Subgroups — #27382644

Order 13568.

1046 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810741	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810739	C₂	1	1	yes	maximal, characteristic
3	#20283486	C₂	1	1	yes	maximal, characteristic
4	#20283137	C₂	1	2	yes	maximal, complemented
5	#108×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274596	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274554	C₂	1	2	yes	maximal, complemented
8	#20274549	C₂	1	2	yes	maximal, complemented
9	#20274519	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133239	C₂²	1	1	yes	characteristic
13	C₂×#13133225	C₂²	1	2	yes	—
14	C₂×#13133223	C₂²	1	2	yes	—
15	#16811091	C₂²	1	2	yes	—
16	#16810741	C₄	1	8	yes	complemented
17	#16810739	C₄	1	8	yes	complemented
18	#16810717	C₄	1	2	yes	complemented
19	#16810710	C₄	1	4	yes	complemented
20	#16810705	C₄	1	2	yes	complemented
21	C₂×#13133153	C₂²	1	1	yes	characteristic
22	C₂×#13133145	C₂²	1	2	yes	—
23	C₂×#13133143	C₂²	1	2	yes	—
24	#16810617	C₂²	1	2	yes	—
25	#16810580	—	2	2	no	—
26	#16810579	C₂²	1	2	yes	—
27	#16810577	—	2	2	no	—
28	#16810575	—	2	2	no	—
29	M₁₆×Dic₅₃	C₂²	1	2	yes	—
30	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₅₃	—	2	2	no	—
36	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
37	#16810387	C₂²	1	2	yes	—
38	#16810382	C₂²	1	2	yes	—
39	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#427	C₂²	1	1	yes	characteristic
41	C₅₃×#405	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#339	C₂²	1	2	yes	—
44	C₂×#11719945	C₂³	1	2	yes	—
45	#13133239	C₂×C₄	1	4	yes	—
46	#13133239	C₂×C₄	1	4	yes	—
47	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719913	C₂×C₄	1	2	yes	—
49	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
50	#13133225	—	2	4	no	—
51	#13133225	C₂×C₄	1	8	yes	complemented
52	#13133223	—	2	4	no	—
53	#13133223	C₂×C₄	1	8	yes	complemented
54	C₂×#11719917	C₂³	1	2	yes	—
55	C₂×#11719912	—	2	2	no	—
56	C₂×#11719912	—	2	2	no	—
57	C₂²×#88322	C₂³	1	1	yes	characteristic
58	C₂²×#88322	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₅₃	—	2	2	no	—
60	C₂×C₈×D₅₃	—	2	2	no	—
61	#13133182	C₂×C₄	1	4	yes	—
62	#13133179	C₂×C₄	1	4	yes	—
63	#13133177	—	2	4	no	—
64	#13133174	—	2	2	no	—
65	C₂×C₄×Dic₅₃	—	2	2	no	—
66	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
68	C₄²×D₅₃	—	2	2	no	—
69	#13133153	C₂×C₄	1	4	yes	complemented
70	#13133145	C₂×C₄	1	8	yes	complemented
71	#13133143	C₂×C₄	1	8	yes	complemented
72	#13133140	C₂×C₄	1	4	yes	—
73	#13133137	C₂×C₄	1	4	yes	—
74	#13133128	—	2	2	no	—
75	#13133127	—	2	2	no	—
76	C₄×#88322	—	2	2	no	—
77	C₄×#88322	—	2	2	no	—
78	C₈×Dic₅₃	—	2	2	no	—
79	C₈×Dic₅₃	—	2	2	no	—
80	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
81	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
82	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
83	C₈×Dic₅₃	D₄	1	1	yes	characteristic
84	C₈×Dic₅₃	D₄	1	1	yes	characteristic
85	C₈×Dic₅₃	D₄	1	1	yes	characteristic
86	C₈×Dic₅₃	D₄	1	1	yes	characteristic
87	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
88	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
90	#117×C₅₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
92	#108×C₅₃	C₂×C₄	1	4	yes	complemented
93	#107×C₅₃	C₂×C₄	1	2	yes	—
94	#106×C₅₃	C₂×C₄	1	2	yes	—
95	#97×C₅₃	—	2	2	no	—
96	C₄×C₈×C₅₃	—	2	2	no	—
97	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
