Subgroups — #27273610

Order 13568.

636 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	#20283343	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810674	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20272553	C₂	1	1	yes	maximal, characteristic, complemented
5	#20272552	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272551	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₅₃	C₄	1	2	yes	—
9	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
10	#16810679	C₄	1	2	yes	—
11	#16810677	—	2	1	no	—
12	#16810676	C₂²	1	1	yes	characteristic
13	#16810674	—	2	1	no	—
14	#16810674	—	2	1	no	—
15	#16810674	—	2	1	no	—
16	#16810674	C₄	1	2	yes	—
17	#16810674	C₄	1	2	yes	—
18	#16810645	C₄	1	2	yes	—
19	C₂×#13133146	—	2	1	no	—
20	#16810585	—	2	1	no	—
21	C₂×#13133129	—	2	1	no	—
22	C₄×#11719917	C₂²	1	1	yes	characteristic
23	#16810575	—	2	1	no	—
24	M₁₆×Dic₅₃	C₄	1	2	yes	—
25	C₄×#11719912	—	2	1	no	—
26	C₄×#11719912	—	2	1	no	—
27	#97×D₅₃	—	2	1	no	—
28	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₅₃	—	2	1	no	—
30	C₅₃×#431	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
36	C₂×#11719917	C₂×C₄	1	2	yes	—
37	C₂×#11719912	—	2	2	no	—
38	C₂×#11719912	—	2	2	no	—
39	M₁₆×D₅₃	—	2	4	no	—
40	M₁₆×D₅₃	—	2	4	no	—
41	C₂²×#88322	—	2	1	no	—
42	C₂×C₈×D₅₃	—	2	2	no	—
43	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
46	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₅₃	D₄	1	1	yes	characteristic
51	C₄²×D₅₃	D₄	1	1	yes	characteristic
52	C₄²×D₅₃	D₄	1	1	yes	characteristic
53	C₄²×D₅₃	D₄	1	1	yes	characteristic
54	C₄⋊#88322	C₂×C₄	1	2	yes	—
55	#13133146	—	2	2	no	—
56	#13133146	—	2	2	no	—
57	#13133146	—	2	2	no	—
58	C₂²⋊#88322	—	2	1	no	—
59	#13133129	—	2	2	no	—
60	#13133129	—	2	2	no	—
61	#13133129	—	2	2	no	—
62	#13133128	—	2	1	no	—
63	#13133127	—	2	2	no	—
64	#13133127	—	2	2	no	—
65	C₄×#88322	—	2	1	no	—
66	C₄×#88322	—	2	1	no	—
67	C₄×#88322	—	2	1	no	—
68	C₄×#88322	C₂×C₄	1	2	yes	—
69	C₈×Dic₅₃	—	2	2	no	—
70	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₅₃	—	2	1	no	—
72	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
74	C₂²⋊C₈×C₅₃	—	2	1	no	—
75	#97×C₅₃	—	2	1	no	—
76	C₄×C₈×C₅₃	—	2	1	no	—
77	C₄×C₈×C₅₃	—	2	1	no	—
78	C₄×C₈×C₅₃	—	2	1	no	—
79	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
80	C₂³×D₅₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	—	2	2	no	—
88	C₂×C₄×D₅₃	—	2	2	no	—
89	C₂×C₄×D₅₃	—	2	4	no	—
90	C₂×C₄×D₅₃	—	4	2	no	—
91	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
103	M₁₆×C₅₃	—	2	2	no	—
104	M₁₆×C₅₃	M₁₆	1	4	yes	complemented
105	C₂×C₈×C₅₃	—	2	2	no	—
106	C₂×C₈×C₅₃	—	2	2	no	—
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	—	4	2	no	—
109	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
113	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
