Subgroups — #27289999

Order 13568.

806 conjugacy classes of subgroups.

The subgroup lattice has 378 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	C₂²×C₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810387	C₂	1	2	yes	maximal
4	#20274408	C₂	1	2	yes	maximal
5	C₂²×#108×C₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11719917	C₂²	1	2	yes	—
7	C₂³×#88322	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₅₃	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	C₂×C₈×Dic₅₃	—	2	2	no	—
13	C₂×C₈×Dic₅₃	—	2	2	no	—
14	C₂×C₈×Dic₅₃	C₄	1	4	yes	—
15	#16810387	—	2	4	no	—
16	#16810377	—	2	4	no	—
17	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
18	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#108×C₅₃	—	2	2	no	—
20	C₂×#108×C₅₃	—	2	2	no	—
21	C₂×#108×C₅₃	C₄	1	4	yes	complemented
22	C₂³×Dic₅₃	Q₈	1	2	yes	—
23	C₂×#11719917	—	2	2	no	—
24	C₂×#11719917	—	2	2	no	—
25	C₂×#11719917	—	2	2	no	—
26	C₂×#11719917	—	2	2	no	—
27	C₂×#11719917	—	2	2	no	—
28	C₂×#11719917	C₂×C₄	1	4	yes	—
29	C₂²×#88322	—	2	1	no	—
30	C₂²×#88322	—	2	1	no	—
31	C₂²×#88322	—	2	2	no	—
32	C₂²×#88322	—	2	1	no	—
33	C₂²×#88322	—	2	1	no	—
34	C₂²×#88322	C₂×C₄	1	2	yes	—
35	C₂²×#88322	D₄	1	2	yes	—
36	C₂²×#88322	Q₈	1	2	yes	—
37	C₂×C₄×Dic₅₃	—	2	1	no	—
38	C₂×C₄×Dic₅₃	—	2	1	no	—
39	C₂×C₄×Dic₅₃	—	2	1	no	—
40	C₂×C₄×Dic₅₃	—	2	1	no	—
41	C₂×C₄×Dic₅₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₅₃	D₄	1	2	yes	—
43	#13133153	—	2	8	no	—
44	C₈×Dic₅₃	—	2	8	no	—
45	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₅₃	—	2	2	no	—
47	C₂×M₁₆×C₅₃	—	2	2	no	—
48	C₂×M₁₆×C₅₃	—	2	2	no	—
49	C₂×M₁₆×C₅₃	—	2	2	no	—
50	C₂×M₁₆×C₅₃	—	2	2	no	—
51	C₂×M₁₆×C₅₃	C₂×C₄	1	4	yes	—
52	C₂²×C₈×C₅₃	—	2	2	no	—
53	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₅₃	D₄	1	2	yes	—
57	C₂²×C₈×C₅₃	D₄	1	2	yes	—
58	C₂²×C₈×C₅₃	D₄	1	2	yes	—
59	C₂²×C₈×C₅₃	Q₈	1	2	yes	—
60	#108×C₅₃	—	2	8	no	—
61	C₂⁴×C₅₃	C₂×Q₈	1	1	yes	characteristic
62	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
76	C₂²×Dic₅₃	—	2	2	no	—
77	C₂²×Dic₅₃	—	2	2	no	—
78	C₂²×Dic₅₃	—	2	8	no	—
79	C₂²×Dic₅₃	C₄⋊C₄	1	4	yes	—
80	M₁₆×C₅₃	—	2	4	no	—
81	M₁₆×C₅₃	—	2	4	no	—
82	M₁₆×C₅₃	—	4	2	no	—
83	M₁₆×C₅₃	—	4	2	no	—
84	C₂×C₈×C₅₃	—	2	4	no	—
85	C₂×C₈×C₅₃	—	4	2	no	—
86	C₂×C₈×C₅₃	—	4	2	no	—
87	C₂×C₈×C₅₃	C₄²	1	4	yes	—
88	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
89	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
90	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
91	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
92	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
93	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
94	C₄×Dic₅₃	—	2	2	no	—
95	C₄×Dic₅₃	—	2	2	no	—
96	C₄×Dic₅₃	—	2	2	no	—
97	C₄×Dic₅₃	—	2	2	no	—
98	#11719917	—	2	4	no	—
99	#11719917	—	2	4	no	—
100	#11719917	—	4	2	no	—
101	#11719917	—	4	2	no	—
102	C₂×#88322	—	2	2	no	—
103	C₂×#88322	—	2	2	no	—
104	C₂×#88322	—	2	2	no	—
105	C₂×#88322	—	2	2	no	—
