Subgroups — C₅₃×#18516 #27226028

Order 13568.

1258 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1639	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1625	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1619	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1540	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₃	—	2	1	no	—
17	C₂×#135×C₅₃	—	2	1	no	—
18	C₅₃×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#548	—	2	1	no	—
21	C₅₃×#547	—	2	1	no	—
22	C₅₃×#547	C₂²	1	1	yes	characteristic
23	C₅₃×#546	—	2	2	no	—
24	C₅₃×#546	—	2	1	no	—
25	D₄²×C₅₃	—	2	1	no	—
26	D₄²×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#532	—	2	1	no	—
28	C₅₃×#532	C₂²	1	1	yes	characteristic
29	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#525	—	2	2	no	—
31	C₅₃×#525	—	2	1	no	—
32	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₃	—	2	1	no	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#480	—	2	1	no	—
40	C₅₃×#474	C₂²	1	1	yes	characteristic
41	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#466	—	2	2	no	—
43	C₅₃×#464	—	2	1	no	—
44	C₅₃×#463	—	2	1	no	—
45	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#459	C₂²	1	1	yes	characteristic
49	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#447	—	2	1	no	—
52	C₄×D₈×C₅₃	—	2	1	no	—
53	C₄×D₈×C₅₃	—	2	1	no	—
54	C₄×D₈×C₅₃	—	2	2	no	—
55	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#416	—	2	1	no	—
58	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#332	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#332	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#331	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#331	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₅₃	—	2	2	no	—
72	C₂×#41×C₅₃	—	2	2	no	—
73	C₂×#41×C₅₃	—	2	1	no	—
74	C₂×#41×C₅₃	—	2	1	no	—
75	C₂×#41×C₅₃	—	2	1	no	—
76	C₂×#41×C₅₃	—	2	1	no	—
77	C₂×#41×C₅₃	—	4	4	no	—
78	C₂×#41×C₅₃	—	4	4	no	—
79	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
80	C₂²×Q₈×C₅₃	—	2	1	no	—
81	C₂²×D₄×C₅₃	—	2	2	no	—
82	C₂²×D₄×C₅₃	—	2	1	no	—
83	C₂²×D₄×C₅₃	—	2	1	no	—
84	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₅₃	—	2	2	no	—
86	C₂³×C₄×C₅₃	—	2	1	no	—
87	#135×C₅₃	—	4	4	no	—
88	C₂×Q₁₆×C₅₃	—	2	1	no	—
89	C₂×SD₁₆×C₅₃	—	2	1	no	—
90	C₂×SD₁₆×C₅₃	—	2	1	no	—
91	C₂×D₈×C₅₃	—	2	2	no	—
92	C₂×D₈×C₅₃	—	2	1	no	—
93	C₂×D₈×C₅₃	—	2	1	no	—
94	C₂×D₈×C₅₃	—	2	1	no	—
95	C₂²×C₈×C₅₃	—	2	1	no	—
96	C₂²×C₈×C₅₃	—	2	1	no	—
97	C₄⋊Q₈×C₅₃	—	2	1	no	—
98	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
100	#127×C₅₃	—	2	1	no	—
101	#127×C₅₃	C₂³	1	1	yes	characteristic
102	#127×C₅₃	C₂³	1	1	yes	characteristic
103	#124×C₅₃	—	2	2	no	—
104	#124×C₅₃	—	2	1	no	—
105	#124×C₅₃	—	2	1	no	—
106	#123×C₅₃	—	2	2	no	—
107	#123×C₅₃	—	2	2	no	—
108	#123×C₅₃	—	2	2	no	—
109	C₂²⋊Q₈×C₅₃	—	2	2	no	—
