Subgroups — C₅₃×#26926 #27234438

Order 13568.

1082 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₅₃	—	2	1	no	—
20	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₅₃	—	2	1	no	—
24	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#480	—	2	4	no	—
28	C₅₃×#459	—	2	4	no	—
29	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#394	—	2	1	no	—
44	C₅₃×#392	—	2	1	no	—
45	C₅₃×#390	C₂²	1	1	yes	characteristic
46	C₅₃×#390	C₂²	1	1	yes	characteristic
47	C₅₃×#389	C₂²	1	1	yes	characteristic
48	C₅₃×#389	C₂²	1	1	yes	characteristic
49	C₅₃×#388	—	2	1	no	—
50	C₅₃×#386	—	2	1	no	—
51	C₅₃×#386	—	2	1	no	—
52	C₅₃×#385	—	2	1	no	—
53	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×#340	C₂²	1	1	yes	characteristic
56	C₅₃×#340	C₂²	1	1	yes	characteristic
57	C₅₃×#340	C₂²	1	1	yes	characteristic
58	C₅₃×#340	C₂²	1	1	yes	characteristic
59	C₅₃×#336	C₂²	1	1	yes	characteristic
60	C₅₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₅₃	—	2	1	no	—
62	C₂²×D₄×C₅₃	—	2	1	no	—
63	C₂²×D₄×C₅₃	—	2	1	no	—
64	C₂²×D₄×C₅₃	—	2	1	no	—
65	C₂²×D₄×C₅₃	—	2	1	no	—
66	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅₃	—	2	1	no	—
70	C₂³×C₄×C₅₃	—	2	1	no	—
71	C₂³×C₄×C₅₃	—	2	1	no	—
72	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂×D₈×C₅₃	—	2	2	no	—
74	C₂×D₈×C₅₃	—	2	2	no	—
75	C₂×D₈×C₅₃	—	2	2	no	—
76	C₂×D₈×C₅₃	—	2	2	no	—
77	C₂×D₈×C₅₃	—	4	1	no	—
78	C₂×D₈×C₅₃	—	4	1	no	—
79	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	#127×C₅₃	—	2	2	no	—
84	#127×C₅₃	—	4	1	no	—
85	#121×C₅₃	—	2	2	no	—
86	#121×C₅₃	—	2	2	no	—
87	#121×C₅₃	—	2	2	no	—
88	#121×C₅₃	—	2	2	no	—
89	#121×C₅₃	—	4	1	no	—
90	#121×C₅₃	—	4	1	no	—
91	#121×C₅₃	—	4	4	no	—
92	C₄×D₄×C₅₃	—	2	2	no	—
93	C₄×D₄×C₅₃	—	2	2	no	—
94	C₄×D₄×C₅₃	—	4	1	no	—
95	C₄×D₄×C₅₃	—	4	1	no	—
96	C₄×D₄×C₅₃	—	4	4	no	—
97	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
101	C₂×C₄⋊C₄×C₅₃	—	4	1	no	—
102	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₅₃	—	2	1	no	—
119	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
121	#107×C₅₃	—	2	2	no	—
122	#107×C₅₃	—	2	2	no	—
123	C₄⋊C₈×C₅₃	—	2	2	no	—
124	#102×C₅₃	—	2	2	no	—
125	#102×C₅₃	—	2	2	no	—
126	#102×C₅₃	—	2	2	no	—
127	#102×C₅₃	—	2	2	no	—
128	#102×C₅₃	—	2	2	no	—
129	#102×C₅₃	—	4	1	no	—
130	#102×C₅₃	—	4	1	no	—
131	#102×C₅₃	D₄	1	4	yes	complemented
132	C₂²⋊C₈×C₅₃	—	2	2	no	—
133	C₂²⋊C₈×C₅₃	—	4	1	no	—
134	C₄×C₈×C₅₃	—	4	1	no	—
