Subgroups — D₅₃×#1670 #27366422

Order 13568.

702 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#475×D₅₃	C₂	1	2	yes	maximal
3	C₈×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20274086	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274085	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274084	C₂	1	2	yes	maximal, complemented
7	#20274083	C₂	1	2	yes	maximal, complemented
8	#20274082	C₂	1	1	yes	maximal, characteristic, complemented
9	#335×D₅₃	C₂	1	1	yes	maximal, characteristic
10	#332×D₅₃	C₂	1	2	yes	maximal
11	C₅₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₅₃	—	2	1	no	—
13	C₂×Q₁₆×D₅₃	—	2	1	no	—
14	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
15	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
16	#16811003	C₂²	1	1	yes	characteristic
17	#16811002	C₂²	1	2	yes	—
18	#16811001	—	2	1	no	—
19	#16811001	—	2	1	no	—
20	#16810909	C₂²	1	2	yes	—
21	#16810908	C₂²	1	2	yes	—
22	#16810907	—	2	2	no	—
23	#16810906	—	2	2	no	—
24	#16810905	C₂²	1	2	yes	—
25	Q₈×#88322	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₀₆	—	2	1	no	—
27	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
28	#16810747	—	2	1	no	—
29	#16810747	C₂²	1	1	yes	characteristic
30	#106×D₅₃	—	2	2	no	—
31	C₄⋊C₈×D₅₃	—	2	1	no	—
32	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
33	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
34	#103×D₅₃	—	2	2	no	—
35	C₄×C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic
38	#16810375	C₂²	1	2	yes	—
39	#16810370	C₂²	1	2	yes	—
40	#16810369	C₂²	1	2	yes	—
41	#16810368	C₂²	1	2	yes	—
42	C₅₃×#494	C₂²	1	1	yes	characteristic
43	C₅₃×#475	C₂²	1	2	yes	—
44	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic
46	C₅₃×#332	C₂²	1	2	yes	—
47	C₂×Q₈×D₅₃	—	2	2	no	—
48	C₂×Q₈×D₅₃	D₄	1	1	yes	characteristic
49	C₂×Dic₂₁₂	—	2	1	no	—
50	C₂×Dic₂₁₂	—	2	1	no	—
51	C₂×#11719925	—	2	2	no	—
52	C₂×#11719925	—	2	2	no	—
53	Q₁₆×D₅₃	—	4	4	no	—
54	Q₁₆×D₅₃	—	4	4	no	—
55	C₂×C₈×D₅₃	—	2	1	no	—
56	C₂×C₈×D₅₃	—	2	2	no	—
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
59	#13133217	C₂³	1	2	yes	—
60	#13133216	—	2	2	no	—
61	#13133216	—	2	2	no	—
62	#13133215	—	2	2	no	—
63	Q₈×Dic₅₃	D₄	1	1	yes	characteristic
64	C₄×Dic₁₀₆	—	2	1	no	—
65	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
66	#13133182	—	2	1	no	—
67	#13133182	D₄	1	1	yes	characteristic
68	C₄⋊C₄×D₅₃	—	2	1	no	—
69	C₄⋊C₄×D₅₃	—	2	2	no	—
70	C₄⋊C₄×D₅₃	—	2	2	no	—
71	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
72	C₄²×D₅₃	—	2	1	no	—
73	C₄²×D₅₃	C₂³	1	1	yes	characteristic
74	#13133149	—	2	2	no	—
75	#13133148	—	2	2	no	—
76	#13133148	—	2	2	no	—
77	C₄⋊#88322	—	2	1	no	—
78	C₄⋊#88322	C₂³	1	1	yes	characteristic
