Subgroups — D₅₃×#2222 #27538651

Order 13568.

638 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×Q₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#504×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#473×D₅₃	C₂	1	2	yes	maximal
4	#20276841	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276840	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276839	C₂	1	2	yes	maximal, complemented
7	#20276838	C₂	1	2	yes	maximal, complemented
8	#20276837	C₂	1	1	yes	maximal, characteristic, complemented
9	#368×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#362×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2222	C₂	1	1	yes	maximal, characteristic, complemented
12	#137×D₅₃	—	2	2	no	—
13	C₂×Q₁₆×D₅₃	C₂²	1	2	yes	—
14	#131×D₅₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₂₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×#13133163	C₂²	1	2	yes	complemented
17	Q₃₂×D₅₃	—	2	1	no	—
18	Q₃₂×D₅₃	—	2	1	no	—
19	Q₃₂×D₅₃	—	2	1	no	—
20	Q₃₂×D₅₃	—	2	1	no	—
21	#16811041	—	2	1	no	—
22	#16811041	C₂²	1	1	yes	characteristic
23	#16811040	C₂²	1	1	yes	characteristic
24	#16811039	—	2	1	no	—
25	#16811039	C₂²	1	1	yes	characteristic
26	M₃₂×D₅₃	—	2	1	no	—
27	M₃₂×D₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₅₃	—	2	1	no	—
29	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
30	#16810899	C₂²	1	2	yes	—
31	#16810898	C₂²	1	2	yes	—
32	#16810897	—	2	2	no	—
33	#16810896	—	2	2	no	—
34	#16810895	C₂²	1	2	yes	—
35	#108×D₅₃	C₂²	1	2	yes	—
36	#101×D₅₃	—	2	2	no	—
37	#16810453	C₂²	1	1	yes	characteristic, complemented
38	#16810452	C₂²	1	2	yes	complemented
39	#16810440	C₂²	1	2	yes	complemented
40	#16810439	C₂²	1	2	yes	complemented
41	#16810438	C₂²	1	2	yes	complemented
42	C₂×Q₃₂×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#504	C₂²	1	1	yes	characteristic
44	C₅₃×#473	C₂²	1	2	yes	—
45	C₅₃×#368	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#362	C₂²	1	2	yes	complemented
47	#41×D₅₃	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₅₃	—	2	2	no	—
49	#13133250	—	2	2	no	—
50	#13133249	—	4	2	no	—
51	#13133248	—	2	2	no	—
52	#13133247	—	2	2	no	—
53	#13133246	—	4	2	no	—
54	C₂×Dic₂₁₂	C₂³	1	2	yes	—
55	C₂×#11719925	—	2	2	no	—
56	Q₁₆×D₅₃	—	2	2	no	—
57	Q₁₆×D₅₃	—	2	2	no	—
58	Q₁₆×D₅₃	—	2	2	no	—
59	Q₁₆×D₅₃	—	2	2	no	—
60	Q₁₆×D₅₃	—	4	2	no	—
61	SD₁₆×D₅₃	—	4	2	no	—
62	#13133225	—	2	1	no	—
63	#13133225	D₄	1	1	yes	characteristic
64	#13133224	D₄	1	1	yes	characteristic