110	C₂²⋊Q₈×C₅₃	—	2	2	no	—
111	C₂²⋊Q₈×C₅₃	—	2	1	no	—
112	C₂²⋊Q₈×C₅₃	—	2	1	no	—
113	#121×C₅₃	—	2	2	no	—
114	#121×C₅₃	—	2	2	no	—
115	#121×C₅₃	—	2	1	no	—
116	#121×C₅₃	—	2	1	no	—
117	#121×C₅₃	—	2	1	no	—
118	#121×C₅₃	—	2	2	no	—
119	#121×C₅₃	—	2	1	no	—
120	#121×C₅₃	—	2	1	no	—
121	#121×C₅₃	—	2	1	no	—
122	#121×C₅₃	—	2	1	no	—
123	#121×C₅₃	D₄	1	2	yes	—
124	#120×C₅₃	—	2	2	no	—
125	#120×C₅₃	—	2	2	no	—
126	#120×C₅₃	—	2	2	no	—
127	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
128	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
129	C₄×D₄×C₅₃	—	2	2	no	—
130	C₄×D₄×C₅₃	—	2	2	no	—
131	C₄×D₄×C₅₃	—	2	2	no	—
132	C₄×D₄×C₅₃	—	2	1	no	—
133	C₄×D₄×C₅₃	—	2	1	no	—
134	C₄×D₄×C₅₃	—	2	1	no	—
135	C₄×D₄×C₅₃	—	2	1	no	—
136	C₄×D₄×C₅₃	—	2	1	no	—
137	C₄×D₄×C₅₃	—	2	1	no	—
138	C₄×D₄×C₅₃	—	2	1	no	—
139	C₄×D₄×C₅₃	—	2	1	no	—
140	C₄×D₄×C₅₃	—	2	1	no	—
141	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
142	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
143	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
144	C₄×D₄×C₅₃	D₄	1	2	yes	—
145	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
148	#117×C₅₃	—	2	1	no	—
149	#117×C₅₃	D₄	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
151	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
153	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
154	C₂×C₄²×C₅₃	—	2	1	no	—
155	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
156	#107×C₅₃	—	2	2	no	—
157	#107×C₅₃	—	2	1	no	—
158	#107×C₅₃	—	2	1	no	—
159	C₄⋊C₈×C₅₃	—	2	1	no	—
160	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
163	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
164	#103×C₅₃	—	2	1	no	—
165	#103×C₅₃	—	2	1	no	—
166	#102×C₅₃	—	2	2	no	—
167	#102×C₅₃	—	2	1	no	—
168	#102×C₅₃	—	2	1	no	—
169	#102×C₅₃	—	2	1	no	—
170	#102×C₅₃	—	2	1	no	—
171	#102×C₅₃	—	2	2	no	—
172	#102×C₅₃	—	2	1	no	—
173	#102×C₅₃	—	2	1	no	—
174	C₂²⋊C₈×C₅₃	—	2	1	no	—
175	C₄×C₈×C₅₃	—	2	1	no	—
176	C₄×C₈×C₅₃	—	2	1	no	—
177	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
179	C₂⁴×C₅₃	—	2	2	no	—
180	C₂⁴×C₅₃	—	2	1	no	—
181	#41×C₅₃	—	2	2	no	—
182	#41×C₅₃	—	4	8	no	—
183	#41×C₅₃	—	4	8	no	—
184	#41×C₅₃	—	4	2	no	—
185	#41×C₅₃	—	4	2	no	—
186	#41×C₅₃	—	4	2	no	—
187	#41×C₅₃	—	4	2	no	—
188	#41×C₅₃	—	4	2	no	—
189	#41×C₅₃	—	4	2	no	—
190	#41×C₅₃	—	4	2	no	—
191	#41×C₅₃	—	4	2	no	—
192	#41×C₅₃	D₈	1	4	yes	complemented
193	C₂×Q₈×C₅₃	—	2	2	no	—
194	C₂×Q₈×C₅₃	—	2	1	no	—
195	C₂×Q₈×C₅₃	—	2	1	no	—
196	C₂×Q₈×C₅₃	—	4	2	no	—
197	C₂×Q₈×C₅₃	—	4	2	no	—
198	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₅₃	—	2	1	no	—
200	C₂×D₄×C₅₃	—	2	2	no	—
201	C₂×D₄×C₅₃	—	2	2	no	—
202	C₂×D₄×C₅₃	—	2	2	no	—
203	C₂×D₄×C₅₃	—	2	2	no	—
204	C₂×D₄×C₅₃	—	2	2	no	—
205	C₂×D₄×C₅₃	—	2	2	no	—
206	C₂×D₄×C₅₃	—	2	2	no	—
207	C₂×D₄×C₅₃	—	2	1	no	—
