Subgroups — #27368037

Order 13568.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285229	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284877	C₂	1	2	yes	maximal
3	#20274119	C₂	1	1	yes	maximal, characteristic, complemented
4	#20274114	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274109	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274104	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274097	C₂	1	2	yes	maximal, complemented
8	#20274090	C₂	1	2	yes	maximal, complemented
9	#20273478	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273423	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₅₃	C₂	1	1	yes	maximal, characteristic
12	#16811180	C₂²	1	2	yes	—
13	#16811028	C₂²	1	1	yes	characteristic
14	#16811028	C₂²	1	1	yes	characteristic
15	#16811025	—	2	1	no	—
16	#16811025	—	2	1	no	—
17	#16811021	C₂²	1	2	yes	—
18	#16810964	—	2	2	no	—
19	#16810918	C₂²	1	2	yes	—
20	#16810913	C₂²	1	2	yes	—
21	#16810833	C₂²	1	2	yes	—
22	#16810828	C₂²	1	2	yes	—
23	#16810785	—	2	2	no	—
24	#16810728	—	2	2	no	—
25	#16810723	—	2	2	no	—
26	#16810680	C₂²	1	2	yes	—
27	#16810661	—	2	1	no	—
28	#16810661	—	2	1	no	—
29	#16810376	C₂²	1	1	yes	characteristic
30	#16810376	C₂²	1	1	yes	characteristic
31	#16810374	C₂²	1	2	yes	—
32	#16810371	C₂²	1	2	yes	—
33	#16810371	C₂²	1	2	yes	—
34	#16810368	C₂²	1	2	yes	—
35	#16810368	C₂²	1	2	yes	—
36	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₅₃	—	2	1	no	—
40	C₈×D₄×C₅₃	—	2	1	no	—
41	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#431	—	2	1	no	—
44	C₅₃×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₅₃	—	2	1	no	—
46	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#11719925	—	2	2	no	—
48	C₂×#11719923	—	2	2	no	—
49	#13133217	C₂³	1	2	yes	—
50	#13133217	C₂³	1	2	yes	—
51	#13133209	—	2	2	no	—
52	#13133196	—	2	2	no	—
53	#13133196	—	2	2	no	—
54	C₄×Dic₁₀₆	—	2	2	no	—
55	C₄×Dic₁₀₆	—	2	2	no	—
56	#13133176	—	2	2	no	—
57	#13133151	—	2	1	no	—
58	#13133151	—	2	1	no	—
59	#13133151	—	2	1	no	—
60	#13133151	—	2	1	no	—
61	#13133150	—	2	2	no	—
62	#13133149	—	2	2	no	—
63	#13133149	—	2	2	no	—
64	#13133148	—	2	2	no	—
65	C₄⋊#88322	C₂³	1	2	yes	—
66	C₄⋊#88322	C₂³	1	2	yes	—
67	#13133141	—	2	2	no	—
68	#13133140	—	2	2	no	—
69	#13133140	—	2	2	no	—
70	#13133138	—	2	2	no	—
71	C₂²⋊#88322	—	2	2	no	—
72	#13133128	—	2	2	no	—
73	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₅₃	—	2	1	no	—
75	C₂²×C₈×C₅₃	—	2	1	no	—
76	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₅₃	—	2	1	no	—
81	C₄×D₄×C₅₃	—	2	1	no	—
82	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
83	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
84	#117×C₅₃	—	2	1	no	—
85	#117×C₅₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₃	—	2	1	no	—
87	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₅₃	—	2	1	no	—
89	C₄⋊C₈×C₅₃	—	2	1	no	—
90	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₅₃	—	2	1	no	—
93	C₂²⋊C₈×C₅₃	—	2	1	no	—
94	C₂²⋊C₈×C₅₃	—	2	1	no	—
95	C₄×C₈×C₅₃	—	2	1	no	—
96	C₄×C₈×C₅₃	—	2	1	no	—
97	C₄×C₈×C₅₃	—	2	1	no	—
98	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	#41×C₅₃	—	2	2	no	—
103	#41×C₅₃	—	2	2	no	—
104	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₅₃	—	2	1	no	—
106	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	—	2	1	no	—
108	C₂²×C₄×C₅₃	—	2	1	no	—
109	C₂²×C₄×C₅₃	—	2	1	no	—
110	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
113	C₂×Dic₁₀₆	—	2	2	no	—
114	C₂×Dic₁₀₆	—	2	2	no	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	—	2	2	no	—
117	C₂×C₈×C₅₃	—	2	1	no	—
118	C₂×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	—	4	2	no	—
120	C₂×C₈×C₅₃	—	4	2	no	—
121	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₅₃	—	2	1	no	—
126	C₄⋊C₄×C₅₃	—	2	1	no	—
127	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₅₃	—	2	1	no	—