106	C₂×#88322	—	2	2	no	—
107	C₂×#88322	—	2	2	no	—
108	C₂×#88322	—	2	4	no	—
109	C₂×#88322	—	4	2	no	—
110	C₂×#88322	—	4	2	no	—
111	C₂×#88322	C₄⋊C₄	1	4	yes	—
112	C₂³×C₅₃	—	2	4	no	—
113	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
115	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
116	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
117	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
118	C₂³×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
119	C₂³×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
120	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
121	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
129	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
137	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
138	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
139	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
140	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
143	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
144	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
145	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
146	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
148	C₂×Dic₅₃	—	2	8	no	—
149	C₂×Dic₅₃	—	2	8	no	—
150	C₂×Dic₅₃	—	2	4	no	—
151	C₂×Dic₅₃	—	2	4	no	—
152	C₂×Dic₅₃	#108	1	8	yes	complemented
153	C₈×C₅₃	—	4	4	no	—
154	C₈×C₅₃	#95	1	8	yes	—
155	#88322	—	2	4	no	—
156	#88322	—	4	4	no	—
157	#10864	—	53	1	no	maximal, Sylow
158	C₂²×C₅₃	—	2	2	no	—
159	C₂²×C₅₃	—	2	2	no	—
160	C₂²×C₅₃	—	2	2	no	—
161	C₂²×C₅₃	—	2	2	no	—
162	C₂²×C₅₃	—	2	2	no	—
163	C₂²×C₅₃	—	2	2	no	—
164	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×C₅₃	#380	1	1	yes	characteristic
166	C₂²×C₅₃	#384	1	1	yes	characteristic
167	C₂²×C₅₃	#389	1	1	yes	characteristic
168	C₂²×C₅₃	#389	1	1	yes	characteristic
169	C₂²×C₅₃	#391	1	1	yes	characteristic
170	C₂²×C₅₃	#391	1	1	yes	characteristic
171	C₂²×C₅₃	C₂×#108	1	4	yes	—
172	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
173	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
174	C₄×C₅₃	#380	1	1	yes	characteristic
175	C₄×C₅₃	#382	1	1	yes	characteristic
176	C₄×C₅₃	#389	1	1	yes	characteristic
177	C₄×C₅₃	#389	1	1	yes	characteristic
178	C₄×C₅₃	#390	1	1	yes	characteristic
179	C₄×C₅₃	#390	1	1	yes	characteristic
180	Dic₅₃	—	2	8	no	—
181	C₂²×#108	—	53	1	no	—
182	C₂²×#108	D₅₃	1	1	yes	characteristic
183	C₂²×C₄×C₈	—	53	1	no	—
184	C₂×#341	—	53	2	no	—
185	#1728	—	53	2	no	—
186	C₂×C₅₃	—	2	1	no	—
187	C₂×C₅₃	—	2	1	no	—
188	C₂×C₅₃	—	2	1	no	—
189	C₂×C₅₃	—	2	1	no	—
190	C₂×C₅₃	C₄⋊#95	1	1	yes	characteristic
191	C₂×C₅₃	C₄×#108	1	2	yes	—
192	C₂×C₅₃	#1810	1	2	yes	—
193	C₂×C₅₃	#1848	1	2	yes	—
194	C₂²×M₁₆	—	53	2	no	—
195	C₂²×M₁₆	C₂×D₅₃	1	2	yes	—
196	C₂³×C₈	—	53	1	no	—
197	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
198	C₂²×C₄²	—	53	1	no	—
199	C₂×#108	—	2	2	no	—
200	C₂×#108	—	2	2	no	—
201	C₂×#108	—	53	4	no	—
202	C₂×#108	—	106	2	no	—