114	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
115	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
125	#11719917	—	2	2	no	—
126	#11719917	M₁₆	1	4	yes	complemented
127	C₂×#88322	—	2	2	no	—
128	C₂×#88322	—	2	2	no	—
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	—	4	2	no	—
131	#11719912	—	2	8	no	—
132	#11719912	—	4	4	no	—
133	C₈×D₅₃	—	2	8	no	—
134	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂²×D₅₃	—	2	2	no	—
136	C₂²×D₅₃	—	2	2	no	—
137	C₂²×D₅₃	—	4	1	no	—
138	C₂²×D₅₃	#95	1	1	yes	characteristic
139	C₂²×D₅₃	#95	1	1	yes	characteristic
140	C₂×C₄×C₅₃	—	2	2	no	—
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
149	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
150	C₂×Dic₅₃	—	2	2	no	—
151	C₂×Dic₅₃	—	2	2	no	—
152	C₂×Dic₅₃	—	4	1	no	—
153	C₂×Dic₅₃	#95	1	1	yes	characteristic
154	C₂×Dic₅₃	#95	1	1	yes	characteristic
155	C₂×Dic₅₃	#95	1	1	yes	characteristic
156	C₂×Dic₅₃	#95	1	1	yes	characteristic
157	C₂×Dic₅₃	#95	1	1	yes	characteristic
158	C₂×Dic₅₃	#95	1	1	yes	characteristic
159	C₄×D₅₃	—	2	2	no	—
160	C₄×D₅₃	—	2	1	no	—
161	C₄×D₅₃	—	2	1	no	—
162	C₄×D₅₃	—	2	1	no	—
163	C₄×D₅₃	—	2	1	no	—
164	C₄×D₅₃	—	2	2	no	—
165	C₄×D₅₃	—	2	2	no	—
166	C₄×D₅₃	—	2	2	no	—
167	C₄×D₅₃	—	2	2	no	—
168	C₄×D₅₃	—	2	2	no	—
169	C₄×D₅₃	—	2	2	no	—
170	C₄×D₅₃	—	4	1	no	—
171	C₄×D₅₃	—	4	1	no	—
172	C₄×D₅₃	#108	1	4	yes	—
173	C₈×C₅₃	—	2	4	no	—
174	C₈×C₅₃	—	4	2	no	—
175	C₈×C₅₃	—	4	2	no	—
176	#88322	—	2	4	no	—
177	#88322	—	4	2	no	—
178	#88322	—	4	2	no	—
179	#7888	—	53	1	no	maximal, Sylow
180	C₂²×C₅₃	—	2	1	no	—
181	C₂²×C₅₃	—	2	1	no	—
182	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
183	C₂²×C₅₃	#423	1	2	yes	—
184	C₂×D₅₃	—	2	1	no	—
185	C₂×D₅₃	—	2	1	no	—
186	C₂×D₅₃	—	2	1	no	—
187	C₂×D₅₃	—	2	1	no	—
188	C₂×D₅₃	—	2	1	no	—
189	C₂×D₅₃	—	4	4	no	—
190	C₂×D₅₃	#341	1	2	yes	—
191	C₄×C₅₃	—	2	1	no	—
192	C₄×C₅₃	—	2	1	no	—
193	C₄×C₅₃	C₄×M₁₆	1	1	yes	characteristic
194	C₄×C₅₃	C₄×M₁₆	1	1	yes	characteristic
195	C₄×C₅₃	#407	1	2	yes	—
196	C₄×C₅₃	#421	1	2	yes	—
197	C₄×C₅₃	C₂×#108	1	2	yes	—
198	Dic₅₃	—	2	1	no	—
199	Dic₅₃	—	2	1	no	—
200	Dic₅₃	—	2	1	no	—
201	Dic₅₃	—	2	1	no	—
202	Dic₅₃	—	2	1	no	—
203	Dic₅₃	#341	1	2	yes	—
204	#2920	—	53	1	no	—
205	C₂×#431	—	53	1	no	—
206	C₂×C₄×M₁₆	—	53	1	no	—
207	#1278	—	53	1	no	—
208	#1278	—	53	1	no	—
209	#1278	—	53	1	no	—
210	#1278	D₅₃	1	1	yes	characteristic, complemented
211	C₂×C₅₃	—	2	2	no	—
212	C₂×C₅₃	#1728	1	1	yes	characteristic
213	C₂×C₅₃	#1733	1	1	yes	characteristic
214	C₂×C₅₃	C₂×#341	1	1	yes	characteristic
215	D₅₃	—	2	2	no	—
216	D₅₃	—	4	1	no	—
217	C₂²×M₁₆	—	53	2	no	—
218	C₂²×C₄²	—	53	1	no	—
219	#432	—	53	2	no	—
220	#432	—	106	1	no	—
221	#431	—	53	2	no	—
222	#431	—	53	2	no	—
223	#431	—	53	1	no	—
224	#431	—	106	1	no	—
225	#431	—	106	1	no	—
226	#431	—	106	1	no	—
227	#431	C₂×D₅₃	1	1	yes	characteristic
228	#423	—	53	2	no	—
