Subgroups — #27368018

Order 13568.

702 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284199	C₂	1	2	yes	maximal
3	C₈×#11719949	C₂	1	1	yes	maximal, characteristic
4	#20274109	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274107	C₂	1	2	yes	maximal, complemented
6	#20274105	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274103	C₂	1	2	yes	maximal, complemented
8	#20274101	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273472	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273385	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133249	—	2	2	no	—
13	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
14	C₄×#11719949	C₂²	1	1	yes	characteristic
15	#16811028	C₂²	1	1	yes	characteristic
16	#16811027	—	2	1	no	—
17	#16811027	—	2	1	no	—
18	#16811026	C₂²	1	2	yes	—
19	#16810833	C₂²	1	2	yes	—
20	#16810831	—	2	2	no	—
21	#16810829	C₂²	1	2	yes	—
22	#16810827	—	2	2	no	—
23	#16810825	C₂²	1	2	yes	—
24	Q₈×#88322	C₂²	1	1	yes	characteristic
25	C₈×D₂₁₂	—	2	1	no	—
26	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
27	#16810688	—	2	1	no	—
28	#16810688	C₂²	1	1	yes	characteristic
29	#16810675	—	2	1	no	—
30	#16810675	C₂²	1	1	yes	characteristic
31	#107×D₅₃	—	2	1	no	—
32	#107×D₅₃	—	2	1	no	—
33	#16810645	C₂²	1	2	yes	—
34	#16810630	—	2	2	no	—
35	C₄×C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic
38	#16810375	C₂²	1	2	yes	—
39	#16810370	C₂²	1	2	yes	—
40	#16810369	C₂²	1	2	yes	—
41	#16810368	C₂²	1	2	yes	—
42	C₅₃×#500	C₂²	1	1	yes	characteristic
43	C₅₃×#462	C₂²	1	2	yes	—
44	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic
46	C₅₃×#332	C₂²	1	2	yes	—
47	C₂×#11719949	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₅₃	—	2	2	no	—
49	#13133249	—	4	8	no	—
50	C₂×#11719925	—	2	2	no	—
51	C₂×#11719913	—	2	2	no	—
52	C₂×#11719924	—	2	2	no	—
53	C₂×#11719912	—	2	2	no	—
54	C₂×C₈×D₅₃	—	2	1	no	—
55	C₂×C₈×D₅₃	—	2	1	no	—
56	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	#13133217	C₂³	1	2	yes	—
59	#13133216	—	2	2	no	—
60	#13133216	—	2	2	no	—
61	#13133215	—	2	2	no	—
62	Q₈×Dic₅₃	D₄	1	1	yes	characteristic
63	C₄×D₂₁₂	—	2	1	no	—
64	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
65	#13133179	—	2	1	no	—
66	#13133179	D₄	1	1	yes	characteristic
67	#13133175	—	2	1	no	—
68	#13133175	D₄	1	1	yes	characteristic
69	C₄⋊C₄×D₅₃	—	2	2	no	—
70	C₄⋊C₄×D₅₃	—	2	2	no	—
71	C₄²×D₅₃	—	2	1	no	—
72	C₄²×D₅₃	C₂³	1	1	yes	characteristic
73	#13133151	—	2	1	no	—
74	#13133151	—	2	1	no	—
75	#13133150	—	2	2	no	—
76	#13133150	—	2	2	no	—
77	C₄⋊#88322	—	2	1	no	—
78	C₄⋊#88322	C₂³	1	2	yes	—
79	C₄⋊#88322	C₂³	1	1	yes	characteristic
80	#13133146	—	2	2	no	—
