅₃	—	4	1	no	—
143	C₄×Dic₅₃	D₈	1	1	yes	characteristic
144	C₄×Dic₅₃	D₈	1	1	yes	characteristic
145	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
146	C₂×#88322	C₂×D₄	1	1	yes	characteristic
147	C₂×#88322	C₂×D₄	1	1	yes	characteristic
148	Dic₂₁₂	—	2	1	no	—
149	Dic₂₁₂	C₂×D₄	1	2	yes	complemented
150	D₄₂₄	—	2	2	no	—
151	D₄₂₄	—	2	2	no	—
152	D₄₂₄	—	4	2	no	—
153	C₈×D₅₃	—	2	2	no	—
154	C₈×D₅₃	C₂×D₄	1	2	yes	—
155	C₈×D₅₃	#41	1	2	yes	—
156	C₁₆×C₅₃	—	2	2	no	—
157	#11719908	—	2	2	no	—
158	C₂³×C₅₃	—	4	2	no	—
159	C₂²×D₅₃	—	4	2	no	—
160	C₂²×D₅₃	—	8	4	no	—
161	C₂²×D₅₃	—	8	4	no	—
162	C₂²×D₅₃	—	8	4	no	—
163	C₂²×D₅₃	C₂×D₈	1	1	yes	characteristic
164	Q₈×C₅₃	—	2	2	no	—
165	Q₈×C₅₃	—	4	1	no	—
166	D₄×C₅₃	—	4	2	no	—
167	D₄×C₅₃	—	4	2	no	—
168	D₄×C₅₃	—	8	2	no	—
169	D₄×C₅₃	—	8	2	no	—
170	C₂×C₄×C₅₃	—	4	1	no	—
171	C₂×C₄×C₅₃	—	4	1	no	—
172	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
175	C₂²⋊D₅₃	—	8	4	no	—
176	C₂²⋊D₅₃	—	8	4	no	—
177	C₂²⋊D₅₃	—	8	4	no	—
178	C₂×Dic₅₃	—	4	1	no	—
179	C₂×Dic₅₃	—	4	1	no	—
180	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
181	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
182	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
183	D₂₁₂	—	4	2	no	—
184	D₂₁₂	—	4	2	no	—
185	D₂₁₂	—	8	2	no	—
186	D₂₁₂	—	8	2	no	—
187	C₄×D₅₃	—	2	2	no	—
188	C₄×D₅₃	—	4	4	no	—
189	C₄×D₅₃	—	8	2	no	—
190	C₄×D₅₃	SD₃₂	1	4	yes	complemented
191	C₄×D₅₃	#121	1	2	yes	—
192	C₄×D₅₃	AGL(1,ℤ/8)	1	2	yes	—
193	Dic₁₀₆	—	2	2	no	—
194	Dic₁₀₆	—	4	1	no	—
195	Dic₁₀₆	—	4	4	no	—
196	C₈×C₅₃	—	2	1	no	—
197	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
199	#88322	—	2	1	no	—
200	#88322	#121	1	2	yes	—
201	C₂×#2207	—	53	1	no	maximal, Sylow
202	C₂²×C₅₃	—	8	2	no	—
203	C₂²×C₅₃	—	8	2	no	—
204	C₂²×C₅₃	—	8	2	no	—
205	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
206	C₂×D₅₃	—	8	2	no	—
207	C₂×D₅₃	—	8	2	no	—
208	C₂×D₅₃	—	8	2	no	—
209	C₂×D₅₃	—	16	8	no	—
210	C₂×D₅₃	#459	1	2	yes	—
211	C₂×D₅₃	C₂×SD₃₂	1	2	yes	—
212	C₂×D₅₃	#509	1	2	yes	—
213	C₄×C₅₃	—	2	1	no	—
214	C₄×C₅₃	—	4	2	no	—
215	C₄×C₅₃	—	8	1	no	—
216	C₄×C₅₃	C₂×SD₃₂	1	2	yes	complemented
217	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
218	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	Dic₅₃	—	2	1	no	—
220	Dic₅₃	—	4	2	no	—
221	Dic₅₃	—	8	1	no	—
222	Dic₅₃	#459	1	2	yes	—
223	Dic₅₃	C₂×SD₃₂	1	2	yes	complemented
224	C₂²×SD₃₂	—	53	2	no	—
225	C₂×#493	—	53	1	no	—
226	C₂×C₄×Q₁₆	—	53	1	no	—
227	#2207	—	53	2	no	—
228	#2207	—	53	1	no	—
229	#2207	—	53	1	no	—
230	#2207	—	53	1	no	—
231	#2207	—	53	2	no	—