65	#13133223	—	2	1	no	—
66	#13133223	C₂³	1	1	yes	characteristic
67	M₁₆×D₅₃	—	2	1	no	—
68	M₁₆×D₅₃	—	2	2	no	—
69	M₁₆×D₅₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	—	2	1	no	—
71	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
72	Dic₄₂₄	—	2	1	no	—
73	Dic₄₂₄	—	2	1	no	—
74	#13133163	—	2	2	no	—
75	#13133163	—	2	2	no	—
76	#13133157	—	2	1	no	—
77	#13133157	C₂³	1	1	yes	characteristic
78	#13133156	—	2	1	no	—
79	#13133156	—	2	1	no	—
80	#13133156	—	2	1	no	—
81	C₂×#11719908	—	2	1	no	—
82	C₂×#11719908	C₂³	1	1	yes	characteristic
83	C₁₆×D₅₃	—	2	1	no	—
84	C₁₆×D₅₃	—	2	1	no	—
85	C₁₆×D₅₃	—	2	1	no	—
86	C₁₆×D₅₃	D₄	1	1	yes	characteristic
87	C₁₆×D₅₃	D₄	1	1	yes	characteristic
88	C₁₆×D₅₃	D₄	1	1	yes	characteristic
89	C₁₆×D₅₃	D₄	1	1	yes	characteristic
90	#13133153	C₂³	1	2	yes	—
91	#13133152	—	2	2	no	—
92	#13133136	—	2	2	no	—
93	#13133135	—	2	2	no	—
94	#13133135	—	2	2	no	—
95	#137×C₅₃	—	2	2	no	—
96	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
97	#131×C₅₃	C₂³	1	1	yes	characteristic
98	Q₃₂×C₅₃	—	2	1	no	—
99	Q₃₂×C₅₃	—	2	1	no	—
100	M₃₂×C₅₃	—	2	1	no	—
101	M₃₂×C₅₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₅₃	—	2	1	no	—
103	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
104	#108×C₅₃	C₂³	1	2	yes	—
105	#101×C₅₃	—	2	2	no	—
106	#41×C₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂×Q₈×C₅₃	—	2	2	no	—
108	#11719949	D₈	1	1	yes	characteristic
109	Q₈×D₅₃	—	4	2	no	—
110	Q₈×D₅₃	—	4	2	no	—
111	Q₈×D₅₃	—	4	2	no	—
112	Q₈×D₅₃	—	4	2	no	—
113	Q₈×D₅₃	D₈	1	1	yes	characteristic
114	#11719947	—	2	1	no	—
115	#11719947	D₈	1	1	yes	characteristic
116	D₄×D₅₃	—	2	1	no	—
117	D₄×D₅₃	D₈	1	1	yes	characteristic
118	#11719945	—	2	1	no	—
119	#11719945	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₅₃	—	2	1	no	—
121	C₂×C₄×D₅₃	—	4	2	no	—
122	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂×Dic₁₀₆	—	2	2	no	—
124	C₂×Dic₁₀₆	—	4	2	no	—
125	Q₁₆×C₅₃	—	2	2	no	—
126	Q₁₆×C₅₃	—	2	2	no	—
127	Q₁₆×C₅₃	—	4	2	no	—
128	SD₁₆×C₅₃	—	4	2	no	—
129	M₁₆×C₅₃	—	2	1	no	—
130	M₁₆×C₅₃	—	2	2	no	—
131	M₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₅₃	—	2	1	no	—
133	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
134	#11719925	—	4	2	no	—
135	#11719925	—	4	2	no	—
136	#11719925	—	4	2	no	—
137	#11719925	—	4	2	no	—
138	#11719924	—	4	2	no	—
139	#11719923	—	4	2	no	—
140	#11719917	—	2	1	no	—
141	#11719917	—	2	2	no	—
142	#11719917	C₂×D₄	1	1	yes	characteristic
