Subgroups — C₅₃×#62247 #27269759

Order 13568.

1914 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3505	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3339	C₂	1	2	yes	maximal, complemented
3	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3301	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3296	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3285	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3280	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3250	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3191	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3187	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3168	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3050	C₂	1	2	yes	maximal, complemented
13	C₂×C₅₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₈×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
17	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₅₃×#553	—	2	4	no	—
22	C₅₃×#553	C₂²	1	4	yes	complemented
23	C₅₃×#552	C₂²	1	4	yes	—
24	C₅₃×#551	—	2	4	no	—
25	C₅₃×#548	C₂²	1	4	yes	complemented
26	C₅₃×#546	C₂²	1	4	yes	—
27	C₅₃×#539	—	2	2	no	—
28	C₅₃×#538	—	2	2	no	—
29	C₅₃×#534	—	2	2	no	—
30	C₅₃×#529	C₂²	1	4	yes	complemented
31	C₅₃×#525	C₂²	1	4	yes	complemented
32	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
33	C₂×#121×C₅₃	C₂²	1	2	yes	—
34	C₅₃×#518	—	2	2	no	—
35	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₅₃×#499	C₂²	1	2	yes	complemented
37	C₅₃×#495	C₂²	1	2	yes	complemented
38	C₅₃×#488	C₂²	1	4	yes	complemented
39	C₅₃×#485	C₂²	1	4	yes	complemented
40	C₅₃×#483	C₂²	1	4	yes	complemented
41	C₅₃×#482	C₂²	1	4	yes	complemented
42	C₅₃×#481	C₂²	1	4	yes	complemented
43	C₅₃×#479	C₂²	1	4	yes	complemented
44	C₅₃×#478	C₂²	1	4	yes	complemented
45	C₅₃×#467	C₂²	1	2	yes	complemented
46	C₅₃×#467	C₂²	1	2	yes	complemented
47	C₅₃×#467	C₂²	1	2	yes	complemented
48	C₅₃×#467	C₂²	1	2	yes	complemented
49	C₅₃×#467	C₂²	1	2	yes	complemented
50	C₅₃×#466	C₂²	1	2	yes	—
51	C₅₃×#466	C₂²	1	2	yes	—
52	C₅₃×#466	C₂²	1	2	yes	complemented
53	C₅₃×#466	C₂²	1	2	yes	complemented
54	C₅₃×#466	C₂²	1	2	yes	complemented
55	C₅₃×#465	C₂²	1	4	yes	complemented
56	C₅₃×#465	C₂²	1	4	yes	complemented
57	C₅₃×#465	C₂²	1	4	yes	complemented
58	C₅₃×#464	C₂²	1	4	yes	complemented
59	C₅₃×#463	C₂²	1	4	yes	complemented
60	C₅₃×#452	C₂²	1	4	yes	complemented
61	C₅₃×#450	C₂²	1	4	yes	complemented
62	C₅₃×#449	C₂²	1	4	yes	complemented
63	C₅₃×#448	C₂²	1	4	yes	complemented
64	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
65	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
66	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
67	C₈×D₄×C₅₃	C₂²	1	2	yes	—
68	C₈×D₄×C₅₃	C₂²	1	2	yes	—
69	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
70	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
71	C₅₃×#427	C₂²	1	2	yes	complemented
72	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
