Subgroups — C₅₃×#61333 #27268845

Order 13568.

1798 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3372	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3370	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3367	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3137	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3083	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3042	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic
13	C₅₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2946	C₂	1	2	yes	maximal, complemented
15	C₂×C₅₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#559	C₂²	1	2	yes	complemented
19	C₅₃×#557	C₂²	1	2	yes	complemented
20	C₅₃×#556	—	2	1	no	—
21	C₅₃×#556	C₂²	1	4	yes	complemented
22	C₅₃×#554	—	2	1	no	—
23	C₅₃×#554	—	2	1	no	—
24	C₅₃×#554	—	2	2	no	—
25	C₅₃×#554	C₂²	1	4	yes	—
26	C₅₃×#554	C₂²	1	2	yes	—
27	C₅₃×#552	—	2	2	no	—
28	D₄×Q₈×C₅₃	—	2	1	no	—
29	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
30	C₅₃×#544	C₂²	1	2	yes	—
31	C₅₃×#543	—	2	2	no	—
32	C₅₃×#539	—	2	2	no	—
33	C₅₃×#536	C₂²	1	2	yes	—
34	C₅₃×#533	C₂²	1	1	yes	characteristic
35	C₅₃×#533	C₂²	1	1	yes	characteristic
36	C₅₃×#532	C₂²	1	1	yes	characteristic
37	C₅₃×#529	—	2	2	no	—
38	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
39	C₅₃×#520	C₂²	1	2	yes	—
40	C₅₃×#518	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#491	C₂²	1	2	yes	complemented
44	C₅₃×#491	C₂²	1	4	yes	complemented
45	C₅₃×#490	C₂²	1	2	yes	complemented
46	C₅₃×#489	C₂²	1	2	yes	complemented
47	C₅₃×#489	C₂²	1	4	yes	complemented
48	C₅₃×#489	C₂²	1	2	yes	complemented
49	C₅₃×#488	C₂²	1	4	yes	complemented
50	C₅₃×#487	C₂²	1	4	yes	complemented
51	C₅₃×#479	C₂²	1	4	yes	complemented
52	C₅₃×#479	C₂²	1	4	yes	complemented
53	C₅₃×#478	C₂²	1	4	yes	complemented
54	C₅₃×#477	C₂²	1	2	yes	complemented
55	C₅₃×#477	C₂²	1	4	yes	complemented
56	C₅₃×#475	C₂²	1	2	yes	complemented
57	C₅₃×#474	C₂²	1	4	yes	complemented
58	C₅₃×#463	C₂²	1	4	yes	—
59	C₅₃×#463	C₂²	1	4	yes	—
60	C₅₃×#463	C₂²	1	4	yes	—
61	C₅₃×#461	C₂²	1	2	yes	—
62	C₅₃×#461	C₂²	1	4	yes	—
63	C₅₃×#461	C₂²	1	4	yes	—
64	C₅₃×#459	C₂²	1	2	yes	—
65	C₅₃×#446	C₂²	1	4	yes	complemented
66	C₅₃×#446	C₂²	1	4	yes	complemented
67	C₅₃×#442	C₂²	1	4	yes	—
68	C₅₃×#440	C₂²	1	4	yes	—
69	C₅₃×#440	C₂²	1	4	yes	—
70	C₅₃×#440	C₂²	1	4	yes	—
71	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
72	C₄×D₈×C₅₃	C₂²	1	4	yes	—
73	C₅₃×#428	C₂²	1	2	yes	—
74	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
75	C₅₃×#424	C₂²	1	2	yes	—
76	C₅₃×#423	C₂²	1	1	yes	characteristic
77	C₅₃×#419	C₂²	1	2	yes	—
78	C₅₃×#417	C₂²	1	2	yes	—
79	C₅₃×#416	C₂²	1	2	yes	—
80	C₅₃×#416	C₂²	1	2	yes	—
81	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
82	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
83	C₅₃×#405	C₂²	1	2	yes	—
84	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
85	C₂×#41×C₅₃	C₂³	1	2	yes	—
86	C₂²×Q₈×C₅₃	—	2	2	no	—
87	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅₃	—	2	1	no	—