81	#13133142	—	2	2	no	—
82	#13133141	—	2	2	no	—
83	#13133140	—	2	2	no	—
84	#13133129	—	2	1	no	—
85	#13133129	—	2	1	no	—
86	#13133129	—	2	1	no	—
87	C₄×#88322	—	2	1	no	—
88	C₄×#88322	C₂³	1	1	yes	characteristic
89	C₈×Dic₅₃	—	2	1	no	—
90	C₈×Dic₅₃	D₄	1	1	yes	characteristic
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₂×Q₁₆×C₅₃	—	2	2	no	—
93	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
94	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
95	#107×C₅₃	—	2	1	no	—
96	#107×C₅₃	—	2	1	no	—
97	C₄⋊C₈×C₅₃	—	2	1	no	—
98	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
99	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
100	#103×C₅₃	—	2	2	no	—
101	C₄×C₈×C₅₃	—	2	1	no	—
102	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₂×Q₈×C₅₃	—	2	2	no	—
104	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
105	#11719949	—	2	2	no	—
106	#11719949	D₈	1	4	yes	—
107	Q₈×D₅₃	—	4	4	no	—
108	Q₈×D₅₃	—	4	4	no	—
109	C₂×D₂₁₂	—	2	1	no	—
110	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	—	2	1	no	—
112	C₂×C₄×D₅₃	—	2	1	no	—
113	C₂×C₄×D₅₃	—	2	1	no	—
114	C₂×C₄×D₅₃	—	4	2	no	—
115	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
118	C₂×Dic₁₀₆	—	2	2	no	—
119	C₂×Dic₁₀₆	—	4	2	no	—
120	Q₁₆×C₅₃	—	4	4	no	—
121	C₂×C₈×C₅₃	—	2	1	no	—
122	C₂×C₈×C₅₃	—	2	2	no	—
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	2	no	—
127	C₄⋊C₄×C₅₃	—	2	2	no	—
128	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₅₃	—	2	1	no	—
130	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
131	#11719925	—	4	4	no	—
132	#11719924	—	4	4	no	—
133	#11719921	—	2	1	no	—
134	#11719921	—	2	1	no	—
135	#11719921	—	2	1	no	—
136	C₄⋊Dic₅₃	—	2	1	no	—
137	C₄⋊Dic₅₃	—	2	2	no	—
138	C₄⋊Dic₅₃	—	2	2	no	—
139	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
140	#11719919	—	4	2	no	—
141	#11719919	—	4	2	no	—
142	C₄×Dic₅₃	—	2	1	no	—
143	C₄×Dic₅₃	—	2	1	no	—
144	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₅₃	#41	1	1	yes	characteristic
147	C₂×#88322	—	2	1	no	—
148	C₂×#88322	—	2	2	no	—
149	C₂×#88322	C₂×D₄	1	1	yes	characteristic
150	C₂×#88322	C₂×D₄	1	1	yes	characteristic
151	#11719913	—	4	4	no	—
152	#11719912	—	4	4	no	—
153	C₈×D₅₃	—	2	2	no	—
154	C₈×D₅₃	—	2	2	no	—
155	C₈×D₅₃	—	4	2	no	—
156	C₈×D₅₃	—	4	2	no	—
157	C₂²×D₅₃	—	2	1	no	—
158	C₂²×D₅₃	#121	1	1	yes	characteristic
159	Q₈×C₅₃	—	2	1	no	—
160	Q₈×C₅₃	—	4	2	no	—
161	Q₈×C₅₃	—	4	2	no	—
162	Q₈×C₅₃	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	4	2	no	—
166	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
169	C₂×Dic₅₃	—	2	1	no	—
170	C₂×Dic₅₃	—	4	2	no	—
171	C₂×Dic₅₃	#121	1	1	yes	characteristic
172	C₂×Dic₅₃	#121	1	1	yes	characteristic