130	C₂²⋊C₄×C₅₃	—	2	1	no	—
131	C₂²⋊C₄×C₅₃	—	2	1	no	—
132	C₄²×C₅₃	—	2	1	no	—
133	C₄²×C₅₃	—	2	1	no	—
134	C₄²×C₅₃	—	2	1	no	—
135	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₅₃	#41	1	1	yes	characteristic
138	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₅₃	—	4	2	no	—
140	#11719925	—	4	4	no	—
141	#11719923	—	4	4	no	—
142	C₄⋊Dic₅₃	—	2	2	no	—
143	C₄⋊Dic₅₃	—	2	2	no	—
144	C₄⋊Dic₅₃	—	2	2	no	—
145	C₄⋊Dic₅₃	—	2	2	no	—
146	#11719919	—	4	2	no	—
147	#11719919	—	4	2	no	—
148	C₄×Dic₅₃	—	4	2	no	—
149	C₂×#88322	—	2	2	no	—
150	C₂×#88322	—	2	2	no	—
151	C₂³×C₅₃	—	2	1	no	—
152	C₂³×C₅₃	#121	1	1	yes	characteristic
153	Q₈×C₅₃	—	2	1	no	—
154	Q₈×C₅₃	#135	1	2	yes	—
155	D₄×C₅₃	—	2	4	no	—
156	D₄×C₅₃	—	2	1	no	—
157	D₄×C₅₃	#135	1	2	yes	—
158	C₂×C₄×C₅₃	—	2	4	no	—
159	C₂×C₄×C₅₃	—	2	1	no	—
160	C₂×C₄×C₅₃	—	2	1	no	—
161	C₂×C₄×C₅₃	—	2	1	no	—
162	C₂×C₄×C₅₃	—	2	1	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	4	1	no	—
167	C₂×C₄×C₅₃	—	4	2	no	—
168	C₂×C₄×C₅₃	—	4	1	no	—
169	C₂×C₄×C₅₃	—	4	1	no	—
170	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₅₃	—	4	2	no	—
177	C₂×Dic₅₃	—	4	2	no	—
178	Dic₁₀₆	—	4	2	no	—
179	Dic₁₀₆	—	4	2	no	—
180	Dic₁₀₆	—	8	2	no	—
181	C₈×C₅₃	—	2	1	no	—
182	C₈×C₅₃	—	2	1	no	—
183	C₈×C₅₃	—	4	1	no	—
184	C₈×C₅₃	—	4	1	no	—
185	C₈×C₅₃	#137	1	2	yes	—
186	C₈×C₅₃	#137	1	2	yes	—
187	#88322	—	4	2	no	—
188	#88322	—	4	2	no	—
189	#19273	—	53	1	no	maximal, Sylow
190	C₂²×C₅₃	—	2	1	no	—
191	C₂²×C₅₃	—	2	1	no	—
192	C₂²×C₅₃	—	2	2	no	—
193	C₂²×C₅₃	—	2	1	no	—
194	C₂²×C₅₃	—	4	1	no	—
195	C₂²×C₅₃	—	4	1	no	—
196	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
197	C₄×C₅₃	—	2	1	no	—
198	C₄×C₅₃	—	2	1	no	—
199	C₄×C₅₃	—	2	2	no	—
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	—	2	1	no	—
202	C₄×C₅₃	—	4	1	no	—
203	C₄×C₅₃	—	4	1	no	—
204	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
205	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
206	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
207	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
208	Dic₅₃	—	8	2	no	—
209	Dic₅₃	—	8	2	no	—
210	#3160	—	53	1	no	—
211	#3116	—	53	2	no	—
212	C₈×#41	D₅₃	1	1	yes	characteristic
213	#1676	—	53	1	no	—
214	#1675	—	53	1	no	—
215	#1674	—	53	1	no	—
216	#1673	—	53	1	no	—
217	#1672	—	53	2	no	—
218	#1671	—	53	2	no	—
219	#1568	—	53	1	no	—
220	#1554	—	53	2	no	—
221	C₂×C₅₃	—	4	1	no	—
222	C₂×C₅₃	—	4	2	no	—
223	C₂×C₅₃	#3039	1	1	yes	characteristic
224	C₂×C₅₃	#3050	1	1	yes	characteristic
225	C₂×C₅₃	#3067	1	1	yes	characteristic
226	#533	—	53	2	no	—
227	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
228	#500	—	53	1	no	—
229	#500	—	53	1	no	—
230	#499	—	106	1	no	—
231	#499	—	106	1	no	—
232	#498	—	53	2	no	—
233	#485	—	106	2	no	—
234	#477	—	53	2	no	—
235	#476	—	53	2	no	—
236	#462	—	53	2	no	—
237	#461	—	53	2	no	—
238	#452	—	106	2	no	—
239	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
240	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
241	#441	—	106	2	no	—
242	#440	—	106	2	no	—
243	C₈×D₄	—	2	1	no	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
246	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
247	#432	—	53	2	no	—
248	#431	—	2	1	no	—
249	#431	C₂×D₅₃	1	1	yes	characteristic
250	#427	—	106	1	no	—
251	#427	—	106	1	no	—
252	C₂×C₄×C₈	—	2	1	no	—
253	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
254	#335	—	53	1	no	—
255	#335	—	53	1	no	—
256	#334	—	53	2	no	—
257	#333	—	53	2	no	—
258	#333	—	53	2	no	—
259	#332	—	53	2	no	—
260	#332	—	53	2	no	—
261	C₅₃	#19273	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	D₂₁₂	1	1	yes	characteristic
263	C₂×Q₁₆	—	106	2	no	—
264	C₂×SD₁₆	—	106	2	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
269	C₄⋊Q₈	—	53	2	no	—
270	C₄⋊Q₈	—	53	2	no	—
271	#125	—	106	2	no	—