90	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
91	C₂×SD₁₆×C₅₃	—	2	4	no	—
92	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
94	C₂×D₈×C₅₃	C₂³	1	4	yes	—
95	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₅₃	—	2	2	no	—
99	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
100	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
101	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
102	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
106	#127×C₅₃	C₂³	1	1	yes	characteristic
107	#126×C₅₃	—	2	4	no	—
108	#126×C₅₃	—	2	4	no	—
109	#125×C₅₃	—	2	2	no	—
110	#125×C₅₃	—	2	4	no	—
111	#125×C₅₃	—	2	2	no	—
112	#125×C₅₃	D₄	1	2	yes	—
113	#125×C₅₃	C₂³	1	4	yes	—
114	#125×C₅₃	C₂³	1	2	yes	—
115	#124×C₅₃	—	2	2	no	—
116	#124×C₅₃	C₂³	1	4	yes	—
117	#124×C₅₃	C₂³	1	2	yes	—
118	#123×C₅₃	—	2	4	no	—
119	#123×C₅₃	—	2	4	no	—
120	C₂²⋊Q₈×C₅₃	—	2	2	no	—
121	C₂²⋊Q₈×C₅₃	—	2	4	no	—
122	C₂²⋊Q₈×C₅₃	—	2	2	no	—
123	C₂²⋊Q₈×C₅₃	—	2	2	no	—
124	C₂²⋊Q₈×C₅₃	—	2	4	no	—
125	C₂²⋊Q₈×C₅₃	—	2	4	no	—
126	C₂²⋊Q₈×C₅₃	—	2	4	no	—
127	C₂²⋊Q₈×C₅₃	—	2	4	no	—
128	C₂²⋊Q₈×C₅₃	—	2	2	no	—
129	C₂²⋊Q₈×C₅₃	—	2	4	no	—
130	C₂²⋊Q₈×C₅₃	—	2	4	no	—
131	C₂²⋊Q₈×C₅₃	—	2	1	no	—
132	C₂²⋊Q₈×C₅₃	—	2	1	no	—
133	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
134	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
135	#121×C₅₃	—	2	1	no	—
136	#121×C₅₃	—	2	1	no	—
137	C₄×Q₈×C₅₃	—	2	1	no	—
138	C₄×Q₈×C₅₃	—	2	1	no	—
139	C₄×Q₈×C₅₃	—	2	1	no	—
140	C₄×Q₈×C₅₃	—	2	1	no	—
141	C₄×Q₈×C₅₃	—	2	2	no	—
142	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
143	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
144	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
145	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
147	C₄×D₄×C₅₃	—	2	2	no	—
148	C₄×D₄×C₅₃	—	2	2	no	—
149	C₄×D₄×C₅₃	—	2	2	no	—
150	C₄×D₄×C₅₃	—	2	4	no	—
151	C₄×D₄×C₅₃	—	2	1	no	—
152	C₄×D₄×C₅₃	—	2	1	no	—
153	C₄×D₄×C₅₃	—	2	1	no	—
154	C₄×D₄×C₅₃	—	2	1	no	—
155	C₄×D₄×C₅₃	C₂³	1	2	yes	—
156	C₄×D₄×C₅₃	C₂³	1	2	yes	—
157	C₄×D₄×C₅₃	C₂³	1	4	yes	—
158	C₄×D₄×C₅₃	C₂³	1	4	yes	—
159	C₄×D₄×C₅₃	C₂³	1	4	yes	—
160	#117×C₅₃	—	2	2	no	—
161	#117×C₅₃	—	2	4	no	—
162	#117×C₅₃	C₂³	1	2	yes	—
163	#117×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
165	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
166	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
167	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
171	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
172	C₂×C₄²×C₅₃	—	2	1	no	—
173	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
174	#107×C₅₃	C₂³	1	4	yes	—
175	#107×C₅₃	C₂³	1	4	yes	—
176	#106×C₅₃	C₂³	1	4	yes	—
177	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
178	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
179	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
180	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
181	#103×C₅₃	C₂³	1	2	yes	—
182	#103×C₅₃	C₂³	1	4	yes	—
183	#103×C₅₃	C₂³	1	4	yes	—
184	#103×C₅₃	C₂³	1	4	yes	—
185	#103×C₅₃	C₂³	1	4	yes	—
186	#103×C₅₃	C₂³	1	2	yes	—