173	C₂×Dic₅₃	#121	1	1	yes	characteristic
174	D₂₁₂	—	2	4	no	—
175	D₂₁₂	—	2	1	no	—
176	D₂₁₂	C₂×D₈	1	2	yes	—
177	C₄×D₅₃	—	2	1	no	—
178	C₄×D₅₃	—	2	1	no	—
179	C₄×D₅₃	—	2	4	no	—
180	C₄×D₅₃	—	2	2	no	—
181	C₄×D₅₃	—	4	1	no	—
182	C₄×D₅₃	—	4	1	no	—
183	C₄×D₅₃	—	4	2	no	—
184	C₄×D₅₃	—	8	4	no	—
185	C₄×D₅₃	C₂×D₈	1	2	yes	—
186	C₄×D₅₃	#135	1	2	yes	—
187	Dic₁₀₆	—	4	2	no	—
188	Dic₁₀₆	—	4	2	no	—
189	Dic₁₀₆	—	8	4	no	—
190	C₈×C₅₃	—	2	1	no	—
191	C₈×C₅₃	—	4	2	no	—
192	C₈×C₅₃	—	4	1	no	—
193	C₈×C₅₃	#137	1	2	yes	complemented
194	#88322	—	2	1	no	—
195	#88322	—	4	2	no	—
196	#88322	—	4	1	no	—
197	#88322	#137	1	2	yes	complemented
198	#19271	—	53	1	no	maximal, Sylow
199	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
200	C₂×D₅₃	—	2	1	no	—
201	C₂×D₅₃	—	2	1	no	—
202	C₂×D₅₃	—	2	2	no	—
203	C₂×D₅₃	—	4	1	no	—
204	C₂×D₅₃	—	4	1	no	—
205	C₂×D₅₃	#466	1	2	yes	—
206	C₄×C₅₃	—	2	2	no	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	—	4	1	no	—
209	C₄×C₅₃	—	8	2	no	—
210	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
212	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
213	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
214	Dic₅₃	—	2	1	no	—
215	Dic₅₃	—	4	1	no	—
216	Dic₅₃	—	8	2	no	—
217	Dic₅₃	#466	1	2	yes	—
218	Dic₅₃	#473	1	2	yes	—
219	C₂×#500	—	53	1	no	—
220	#3039	—	53	2	no	—
221	C₈×#41	—	53	1	no	—
222	#1674	—	53	2	no	—
223	#1674	—	53	1	no	—
224	#1674	D₅₃	1	1	yes	characteristic, complemented
225	#1673	—	53	1	no	—
226	#1673	—	53	1	no	—
227	#1673	—	53	2	no	—
228	#1567	—	53	1	no	—
229	#1546	—	53	2	no	—
230	C₂×C₅₃	#3039	1	1	yes	characteristic
231	C₂×C₅₃	C₂×#466	1	1	yes	characteristic
232	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
233	D₅₃	—	2	2	no	—
234	D₅₃	—	4	2	no	—
235	C₂×#137	—	106	2	no	—
236	C₂×C₄⋊Q₈	—	53	2	no	—
237	C₄×#41	—	53	1	no	—
238	#500	—	53	2	no	—
239	#500	—	53	1	no	—
240	#500	—	106	1	no	—
241	#500	—	106	1	no	—
242	#500	C₂×D₅₃	1	1	yes	characteristic
243	#462	—	53	2	no	—
244	#462	—	106	2	no	—
245	#462	C₂×D₅₃	1	2	yes	—
246	#461	—	53	2	no	—
247	#461	—	53	2	no	—
248	#461	—	106	2	no	—
249	C₈×Q₈	—	53	1	no	—
250	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
251	C₈×D₄	—	53	1	no	—
252	C₈×D₄	—	53	1	no	—
253	C₈×D₄	—	106	1	no	—
254	C₈×D₄	—	106	1	no	—
255	#431	—	53	1	no	—
256	#431	—	106	1	no	—
257	C₂×#107	—	106	1	no	—
258	C₂×#107	—	106	1	no	—
259	#423	—	53	2	no	—
260	#419	—	106	2	no	—
261	C₂×C₄×C₈	—	53	1	no	—
262	C₂×C₄×C₈	—	106	1	no	—
263	#335	—	53	2	no	—
264	#335	—	53	1	no	—
265	#335	C₂×D₅₃	1	1	yes	characteristic
266	#332	—	53	2	no	—
267	#332	—	53	2	no	—
268	#332	—	53	2	no	—
269	#332	C₂×D₅₃	1	2	yes	—
