Subgroups — #27398019

Order 13568.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285201	C₂	1	1	yes	maximal, characteristic
2	#20283631	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283566	C₂	1	1	yes	maximal, characteristic, complemented
4	#20275623	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275611	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275246	C₂	1	2	yes	maximal, complemented
7	#20275241	C₂	1	2	yes	maximal, complemented
8	#20275201	C₂	1	2	yes	maximal, complemented
9	#20275194	C₂	1	2	yes	maximal, complemented
10	#20274470	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133245	C₂²	1	2	yes	—
13	C₂×#13133239	C₂²	1	1	yes	characteristic
14	C₂²×D₄₂₄	C₂²	1	1	yes	characteristic
15	#16811389	C₂²	1	2	yes	—
16	#16811192	C₂²	1	2	yes	—
17	#16811097	C₂²	1	2	yes	—
18	#16811012	C₄	1	4	yes	complemented
19	#16811007	C₄	1	2	yes	complemented
20	#16811000	C₄	1	2	yes	complemented
21	#16810744	—	2	2	no	—
22	#16810739	—	2	2	no	—
23	#16810734	—	2	2	no	—
24	#16810705	—	2	2	no	—
25	#16810641	C₂²	1	2	yes	—
26	#16810639	C₂²	1	2	yes	—
27	#16810629	C₂²	1	2	yes	—
28	#16810627	C₂²	1	2	yes	—
29	C₂×#13133133	C₂²	1	2	yes	—
30	#16810596	C₂²	1	2	yes	—
31	#16810578	C₂²	1	1	yes	characteristic
32	#16810578	C₂²	1	1	yes	characteristic
33	#16810381	C₂²	1	1	yes	characteristic
34	#16810380	C₂²	1	1	yes	characteristic
35	#16810379	C₂²	1	1	yes	characteristic
36	#16810379	C₂²	1	1	yes	characteristic
37	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#427	C₂²	1	1	yes	characteristic
39	C₅₃×#405	C₂²	1	1	yes	characteristic
40	C₅₃×#344	C₂²	1	2	yes	—
41	C₅₃×H(3,ℤ/4)	C₂²	1	2	yes	—
42	C₂×#11719945	C₂³	1	2	yes	—
43	C₂²×D₂₁₂	C₂³	1	2	yes	—
44	#13133245	—	4	2	no	—
45	#13133245	—	4	2	no	—
46	#13133239	—	2	1	no	—
47	#13133239	—	2	1	no	—
48	#13133239	—	2	1	no	—
49	#13133239	—	2	1	no	—
50	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#11719913	C₂×C₄	1	2	yes	complemented
52	C₂×#11719913	C₂×C₄	1	4	yes	complemented
53	C₂×D₄₂₄	—	2	1	no	—
54	C₂×D₄₂₄	—	2	1	no	—
55	C₂×D₄₂₄	—	2	1	no	—
56	C₂×D₄₂₄	—	2	1	no	—
57	C₂×D₄₂₄	C₂×C₄	1	2	yes	—
58	C₂×D₄₂₄	C₂×C₄	1	2	yes	—
59	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×D₄₂₄	C₂×C₄	1	4	yes	complemented
61	#13133225	—	2	4	no	—
62	#13133223	—	4	2	no	—
63	C₂×#11719917	C₂³	1	1	yes	characteristic
64	C₂×#11719917	C₂³	1	1	yes	characteristic
65	M₁₆×D₅₃	—	4	2	no	—
66	#13133214	C₂×C₄	1	4	yes	complemented
67	#13133205	C₂×C₄	1	4	yes	complemented
68	#13133192	—	4	2	no	—
69	#13133187	—	4	2	no	—
70	C₄×D₂₁₂	—	4	2	no	—
71	#13133179	—	2	4	no	—
72	#13133176	C₂³	1	1	yes	characteristic
73	#13133176	C₂³	1	1	yes	characteristic
74	C₂²⋊C₄×D₅₃	—	4	2	no	—
75	#13133145	—	4	2	no	—
76	#13133143	—	2	4	no	—
77	#13133139	—	4	2	no	—
78	#13133137	—	2	4	no	—