232	#2207	D₅₃	1	1	yes	characteristic, direct product factor
233	C₂×C₄⋊C₁₆	—	53	1	no	—
234	C₂×#357	—	53	2	no	—
235	C₂×C₅₃	—	16	2	no	—
236	C₂×C₅₃	C₂×#459	1	1	yes	characteristic
237	C₂×C₅₃	C₂²×SD₃₂	1	1	yes	characteristic
238	C₂×C₅₃	C₂×#509	1	1	yes	characteristic
239	D₅₃	—	16	2	no	—
240	D₅₃	#2207	1	4	yes	direct product factor
241	C₂²×Q₁₆	—	53	1	no	—
242	C₂²×D₈	—	53	2	no	—
243	C₂²×D₈	—	106	1	no	—
244	C₂×#127	—	106	1	no	—
245	C₂×C₄×Q₈	—	106	1	no	—
246	C₂×SD₃₂	—	53	2	no	—
247	C₂×SD₃₂	—	53	2	no	—
248	C₂×SD₃₂	—	53	2	no	—
249	C₂×SD₃₂	—	106	8	no	—
250	C₂×SD₃₂	C₂×D₅₃	1	2	yes	complemented
251	C₂²×C₁₆	—	53	2	no	—
252	#493	—	53	2	no	—
253	#493	—	53	1	no	—
254	#493	—	106	1	no	—
255	#493	—	106	1	no	—
256	#493	C₂×D₅₃	1	1	yes	characteristic
257	C₄×Q₁₆	—	53	1	no	—
258	C₄×Q₁₆	—	53	1	no	—
259	C₄×Q₁₆	—	53	1	no	—
260	C₄×Q₁₆	—	106	1	no	—
261	C₄×Q₁₆	—	106	1	no	—
262	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
263	C₂×#107	—	53	1	no	—
264	C₂×#103	—	106	1	no	—
265	C₂×C₄×C₈	—	53	1	no	—
266	C₄⋊C₁₆	—	53	2	no	—
267	C₄⋊C₁₆	—	53	1	no	—
268	C₄⋊C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
269	#357	—	53	2	no	—
270	#357	—	53	2	no	—
271	#357	—	53	2	no	—
272	#357	C₂×D₅₃	1	2	yes	complemented
273	C₅₃	C₂×#2207	1	1	yes	characteristic, complemented, Sylow
274	C₂²×Q₈	—	106	1	no	—
275	C₂²×D₄	—	106	2	no	—
276	C₂²×D₄	—	212	1	no	—
277	C₂²×D₄	—	212	1	no	—
278	C₂×Q₁₆	—	53	4	no	—
279	C₂×Q₁₆	—	53	1	no	—
280	C₂×Q₁₆	—	106	2	no	—
281	C₂×Q₁₆	—	106	1	no	—
282	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	53	2	no	—
285	C₂×D₈	—	106	4	no	—
286	C₂×D₈	—	106	4	no	—
287	C₂×D₈	—	106	2	no	—
288	C₂×D₈	—	106	2	no	—
289	C₂×D₈	—	106	1	no	—
290	C₂×D₈	—	212	4	no	—
291	C₂×D₈	C₂²×D₅₃	1	2	yes	—
292	C₂²×C₈	—	53	1	no	—
293	C₂²×C₈	—	53	1	no	—
294	#127	—	2	1	no	—
295	#127	—	106	2	no	—
296	#127	—	106	1	no	—
297	#127	—	212	1	no	—
298	#127	—	212	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	106	1	no	—
301	C₄×Q₈	—	106	1	no	—
302	C₄×Q₈	—	106	1	no	—
303	C₄×Q₈	—	212	1	no	—
304	C₄×Q₈	—	212	1	no	—
305	C₂×C₄⋊C₄	—	106	1	no	—
306	C₂×C₄⋊C₄	—	212	1	no	—
307	C₂×C₄²	—	53	1	no	—
308	C₂×C₄²	—	212	1	no	—
309	SD₃₂	—	2	4	no	—
310	SD₃₂	—	106	4	no	—
311	SD₃₂	—	106	4	no	—
312	SD₃₂	—	106	4	no	—
313	C₂×C₁₆	—	53	2	no	—
314	C₂×C₁₆	—	106	4	no	—
315	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
316	#107	—	53	1	no	—
317	#107	—	106	1	no	—
318	#107	C₂²×D₅₃	1	1	yes	characteristic
319	#103	—	2	1	no	—
320	#103	—	106	1	no	—
321	#103	—	106	1	no	—
322	#103	—	106	1	no	—
323	C₄×C₈	—	53	1	no	—
