Subgroups — #27290040

Order 13568.

714 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133153	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810578	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810394	C₂	1	2	yes	maximal
4	#20274441	C₂	1	2	yes	maximal
5	C₂²×#108×C₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11719917	C₂²	1	2	yes	—
7	C₂²×#11719917	C₂²	1	1	yes	characteristic
8	C₂×#13133176	C₂²	1	1	yes	characteristic
9	C₂×#13133153	—	2	2	no	—
10	C₂×#13133153	—	2	2	no	—
11	C₂×#13133153	C₄	1	4	yes	complemented
12	#16810578	—	2	2	no	—
13	#16810578	C₄	1	4	yes	—
14	C₂×#13133127	—	2	1	no	—
15	C₂×C₈×Dic₅₃	—	2	1	no	—
16	#16810394	—	2	4	no	—
17	#16810387	—	2	4	no	—
18	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
19	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×#108×C₅₃	—	2	1	no	—
21	C₂×#108×C₅₃	—	2	1	no	—
22	C₂×#108×C₅₃	—	2	2	no	—
23	C₂×#108×C₅₃	C₄	1	4	yes	complemented
24	C₂×#11719917	—	2	1	no	—
25	C₂×#11719917	—	2	2	no	—
26	C₂×#11719917	—	2	2	no	—
27	C₂×#11719917	—	2	2	no	—
28	C₂×#11719917	—	2	1	no	—
29	C₂×#11719917	—	2	1	no	—
30	C₂×#11719917	—	2	2	no	—
31	C₂×#11719917	—	2	2	no	—
32	C₂×#11719917	C₂×C₄	1	4	yes	—
33	C₂×#11719917	C₂×C₄	1	2	yes	—
34	C₂×#11719917	D₄	1	2	yes	—
35	C₂×#11719917	Q₈	1	2	yes	—
36	C₂²×#88322	—	2	1	no	—
37	C₂²×#88322	—	2	2	no	—
38	#13133176	—	2	1	no	—
39	#13133176	—	2	1	no	—
40	#13133176	C₂×C₄	1	2	yes	—
41	#13133176	D₄	1	2	yes	—
42	C₂×C₄⋊Dic₅₃	—	2	1	no	—
43	C₂×C₂²⋊Dic₅₃	Q₈	1	2	yes	—
44	C₂×C₄×Dic₅₃	—	2	1	no	—
45	#13133153	—	2	8	no	—
46	#13133127	—	2	4	no	—
47	C₈×Dic₅₃	—	2	4	no	—
48	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₅₃	—	2	2	no	—
50	C₂×M₁₆×C₅₃	—	2	2	no	—
51	C₂×M₁₆×C₅₃	—	2	2	no	—
52	C₂×M₁₆×C₅₃	—	2	2	no	—
53	C₂×M₁₆×C₅₃	—	2	2	no	—
54	C₂×M₁₆×C₅₃	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₅₃	—	2	2	no	—
56	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
57	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
58	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₅₃	D₄	1	2	yes	—
60	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₅₃	D₄	1	2	yes	—
63	C₂²×C₈×C₅₃	Q₈	1	2	yes	—
64	#108×C₅₃	—	2	4	no	—
65	#108×C₅₃	—	2	4	no	—
66	C₂⁴×C₅₃	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
81	C₂²×Dic₅₃	—	2	2	no	—
82	M₁₆×C₅₃	—	2	4	no	—
83	M₁₆×C₅₃	—	2	4	no	—
84	M₁₆×C₅₃	—	4	2	no	—
85	M₁₆×C₅₃	—	4	2	no	—
86	C₂×C₈×C₅₃	—	2	4	no	—
87	C₂×C₈×C₅₃	—	4	2	no	—
88	C₂×C₈×C₅₃	—	4	2	no	—
89	C₂×C₈×C₅₃	C₄²	1	4	yes	—
90	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
91	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
92	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
93	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
94	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
95	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
96	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
97	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