98	C₂²×C₄×C₅₃	—	2	1	no	—
99	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
100	C₂×C₂²⋊D₅₃	—	2	2	no	—
101	C₂²×Dic₅₃	—	2	1	no	—
102	C₂²×Dic₅₃	#41	1	2	yes	—
103	#11719945	—	2	2	no	—
104	#11719945	—	2	2	no	—
105	#11719945	C₂²×C₄	1	4	yes	—
106	#11719945	C₂²×C₄	1	4	yes	—
107	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₅₃	—	2	2	no	—
109	C₂×C₄×D₅₃	—	2	4	no	—
110	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
111	M₁₆×C₅₃	—	2	2	no	—
112	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₅₃	—	2	2	no	—
114	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	#41	1	2	yes	—
122	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₅₃	—	2	2	no	—
124	C₄²×C₅₃	—	2	2	no	—
125	C₄²×C₅₃	—	2	1	no	—
126	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
127	#11719921	—	2	4	no	—
128	#11719919	—	2	4	no	—
129	C₄×Dic₅₃	—	2	8	no	—
130	C₄×Dic₅₃	—	2	1	no	—
131	C₄×Dic₅₃	—	2	4	no	—
132	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
133	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
134	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
136	#11719917	—	2	2	no	—
137	#11719917	C₂²×C₄	1	4	yes	—
138	C₂×#88322	—	2	2	no	—
139	C₂×#88322	—	2	1	no	—
140	C₂×#88322	—	2	1	no	—
141	C₂×#88322	C₂²×C₄	1	2	yes	—
142	C₂×#88322	C₂²×C₄	1	2	yes	—
143	C₂×#88322	C₂×D₄	1	1	yes	characteristic
144	C₂×#88322	C₂×D₄	1	1	yes	characteristic
145	C₂×#88322	#41	1	2	yes	—
146	Dic₂₁₂	C₄²	1	4	yes	complemented
147	D₄₂₄	C₄²	1	4	yes	complemented
148	#11719913	C₄²	1	8	yes	complemented
149	#11719912	—	2	8	no	—
150	#11719912	—	2	8	no	—
151	C₈×D₅₃	—	2	8	no	—
152	C₈×D₅₃	—	2	8	no	—
153	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
154	C₂²×D₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	4	no	—
156	C₂×C₄×C₅₃	—	2	2	no	—
157	C₂×C₄×C₅₃	—	2	4	no	—
158	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
164	C₂²⋊D₅₃	—	2	4	no	—
165	C₂²⋊D₅₃	—	2	4	no	—
166	C₂×Dic₅₃	—	2	4	no	—
167	C₂×Dic₅₃	—	2	2	no	—
168	C₂×Dic₅₃	—	2	2	no	—
169	C₂×Dic₅₃	—	2	4	no	—
170	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
171	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
172	D₂₁₂	—	2	2	no	—
173	D₂₁₂	C₂×C₄²	1	4	yes	—
174	C₄×D₅₃	—	2	4	no	—
175	C₄×D₅₃	—	2	4	no	—
176	C₄×D₅₃	—	4	8	no	—
177	Dic₁₀₆	—	2	2	no	—
178	Dic₁₀₆	C₂×C₄²	1	4	yes	—
179	C₈×C₅₃	—	2	4	no	—
180	C₈×C₅₃	C₂×C₄²	1	2	yes	—
181	C₈×C₅₃	C₂×C₄²	1	2	yes	—
182	C₈×C₅₃	C₄×D₄	1	2	yes	—
183	C₈×C₅₃	C₄×D₄	1	2	yes	—
184	#88322	—	2	4	no	—
185	#88322	—	2	2	no	—
186	#88322	C₄×D₄	1	2	yes	—
187	#88322	C₄×D₄	1	2	yes	—
188	C₄×#443	—	53	1	no	maximal, Sylow
189	C₂²×C₅₃	—	2	2	no	—
190	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
192	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
193	C₂×D₅₃	—	2	4	no	—
194	C₂×D₅₃	—	4	4	no	—
195	C₄×C₅₃	—	2	4	no	—
196	C₄×C₅₃	—	4	4	no	—
197	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
198	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
200	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
201	Dic₅₃	—	2	4	no	—
202	Dic₅₃	—	2	2	no	—
203	Dic₅₃	—	2	4	no	—
204	Dic₅₃	#443	1	4	yes	complemented
205	C₂×#443	—	53	1	no	—
206	C₂×#443	—	53	1	no	—
207	C₄×#135	—	53	1	no	—
208	C₄×#131	—	53	2	no	—
209	C₄×#108	—	53	1	no	—
210	#1772	—	53	1	no	—
211	#1772	D₅₃	1	1	yes	characteristic, complemented
212	#1764	—	53	2	no	—
213	#1764	—	53	2	no	—
214	C₄×#104	—	53	2	no	—
215	C₄²×C₈	—	53	1	no	—
216	C₂×C₅₃	—	2	1	no	—
