Subgroups — #27537345

Order 13568.

648 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20287817	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16810738	C₂	1	1	yes	maximal, characteristic
3	#20276555	C₂	1	4	yes	maximal, complemented
4	#20276550	C₂	1	4	yes	maximal, complemented
5	C₂×#16810443	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276344	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276343	C₂	1	1	yes	maximal, characteristic, complemented
8	M₃₂×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13133237	C₄	1	1	yes	characteristic
11	C₂×#13133223	C₂²	1	1	yes	characteristic
12	#16811041	—	2	2	no	—
13	#16811039	C₂²	1	4	yes	complemented
14	C₂×#13133157	C₂²	1	1	yes	characteristic
15	C₂×#13133157	C₂²	1	1	yes	characteristic
16	M₃₂×D₅₃	—	2	2	no	—
17	#16810738	C₄	1	2	yes	—
18	#16810738	C₄	1	2	yes	—
19	#16810738	C₂²	1	2	yes	—
20	#16810738	C₂²	1	2	yes	—
21	C₂×#13133152	C₄	1	1	yes	characteristic
22	C₂×#13133144	C₄	1	1	yes	characteristic
23	C₂×#13133143	C₄	1	1	yes	characteristic
24	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
25	#16810443	C₂²	1	2	yes	complemented
26	#16810443	C₂²	1	2	yes	complemented
27	#16810408	C₂²	1	4	yes	complemented
28	#16810407	C₂²	1	4	yes	complemented
29	#16810398	C₂²	1	2	yes	complemented
30	C₁₆×Dic₅₃	C₂²	1	2	yes	complemented
31	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#504	—	2	2	no	—
33	C₅₃×#504	C₂²	1	4	yes	complemented
34	C₂×M₃₂×C₅₃	—	2	2	no	—
35	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
38	#13133237	C₈	1	2	yes	—
39	#13133237	C₈	1	2	yes	—
40	#13133237	C₂×C₄	1	2	yes	—
41	#13133237	C₂×C₄	1	2	yes	—
42	C₂×#11719925	C₈	1	1	yes	characteristic
43	C₂×#11719923	C₈	1	1	yes	characteristic
44	C₂×#11719924	C₈	1	1	yes	characteristic
45	C₂×#11719922	C₈	1	1	yes	characteristic
46	#13133223	—	2	1	no	—
47	#13133223	—	2	1	no	—
48	#13133223	C₂×C₄	1	2	yes	—
49	#13133223	C₂³	1	2	yes	—
50	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
51	C₂×#11719912	—	2	1	no	—
52	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	—	2	1	no	—
54	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
55	#13133157	—	2	1	no	—
56	#13133157	—	2	1	no	—
57	#13133157	—	2	1	no	—
58	#13133157	C₂³	1	2	yes	—
59	#13133156	—	2	4	no	—
60	C₂×#11719908	—	2	1	no	—
61	C₂×#11719908	C₂³	1	2	yes	—
62	C₁₆×D₅₃	—	2	4	no	—
63	#13133152	C₂×C₄	1	2	yes	—
64	#13133152	C₂×C₄	1	2	yes	—
65	#13133144	C₂×C₄	1	2	yes	—
66	#13133144	C₂×C₄	1	2	yes	—
67	#13133143	C₂×C₄	1	2	yes	—
68	#13133143	C₂×C₄	1	2	yes	—
69	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
72	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
73	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
74	#131×C₅₃	—	2	1	no	—
75	#131×C₅₃	—	2	1	no	—
76	#131×C₅₃	C₂×C₄	1	2	yes	—
77	#131×C₅₃	C₂³	1	2	yes	—
78	C₂×M₁₆×C₅₃	—	2	1	no	—
79	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₅₃	—	2	1	no	—
81	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	M₃₂×C₅₃	—	2	1	no	—
83	M₃₂×C₅₃	—	2	4	no	—
84	M₃₂×C₅₃	D₄	1	2	yes	—
85	M₃₂×C₅₃	D₄	1	2	yes	—
86	M₃₂×C₅₃	C₂³	1	2	yes	—
87	C₂×C₁₆×C₅₃	—	2	1	no	—
88	C₂×C₁₆×C₅₃	—	2	4	no	—
89	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
90	#41×C₅₃	—	2	1	no	—
91	#41×C₅₃	—	2	1	no	—
92	#41×C₅₃	C₂×C₈	1	2	yes	—
93	#41×C₅₃	C₂²×C₄	1	2	yes	—
94	C₂×Q₈×C₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₅₃	—	2	1	no	—