143	C₂×#88322	—	2	1	no	—
144	C₂×#88322	C₂×D₄	1	1	yes	characteristic
145	Dic₂₁₂	—	2	2	no	—
146	Dic₂₁₂	—	2	2	no	—
147	Dic₂₁₂	—	4	2	no	—
148	#11719913	—	4	2	no	—
149	#11719912	—	2	1	no	—
150	#11719912	—	2	1	no	—
151	#11719912	—	2	1	no	—
152	#11719912	—	4	2	no	—
153	C₈×D₅₃	—	2	1	no	—
154	C₈×D₅₃	—	2	1	no	—
155	C₈×D₅₃	—	2	1	no	—
156	C₈×D₅₃	—	4	2	no	—
157	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
158	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
159	C₈×D₅₃	#41	1	1	yes	characteristic
160	C₈×D₅₃	#41	1	1	yes	characteristic
161	C₁₆×C₅₃	—	2	1	no	—
162	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
163	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
164	#11719908	—	2	1	no	—
165	#11719908	C₂×D₄	1	1	yes	characteristic
166	#11719908	C₂×D₄	1	1	yes	characteristic
167	C₂²×D₅₃	—	2	1	no	—
168	C₂²×D₅₃	#135	1	1	yes	characteristic
169	Q₈×C₅₃	—	4	2	no	—
170	Q₈×C₅₃	—	4	2	no	—
171	Q₈×C₅₃	C₂×D₈	1	1	yes	characteristic
172	D₄×C₅₃	—	2	1	no	—
173	D₄×C₅₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₅₃	—	2	1	no	—
175	C₂×C₄×C₅₃	—	4	2	no	—
176	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
177	C₂²⋊D₅₃	—	2	1	no	—
178	C₂²⋊D₅₃	—	2	1	no	—
179	C₂²⋊D₅₃	—	2	1	no	—
180	C₂×Dic₅₃	—	2	1	no	—
181	C₂×Dic₅₃	—	4	2	no	—
182	C₂×Dic₅₃	#135	1	1	yes	characteristic
183	D₂₁₂	—	2	1	no	—
184	D₂₁₂	C₂×D₈	1	1	yes	characteristic
185	C₄×D₅₃	—	2	1	no	—
186	C₄×D₅₃	—	2	1	no	—
187	C₄×D₅₃	—	2	1	no	—
188	C₄×D₅₃	—	8	2	no	—
189	C₄×D₅₃	—	8	2	no	—
190	C₄×D₅₃	#121	1	1	yes	characteristic
191	C₄×D₅₃	#121	1	1	yes	characteristic
192	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
193	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
194	Dic₁₀₆	—	2	1	no	—
195	Dic₁₀₆	—	4	2	no	—
196	Dic₁₀₆	—	4	2	no	—
197	Dic₁₀₆	—	8	2	no	—
198	Dic₁₀₆	—	8	2	no	—
199	Dic₁₀₆	C₂×D₈	1	1	yes	characteristic
200	C₈×C₅₃	—	2	1	no	—
201	C₈×C₅₃	—	4	2	no	—
202	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
204	#88322	—	2	1	no	—
205	#88322	—	4	2	no	—
206	#88322	#121	1	1	yes	characteristic
207	#88322	#121	1	1	yes	characteristic
208	C₂×#2222	—	53	1	no	maximal, Sylow
209	C₂²×C₅₃	—	2	1	no	—
210	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
211	C₂×D₅₃	—	2	2	no	—
212	C₂×D₅₃	—	2	1	no	—
213	C₂×D₅₃	—	4	2	no	—
214	C₂×D₅₃	#466	1	1	yes	characteristic
215	C₂×D₅₃	#466	1	1	yes	characteristic
216	C₄×C₅₃	—	2	1	no	—
217	C₄×C₅₃	—	8	2	no	—
218	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
