Subgroups — #27354705

Order 13568.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285315	C₂	1	1	yes	maximal, characteristic
2	#20283684	C₂	1	1	yes	maximal, characteristic
3	#20283650	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273609	C₂	1	2	yes	maximal, complemented
5	#20273602	C₂	1	2	yes	maximal, complemented
6	#20273531	C₂	1	2	yes	maximal, complemented
7	#20273530	C₂	1	2	yes	maximal, complemented
8	#20273483	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273181	C₂	1	1	yes	maximal, characteristic
10	#20272996	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1497	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811157	C₂²	1	1	yes	characteristic
13	#16811029	C₄	1	1	yes	characteristic
14	#16811015	C₄	1	1	yes	characteristic
15	#16810991	C₄	1	1	yes	characteristic
16	#16810985	C₄	1	1	yes	characteristic
17	#16810879	C₄	1	2	yes	—
18	#16810871	C₄	1	2	yes	—
19	#16810754	—	2	1	no	—
20	#16810754	C₂²	1	2	yes	—
21	#16810750	C₂²	1	1	yes	characteristic
22	Q₈×#88322	—	2	1	no	—
23	Q₈×#88322	C₂²	1	2	yes	—
24	#16810747	C₂²	1	1	yes	characteristic
25	C₄×#11719925	C₂²	1	2	yes	—
26	C₄×#11719924	C₂²	1	2	yes	—
27	#16810700	C₂²	1	1	yes	characteristic
28	#16810691	—	2	1	no	—
29	#16810688	C₂²	1	1	yes	characteristic
30	#16810686	—	2	1	no	—
31	#16810685	—	2	1	no	—
32	#16810650	—	2	1	no	—
33	#16810647	C₂²	1	1	yes	characteristic
34	#16810580	—	2	1	no	—
35	#16810579	—	2	1	no	—
36	C₄×#11719917	C₂²	1	1	yes	characteristic
37	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
38	#16810375	C₂²	1	2	yes	—
39	#16810373	C₂²	1	2	yes	—
40	#16810355	C₂²	1	2	yes	—
41	#16810352	C₂²	1	2	yes	—
42	#16810345	C₂²	1	2	yes	—
43	C₈×#88322	C₂²	1	2	yes	—
44	C₅₃×#533	C₂²	1	1	yes	characteristic
45	C₅₃×#432	C₂²	1	1	yes	characteristic
46	C₅₃×#431	C₂²	1	1	yes	characteristic
47	C₅₃×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₅₃×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₂×#11719925	C₂×C₄	1	2	yes	—
50	C₂×#11719924	C₂×C₄	1	2	yes	—
51	C₂×#11719917	—	2	1	no	—
52	C₂×#11719917	C₂×C₄	1	2	yes	—
53	C₂×#11719912	—	2	1	no	—
54	C₂²×#88322	D₄	1	1	yes	characteristic
55	C₂²×#88322	D₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	—	2	1	no	—
57	#13133211	—	2	1	no	—
58	#13133209	C₂×C₄	1	1	yes	characteristic
59	#13133205	C₂×C₄	1	1	yes	characteristic
60	#13133200	—	2	1	no	—
61	#13133196	C₂×C₄	1	1	yes	characteristic
62	#13133191	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
64	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₅₃	—	2	1	no	—
66	#13133174	—	2	1	no	—
67	#13133150	C₂×C₄	1	2	yes	—
68	#13133148	C₂×C₄	1	2	yes	—
69	C₄⋊#88322	—	2	1	no	—
70	C₄⋊#88322	—	2	2	no	—
71	C₄⋊#88322	—	2	2	no	—
72	C₄⋊#88322	C₂³	1	2	yes	—
73	#13133146	—	2	1	no	—
74	#13133146	—	2	1	no	—
75	#13133141	C₂×C₄	1	2	yes	—
76	#13133141	C₂×C₄	1	2	yes	—
77	#13133140	C₂×C₄	1	2	yes	—
78	#13133137	C₂×C₄	1	2	yes	—
79	#13133129	—	2	1	no	—
80	#13133129	—	2	1	no	—
81	#13133128	—	2	2	no	—
82	#13133128	C₂×C₄	1	1	yes	characteristic
83	#13133128	C₂×C₄	1	1	yes	characteristic
84	#13133127	—	2	1	no	—
85	C₄×#88322	—	2	2	no	—
86	C₄×#88322	D₄	1	1	yes	characteristic
87	C₄×#88322	D₄	1	1	yes	characteristic
88	C₄×#88322	C₂³	1	2	yes	—
