Subgroups — #27353102

Order 13568.

762 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283345	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20273478	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273476	C₂	1	2	yes	maximal, complemented
5	#20273472	C₂	1	2	yes	maximal, complemented
6	#20273469	C₂	1	2	yes	maximal, complemented
7	#20273462	C₂	1	2	yes	maximal, complemented
8	#20273460	C₂	1	2	yes	maximal, complemented
9	C₅₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₅₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₅₃	C₄	1	1	yes	characteristic
12	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
13	#16810680	C₂²	1	2	yes	—
14	#16810678	—	2	2	no	—
15	#16810675	C₂²	1	4	yes	—
16	#16810673	—	2	2	no	—
17	#16810645	C₂²	1	4	yes	—
18	#16810585	—	2	2	no	—
19	#16810575	—	2	2	no	—
20	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic
23	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
25	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
27	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	#16810376	C₂²	1	2	yes	complemented
32	#16810375	C₂²	1	4	yes	complemented
33	#16810374	C₂²	1	2	yes	complemented
34	#16810373	C₂²	1	4	yes	complemented
35	C₅₃×#432	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#335	C₂²	1	2	yes	complemented
38	C₅₃×#334	C₂²	1	2	yes	complemented
39	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
42	C₂×#11719912	—	2	4	no	—
43	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
44	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₅₃	—	2	4	no	—
46	C₂×C₈×D₅₃	—	2	4	no	—
47	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
58	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₅₃	D₄	1	1	yes	characteristic
61	C₄²×D₅₃	D₄	1	1	yes	characteristic
62	C₄²×D₅₃	Q₈	1	1	yes	characteristic
63	C₄²×D₅₃	Q₈	1	1	yes	characteristic
64	C₄²×D₅₃	C₂³	1	1	yes	characteristic
65	C₄²×D₅₃	C₂³	1	1	yes	characteristic
66	C₄⋊#88322	C₂³	1	4	yes	—
67	#13133146	—	2	4	no	—
68	C₂²⋊#88322	—	2	2	no	—
69	#13133129	—	2	4	no	—
70	#13133128	—	2	2	no	—
71	C₄×#88322	C₂×C₄	1	1	yes	characteristic
72	C₄×#88322	C₂×C₄	1	1	yes	characteristic
73	C₄×#88322	C₂³	1	1	yes	characteristic
74	C₄×#88322	C₂³	1	1	yes	characteristic
75	C₈×Dic₅₃	—	2	4	no	—
76	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
88	C₂²⋊C₈×C₅₃	—	2	2	no	—
89	#97×C₅₃	—	2	2	no	—
90	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₂³×D₅₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
98	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	—	2	4	no	—
102	C₂×C₄×D₅₃	—	2	2	no	—
103	C₂×C₄×D₅₃	—	2	2	no	—
104	C₂×C₄×D₅₃	—	2	4	no	—
105	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₈×C₅₃	—	2	2	no	—
118	C₂×C₈×C₅₃	—	2	2	no	—
119	C₂×C₈×C₅₃	—	2	4	no	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
128	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
139	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
140	C₂×#88322	—	2	2	no	—
141	C₂×#88322	—	2	2	no	—
142	C₂×#88322	—	2	4	no	—
143	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
144	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