208	C₂×D₄×C₅₃	—	2	1	no	—
209	C₂×D₄×C₅₃	—	2	1	no	—
210	C₂×D₄×C₅₃	—	2	1	no	—
211	C₂×D₄×C₅₃	—	2	1	no	—
212	C₂×D₄×C₅₃	—	2	1	no	—
213	C₂×D₄×C₅₃	—	4	1	no	—
214	C₂×D₄×C₅₃	—	4	2	no	—
215	C₂×D₄×C₅₃	—	4	8	no	—
216	C₂×D₄×C₅₃	—	4	2	no	—
217	C₂×D₄×C₅₃	—	4	2	no	—
218	C₂×D₄×C₅₃	—	4	2	no	—
219	C₂×D₄×C₅₃	—	4	1	no	—
220	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₅₃	—	2	1	no	—
225	C₂²×C₄×C₅₃	—	2	2	no	—
226	C₂²×C₄×C₅₃	—	2	2	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	2	1	no	—
229	C₂²×C₄×C₅₃	—	2	1	no	—
230	C₂²×C₄×C₅₃	—	2	2	no	—
231	C₂²×C₄×C₅₃	—	2	1	no	—
232	C₂²×C₄×C₅₃	—	2	1	no	—
233	C₂²×C₄×C₅₃	—	2	1	no	—
234	C₂²×C₄×C₅₃	—	2	1	no	—
235	C₂²×C₄×C₅₃	—	2	1	no	—
236	C₂²×C₄×C₅₃	—	4	8	no	—
237	C₂²×C₄×C₅₃	—	4	2	no	—
238	C₂²×C₄×C₅₃	—	4	2	no	—
239	C₂²×C₄×C₅₃	—	4	1	no	—
240	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
243	Q₁₆×C₅₃	—	4	2	no	—
244	SD₁₆×C₅₃	—	4	2	no	—
245	SD₁₆×C₅₃	—	4	2	no	—
246	D₈×C₅₃	—	4	4	no	—
247	D₈×C₅₃	—	4	2	no	—
248	D₈×C₅₃	—	4	2	no	—
249	D₈×C₅₃	—	4	2	no	—
250	C₂×C₈×C₅₃	—	2	1	no	—
251	C₂×C₈×C₅₃	—	2	1	no	—
252	C₂×C₈×C₅₃	—	2	1	no	—
253	C₂×C₈×C₅₃	—	2	1	no	—
254	C₂×C₈×C₅₃	—	2	1	no	—
255	C₂×C₈×C₅₃	—	2	1	no	—
256	C₂×C₈×C₅₃	—	4	2	no	—
257	C₂×C₈×C₅₃	—	4	2	no	—
258	C₄⋊C₄×C₅₃	—	2	2	no	—
259	C₄⋊C₄×C₅₃	—	2	2	no	—
260	C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₄⋊C₄×C₅₃	—	2	1	no	—
262	C₄⋊C₄×C₅₃	—	2	1	no	—
263	C₄⋊C₄×C₅₃	—	2	1	no	—
264	C₄⋊C₄×C₅₃	—	2	1	no	—
265	C₄⋊C₄×C₅₃	—	2	1	no	—
266	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
269	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
270	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂²⋊C₄×C₅₃	—	2	2	no	—
273	C₂²⋊C₄×C₅₃	—	2	2	no	—
274	C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂²⋊C₄×C₅₃	—	2	1	no	—
276	C₂²⋊C₄×C₅₃	—	2	1	no	—
277	C₂²⋊C₄×C₅₃	—	2	2	no	—
278	C₂²⋊C₄×C₅₃	—	2	1	no	—
279	C₂²⋊C₄×C₅₃	—	2	1	no	—
280	C₂²⋊C₄×C₅₃	—	2	2	no	—
281	C₂²⋊C₄×C₅₃	—	2	1	no	—
282	C₂²⋊C₄×C₅₃	—	2	1	no	—
283	C₂²⋊C₄×C₅₃	—	2	1	no	—
284	C₂²⋊C₄×C₅₃	—	4	1	no	—
285	C₂²⋊C₄×C₅₃	—	4	1	no	—
286	C₄²×C₅₃	—	2	1	no	—
287	C₄²×C₅₃	—	2	1	no	—
288	C₄²×C₅₃	—	2	1	no	—
289	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
293	C₂³×C₅₃	—	2	1	no	—
294	C₂³×C₅₃	—	2	1	no	—
295	C₂³×C₅₃	—	2	1	no	—
296	C₂³×C₅₃	—	2	2	no	—
297	C₂³×C₅₃	—	4	2	no	—
298	C₂³×C₅₃	—	4	4	no	—
299	C₂³×C₅₃	—	4	4	no	—
300	C₂³×C₅₃	—	4	2	no	—
301	C₂³×C₅₃	—	4	1	no	—
302	C₂³×C₅₃	—	8	1	no	—
303	C₂³×C₅₃	—	8	2	no	—
304	C₂³×C₅₃	#120	1	1	yes	characteristic
305	Q₈×C₅₃	—	2	1	no	—
306	Q₈×C₅₃	—	4	4	no	—
307	Q₈×C₅₃	—	4	1	no	—
308	Q₈×C₅₃	—	4	1	no	—
309	Q₈×C₅₃	—	4	1	no	—
310	Q₈×C₅₃	—	4	1	no	—
311	Q₈×C₅₃	C₂×D₈	1	2	yes	—
312	D₄×C₅₃	—	2	4	no	—
313	D₄×C₅₃	—	2	1	no	—
314	D₄×C₅₃	—	2	1	no	—
315	D₄×C₅₃	—	2	1	no	—
316	D₄×C₅₃	—	2	1	no	—
317	D₄×C₅₃	—	4	2	no	—
318	D₄×C₅₃	—	4	2	no	—
319	D₄×C₅₃	—	4	4	no	—