73	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#416	C₂²	1	4	yes	complemented
76	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
77	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
78	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
79	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×#41×C₅₃	C₂³	1	4	yes	—
82	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₅₃	—	2	2	no	—
84	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
88	#135×C₅₃	—	4	4	no	—
89	C₂×Q₁₆×C₅₃	—	4	2	no	—
90	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
91	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
94	C₂×D₈×C₅₃	—	4	2	no	—
95	C₂×D₈×C₅₃	C₂³	1	2	yes	—
96	C₂×D₈×C₅₃	C₂³	1	2	yes	—
97	C₂²×C₈×C₅₃	—	4	2	no	—
98	C₂²×C₈×C₅₃	—	4	2	no	—
99	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
109	#126×C₅₃	—	2	4	no	—
110	#126×C₅₃	—	2	4	no	—
111	#126×C₅₃	—	2	4	no	—
112	#125×C₅₃	—	2	4	no	—
113	#125×C₅₃	C₂³	1	4	yes	—
114	#124×C₅₃	—	2	4	no	—
115	#124×C₅₃	C₂³	1	4	yes	—
116	#123×C₅₃	—	2	4	no	—
117	#123×C₅₃	—	2	4	no	—
118	#123×C₅₃	—	2	4	no	—
119	#123×C₅₃	—	2	4	no	—
120	#123×C₅₃	—	2	4	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	C₂³	1	4	yes	—
125	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
126	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
127	#121×C₅₃	—	2	4	no	—
128	#121×C₅₃	—	2	4	no	—
129	#121×C₅₃	—	2	4	no	—
130	#121×C₅₃	—	2	2	no	—
131	#121×C₅₃	—	2	2	no	—
132	#121×C₅₃	C₂³	1	4	yes	—
133	#121×C₅₃	C₂³	1	4	yes	—
134	#121×C₅₃	C₂³	1	4	yes	—
135	#120×C₅₃	—	2	4	no	—
136	#120×C₅₃	—	2	4	no	—
137	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
138	C₄×D₄×C₅₃	—	2	4	no	—
139	C₄×D₄×C₅₃	—	2	4	no	—
140	C₄×D₄×C₅₃	—	2	4	no	—
141	C₄×D₄×C₅₃	—	2	4	no	—
142	C₄×D₄×C₅₃	—	2	4	no	—
143	C₄×D₄×C₅₃	D₄	1	2	yes	—
144	C₄×D₄×C₅₃	D₄	1	2	yes	—
145	C₄×D₄×C₅₃	C₂³	1	4	yes	—
146	C₄×D₄×C₅₃	C₂³	1	2	yes	—
147	C₄×D₄×C₅₃	C₂³	1	2	yes	—
148	#117×C₅₃	—	2	4	no	—
149	#117×C₅₃	—	2	4	no	—
150	#117×C₅₃	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
152	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
156	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
157	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
158	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
161	#107×C₅₃	C₂³	1	2	yes	—
162	#107×C₅₃	C₂³	1	2	yes	—
163	#107×C₅₃	C₂³	1	2	yes	—
164	#107×C₅₃	C₂³	1	2	yes	—
165	#106×C₅₃	C₂³	1	4	yes	—
166	#106×C₅₃	C₂³	1	4	yes	—
167	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
168	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
169	#103×C₅₃	C₂³	1	4	yes	—
170	#103×C₅₃	C₂³	1	4	yes	—
171	#103×C₅₃	C₂³	1	4	yes	—
172	#103×C₅₃	C₂³	1	4	yes	—
173	#102×C₅₃	C₂³	1	4	yes	—
174	#102×C₅₃	C₂³	1	4	yes	—
175	#102×C₅₃	C₂³	1	4	yes	—
176	#102×C₅₃	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
178	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
179	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
180	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
