Subgroups — #27353333

Order 13568.

610 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#88322	C₂	1	1	yes	maximal, characteristic
2	#20283381	C₂	1	1	yes	maximal, characteristic
3	#20273496	C₂	1	2	yes	maximal, complemented
4	#20273493	C₂	1	2	yes	maximal, complemented
5	#20273487	C₂	1	1	yes	maximal, characteristic, complemented
6	#20273485	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273476	C₂	1	2	yes	maximal, complemented
8	#20273473	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273461	C₂	1	2	yes	maximal, complemented
10	C₂×#16810375	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic
12	Q₈×#88322	C₄	1	1	yes	characteristic
13	Q₈×#88322	C₄	1	1	yes	characteristic
14	D₄×#88322	C₄	1	1	yes	characteristic
15	D₄×#88322	C₄	1	2	yes	—
16	D₄×#88322	C₄	1	1	yes	characteristic
17	D₄×#88322	C₄	1	2	yes	—
18	#16810684	—	2	2	no	—
19	#16810680	C₂²	1	2	yes	—
20	#16810676	C₂²	1	2	yes	—
21	#16810676	C₂²	1	1	yes	characteristic
22	#16810676	C₂²	1	2	yes	—
23	#16810647	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
25	#16810590	—	2	1	no	—
26	#16810579	—	2	1	no	—
27	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
28	C₂×C₄×#88322	C₂²	1	2	yes	—
29	#16810375	C₂²	1	1	yes	characteristic
30	#16810375	C₂²	1	1	yes	characteristic
31	#16810375	C₂²	1	1	yes	characteristic
32	#16810375	C₂²	1	1	yes	characteristic
33	#16810375	C₂²	1	2	yes	—
34	#16810375	C₂²	1	2	yes	—
35	#16810373	C₂²	1	2	yes	—
36	#16810373	C₂²	1	2	yes	—
37	#16810373	C₂²	1	2	yes	—
38	#16810373	C₂²	1	2	yes	—
39	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#433	—	2	2	no	—
41	C₅₃×#432	C₂²	1	2	yes	—
42	C₅₃×#431	C₂²	1	2	yes	—
43	C₅₃×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#408	—	2	1	no	—
46	C₅₃×#405	—	2	1	no	—
47	C₂×#11719917	—	2	1	no	—
48	C₂²×#88322	—	2	1	no	—
49	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
50	C₂²×#88322	C₂×C₄	1	2	yes	—
51	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
52	C₂²×#88322	C₂×C₄	1	2	yes	—
53	C₄⋊#88322	—	2	1	no	—
54	C₄⋊#88322	—	2	1	no	—
55	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
56	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
57	C₄⋊#88322	C₂×C₄	1	2	yes	—
58	C₄⋊#88322	C₂×C₄	1	2	yes	—
59	C₄⋊#88322	C₂³	1	1	yes	characteristic
60	C₄⋊#88322	C₂³	1	1	yes	characteristic
61	C₄⋊#88322	C₂³	1	2	yes	—
62	C₂²⋊#88322	—	2	2	no	—
63	C₂²⋊#88322	—	2	2	no	—
64	C₂²⋊#88322	C₂×C₄	1	2	yes	—
65	C₂²⋊#88322	C₂×C₄	1	2	yes	—
66	C₂²⋊#88322	C₂×C₄	1	2	yes	—
67	#13133128	—	2	2	no	—
68	C₄×#88322	—	2	2	no	—
69	C₄×#88322	C₂×C₄	1	1	yes	characteristic
70	C₄×#88322	C₂×C₄	1	2	yes	—
71	C₄×#88322	C₂×C₄	1	1	yes	characteristic
72	C₄×#88322	C₂×C₄	1	2	yes	—
73	C₄×#88322	C₂³	1	1	yes	characteristic
74	C₄×#88322	C₂³	1	2	yes	—
75	C₄×#88322	C₂³	1	1	yes	characteristic
76	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
77	C₂×M₁₆×C₅₃	—	2	1	no	—
78	C₂²×C₈×C₅₃	—	2	1	no	—
79	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₅₃	Q₈	1	1	yes	characteristic
81	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