320	D₄×C₅₃	—	4	2	no	—
321	D₄×C₅₃	—	4	4	no	—
322	D₄×C₅₃	—	4	4	no	—
323	D₄×C₅₃	—	4	4	no	—
324	D₄×C₅₃	—	4	4	no	—
325	D₄×C₅₃	—	4	1	no	—
326	D₄×C₅₃	—	4	1	no	—
327	D₄×C₅₃	—	4	1	no	—
328	D₄×C₅₃	—	4	1	no	—
329	D₄×C₅₃	—	4	1	no	—
330	D₄×C₅₃	—	4	1	no	—
331	D₄×C₅₃	—	4	1	no	—
332	D₄×C₅₃	—	4	1	no	—
333	D₄×C₅₃	—	8	2	no	—
334	D₄×C₅₃	—	8	2	no	—
335	D₄×C₅₃	C₂×D₈	1	2	yes	—
336	D₄×C₅₃	#135	1	2	yes	complemented
337	C₂×C₄×C₅₃	—	2	1	no	—
338	C₂×C₄×C₅₃	—	2	1	no	—
339	C₂×C₄×C₅₃	—	2	1	no	—
340	C₂×C₄×C₅₃	—	2	4	no	—
341	C₂×C₄×C₅₃	—	2	1	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	1	no	—
344	C₂×C₄×C₅₃	—	2	1	no	—
345	C₂×C₄×C₅₃	—	2	1	no	—
346	C₂×C₄×C₅₃	—	4	1	no	—
347	C₂×C₄×C₅₃	—	4	4	no	—
348	C₂×C₄×C₅₃	—	4	4	no	—
349	C₂×C₄×C₅₃	—	4	4	no	—
350	C₂×C₄×C₅₃	—	4	2	no	—
351	C₂×C₄×C₅₃	—	4	1	no	—
352	C₂×C₄×C₅₃	—	4	1	no	—
353	C₂×C₄×C₅₃	—	4	1	no	—
354	C₂×C₄×C₅₃	—	4	1	no	—
355	C₂×C₄×C₅₃	—	4	1	no	—
356	C₂×C₄×C₅₃	—	4	1	no	—
357	C₂×C₄×C₅₃	—	4	2	no	—
358	C₂×C₄×C₅₃	—	4	4	no	—
359	C₂×C₄×C₅₃	—	4	2	no	—
360	C₂×C₄×C₅₃	—	4	1	no	—
361	C₂×C₄×C₅₃	—	8	1	no	—
362	C₂×C₄×C₅₃	—	8	2	no	—
363	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
364	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
365	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
366	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
367	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
371	C₈×C₅₃	—	2	2	no	—
372	C₈×C₅₃	—	4	1	no	—
373	C₈×C₅₃	—	4	1	no	—
374	C₈×C₅₃	—	4	1	no	—
375	C₈×C₅₃	—	4	1	no	—
376	C₈×C₅₃	—	4	1	no	—
377	#18516	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂²×C₅₃	—	2	1	no	—
379	C₂²×C₅₃	—	2	1	no	—
380	C₂²×C₅₃	—	2	2	no	—
381	C₂²×C₅₃	—	2	2	no	—
382	C₂²×C₅₃	—	4	1	no	—
383	C₂²×C₅₃	—	4	1	no	—
384	C₂²×C₅₃	—	4	1	no	—
385	C₂²×C₅₃	—	4	1	no	—
386	C₂²×C₅₃	—	4	2	no	—
387	C₂²×C₅₃	—	4	1	no	—
388	C₂²×C₅₃	—	4	1	no	—
389	C₂²×C₅₃	—	4	2	no	—
390	C₂²×C₅₃	—	4	2	no	—
391	C₂²×C₅₃	—	4	1	no	—
392	C₂²×C₅₃	—	8	4	no	—
393	C₂²×C₅₃	—	8	8	no	—
394	C₂²×C₅₃	—	8	1	no	—
395	C₂²×C₅₃	—	8	1	no	—
396	C₂²×C₅₃	—	8	1	no	—
397	C₂²×C₅₃	#447	1	2	yes	—
398	C₂²×C₅₃	C₂×#120	1	1	yes	characteristic
399	C₄×C₅₃	—	2	2	no	—
400	C₄×C₅₃	—	2	1	no	—
401	C₄×C₅₃	—	2	1	no	—
402	C₄×C₅₃	—	2	1	no	—
403	C₄×C₅₃	—	4	1	no	—
404	C₄×C₅₃	—	4	2	no	—
405	C₄×C₅₃	—	4	1	no	—
406	C₄×C₅₃	—	4	1	no	—
407	C₄×C₅₃	—	4	1	no	—
408	C₄×C₅₃	—	8	1	no	—
409	C₄×C₅₃	#447	1	2	yes	—
410	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
411	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
412	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
413	C₄×C₅₃	#575	1	1	yes	characteristic
414	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
415	#3169	C₂×C₅₃	1	1	yes	characteristic, complemented
416	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
417	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