181	C₄×C₈×C₅₃	C₂³	1	2	yes	—
182	C₄×C₈×C₅₃	C₂³	1	2	yes	—
183	C₂⁴×C₅₃	—	2	2	no	—
184	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
185	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
186	#41×C₅₃	—	4	4	no	—
187	#41×C₅₃	—	4	4	no	—
188	C₂×Q₈×C₅₃	—	2	2	no	—
189	C₂×Q₈×C₅₃	—	4	2	no	—
190	C₂×Q₈×C₅₃	—	4	2	no	—
191	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
192	C₂×D₄×C₅₃	—	2	4	no	—
193	C₂×D₄×C₅₃	—	2	4	no	—
194	C₂×D₄×C₅₃	—	2	4	no	—
195	C₂×D₄×C₅₃	—	2	4	no	—
196	C₂×D₄×C₅₃	—	2	4	no	—
197	C₂×D₄×C₅₃	—	2	2	no	—
198	C₂×D₄×C₅₃	—	4	2	no	—
199	C₂×D₄×C₅₃	—	4	2	no	—
200	C₂×D₄×C₅₃	—	4	8	no	—
201	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
203	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₅₃	—	2	2	no	—
205	C₂²×C₄×C₅₃	—	2	2	no	—
206	C₂²×C₄×C₅₃	—	2	2	no	—
207	C₂²×C₄×C₅₃	—	2	4	no	—
208	C₂²×C₄×C₅₃	—	2	4	no	—
209	C₂²×C₄×C₅₃	—	4	1	no	—
210	C₂²×C₄×C₅₃	—	4	1	no	—
211	C₂²×C₄×C₅₃	—	4	1	no	—
212	C₂²×C₄×C₅₃	—	4	1	no	—
213	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
224	Q₁₆×C₅₃	—	2	4	no	—
225	Q₁₆×C₅₃	—	4	2	no	—
226	SD₁₆×C₅₃	—	4	4	no	—
227	SD₁₆×C₅₃	—	4	4	no	—
228	D₈×C₅₃	—	2	4	no	—
229	D₈×C₅₃	—	4	2	no	—
230	C₂×C₈×C₅₃	—	2	2	no	—
231	C₂×C₈×C₅₃	—	2	2	no	—
232	C₂×C₈×C₅₃	—	2	2	no	—
233	C₂×C₈×C₅₃	—	2	4	no	—
234	C₂×C₈×C₅₃	—	4	1	no	—
235	C₂×C₈×C₅₃	—	4	2	no	—
236	C₂×C₈×C₅₃	—	4	1	no	—
237	C₂×C₈×C₅₃	—	4	1	no	—
238	C₂×C₈×C₅₃	—	4	1	no	—
239	C₂×C₈×C₅₃	—	4	1	no	—
240	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
241	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₅₃	—	2	4	no	—
247	C₄⋊C₄×C₅₃	—	2	4	no	—
248	C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₄⋊C₄×C₅₃	—	2	2	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
257	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
258	C₂²⋊C₄×C₅₃	—	2	4	no	—
259	C₂²⋊C₄×C₅₃	—	2	4	no	—
260	C₂²⋊C₄×C₅₃	—	2	4	no	—
261	C₂²⋊C₄×C₅₃	—	2	4	no	—
262	C₂²⋊C₄×C₅₃	—	2	4	no	—
263	C₂²⋊C₄×C₅₃	—	2	4	no	—
264	C₂²⋊C₄×C₅₃	—	2	4	no	—
265	C₂²⋊C₄×C₅₃	—	2	4	no	—
266	C₂²⋊C₄×C₅₃	—	2	4	no	—
267	C₂²⋊C₄×C₅₃	—	2	4	no	—
268	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
269	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
270	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
272	C₄²×C₅₃	—	2	4	no	—
273	C₄²×C₅₃	—	2	4	no	—
274	C₄²×C₅₃	C₂×D₄	1	2	yes	—
275	C₄²×C₅₃	C₂⁴	1	2	yes	—
276	C₂³×C₅₃	—	2	2	no	—
277	C₂³×C₅₃	—	2	4	no	—
278	C₂³×C₅₃	—	4	1	no	—
279	C₂³×C₅₃	—	4	1	no	—
280	C₂³×C₅₃	—	4	1	no	—
281	C₂³×C₅₃	—	4	1	no	—
282	C₂³×C₅₃	—	4	4	no	—
283	C₂³×C₅₃	—	8	2	no	—
284	C₂³×C₅₃	—	8	2	no	—
285	C₂³×C₅₃	#135	1	4	yes	complemented
286	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
288	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
289	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₅₃	—	2	4	no	—
291	Q₈×C₅₃	—	2	4	no	—
292	Q₈×C₅₃	—	8	2	no	—
293	D₄×C₅₃	—	2	4	no	—
294	D₄×C₅₃	—	2	4	no	—
295	D₄×C₅₃	—	2	4	no	—
296	D₄×C₅₃	—	2	4	no	—
297	D₄×C₅₃	—	4	8	no	—
298	D₄×C₅₃	—	4	8	no	—
299	D₄×C₅₃	—	8	2	no	—