187	#103×C₅₃	C₂³	1	2	yes	—
188	#103×C₅₃	C₂³	1	2	yes	—
189	#102×C₅₃	C₂³	1	2	yes	—
190	#102×C₅₃	C₂³	1	4	yes	—
191	#102×C₅₃	C₂³	1	2	yes	—
192	#102×C₅₃	C₂³	1	2	yes	—
193	#102×C₅₃	C₂³	1	2	yes	—
194	#102×C₅₃	C₂³	1	4	yes	—
195	#97×C₅₃	C₂³	1	2	yes	—
196	#97×C₅₃	C₂³	1	4	yes	—
197	#97×C₅₃	C₂³	1	2	yes	—
198	C₄×C₈×C₅₃	C₂³	1	4	yes	—
199	C₂⁴×C₅₃	—	2	1	no	—
200	#41×C₅₃	—	2	4	no	—
201	#41×C₅₃	—	2	4	no	—
202	C₂×Q₈×C₅₃	—	2	1	no	—
203	C₂×Q₈×C₅₃	—	2	1	no	—
204	C₂×Q₈×C₅₃	—	2	1	no	—
205	C₂×Q₈×C₅₃	—	2	4	no	—
206	C₂×Q₈×C₅₃	—	2	2	no	—
207	C₂×Q₈×C₅₃	—	2	2	no	—
208	C₂×Q₈×C₅₃	—	8	4	no	—
209	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
213	C₂×D₄×C₅₃	—	2	2	no	—
214	C₂×D₄×C₅₃	—	2	1	no	—
215	C₂×D₄×C₅₃	—	2	1	no	—
216	C₂×D₄×C₅₃	—	2	1	no	—
217	C₂×D₄×C₅₃	—	2	2	no	—
218	C₂×D₄×C₅₃	#41	1	4	yes	—
219	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₃	—	2	1	no	—
222	C₂²×C₄×C₅₃	—	2	1	no	—
223	C₂²×C₄×C₅₃	—	2	1	no	—
224	C₂²×C₄×C₅₃	—	2	2	no	—
225	C₂²×C₄×C₅₃	—	2	2	no	—
226	C₂²×C₄×C₅₃	—	2	4	no	—
227	C₂²×C₄×C₅₃	—	2	4	no	—
228	C₂²×C₄×C₅₃	—	2	2	no	—
229	C₂²×C₄×C₅₃	—	2	4	no	—
230	C₂²×C₄×C₅₃	—	8	2	no	—
231	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
234	SD₁₆×C₅₃	—	2	8	no	—
235	SD₁₆×C₅₃	—	2	8	no	—
236	D₈×C₅₃	—	2	8	no	—
237	M₁₆×C₅₃	—	2	4	no	—
238	C₂×C₈×C₅₃	—	2	2	no	—
239	C₂×C₈×C₅₃	—	2	2	no	—
240	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
241	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
242	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₄⋊C₄×C₅₃	—	2	2	no	—
245	C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₄⋊C₄×C₅₃	—	2	4	no	—
247	C₄⋊C₄×C₅₃	—	2	2	no	—
248	C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₄⋊C₄×C₅₃	—	2	4	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	1	no	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₄⋊C₄×C₅₃	—	2	2	no	—
257	C₄⋊C₄×C₅₃	—	2	1	no	—
258	C₄⋊C₄×C₅₃	—	2	4	no	—
259	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
269	C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂²⋊C₄×C₅₃	—	2	4	no	—
273	C₂²⋊C₄×C₅₃	—	2	4	no	—
274	C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂²⋊C₄×C₅₃	—	2	4	no	—
276	C₂²⋊C₄×C₅₃	—	2	4	no	—
277	C₂²⋊C₄×C₅₃	—	2	2	no	—
278	C₂²⋊C₄×C₅₃	—	2	4	no	—
279	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
280	C₄²×C₅₃	—	2	2	no	—
281	C₄²×C₅₃	—	2	2	no	—
282	C₄²×C₅₃	—	2	4	no	—
283	C₄²×C₅₃	—	2	2	no	—
284	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₅₃	C₂⁴	1	4	yes	—
287	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
288	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
289	C₂³×C₅₃	—	2	2	no	—
290	C₂³×C₅₃	—	2	4	no	—
291	C₂³×C₅₃	—	2	2	no	—
292	C₂³×C₅₃	—	8	1	no	—
293	C₂³×C₅₃	—	8	1	no	—
294	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₅₃	—	2	2	no	—
296	Q₈×C₅₃	—	2	2	no	—
297	Q₈×C₅₃	—	2	2	no	—
298	Q₈×C₅₃	—	2	2	no	—
299	Q₈×C₅₃	—	4	2	no	—
300	Q₈×C₅₃	—	4	2	no	—
301	Q₈×C₅₃	—	4	2	no	—
302	Q₈×C₅₃	—	4	2	no	—
303	Q₈×C₅₃	—	8	1	no	—
304	Q₈×C₅₃	—	8	4	no	—
305	D₄×C₅₃	—	2	4	no	—
306	D₄×C₅₃	—	2	2	no	—
307	D₄×C₅₃	—	2	2	no	—