418	#1649	C₂×C₅₃	1	1	yes	characteristic, complemented
419	#1647	C₂×C₅₃	1	1	yes	characteristic, complemented
420	#1641	C₂×C₅₃	1	1	yes	characteristic, complemented
421	#1639	C₂×C₅₃	1	1	yes	characteristic, complemented
422	#1627	C₂×C₅₃	1	1	yes	characteristic, complemented
423	#1625	C₂×C₅₃	1	1	yes	characteristic, complemented
424	#1621	C₂×C₅₃	1	1	yes	characteristic, complemented
425	#1619	C₂×C₅₃	1	1	yes	characteristic, complemented
426	#1540	C₂×C₅₃	1	1	yes	characteristic, complemented
427	#1476	C₂×C₅₃	1	1	yes	characteristic, complemented
428	C₂×D₄⋊C₈	C₂×C₅₃	1	1	yes	characteristic, complemented
429	C₂×C₅₃	—	2	2	no	—
430	C₂×C₅₃	—	4	2	no	—
431	C₂×C₅₃	—	4	2	no	—
432	C₂×C₅₃	—	8	1	no	—
433	C₂×C₅₃	—	8	2	no	—
434	C₂×C₅₃	—	16	1	no	—
435	C₂×C₅₃	C₂×#447	1	1	yes	characteristic
436	C₂×C₅₃	#3002	1	1	yes	characteristic
437	C₂×C₅₃	#3018	1	1	yes	characteristic
438	C₂²×#41	—	2	1	no	—
439	C₂×#135	—	2	1	no	—
440	#550	C₂²×C₅₃	1	1	yes	characteristic
441	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
442	#548	—	2	1	no	—
443	#547	—	2	1	no	—
444	#547	C₂²×C₅₃	1	1	yes	characteristic
445	#546	—	2	2	no	—
446	#546	—	2	1	no	—
447	D₄²	—	2	1	no	—
448	D₄²	C₂²×C₅₃	1	1	yes	characteristic
449	#532	—	2	1	no	—
450	#532	C₂²×C₅₃	1	1	yes	characteristic
451	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
452	#525	—	2	2	no	—
453	#525	—	2	1	no	—
454	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
455	C₂×C₄×D₄	—	2	1	no	—
456	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
457	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
458	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
459	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
460	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
461	#480	—	2	1	no	—
462	#474	C₂²×C₅₃	1	1	yes	characteristic
463	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
464	#466	—	2	2	no	—
465	#464	—	2	1	no	—
466	#463	—	2	1	no	—
467	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
468	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
469	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
470	#459	C₂²×C₅₃	1	1	yes	characteristic
471	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
472	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
473	#447	—	2	1	no	—
474	C₄×D₈	—	2	1	no	—
475	C₄×D₈	—	2	1	no	—
476	C₄×D₈	—	2	2	no	—
477	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
478	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
479	#416	—	2	1	no	—
480	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
481	#332	C₂²×C₅₃	1	1	yes	characteristic, complemented
482	#332	C₂²×C₅₃	1	1	yes	characteristic, complemented
483	#331	C₂²×C₅₃	1	1	yes	characteristic, complemented
484	#331	C₂²×C₅₃	1	1	yes	characteristic, complemented