300	D₄×C₅₃	—	8	4	no	—
301	D₄×C₅₃	—	8	4	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	2	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	2	1	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	4	no	—
312	C₂×C₄×C₅₃	—	2	4	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	4	2	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	4	no	—
321	C₂×C₄×C₅₃	—	8	4	no	—
322	C₂×C₄×C₅₃	—	8	4	no	—
323	C₂×C₄×C₅₃	—	8	2	no	—
324	C₂×C₄×C₅₃	—	8	2	no	—
325	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
332	C₈×C₅₃	—	2	1	no	—
333	C₈×C₅₃	—	2	1	no	—
334	C₈×C₅₃	—	2	2	no	—
335	C₈×C₅₃	—	2	1	no	—
336	C₈×C₅₃	—	2	2	no	—
337	C₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
338	#62247	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂²×C₅₃	—	2	1	no	—
340	C₂²×C₅₃	—	2	1	no	—
341	C₂²×C₅₃	—	2	1	no	—
342	C₂²×C₅₃	—	2	1	no	—
343	C₂²×C₅₃	—	2	1	no	—
344	C₂²×C₅₃	—	2	1	no	—
345	C₂²×C₅₃	—	2	2	no	—
346	C₂²×C₅₃	—	2	2	no	—
347	C₂²×C₅₃	—	2	2	no	—
348	C₂²×C₅₃	—	4	4	no	—
349	C₂²×C₅₃	—	4	4	no	—
350	C₂²×C₅₃	—	4	4	no	—
351	C₂²×C₅₃	—	4	4	no	—
352	C₂²×C₅₃	—	4	4	no	—
353	C₂²×C₅₃	—	16	4	no	—
354	C₂²×C₅₃	C₂×#135	1	2	yes	—
355	C₂²×C₅₃	C₂×#135	1	2	yes	—
356	C₂²×C₅₃	C₂×#135	1	2	yes	—
357	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₅₃	—	2	2	no	—
359	C₄×C₅₃	—	2	1	no	—
360	C₄×C₅₃	—	2	2	no	—
361	C₄×C₅₃	—	2	1	no	—
362	C₄×C₅₃	—	2	1	no	—
363	C₄×C₅₃	—	2	2	no	—
364	C₄×C₅₃	—	4	4	no	—
365	C₄×C₅₃	—	4	4	no	—
366	C₄×C₅₃	—	4	4	no	—
367	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₄×C₅₃	#585	1	1	yes	characteristic
369	#3505	C₂×C₅₃	1	2	yes	complemented
370	#3339	C₂×C₅₃	1	2	yes	complemented
371	#3336	C₂×C₅₃	1	2	yes	complemented
372	#3301	C₂×C₅₃	1	4	yes	complemented
373	#3296	C₂×C₅₃	1	4	yes	complemented
374	#3285	C₂×C₅₃	1	2	yes	complemented
375	#3280	C₂×C₅₃	1	2	yes	complemented
376	#3250	C₂×C₅₃	1	2	yes	complemented
377	#3191	C₂×C₅₃	1	2	yes	complemented
378	#3187	C₂×C₅₃	1	2	yes	complemented
379	#3168	C₂×C₅₃	1	2	yes	complemented
380	#3050	C₂×C₅₃	1	2	yes	complemented
381	C₂×#467	C₂×C₅₃	1	1	yes	characteristic, complemented
382	C₂×#466	C₂×C₅₃	1	1	yes	characteristic, complemented
383	C₂×C₈×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
384	C₂×C₅₃	—	2	2	no	—
385	C₂×C₅₃	—	2	2	no	—
386	C₂×C₅₃	—	2	2	no	—
387	C₂×C₅₃	—	4	2	no	—
388	C₂×C₅₃	—	8	4	no	—
389	C₂×C₅₃	#3496	1	1	yes	characteristic
390	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
391	C₂×C₅₃	#3584	1	1	yes	characteristic
392	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
393	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
394	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
395	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
396	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
397	#553	—	2	4	no	—
398	#553	C₂²×C₅₃	1	4	yes	complemented
399	#552	C₂²×C₅₃	1	4	yes	—
400	#551	—	2	4	no	—
401	#548	C₂²×C₅₃	1	4	yes	complemented
402	#546	C₂²×C₅₃	1	4	yes	—
403	#539	—	2	2	no	—