270	C₅₃	#19271	1	1	yes	characteristic, complemented, Sylow
271	C₂×#41	—	53	1	no	—
272	C₂²×Q₈	—	106	2	no	—
273	#137	—	212	8	no	—
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×Q₁₆	—	106	2	no	—
276	C₂×SD₁₆	—	106	2	no	—
277	C₂×SD₁₆	—	106	2	no	—
278	C₂×M₁₆	—	106	2	no	—
279	C₂²×C₈	—	53	1	no	—
280	C₂²×C₈	—	53	1	no	—
281	C₂²×C₈	—	106	1	no	—
282	C₂²×C₈	—	106	1	no	—
283	C₄⋊Q₈	—	53	2	no	—
284	C₄⋊Q₈	—	106	2	no	—
285	C₄⋊Q₈	—	106	2	no	—
286	C₄⋊Q₈	—	106	2	no	—
287	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
288	C₄×Q₈	—	53	1	no	—
289	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
290	C₄×D₄	—	53	1	no	—
291	C₄×D₄	—	53	1	no	—
292	C₄×D₄	—	106	1	no	—
293	C₄×D₄	—	106	1	no	—
294	#117	—	53	1	no	—
295	#117	—	106	1	no	—
296	C₂×C₄⋊C₄	—	106	2	no	—
297	C₂×C₄⋊C₄	—	106	2	no	—
298	C₂×C₄²	—	53	1	no	—
299	C₂×C₄²	—	106	1	no	—
300	#107	—	2	1	no	—
301	#107	—	2	1	no	—
302	#107	—	106	2	no	—
303	#107	—	106	2	no	—
304	#107	—	106	1	no	—
305	#107	—	106	1	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	53	1	no	—
308	C₄⋊C₈	—	53	2	no	—
309	C₄⋊C₈	—	106	1	no	—
310	C₄⋊C₈	—	106	2	no	—
311	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	106	2	no	—
315	#103	—	106	2	no	—
316	#103	—	106	2	no	—
317	C₂²⋊C₈	—	106	1	no	—
318	C₂²⋊C₈	—	106	1	no	—
319	C₂²⋊C₈	—	106	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	53	1	no	—
322	C₄×C₈	—	53	1	no	—
323	C₄×C₈	—	53	1	no	—
324	C₄×C₈	—	106	1	no	—
325	C₄×C₈	—	106	1	no	—
326	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
327	#41	—	53	4	no	—
328	#41	—	106	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	106	2	no	—
331	C₂×Q₈	—	212	2	no	—
332	C₂×Q₈	—	212	4	no	—
333	C₂×Q₈	—	212	4	no	—
334	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
335	C₂×D₄	—	53	1	no	—
336	C₂×D₄	—	106	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	—	53	1	no	—
339	C₂²×C₄	—	53	1	no	—
340	C₂²×C₄	—	106	1	no	—
341	C₂²×C₄	—	106	1	no	—
342	C₂²×C₄	—	106	1	no	—
343	C₂²×C₄	—	212	2	no	—
344	Q₁₆	—	4	4	no	—
345	Q₁₆	—	212	4	no	—
346	SD₁₆	—	212	4	no	—
347	SD₁₆	—	212	4	no	—
348	M₁₆	—	212	4	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	53	1	no	—
352	C₂×C₈	—	53	1	no	—
353	C₂×C₈	—	106	2	no	—
354	C₂×C₈	—	106	2	no	—
355	C₂×C₈	—	106	1	no	—
356	C₂×C₈	—	106	2	no	—
357	C₂×C₈	—	212	2	no	—
358	C₂×C₈	—	212	2	no	—
359	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
360	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	53	1	no	—
365	C₄⋊C₄	—	106	1	no	—
366	C₄⋊C₄	—	106	2	no	—
367	C₄⋊C₄	—	106	2	no	—
368	C₄⋊C₄	—	212	2	no	—
369	C₄⋊C₄	—	212	2	no	—
370	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
371	C₂²⋊C₄	—	106	1	no	—