96	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₅₃	—	2	1	no	—
98	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₅₃	—	2	1	no	—
100	C₂²×Dic₅₃	—	2	1	no	—
101	#11719945	—	2	1	no	—
102	#11719945	—	2	1	no	—
103	#11719945	C₂×C₈	1	2	yes	—
104	#11719945	C₂²×C₄	1	2	yes	—
105	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₅₃	—	2	1	no	—
107	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
108	M₁₆×C₅₃	—	2	1	no	—
109	M₁₆×C₅₃	—	2	2	no	—
110	M₁₆×C₅₃	—	2	2	no	—
111	M₁₆×C₅₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₅₃	—	2	1	no	—
113	C₂×C₈×C₅₃	—	2	2	no	—
114	C₂×C₈×C₅₃	—	2	2	no	—
115	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
119	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
121	#11719925	C₂×C₈	1	2	yes	—
122	#11719925	C₂×C₈	1	2	yes	—
123	#11719924	C₂×C₈	1	2	yes	—
124	#11719924	C₂×C₈	1	2	yes	—
125	#11719923	C₂×C₈	1	2	yes	—
126	#11719923	C₂×C₈	1	2	yes	—
127	#11719922	C₂×C₈	1	2	yes	—
128	#11719922	C₂×C₈	1	2	yes	—
129	C₄×Dic₅₃	—	2	1	no	—
130	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
132	#11719917	—	2	1	no	—
133	#11719917	C₂²×C₄	1	2	yes	—
134	C₂×#88322	—	2	1	no	—
135	C₂×#88322	C₂×C₈	1	1	yes	characteristic
136	C₂×#88322	C₂×C₈	1	1	yes	characteristic
137	C₂×#88322	C₂×C₈	1	1	yes	characteristic
138	C₂×#88322	C₂×C₈	1	1	yes	characteristic
139	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
140	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
141	#11719912	—	2	2	no	—
142	#11719912	—	2	2	no	—
143	C₈×D₅₃	—	2	2	no	—
144	C₈×D₅₃	—	2	2	no	—
145	C₁₆×C₅₃	—	2	2	no	—
146	C₁₆×C₅₃	C₂×D₄	1	4	yes	—
147	#11719908	—	2	2	no	—
148	#11719908	—	2	2	no	—
149	C₂³×C₅₃	—	2	1	no	—
150	C₂³×C₅₃	#131	1	1	yes	characteristic
151	C₂²×D₅₃	—	2	1	no	—
152	Q₈×C₅₃	—	2	1	no	—
153	Q₈×C₅₃	C₂²×C₈	1	2	yes	—
154	D₄×C₅₃	—	2	2	no	—
155	D₄×C₅₃	—	2	2	no	—
156	D₄×C₅₃	—	2	1	no	—
157	D₄×C₅₃	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	2	2	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
167	C₂²⋊D₅₃	—	2	2	no	—
168	C₂²⋊D₅₃	—	2	2	no	—
169	C₂×Dic₅₃	—	2	1	no	—
170	C₂×Dic₅₃	—	2	1	no	—
171	C₂×Dic₅₃	—	2	1	no	—
172	C₂×Dic₅₃	—	4	2	no	—
173	D₂₁₂	—	2	1	no	—
174	D₂₁₂	C₂²×C₈	1	2	yes	—
175	C₄×D₅₃	—	2	2	no	—
176	C₄×D₅₃	—	2	2	no	—
177	Dic₁₀₆	—	2	1	no	—
178	Dic₁₀₆	C₂²×C₈	1	2	yes	—
179	C₈×C₅₃	—	2	2	no	—
180	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
181	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
182	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
184	#88322	—	2	2	no	—
185	#88322	C₂²×C₈	1	1	yes	characteristic
186	#88322	C₂²×C₈	1	1	yes	characteristic
187	#88322	C₂²×C₈	1	1	yes	characteristic
188	#88322	C₂²×C₈	1	1	yes	characteristic
189	#33443	—	53	1	no	maximal, Sylow
190	C₂²×C₅₃	—	2	2	no	—
191	C₂²×C₅₃	—	4	1	no	—
192	C₂²×C₅₃	—	8	1	no	—
193	C₂²×C₅₃	C₈×D₄	1	1	yes	characteristic
194	C₂²×C₅₃	C₈×D₄	1	1	yes	characteristic
195	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
196	C₂×D₅₃	—	2	2	no	—
197	C₂×D₅₃	—	8	1	no	—
198	C₄×C₅₃	—	2	2	no	—
199	C₄×C₅₃	C₈×D₄	1	1	yes	characteristic
200	C₄×C₅₃	C₈×D₄	1	1	yes	characteristic
201	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
203	Dic₅₃	—	2	2	no	—
204	Dic₅₃	—	2	2	no	—
205	Dic₅₃	—	4	1	no	—
206	#3407	—	53	1	no	—
207	#3407	D₅₃	1	1	yes	characteristic, complemented
208	C₂×#443	—	53	1	no	—
209	#2171	—	53	4	no	—