79	#13133133	—	4	2	no	—
80	#13133131	—	4	2	no	—
81	#13133127	—	2	1	no	—
82	#13133127	D₄	1	2	yes	complemented
83	C₈×Dic₅₃	—	2	1	no	—
84	C₈×Dic₅₃	D₄	1	2	yes	complemented
85	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
86	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
88	#117×C₅₃	C₂³	1	2	yes	—
89	#117×C₅₃	C₂³	1	1	yes	characteristic
90	#108×C₅₃	—	2	1	no	—
91	#108×C₅₃	—	2	1	no	—
92	#107×C₅₃	—	2	1	no	—
93	#106×C₅₃	—	2	1	no	—
94	#97×C₅₃	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
96	C₂³×D₅₃	—	2	2	no	—
97	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₂²⋊D₅₃	—	2	2	no	—
99	#11719945	—	2	2	no	—
100	#11719945	—	2	2	no	—
101	#11719945	—	2	2	no	—
102	#11719945	—	2	2	no	—
103	C₂×D₂₁₂	—	2	2	no	—
104	C₂×D₂₁₂	—	2	2	no	—
105	C₂×D₂₁₂	—	2	2	no	—
106	C₂×D₂₁₂	—	2	2	no	—
107	C₂×D₂₁₂	—	2	2	no	—
108	C₂×D₂₁₂	—	4	4	no	—
109	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
110	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₅₃	—	2	2	no	—
112	C₂×C₄×D₅₃	—	4	4	no	—
113	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
114	M₁₆×C₅₃	—	2	1	no	—
115	M₁₆×C₅₃	—	2	1	no	—
116	M₁₆×C₅₃	—	2	2	no	—
117	M₁₆×C₅₃	—	2	2	no	—
118	C₂×C₈×C₅₃	—	2	2	no	—
119	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂²×C₄	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	#41	1	1	yes	characteristic
125	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
126	C₄⋊C₄×C₅₃	—	2	1	no	—
127	C₄⋊C₄×C₅₃	—	2	2	no	—
128	C₂²⋊C₄×C₅₃	—	2	1	no	—
129	C₂²⋊C₄×C₅₃	—	2	2	no	—
130	C₄²×C₅₃	—	2	2	no	—
131	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
132	C₂²⋊Dic₅₃	—	2	1	no	—
133	C₂²⋊Dic₅₃	—	2	1	no	—
134	#11719921	—	4	4	no	—
135	#11719921	—	4	4	no	—
136	C₄⋊Dic₅₃	—	2	1	no	—
137	C₄⋊Dic₅₃	—	2	1	no	—
138	C₄×Dic₅₃	—	2	1	no	—
139	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
140	#11719917	—	2	1	no	—
141	#11719917	—	2	1	no	—
142	#11719917	—	2	1	no	—
143	#11719917	—	2	1	no	—
144	C₂×#88322	—	2	1	no	—
145	C₂×#88322	C₂×D₄	1	2	yes	—
146	Dic₂₁₂	—	2	1	no	—
147	Dic₂₁₂	—	2	1	no	—
148	D₄₂₄	—	2	2	no	—
149	D₄₂₄	—	2	2	no	—
150	D₄₂₄	—	2	2	no	—
151	D₄₂₄	—	2	2	no	—
152	D₄₂₄	—	2	1	no	—
153	D₄₂₄	—	2	1	no	—
154	D₄₂₄	—	4	4	no	—
155	#11719913	—	2	2	no	—
156	#11719913	—	2	2	no	—
157	#11719913	—	4	4	no	—
158	#11719912	—	4	4	no	—
159	C₈×D₅₃	—	4	4	no	—
160	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₅₃	—	2	2	no	—
162	C₂²×D₅₃	—	2	4	no	—
163	C₂²×D₅₃	—	4	2	no	—
164	C₂²×D₅₃	—	4	2	no	—
165	C₂²×D₅₃	—	16	2	no	—
166	C₂×C₄×C₅₃	—	2	2	no	—
167	C₂×C₄×C₅₃	—	4	2	no	—
168	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²⋊D₅₃	—	4	2	no	—
175	C₂²⋊D₅₃	—	4	2	no	—
176	C₂×Dic₅₃	—	2	2	no	—
177	C₂×Dic₅₃	—	2	2	no	—
178	C₂×Dic₅₃	—	4	1	no	—
179	D₂₁₂	—	2	4	no	—
180	D₂₁₂	—	2	2	no	—
181	D₂₁₂	—	2	4	no	—