308	D₄×C₅₃	—	2	2	no	—
309	D₄×C₅₃	—	4	2	no	—
310	D₄×C₅₃	—	4	4	no	—
311	D₄×C₅₃	—	8	1	no	—
312	D₄×C₅₃	C₂×#41	1	4	yes	—
313	C₂×C₄×C₅₃	—	2	2	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	2	no	—
317	C₂×C₄×C₅₃	—	2	2	no	—
318	C₂×C₄×C₅₃	—	2	2	no	—
319	C₂×C₄×C₅₃	—	4	1	no	—
320	C₂×C₄×C₅₃	—	4	1	no	—
321	C₂×C₄×C₅₃	—	4	4	no	—
322	C₂×C₄×C₅₃	—	4	2	no	—
323	C₂×C₄×C₅₃	—	4	4	no	—
324	C₂×C₄×C₅₃	—	8	4	no	—
325	C₂×C₄×C₅₃	—	8	4	no	—
326	C₂×C₄×C₅₃	—	8	2	no	—
327	C₂×C₄×C₅₃	—	8	4	no	—
328	C₂×C₄×C₅₃	—	8	1	no	—
329	C₂×C₄×C₅₃	—	8	1	no	—
330	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
338	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
339	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
340	C₈×C₅₃	—	2	2	no	—
341	C₈×C₅₃	—	2	4	no	—
342	C₈×C₅₃	—	2	2	no	—
343	#61333	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂²×C₅₃	—	2	1	no	—
345	C₂²×C₅₃	—	2	1	no	—
346	C₂²×C₅₃	—	2	4	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	—	8	4	no	—
353	C₂²×C₅₃	#548	1	2	yes	—
354	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₅₃	—	2	1	no	—
356	C₄×C₅₃	—	2	1	no	—
357	C₄×C₅₃	—	2	4	no	—
358	C₄×C₅₃	—	2	1	no	—
359	C₄×C₅₃	—	2	1	no	—
360	C₄×C₅₃	—	2	4	no	—
361	C₄×C₅₃	—	4	2	no	—
362	C₄×C₅₃	—	4	2	no	—
363	C₄×C₅₃	—	4	2	no	—
364	C₄×C₅₃	—	4	2	no	—
365	C₄×C₅₃	—	4	2	no	—
366	C₄×C₅₃	—	4	2	no	—
367	C₄×C₅₃	#548	1	2	yes	—
368	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
369	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
370	#3507	C₂×C₅₃	1	1	yes	characteristic, complemented
371	#3501	C₂×C₅₃	1	1	yes	characteristic, complemented
372	#3376	C₂×C₅₃	1	4	yes	complemented
373	#3372	C₂×C₅₃	1	4	yes	complemented
374	#3370	C₂×C₅₃	1	4	yes	complemented
375	#3367	C₂×C₅₃	1	4	yes	complemented
376	#3137	C₂×C₅₃	1	2	yes	complemented
377	#3135	C₂×C₅₃	1	1	yes	characteristic, complemented
378	#3083	C₂×C₅₃	1	2	yes	complemented
379	#3078	C₂×C₅₃	1	1	yes	characteristic, complemented
380	#3042	C₂×C₅₃	1	2	yes	complemented
381	#3036	C₂×C₅₃	1	1	yes	characteristic
382	#2961	C₂×C₅₃	1	1	yes	characteristic, complemented
383	#2946	C₂×C₅₃	1	2	yes	complemented
384	C₂×#440	C₂×C₅₃	1	1	yes	characteristic, complemented
385	C₂×C₅₃	—	2	2	no	—
386	C₂×C₅₃	—	4	4	no	—
387	C₂×C₅₃	—	8	2	no	—
388	C₂×C₅₃	C₂×#548	1	1	yes	characteristic
389	C₂×C₅₃	#3585	1	1	yes	characteristic
390	C₂×C₅₃	#3586	1	1	yes	characteristic
391	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
392	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
393	#559	C₂²×C₅₃	1	2	yes	complemented
394	#557	C₂²×C₅₃	1	2	yes	complemented
395	#556	—	2	1	no	—
396	#556	C₂²×C₅₃	1	4	yes	complemented
397	#554	—	2	1	no	—
398	#554	—	2	1	no	—
399	#554	—	2	2	no	—
400	#554	C₂²×C₅₃	1	4	yes	—
401	#554	C₂²×C₅₃	1	2	yes	—
402	#552	—	2	2	no	—
403	D₄×Q₈	—	2	1	no	—
404	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
405	#544	C₂²×C₅₃	1	2	yes	—
406	#543	—	2	2	no	—
407	#539	—	2	2	no	—
408	#536	C₂²×C₅₃	1	2	yes	—
409	#533	C₂²×C₅₃	1	1	yes	characteristic
410	#533	C₂²×C₅₃	1	1	yes	characteristic
