Subgroups — #444×Dic₅₃ #27382666

Order 13568.

1022 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810745	C₂	1	1	yes	maximal, characteristic
2	#135×Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	#131×Dic₅₃	C₂	1	2	yes	maximal, complemented
4	#108×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274602	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274599	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274560	C₂	1	2	yes	maximal, complemented
8	#20274557	C₂	1	2	yes	maximal, complemented
9	#104×Dic₅₃	C₂	1	2	yes	maximal, complemented
10	#97×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#444	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133224	C₂²	1	2	yes	—
13	#41×Dic₅₃	C₂²	1	2	yes	—
14	#16810745	C₄	1	8	yes	complemented
15	Q₁₆×Dic₅₃	C₄	1	2	yes	complemented
16	SD₁₆×Dic₅₃	C₄	1	4	yes	complemented
17	D₈×Dic₅₃	C₄	1	2	yes	complemented
18	C₂×#13133153	C₂²	1	1	yes	characteristic
19	#16810661	C₂²	1	1	yes	characteristic
20	C₂×#13133144	C₂²	1	2	yes	—
21	#16810619	C₂²	1	2	yes	—
22	#16810581	—	2	2	no	—
23	#16810581	C₂²	1	2	yes	—
24	#16810578	—	2	2	no	—
25	#16810578	C₂²	1	2	yes	—
26	M₁₆×Dic₅₃	—	2	2	no	—
27	M₁₆×Dic₅₃	C₂²	1	2	yes	—
28	C₂×#13133128	C₂²	1	1	yes	characteristic
29	C₂×#13133127	C₂²	1	1	yes	characteristic
30	C₂×#13133127	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₅₃	—	2	2	no	—
32	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
34	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
35	#16810387	C₂²	1	2	yes	—
36	#16810384	C₂²	1	2	yes	—
37	#16810383	C₂²	1	2	yes	—
38	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#131×C₅₃	C₂²	1	2	yes	—
40	C₅₃×#444	C₄	1	8	yes	complemented
41	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#104×C₅₃	C₂²	1	2	yes	—
43	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
44	#13133224	—	2	4	no	—
45	#13133224	C₂×C₄	1	8	yes	complemented
46	C₂×#11719917	—	2	2	no	—
47	C₂×#11719917	C₂³	1	2	yes	—
48	C₂²×#88322	—	2	2	no	—
49	C₂²×#88322	C₂³	1	1	yes	characteristic
50	C₂²×#88322	C₂³	1	1	yes	characteristic
51	Q₈×Dic₅₃	C₂×C₄	1	4	yes	—
52	D₄×Dic₅₃	—	2	4	no	—
53	D₄×Dic₅₃	C₂×C₄	1	4	yes	—
54	#13133176	—	2	2	no	—
55	#13133176	C₂³	1	2	yes	—
56	C₂×C₄×Dic₅₃	—	2	2	no	—
57	C₂×C₄×Dic₅₃	—	2	2	no	—
58	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
60	#13133153	C₂×C₄	1	4	yes	complemented
61	#13133151	C₂×C₄	1	2	yes	—
62	#13133149	C₂×C₄	1	2	yes	—
63	#13133144	C₂×C₄	1	8	yes	complemented
64	#13133141	C₂×C₄	1	4	yes	—
65	#13133138	C₂×C₄	1	4	yes	—
66	#13133128	—	2	2	no	—
67	#13133127	—	2	2	no	—
68	#13133127	—	2	2	no	—
69	#13133127	—	2	2	no	—
70	#13133127	—	2	2	no	—
71	#13133127	C₂×C₄	1	4	yes	complemented
72	C₈×Dic₅₃	—	2	2	no	—
73	C₈×Dic₅₃	—	2	2	no	—
74	C₈×Dic₅₃	—	2	2	no	—
75	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
76	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
77	C₈×Dic₅₃	D₄	1	2	yes	—
78	C₈×Dic₅₃	D₄	1	2	yes	—
79	C₂×#41×C₅₃	C₂³	1	2	yes	—
80	#135×C₅₃	C₂×C₄	1	4	yes	—
81	#135×C₅₃	C₂×C₄	1	4	yes	—
82	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
83	C₂×SD₁₆×C₅₃	C₂×C₄	1	2	yes	—
84	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
85	#131×C₅₃	—	2	4	no	—
86	#131×C₅₃	C₂×C₄	1	8	yes	complemented
87	C₂×M₁₆×C₅₃	—	2	2	no	—
88	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
89	C₂²×C₈×C₅₃	—	2	2	no	—
90	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