219	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
220	Dic₅₃	—	2	1	no	—
221	Dic₅₃	—	8	2	no	—
222	Dic₅₃	#466	1	1	yes	characteristic
223	Dic₅₃	#466	1	1	yes	characteristic
224	C₂²×Q₃₂	—	53	1	no	—
225	C₂×#504	—	53	1	no	—
226	C₂×#473	—	53	2	no	—
227	#2222	—	53	1	no	—
228	#2222	—	53	1	no	—
229	#2222	—	53	2	no	—
230	#2222	—	53	1	no	—
231	#2222	—	53	2	no	—
232	#2222	D₅₃	1	1	yes	characteristic, direct product factor
233	C₂×#368	—	53	1	no	—
234	C₂×#362	—	53	2	no	—
235	C₂×C₅₃	—	2	1	no	—
236	C₂×C₅₃	—	4	1	no	—
237	C₂×C₅₃	C₂×#466	1	1	yes	characteristic
238	D₅₃	—	2	1	no	—
239	D₅₃	—	4	1	no	—
240	D₅₃	#2222	1	2	yes	direct product factor
241	C₂×#137	—	106	2	no	—
242	C₂²×Q₁₆	—	53	2	no	—
243	C₂×#131	—	53	1	no	—
244	C₂×Q₃₂	—	53	2	no	—
245	C₂×Q₃₂	—	53	1	no	—
246	C₂×Q₃₂	—	106	1	no	—
247	C₂×Q₃₂	—	106	1	no	—
248	C₂×Q₃₂	—	106	1	no	—
249	C₂×Q₃₂	—	106	1	no	—
250	C₂×Q₃₂	C₂×D₅₃	1	1	yes	characteristic, complemented
251	#504	—	53	1	no	—
252	#504	—	53	1	no	—
253	#504	—	53	1	no	—
254	#504	—	106	1	no	—
255	#504	—	106	1	no	—
256	#504	C₂×D₅₃	1	1	yes	characteristic
257	C₂×M₃₂	—	53	1	no	—
258	C₂×M₃₂	—	106	1	no	—
259	C₂²×C₁₆	—	53	1	no	—
260	C₂²×C₁₆	—	106	1	no	—
261	#473	—	53	2	no	—
262	#473	—	53	2	no	—
263	#473	—	53	2	no	—
264	#473	—	106	2	no	—
265	#473	—	106	2	no	—
266	#473	C₂×D₅₃	1	2	yes	—
267	C₂×#108	—	53	2	no	—
268	C₂×#101	—	106	2	no	—
269	#368	—	53	1	no	—
270	#368	—	53	2	no	—
271	#368	C₂×D₅₃	1	1	yes	characteristic, complemented
272	#362	—	53	2	no	—
273	#362	—	53	2	no	—
274	#362	—	53	2	no	—
275	#362	C₂×D₅₃	1	2	yes	complemented
276	C₅₃	C₂×#2222	1	1	yes	characteristic, complemented, Sylow
277	C₂×#41	—	53	1	no	—
278	C₂²×Q₈	—	106	2	no	—
279	#137	—	2	2	no	—
280	#137	—	106	2	no	—
281	#137	—	106	2	no	—
282	#137	—	106	2	no	—
283	#137	—	212	2	no	—
284	#137	—	212	2	no	—
285	C₂×Q₁₆	—	53	2	no	—
286	C₂×Q₁₆	—	106	2	no	—
287	C₂×Q₁₆	—	106	2	no	—
288	C₂×Q₁₆	—	106	2	no	—
289	C₂×Q₁₆	—	106	2	no	—
290	C₂×Q₁₆	—	106	2	no	—
291	C₂×Q₁₆	—	212	2	no	—
292	C₂×Q₁₆	C₂²×D₅₃	1	2	yes	—
293	C₂×SD₁₆	—	212	2	no	—
294	#131	—	53	1	no	—
295	#131	—	53	1	no	—
296	#131	—	53	1	no	—
297	#131	—	106	1	no	—
298	#131	—	106	1	no	—
299	#131	C₂²×D₅₃	1	1	yes	characteristic
300	C₂×M₁₆	—	53	1	no	—
301	C₂×M₁₆	—	106	1	no	—
302	C₂×M₁₆	—	106	2	no	—
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	106	1	no	—
305	Q₃₂	—	2	1	no	—
306	Q₃₂	—	2	1	no	—
307	Q₃₂	—	106	2	no	—
308	Q₃₂	—	106	2	no	—
309	Q₃₂	—	106	1	no	—
310	Q₃₂	—	106	1	no	—
311	M₃₂	—	2	1	no	—