485	Q₈⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
486	Q₈⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
487	D₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
488	D₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
489	D₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
490	D₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
491	D₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
492	D₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
493	C₅₃	#18516	1	1	yes	characteristic, direct product factor, Sylow
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	1	no	—
497	C₂×#41	—	2	1	no	—
498	C₂×#41	—	2	1	no	—
499	C₂×#41	—	2	1	no	—
500	C₂×#41	—	4	4	no	—
501	C₂×#41	—	4	4	no	—
502	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×D₄	—	2	2	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
508	C₂³×C₄	—	2	2	no	—
509	C₂³×C₄	—	2	1	no	—
510	#135	—	4	4	no	—
511	C₂×Q₁₆	—	2	1	no	—
512	C₂×SD₁₆	—	2	1	no	—
513	C₂×SD₁₆	—	2	1	no	—
514	C₂×D₈	—	2	1	no	—
515	C₂×D₈	—	2	1	no	—
516	C₂×D₈	—	2	1	no	—
517	C₂×D₈	—	2	2	no	—
518	C₂²×C₈	—	2	1	no	—
519	C₂²×C₈	—	2	1	no	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
523	#127	—	2	1	no	—
524	#127	C₂³×C₅₃	1	1	yes	characteristic
525	#127	C₂³×C₅₃	1	1	yes	characteristic
526	#124	—	2	2	no	—
527	#124	—	2	1	no	—
528	#124	—	2	1	no	—
529	#123	—	2	2	no	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#121	D₄×C₅₃	1	2	yes	—
547	#120	—	2	2	no	—
548	#120	—	2	2	no	—
549	#120	—	2	2	no	—
550	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
565	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
566	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
567	C₄×D₄	D₄×C₅₃	1	2	yes	—
568	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
569	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
570	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
571	#117	—	2	1	no	—
572	#117	D₄×C₅₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	—	2	2	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₄²	—	2	1	no	—
578	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
579	#107	—	2	2	no	—
580	#107	—	2	1	no	—
581	#107	—	2	1	no	—
582	C₄⋊C₈	—	2	1	no	—
583	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
584	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
585	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
586	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
587	#103	—	2	1	no	—
588	#103	—	2	1	no	—
589	#102	—	2	1	no	—
590	#102	—	2	1	no	—
591	#102	—	2	2	no	—
592	#102	—	2	1	no	—
593	#102	—	2	1	no	—
594	#102	—	2	1	no	—
595	#102	—	2	1	no	—
596	#102	—	2	2	no	—
597	C₂²⋊C₈	—	2	1	no	—
598	C₄×C₈	—	2	1	no	—
599	C₄×C₈	—	2	1	no	—
600	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