135	#95×C₅₃	—	2	1	no	—
136	#95×C₅₃	—	2	1	no	—
137	#95×C₅₃	—	2	1	no	—
138	#95×C₅₃	D₄	1	1	yes	characteristic
139	#95×C₅₃	D₄	1	1	yes	characteristic
140	C₂⁴×C₅₃	—	2	1	no	—
141	C₂⁴×C₅₃	—	2	1	no	—
142	C₂⁴×C₅₃	—	2	1	no	—
143	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₅₃	—	2	4	no	—
145	C₂×D₄×C₅₃	—	2	1	no	—
146	C₂×D₄×C₅₃	—	2	1	no	—
147	C₂×D₄×C₅₃	—	2	1	no	—
148	C₂×D₄×C₅₃	—	2	1	no	—
149	C₂×D₄×C₅₃	—	2	1	no	—
150	C₂×D₄×C₅₃	—	2	1	no	—
151	C₂×D₄×C₅₃	—	2	1	no	—
152	C₂×D₄×C₅₃	—	2	1	no	—
153	C₂×D₄×C₅₃	—	2	1	no	—
154	C₂×D₄×C₅₃	—	2	1	no	—
155	C₂×D₄×C₅₃	—	2	1	no	—
156	C₂×D₄×C₅₃	—	2	1	no	—
157	C₂×D₄×C₅₃	—	2	1	no	—
158	C₂×D₄×C₅₃	—	2	1	no	—
159	C₂×D₄×C₅₃	—	2	1	no	—
160	C₂×D₄×C₅₃	—	2	1	no	—
161	C₂×D₄×C₅₃	—	4	2	no	—
162	C₂×D₄×C₅₃	—	4	2	no	—
163	C₂×D₄×C₅₃	—	4	2	no	—
164	C₂×D₄×C₅₃	—	4	2	no	—
165	C₂×D₄×C₅₃	—	4	2	no	—
166	C₂×D₄×C₅₃	—	4	2	no	—
167	C₂×D₄×C₅₃	—	4	2	no	—
168	C₂×D₄×C₅₃	—	4	2	no	—
169	C₂×D₄×C₅₃	—	4	2	no	—
170	C₂×D₄×C₅₃	—	4	2	no	—
171	C₂×D₄×C₅₃	—	8	1	no	—
172	C₂×D₄×C₅₃	—	8	1	no	—
173	C₂×D₄×C₅₃	—	8	1	no	—
174	C₂×D₄×C₅₃	—	8	1	no	—
175	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₅₃	#41	1	2	yes	—
177	C₂²×C₄×C₅₃	—	2	1	no	—
178	C₂²×C₄×C₅₃	—	2	1	no	—
179	C₂²×C₄×C₅₃	—	2	1	no	—
180	C₂²×C₄×C₅₃	—	2	1	no	—
181	C₂²×C₄×C₅₃	—	2	1	no	—
182	C₂²×C₄×C₅₃	—	2	1	no	—
183	C₂²×C₄×C₅₃	—	2	1	no	—
184	C₂²×C₄×C₅₃	—	2	1	no	—
185	C₂²×C₄×C₅₃	—	2	1	no	—
186	C₂²×C₄×C₅₃	—	2	1	no	—
187	C₂²×C₄×C₅₃	—	2	1	no	—
188	C₂²×C₄×C₅₃	—	4	2	no	—
189	C₂²×C₄×C₅₃	—	4	2	no	—
190	C₂²×C₄×C₅₃	—	4	2	no	—
191	C₂²×C₄×C₅₃	—	4	2	no	—
192	C₂²×C₄×C₅₃	—	4	2	no	—
193	C₂²×C₄×C₅₃	—	4	2	no	—
194	C₂²×C₄×C₅₃	—	8	1	no	—
195	C₂²×C₄×C₅₃	—	8	1	no	—
196	C₂²×C₄×C₅₃	—	8	1	no	—
197	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
203	D₈×C₅₃	—	4	4	no	—
204	D₈×C₅₃	—	4	4	no	—
205	C₂×C₈×C₅₃	—	2	1	no	—
206	C₂×C₈×C₅₃	—	2	1	no	—
207	C₂×C₈×C₅₃	—	2	1	no	—
208	C₂×C₈×C₅₃	—	2	1	no	—
209	C₂×C₈×C₅₃	—	2	1	no	—
210	C₂×C₈×C₅₃	—	2	1	no	—
211	C₂×C₈×C₅₃	—	2	1	no	—
212	C₂×C₈×C₅₃	—	2	1	no	—
213	C₂×C₈×C₅₃	—	2	1	no	—
214	C₂×C₈×C₅₃	—	2	1	no	—
215	C₂×C₈×C₅₃	—	2	1	no	—
216	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
217	C₄⋊C₄×C₅₃	—	2	1	no	—
218	C₄⋊C₄×C₅₃	—	2	1	no	—
219	C₄⋊C₄×C₅₃	—	2	1	no	—
220	C₄⋊C₄×C₅₃	—	2	1	no	—
221	C₄⋊C₄×C₅₃	—	2	1	no	—
222	C₄⋊C₄×C₅₃	—	2	1	no	—
223	C₄⋊C₄×C₅₃	—	2	1	no	—
224	C₄⋊C₄×C₅₃	—	4	2	no	—
225	C₄⋊C₄×C₅₃	—	4	2	no	—