210	#2170	—	53	4	no	—
211	C₂×#364	—	53	1	no	—
212	#2117	—	53	1	no	—
213	#2117	—	53	1	no	—
214	C₄×M₃₂	—	53	1	no	—
215	C₂×C₅₃	—	2	1	no	—
216	C₂×C₅₃	—	2	1	no	—
217	C₂×C₅₃	—	2	1	no	—
218	C₂×C₅₃	—	4	2	no	—
219	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
220	D₅₃	—	4	2	no	—
221	C₂×#135	—	53	1	no	—
222	C₂×#131	—	53	1	no	—
223	C₂×#131	C₂×D₅₃	1	1	yes	characteristic
224	#504	—	2	2	no	—
225	#504	—	53	4	no	—
226	#504	—	106	2	no	—
227	#504	C₂×D₅₃	1	4	yes	complemented
228	C₂×M₃₂	—	2	2	no	—
229	C₂×M₃₂	—	53	1	no	—
230	C₂×M₃₂	—	53	1	no	—
231	C₂×M₃₂	—	106	2	no	—
232	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
233	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
234	#443	—	53	2	no	—
235	#443	—	53	2	no	—
236	#443	—	53	2	no	—
237	#443	—	53	2	no	—
238	C₂×#108	—	53	1	no	—
239	C₂×#104	—	53	1	no	—
240	C₂×#104	—	53	1	no	—
241	C₂×C₄×C₈	—	53	1	no	—
242	#364	—	53	2	no	—
243	#364	—	53	2	no	—
244	#350	—	53	4	no	—
245	#350	—	53	4	no	—
246	#346	—	53	2	no	—
247	C₄×C₁₆	—	53	2	no	—
248	C₅₃	#33443	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	53	1	no	—
250	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
251	#135	—	53	2	no	—
252	#135	—	53	2	no	—
253	#135	—	53	2	no	—
254	#135	—	53	2	no	—
255	C₂×Q₁₆	—	53	1	no	—
256	C₂×SD₁₆	—	53	1	no	—
257	C₂×SD₁₆	—	53	1	no	—
258	C₂×D₈	—	53	1	no	—
259	#131	—	2	1	no	—
260	#131	—	2	1	no	—
261	#131	—	53	2	no	—
262	#131	—	53	2	no	—
263	#131	—	106	1	no	—
264	#131	—	106	1	no	—
265	#131	C₄×D₅₃	1	2	yes	—
266	#131	C₂²×D₅₃	1	2	yes	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	53	1	no	—
269	C₂×M₁₆	—	106	1	no	—
270	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	53	1	no	—
273	C₂²×C₈	—	106	1	no	—
274	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
275	C₂×C₄²	—	53	1	no	—
276	M₃₂	—	2	1	no	—
277	M₃₂	—	2	4	no	—
278	M₃₂	—	53	2	no	—
279	M₃₂	—	106	1	no	—
280	M₃₂	—	106	1	no	—
281	M₃₂	—	106	1	no	—
282	M₃₂	—	106	4	no	—
283	M₃₂	C₂²⋊D₅₃	1	2	yes	—
284	M₃₂	C₂²⋊D₅₃	1	2	yes	—
285	M₃₂	C₂²×D₅₃	1	2	yes	—
286	C₂×C₁₆	—	2	1	no	—
287	C₂×C₁₆	—	2	4	no	—
288	C₂×C₁₆	—	53	2	no	—
289	C₂×C₁₆	—	106	1	no	—
290	C₂×C₁₆	—	106	4	no	—
291	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
292	#108	—	53	2	no	—
293	#108	—	53	2	no	—
294	#104	—	53	2	no	—
295	#104	—	53	2	no	—
296	#104	—	53	2	no	—
297	#104	—	53	2	no	—
298	C₄×C₈	—	53	1	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	53	1	no	—
301	C₄×C₈	—	53	1	no	—
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	—	53	2	no	—
305	#41	—	53	2	no	—
306	#41	—	106	1	no	—
307	#41	—	106	1	no	—
308	#41	C₈×D₅₃	1	2	yes	—
309	#41	C₂×C₄×D₅₃	1	2	yes	—
310	C₂×Q₈	—	53	1	no	—
311	C₂×Q₈	C₈×D₅₃	1	1	yes	characteristic
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	53	1	no	—
314	C₂×D₄	—	106	1	no	—
315	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	106	1	no	—
318	C₂²×C₄	—	106	1	no	—
319	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
320	Q₁₆	—	53	2	no	—
321	Q₁₆	—	53	2	no	—
322	SD₁₆	—	53	2	no	—
323	SD₁₆	—	53	2	no	—
324	SD₁₆	—	53	2	no	—
325	SD₁₆	—	53	2	no	—
326	D₈	—	53	2	no	—
327	D₈	—	53	2	no	—
328	M₁₆	—	2	1	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	53	2	no	—
332	M₁₆	—	106	1	no	—
333	M₁₆	—	106	2	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	C₂×C₄×D₅₃	1	2	yes	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	1	no	—