98	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
99	C₂²⋊Dic₅₃	—	2	2	no	—
100	C₂²⋊Dic₅₃	C₄⋊C₄	1	4	yes	—
101	C₄⋊Dic₅₃	—	2	2	no	—
102	C₄⋊Dic₅₃	—	2	2	no	—
103	C₄×Dic₅₃	—	2	2	no	—
104	C₄×Dic₅₃	—	2	2	no	—
105	#11719917	—	2	2	no	—
106	#11719917	—	2	2	no	—
107	#11719917	—	2	2	no	—
108	#11719917	—	2	4	no	—
109	#11719917	—	2	4	no	—
110	#11719917	—	4	2	no	—
111	#11719917	—	4	2	no	—
112	#11719917	C₄⋊C₄	1	4	yes	—
113	C₂×#88322	—	2	2	no	—
114	C₂×#88322	—	2	2	no	—
115	C₂×#88322	—	2	2	no	—
116	C₂×#88322	—	2	4	no	—
117	C₂×#88322	—	4	2	no	—
118	C₂×#88322	—	4	2	no	—
119	C₂³×C₅₃	—	4	2	no	—
120	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
122	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
123	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
124	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
126	C₂³×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
128	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
136	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
144	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
145	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
146	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
150	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
151	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
152	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
153	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
155	C₂×Dic₅₃	—	2	4	no	—
156	C₂×Dic₅₃	—	4	4	no	—
157	C₈×C₅₃	—	4	4	no	—
158	C₈×C₅₃	#95	1	4	yes	—
159	C₈×C₅₃	#95	1	4	yes	—
160	#88322	—	2	4	no	—
161	#88322	—	4	4	no	—
162	#10873	—	53	1	no	maximal, Sylow
163	C₂²×C₅₃	—	2	2	no	—
164	C₂²×C₅₃	—	2	2	no	—
165	C₂²×C₅₃	—	2	2	no	—
166	C₂²×C₅₃	—	4	1	no	—
167	C₂²×C₅₃	—	4	1	no	—
168	C₂²×C₅₃	—	4	1	no	—
169	C₂²×C₅₃	—	4	1	no	—
170	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×C₅₃	#380	1	1	yes	characteristic
172	C₂²×C₅₃	#384	1	1	yes	characteristic
173	C₂²×C₅₃	#389	1	1	yes	characteristic
174	C₂²×C₅₃	#389	1	1	yes	characteristic
175	C₂²×C₅₃	#391	1	1	yes	characteristic
176	C₂²×C₅₃	#391	1	1	yes	characteristic
177	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
178	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
179	C₄×C₅₃	#380	1	1	yes	characteristic
180	C₄×C₅₃	#382	1	1	yes	characteristic
181	C₄×C₅₃	#389	1	1	yes	characteristic
182	C₄×C₅₃	#389	1	1	yes	characteristic
183	C₄×C₅₃	#390	1	1	yes	characteristic
184	C₄×C₅₃	#390	1	1	yes	characteristic
185	Dic₅₃	—	4	4	no	—
186	C₂²×#108	—	53	1	no	—
187	C₂²×#108	D₅₃	1	1	yes	characteristic
188	C₂×#405	—	53	1	no	—
189	C₂×#344	—	53	2	no	—
190	#1738	—	53	2	no	—
191	C₂×C₅₃	—	2	1	no	—
192	C₂×C₅₃	—	2	1	no	—
193	C₂×C₅₃	—	2	1	no	—
194	C₂×C₅₃	—	2	1	no	—
195	C₂×C₅₃	—	2	1	no	—
196	C₂×C₅₃	—	2	1	no	—
197	C₂×C₅₃	C₄⋊#95	1	1	yes	characteristic
198	C₂×C₅₃	#1953	1	2	yes	—
199	C₂²×M₁₆	—	53	1	no	—
200	C₂²×M₁₆	—	53	2	no	—
201	C₂²×M₁₆	C₂×D₅₃	1	2	yes	—
202	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