226	C₄⋊C₄×C₅₃	—	4	2	no	—
227	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
228	C₄⋊C₄×C₅₃	#41	1	2	yes	—
229	C₄⋊C₄×C₅₃	#41	1	2	yes	—
230	C₂²⋊C₄×C₅₃	—	2	4	no	—
231	C₂²⋊C₄×C₅₃	—	4	1	no	—
232	C₂²⋊C₄×C₅₃	—	4	2	no	—
233	C₂²⋊C₄×C₅₃	—	4	2	no	—
234	C₂²⋊C₄×C₅₃	—	4	2	no	—
235	C₂²⋊C₄×C₅₃	—	4	2	no	—
236	C₂²⋊C₄×C₅₃	—	4	2	no	—
237	C₂²⋊C₄×C₅₃	—	4	2	no	—
238	C₂²⋊C₄×C₅₃	—	8	1	no	—
239	C₂²⋊C₄×C₅₃	—	8	1	no	—
240	C₂²⋊C₄×C₅₃	D₈	1	4	yes	complemented
241	C₄²×C₅₃	—	2	1	no	—
242	C₄²×C₅₃	—	2	1	no	—
243	C₄²×C₅₃	—	2	1	no	—
244	C₄²×C₅₃	—	2	1	no	—
245	C₄²×C₅₃	—	4	2	no	—
246	C₂³×C₅₃	—	2	1	no	—
247	C₂³×C₅₃	—	2	1	no	—
248	C₂³×C₅₃	—	2	1	no	—
249	C₂³×C₅₃	—	2	1	no	—
250	C₂³×C₅₃	—	2	1	no	—
251	C₂³×C₅₃	—	2	1	no	—
252	C₂³×C₅₃	—	2	2	no	—
253	C₂³×C₅₃	—	2	2	no	—
254	C₂³×C₅₃	—	4	1	no	—
255	C₂³×C₅₃	—	4	1	no	—
256	C₂³×C₅₃	—	4	1	no	—
257	C₂³×C₅₃	—	4	1	no	—
258	C₂³×C₅₃	—	4	1	no	—
259	C₂³×C₅₃	—	4	1	no	—
260	C₂³×C₅₃	—	4	1	no	—
261	C₂³×C₅₃	—	4	1	no	—
262	C₂³×C₅₃	—	4	1	no	—
263	C₂³×C₅₃	—	4	1	no	—
264	C₂³×C₅₃	—	4	1	no	—
265	C₂³×C₅₃	—	4	1	no	—
266	C₂³×C₅₃	—	4	1	no	—
267	C₂³×C₅₃	—	4	1	no	—
268	C₂³×C₅₃	—	4	1	no	—
269	C₂³×C₅₃	—	4	1	no	—
270	C₂³×C₅₃	—	4	1	no	—
271	C₂³×C₅₃	—	4	1	no	—
272	C₂³×C₅₃	—	4	1	no	—
273	C₂³×C₅₃	C₂×D₈	1	2	yes	—
274	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
275	D₄×C₅₃	—	2	2	no	—
276	D₄×C₅₃	—	2	2	no	—
277	D₄×C₅₃	—	2	2	no	—
278	D₄×C₅₃	—	2	2	no	—
279	D₄×C₅₃	—	4	8	no	—
280	D₄×C₅₃	—	4	1	no	—
281	D₄×C₅₃	—	4	1	no	—
282	D₄×C₅₃	—	4	1	no	—
283	D₄×C₅₃	—	4	1	no	—
284	D₄×C₅₃	—	4	1	no	—
285	D₄×C₅₃	—	4	1	no	—
286	D₄×C₅₃	—	4	1	no	—
287	D₄×C₅₃	—	4	1	no	—
288	D₄×C₅₃	—	8	4	no	—
289	D₄×C₅₃	—	8	4	no	—
290	D₄×C₅₃	—	8	4	no	—
291	D₄×C₅₃	—	8	4	no	—
292	C₂×C₄×C₅₃	—	2	1	no	—
293	C₂×C₄×C₅₃	—	2	1	no	—
294	C₂×C₄×C₅₃	—	2	1	no	—
295	C₂×C₄×C₅₃	—	2	1	no	—
296	C₂×C₄×C₅₃	—	2	1	no	—
297	C₂×C₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	1	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	1	no	—
301	C₂×C₄×C₅₃	—	2	1	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	1	no	—
304	C₂×C₄×C₅₃	—	2	1	no	—
305	C₂×C₄×C₅₃	—	2	1	no	—
306	C₂×C₄×C₅₃	—	2	1	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	—	4	1	no	—
309	C₂×C₄×C₅₃	—	4	1	no	—
310	C₂×C₄×C₅₃	—	4	1	no	—
311	C₂×C₄×C₅₃	—	4	1	no	—
312	C₂×C₄×C₅₃	—	4	1	no	—
313	C₂×C₄×C₅₃	—	4	1	no	—
314	C₂×C₄×C₅₃	—	4	1	no	—
315	C₂×C₄×C₅₃	—	4	1	no	—
316	C₂×C₄×C₅₃	—	4	1	no	—