404	#538	—	2	2	no	—
405	#534	—	2	2	no	—
406	#529	C₂²×C₅₃	1	4	yes	complemented
407	#525	C₂²×C₅₃	1	4	yes	complemented
408	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
409	C₂×#121	C₂²×C₅₃	1	2	yes	—
410	#518	—	2	2	no	—
411	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
412	#499	C₂²×C₅₃	1	2	yes	complemented
413	#495	C₂²×C₅₃	1	2	yes	complemented
414	#488	C₂²×C₅₃	1	4	yes	complemented
415	#485	C₂²×C₅₃	1	4	yes	complemented
416	#483	C₂²×C₅₃	1	4	yes	complemented
417	#482	C₂²×C₅₃	1	4	yes	complemented
418	#481	C₂²×C₅₃	1	4	yes	complemented
419	#479	C₂²×C₅₃	1	4	yes	complemented
420	#478	C₂²×C₅₃	1	4	yes	complemented
421	#467	C₂²×C₅₃	1	2	yes	complemented
422	#467	C₂²×C₅₃	1	2	yes	complemented
423	#467	C₂²×C₅₃	1	2	yes	complemented
424	#467	C₂²×C₅₃	1	2	yes	complemented
425	#467	C₂²×C₅₃	1	2	yes	complemented
426	#466	C₂²×C₅₃	1	2	yes	—
427	#466	C₂²×C₅₃	1	2	yes	—
428	#466	C₂²×C₅₃	1	2	yes	complemented
429	#466	C₂²×C₅₃	1	2	yes	complemented
430	#466	C₂²×C₅₃	1	2	yes	complemented
431	#465	C₂²×C₅₃	1	4	yes	complemented
432	#465	C₂²×C₅₃	1	4	yes	complemented
433	#465	C₂²×C₅₃	1	4	yes	complemented
434	#464	C₂²×C₅₃	1	4	yes	complemented
435	#463	C₂²×C₅₃	1	4	yes	complemented
436	#452	C₂²×C₅₃	1	4	yes	complemented
437	#450	C₂²×C₅₃	1	4	yes	complemented
438	#449	C₂²×C₅₃	1	4	yes	complemented
439	#448	C₂²×C₅₃	1	4	yes	complemented
440	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
441	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
442	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
443	C₈×D₄	C₂²×C₅₃	1	2	yes	—
444	C₈×D₄	C₂²×C₅₃	1	2	yes	—
445	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
446	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
447	#427	C₂²×C₅₃	1	2	yes	complemented
448	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
449	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
450	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
451	#416	C₂²×C₅₃	1	4	yes	complemented
452	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
453	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
454	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
455	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
456	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
457	C₅₃	#62247	1	1	yes	characteristic, direct product factor, Sylow
458	C₂×#41	C₂³×C₅₃	1	4	yes	—
459	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
460	C₂²×D₄	—	2	2	no	—
461	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
462	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
463	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
465	#135	—	4	4	no	—
466	C₂×Q₁₆	—	4	2	no	—
467	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
468	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
469	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
471	C₂×D₈	—	4	2	no	—
472	C₂×D₈	C₂³×C₅₃	1	2	yes	—
473	C₂×D₈	C₂³×C₅₃	1	2	yes	—
474	C₂²×C₈	—	4	2	no	—