312	M₃₂	—	53	1	no	—
313	M₃₂	—	106	1	no	—
314	M₃₂	—	106	1	no	—
315	M₃₂	—	106	1	no	—
316	M₃₂	—	106	1	no	—
317	M₃₂	C₂²×D₅₃	1	1	yes	characteristic
318	C₂×C₁₆	—	2	1	no	—
319	C₂×C₁₆	—	53	1	no	—
320	C₂×C₁₆	—	53	1	no	—
321	C₂×C₁₆	—	53	1	no	—
322	C₂×C₁₆	—	53	1	no	—
323	C₂×C₁₆	—	53	1	no	—
324	C₂×C₁₆	—	106	1	no	—
325	C₂×C₁₆	—	106	1	no	—
326	C₂×C₁₆	—	106	1	no	—
327	C₂×C₁₆	—	106	1	no	—
328	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
329	#108	—	53	2	no	—
330	#108	—	106	2	no	—
331	#108	C₂²×D₅₃	1	2	yes	—
332	#101	—	2	2	no	—
333	#101	—	106	2	no	—
334	#101	—	106	2	no	—
335	#101	—	106	2	no	—
336	#41	—	53	1	no	—
337	#41	—	53	1	no	—
338	#41	—	53	1	no	—
339	#41	—	106	1	no	—
340	#41	—	106	1	no	—
341	#41	D₄×D₅₃	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	53	1	no	—
344	C₂×Q₈	—	106	2	no	—
345	C₂×Q₈	—	212	2	no	—
346	C₂×Q₈	—	212	2	no	—
347	C₂×Q₈	—	212	2	no	—
348	C₂×Q₈	—	212	2	no	—
349	C₂×Q₈	—	212	2	no	—
350	C₂×D₄	—	53	1	no	—
351	C₂×D₄	—	106	1	no	—
352	C₂²×C₄	—	53	1	no	—
353	C₂²×C₄	—	106	1	no	—
354	C₂²×C₄	—	212	2	no	—
355	Q₁₆	—	2	2	no	—
356	Q₁₆	—	2	2	no	—
357	Q₁₆	—	4	2	no	—
358	Q₁₆	—	106	2	no	—
359	Q₁₆	—	106	2	no	—
360	Q₁₆	—	212	2	no	—
361	Q₁₆	—	212	2	no	—
362	Q₁₆	—	212	2	no	—
363	Q₁₆	—	212	2	no	—
364	Q₁₆	—	212	2	no	—
365	SD₁₆	—	4	2	no	—
366	SD₁₆	—	212	2	no	—
367	SD₁₆	—	212	2	no	—
368	SD₁₆	—	212	2	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	53	1	no	—
372	M₁₆	—	106	1	no	—
373	M₁₆	—	106	1	no	—
374	M₁₆	—	106	1	no	—
375	M₁₆	—	106	1	no	—
376	M₁₆	—	106	2	no	—
377	M₁₆	—	212	2	no	—
378	M₁₆	D₄×D₅₃	1	1	yes	characteristic
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	53	1	no	—
381	C₂×C₈	—	53	1	no	—
382	C₂×C₈	—	53	1	no	—
383	C₂×C₈	—	53	1	no	—
384	C₂×C₈	—	53	1	no	—
385	C₂×C₈	—	106	1	no	—
386	C₂×C₈	—	106	1	no	—
387	C₂×C₈	—	106	1	no	—
388	C₂×C₈	—	106	1	no	—
389	C₂×C₈	—	212	2	no	—
390	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
391	C₁₆	—	2	1	no	—
392	C₁₆	—	53	1	no	—
393	C₁₆	—	53	1	no	—
394	C₁₆	—	106	1	no	—
395	C₁₆	D₄×D₅₃	1	1	yes	characteristic
396	C₁₆	D₄×D₅₃	1	1	yes	characteristic
397	C₂³	—	53	1	no	—
398	C₂³	—	106	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	53	1	no	—
402	Q₈	—	106	1	no	—
403	Q₈	—	424	2	no	—
404	Q₈	—	424	2	no	—
405	Q₈	—	212	2	no	—
406	Q₈	—	212	2	no	—
407	Q₈	D₈×D₅₃	1	1	yes	characteristic
408	D₄	—	2	1	no	—
409	D₄	—	53	1	no	—
410	D₄	—	106	1	no	—
411	D₄	—	106	1	no	—
412	D₄	—	106	1	no	—
413	D₄	—	106	1	no	—