229	C₂×C₄⋊C₈	—	106	1	no	—
230	#407	—	106	1	no	—
231	C₂×C₂²⋊C₈	—	106	1	no	—
232	C₄×M₁₆	—	53	2	no	—
233	C₄×M₁₆	—	53	1	no	—
234	C₄×M₁₆	—	106	1	no	—
235	C₄×M₁₆	—	106	1	no	—
236	C₄×M₁₆	—	106	1	no	—
237	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
238	C₂×#97	—	106	1	no	—
239	C₂×C₄×C₈	—	53	1	no	—
240	C₂×C₄×C₈	—	106	1	no	—
241	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
242	C₅₃	#7888	1	1	yes	characteristic, complemented, Sylow
243	C₂³×C₄	—	53	1	no	—
244	C₂³×C₄	—	53	1	no	—
245	C₂³×C₄	—	53	1	no	—
246	C₂×M₁₆	—	53	2	no	—
247	C₂×M₁₆	—	106	2	no	—
248	C₂×M₁₆	—	106	2	no	—
249	C₂×M₁₆	—	106	4	no	—
250	C₂×M₁₆	—	106	4	no	—
251	C₂×M₁₆	C₄×D₅₃	1	2	yes	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	106	2	no	—
254	C₂²×C₈	—	106	1	no	—
255	C₂×C₄²	—	53	1	no	—
256	C₂×C₄²	—	53	1	no	—
257	C₂×C₄²	—	53	1	no	—
258	C₂×C₄²	—	53	1	no	—
259	C₂×C₄²	—	53	1	no	—
260	C₂×C₄²	—	53	1	no	—
261	C₂×C₄²	—	53	1	no	—
262	C₂×C₄²	—	53	1	no	—
263	C₂×C₄²	—	53	1	no	—
264	C₂×C₄²	—	53	1	no	—
265	C₂×C₄²	—	53	1	no	—
266	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
267	C₄⋊C₈	—	53	2	no	—
268	C₄⋊C₈	—	106	2	no	—
269	C₄⋊C₈	—	106	2	no	—
270	C₄⋊C₈	—	106	2	no	—
271	C₄⋊C₈	C₄×D₅₃	1	2	yes	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	106	2	no	—
274	C₂²⋊C₈	—	106	2	no	—
275	C₂²⋊C₈	—	106	2	no	—
276	C₂²⋊C₈	—	106	1	no	—
277	#97	—	2	1	no	—
278	#97	—	106	2	no	—
279	#97	—	106	2	no	—
280	#97	—	106	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	—	53	2	no	—
285	C₄×C₈	—	106	2	no	—
286	C₄×C₈	—	106	1	no	—
287	C₄×C₈	—	106	1	no	—
288	C₄×C₈	—	106	1	no	—
289	C₄×C₈	C₄×D₅₃	1	2	yes	—
290	C₂⁴	—	53	1	no	—
291	C₂²×C₄	—	53	1	no	—
292	C₂²×C₄	—	53	1	no	—
293	C₂²×C₄	—	53	1	no	—
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	1	no	—
296	C₂²×C₄	—	53	1	no	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	1	no	—
301	C₂²×C₄	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	106	4	no	—
307	C₂²×C₄	—	106	2	no	—
308	C₂²×C₄	—	106	2	no	—
309	C₂²×C₄	—	212	2	no	—
310	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
312	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
313	M₁₆	—	2	2	no	—
314	M₁₆	—	53	4	no	—
315	M₁₆	—	106	8	no	—
316	M₁₆	—	106	2	no	—
317	M₁₆	—	212	4	no	—
318	M₁₆	#11719912	1	4	yes	complemented
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	106	8	no	—
324	C₂×C₈	—	106	2	no	—
325	C₂×C₈	—	106	2	no	—
326	C₂×C₈	—	106	2	no	—
327	C₂×C₈	—	212	2	no	—
328	C₄²	—	53	1	no	—
329	C₄²	—	53	1	no	—
330	C₄²	—	53	1	no	—
331	C₄²	—	53	1	no	—
332	C₄²	—	53	1	no	—
333	C₄²	—	53	1	no	—
334	C₄²	—	53	1	no	—
335	C₄²	—	53	1	no	—
336	C₄²	—	53	1	no	—
337	C₄²	—	53	1	no	—
338	C₄²	—	53	1	no	—
339	C₄²	—	53	1	no	—
340	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
341	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
342	C₄²	D₄×D₅₃	1	1	yes	characteristic