217	C₂×C₅₃	—	2	1	no	—
218	C₂×C₅₃	C₄²×D₄	1	1	yes	characteristic
219	C₂×C₅₃	C₂×#443	1	2	yes	—
220	D₅₃	—	4	4	no	—
221	C₂×#135	—	53	1	no	—
222	C₂×#131	—	53	2	no	—
223	C₂×#131	—	53	2	no	—
224	C₄×#41	—	53	2	no	—
225	#443	—	53	8	no	—
226	#443	—	53	8	no	—
227	C₄×Q₁₆	—	53	2	no	—
228	C₄×SD₁₆	—	53	4	no	—
229	C₄×D₈	—	53	2	no	—
230	C₂×#108	—	53	1	no	—
231	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
232	#427	C₂×D₅₃	1	1	yes	characteristic
233	C₂×#104	—	53	2	no	—
234	C₂×#104	—	53	2	no	—
235	#416	—	53	2	no	—
236	#405	—	53	2	no	—
237	#405	—	106	2	no	—
238	#405	—	106	2	no	—
239	#405	C₂×D₅₃	1	2	yes	—
240	C₄×M₁₆	—	53	2	no	—
241	C₄×M₁₆	—	106	2	no	—
242	C₂×C₄×C₈	—	53	1	no	—
243	C₂×C₄×C₈	—	53	1	no	—
244	C₂×C₄×C₈	—	53	1	no	—
245	C₂×C₄×C₈	—	53	1	no	—
246	C₂×C₄×C₈	—	53	1	no	—
247	C₂×C₄×C₈	—	106	2	no	—
248	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
249	C₄³	—	53	1	no	—
250	#341	—	53	2	no	—
251	#339	—	53	2	no	—
252	#339	C₂×D₅₃	1	2	yes	—
253	C₅₃	C₄×#443	1	1	yes	characteristic, complemented, Sylow
254	C₂×#41	—	53	2	no	—
255	#135	—	53	4	no	—
256	#135	—	53	4	no	—
257	C₂×Q₁₆	—	53	1	no	—
258	C₂×SD₁₆	—	53	2	no	—
259	C₂×D₈	—	53	1	no	—
260	#131	—	53	8	no	—
261	#131	—	53	8	no	—
262	#131	—	106	4	no	—
263	#131	—	106	4	no	—
264	C₂×M₁₆	—	53	2	no	—
265	C₂×M₁₆	—	106	2	no	—
266	C₂×M₁₆	—	106	2	no	—
267	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
268	C₂²×C₈	—	53	1	no	—
269	C₂²×C₈	—	53	1	no	—
270	C₂²×C₈	—	106	2	no	—
271	C₂²×C₈	—	106	2	no	—
272	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
274	C₄×Q₈	—	53	4	no	—
275	C₄×D₄	—	53	4	no	—
276	C₄×D₄	—	106	4	no	—
277	#117	—	106	2	no	—
278	#117	C₂²×D₅₃	1	2	yes	—
279	C₂×C₄²	—	53	1	no	—
280	C₂×C₄²	—	53	1	no	—
281	C₂×C₄²	—	106	2	no	—
282	C₂×C₄²	—	106	2	no	—
283	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
284	#108	—	53	4	no	—
285	#108	C₄×D₅₃	1	4	yes	complemented
286	#107	C₄×D₅₃	1	2	yes	—
287	#106	C₄×D₅₃	1	2	yes	—
288	#104	—	53	8	no	—
289	#104	—	53	8	no	—
290	#103	—	53	4	no	—
291	#102	—	53	4	no	—
292	#97	—	2	2	no	—
293	#97	—	106	2	no	—
294	#97	—	106	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	53	2	no	—
297	C₄×C₈	—	53	2	no	—
298	C₄×C₈	—	53	4	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	53	1	no	—
301	C₄×C₈	—	53	1	no	—
302	C₄×C₈	—	53	1	no	—
303	C₄×C₈	—	106	2	no	—
304	C₄×C₈	—	106	2	no	—
305	C₄×C₈	—	106	2	no	—
306	C₄×C₈	—	106	2	no	—
307	C₄×C₈	C₄×D₅₃	1	4	yes	complemented
308	#41	—	53	4	no	—
309	#41	—	53	4	no	—
310	#41	—	106	2	no	—
311	#41	—	106	2	no	—
312	C₂×Q₈	—	53	2	no	—
313	C₂×D₄	—	53	2	no	—
314	C₂×D₄	—	106	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	53	2	no	—
317	C₂²×C₄	—	106	4	no	—
318	C₂²×C₄	—	106	1	no	—
319	C₂²×C₄	—	106	2	no	—
320	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
321	Q₁₆	—	53	4	no	—
322	SD₁₆	—	53	8	no	—
323	D₈	—	53	4	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	53	4	no	—
326	M₁₆	—	106	8	no	—
327	M₁₆	—	106	2	no	—
328	M₁₆	—	106	8	no	—
329	M₁₆	C₂×C₄×D₅₃	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	53	2	no	—
332	C₂×C₈	—	53	1	no	—
333	C₂×C₈	—	53	1	no	—
334	C₂×C₈	—	53	2	no	—
335	C₂×C₈	—	53	2	no	—
336	C₂×C₈	—	106	8	no	—
337	C₂×C₈	—	106	2	no	—
338	C₂×C₈	—	106	1	no	—
339	C₂×C₈	—	106	1	no	—
340	C₂×C₈	—	106	8	no	—
341	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
342	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