89	C₄×#88322	C₂³	1	1	yes	characteristic
90	C₄×#88322	C₂³	1	1	yes	characteristic
91	C₈×Dic₅₃	—	2	1	no	—
92	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
94	#125×C₅₃	—	2	1	no	—
95	C₂²⋊Q₈×C₅₃	—	2	1	no	—
96	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₅₃	—	2	1	no	—
98	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
99	#117×C₅₃	—	2	1	no	—
100	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₅₃	—	2	1	no	—
102	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₅₃	—	2	1	no	—
105	C₂²⋊C₈×C₅₃	—	2	1	no	—
106	#97×C₅₃	—	2	1	no	—
107	C₄×C₈×C₅₃	C₂³	1	2	yes	—
108	C₂×Q₈×C₅₃	—	2	1	no	—
109	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅₃	C₂²×C₄	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×C₂²⋊D₅₃	—	2	1	no	—
114	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₅₃	—	2	1	no	—
116	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	—	2	1	no	—
118	C₂×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	—	2	2	no	—
120	C₄⋊C₄×C₅₃	—	2	1	no	—
121	C₄⋊C₄×C₅₃	—	2	1	no	—
122	C₄⋊C₄×C₅₃	—	2	1	no	—
123	C₄⋊C₄×C₅₃	—	2	2	no	—
124	C₄⋊C₄×C₅₃	—	2	2	no	—
125	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₅₃	—	2	2	no	—
127	C₄²×C₅₃	—	2	2	no	—
128	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅₃	#41	1	1	yes	characteristic
131	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₅₃	—	2	1	no	—
133	#11719925	—	2	4	no	—
134	#11719924	—	2	4	no	—
135	#11719921	—	2	1	no	—
136	#11719921	—	2	1	no	—
137	#11719921	—	2	1	no	—
138	#11719921	—	2	1	no	—
139	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
141	#11719919	—	2	1	no	—
142	#11719919	—	2	1	no	—
143	#11719919	—	2	1	no	—
144	#11719919	—	2	1	no	—
145	C₄×Dic₅₃	—	2	1	no	—
146	#11719917	—	2	4	no	—
147	#11719917	—	4	2	no	—
148	C₂×#88322	—	2	2	no	—
149	C₂×#88322	—	2	2	no	—
150	C₂×#88322	—	4	1	no	—
151	C₂×#88322	C₂²×C₄	1	2	yes	—
152	C₂×#88322	C₂²×C₄	1	2	yes	—
153	C₂×#88322	C₂×D₄	1	1	yes	characteristic
154	C₂×#88322	C₂×D₄	1	1	yes	characteristic
155	C₂×#88322	C₂×D₄	1	1	yes	characteristic
156	C₂×#88322	C₂×D₄	1	1	yes	characteristic
157	#11719912	—	4	2	no	—
158	C₈×D₅₃	—	4	2	no	—
159	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₅₃	—	2	1	no	—
161	Q₈×C₅₃	—	2	2	no	—
162	Q₈×C₅₃	—	2	2	no	—
163	Q₈×C₅₃	—	4	2	no	—
164	C₂×C₄×C₅₃	—	2	2	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	2	2	no	—
168	C₂×C₄×C₅₃	—	2	2	no	—
169	C₂×C₄×C₅₃	—	4	1	no	—
170	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂³×C₄	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	C₂²⋊D₅₃	—	4	2	no	—
177	C₂×Dic₅₃	—	2	1	no	—
178	C₂×Dic₅₃	—	2	1	no	—
179	C₂×Dic₅₃	—	2	1	no	—
180	D₂₁₂	—	2	2	no	—
181	C₄×D₅₃	—	4	1	no	—
182	C₄×D₅₃	—	4	1	no	—
183	Dic₁₀₆	—	2	2	no	—
184	C₈×C₅₃	—	4	2	no	—
185	C₈×C₅₃	—	4	1	no	—
186	C₈×C₅₃	—	4	1	no	—
187	#88322	—	2	2	no	—
188	#88322	—	2	1	no	—
189	#88322	—	2	1	no	—
190	#88322	—	2	1	no	—
191	#88322	—	4	2	no	—
192	#88322	#131	1	4	yes	—
193	#88322	#137	1	2	yes	—
194	#17967	—	53	1	no	maximal, Sylow
195	C₂²×C₅₃	—	2	1	no	—
196	C₂²×C₅₃	—	2	1	no	—
197	C₂²×C₅₃	—	2	1	no	—
198	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×D₅₃	—	4	1	no	—
200	C₂×D₅₃	—	4	1	no	—
201	C₂×D₅₃	—	4	1	no	—
202	C₄×C₅₃	—	2	1	no	—