475	C₂²×C₈	—	4	2	no	—
476	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
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	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
485	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
486	#126	—	2	4	no	—
487	#126	—	2	4	no	—
488	#126	—	2	4	no	—
489	#125	—	2	4	no	—
490	#125	C₂³×C₅₃	1	4	yes	—
491	#124	—	2	4	no	—
492	#124	C₂³×C₅₃	1	4	yes	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
502	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
503	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
504	#121	—	2	4	no	—
505	#121	—	2	4	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	4	no	—
509	#121	C₂³×C₅₃	1	4	yes	—
510	#121	C₂³×C₅₃	1	4	yes	—
511	#121	C₂³×C₅₃	1	4	yes	—
512	#120	—	2	4	no	—
513	#120	—	2	4	no	—
514	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	2	4	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	D₄×C₅₃	1	2	yes	—
521	C₄×D₄	D₄×C₅₃	1	2	yes	—
522	C₄×D₄	C₂³×C₅₃	1	4	yes	—
523	C₄×D₄	C₂³×C₅₃	1	2	yes	—
524	C₄×D₄	C₂³×C₅₃	1	2	yes	—
525	#117	—	2	4	no	—
526	#117	—	2	4	no	—
527	#117	C₂³×C₅₃	1	4	yes	—
528	C₂×C₄⋊C₄	—	2	2	no	—
529	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
532	C₂×C₂²⋊C₄	—	2	2	no	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	C₂×C₂²⋊C₄	—	2	4	no	—
535	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
538	#107	C₂³×C₅₃	1	2	yes	—
539	#107	C₂³×C₅₃	1	2	yes	—
540	#107	C₂³×C₅₃	1	2	yes	—
541	#107	C₂³×C₅₃	1	2	yes	—
542	#106	C₂³×C₅₃	1	4	yes	—
543	#106	C₂³×C₅₃	1	4	yes	—
544	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
545	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
546	#103	C₂³×C₅₃	1	4	yes	—
547	#103	C₂³×C₅₃	1	4	yes	—
548	#103	C₂³×C₅₃	1	4	yes	—
549	#103	C₂³×C₅₃	1	4	yes	—
550	#102	C₂³×C₅₃	1	4	yes	—
551	#102	C₂³×C₅₃	1	4	yes	—
552	#102	C₂³×C₅₃	1	4	yes	—
553	#102	C₂³×C₅₃	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
556	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
558	C₄×C₈	C₂³×C₅₃	1	2	yes	—
559	C₄×C₈	C₂³×C₅₃	1	2	yes	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
562	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
563	#41	—	4	4	no	—
564	#41	—	4	4	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	—	4	2	no	—
568	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	8	no	—
578	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
579	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
580	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
601	Q₁₆	—	2	4	no	—
602	Q₁₆	—	4	2	no	—
603	SD₁₆	—	4	4	no	—
604	SD₁₆	—	4	4	no	—
605	D₈	—	2	4	no	—
606	D₈	—	4	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	4	1	no	—
612	C₂×C₈	—	4	2	no	—
613	C₂×C₈	—	4	1	no	—
614	C₂×C₈	—	4	1	no	—
615	C₂×C₈	—	4	1	no	—
616	C₂×C₈	—	4	1	no	—
617	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
621	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
634	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