82	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₅₃	Q₈	1	1	yes	characteristic
84	C₄×D₄×C₅₃	Q₈	1	2	yes	—
85	#117×C₅₃	D₄	1	1	yes	characteristic
86	#117×C₅₃	D₄	1	2	yes	—
87	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
89	C₄⋊C₈×C₅₃	—	2	1	no	—
90	C₄⋊C₈×C₅₃	—	2	1	no	—
91	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
94	C₂²⋊C₈×C₅₃	—	2	2	no	—
95	C₂²⋊C₈×C₅₃	—	2	2	no	—
96	#97×C₅₃	—	2	2	no	—
97	C₄×C₈×C₅₃	—	2	2	no	—
98	#41×C₅₃	—	2	2	no	—
99	#41×C₅₃	—	2	2	no	—
100	C₂×Q₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₅₃	C₄⋊C₄	1	2	yes	—
102	C₂×D₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
109	M₁₆×C₅₃	—	4	2	no	—
110	C₂×C₈×C₅₃	—	2	1	no	—
111	C₂×C₈×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	—	2	1	no	—
113	C₂×C₈×C₅₃	—	4	2	no	—
114	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
115	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
117	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
120	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
121	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
122	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅₃	C₂×D₄	1	2	yes	—
124	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
126	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
128	#11719917	—	4	2	no	—
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	—	2	4	no	—
131	C₂×#88322	—	2	1	no	—
132	C₂×#88322	—	2	2	no	—
133	C₂×#88322	—	2	1	no	—
134	C₂×#88322	—	4	1	no	—
135	C₂×#88322	—	4	2	no	—
136	C₂×#88322	—	4	2	no	—
137	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
138	C₂×#88322	C₂²×C₄	1	2	yes	—
139	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
140	C₂×#88322	C₂²×C₄	1	2	yes	—
141	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
142	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
143	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	Q₈×C₅₃	—	2	2	no	—
146	D₄×C₅₃	—	2	4	no	—
147	D₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	2	1	no	—
149	C₂×C₄×C₅₃	—	2	2	no	—
150	C₂×C₄×C₅₃	—	2	1	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	—	4	1	no	—
155	C₂×C₄×C₅₃	—	4	2	no	—
156	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	#135	1	2	yes	—
163	C₂×C₄×C₅₃	#135	1	2	yes	—
164	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
167	C₈×C₅₃	—	4	1	no	—
168	C₈×C₅₃	—	4	1	no	—
169	C₈×C₅₃	—	4	2	no	—
170	#88322	—	2	2	no	—
171	#88322	—	2	1	no	—
172	#88322	—	2	1	no	—
173	#88322	—	2	2	no	—
174	#88322	—	2	1	no	—
175	#88322	—	4	1	no	—
176	#88322	—	4	1	no	—
177	#88322	—	4	2	no	—
178	#88322	#131	1	2	yes	—
179	#17829	—	53	1	no	maximal, Sylow
180	C₂²×C₅₃	—	2	1	no	—
181	C₂²×C₅₃	—	2	1	no	—
182	C₂²×C₅₃	—	2	2	no	—
183	C₂²×C₅₃	—	2	2	no	—
184	C₂²×C₅₃	—	2	2	no	—
185	C₂²×C₅₃	#427	1	2	yes	—
186	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	—	2	2	no	—
189	C₄×C₅₃	—	2	2	no	—
190	C₄×C₅₃	—	2	1	no	—
191	C₄×C₅₃	—	2	1	no	—
192	C₄×C₅₃	—	2	2	no	—
193	C₄×C₅₃	#427	1	2	yes	—
194	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
195	C₄×C₅₃	#568	1	1	yes	characteristic