93	#108×C₅₃	C₂×C₄	1	4	yes	complemented
94	#104×C₅₃	C₂×C₄	1	8	yes	complemented
95	#97×C₅₃	C₂×C₄	1	4	yes	complemented
96	#41×C₅₃	—	2	2	no	—
97	#41×C₅₃	—	2	2	no	—
98	#41×C₅₃	C₂²×C₄	1	4	yes	—
99	#41×C₅₃	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₅₃	—	2	2	no	—
102	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅₃	—	2	2	no	—
104	C₂²×C₄×C₅₃	—	2	1	no	—
105	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₅₃	—	2	1	no	—
107	C₂²×Dic₅₃	—	2	4	no	—
108	C₂²×Dic₅₃	#41	1	2	yes	—
109	Q₁₆×C₅₃	C₄²	1	4	yes	complemented
110	SD₁₆×C₅₃	C₄²	1	8	yes	complemented
111	D₈×C₅₃	C₄²	1	4	yes	complemented
112	M₁₆×C₅₃	—	2	2	no	—
113	M₁₆×C₅₃	—	2	8	no	—
114	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	—	2	8	no	—
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₅₃	#41	1	2	yes	—
124	C₄²×C₅₃	—	2	1	no	—
125	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
126	C₂²⋊Dic₅₃	—	2	2	no	—
127	C₂²⋊Dic₅₃	—	2	4	no	—
128	C₄⋊Dic₅₃	—	2	4	no	—
129	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
130	C₄×Dic₅₃	—	2	2	no	—
131	C₄×Dic₅₃	—	2	1	no	—
132	C₄×Dic₅₃	—	2	4	no	—
133	C₄×Dic₅₃	—	4	4	no	—
134	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
135	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
136	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
138	#11719917	—	2	2	no	—
139	#11719917	—	2	8	no	—
140	#11719917	C₂²×C₄	1	4	yes	—
141	C₂×#88322	—	2	2	no	—
142	C₂×#88322	—	2	1	no	—
143	C₂×#88322	—	2	1	no	—
144	C₂×#88322	—	2	8	no	—
145	C₂×#88322	C₂²×C₄	1	2	yes	—
146	C₂×#88322	C₂²×C₄	1	2	yes	—
147	C₂×#88322	C₂×D₄	1	2	yes	—
148	C₂×#88322	#41	1	2	yes	—
149	C₂³×C₅₃	—	2	2	no	—
150	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
151	Q₈×C₅₃	—	2	2	no	—
152	Q₈×C₅₃	C₂×C₄²	1	4	yes	—
153	D₄×C₅₃	—	2	4	no	—
154	D₄×C₅₃	—	2	4	no	—
155	D₄×C₅₃	—	2	2	no	—
156	D₄×C₅₃	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₅₃	—	2	2	no	—
158	C₂×C₄×C₅₃	—	2	4	no	—
159	C₂×C₄×C₅₃	—	2	4	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	—	4	2	no	—
162	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
168	C₂×Dic₅₃	—	2	4	no	—
169	C₂×Dic₅₃	—	2	4	no	—
170	C₂×Dic₅₃	—	2	2	no	—
171	C₂×Dic₅₃	—	4	2	no	—
172	C₂×Dic₅₃	—	4	8	no	—
173	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
174	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
175	C₈×C₅₃	—	2	4	no	—
176	C₈×C₅₃	C₂×C₄²	1	2	yes	—
177	C₈×C₅₃	C₂×C₄²	1	2	yes	—
178	C₈×C₅₃	C₄×D₄	1	4	yes	—
179	#88322	—	2	4	no	—
180	#88322	—	2	2	no	—
181	#88322	C₄×D₄	1	4	yes	—
182	C₄×#444	—	53	1	no	maximal, Sylow
183	C₂²×C₅₃	—	2	2	no	—
184	C₂²×C₅₃	—	2	4	no	—
185	C₂²×C₅₃	—	4	4	no	—
186	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
188	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
189	C₄×C₅₃	—	2	4	no	—
190	C₄×C₅₃	—	4	2	no	—
191	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
192	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
195	Dic₅₃	—	2	2	no	—
196	Dic₅₃	—	4	2	no	—
197	Dic₅₃	—	4	4	no	—
198	Dic₅₃	#444	1	4	yes	direct product factor
199	C₂×#444	—	53	1	no	—
200	C₂×#444	D₅₃	1	1	yes	characteristic
201	C₄×#135	—	53	1	no	—
202	C₄×#131	—	53	2	no	—
203	C₄×#108	—	53	1	no	—
204	#1773	—	53	1	no	—
205	#1773	—	53	1	no	—
206	#1765	—	53	2	no	—
207	#1765	—	53	2	no	—
208	C₄×#104	—	53	2	no	—
209	C₄×#97	—	53	1	no	—
210	C₂×C₅₃	—	2	1	no	—
211	C₂×C₅₃	—	2	1	no	—
212	C₂×C₅₃	—	4	4	no	—