324	C₄×C₈	—	53	1	no	—
325	C₄×C₈	—	53	1	no	—
326	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
327	C₂⁴	—	212	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	106	4	no	—
330	C₂×Q₈	—	106	1	no	—
331	C₂×Q₈	—	212	1	no	—
332	C₂×Q₈	—	212	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	106	2	no	—
337	C₂×D₄	—	424	4	no	—
338	C₂×D₄	—	424	4	no	—
339	C₂×D₄	—	212	4	no	—
340	C₂×D₄	—	212	4	no	—
341	C₂×D₄	—	212	2	no	—
342	C₂×D₄	—	212	2	no	—
343	C₂×D₄	—	212	2	no	—
344	C₂×D₄	—	212	1	no	—
345	C₂×D₄	—	212	1	no	—
346	C₂²×C₄	—	53	1	no	—
347	C₂²×C₄	—	53	1	no	—
348	C₂²×C₄	—	53	1	no	—
349	C₂²×C₄	—	212	1	no	—
350	C₂²×C₄	—	212	1	no	—
351	Q₁₆	—	2	1	no	—
352	Q₁₆	—	53	2	no	—
353	Q₁₆	—	106	4	no	—
354	Q₁₆	—	106	1	no	—
355	Q₁₆	D₄×D₅₃	1	2	yes	complemented
356	D₈	—	2	2	no	—
357	D₈	—	2	2	no	—
358	D₈	—	4	2	no	—
359	D₈	—	106	2	no	—
360	D₈	—	106	2	no	—
361	D₈	—	212	2	no	—
362	D₈	—	212	4	no	—
363	D₈	—	212	4	no	—
364	C₂×C₈	—	53	1	no	—
365	C₂×C₈	—	53	2	no	—
366	C₂×C₈	—	53	2	no	—
367	C₂×C₈	—	53	1	no	—
368	C₂×C₈	—	106	2	no	—
369	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
370	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	106	1	no	—
374	C₄⋊C₄	—	212	1	no	—
375	C₄⋊C₄	—	212	1	no	—
376	C₄⋊C₄	—	212	1	no	—
377	C₄⋊C₄	—	212	1	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	53	1	no	—
380	C₄²	—	53	1	no	—
381	C₄²	—	53	1	no	—
382	C₄²	—	212	1	no	—
383	C₄²	—	212	1	no	—
384	C₄²	—	212	1	no	—
385	C₄²	D₄×D₅₃	1	1	yes	characteristic
386	C₁₆	—	2	2	no	—
387	C₁₆	—	106	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	53	1	no	—
390	C₂³	—	424	4	no	—
391	C₂³	—	424	4	no	—
392	C₂³	—	424	4	no	—
393	C₂³	—	212	2	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	106	2	no	—
397	Q₈	—	212	4	no	—
398	Q₈	—	212	1	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	424	2	no	—
404	D₄	—	424	4	no	—
405	D₄	—	424	4	no	—
406	D₄	—	424	4	no	—
407	D₄	—	424	2	no	—
408	D₄	—	212	2	no	—
409	D₄	—	212	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	53	1	no	—
413	C₂×C₄	—	53	1	no	—
414	C₂×C₄	—	53	4	no	—
415	C₂×C₄	—	53	2	no	—
416	C₂×C₄	—	53	2	no	—
417	C₂×C₄	—	53	1	no	—
418	C₂×C₄	—	106	2	no	—
419	C₂×C₄	—	424	2	no	—
420	C₂×C₄	—	212	4	no	—
421	C₂×C₄	—	212	1	no	—
422	C₂×C₄	—	212	1	no	—
423	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
424	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
425	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	53	2	no	—
428	C₈	—	106	1	no	—
429	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
430	C₈	#41×D₅₃	1	1	yes	characteristic