601	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	1	no	—
604	#41	—	2	2	no	—
605	#41	—	4	8	no	—
606	#41	—	4	8	no	—
607	#41	—	4	2	no	—
608	#41	—	4	2	no	—
609	#41	—	4	2	no	—
610	#41	—	4	2	no	—
611	#41	—	4	2	no	—
612	#41	—	4	2	no	—
613	#41	—	4	2	no	—
614	#41	—	4	2	no	—
615	#41	D₈×C₅₃	1	4	yes	complemented
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	—	4	2	no	—
621	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	4	1	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	8	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	1	no	—
643	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
644	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
645	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
646	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	4	8	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
666	Q₁₆	—	4	2	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	D₈	—	4	4	no	—
670	D₈	—	4	2	no	—
671	D₈	—	4	2	no	—
672	D₈	—	4	2	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	4	2	no	—
680	C₂×C₈	—	4	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
690	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
691	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
692	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	4	1	no	—
708	C₂²⋊C₄	—	4	1	no	—
709	C₄²	—	2	1	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
713	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
715	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	4	2	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	4	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	8	1	no	—
726	C₂³	—	8	2	no	—
727	C₂³	#120×C₅₃	1	1	yes	characteristic
728	Q₈	—	2	1	no	—
729	Q₈	—	4	4	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	Q₈	—	4	1	no	—
734	Q₈	C₂×D₈×C₅₃	1	2	yes	—
735	D₄	—	2	4	no	—
736	D₄	—	2	1	no	—
737	D₄	—	2	1	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	1	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	4	no	—
745	D₄	—	4	4	no	—
746	D₄	—	4	4	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	1	no	—
754	D₄	—	4	1	no	—
755	D₄	—	4	1	no	—
756	D₄	—	8	2	no	—
757	D₄	—	8	2	no	—
758	D₄	C₂×D₈×C₅₃	1	2	yes	—
759	D₄	#135×C₅₃	1	2	yes	complemented
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	8	1	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
787	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
788	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
789	C₂×C₄	C₂×D₈×C₅₃	1	2	yes	—
790	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
794	C₈	—	2	2	no	—
795	C₈	—	4	1	no	—
796	C₈	—	4	1	no	—
797	C₈	—	4	1	no	—
798	C₈	—	4	1	no	—
799	C₈	—	4	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	8	4	no	—
815	C₂²	—	8	8	no	—
816	C₂²	—	8	1	no	—