145	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
146	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
147	#11719912	—	4	8	no	—
148	C₈×D₅₃	—	2	2	no	—
149	C₈×D₅₃	—	2	2	no	—
150	C₈×D₅₃	—	2	2	no	—
151	C₈×D₅₃	—	2	2	no	—
152	C₈×D₅₃	—	2	2	no	—
153	C₈×D₅₃	—	2	2	no	—
154	C₈×D₅₃	M₁₆	1	4	yes	complemented
155	C₈×D₅₃	M₁₆	1	4	yes	complemented
156	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×D₅₃	—	2	2	no	—
158	C₂²×D₅₃	—	2	2	no	—
159	C₂²×D₅₃	—	2	2	no	—
160	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	—	2	2	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	2	no	—
166	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂×Dic₅₃	—	2	2	no	—
173	C₂×Dic₅₃	—	2	2	no	—
174	C₂×Dic₅₃	#108	1	4	yes	—
175	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₄×D₅₃	—	2	2	no	—
182	C₄×D₅₃	—	2	2	no	—
183	C₄×D₅₃	—	2	1	no	—
184	C₄×D₅₃	—	2	1	no	—
185	C₄×D₅₃	—	2	2	no	—
186	C₄×D₅₃	—	2	2	no	—
187	C₄×D₅₃	—	2	2	no	—
188	C₄×D₅₃	—	2	2	no	—
189	C₄×D₅₃	—	2	2	no	—
190	C₄×D₅₃	—	2	2	no	—
191	C₄×D₅₃	—	2	2	no	—
192	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
193	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
194	C₄×D₅₃	#135	1	4	yes	—
195	C₈×C₅₃	—	2	1	no	—
196	C₈×C₅₃	—	2	1	no	—
197	C₈×C₅₃	—	4	4	no	—
198	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
199	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
200	#88322	—	2	1	no	—
201	#88322	—	2	1	no	—
202	#88322	—	4	4	no	—
203	#88322	C₂×M₁₆	1	2	yes	—
204	#88322	C₂×M₁₆	1	2	yes	—
205	#17793	—	53	1	no	maximal, Sylow
206	C₂²×C₅₃	—	2	1	no	—
207	C₂²×C₅₃	—	2	1	no	—
208	C₂²×C₅₃	C₂×#108	1	2	yes	—
209	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
210	C₂×D₅₃	—	2	8	no	—
211	C₂×D₅₃	—	2	1	no	—
212	C₂×D₅₃	—	2	1	no	—
213	C₂×D₅₃	—	2	1	no	—
214	C₂×D₅₃	—	2	1	no	—
215	C₂×D₅₃	#423	1	2	yes	—
216	C₂×D₅₃	#427	1	2	yes	—
217	C₄×C₅₃	—	2	1	no	—
218	C₄×C₅₃	—	2	1	no	—
219	C₄×C₅₃	—	2	1	no	—
220	C₄×C₅₃	—	2	1	no	—
221	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
222	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
223	C₄×C₅₃	C₂×#135	1	2	yes	—
224	Dic₅₃	—	2	1	no	—
225	Dic₅₃	—	2	1	no	—
226	Dic₅₃	#423	1	2	yes	—
227	Dic₅₃	#427	1	2	yes	—
228	Dic₅₃	C₂×#108	1	2	yes	—
229	Dic₅₃	C₂×#108	1	2	yes	—
230	#2920	—	53	2	no	—
231	C₂²×C₄×C₈	—	53	1	no	—
232	#1568	—	53	2	no	—
233	#1568	—	53	1	no	—
234	#1568	D₅₃	1	1	yes	characteristic, complemented
235	#1567	—	53	2	no	—
236	#1566	—	53	2	no	—
237	#1564	—	53	2	no	—
238	#1564	—	53	2	no	—
239	C₂×C₅₃	—	2	2	no	—
240	C₂×C₅₃	C₂×#423	1	1	yes	characteristic
241	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
242	C₂×C₅₃	C₂²×#108	1	1	yes	characteristic
243	D₅₃	—	2	2	no	—
244	D₅₃	—	2	2	no	—
245	C₂³×C₈	—	53	1	no	—
246	C₂³×C₈	—	53	1	no	—
247	C₂²×C₄²	—	53	1	no	—
248	#432	—	53	2	no	—
249	#432	—	106	2	no	—
250	#432	C₂×D₅₃	1	2	yes	—
251	#431	—	53	4	no	—
252	#431	—	106	2	no	—
253	#423	—	53	4	no	—
254	#407	—	106	2	no	—
255	C₄×M₁₆	—	106	2	no	—
256	C₂×C₄×C₈	—	53	1	no	—
257	C₂×C₄×C₈	—	53	1	no	—
258	C₂×C₄×C₈	—	53	1	no	—
259	C₂×C₄×C₈	—	53	1	no	—
260	C₂×C₄×C₈	—	53	1	no	—
261	C₂×C₄×C₈	—	53	1	no	—
262	C₂×C₄×C₈	—	53	1	no	—
263	C₂×C₄×C₈	—	53	1	no	—