79	C₄⋊#88322	C₂³	1	2	yes	—
80	#13133146	—	2	1	no	—
81	#13133146	—	2	2	no	—
82	#13133146	—	2	1	no	—
83	#13133146	—	2	1	no	—
84	#13133142	—	2	2	no	—
85	#13133141	—	2	2	no	—
86	#13133140	—	2	2	no	—
87	C₄×#88322	—	2	1	no	—
88	C₄×#88322	C₂³	1	1	yes	characteristic
89	C₈×Dic₅₃	—	2	1	no	—
90	C₈×Dic₅₃	—	2	1	no	—
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₈×Dic₅₃	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₅₃	—	2	1	no	—
94	C₂×Q₁₆×C₅₃	—	2	1	no	—
95	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
96	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
97	#106×C₅₃	—	2	2	no	—
98	C₄⋊C₈×C₅₃	—	2	1	no	—
99	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
101	#103×C₅₃	—	2	2	no	—
102	C₄×C₈×C₅₃	—	2	1	no	—
103	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×Q₈×C₅₃	—	2	2	no	—
105	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
106	Q₈×D₅₃	—	2	2	no	—
107	Q₈×D₅₃	—	4	4	no	—
108	Q₈×D₅₃	—	4	4	no	—
109	Q₈×D₅₃	Q₁₆	1	4	yes	complemented
110	C₂×C₄×D₅₃	—	2	1	no	—
111	C₂×C₄×D₅₃	—	2	1	no	—
112	C₂×C₄×D₅₃	—	4	2	no	—
113	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
116	C₂×Dic₁₀₆	—	2	1	no	—
117	C₂×Dic₁₀₆	—	2	2	no	—
118	C₂×Dic₁₀₆	—	4	2	no	—
119	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
120	Q₁₆×C₅₃	—	4	2	no	—
121	Q₁₆×C₅₃	—	4	2	no	—
122	C₂×C₈×C₅₃	—	2	1	no	—
123	C₂×C₈×C₅₃	—	2	2	no	—
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₅₃	—	2	1	no	—
127	C₄⋊C₄×C₅₃	—	2	2	no	—
128	C₄⋊C₄×C₅₃	—	2	2	no	—
129	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅₃	—	2	1	no	—
131	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
132	#11719925	—	4	4	no	—
133	#11719925	—	4	4	no	—
134	C₄⋊Dic₅₃	—	2	1	no	—
135	C₄⋊Dic₅₃	—	2	2	no	—
136	C₄⋊Dic₅₃	—	2	2	no	—
137	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
138	#11719919	—	2	1	no	—
139	#11719919	—	2	1	no	—
140	#11719919	—	2	1	no	—
141	#11719919	—	4	2	no	—
142	#11719919	—	4	2	no	—
143	C₄×Dic₅₃	—	2	1	no	—
144	C₄×Dic₅₃	—	2	1	no	—
145	C₄×Dic₅₃	—	2	1	no	—
146	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
147	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₅₃	#41	1	1	yes	characteristic
149	C₂×#88322	—	2	1	no	—
150	C₂×#88322	—	2	2	no	—
151	C₂×#88322	C₂×D₄	1	1	yes	characteristic
152	C₂×#88322	C₂×D₄	1	1	yes	characteristic
153	Dic₂₁₂	—	4	2	no	—
154	Dic₂₁₂	—	4	2	no	—
155	C₈×D₅₃	—	2	2	no	—
156	C₈×D₅₃	—	4	4	no	—
157	C₈×D₅₃	—	4	2	no	—
158	C₈×D₅₃	SD₁₆	1	4	yes	—
159	C₂²×D₅₃	#121	1	1	yes	characteristic
160	Q₈×C₅₃	—	2	1	no	—
161	Q₈×C₅₃	—	4	2	no	—
162	Q₈×C₅₃	—	4	2	no	—
163	Q₈×C₅₃	C₂×Q₁₆	1	2	yes	complemented
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	4	2	no	—