213	C₂×C₅₃	C₄²×D₄	1	1	yes	characteristic
214	C₂×C₅₃	C₂×#444	1	2	yes	—
215	C₂×#135	C₂×D₅₃	1	1	yes	characteristic
216	C₂×#131	—	53	2	no	—
217	C₂×#131	C₂×D₅₃	1	2	yes	—
218	C₄×#41	—	53	2	no	—
219	#444	—	53	8	no	—
220	#444	Dic₅₃	1	8	yes	direct product factor
221	C₄×Q₁₆	—	53	2	no	—
222	C₄×SD₁₆	—	53	4	no	—
223	C₄×D₈	—	53	2	no	—
224	C₂×#108	—	53	1	no	—
225	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
226	#427	—	53	1	no	—
227	C₂×#104	—	53	2	no	—
228	C₂×#104	C₂×D₅₃	1	2	yes	—
229	#416	—	53	2	no	—
230	#405	—	53	2	no	—
231	#405	—	53	2	no	—
232	#405	—	106	2	no	—
233	#405	—	106	2	no	—
234	C₄×M₁₆	—	53	2	no	—
235	C₄×M₁₆	—	106	2	no	—
236	C₂×#97	—	53	1	no	—
237	C₂×#97	—	53	1	no	—
238	C₂×#97	—	53	1	no	—
239	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
240	C₂×C₄×C₈	—	53	1	no	—
241	C₂×C₄×C₈	—	53	1	no	—
242	C₂×C₄×C₈	—	106	2	no	—
243	C₄³	—	53	1	no	—
244	#341	—	53	2	no	—
245	#339	—	53	2	no	—
246	#339	—	53	2	no	—
247	C₅₃	C₄×#444	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	C₂²×D₅₃	1	2	yes	—
249	#135	C₄×D₅₃	1	4	yes	—
250	#135	C₂×Dic₅₃	1	4	yes	—
251	C₂×Q₁₆	C₄×D₅₃	1	1	yes	characteristic
252	C₂×SD₁₆	C₄×D₅₃	1	2	yes	—
253	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
254	#131	—	2	4	no	—
255	#131	—	53	8	no	—
256	#131	—	106	4	no	—
257	#131	C₂×Dic₅₃	1	8	yes	complemented
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	53	2	no	—
260	C₂×M₁₆	—	106	2	no	—
261	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	53	1	no	—
265	C₂²×C₈	—	106	2	no	—
266	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
268	C₄×Q₈	—	53	4	no	—
269	C₄×D₄	—	53	4	no	—
270	C₄×D₄	—	106	4	no	—
271	#117	—	53	2	no	—
272	#117	—	106	2	no	—
273	C₂×C₄²	—	53	1	no	—
274	C₂×C₄²	—	53	1	no	—
275	C₂×C₄²	—	106	2	no	—
276	C₂×C₄²	—	106	2	no	—
277	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
278	#108	—	53	4	no	—
279	#108	C₂×Dic₅₃	1	4	yes	complemented
280	#107	—	53	2	no	—
281	#106	—	53	2	no	—
282	#104	—	53	8	no	—
283	#104	C₂×Dic₅₃	1	8	yes	complemented
284	#103	—	53	4	no	—
285	#102	—	53	4	no	—
286	#97	—	53	4	no	—
287	#97	—	106	2	no	—
288	#97	—	106	2	no	—
289	#97	—	106	2	no	—
290	#97	—	106	2	no	—
291	#97	—	106	2	no	—
292	#97	C₂×Dic₅₃	1	4	yes	complemented
293	C₄×C₈	—	53	2	no	—
294	C₄×C₈	—	53	2	no	—
295	C₄×C₈	—	53	2	no	—
296	C₄×C₈	—	53	2	no	—
297	C₄×C₈	—	106	2	no	—
298	C₄×C₈	—	106	2	no	—
299	C₄×C₈	—	106	2	no	—
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	#41	C₂×C₄×D₅₃	1	4	yes	—
303	#41	C₂²×Dic₅₃	1	4	yes	—
304	C₂×Q₈	C₂×C₄×D₅₃	1	2	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	53	2	no	—
310	C₂²×C₄	—	106	4	no	—
311	C₂²×C₄	—	106	1	no	—
312	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
313	Q₁₆	C₄×Dic₅₃	1	4	yes	complemented
314	SD₁₆	C₄×Dic₅₃	1	8	yes	complemented
315	D₈	C₄×Dic₅₃	1	4	yes	complemented
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	8	no	—
318	M₁₆	—	53	4	no	—
319	M₁₆	—	106	8	no	—
320	M₁₆	—	106	2	no	—
321	M₁₆	C₂²×Dic₅₃	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	—	53	2	no	—
325	C₂×C₈	—	53	2	no	—
326	C₂×C₈	—	53	2	no	—
327	C₂×C₈	—	53	2	no	—
328	C₂×C₈	—	106	8	no	—
329	C₂×C₈	—	106	2	no	—
330	C₂×C₈	—	106	1	no	—
331	C₂×C₈	—	106	1	no	—
332	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
335	C₂×C₈	D₄×D₅₃	1	2	yes	—
336	C₂×C₈	#11719947	1	2	yes	—
337	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