646	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
647	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
648	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	C₂×D₄×C₅₃	1	2	yes	—
652	C₄²	C₂⁴×C₅₃	1	2	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	8	2	no	—
661	C₂³	—	8	2	no	—
662	C₂³	#135×C₅₃	1	4	yes	complemented
663	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
664	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
665	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
667	Q₈	—	2	4	no	—
668	Q₈	—	2	4	no	—
669	Q₈	—	8	2	no	—
670	D₄	—	2	4	no	—
671	D₄	—	2	4	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	4	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	8	no	—
676	D₄	—	8	2	no	—
677	D₄	—	8	4	no	—
678	D₄	—	8	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	8	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	—	8	2	no	—
701	C₂×C₄	—	8	2	no	—
702	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
708	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
709	C₈	—	2	1	no	—
710	C₈	—	2	1	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	16	4	no	—
730	C₂²	C₂×#135×C₅₃	1	2	yes	—
731	C₂²	C₂×#135×C₅₃	1	2	yes	—
732	C₂²	C₂×#135×C₅₃	1	2	yes	—
733	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
744	C₄	C₅₃×#585	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	2	2	no	—
747	C₂	—	2	2	no	—
748	C₂	—	4	2	no	—
749	C₂	—	8	4	no	—
750	C₂	C₅₃×#3496	1	1	yes	characteristic
751	C₂	C₂²×#135×C₅₃	1	1	yes	characteristic
752	C₂	C₅₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3505	C₂	semidirect
2. C₅₃×#3339	C₂	semidirect
3. C₅₃×#3336	C₂	semidirect
4. C₅₃×#3301	C₂	semidirect
5. C₅₃×#3296	C₂	semidirect
6. C₅₃×#3285	C₂	semidirect
7. C₅₃×#3280	C₂	semidirect
8. C₅₃×#3250	C₂	semidirect
9. C₅₃×#3191	C₂	semidirect
10. C₅₃×#3187	C₂	semidirect
11. C₅₃×#3168	C₂	semidirect
12. C₅₃×#3050	C₂	semidirect
13. C₂×C₅₃×#467	C₂	semidirect
14. C₂×C₅₃×#466	C₂	semidirect
15. C₂×C₈×D₄×C₅₃	C₂	semidirect
16. C₂×#135×C₅₃	C₂²	semidirect
17. C₂²×Q₁₆×C₅₃	C₂²	semidirect
18. C₂²×D₈×C₅₃	C₂²	semidirect
20. C₂³×C₈×C₅₃	C₂²	semidirect
22. C₅₃×#553	C₂²	semidirect
25. C₅₃×#548	C₂²	semidirect
30. C₅₃×#529	C₂²	semidirect
31. C₅₃×#525	C₂²	semidirect
36. C₅₃×#499	C₂²	semidirect
37. C₅₃×#495	C₂²	semidirect
38. C₅₃×#488	C₂²	semidirect
39. C₅₃×#485	C₂²	semidirect
40. C₅₃×#483	C₂²	semidirect
41. C₅₃×#482	C₂²	semidirect
42. C₅₃×#481	C₂²	semidirect
43. C₅₃×#479	C₂²	semidirect
44. C₅₃×#478	C₂²	semidirect
45. C₅₃×#467	C₂²	semidirect
46. C₅₃×#467	C₂²	semidirect
47. C₅₃×#467	C₂²	semidirect
48. C₅₃×#467	C₂²	semidirect
49. C₅₃×#467	C₂²	semidirect
52. C₅₃×#466	C₂²	semidirect
53. C₅₃×#466	C₂²	semidirect
54. C₅₃×#466	C₂²	semidirect
55. C₅₃×#465	C₂²	semidirect
56. C₅₃×#465	C₂²	semidirect
57. C₅₃×#465	C₂²	semidirect
58. C₅₃×#464	C₂²	semidirect
59. C₅₃×#463	C₂²	semidirect
60. C₅₃×#452	C₂²	semidirect
61. C₅₃×#450	C₂²	semidirect
62. C₅₃×#449	C₂²	semidirect