167	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₅₃	—	2	1	no	—
171	C₂×Dic₅₃	—	2	1	no	—
172	C₂×Dic₅₃	—	4	2	no	—
173	C₂×Dic₅₃	#121	1	1	yes	characteristic
174	C₂×Dic₅₃	#121	1	1	yes	characteristic
175	C₂×Dic₅₃	#121	1	1	yes	characteristic
176	C₄×D₅₃	—	2	4	no	—
177	C₄×D₅₃	—	2	2	no	—
178	C₄×D₅₃	—	4	2	no	—
179	C₄×D₅₃	—	8	4	no	—
180	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
181	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
182	C₄×D₅₃	#135	1	2	yes	—
183	C₄×D₅₃	AGL(1,ℤ/8)	1	2	yes	—
184	Dic₁₀₆	—	2	1	no	—
185	Dic₁₀₆	—	2	4	no	—
186	Dic₁₀₆	—	4	2	no	—
187	Dic₁₀₆	—	4	2	no	—
188	Dic₁₀₆	—	8	4	no	—
189	Dic₁₀₆	C₂×Q₁₆	1	2	yes	complemented
190	C₈×C₅₃	—	2	1	no	—
191	C₈×C₅₃	—	4	2	no	—
192	C₈×C₅₃	—	4	1	no	—
193	C₈×C₅₃	C₂×SD₁₆	1	2	yes	—
194	#88322	—	2	1	no	—
195	#88322	—	4	2	no	—
196	#88322	—	4	1	no	—
197	#88322	C₂×SD₁₆	1	2	yes	—
198	C₂×#1670	—	53	1	no	maximal, Sylow
199	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
200	C₂×D₅₃	#460	1	2	yes	—
201	C₂×D₅₃	#467	1	2	yes	—
202	C₂×D₅₃	#473	1	2	yes	—
203	C₄×C₅₃	—	2	2	no	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	—	4	1	no	—
206	C₄×C₅₃	—	8	2	no	—
207	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
208	C₄×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
209	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
210	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	Dic₅₃	—	2	2	no	—
212	Dic₅₃	—	2	1	no	—
213	Dic₅₃	—	4	1	no	—
214	Dic₅₃	—	8	2	no	—
215	Dic₅₃	#460	1	2	yes	—
216	Dic₅₃	#467	1	2	yes	—
217	C₂×#494	—	53	1	no	—
218	C₂×#475	—	53	2	no	—
219	C₂×C₈×Q₈	—	53	1	no	—
220	#1670	—	53	1	no	—
221	#1670	—	53	2	no	—
222	#1670	—	53	1	no	—
223	#1670	—	53	1	no	—
224	#1670	—	53	2	no	—
225	#1670	D₅₃	1	1	yes	characteristic, direct product factor
226	C₂×#335	—	53	1	no	—
227	C₂×#332	—	53	2	no	—
228	C₂×C₅₃	C₂×#460	1	1	yes	characteristic
229	C₂×C₅₃	C₂×#467	1	1	yes	characteristic
230	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
231	D₅₃	#1670	1	4	yes	direct product factor
232	C₂²×Q₁₆	—	106	1	no	—
233	C₂²×Q₁₆	—	106	1	no	—
234	C₂×C₄⋊Q₈	—	53	2	no	—
235	C₂×C₄×Q₈	—	53	1	no	—
236	#494	—	53	2	no	—
237	#494	—	53	1	no	—
238	#494	—	106	1	no	—
239	#494	—	106	1	no	—
240	#494	C₂×D₅₃	1	1	yes	characteristic
241	#475	—	53	2	no	—
242	#475	—	53	2	no	—
243	#475	—	53	2	no	—
244	#475	—	106	2	no	—
245	#475	—	106	2	no	—
246	#475	C₂×D₅₃	1	2	yes	—
247	C₈×Q₈	—	53	1	no	—
248	C₈×Q₈	—	53	1	no	—
249	C₈×Q₈	—	53	1	no	—
250	C₈×Q₈	—	106	1	no	—
251	C₈×Q₈	—	106	1	no	—
252	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
253	C₂×#106	—	106	2	no	—
254	C₂×C₄⋊C₈	—	53	2	no	—
255	C₂×C₄⋊C₈	—	53	1	no	—
256	C₂×C₄⋊C₈	—	106	1	no	—
257	C₂×#103	—	106	2	no	—