411	#532	C₂²×C₅₃	1	1	yes	characteristic
412	#529	—	2	2	no	—
413	C₂×C₂²⋊Q₈	—	2	2	no	—
414	#520	C₂²×C₅₃	1	2	yes	—
415	#518	C₂²×C₅₃	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
418	#491	C₂²×C₅₃	1	2	yes	complemented
419	#491	C₂²×C₅₃	1	4	yes	complemented
420	#490	C₂²×C₅₃	1	2	yes	complemented
421	#489	C₂²×C₅₃	1	2	yes	complemented
422	#489	C₂²×C₅₃	1	4	yes	complemented
423	#489	C₂²×C₅₃	1	2	yes	complemented
424	#488	C₂²×C₅₃	1	4	yes	complemented
425	#487	C₂²×C₅₃	1	4	yes	complemented
426	#479	C₂²×C₅₃	1	4	yes	complemented
427	#479	C₂²×C₅₃	1	4	yes	complemented
428	#478	C₂²×C₅₃	1	4	yes	complemented
429	#477	C₂²×C₅₃	1	2	yes	complemented
430	#477	C₂²×C₅₃	1	4	yes	complemented
431	#475	C₂²×C₅₃	1	2	yes	complemented
432	#474	C₂²×C₅₃	1	4	yes	complemented
433	#463	C₂²×C₅₃	1	4	yes	—
434	#463	C₂²×C₅₃	1	4	yes	—
435	#463	C₂²×C₅₃	1	4	yes	—
436	#461	C₂²×C₅₃	1	4	yes	—
437	#461	C₂²×C₅₃	1	2	yes	—
438	#461	C₂²×C₅₃	1	4	yes	—
439	#459	C₂²×C₅₃	1	2	yes	—
440	#446	C₂²×C₅₃	1	4	yes	complemented
441	#446	C₂²×C₅₃	1	4	yes	complemented
442	#442	C₂²×C₅₃	1	4	yes	—
443	#440	C₂²×C₅₃	1	4	yes	—
444	#440	C₂²×C₅₃	1	4	yes	—
445	#440	C₂²×C₅₃	1	4	yes	—
446	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
447	C₄×D₈	C₂²×C₅₃	1	4	yes	—
448	#428	C₂²×C₅₃	1	2	yes	—
449	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
450	#424	C₂²×C₅₃	1	2	yes	—
451	#423	C₂²×C₅₃	1	1	yes	characteristic
452	#419	C₂²×C₅₃	1	2	yes	—
453	#417	C₂²×C₅₃	1	2	yes	—
454	#416	C₂²×C₅₃	1	2	yes	—
455	#416	C₂²×C₅₃	1	2	yes	—
456	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
457	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
458	#405	C₂²×C₅₃	1	2	yes	—
459	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
460	C₅₃	#61333	1	1	yes	characteristic, direct product factor, Sylow
461	C₂×#41	C₂³×C₅₃	1	2	yes	—
462	C₂²×Q₈	—	2	2	no	—
463	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
465	C₂³×C₄	—	2	1	no	—
466	AGL(1,ℤ/8)	—	2	8	no	—
467	C₂×SD₁₆	—	2	4	no	—
468	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
470	C₂×D₈	C₂³×C₅₃	1	4	yes	—
471	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
472	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
476	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
479	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
482	#127	C₂³×C₅₃	1	1	yes	characteristic
483	#126	—	2	4	no	—
484	#126	—	2	4	no	—
485	#125	—	2	2	no	—
486	#125	—	2	4	no	—
487	#125	—	2	2	no	—
488	#125	D₄×C₅₃	1	2	yes	—
489	#125	C₂³×C₅₃	1	2	yes	—
490	#125	C₂³×C₅₃	1	4	yes	—
491	#124	—	2	2	no	—
492	#124	C₂³×C₅₃	1	2	yes	—
493	#124	C₂³×C₅₃	1	4	yes	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	—	2	4	no	—
509	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
510	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
511	#121	—	2	1	no	—
512	#121	—	2	1	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
519	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
520	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