196	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
197	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
198	C₈×#41	—	53	1	no	—
199	#2925	—	53	1	no	—
200	#2925	D₅₃	1	1	yes	characteristic
201	#1572	—	53	2	no	—
202	#1572	—	53	2	no	—
203	#1570	—	53	1	no	—
204	#1570	—	53	1	no	—
205	#1568	—	53	2	no	—
206	#1567	—	53	1	no	—
207	#1564	—	53	2	no	—
208	C₂×#335	—	53	1	no	—
209	C₂×C₅₃	—	2	2	no	—
210	C₂×C₅₃	—	4	2	no	—
211	C₂×C₅₃	#2906	1	1	yes	characteristic
212	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
213	C₂×C₅₃	#2916	1	1	yes	characteristic
214	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
215	C₈×Q₈	—	53	1	no	—
216	C₈×Q₈	—	53	1	no	—
217	C₈×D₄	—	53	1	no	—
218	C₈×D₄	—	53	2	no	—
219	C₈×D₄	—	53	1	no	—
220	C₈×D₄	—	53	2	no	—
221	#433	—	2	2	no	—
222	#433	—	106	2	no	—
223	#432	—	53	2	no	—
224	#432	C₂×D₅₃	1	2	yes	—
225	#431	—	53	1	no	—
226	#431	—	53	2	no	—
227	#431	—	53	2	no	—
228	#431	C₂×D₅₃	1	2	yes	—
229	#423	—	53	1	no	—
230	#423	C₂×D₅₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	—	53	1	no	—
232	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
233	#408	—	2	1	no	—
234	#408	—	106	1	no	—
235	#405	—	2	1	no	—
236	#405	—	106	1	no	—
237	C₂×C₄×C₈	—	53	1	no	—
238	C₂×C₄×C₈	—	53	2	no	—
239	#335	—	53	1	no	—
240	#335	—	53	1	no	—
241	#335	—	53	1	no	—
242	#335	—	53	1	no	—
243	#335	—	53	2	no	—
244	#335	—	53	2	no	—
245	#334	—	53	2	no	—
246	#334	—	53	2	no	—
247	#334	—	53	2	no	—
248	#334	—	53	2	no	—
249	C₅₃	#17829	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	C₂²⋊D₅₃	1	1	yes	characteristic
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	106	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	53	1	no	—
255	C₂²×C₈	—	53	2	no	—
256	C₂²×C₈	—	53	1	no	—
257	C₂²×C₈	—	53	2	no	—
258	C₂²×C₈	—	106	1	no	—
259	C₄×Q₈	Dic₁₀₆	1	1	yes	characteristic
260	C₄×Q₈	C₄×D₅₃	1	1	yes	characteristic
261	C₄×D₄	Dic₁₀₆	1	2	yes	—
262	C₄×D₄	Dic₁₀₆	1	1	yes	characteristic
263	C₄×D₄	C₄×D₅₃	1	2	yes	—
264	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
265	#117	C₂²⋊D₅₃	1	1	yes	characteristic
266	#117	C₂²⋊D₅₃	1	2	yes	—
267	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	53	1	no	—
272	C₄⋊C₈	—	53	1	no	—
273	C₄⋊C₈	—	53	2	no	—
274	C₄⋊C₈	—	53	2	no	—
275	C₄⋊C₈	—	53	1	no	—
276	C₄⋊C₈	—	53	1	no	—
277	C₄⋊C₈	—	53	2	no	—
278	C₄⋊C₈	—	106	1	no	—
279	C₄⋊C₈	—	106	1	no	—
280	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	53	2	no	—
286	C₂²⋊C₈	—	53	2	no	—
287	C₂²⋊C₈	—	53	2	no	—
288	C₂²⋊C₈	—	106	2	no	—
289	C₂²⋊C₈	—	106	2	no	—
290	#97	—	2	2	no	—
291	#97	—	106	2	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	53	1	no	—
294	C₄×C₈	—	53	2	no	—
295	C₄×C₈	—	53	1	no	—
296	C₄×C₈	—	53	2	no	—
297	C₄×C₈	—	53	2	no	—
298	C₄×C₈	—	53	1	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	106	2	no	—
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	#11719919	1	1	yes	characteristic
304	C₂×D₄	#11719919	1	2	yes	—
305	C₂×D₄	#11719919	1	1	yes	characteristic
306	C₂²×C₄	C₂×Dic₁₀₆	1	2	yes	—
307	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