343	C₂×C₈	—	53	1	no	—
344	C₂×C₈	—	53	1	no	—
345	C₂×C₈	—	106	1	no	—
346	C₂×C₈	—	106	2	no	—
347	C₂×C₈	—	106	2	no	—
348	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
349	C₂×C₈	#11719945	1	1	yes	characteristic
350	C₂×C₈	#11719945	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
354	C₄²	—	53	1	no	—
355	C₄²	—	53	1	no	—
356	C₄²	—	106	1	no	—
357	C₁₆	—	2	2	no	—
358	C₁₆	—	106	2	no	—
359	C₁₆	—	106	2	no	—
360	C₁₆	C₂×C₂²⋊D₅₃	1	4	yes	—
361	C₂³	—	2	1	no	—
362	C₂³	—	106	1	no	—
363	C₂³	#13133223	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	—	53	2	no	—
366	Q₈	—	106	1	no	—
367	Q₈	C₂×C₈×D₅₃	1	2	yes	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	2	1	no	—
371	D₄	—	53	2	no	—
372	D₄	—	106	2	no	—
373	D₄	—	106	2	no	—
374	D₄	—	106	1	no	—
375	D₄	C₂×C₈×D₅₃	1	2	yes	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	106	1	no	—
380	C₂×C₄	—	106	1	no	—
381	C₂×C₄	—	106	2	no	—
382	C₂×C₄	—	106	2	no	—
383	C₂×C₄	—	106	1	no	—
384	C₂×C₄	—	212	2	no	—
385	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
387	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
389	C₂×C₄	#13133223	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	53	1	no	—
393	C₈	—	53	1	no	—
394	C₈	—	53	1	no	—
395	C₈	—	53	1	no	—
396	C₈	—	106	2	no	—
397	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
398	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
399	C₈	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
400	C₈	C₂×#11719945	1	1	yes	characteristic
401	C₂²	—	2	2	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	106	2	no	—
405	C₂²	—	424	1	no	—
406	C₂²	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
407	C₂²	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
408	C₂²	C₂×#13133223	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	106	2	no	—
411	C₄	—	106	2	no	—
412	C₄	—	212	1	no	—
413	C₄	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
414	C₄	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
415	C₄	C₂×C₄×C₂²⋊D₅₃	1	1	yes	characteristic
416	C₄	C₂²×C₈×D₅₃	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	4	2	no	—
421	C₂	—	212	2	no	—
422	C₂	C₂×C₈×C₂²⋊D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²×C₂²⋊D₅₃
commutator	C₄×C₅₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#3407	C₂
socle	C₂×C₅₃	C₂×C₈×D₄
prime radical	C₂×#13133237	C₄
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#3407	D₅₃
hypocenter	C₅₃	#33443
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂ ◁ #3407

Complements

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

N	H ≅ G/N	type
1. #20287817	C₂	semidirect
3. #20276555	C₂	semidirect
4. #20276550	C₂	semidirect
5. C₂×#16810443	C₂	semidirect
6. #20276344	C₂	semidirect
7. #20276343	C₂	semidirect
8. M₃₂×Dic₅₃	C₂	semidirect
9. C₅₃×#3407	C₂	semidirect
13. #16811039	C₂²	semidirect
25. #16810443	C₂²	semidirect
26. #16810443	C₂²	semidirect
27. #16810408	C₂²	semidirect
28. #16810407	C₂²	semidirect
29. #16810398	C₂²	semidirect
30. C₁₆×Dic₅₃	C₂²	semidirect
33. C₅₃×#504	C₂²	semidirect
207. #3407	D₅₃	semidirect
227. #504	C₂×D₅₃	semidirect
248. C₅₃	#33443	semidirect

Maximal subgroups

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

subgroup	index
#20287817	2
C₂×#16810738	2
#20276555	2
#20276550	2
C₂×#16810443	2
#20276344	2
#20276343	2
M₃₂×Dic₅₃	2
C₅₃×#3407	2
#33443	53