182	D₂₁₂	—	2	2	no	—
183	D₂₁₂	—	4	2	no	—
184	D₂₁₂	—	4	2	no	—
185	D₂₁₂	—	16	4	no	—
186	C₄×D₅₃	—	4	2	no	—
187	C₄×D₅₃	—	4	2	no	—
188	C₄×D₅₃	—	16	4	no	—
189	Dic₁₀₆	—	2	2	no	—
190	Dic₁₀₆	—	2	2	no	—
191	C₈×C₅₃	—	2	2	no	—
192	C₈×C₅₃	—	4	2	no	—
193	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
194	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
195	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
196	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
197	#88322	—	2	2	no	—
198	#88322	—	4	1	no	—
199	#22286	—	53	1	no	maximal, Sylow
200	C₂²×C₅₃	—	4	1	no	—
201	C₂²×C₅₃	#518	1	1	yes	characteristic
202	C₂²×C₅₃	#535	1	1	yes	characteristic
203	C₂²×C₅₃	#540	1	1	yes	characteristic
204	C₂×D₅₃	—	4	2	no	—
205	C₂×D₅₃	—	4	4	no	—
206	C₂×D₅₃	—	8	4	no	—
207	C₂×D₅₃	—	8	2	no	—
208	C₂×D₅₃	—	8	4	no	—
209	C₂×D₅₃	—	16	2	no	—
210	C₄×C₅₃	—	4	2	no	—
211	C₄×C₅₃	—	8	2	no	—
212	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₅₃	#518	1	1	yes	characteristic
214	C₄×C₅₃	#535	1	1	yes	characteristic
215	C₄×C₅₃	#540	1	1	yes	characteristic
216	Dic₅₃	—	4	2	no	—
217	Dic₅₃	—	4	2	no	—
218	Dic₅₃	—	8	1	no	—
219	#3155	—	53	1	no	—
220	#2957	—	53	1	no	—
221	#2948	—	53	1	no	—
222	#1978	—	53	1	no	—
223	#1976	—	53	1	no	—
224	#1911	—	53	2	no	—
225	#1910	—	53	2	no	—
226	#1904	—	53	2	no	—
227	#1903	—	53	2	no	—
228	#1833	D₅₃	1	1	yes	characteristic, complemented
229	#1747	—	53	1	no	—
230	C₂×C₅₃	—	2	1	no	—
231	C₂×C₅₃	—	2	1	no	—
232	C₂×C₅₃	—	2	1	no	—
233	C₂×C₅₃	#2328	1	1	yes	characteristic
234	D₅₃	—	8	2	no	—
235	D₅₃	—	8	4	no	—
236	C₂×AGL(1,ℤ/8)	—	53	2	no	—
237	C₂×#135	—	53	1	no	—
238	C₂²×D₈	—	53	1	no	—
239	#568	—	53	2	no	—
240	#535	—	53	2	no	—
241	#518	—	53	2	no	—
242	#496	—	53	4	no	—
243	#495	—	53	2	no	—
244	#493	—	53	2	no	—
245	#444	—	106	2	no	—
246	#443	—	106	2	no	—
247	#442	—	106	2	no	—
248	C₄×D₈	—	106	2	no	—
249	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
250	#427	C₂×D₅₃	1	1	yes	characteristic
251	#421	—	53	2	no	—
252	#421	—	53	2	no	—
253	#418	—	53	2	no	—
254	#418	—	53	2	no	—
255	C₂×#100	—	53	2	no	—
256	#410	—	53	2	no	—
257	#405	—	53	1	no	—
258	#405	—	53	1	no	—
259	#405	C₂×D₅₃	1	1	yes	characteristic
260	#344	C₂×D₅₃	1	2	yes	—
261	#338	—	53	1	no	—
262	H(3,ℤ/4)	—	53	1	no	—
263	H(3,ℤ/4)	—	53	1	no	—
264	H(3,ℤ/4)	—	53	1	no	—
265	H(3,ℤ/4)	C₂×D₅₃	1	2	yes	—
266	C₅₃	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	53	2	no	—
268	C₂²×D₄	—	53	2	no	—
269	AGL(1,ℤ/8)	—	212	2	no	—
270	AGL(1,ℤ/8)	—	212	2	no	—
271	#135	—	106	1	no	—
272	#135	—	106	1	no	—
273	#135	—	106	1	no	—
274	#135	—	106	1	no	—
275	C₂×Q₁₆	—	53	1	no	—
276	C₂×SD₁₆	—	53	2	no	—
277	C₂×SD₁₆	—	53	4	no	—
278	C₂×D₈	—	53	2	no	—
279	C₂×D₈	—	53	2	no	—
280	C₂×D₈	—	53	1	no	—
281	C₂×D₈	—	53	4	no	—
282	C₂×D₈	—	106	1	no	—