203	C₄×C₅₃	—	2	1	no	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	4	2	no	—
207	C₄×C₅₃	—	4	2	no	—
208	C₄×C₅₃	C₂×#131	1	2	yes	—
209	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
210	C₄×C₅₃	#575	1	1	yes	characteristic
211	Dic₅₃	—	4	1	no	—
212	Dic₅₃	—	4	1	no	—
213	Dic₅₃	—	4	1	no	—
214	#3172	—	53	1	no	—
215	#2966	—	53	1	no	—
216	#2960	—	53	1	no	—
217	#1591	—	53	2	no	—
218	#1590	—	53	2	no	—
219	#1579	—	53	2	no	—
220	SD₁₆⋊C₈	—	53	2	no	—
221	#1569	—	53	1	no	—
222	#1497	D₅₃	1	1	yes	characteristic, complemented
223	#1495	—	53	1	no	—
224	C₈×M₁₆	—	53	1	no	—
225	C₂×C₅₃	—	4	1	no	—
226	C₂×C₅₃	#2931	1	1	yes	characteristic
227	C₂×C₅₃	C₄×#137	1	1	yes	characteristic
228	C₂×C₅₃	#2955	1	1	yes	characteristic
229	D₅₃	—	8	1	no	—
230	#533	C₂×D₅₃	1	1	yes	characteristic
231	#529	—	53	1	no	—
232	#501	—	53	1	no	—
233	#497	—	53	1	no	—
234	#491	—	53	1	no	—
235	#489	—	53	1	no	—
236	#470	—	53	2	no	—
237	#468	—	53	2	no	—
238	#446	—	53	2	no	—
239	#446	—	53	1	no	—
240	#446	—	106	1	no	—
241	C₈×Q₈	—	53	2	no	—
242	C₈×Q₈	—	53	1	no	—
243	C₈×Q₈	—	106	1	no	—
244	C₄×Q₁₆	—	53	2	no	—
245	C₄×SD₁₆	—	53	2	no	—
246	#436	—	53	1	no	—
247	#435	—	106	1	no	—
248	C₈×D₄	—	53	1	no	—
249	C₈×D₄	—	106	1	no	—
250	#433	—	106	1	no	—
251	#432	C₂×D₅₃	1	1	yes	characteristic
252	#431	C₂×D₅₃	1	1	yes	characteristic
253	#424	—	106	1	no	—
254	#423	—	53	1	no	—
255	#405	—	106	1	no	—
256	#405	—	106	1	no	—
257	C₄×M₁₆	—	53	1	no	—
258	C₂×C₄×C₈	—	53	1	no	—
259	#335	—	53	2	no	—
260	#334	—	53	2	no	—
261	Q₈⋊C₈	—	53	2	no	—
262	Q₈⋊C₈	C₂×D₅₃	1	2	yes	—
263	Q₈⋊C₈	C₂×D₅₃	1	2	yes	—
264	D₄⋊C₈	—	53	2	no	—
265	#322	—	53	2	no	—
266	C₈²	—	53	2	no	—
267	C₅₃	#17967	1	1	yes	characteristic, complemented, Sylow
268	C₂×Q₁₆	—	53	2	no	—
269	C₂×SD₁₆	—	53	2	no	—
270	C₂×M₁₆	—	53	2	no	—
271	C₂×M₁₆	—	106	1	no	—
272	C₂×M₁₆	—	106	1	no	—
273	C₂²×C₈	—	53	1	no	—
274	C₂²×C₈	—	53	1	no	—
275	C₂²×C₈	—	106	1	no	—
276	C₄⋊Q₈	C₄×D₅₃	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₅₃	1	1	yes	characteristic
278	#126	—	106	1	no	—
279	#125	—	2	1	no	—
280	#125	—	53	1	no	—
281	#124	—	53	1	no	—
282	#123	—	106	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	53	1	no	—
285	C₂²⋊Q₈	C₄×D₅₃	1	2	yes	—
286	#121	—	53	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	53	1	no	—
289	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
290	C₄×D₄	—	53	1	no	—
291	C₄×D₄	—	106	1	no	—
292	#117	—	2	1	no	—
293	#117	—	106	1	no	—
294	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
295	#107	—	53	2	no	—
296	#106	—	53	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	53	2	no	—
299	C₄⋊C₈	—	106	2	no	—
300	C₄⋊C₈	—	106	2	no	—
301	C₄⋊C₈	—	106	1	no	—
302	C₄⋊C₈	—	106	1	no	—
303	C₄⋊C₈	—	106	1	no	—
304	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
306	#103	—	53	2	no	—
307	#103	—	53	2	no	—
308	#103	—	53	2	no	—
309	#102	—	53	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	106	1	no	—
313	C₂²⋊C₈	—	106	1	no	—
314	#97	—	2	1	no	—
315	#97	—	53	1	no	—
316	#97	—	53	1	no	—
317	#97	—	106	2	no	—
318	#97	—	106	1	no	—
319	C₄×C₈	—	53	1	no	—
320	C₄×C₈	—	53	1	no	—
321	C₄×C₈	—	53	1	no	—
322	C₄×C₈	—	53	2	no	—
323	C₄×C₈	—	53	1	no	—
324	C₄×C₈	—	106	2	no	—
325	C₄×C₈	—	106	1	no	—
326	C₄×C₈	C₂²×D₅₃	1	2	yes	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	53	1	no	—