203	C₂×#108	—	106	2	no	—
204	C₂×#108	Dic₅₃	1	4	yes	complemented
205	C₂×C₄×C₈	—	53	4	no	—
206	C₂×C₄×C₈	—	106	2	no	—
207	C₂×C₄×C₈	—	106	2	no	—
208	#341	—	106	4	no	—
209	#336	—	106	4	no	—
210	C₅₃	#10864	1	1	yes	characteristic, complemented, Sylow
211	C₂³×C₄	—	53	2	no	—
212	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	53	4	no	—
219	C₂×M₁₆	—	106	2	no	—
220	C₂×M₁₆	—	106	2	no	—
221	C₂×M₁₆	—	106	2	no	—
222	C₂×M₁₆	—	106	2	no	—
223	C₂×M₁₆	—	106	2	no	—
224	C₂×M₁₆	C₂×Dic₅₃	1	4	yes	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	53	2	no	—
227	C₂²×C₈	—	53	2	no	—
228	C₂²×C₈	—	53	2	no	—
229	C₂²×C₈	—	106	1	no	—
230	C₂²×C₈	—	106	1	no	—
231	C₂²×C₈	—	106	1	no	—
232	C₂²×C₈	—	106	1	no	—
233	C₂²×C₈	—	106	2	no	—
234	C₂²×C₈	Dic₁₀₆	1	2	yes	—
235	C₂²×C₈	C₄×D₅₃	1	2	yes	—
236	C₂²×C₈	C₄×D₅₃	1	2	yes	—
237	C₂²×C₈	D₂₁₂	1	2	yes	—
238	C₂²×C₈	C₂×Dic₅₃	1	2	yes	—
239	C₂²×C₈	C₂²⋊D₅₃	1	2	yes	—
240	C₂²×C₈	C₂²⋊D₅₃	1	2	yes	—
241	C₂×C₄²	—	53	2	no	—
242	C₂×C₄²	—	53	2	no	—
243	C₂×C₄²	—	106	1	no	—
244	C₂×C₄²	—	106	1	no	—
245	C₂×C₄²	—	106	1	no	—
246	C₂×C₄²	—	106	1	no	—
247	#108	—	2	8	no	—
248	#108	—	106	8	no	—
249	C₄×C₈	—	106	8	no	—
250	C₂⁴	Q₈×D₅₃	1	1	yes	characteristic
251	C₂²×C₄	—	53	4	no	—
252	C₂²×C₄	—	106	8	no	—
253	C₂²×C₄	—	106	2	no	—
254	C₂²×C₄	—	106	2	no	—
255	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
259	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
260	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
261	C₂²×C₄	#11719947	1	1	yes	characteristic
262	C₂²×C₄	#11719947	1	1	yes	characteristic
263	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
264	C₂²×C₄	#11719949	1	1	yes	characteristic
265	C₂²×C₄	#11719949	1	1	yes	characteristic
266	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
269	M₁₆	—	2	4	no	—
270	M₁₆	—	2	4	no	—
271	M₁₆	—	4	2	no	—
272	M₁₆	—	4	2	no	—
273	M₁₆	—	106	4	no	—
274	M₁₆	—	106	4	no	—
275	M₁₆	—	212	2	no	—
276	M₁₆	—	212	2	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	4	2	no	—
279	C₂×C₈	—	4	2	no	—
280	C₂×C₈	—	53	4	no	—
281	C₂×C₈	—	106	2	no	—
282	C₂×C₈	—	106	2	no	—
283	C₂×C₈	—	106	2	no	—
284	C₂×C₈	—	106	2	no	—
285	C₂×C₈	—	106	2	no	—
286	C₂×C₈	—	106	2	no	—
287	C₂×C₈	—	106	4	no	—
288	C₂×C₈	—	212	2	no	—
289	C₂×C₈	—	212	2	no	—
290	C₂×C₈	C₄×Dic₅₃	1	4	yes	—
291	C₂×C₈	#11719919	1	4	yes	—
292	C₂×C₈	#11719919	1	4	yes	—
293	C₂×C₈	C₄⋊Dic₅₃	1	4	yes	—
294	C₂×C₈	#11719921	1	4	yes	—
295	C₂×C₈	#11719921	1	4	yes	—
296	C₂×C₈	C₂²⋊Dic₅₃	1	4	yes	—
297	C₄²	—	106	2	no	—
298	C₄²	—	106	2	no	—
299	C₄²	—	106	2	no	—
300	C₄²	—	106	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
303	C₂³	#13133182	1	1	yes	characteristic
304	C₂³	Q₈×Dic₅₃	1	1	yes	characteristic
305	C₂³	#13133193	1	1	yes	characteristic
306	C₂³	#13133197	1	1	yes	characteristic
307	C₂³	#13133215	1	1	yes	characteristic
308	C₂³	#13133216	1	1	yes	characteristic
309	C₂×C₄	—	53	8	no	—
310	C₂×C₄	—	106	8	no	—
311	C₂×C₄	—	106	8	no	—
312	C₂×C₄	—	106	4	no	—