521	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
522	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	C₂³×C₅₃	1	2	yes	—
532	C₄×D₄	C₂³×C₅₃	1	2	yes	—
533	C₄×D₄	C₂³×C₅₃	1	4	yes	—
534	C₄×D₄	C₂³×C₅₃	1	4	yes	—
535	C₄×D₄	C₂³×C₅₃	1	4	yes	—
536	#117	—	2	2	no	—
537	#117	—	2	4	no	—
538	#117	C₂³×C₅₃	1	2	yes	—
539	#117	C₂³×C₅₃	1	2	yes	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	—	2	4	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	4	no	—
548	C₂×C₄²	—	2	1	no	—
549	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
550	#107	C₂³×C₅₃	1	4	yes	—
551	#107	C₂³×C₅₃	1	4	yes	—
552	#106	C₂³×C₅₃	1	4	yes	—
553	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
554	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
555	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
556	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
557	#103	C₂³×C₅₃	1	4	yes	—
558	#103	C₂³×C₅₃	1	2	yes	—
559	#103	C₂³×C₅₃	1	2	yes	—
560	#103	C₂³×C₅₃	1	2	yes	—
561	#103	C₂³×C₅₃	1	2	yes	—
562	#103	C₂³×C₅₃	1	4	yes	—
563	#103	C₂³×C₅₃	1	4	yes	—
564	#103	C₂³×C₅₃	1	4	yes	—
565	#102	C₂³×C₅₃	1	4	yes	—
566	#102	C₂³×C₅₃	1	2	yes	—
567	#102	C₂³×C₅₃	1	2	yes	—
568	#102	C₂³×C₅₃	1	2	yes	—
569	#102	C₂³×C₅₃	1	2	yes	—
570	#102	C₂³×C₅₃	1	4	yes	—
571	#97	C₂³×C₅₃	1	2	yes	—
572	#97	C₂³×C₅₃	1	2	yes	—
573	#97	C₂³×C₅₃	1	4	yes	—
574	C₄×C₈	C₂³×C₅₃	1	4	yes	—
575	C₂⁴	—	2	1	no	—
576	#41	—	2	4	no	—
577	#41	—	2	4	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	8	4	no	—
585	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
586	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
587	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
588	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	#41×C₅₃	1	4	yes	—
595	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
596	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	8	2	no	—
607	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
610	SD₁₆	—	2	8	no	—
611	SD₁₆	—	2	8	no	—
612	D₈	—	2	8	no	—
613	M₁₆	—	2	4	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
617	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
618	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
637	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
639	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
640	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
662	C₄²	C₂⁴×C₅₃	1	4	yes	—
663	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
664	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	8	1	no	—
669	C₂³	—	8	1	no	—
670	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	4	2	no	—
678	Q₈	—	4	2	no	—
679	Q₈	—	8	1	no	—
680	Q₈	—	8	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	4	no	—
687	D₄	—	8	1	no	—
688	D₄	C₂×#41×C₅₃	1	4	yes	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	2	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
712	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
713	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
714	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