343	C₄²	D₄×D₅₃	1	1	yes	characteristic
344	C₂³	—	53	1	no	—
345	C₂³	—	53	1	no	—
346	C₂³	—	106	2	no	—
347	C₂³	—	106	2	no	—
348	C₂³	—	212	1	no	—
349	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	53	1	no	—
353	C₂×C₄	—	53	4	no	—
354	C₂×C₄	—	53	1	no	—
355	C₂×C₄	—	53	1	no	—
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	53	1	no	—
358	C₂×C₄	—	53	1	no	—
359	C₂×C₄	—	106	2	no	—
360	C₂×C₄	—	106	2	no	—
361	C₂×C₄	—	106	2	no	—
362	C₂×C₄	—	106	2	no	—
363	C₂×C₄	—	106	1	no	—
364	C₂×C₄	—	106	1	no	—
365	C₂×C₄	—	106	1	no	—
366	C₂×C₄	—	106	1	no	—
367	C₂×C₄	—	106	2	no	—
368	C₂×C₄	—	106	2	no	—
369	C₂×C₄	—	106	2	no	—
370	C₂×C₄	—	106	2	no	—
371	C₂×C₄	—	106	2	no	—
372	C₂×C₄	—	212	1	no	—
373	C₂×C₄	—	212	1	no	—
374	C₂×C₄	—	212	1	no	—
375	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
376	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
377	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
378	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
379	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
380	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
381	C₂×C₄	M₁₆×D₅₃	1	2	yes	—
382	C₂×C₄	C₂×#11719912	1	2	yes	—
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	106	4	no	—
387	C₈	—	212	2	no	—
388	C₈	—	212	2	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	53	2	no	—
392	C₂²	—	106	1	no	—
393	C₂²	—	106	1	no	—
394	C₂²	—	106	1	no	—
395	C₂²	—	106	1	no	—
396	C₂²	—	106	1	no	—
397	C₂²	—	212	4	no	—
398	C₂²	#95×D₅₃	1	1	yes	characteristic
399	C₂²	#16810645	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	53	2	no	—
403	C₄	—	106	1	no	—
404	C₄	—	106	1	no	—
405	C₄	—	106	1	no	—
406	C₄	—	106	1	no	—
407	C₄	—	106	1	no	—
408	C₄	C₄×#11719912	1	1	yes	characteristic
409	C₄	#16810575	1	1	yes	characteristic
410	C₄	#16810585	1	2	yes	—
411	C₄	#16810638	1	2	yes	—
412	C₄	#108×D₅₃	1	2	yes	—
413	C₂	—	2	2	no	—
414	C₂	—	106	2	no	—
415	C₂	—	212	1	no	—
416	C₂	#20274407	1	1	yes	characteristic
417	C₂	#20274423	1	1	yes	characteristic
418	C₂	#341×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1278	C₂
socle	C₂²×C₅₃	C₂×#95
prime radical	C₂³×D₅₃	C₄⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1278	D₅₃
hypocenter	C₅₃	#7888
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1278

Complements

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

N	H ≅ G/N	type
4. #20272553	C₂	semidirect
5. #20272552	C₂	semidirect
6. #20272551	C₂	semidirect
7. C₅₃×#1278	C₂	semidirect
104. M₁₆×C₅₃	M₁₆	semidirect
126. #11719917	M₁₆	semidirect
210. #1278	D₅₃	semidirect
242. C₅₃	#7888	semidirect
318. M₁₆	#11719912	semidirect

Maximal subgroups

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

subgroup	index
#20283343	2
C₂×#16810674	2
C₄×M₁₆×D₅₃	2
#20272553	2
#20272552	2
#20272551	2
C₅₃×#1278	2
#7888	53