258	C₂×C₄×C₈	—	53	1	no	—
259	C₂×C₄×C₈	—	106	1	no	—
260	#335	—	53	2	no	—
261	#335	—	53	1	no	—
262	#335	C₂×D₅₃	1	1	yes	characteristic
263	#332	—	53	2	no	—
264	#332	—	53	2	no	—
265	#332	—	53	2	no	—
266	#332	C₂×D₅₃	1	2	yes	—
267	C₅₃	C₂×#1670	1	1	yes	characteristic, complemented, Sylow
268	C₂²×Q₈	—	53	1	no	—
269	C₂²×Q₈	—	106	2	no	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	106	2	no	—
273	C₂×Q₁₆	—	106	2	no	—
274	C₂×Q₁₆	—	106	1	no	—
275	C₂×Q₁₆	—	106	1	no	—
276	C₂×Q₁₆	—	212	4	no	—
277	C₂×Q₁₆	—	212	4	no	—
278	C₂²×C₈	—	53	1	no	—
279	C₂²×C₈	—	53	1	no	—
280	C₂²×C₈	—	106	1	no	—
281	C₂²×C₈	—	106	2	no	—
282	C₄⋊Q₈	—	53	2	no	—
283	C₄⋊Q₈	—	106	2	no	—
284	C₄⋊Q₈	—	106	2	no	—
285	C₄⋊Q₈	—	106	2	no	—
286	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
287	C₄×Q₈	—	53	1	no	—
288	C₄×Q₈	—	53	1	no	—
289	C₄×Q₈	—	53	1	no	—
290	C₄×Q₈	—	106	1	no	—
291	C₄×Q₈	—	106	1	no	—
292	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	53	1	no	—
294	C₂×C₄⋊C₄	—	106	1	no	—
295	C₂×C₄⋊C₄	—	106	2	no	—
296	C₂×C₄⋊C₄	—	106	2	no	—
297	C₂×C₄²	—	53	1	no	—
298	C₂×C₄²	—	106	1	no	—
299	#106	—	2	2	no	—
300	#106	—	106	2	no	—
301	#106	—	106	2	no	—
302	#106	—	106	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	53	1	no	—
305	C₄⋊C₈	—	53	2	no	—
306	C₄⋊C₈	—	106	1	no	—
307	C₄⋊C₈	—	106	1	no	—
308	C₄⋊C₈	—	106	2	no	—
309	C₄⋊C₈	—	106	1	no	—
310	C₄⋊C₈	—	106	1	no	—
311	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	106	2	no	—
315	#103	—	106	2	no	—
316	#103	—	106	2	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	—	53	1	no	—
319	C₄×C₈	—	53	1	no	—
320	C₄×C₈	—	53	1	no	—
321	C₄×C₈	—	106	1	no	—
322	C₄×C₈	—	106	1	no	—
323	C₄×C₈	—	106	1	no	—
324	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	53	4	no	—
327	C₂×Q₈	—	53	1	no	—
328	C₂×Q₈	—	106	1	no	—
329	C₂×Q₈	—	106	2	no	—
330	C₂×Q₈	—	106	2	no	—
331	C₂×Q₈	—	212	2	no	—
332	C₂×Q₈	—	212	4	no	—
333	C₂×Q₈	—	212	4	no	—
334	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
335	C₂²×C₄	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	—	106	1	no	—
339	C₂²×C₄	—	106	1	no	—
340	C₂²×C₄	—	212	2	no	—
341	Q₁₆	—	4	2	no	—
342	Q₁₆	—	4	2	no	—
343	Q₁₆	—	212	2	no	—
344	Q₁₆	—	212	4	no	—
345	Q₁₆	—	212	4	no	—
346	Q₁₆	—	212	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	53	1	no	—
350	C₂×C₈	—	53	4	no	—
351	C₂×C₈	—	53	1	no	—
352	C₂×C₈	—	106	2	no	—
353	C₂×C₈	—	106	1	no	—
354	C₂×C₈	—	106	2	no	—
355	C₂×C₈	—	212	4	no	—
356	C₂×C₈	—	212	2	no	—
357	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
358	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	53	1	no	—
363	C₄⋊C₄	—	106	1	no	—
364	C₄⋊C₄	—	106	1	no	—
365	C₄⋊C₄	—	106	1	no	—
366	C₄⋊C₄	—	106	1	no	—