338	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
339	C₄⋊C₄	—	53	4	no	—
340	C₄⋊C₄	—	106	4	no	—
341	C₂²⋊C₄	—	106	4	no	—
342	C₂²⋊C₄	—	106	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	53	2	no	—
345	C₄²	—	53	1	no	—
346	C₄²	—	53	1	no	—
347	C₄²	—	53	2	no	—
348	C₄²	—	106	4	no	—
349	C₄²	—	106	2	no	—
350	C₄²	—	106	1	no	—
351	C₄²	—	212	4	no	—
352	C₄²	C₂²×Dic₅₃	1	2	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	#41×D₅₃	1	1	yes	characteristic
355	Q₈	—	2	2	no	—
356	Q₈	C₂×C₄×Dic₅₃	1	4	yes	—
357	D₄	—	2	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	2	no	—
360	D₄	C₂×C₄×Dic₅₃	1	4	yes	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	53	2	no	—
367	C₂×C₄	—	53	2	no	—
368	C₂×C₄	—	106	4	no	—
369	C₂×C₄	—	106	4	no	—
370	C₂×C₄	—	106	2	no	—
371	C₂×C₄	—	212	8	no	—
372	C₂×C₄	—	212	2	no	—
373	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
375	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
377	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
378	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	53	4	no	—
381	C₈	—	106	4	no	—
382	C₈	—	106	2	no	—
383	C₈	C₂×C₄×Dic₅₃	1	2	yes	—
384	C₈	C₂×C₄×Dic₅₃	1	2	yes	—
385	C₈	D₄×Dic₅₃	1	4	yes	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
390	C₂²	C₄×#11719947	1	1	yes	characteristic
391	C₂²	#41×Dic₅₃	1	1	yes	characteristic
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	53	4	no	—
395	C₄	—	106	2	no	—
396	C₄	—	212	2	no	—
397	C₄	—	212	4	no	—
398	C₄	C₂²×C₄×Dic₅₃	1	1	yes	characteristic
399	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
400	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
401	C₄	C₄×#11719947	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	4	4	no	—
405	C₂	C₄×D₄×Dic₅₃	1	1	yes	characteristic
406	C₂	#444×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₂×C₅₃×#444	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#135×C₅₃	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	C₂×#444	D₅₃
hypocenter	C₅₃	C₄×#444
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
3. #131×Dic₅₃	C₂	semidirect
4. #108×Dic₅₃	C₂	semidirect
5. #20274602	C₂	semidirect
6. #20274599	C₂	semidirect
7. #20274560	C₂	semidirect
8. #20274557	C₂	semidirect
9. #104×Dic₅₃	C₂	semidirect
10. #97×Dic₅₃	C₂	semidirect
14. #16810745	C₄	semidirect
15. Q₁₆×Dic₅₃	C₄	semidirect
16. SD₁₆×Dic₅₃	C₄	semidirect
17. D₈×Dic₅₃	C₄	semidirect
40. C₅₃×#444	C₄	semidirect
45. #13133224	C₂×C₄	semidirect
60. #13133153	C₂×C₄	semidirect
63. #13133144	C₂×C₄	semidirect
71. #13133127	C₂×C₄	semidirect
86. #131×C₅₃	C₂×C₄	semidirect
93. #108×C₅₃	C₂×C₄	semidirect
94. #104×C₅₃	C₂×C₄	semidirect
95. #97×C₅₃	C₂×C₄	semidirect
109. Q₁₆×C₅₃	C₄²	semidirect
110. SD₁₆×C₅₃	C₄²	semidirect
111. D₈×C₅₃	C₄²	semidirect
198. Dic₅₃	#444	direct (N × H)
220. #444	Dic₅₃	direct (N × H)
247. C₅₃	C₄×#444	semidirect
257. #131	C₂×Dic₅₃	semidirect
279. #108	C₂×Dic₅₃	semidirect
283. #104	C₂×Dic₅₃	semidirect
292. #97	C₂×Dic₅₃	semidirect
313. Q₁₆	C₄×Dic₅₃	semidirect
314. SD₁₆	C₄×Dic₅₃	semidirect
315. D₈	C₄×Dic₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810745	2
#135×Dic₅₃	2
#131×Dic₅₃	2
#108×Dic₅₃	2
#20274602	2
#20274599	2
#20274560	2
#20274557	2
#104×Dic₅₃	2
#97×Dic₅₃	2
C₂×C₅₃×#444	2
C₄×#444	53

Subgroups — #444×Dic53 #27382666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #444×Dic₅₃ #27382666