313	C₂×C₄	—	106	4	no	—
314	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
315	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
316	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
317	C₂×C₄	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
318	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
319	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
320	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
322	C₂×C₄	#13133175	1	1	yes	characteristic
323	C₂×C₄	#13133175	1	1	yes	characteristic
324	C₂×C₄	#13133179	1	1	yes	characteristic
325	C₂×C₄	#13133179	1	1	yes	characteristic
326	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
327	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
328	C₂×C₄	#13133182	1	1	yes	characteristic
329	C₂×C₄	Q₈×Dic₅₃	1	1	yes	characteristic
330	C₂×C₄	#13133188	1	1	yes	characteristic
331	C₂×C₄	#13133188	1	1	yes	characteristic
332	C₂×C₄	#13133192	1	1	yes	characteristic
333	C₂×C₄	#13133192	1	1	yes	characteristic
334	C₂×C₄	#13133193	1	1	yes	characteristic
335	C₂×C₄	#13133197	1	1	yes	characteristic
336	C₂×C₄	#13133204	1	1	yes	characteristic
337	C₂×C₄	#13133206	1	1	yes	characteristic
338	C₂×C₄	#13133208	1	1	yes	characteristic
339	C₂×C₄	#13133208	1	1	yes	characteristic
340	C₂×C₄	#13133213	1	1	yes	characteristic
341	C₂×C₄	#13133216	1	1	yes	characteristic
342	C₈	—	4	4	no	—
343	C₈	—	106	4	no	—
344	C₈	—	212	4	no	—
345	C₈	#13133124	1	8	yes	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	C₄⋊C₄×Dic₅₃	1	1	yes	characteristic
353	C₂²	#16810480	1	1	yes	characteristic
354	C₂²	#16810492	1	1	yes	characteristic
355	C₂²	#16810519	1	1	yes	characteristic
356	C₂²	#16810522	1	1	yes	characteristic
357	C₂²	#16810528	1	1	yes	characteristic
358	C₂²	#16810530	1	1	yes	characteristic
359	C₂²	#108×D₅₃	1	4	yes	—
360	C₄	—	106	8	no	—
361	C₄	C₂×#13133124	1	1	yes	characteristic
362	C₄	C₄⋊C₄×Dic₅₃	1	1	yes	characteristic
363	C₄	#16810480	1	1	yes	characteristic
364	C₄	#16810488	1	1	yes	characteristic
365	C₄	#16810519	1	1	yes	characteristic
366	C₄	#16810522	1	1	yes	characteristic
367	C₄	#16810524	1	1	yes	characteristic
368	C₄	#16810526	1	1	yes	characteristic
369	C₂	—	2	1	no	—
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	2	1	no	—
373	C₂	#20272944	1	1	yes	characteristic
374	C₂	#108×Dic₅₃	1	2	yes	—
375	C₂	#20274750	1	2	yes	—
376	C₂	#20274885	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₃
Fitting	C₂²×#108×C₅₃	C₂
socle	C₂³×C₅₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₅₃	C₂×Q₈
cosocle	C₂³×C₄×C₅₃	C₂³
hypercenter	C₂²×#108	D₅₃
hypocenter	C₅₃	#10864
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×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
21. C₂×#108×C₅₃	C₄	semidirect
152. C₂×Dic₅₃	#108	semidirect
204. C₂×#108	Dic₅₃	semidirect
210. C₅₃	#10864	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
C₂²×C₈×Dic₅₃	2
C₂×#16810387	2
#20274408	2
C₂²×#108×C₅₃	2
#10864	53