309	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
311	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
312	M₁₆	—	4	2	no	—
313	M₁₆	—	212	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	53	1	no	—
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	53	2	no	—
321	C₂×C₈	—	53	1	no	—
322	C₂×C₈	—	53	2	no	—
323	C₂×C₈	—	53	1	no	—
324	C₂×C₈	—	106	2	no	—
325	C₂×C₈	—	106	4	no	—
326	C₂×C₈	—	106	1	no	—
327	C₂×C₈	—	106	2	no	—
328	C₂×C₈	—	106	1	no	—
329	C₂×C₈	—	212	1	no	—
330	C₂×C₈	—	212	2	no	—
331	C₂×C₈	—	212	2	no	—
332	C₄⋊C₄	#11719919	1	2	yes	—
333	C₄⋊C₄	#11719919	1	1	yes	characteristic
334	C₄⋊C₄	#11719919	1	2	yes	—
335	C₄⋊C₄	#11719919	1	1	yes	characteristic
336	C₂²⋊C₄	#11719919	1	2	yes	—
337	C₂²⋊C₄	#11719919	1	2	yes	—
338	C₂²⋊C₄	#11719919	1	2	yes	—
339	C₄²	C₂×Dic₁₀₆	1	2	yes	—
340	C₄²	C₂×Dic₁₀₆	1	1	yes	characteristic
341	C₄²	C₂×C₄×D₅₃	1	2	yes	—
342	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
343	C₄²	C₂×C₂²⋊D₅₃	1	2	yes	—
344	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
345	C₄²	C₂³×D₅₃	1	1	yes	characteristic
346	C₂³	C₂×#11719919	1	2	yes	—
347	C₂³	C₂×#11719919	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×#11719919	1	2	yes	—
360	C₂×C₄	C₂×#11719919	1	2	yes	—
361	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
362	C₂×C₄	C₂×#11719919	1	2	yes	—
363	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
364	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
365	C₂×C₄	#13133237	1	2	yes	—
366	C₂×C₄	#13133237	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×Dic₁₀₆	1	1	yes	characteristic
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	53	2	no	—
374	C₈	—	106	2	no	—
375	C₈	—	106	1	no	—
376	C₈	—	106	2	no	—
377	C₈	—	106	1	no	—
378	C₈	—	106	1	no	—
379	C₈	—	212	1	no	—
380	C₈	—	212	1	no	—
381	C₈	—	212	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#16810659	1	2	yes	—
388	C₂²	C₂²×#11719919	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	#16810659	1	2	yes	—
396	C₄	#131×D₅₃	1	1	yes	characteristic
397	C₄	#16811388	1	1	yes	characteristic
398	C₄	C₂×#13133237	1	1	yes	characteristic
399	C₄	C₂×#13133237	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	#20283281	1	1	yes	characteristic
403	C₂	C₂×#16810659	1	1	yes	characteristic
404	C₂	#20283324	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#2925	C₂
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₅₃	D₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#2925	D₅₃
hypocenter	C₅₃	#17829
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #20273496	C₂	semidirect
4. #20273493	C₂	semidirect
5. #20273487	C₂	semidirect
6. #20273485	C₂	semidirect
7. #20273476	C₂	semidirect
8. #20273473	C₂	semidirect
9. #20273461	C₂	semidirect
10. C₂×#16810375	C₂	semidirect
249. C₅₃	#17829	semidirect

Maximal subgroups

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

subgroup	index
#41×#88322	2
#20283381	2
#20273496	2
#20273493	2
#20273487	2
#20273485	2
#20273476	2
#20273473	2
#20273461	2
C₂×#16810375	2
C₅₃×#2925	2
#17829	53