367	C₄⋊C₄	—	106	2	no	—
368	C₄⋊C₄	—	106	2	no	—
369	C₄⋊C₄	—	212	2	no	—
370	C₄⋊C₄	—	212	2	no	—
371	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
372	C₄²	—	2	1	no	—
373	C₄²	—	53	1	no	—
374	C₄²	—	53	1	no	—
375	C₄²	—	53	1	no	—
376	C₄²	—	106	1	no	—
377	C₄²	—	106	1	no	—
378	C₄²	—	106	1	no	—
379	C₄²	C₂³×D₅₃	1	1	yes	characteristic
380	C₂³	—	53	1	no	—
381	Q₈	—	2	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	53	2	no	—
385	Q₈	—	106	4	no	—
386	Q₈	—	106	1	no	—
387	Q₈	—	424	4	no	—
388	Q₈	—	212	2	no	—
389	Q₈	—	212	2	no	—
390	Q₈	Q₁₆×D₅₃	1	2	yes	complemented
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	2	no	—
397	C₂×C₄	—	53	2	no	—
398	C₂×C₄	—	53	2	no	—
399	C₂×C₄	—	53	2	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	106	2	no	—
402	C₂×C₄	—	106	4	no	—
403	C₂×C₄	—	106	1	no	—
404	C₂×C₄	—	106	1	no	—
405	C₂×C₄	—	424	4	no	—
406	C₂×C₄	—	212	2	no	—
407	C₂×C₄	—	212	2	no	—
408	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
410	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	53	2	no	—
415	C₈	—	106	1	no	—
416	C₈	—	212	2	no	—
417	C₈	—	212	1	no	—
418	C₈	SD₁₆×D₅₃	1	2	yes	—
419	C₂²	—	53	2	no	—
420	C₂²	—	53	2	no	—
421	C₂²	—	53	2	no	—
422	C₂²	#121×D₅₃	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	8	2	no	—
427	C₄	—	53	2	no	—
428	C₄	—	53	2	no	—
429	C₄	—	106	1	no	—
430	C₄	—	106	2	no	—
431	C₄	—	424	2	no	—
432	C₄	—	212	1	no	—
433	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
434	C₄	C₂×Q₁₆×D₅₃	1	1	yes	characteristic
435	C₄	#135×D₅₃	1	1	yes	characteristic
436	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
437	C₂	—	53	4	no	—
438	C₂	#460×D₅₃	1	1	yes	characteristic
439	C₂	#467×D₅₃	1	1	yes	characteristic
440	C₂	#473×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1670	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂²×D₅₃	#121
hypercenter	#1670	D₅₃
hypocenter	C₅₃	C₂×#1670
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1670

Complements

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

N	H ≅ G/N	type
4. #20274086	C₂	semidirect
5. #20274085	C₂	semidirect
6. #20274084	C₂	semidirect
7. #20274083	C₂	semidirect
8. #20274082	C₂	semidirect
11. C₅₃×#1670	C₂	semidirect
109. Q₈×D₅₃	Q₁₆	semidirect
163. Q₈×C₅₃	C₂×Q₁₆	semidirect
189. Dic₁₀₆	C₂×Q₁₆	semidirect
225. #1670	D₅₃	direct (N × H)
231. D₅₃	#1670	direct (N × H)
267. C₅₃	C₂×#1670	semidirect
390. Q₈	Q₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#494×D₅₃	2
#475×D₅₃	2
C₈×Q₈×D₅₃	2
#20274086	2
#20274085	2
#20274084	2
#20274083	2
#20274082	2
#335×D₅₃	2
#332×D₅₃	2
C₅₃×#1670	2
C₂×#1670	53

Subgroups — D53×#1670 #27366422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1670 #27366422