329	C₂×Q₈	C₂×C₄×D₅₃	1	2	yes	—
330	C₂×D₄	—	53	1	no	—
331	C₂×D₄	—	106	1	no	—
332	C₂²×C₄	—	106	1	no	—
333	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
335	C₂²×C₄	#11719947	1	1	yes	characteristic
336	Q₁₆	—	106	4	no	—
337	SD₁₆	—	106	4	no	—
338	M₁₆	—	106	4	no	—
339	M₁₆	—	212	2	no	—
340	M₁₆	—	212	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	53	2	no	—
345	C₂×C₈	—	53	1	no	—
346	C₂×C₈	—	53	2	no	—
347	C₂×C₈	—	53	1	no	—
348	C₂×C₈	—	53	1	no	—
349	C₂×C₈	—	53	1	no	—
350	C₂×C₈	—	106	2	no	—
351	C₂×C₈	—	106	2	no	—
352	C₂×C₈	—	212	2	no	—
353	C₂×C₈	—	212	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	53	1	no	—
360	C₄⋊C₄	—	53	1	no	—
361	C₄⋊C₄	—	106	1	no	—
362	C₄⋊C₄	—	106	1	no	—
363	C₄⋊C₄	—	106	1	no	—
364	C₄⋊C₄	—	106	1	no	—
365	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	106	1	no	—
368	C₂²⋊C₄	—	106	1	no	—
369	C₂²⋊C₄	—	106	1	no	—
370	C₂²⋊C₄	—	106	1	no	—
371	C₂²⋊C₄	—	106	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	106	1	no	—
374	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
375	C₄²	D₄×D₅₃	1	1	yes	characteristic
376	C₄²	#11719947	1	1	yes	characteristic
377	C₄²	C₂³×D₅₃	1	1	yes	characteristic
378	C₂³	—	106	1	no	—
379	C₂³	#13133177	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	106	2	no	—
384	D₄	—	106	2	no	—
385	D₄	—	212	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	106	1	no	—
393	C₂×C₄	—	106	1	no	—
394	C₂×C₄	—	106	1	no	—
395	C₂×C₄	—	212	1	no	—
396	C₂×C₄	—	212	1	no	—
397	C₂×C₄	#13133177	1	1	yes	characteristic
398	C₂×C₄	#13133177	1	1	yes	characteristic
399	C₂×C₄	#13133177	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
402	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	53	4	no	—
407	C₈	—	53	2	no	—
408	C₈	—	106	2	no	—
409	C₈	—	106	1	no	—
410	C₈	—	106	1	no	—
411	C₈	—	106	1	no	—
412	C₈	—	212	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	212	1	no	—
417	C₂²	—	212	1	no	—
418	C₂²	—	212	1	no	—
419	C₂²	C₂×#13133177	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	212	1	no	—
427	C₄	—	212	1	no	—
428	C₄	—	212	1	no	—
429	C₄	#131×D₅₃	1	2	yes	—
430	C₄	#137×D₅₃	1	1	yes	characteristic
431	C₄	#16811422	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	424	1	no	—
434	C₂	#20283423	1	1	yes	characteristic
435	C₂	#20283530	1	1	yes	characteristic
436	C₂	#20283614	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1497	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	#13133191	C₂×C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1497	D₅₃
hypocenter	C₅₃	#17967
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1497

Complements

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

N	H ≅ G/N	type
3. #20283650	C₂	semidirect
4. #20273609	C₂	semidirect
5. #20273602	C₂	semidirect
6. #20273531	C₂	semidirect
7. #20273530	C₂	semidirect
8. #20273483	C₂	semidirect
10. #20272996	C₂	semidirect
11. C₅₃×#1497	C₂	semidirect
222. #1497	D₅₃	semidirect
267. C₅₃	#17967	semidirect

Maximal subgroups

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

subgroup	index
#20285315	2
#20283684	2
#20283650	2
#20273609	2
#20273602	2
#20273531	2
#20273530	2
#20273483	2
#20273181	2
#20272996	2
C₅₃×#1497	2
#17967	53