264	C₂×C₄×C₈	—	53	1	no	—
265	C₂×C₄×C₈	—	53	1	no	—
266	C₂×C₄×C₈	—	53	1	no	—
267	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
268	#335	—	53	4	no	—
269	#335	—	53	2	no	—
270	#335	C₂×D₅₃	1	2	yes	complemented
271	#334	—	53	4	no	—
272	#334	—	53	2	no	—
273	#334	C₂×D₅₃	1	2	yes	complemented
274	C₅₃	#17793	1	1	yes	characteristic, complemented, Sylow
275	C₂³×C₄	—	53	1	no	—
276	C₂³×C₄	—	53	1	no	—
277	C₂³×C₄	—	53	1	no	—
278	C₂×M₁₆	—	106	4	no	—
279	C₂²×C₈	—	53	1	no	—
280	C₂²×C₈	—	53	1	no	—
281	C₂²×C₈	—	53	1	no	—
282	C₂²×C₈	—	53	1	no	—
283	C₂²×C₈	—	53	1	no	—
284	C₂²×C₈	—	53	1	no	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	53	1	no	—
287	C₂²×C₈	—	53	1	no	—
288	C₂²×C₈	—	53	1	no	—
289	C₂²×C₈	—	106	4	no	—
290	C₂²×C₈	—	106	4	no	—
291	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
292	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
293	C₂×C₄²	—	53	1	no	—
294	C₂×C₄²	—	53	1	no	—
295	C₂×C₄²	—	53	1	no	—
296	C₂×C₄²	—	53	1	no	—
297	C₂×C₄²	—	53	1	no	—
298	C₂×C₄²	—	53	1	no	—
299	C₂×C₄²	—	53	1	no	—
300	C₂×C₄²	—	53	1	no	—
301	C₂×C₄²	—	53	1	no	—
302	C₂×C₄²	—	53	1	no	—
303	C₂×C₄²	—	53	1	no	—
304	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
305	C₄⋊C₈	—	53	4	no	—
306	C₄⋊C₈	—	106	4	no	—
307	C₄⋊C₈	C₂²×D₅₃	1	4	yes	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	106	4	no	—
310	C₂²⋊C₈	—	106	2	no	—
311	#97	—	2	2	no	—
312	#97	—	106	2	no	—
313	C₄×C₈	—	53	1	no	—
314	C₄×C₈	—	53	1	no	—
315	C₄×C₈	—	53	1	no	—
316	C₄×C₈	—	53	1	no	—
317	C₄×C₈	—	53	1	no	—
318	C₄×C₈	—	53	1	no	—
319	C₄×C₈	—	53	1	no	—
320	C₄×C₈	—	53	1	no	—
321	C₄×C₈	—	53	1	no	—
322	C₄×C₈	—	53	1	no	—
323	C₄×C₈	—	53	1	no	—
324	C₄×C₈	—	53	1	no	—
325	C₄×C₈	—	106	4	no	—
326	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
327	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
330	C₂⁴	—	53	1	no	—
331	C₂²×C₄	—	53	1	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	1	no	—
334	C₂²×C₄	—	53	1	no	—
335	C₂²×C₄	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	—	53	1	no	—
339	C₂²×C₄	—	53	1	no	—
340	C₂²×C₄	—	53	1	no	—
341	C₂²×C₄	—	53	1	no	—
342	C₂²×C₄	—	53	1	no	—
343	C₂²×C₄	—	53	1	no	—
344	C₂²×C₄	—	53	1	no	—
345	C₂²×C₄	—	53	1	no	—
346	C₂²×C₄	—	106	2	no	—
347	C₂²×C₄	—	106	2	no	—
348	C₂²×C₄	—	106	4	no	—
349	C₂²×C₄	—	106	4	no	—
350	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
352	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
353	M₁₆	—	212	8	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	53	1	no	—
358	C₂×C₈	—	53	1	no	—
359	C₂×C₈	—	53	4	no	—
360	C₂×C₈	—	53	4	no	—
361	C₂×C₈	—	53	1	no	—
362	C₂×C₈	—	53	1	no	—
363	C₂×C₈	—	106	2	no	—
364	C₂×C₈	—	106	2	no	—
365	C₂×C₈	—	106	2	no	—
366	C₂×C₈	—	106	2	no	—
367	C₂×C₈	—	106	2	no	—
368	C₂×C₈	—	106	2	no	—
369	C₂×C₈	—	106	2	no	—
370	C₂×C₈	—	106	2	no	—
371	C₂×C₈	—	106	4	no	—
372	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
374	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
375	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
376	C₄²	—	53	1	no	—
377	C₄²	—	53	1	no	—
378	C₄²	—	53	1	no	—
379	C₄²	—	53	1	no	—
380	C₄²	—	53	1	no	—
381	C₄²	—	53	1	no	—