372	C₂²⋊C₄	—	106	1	no	—
373	C₂²⋊C₄	—	106	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	53	1	no	—
376	C₄²	—	53	1	no	—
377	C₄²	—	53	1	no	—
378	C₄²	—	106	1	no	—
379	C₄²	—	106	1	no	—
380	C₄²	C₂³×D₅₃	1	1	yes	characteristic
381	C₂³	—	53	1	no	—
382	C₂³	—	106	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	424	4	no	—
387	Q₈	—	212	2	no	—
388	Q₈	—	212	2	no	—
389	Q₈	D₈×D₅₃	1	2	yes	—
390	D₄	—	53	2	no	—
391	D₄	—	106	4	no	—
392	D₄	—	106	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	53	1	no	—
397	C₂×C₄	—	53	1	no	—
398	C₂×C₄	—	53	2	no	—
399	C₂×C₄	—	53	2	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	106	2	no	—
402	C₂×C₄	—	106	4	no	—
403	C₂×C₄	—	106	1	no	—
404	C₂×C₄	—	106	1	no	—
405	C₂×C₄	—	106	1	no	—
406	C₂×C₄	—	424	4	no	—
407	C₂×C₄	—	212	2	no	—
408	C₂×C₄	—	212	2	no	—
409	C₂×C₄	—	212	1	no	—
410	C₂×C₄	—	212	1	no	—
411	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
413	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	53	2	no	—
418	C₈	—	106	1	no	—
419	C₈	—	212	2	no	—
420	C₈	—	212	1	no	—
421	C₈	#13133249	1	2	yes	complemented
422	C₂²	—	53	2	no	—
423	C₂²	—	106	1	no	—
424	C₂²	—	106	1	no	—
425	C₂²	—	106	2	no	—
426	C₂²	—	212	1	no	—
427	C₂²	—	212	1	no	—
428	C₂²	#121×D₅₃	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	53	2	no	—
434	C₄	—	53	2	no	—
435	C₄	—	106	1	no	—
436	C₄	—	424	2	no	—
437	C₄	—	212	1	no	—
438	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
439	C₄	#135×D₅₃	1	1	yes	characteristic
440	C₄	#137×D₅₃	1	1	yes	characteristic
441	C₄	C₂×#13133249	1	1	yes	characteristic
442	C₂	—	106	2	no	—
443	C₂	—	212	2	no	—
444	C₂	#20284199	1	1	yes	characteristic
445	C₂	#466×D₅₃	1	1	yes	characteristic
446	C₂	#473×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1674	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#11719949	D₄
hypercenter	#1674	D₅₃
hypocenter	C₅₃	#19271
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1674

Complements

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

N	H ≅ G/N	type
1. #500×D₅₃	C₂	semidirect
4. #20274109	C₂	semidirect
5. #20274107	C₂	semidirect
6. #20274105	C₂	semidirect
7. #20274103	C₂	semidirect
8. #20274101	C₂	semidirect
9. #20273472	C₂	semidirect
10. #20273385	C₂	semidirect
11. C₅₃×#1674	C₂	semidirect
193. C₈×C₅₃	#137	semidirect
197. #88322	#137	semidirect
224. #1674	D₅₃	semidirect
270. C₅₃	#19271	semidirect
421. C₈	#13133249	semidirect

Maximal subgroups

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

subgroup	index
#500×D₅₃	2
#20284199	2
C₈×#11719949	2
#20274109	2
#20274107	2
#20274105	2
#20274103	2
#20274101	2
#20273472	2
#20273385	2
C₅₃×#1674	2
#19271	53