715	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	4	no	—
718	C₈	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	C₅₃×#548	1	2	yes	—
729	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	4	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	C₅₃×#548	1	2	yes	—
743	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
744	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	4	4	no	—
747	C₂	—	8	2	no	—
748	C₂	C₂×C₅₃×#548	1	1	yes	characteristic
749	C₂	C₅₃×#3585	1	1	yes	characteristic
750	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3036	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3507	C₂	semidirect
2. C₅₃×#3501	C₂	semidirect
3. C₅₃×#3376	C₂	semidirect
4. C₅₃×#3372	C₂	semidirect
5. C₅₃×#3370	C₂	semidirect
6. C₅₃×#3367	C₂	semidirect
7. C₅₃×#3137	C₂	semidirect
8. C₅₃×#3135	C₂	semidirect
9. C₅₃×#3083	C₂	semidirect
10. C₅₃×#3078	C₂	semidirect
11. C₅₃×#3042	C₂	semidirect
13. C₅₃×#2961	C₂	semidirect
14. C₅₃×#2946	C₂	semidirect
15. C₂×C₅₃×#440	C₂	semidirect
18. C₅₃×#559	C₂²	semidirect
19. C₅₃×#557	C₂²	semidirect
21. C₅₃×#556	C₂²	semidirect
43. C₅₃×#491	C₂²	semidirect
44. C₅₃×#491	C₂²	semidirect
45. C₅₃×#490	C₂²	semidirect
46. C₅₃×#489	C₂²	semidirect
47. C₅₃×#489	C₂²	semidirect
48. C₅₃×#489	C₂²	semidirect
49. C₅₃×#488	C₂²	semidirect
50. C₅₃×#487	C₂²	semidirect
51. C₅₃×#479	C₂²	semidirect
52. C₅₃×#479	C₂²	semidirect
53. C₅₃×#478	C₂²	semidirect
54. C₅₃×#477	C₂²	semidirect
55. C₅₃×#477	C₂²	semidirect
56. C₅₃×#475	C₂²	semidirect
57. C₅₃×#474	C₂²	semidirect
65. C₅₃×#446	C₂²	semidirect
66. C₅₃×#446	C₂²	semidirect
343. #61333	C₅₃	direct (N × H)
370. #3507	C₂×C₅₃	semidirect
371. #3501	C₂×C₅₃	semidirect
372. #3376	C₂×C₅₃	semidirect
373. #3372	C₂×C₅₃	semidirect
374. #3370	C₂×C₅₃	semidirect
375. #3367	C₂×C₅₃	semidirect
376. #3137	C₂×C₅₃	semidirect
377. #3135	C₂×C₅₃	semidirect
378. #3083	C₂×C₅₃	semidirect
379. #3078	C₂×C₅₃	semidirect
380. #3042	C₂×C₅₃	semidirect
382. #2961	C₂×C₅₃	semidirect
383. #2946	C₂×C₅₃	semidirect
384. C₂×#440	C₂×C₅₃	semidirect
393. #559	C₂²×C₅₃	semidirect
394. #557	C₂²×C₅₃	semidirect
396. #556	C₂²×C₅₃	semidirect
418. #491	C₂²×C₅₃	semidirect
419. #491	C₂²×C₅₃	semidirect
420. #490	C₂²×C₅₃	semidirect
421. #489	C₂²×C₅₃	semidirect
422. #489	C₂²×C₅₃	semidirect
423. #489	C₂²×C₅₃	semidirect
424. #488	C₂²×C₅₃	semidirect
425. #487	C₂²×C₅₃	semidirect
426. #479	C₂²×C₅₃	semidirect
427. #479	C₂²×C₅₃	semidirect
428. #478	C₂²×C₅₃	semidirect
429. #477	C₂²×C₅₃	semidirect
430. #477	C₂²×C₅₃	semidirect
431. #475	C₂²×C₅₃	semidirect
432. #474	C₂²×C₅₃	semidirect
440. #446	C₂²×C₅₃	semidirect
441. #446	C₂²×C₅₃	semidirect
460. C₅₃	#61333	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3507	2
C₅₃×#3501	2
C₅₃×#3376	2
C₅₃×#3372	2
C₅₃×#3370	2
C₅₃×#3367	2
C₅₃×#3137	2
C₅₃×#3135	2
C₅₃×#3083	2
C₅₃×#3078	2
C₅₃×#3042	2
C₅₃×#3036	2
C₅₃×#2961	2
C₅₃×#2946	2
C₂×C₅₃×#440	2
#61333	53

Subgroups — C53×#61333 #27268845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61333 #27268845