344	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
345	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
346	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
347	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
348	C₂×C₈	#11719949	1	2	yes	—
349	C₄⋊C₄	—	106	4	no	—
350	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	106	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	53	2	no	—
356	C₄²	—	53	1	no	—
357	C₄²	—	53	1	no	—
358	C₄²	—	53	2	no	—
359	C₄²	—	106	4	no	—
360	C₄²	—	106	8	no	—
361	C₄²	—	106	1	no	—
362	C₄²	C₂×C₄×D₅₃	1	2	yes	—
363	C₂³	—	106	2	no	—
364	C₂³	#41×D₅₃	1	1	yes	characteristic
365	Q₈	—	53	4	no	—
366	Q₈	—	106	2	no	—
367	D₄	—	53	4	no	—
368	D₄	—	106	4	no	—
369	D₄	—	106	4	no	—
370	D₄	—	106	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	53	2	no	—
375	C₂×C₄	—	53	2	no	—
376	C₂×C₄	—	106	4	no	—
377	C₂×C₄	—	106	4	no	—
378	C₂×C₄	—	106	2	no	—
379	C₂×C₄	—	106	2	no	—
380	C₂×C₄	—	106	4	no	—
381	C₂×C₄	—	106	4	no	—
382	C₂×C₄	—	212	8	no	—
383	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
387	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
388	C₂×C₄	C₂×#11719949	1	1	yes	characteristic
389	C₈	—	2	4	no	—
390	C₈	—	53	2	no	—
391	C₈	—	53	2	no	—
392	C₈	—	106	4	no	—
393	C₈	—	106	2	no	—
394	C₈	C₄²×D₅₃	1	2	yes	—
395	C₈	C₄²×D₅₃	1	2	yes	—
396	C₈	#13133179	1	2	yes	—
397	C₈	#13133179	1	2	yes	—
398	C₂²	—	2	2	no	—
399	C₂²	—	106	4	no	—
400	C₂²	—	212	4	no	—
401	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
402	C₂²	#16811091	1	1	yes	characteristic
403	C₂²	C₄×#11719949	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	53	4	no	—
407	C₄	—	106	4	no	—
408	C₄	—	106	4	no	—
409	C₄	—	106	2	no	—
410	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
411	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
412	C₄	C₂×#13133179	1	1	yes	characteristic
413	C₄	C₄×#11719949	1	1	yes	characteristic
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	212	4	no	—
417	C₂	C₄×#13133179	1	1	yes	characteristic
418	C₂	#443×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₅₃
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1772	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#13133239	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1772	D₅₃
hypocenter	C₅₃	C₄×#443
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
4. #20283137	C₂	semidirect
5. #108×Dic₅₃	C₂	semidirect
6. #20274596	C₂	semidirect
7. #20274554	C₂	semidirect
8. #20274549	C₂	semidirect
9. #20274519	C₂	semidirect
10. C₄×C₈×Dic₅₃	C₂	semidirect
11. C₅₃×#1772	C₂	semidirect
16. #16810741	C₄	semidirect
17. #16810739	C₄	semidirect
18. #16810717	C₄	semidirect
19. #16810710	C₄	semidirect
20. #16810705	C₄	semidirect
51. #13133225	C₂×C₄	semidirect
53. #13133223	C₂×C₄	semidirect
69. #13133153	C₂×C₄	semidirect
70. #13133145	C₂×C₄	semidirect
71. #13133143	C₂×C₄	semidirect
82. C₈×Dic₅₃	C₂×C₄	semidirect
92. #108×C₅₃	C₂×C₄	semidirect
97. C₄×C₈×C₅₃	C₂×C₄	semidirect
146. Dic₂₁₂	C₄²	semidirect
147. D₄₂₄	C₄²	semidirect
148. #11719913	C₄²	semidirect
204. Dic₅₃	#443	semidirect
211. #1772	D₅₃	semidirect
253. C₅₃	C₄×#443	semidirect
285. #108	C₄×D₅₃	semidirect
307. C₄×C₈	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810741	2
C₂×#16810739	2
#20283486	2
#20283137	2
#108×Dic₅₃	2
#20274596	2
#20274554	2
#20274549	2
#20274519	2
C₄×C₈×Dic₅₃	2
C₅₃×#1772	2
C₄×#443	53