317	C₂×C₄×C₅₃	—	4	1	no	—
318	C₂×C₄×C₅₃	—	4	1	no	—
319	C₂×C₄×C₅₃	—	4	1	no	—
320	C₂×C₄×C₅₃	—	4	1	no	—
321	C₂×C₄×C₅₃	—	4	1	no	—
322	C₂×C₄×C₅₃	—	4	1	no	—
323	C₂×C₄×C₅₃	—	4	1	no	—
324	C₂×C₄×C₅₃	—	8	4	no	—
325	C₂×C₄×C₅₃	—	8	4	no	—
326	C₂×C₄×C₅₃	—	8	4	no	—
327	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
328	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
329	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
335	C₈×C₅₃	—	2	2	no	—
336	C₈×C₅₃	—	4	1	no	—
337	C₈×C₅₃	—	4	1	no	—
338	C₈×C₅₃	—	4	1	no	—
339	#26926	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂²×C₅₃	—	2	2	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	2	2	no	—
343	C₂²×C₅₃	—	4	1	no	—
344	C₂²×C₅₃	—	4	1	no	—
345	C₂²×C₅₃	—	4	1	no	—
346	C₂²×C₅₃	—	4	1	no	—
347	C₂²×C₅₃	—	4	2	no	—
348	C₂²×C₅₃	—	4	2	no	—
349	C₂²×C₅₃	—	4	2	no	—
350	C₂²×C₅₃	—	4	2	no	—
351	C₂²×C₅₃	—	4	2	no	—
352	C₂²×C₅₃	—	4	2	no	—
353	C₂²×C₅₃	—	8	1	no	—
354	C₂²×C₅₃	—	8	1	no	—
355	C₂²×C₅₃	—	8	1	no	—
356	C₂²×C₅₃	—	8	1	no	—
357	C₂²×C₅₃	—	8	1	no	—
358	C₂²×C₅₃	—	8	1	no	—
359	C₂²×C₅₃	—	8	1	no	—
360	C₂²×C₅₃	—	8	1	no	—
361	C₂²×C₅₃	—	8	1	no	—
362	C₂²×C₅₃	—	8	1	no	—
363	C₂²×C₅₃	—	8	1	no	—
364	C₂²×C₅₃	—	8	1	no	—
365	C₂²×C₅₃	—	8	1	no	—
366	C₂²×C₅₃	—	8	1	no	—
367	C₂²×C₅₃	—	8	1	no	—
368	C₂²×C₅₃	#525	1	1	yes	characteristic
369	C₂²×C₅₃	D₄²	1	1	yes	characteristic
370	C₂²×C₅₃	#546	1	1	yes	characteristic
371	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
372	C₂²×C₅₃	#575	1	1	yes	characteristic
373	C₂²×C₅₃	#576	1	1	yes	characteristic
374	C₂²×C₅₃	#577	1	1	yes	characteristic
375	C₄×C₅₃	—	2	2	no	—
376	C₄×C₅₃	—	2	2	no	—
377	C₄×C₅₃	—	4	2	no	—
378	C₄×C₅₃	—	4	1	no	—
379	C₄×C₅₃	—	4	1	no	—
380	C₄×C₅₃	—	4	2	no	—
381	C₄×C₅₃	—	4	2	no	—
382	C₄×C₅₃	—	4	1	no	—
383	C₄×C₅₃	—	8	1	no	—
384	C₄×C₅₃	—	8	1	no	—
385	C₄×C₅₃	#532	1	1	yes	characteristic
386	C₄×C₅₃	#540	1	1	yes	characteristic
387	C₄×C₅₃	#546	1	1	yes	characteristic
388	C₄×C₅₃	#553	1	1	yes	characteristic
389	C₂×#480	C₂×C₅₃	1	1	yes	characteristic, complemented
390	C₂×#459	C₂×C₅₃	1	1	yes	characteristic, complemented
391	#2428	C₂×C₅₃	1	1	yes	characteristic, complemented
392	#2361	C₂×C₅₃	1	1	yes	characteristic, complemented
393	#2086	C₂×C₅₃	1	1	yes	characteristic, complemented
394	#2041	C₂×C₅₃	1	1	yes	characteristic, complemented
395	#1999	C₂×C₅₃	1	1	yes	characteristic, complemented
396	#1999	C₂×C₅₃	1	1	yes	characteristic, complemented