203	C₂×#117	—	53	1	no	—
204	C₂×#108	—	2	1	no	—
205	C₂×#108	—	2	1	no	—
206	C₂×#108	—	2	2	no	—
207	C₂×#108	—	53	4	no	—
208	C₂×#108	—	106	2	no	—
209	C₂×#108	—	106	2	no	—
210	C₂×#108	Dic₅₃	1	4	yes	complemented
211	#405	—	53	4	no	—
212	#405	—	106	2	no	—
213	C₂×#97	—	106	1	no	—
214	C₂×C₄×C₈	—	106	1	no	—
215	#344	—	106	4	no	—
216	#341	—	106	4	no	—
217	C₅₃	#10873	1	1	yes	characteristic, complemented, Sylow
218	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	53	2	no	—
225	C₂×M₁₆	—	53	2	no	—
226	C₂×M₁₆	—	53	2	no	—
227	C₂×M₁₆	—	53	4	no	—
228	C₂×M₁₆	—	106	1	no	—
229	C₂×M₁₆	—	106	1	no	—
230	C₂×M₁₆	—	106	1	no	—
231	C₂×M₁₆	—	106	2	no	—
232	C₂×M₁₆	—	106	2	no	—
233	C₂×M₁₆	—	106	2	no	—
234	C₂×M₁₆	—	106	2	no	—
235	C₂×M₁₆	—	106	2	no	—
236	C₂×M₁₆	C₂×Dic₅₃	1	4	yes	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	106	1	no	—
239	C₂²×C₈	—	106	2	no	—
240	C₂²×C₈	Dic₁₀₆	1	2	yes	—
241	C₂²×C₈	C₄×D₅₃	1	2	yes	—
242	C₂²×C₈	C₄×D₅₃	1	2	yes	—
243	C₂²×C₈	D₂₁₂	1	2	yes	—
244	C₂²×C₈	C₂×Dic₅₃	1	2	yes	—
245	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
246	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
247	C₂²×C₈	C₂²⋊D₅₃	1	2	yes	—
248	#117	—	53	2	no	—
249	#117	—	53	2	no	—
250	#117	—	106	1	no	—
251	#117	—	106	1	no	—
252	C₂×C₄⋊C₄	—	106	1	no	—
253	C₂×C₂²⋊C₄	—	53	2	no	—
254	C₂×C₄²	—	106	1	no	—
255	#108	—	2	4	no	—
256	#108	—	2	4	no	—
257	#108	—	106	8	no	—
258	#97	—	106	4	no	—
259	C₄×C₈	—	106	4	no	—
260	C₂⁴	Q₈×D₅₃	1	1	yes	characteristic
261	C₂²×C₄	—	106	2	no	—
262	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
266	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
267	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
268	C₂²×C₄	#11719947	1	1	yes	characteristic
269	C₂²×C₄	#11719947	1	1	yes	characteristic
270	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
271	C₂²×C₄	#11719949	1	1	yes	characteristic
272	C₂²×C₄	#11719949	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	—	4	2	no	—
279	M₁₆	—	4	2	no	—
280	M₁₆	—	53	4	no	—
281	M₁₆	—	106	2	no	—
282	M₁₆	—	106	2	no	—
283	M₁₆	—	106	2	no	—
284	M₁₆	—	106	4	no	—
285	M₁₆	—	106	4	no	—
286	M₁₆	—	212	2	no	—
287	M₁₆	—	212	2	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	106	2	no	—
292	C₂×C₈	—	106	2	no	—
293	C₂×C₈	—	106	2	no	—
294	C₂×C₈	—	106	4	no	—
295	C₂×C₈	—	212	2	no	—
296	C₂×C₈	—	212	2	no	—
297	C₂×C₈	C₄×Dic₅₃	1	4	yes	—
298	C₂×C₈	#11719919	1	2	yes	—
299	C₂×C₈	#11719919	1	2	yes	—
300	C₂×C₈	#11719919	1	4	yes	—
301	C₂×C₈	C₄⋊Dic₅₃	1	4	yes	—
302	C₂×C₈	#11719921	1	2	yes	—
303	C₂×C₈	#11719921	1	2	yes	—
304	C₂×C₈	#11719921	1	4	yes	—
305	C₂×C₈	C₂²⋊Dic₅₃	1	2	yes	—
306	C₂×C₈	C₂²⋊Dic₅₃	1	2	yes	—
307	C₄⋊C₄	—	106	2	no	—
308	C₄⋊C₄	—	106	2	no	—
309	C₂²⋊C₄	—	53	4	no	—
310	C₂²⋊C₄	—	106	2	no	—
311	C₄²	—	106	2	no	—
312	C₄²	—	106	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
315	C₂³	#13133182	1	1	yes	characteristic
316	C₂³	Q₈×Dic₅₃	1	1	yes	characteristic
317	C₂³	#13133193	1	1	yes	characteristic