414	D₄	D₈×D₅₃	1	1	yes	characteristic
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	53	1	no	—
418	C₂×C₄	—	53	1	no	—
419	C₂×C₄	—	53	1	no	—
420	C₂×C₄	—	53	1	no	—
421	C₂×C₄	—	53	1	no	—
422	C₂×C₄	—	106	1	no	—
423	C₂×C₄	—	106	1	no	—
424	C₂×C₄	—	106	1	no	—
425	C₂×C₄	—	106	1	no	—
426	C₂×C₄	—	424	2	no	—
427	C₂×C₄	—	424	2	no	—
428	C₂×C₄	—	212	2	no	—
429	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	53	1	no	—
433	C₈	—	53	1	no	—
434	C₈	—	106	1	no	—
435	C₈	—	212	2	no	—
436	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
437	C₈	#41×D₅₃	1	1	yes	characteristic
438	C₂²	—	2	1	no	—
439	C₂²	—	53	1	no	—
440	C₂²	—	53	1	no	—
441	C₂²	—	106	2	no	—
442	C₂²	—	106	1	no	—
443	C₂²	—	212	2	no	—
444	C₂²	#135×D₅₃	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	53	1	no	—
448	C₄	—	53	1	no	—
449	C₄	—	106	1	no	—
450	C₄	—	424	2	no	—
451	C₄	#121×D₅₃	1	1	yes	characteristic
452	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	4	1	no	—
455	C₂	—	53	2	no	—
456	C₂	—	106	1	no	—
457	C₂	—	212	1	no	—
458	C₂	#466×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#466×D₅₃
commutator, cosocle	C₂×C₈×C₅₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2222	C₂
socle	C₂×C₅₃	C₂×#466
prime radical	#41×D₅₃	D₄
hypercenter	#2222	D₅₃
hypocenter	C₅₃	C₂×#2222
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2222

Complements

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

N	H ≅ G/N	type
1. C₂×Q₃₂×D₅₃	C₂	semidirect
4. #20276841	C₂	semidirect
5. #20276840	C₂	semidirect
6. #20276839	C₂	semidirect
7. #20276838	C₂	semidirect
8. #20276837	C₂	semidirect
9. #368×D₅₃	C₂	semidirect
10. #362×D₅₃	C₂	semidirect
11. C₅₃×#2222	C₂	semidirect
15. C₂×Dic₄₂₄	C₂²	semidirect
16. C₂×#13133163	C₂²	semidirect
37. #16810453	C₂²	semidirect
38. #16810452	C₂²	semidirect
39. #16810440	C₂²	semidirect
40. #16810439	C₂²	semidirect
41. #16810438	C₂²	semidirect
42. C₂×Q₃₂×C₅₃	C₂²	semidirect
45. C₅₃×#368	C₂²	semidirect
46. C₅₃×#362	C₂²	semidirect
232. #2222	D₅₃	direct (N × H)
240. D₅₃	#2222	direct (N × H)
250. C₂×Q₃₂	C₂×D₅₃	semidirect
271. #368	C₂×D₅₃	semidirect
275. #362	C₂×D₅₃	semidirect
276. C₅₃	C₂×#2222	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×D₅₃	2
#504×D₅₃	2
#473×D₅₃	2
#20276841	2
#20276840	2
#20276839	2
#20276838	2
#20276837	2
#368×D₅₃	2
#362×D₅₃	2
C₅₃×#2222	2
C₂×#2222	53

Subgroups — D53×#2222 #27538651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2222 #27538651