397	#1970	C₂×C₅₃	1	1	yes	characteristic, complemented
398	#1925	C₂×C₅₃	1	1	yes	characteristic, complemented
399	#1923	C₂×C₅₃	1	1	yes	characteristic, complemented
400	#1879	C₂×C₅₃	1	1	yes	characteristic, complemented
401	#1874	C₂×C₅₃	1	1	yes	characteristic, complemented
402	#1862	C₂×C₅₃	1	1	yes	characteristic, complemented
403	C₄×#102	C₂×C₅₃	1	1	yes	characteristic, complemented
404	C₂×C₅₃	—	4	2	no	—
405	C₂×C₅₃	—	8	2	no	—
406	C₂×C₅₃	—	8	2	no	—
407	C₂×C₅₃	—	16	1	no	—
408	C₂×C₅₃	#2464	1	1	yes	characteristic
409	C₂×C₅₃	#3100	1	1	yes	characteristic
410	C₂×C₅₃	#3119	1	1	yes	characteristic
411	C₂×C₅₃	#3275	1	1	yes	characteristic
412	C₂×C₅₃	D₄×D₈	1	1	yes	characteristic
413	C₂×C₅₃	#3294	1	1	yes	characteristic
414	C₂×C₅₃	#3309	1	1	yes	characteristic
415	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
417	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
418	C₂×#121	—	2	1	no	—
419	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
420	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
421	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
422	C₂×C₄×D₄	—	2	1	no	—
423	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
426	#480	—	2	4	no	—
427	#459	—	2	4	no	—
428	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
429	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
430	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
431	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
434	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
436	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
438	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
441	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
442	#394	—	2	1	no	—
443	#392	—	2	1	no	—
444	#390	C₂²×C₅₃	1	1	yes	characteristic
445	#390	C₂²×C₅₃	1	1	yes	characteristic
446	#389	C₂²×C₅₃	1	1	yes	characteristic
447	#389	C₂²×C₅₃	1	1	yes	characteristic
448	#388	—	2	1	no	—
449	#386	—	2	1	no	—
450	#386	—	2	1	no	—
451	#385	—	2	1	no	—
452	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
454	#340	C₂²×C₅₃	1	1	yes	characteristic
455	#340	C₂²×C₅₃	1	1	yes	characteristic
456	#340	C₂²×C₅₃	1	1	yes	characteristic
457	#340	C₂²×C₅₃	1	1	yes	characteristic
458	#336	C₂²×C₅₃	1	1	yes	characteristic
459	#336	C₂²×C₅₃	1	1	yes	characteristic
460	C₅₃	#26926	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	—	2	2	no	—