283	C₂×D₈	—	106	1	no	—
284	C₂×D₈	—	106	1	no	—
285	C₂×D₈	—	106	1	no	—
286	#131	—	106	4	no	—
287	#131	—	212	2	no	—
288	C₂×M₁₆	—	53	1	no	—
289	C₂×M₁₆	—	53	1	no	—
290	C₂×M₁₆	—	212	2	no	—
291	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
292	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
294	#127	—	53	4	no	—
295	#124	—	53	4	no	—
296	#121	—	212	2	no	—
297	#120	—	212	2	no	—
298	C₄×D₄	—	106	4	no	—
299	C₄×D₄	—	212	2	no	—
300	#117	—	53	1	no	—
301	#117	—	53	1	no	—
302	#117	C₂²×D₅₃	1	2	yes	—
303	#117	C₂²×D₅₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	212	2	no	—
305	#108	—	2	1	no	—
306	#108	—	2	1	no	—
307	#107	—	2	1	no	—
308	#106	—	2	1	no	—
309	#104	—	106	4	no	—
310	#104	—	212	2	no	—
311	#102	—	106	4	no	—
312	#102	—	212	2	no	—
313	#100	—	212	2	no	—
314	#99	—	212	2	no	—
315	#97	—	53	2	no	—
316	#97	—	106	1	no	—
317	#97	C₄×D₅₃	1	2	yes	complemented
318	C₄×C₈	—	53	2	no	—
319	C₄×C₈	—	106	1	no	—
320	C₄×C₈	C₄×D₅₃	1	2	yes	complemented
321	C₂⁴	—	106	2	no	—
322	#41	—	106	2	no	—
323	#41	—	106	2	no	—
324	#41	—	106	2	no	—
325	#41	—	106	2	no	—
326	C₂×Q₈	—	53	2	no	—
327	C₂×D₄	—	53	4	no	—
328	C₂×D₄	—	53	2	no	—
329	C₂×D₄	—	106	2	no	—
330	C₂×D₄	—	106	2	no	—
331	C₂×D₄	—	106	2	no	—
332	C₂×D₄	—	106	2	no	—
333	C₂×D₄	—	106	2	no	—
334	C₂×D₄	—	106	2	no	—
335	C₂×D₄	—	212	4	no	—
336	C₂²×C₄	—	106	2	no	—
337	C₂²×C₄	—	212	4	no	—
338	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
339	Q₁₆	—	106	1	no	—
340	Q₁₆	—	106	1	no	—
341	SD₁₆	—	106	2	no	—
342	SD₁₆	—	106	2	no	—
343	SD₁₆	—	212	4	no	—
344	D₈	—	106	2	no	—
345	D₈	—	106	2	no	—
346	D₈	—	106	2	no	—
347	D₈	—	106	2	no	—
348	D₈	—	106	1	no	—
349	D₈	—	106	1	no	—
350	D₈	—	212	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	106	1	no	—
356	M₁₆	—	106	1	no	—
357	M₁₆	—	106	1	no	—
358	M₁₆	—	106	1	no	—
359	M₁₆	—	212	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	53	2	no	—
362	C₂×C₈	—	106	1	no	—
363	C₂×C₈	—	212	4	no	—
364	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
367	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
368	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
369	C₂×C₈	#11719949	1	1	yes	characteristic
370	C₂×C₈	#11719949	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	106	1	no	—
374	C₄⋊C₄	—	106	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	106	1	no	—
378	C₂²⋊C₄	—	106	1	no	—
379	C₂²⋊C₄	—	212	4	no	—
380	C₂²⋊C₄	—	212	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	53	2	no	—
383	C₄²	—	106	1	no	—
384	C₄²	C₂×C₄×D₅₃	1	2	yes	—
385	C₂³	—	848	2	no	—
386	C₂³	—	106	4	no	—
387	C₂³	—	106	2	no	—
388	C₂³	—	212	2	no	—
389	C₂³	—	212	2	no	—
390	C₂³	#13133263	1	1	yes	characteristic
391	Q₈	—	106	2	no	—
392	Q₈	—	106	2	no	—
393	D₄	—	848	4	no	—
394	D₄	—	106	4	no	—
395	D₄	—	106	2	no	—