272	C₂²⋊Q₈	—	106	2	no	—
273	C₂²⋊Q₈	—	106	2	no	—
274	C₄×Q₈	—	106	2	no	—
275	C₄×Q₈	—	106	2	no	—
276	C₄×Q₈	D₂₁₂	1	1	yes	characteristic
277	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₂₁₂	1	1	yes	characteristic
281	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	106	2	no	—
284	#117	D₂₁₂	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
287	#107	—	106	1	no	—
288	#107	—	106	1	no	—
289	#107	—	106	1	no	—
290	#107	—	106	1	no	—
291	#107	—	106	2	no	—
292	#106	—	106	2	no	—
293	#106	—	106	2	no	—
294	#106	—	106	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	53	2	no	—
298	C₄⋊C₈	—	53	2	no	—
299	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
300	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
301	#103	—	106	2	no	—
302	#103	—	106	2	no	—
303	#103	—	106	2	no	—
304	#102	—	106	2	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	106	2	no	—
309	#97	—	106	2	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
314	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	—	106	2	no	—
320	C₂×Q₈	—	106	2	no	—
321	C₂×Q₈	C₂×D₂₁₂	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
328	C₂²×C₄	#11719945	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
330	Q₁₆	—	212	4	no	—
331	SD₁₆	—	212	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	106	2	no	—
339	C₂×C₈	—	106	2	no	—
340	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	106	2	no	—
347	C₄⋊C₄	—	106	2	no	—
348	C₄⋊C₄	—	106	2	no	—
349	C₄⋊C₄	—	106	2	no	—
350	C₄⋊C₄	—	212	2	no	—
351	C₄⋊C₄	—	212	2	no	—
352	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
353	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	212	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	212	2	no	—
362	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
363	C₄²	#11719945	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
365	C₄²	C₂³×D₅₃	1	1	yes	characteristic
366	C₂³	—	2	1	no	—
367	C₂³	#13133191	1	1	yes	characteristic
368	Q₈	—	2	1	no	—
369	Q₈	—	424	2	no	—
370	Q₈	—	212	2	no	—
371	Q₈	—	212	2	no	—
372	Q₈	#13133239	1	2	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	1	no	—
375	D₄	#13133239	1	2	yes	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	212	2	no	—
389	C₂×C₄	—	212	2	no	—
390	C₂×C₄	#13133191	1	1	yes	characteristic
391	C₂×C₄	#13133191	1	1	yes	characteristic
392	C₂×C₄	#13133191	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
395	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	212	2	no	—
401	C₈	—	212	2	no	—
402	C₈	#13133247	1	2	yes	—
403	C₈	#13133247	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×#13133191	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	424	2	no	—
419	C₄	—	424	2	no	—
420	C₄	C₂×#13133239	1	1	yes	characteristic
421	C₄	C₂×#13133239	1	1	yes	characteristic
422	C₄	C₂×#13133247	1	1	yes	characteristic
423	C₄	C₂×#13133247	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#20284202	1	1	yes	characteristic
427	C₂	#20284296	1	1	yes	characteristic
428	C₂	#20284435	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13133191
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₈×#41×C₅₃	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#41×C₅₃	D₄
hypercenter	C₈×#41	D₅₃
hypocenter	C₅₃	#19273
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #20285229	C₂	semidirect
3. #20274119	C₂	semidirect
4. #20274114	C₂	semidirect
5. #20274109	C₂	semidirect
6. #20274104	C₂	semidirect
7. #20274097	C₂	semidirect
8. #20274090	C₂	semidirect
9. #20273478	C₂	semidirect
10. #20273423	C₂	semidirect
261. C₅₃	#19273	semidirect

Maximal subgroups

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

subgroup	index
#20285229	2
#20284877	2
#20274119	2
#20274114	2
#20274109	2
#20274104	2
#20274097	2
#20274090	2
#20273478	2
#20273423	2
C₈×#41×C₅₃	2
#19273	53