476	C₂×D₈	—	2	2	no	—
477	C₂×D₈	—	4	1	no	—
478	C₂×D₈	—	4	1	no	—
479	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
483	#127	—	2	2	no	—
484	#127	—	4	1	no	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	—	4	1	no	—
490	#121	—	4	1	no	—
491	#121	—	4	4	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	4	1	no	—
495	C₄×D₄	—	4	1	no	—
496	C₄×D₄	—	4	4	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	4	1	no	—
502	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
521	#107	—	2	2	no	—
522	#107	—	2	2	no	—
523	C₄⋊C₈	—	2	2	no	—
524	#102	—	2	2	no	—
525	#102	—	2	2	no	—
526	#102	—	2	2	no	—
527	#102	—	2	2	no	—
528	#102	—	2	2	no	—
529	#102	—	4	1	no	—
530	#102	—	4	1	no	—
531	#102	D₄×C₅₃	1	4	yes	complemented
532	C₂²⋊C₈	—	2	2	no	—
533	C₂²⋊C₈	—	4	1	no	—
534	C₄×C₈	—	4	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	#95	D₄×C₅₃	1	1	yes	characteristic
539	#95	D₄×C₅₃	1	1	yes	characteristic
540	C₂⁴	—	2	1	no	—
541	C₂⁴	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	8	1	no	—
572	C₂×D₄	—	8	1	no	—
573	C₂×D₄	—	8	1	no	—
574	C₂×D₄	—	8	1	no	—
575	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
576	C₂×D₄	#41×C₅₃	1	2	yes	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	8	1	no	—
595	C₂²×C₄	—	8	1	no	—
596	C₂²×C₄	—	8	1	no	—
597	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
603	D₈	—	4	4	no	—
604	D₈	—	4	4	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
628	C₄⋊C₄	#41×C₅₃	1	2	yes	—
629	C₄⋊C₄	#41×C₅₃	1	2	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	8	1	no	—
639	C₂²⋊C₄	—	8	1	no	—
640	C₂²⋊C₄	D₈×C₅₃	1	4	yes	complemented
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	4	2	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	C₂×D₈×C₅₃	1	2	yes	—
674	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	4	8	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	4	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	C₂×D₈×C₅₃	1	2	yes	—
728	C₂×C₄	C₂×D₈×C₅₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
730	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
732	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
733	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
734	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
735	C₈	—	2	2	no	—
736	C₈	—	4	1	no	—
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	C₅₃×#525	1	1	yes	characteristic