318	C₂³	#13133197	1	1	yes	characteristic
319	C₂³	#13133215	1	1	yes	characteristic
320	C₂³	#13133216	1	1	yes	characteristic
321	C₂×C₄	—	106	4	no	—
322	C₂×C₄	—	212	4	no	—
323	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
324	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
325	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
326	C₂×C₄	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
327	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
328	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
329	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
331	C₂×C₄	#13133175	1	1	yes	characteristic
332	C₂×C₄	#13133175	1	1	yes	characteristic
333	C₂×C₄	#13133179	1	1	yes	characteristic
334	C₂×C₄	#13133179	1	1	yes	characteristic
335	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
336	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
337	C₂×C₄	#13133182	1	1	yes	characteristic
338	C₂×C₄	Q₈×Dic₅₃	1	1	yes	characteristic
339	C₂×C₄	#13133188	1	1	yes	characteristic
340	C₂×C₄	#13133188	1	1	yes	characteristic
341	C₂×C₄	#13133192	1	1	yes	characteristic
342	C₂×C₄	#13133192	1	1	yes	characteristic
343	C₂×C₄	#13133193	1	1	yes	characteristic
344	C₂×C₄	#13133197	1	1	yes	characteristic
345	C₂×C₄	#13133204	1	1	yes	characteristic
346	C₂×C₄	#13133206	1	1	yes	characteristic
347	C₂×C₄	#13133208	1	1	yes	characteristic
348	C₂×C₄	#13133208	1	1	yes	characteristic
349	C₂×C₄	#13133213	1	1	yes	characteristic
350	C₂×C₄	#13133216	1	1	yes	characteristic
351	C₈	—	4	4	no	—
352	C₈	—	106	4	no	—
353	C₈	—	212	4	no	—
354	C₈	#13133124	1	4	yes	—
355	C₈	#13133124	1	4	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₄⋊C₄×Dic₅₃	1	1	yes	characteristic
364	C₂²	#16810480	1	1	yes	characteristic
365	C₂²	#16810492	1	1	yes	characteristic
366	C₂²	#16810519	1	1	yes	characteristic
367	C₂²	#16810522	1	1	yes	characteristic
368	C₂²	#16810528	1	1	yes	characteristic
369	C₂²	#16810530	1	1	yes	characteristic
370	C₄	—	212	4	no	—
371	C₄	C₂×#13133124	1	1	yes	characteristic
372	C₄	C₄⋊C₄×Dic₅₃	1	1	yes	characteristic
373	C₄	#16810480	1	1	yes	characteristic
374	C₄	#16810488	1	1	yes	characteristic
375	C₄	#16810519	1	1	yes	characteristic
376	C₄	#16810522	1	1	yes	characteristic
377	C₄	#16810524	1	1	yes	characteristic
378	C₄	#16810526	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	#20272944	1	1	yes	characteristic
386	C₂	#20275503	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13133188
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₃
Fitting	C₂²×#108×C₅₃	C₂
socle	C₂²×C₅₃	#389
prime radical	C₂⁴×C₅₃	C₂×Q₈
cosocle	C₂³×C₄×C₅₃	C₂³
hypercenter	C₂²×#108	D₅₃
hypocenter	C₅₃	#10873
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
11. C₂×#13133153	C₄	semidirect
23. C₂×#108×C₅₃	C₄	semidirect
210. C₂×#108	Dic₅₃	semidirect
217. C₅₃	#10873	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133153	2
C₂×#16810578	2
C₂×#16810394	2
#20274441	2
C₂²×#108×C₅₃	2
#10873	53