63. C₅₃×#448	C₂²	semidirect
64. C₄×Q₁₆×C₅₃	C₂²	semidirect
65. C₄×SD₁₆×C₅₃	C₂²	semidirect
66. C₄×D₈×C₅₃	C₂²	semidirect
69. C₈×D₄×C₅₃	C₂²	semidirect
70. C₈×D₄×C₅₃	C₂²	semidirect
71. C₅₃×#427	C₂²	semidirect
72. C₂×#107×C₅₃	C₂²	semidirect
73. C₂×#107×C₅₃	C₂²	semidirect
74. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
75. C₅₃×#416	C₂²	semidirect
76. C₂×#103×C₅₃	C₂²	semidirect
77. C₂×#102×C₅₃	C₂²	semidirect
79. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
80. C₂×C₄×C₈×C₅₃	C₂²	semidirect
285. C₂³×C₅₃	#135	semidirect
338. #62247	C₅₃	direct (N × H)
369. #3505	C₂×C₅₃	semidirect
370. #3339	C₂×C₅₃	semidirect
371. #3336	C₂×C₅₃	semidirect
372. #3301	C₂×C₅₃	semidirect
373. #3296	C₂×C₅₃	semidirect
374. #3285	C₂×C₅₃	semidirect
375. #3280	C₂×C₅₃	semidirect
376. #3250	C₂×C₅₃	semidirect
377. #3191	C₂×C₅₃	semidirect
378. #3187	C₂×C₅₃	semidirect
379. #3168	C₂×C₅₃	semidirect
380. #3050	C₂×C₅₃	semidirect
381. C₂×#467	C₂×C₅₃	semidirect
382. C₂×#466	C₂×C₅₃	semidirect
383. C₂×C₈×D₄	C₂×C₅₃	semidirect
392. C₂×#135	C₂²×C₅₃	semidirect
393. C₂²×Q₁₆	C₂²×C₅₃	semidirect
394. C₂²×D₈	C₂²×C₅₃	semidirect
396. C₂³×C₈	C₂²×C₅₃	semidirect
398. #553	C₂²×C₅₃	semidirect
401. #548	C₂²×C₅₃	semidirect
406. #529	C₂²×C₅₃	semidirect
407. #525	C₂²×C₅₃	semidirect
412. #499	C₂²×C₅₃	semidirect
413. #495	C₂²×C₅₃	semidirect
414. #488	C₂²×C₅₃	semidirect
415. #485	C₂²×C₅₃	semidirect
416. #483	C₂²×C₅₃	semidirect
417. #482	C₂²×C₅₃	semidirect
418. #481	C₂²×C₅₃	semidirect
419. #479	C₂²×C₅₃	semidirect
420. #478	C₂²×C₅₃	semidirect
421. #467	C₂²×C₅₃	semidirect
422. #467	C₂²×C₅₃	semidirect
423. #467	C₂²×C₅₃	semidirect
424. #467	C₂²×C₅₃	semidirect
425. #467	C₂²×C₅₃	semidirect
428. #466	C₂²×C₅₃	semidirect
429. #466	C₂²×C₅₃	semidirect
430. #466	C₂²×C₅₃	semidirect
431. #465	C₂²×C₅₃	semidirect
432. #465	C₂²×C₅₃	semidirect
433. #465	C₂²×C₅₃	semidirect
434. #464	C₂²×C₅₃	semidirect
435. #463	C₂²×C₅₃	semidirect
436. #452	C₂²×C₅₃	semidirect
437. #450	C₂²×C₅₃	semidirect
438. #449	C₂²×C₅₃	semidirect
439. #448	C₂²×C₅₃	semidirect
440. C₄×Q₁₆	C₂²×C₅₃	semidirect
441. C₄×SD₁₆	C₂²×C₅₃	semidirect
442. C₄×D₈	C₂²×C₅₃	semidirect
445. C₈×D₄	C₂²×C₅₃	semidirect
446. C₈×D₄	C₂²×C₅₃	semidirect
447. #427	C₂²×C₅₃	semidirect
448. C₂×#107	C₂²×C₅₃	semidirect
449. C₂×#107	C₂²×C₅₃	semidirect
450. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
451. #416	C₂²×C₅₃	semidirect
452. C₂×#103	C₂²×C₅₃	semidirect
453. C₂×#102	C₂²×C₅₃	semidirect
455. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
456. C₂×C₄×C₈	C₂²×C₅₃	semidirect
457. C₅₃	#62247	direct (N × H)
662. C₂³	#135×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3505	2
C₅₃×#3339	2
C₅₃×#3336	2
C₅₃×#3301	2
C₅₃×#3296	2
C₅₃×#3285	2
C₅₃×#3280	2
C₅₃×#3250	2
C₅₃×#3191	2
C₅₃×#3187	2
C₅₃×#3168	2
C₅₃×#3050	2
C₂×C₅₃×#467	2
C₂×C₅₃×#466	2
C₂×C₈×D₄×C₅₃	2
#62247	53

Subgroups — C53×#62247 #27269759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62247 #27269759