768	C₂²	D₄²×C₅₃	1	1	yes	characteristic
769	C₂²	C₅₃×#546	1	1	yes	characteristic
770	C₂²	C₂²×D₈×C₅₃	1	1	yes	characteristic
771	C₂²	C₅₃×#575	1	1	yes	characteristic
772	C₂²	C₅₃×#576	1	1	yes	characteristic
773	C₂²	C₅₃×#577	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	2	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	C₅₃×#532	1	1	yes	characteristic
785	C₄	C₅₃×#540	1	1	yes	characteristic
786	C₄	C₅₃×#546	1	1	yes	characteristic
787	C₄	C₅₃×#553	1	1	yes	characteristic
788	C₂	—	4	2	no	—
789	C₂	—	8	2	no	—
790	C₂	—	8	2	no	—
791	C₂	—	16	1	no	—
792	C₂	C₅₃×#2464	1	1	yes	characteristic
793	C₂	C₅₃×#3100	1	1	yes	characteristic
794	C₂	C₅₃×#3119	1	1	yes	characteristic
795	C₂	C₅₃×#3275	1	1	yes	characteristic
796	C₂	D₄×D₈×C₅₃	1	1	yes	characteristic
797	C₂	C₅₃×#3294	1	1	yes	characteristic
798	C₂	C₅₃×#3309	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₄×C₂²⋊C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#480	C₂	semidirect
2. C₂×C₅₃×#459	C₂	semidirect
3. C₅₃×#2428	C₂	semidirect
4. C₅₃×#2361	C₂	semidirect
5. C₅₃×#2086	C₂	semidirect
6. C₅₃×#2041	C₂	semidirect
7. C₅₃×#1999	C₂	semidirect
8. C₅₃×#1999	C₂	semidirect
9. C₅₃×#1970	C₂	semidirect
10. C₅₃×#1925	C₂	semidirect
11. C₅₃×#1923	C₂	semidirect
12. C₅₃×#1879	C₂	semidirect
13. C₅₃×#1874	C₂	semidirect
14. C₅₃×#1862	C₂	semidirect
15. C₄×#102×C₅₃	C₂	semidirect
131. #102×C₅₃	D₄	semidirect
240. C₂²⋊C₄×C₅₃	D₈	semidirect
339. #26926	C₅₃	direct (N × H)
389. C₂×#480	C₂×C₅₃	semidirect
390. C₂×#459	C₂×C₅₃	semidirect
391. #2428	C₂×C₅₃	semidirect
392. #2361	C₂×C₅₃	semidirect
393. #2086	C₂×C₅₃	semidirect
394. #2041	C₂×C₅₃	semidirect
395. #1999	C₂×C₅₃	semidirect
396. #1999	C₂×C₅₃	semidirect
397. #1970	C₂×C₅₃	semidirect
398. #1925	C₂×C₅₃	semidirect
399. #1923	C₂×C₅₃	semidirect
400. #1879	C₂×C₅₃	semidirect
401. #1874	C₂×C₅₃	semidirect
402. #1862	C₂×C₅₃	semidirect
403. C₄×#102	C₂×C₅₃	semidirect
460. C₅₃	#26926	direct (N × H)
531. #102	D₄×C₅₃	semidirect
640. C₂²⋊C₄	D₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#480	2
C₂×C₅₃×#459	2
C₅₃×#2428	2
C₅₃×#2361	2
C₅₃×#2086	2
C₅₃×#2041	2
C₅₃×#1999	2
C₅₃×#1970	2
C₅₃×#1925	2
C₅₃×#1923	2
C₅₃×#1879	2
C₅₃×#1874	2
C₅₃×#1862	2
C₄×#102×C₅₃	2
#26926	53

Subgroups — C53×#26926 #27234438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#26926 #27234438