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	53	2	no	—
435	C₂²	—	53	2	no	—
436	C₂²	—	53	2	no	—
437	C₂²	—	848	8	no	—
438	C₂²	—	424	2	no	—
439	C₂²	—	424	2	no	—
440	C₂²	—	424	2	no	—
441	C₂²	C₂×D₈×D₅₃	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	53	2	no	—
446	C₄	—	53	2	no	—
447	C₄	—	106	1	no	—
448	C₄	—	424	1	no	—
449	C₄	—	212	2	no	—
450	C₄	SD₃₂×D₅₃	1	2	yes	complemented
451	C₄	#121×D₅₃	1	1	yes	characteristic
452	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
453	C₂	—	16	2	no	—
454	C₂	—	53	4	no	—
455	C₂	—	848	2	no	—
456	C₂	#459×D₅₃	1	1	yes	characteristic
457	C₂	C₂×SD₃₂×D₅₃	1	1	yes	characteristic
458	C₂	#509×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₅₃
commutator, cosocle	C₂×C₈×C₅₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2207	C₂
socle	C₂²×C₅₃	C₂²×D₈
prime radical	#493×D₅₃	C₂
hypercenter	#2207	D₅₃
hypocenter	C₅₃	C₂×#2207
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2207

Complements

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

N	H ≅ G/N	type
1. C₂×SD₃₂×D₅₃	C₂	semidirect
3. C₄×Q₁₆×D₅₃	C₂	semidirect
4. #20276756	C₂	semidirect
5. #20276755	C₂	semidirect
6. #20276754	C₂	semidirect
7. #20276753	C₂	semidirect
8. #20276752	C₂	semidirect
9. C₄⋊C₁₆×D₅₃	C₂	semidirect
10. #357×D₅₃	C₂	semidirect
11. C₅₃×#2207	C₂	semidirect
17. C₂×#13133162	C₂²	semidirect
18. C₂×#13133161	C₂²	semidirect
19. C₂×#13133160	C₂²	semidirect
26. C₄×Dic₂₁₂	C₂²	semidirect
27. Q₁₆×Dic₅₃	C₂²	semidirect
28. #16810717	C₂²	semidirect
34. C₄⋊#11719908	C₂²	semidirect
35. #16810441	C₂²	semidirect
36. #16810425	C₂²	semidirect
37. #16810424	C₂²	semidirect
38. #16810423	C₂²	semidirect
39. C₂×SD₃₂×C₅₃	C₂²	semidirect
41. C₄×Q₁₆×C₅₃	C₂²	semidirect
42. C₅₃×C₄⋊C₁₆	C₂²	semidirect
43. C₅₃×#357	C₂²	semidirect
51. Q₁₆×D₅₃	D₄	semidirect
122. Q₁₆×C₅₃	C₂×D₄	semidirect
149. Dic₂₁₂	C₂×D₄	semidirect
190. C₄×D₅₃	SD₃₂	semidirect
216. C₄×C₅₃	C₂×SD₃₂	semidirect
223. Dic₅₃	C₂×SD₃₂	semidirect
232. #2207	D₅₃	direct (N × H)
240. D₅₃	#2207	direct (N × H)
250. C₂×SD₃₂	C₂×D₅₃	semidirect
262. C₄×Q₁₆	C₂×D₅₃	semidirect
268. C₄⋊C₁₆	C₂×D₅₃	semidirect
272. #357	C₂×D₅₃	semidirect
273. C₅₃	C₂×#2207	semidirect
355. Q₁₆	D₄×D₅₃	semidirect
450. C₄	SD₃₂×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₃₂×D₅₃	2
#493×D₅₃	2
C₄×Q₁₆×D₅₃	2
#20276756	2
#20276755	2
#20276754	2
#20276753	2
#20276752	2
C₄⋊C₁₆×D₅₃	2
#357×D₅₃	2
C₅₃×#2207	2
C₂×#2207	53

Subgroups — D53×#2207 #27538332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2207 #27538332