382	C₄²	—	53	1	no	—
383	C₄²	—	53	1	no	—
384	C₄²	—	53	1	no	—
385	C₄²	—	53	1	no	—
386	C₄²	—	53	1	no	—
387	C₄²	—	53	1	no	—
388	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
389	C₄²	D₄×D₅₃	1	1	yes	characteristic
390	C₄²	Q₈×D₅₃	1	1	yes	characteristic
391	C₄²	C₂³×D₅₃	1	1	yes	characteristic
392	C₂³	—	53	1	no	—
393	C₂³	—	53	1	no	—
394	C₂³	—	106	2	no	—
395	C₂³	—	106	2	no	—
396	C₂³	—	106	2	no	—
397	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	53	1	no	—
403	C₂×C₄	—	53	1	no	—
404	C₂×C₄	—	53	1	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	4	no	—
407	C₂×C₄	—	53	2	no	—
408	C₂×C₄	—	53	2	no	—
409	C₂×C₄	—	53	4	no	—
410	C₂×C₄	—	53	1	no	—
411	C₂×C₄	—	53	1	no	—
412	C₂×C₄	—	106	2	no	—
413	C₂×C₄	—	106	2	no	—
414	C₂×C₄	—	106	2	no	—
415	C₂×C₄	—	106	2	no	—
416	C₂×C₄	—	106	2	no	—
417	C₂×C₄	—	106	2	no	—
418	C₂×C₄	—	106	2	no	—
419	C₂×C₄	—	106	2	no	—
420	C₂×C₄	—	106	2	no	—
421	C₂×C₄	—	106	2	no	—
422	C₂×C₄	—	106	1	no	—
423	C₂×C₄	—	106	1	no	—
424	C₂×C₄	—	106	2	no	—
425	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
426	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
427	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
430	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	4	no	—
434	C₈	—	53	2	no	—
435	C₈	—	53	2	no	—
436	C₈	—	106	1	no	—
437	C₈	—	106	1	no	—
438	C₈	—	212	4	no	—
439	C₈	M₁₆×D₅₃	1	2	yes	—
440	C₈	M₁₆×D₅₃	1	2	yes	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	53	2	no	—
444	C₂²	—	53	2	no	—
445	C₂²	—	106	8	no	—
446	C₂²	—	106	1	no	—
447	C₂²	—	106	1	no	—
448	C₂²	—	106	1	no	—
449	C₂²	—	106	1	no	—
450	C₂²	#108×D₅₃	1	2	yes	—
451	C₂²	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	53	2	no	—
457	C₄	—	53	2	no	—
458	C₄	—	53	2	no	—
459	C₄	—	53	2	no	—
460	C₄	—	106	1	no	—
461	C₄	—	106	1	no	—
462	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
463	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
464	C₄	#135×D₅₃	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	106	2	no	—
467	C₂	—	106	2	no	—
468	C₂	#423×D₅₃	1	1	yes	characteristic
469	C₂	#427×D₅₃	1	1	yes	characteristic
470	C₂	C₂×#108×D₅₃	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×#1568	C₂
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₅₃	C₄⋊C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1568	D₅₃
hypocenter	C₅₃	#17793
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #20273478	C₂	semidirect
4. #20273476	C₂	semidirect
5. #20273472	C₂	semidirect
6. #20273469	C₂	semidirect
7. #20273462	C₂	semidirect
8. #20273460	C₂	semidirect
9. C₅₃×#1568	C₂	semidirect
31. #16810376	C₂²	semidirect
32. #16810375	C₂²	semidirect
33. #16810374	C₂²	semidirect
34. #16810373	C₂²	semidirect
37. C₅₃×#335	C₂²	semidirect
38. C₅₃×#334	C₂²	semidirect
154. C₈×D₅₃	M₁₆	semidirect
155. C₈×D₅₃	M₁₆	semidirect
234. #1568	D₅₃	semidirect
270. #335	C₂×D₅₃	semidirect
273. #334	C₂×D₅₃	semidirect
274. C₅₃	#17793	semidirect

Maximal subgroups

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

subgroup	index
#20283345	2
C₂×C₄×C₈×D₅₃	2
#20273478	2
#20273476	2
#20273472	2
#20273469	2
#20273462	2
#20273460	2
C₅₃×#1568	2
#17793	53