396	D₄	—	106	2	no	—
397	D₄	—	106	4	no	—
398	D₄	—	212	2	no	—
399	D₄	—	212	2	no	—
400	D₄	—	212	2	no	—
401	D₄	—	212	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	848	4	no	—
405	C₂×C₄	—	106	2	no	—
406	C₂×C₄	—	106	2	no	—
407	C₂×C₄	—	212	1	no	—
408	C₂×C₄	—	212	2	no	—
409	C₂×C₄	—	212	2	no	—
410	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#11719949	1	1	yes	characteristic
413	C₂×C₄	#13133263	1	1	yes	characteristic
414	C₂×C₄	#13133263	1	1	yes	characteristic
415	C₂×C₄	#13133263	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	106	2	no	—
419	C₈	—	212	1	no	—
420	C₈	#13133179	1	1	yes	characteristic
421	C₈	#13133179	1	1	yes	characteristic
422	C₈	#13133179	1	1	yes	characteristic
423	C₈	#13133179	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	848	2	no	—
426	C₂²	—	424	2	no	—
427	C₂²	—	424	4	no	—
428	C₂²	—	424	4	no	—
429	C₂²	—	212	2	no	—
430	C₂²	—	212	4	no	—
431	C₂²	#16811097	1	1	yes	characteristic
432	C₂²	#16811191	1	1	yes	characteristic
433	C₂²	#16811229	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	424	1	no	—
437	C₄	—	212	2	no	—
438	C₄	—	212	2	no	—
439	C₄	C₂×#13133179	1	1	yes	characteristic
440	C₄	#16811097	1	1	yes	characteristic
441	C₄	#16811191	1	1	yes	characteristic
442	C₄	#16811229	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	424	4	no	—
447	C₂	—	424	2	no	—
448	C₂	#20277438	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20277438
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1833	C₂
socle	C₂×C₅₃	#2328
prime radical	#20285201	C₂
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1833	D₅₃
hypocenter	C₅₃	#22286
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1833

Complements

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

N	H ≅ G/N	type
2. #20283631	C₂	semidirect
3. #20283566	C₂	semidirect
4. #20275623	C₂	semidirect
5. #20275611	C₂	semidirect
6. #20275246	C₂	semidirect
7. #20275241	C₂	semidirect
8. #20275201	C₂	semidirect
9. #20275194	C₂	semidirect
10. #20274470	C₂	semidirect
11. C₅₃×#1833	C₂	semidirect
18. #16811012	C₄	semidirect
19. #16811007	C₄	semidirect
20. #16811000	C₄	semidirect
50. C₂×Dic₂₁₂	C₂×C₄	semidirect
51. C₂×#11719913	C₂×C₄	semidirect
52. C₂×#11719913	C₂×C₄	semidirect
59. C₂×D₄₂₄	C₂×C₄	semidirect
60. C₂×D₄₂₄	C₂×C₄	semidirect
66. #13133214	C₂×C₄	semidirect
67. #13133205	C₂×C₄	semidirect
82. #13133127	D₄	semidirect
84. C₈×Dic₅₃	D₄	semidirect
94. #97×C₅₃	C₂×C₄	semidirect
95. C₄×C₈×C₅₃	C₂×C₄	semidirect
228. #1833	D₅₃	semidirect
266. C₅₃	#22286	semidirect
317. #97	C₄×D₅₃	semidirect
320. C₄×C₈	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20285201	2
#20283631	2
#20283566	2
#20275623	2
#20275611	2
#20275246	2
#20275241	2
#20275201	2
#20275194	2
#20274470	2
C₅₃×#1833	2
#22286	53