817	C₂²	—	8	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	C₅₃×#447	1	2	yes	—
820	C₂²	C₂×#120×C₅₃	1	1	yes	characteristic
821	C₄	—	2	2	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	8	1	no	—
831	C₄	C₅₃×#447	1	2	yes	—
832	C₄	C₂²×D₈×C₅₃	1	1	yes	characteristic
833	C₄	C₂×#135×C₅₃	1	1	yes	characteristic
834	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
835	C₄	C₅₃×#575	1	1	yes	characteristic
836	C₂	—	2	2	no	—
837	C₂	—	4	2	no	—
838	C₂	—	4	2	no	—
839	C₂	—	8	1	no	—
840	C₂	—	8	2	no	—
841	C₂	—	16	1	no	—
842	C₂	C₂×C₅₃×#447	1	1	yes	characteristic
843	C₂	C₅₃×#3002	1	1	yes	characteristic
844	C₂	C₅₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
socle	C₂²×C₅₃	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. D₄×#41×C₅₃	C₂	semidirect
2. C₅₃×#3169	C₂	semidirect
3. C₅₃×#3100	C₂	semidirect
4. C₅₃×#3035	C₂	semidirect
5. C₅₃×#1649	C₂	semidirect
6. C₅₃×#1647	C₂	semidirect
7. C₅₃×#1641	C₂	semidirect
8. C₅₃×#1639	C₂	semidirect
9. C₅₃×#1627	C₂	semidirect
10. C₅₃×#1625	C₂	semidirect
11. C₅₃×#1621	C₂	semidirect
12. C₅₃×#1619	C₂	semidirect
13. C₅₃×#1540	C₂	semidirect
14. C₅₃×#1476	C₂	semidirect
15. C₂×C₅₃×D₄⋊C₈	C₂	semidirect
29. C₅₃×#532	C₂²	semidirect
35. C₅₃×#500	C₂²	semidirect
36. C₅₃×#493	C₂²	semidirect
37. C₅₃×#486	C₂²	semidirect
38. C₅₃×#486	C₂²	semidirect
41. C₅₃×#474	C₂²	semidirect
45. C₅₃×#462	C₂²	semidirect
46. C₅₃×#461	C₂²	semidirect
47. C₅₃×#460	C₂²	semidirect
49. C₅₃×#459	C₂²	semidirect
50. C₅₃×#459	C₂²	semidirect
55. C₅₃×#431	C₂²	semidirect
56. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
58. C₂×C₄×C₈×C₅₃	C₂²	semidirect
59. C₅₃×#332	C₂²	semidirect
60. C₅₃×#332	C₂²	semidirect
61. C₅₃×#331	C₂²	semidirect
62. C₅₃×#331	C₂²	semidirect
63. C₅₃×Q₈⋊C₈	C₂²	semidirect
64. C₅₃×Q₈⋊C₈	C₂²	semidirect
67. C₅₃×D₄⋊C₈	C₂²	semidirect
68. C₅₃×D₄⋊C₈	C₂²	semidirect
69. C₅₃×D₄⋊C₈	C₂²	semidirect
70. C₅₃×D₄⋊C₈	C₂²	semidirect
192. #41×C₅₃	D₈	semidirect
336. D₄×C₅₃	#135	semidirect
377. #18516	C₅₃	direct (N × H)
414. D₄×#41	C₂×C₅₃	semidirect
415. #3169	C₂×C₅₃	semidirect
416. #3100	C₂×C₅₃	semidirect
417. #3035	C₂×C₅₃	semidirect
418. #1649	C₂×C₅₃	semidirect
419. #1647	C₂×C₅₃	semidirect
420. #1641	C₂×C₅₃	semidirect
421. #1639	C₂×C₅₃	semidirect
422. #1627	C₂×C₅₃	semidirect
423. #1625	C₂×C₅₃	semidirect
424. #1621	C₂×C₅₃	semidirect
425. #1619	C₂×C₅₃	semidirect
426. #1540	C₂×C₅₃	semidirect
427. #1476	C₂×C₅₃	semidirect
428. C₂×D₄⋊C₈	C₂×C₅₃	semidirect
451. #532	C₂²×C₅₃	semidirect
457. #500	C₂²×C₅₃	semidirect
458. #493	C₂²×C₅₃	semidirect
459. #486	C₂²×C₅₃	semidirect
460. #486	C₂²×C₅₃	semidirect
463. #474	C₂²×C₅₃	semidirect
467. #462	C₂²×C₅₃	semidirect
468. #461	C₂²×C₅₃	semidirect
469. #460	C₂²×C₅₃	semidirect
471. #459	C₂²×C₅₃	semidirect
472. #459	C₂²×C₅₃	semidirect
477. #431	C₂²×C₅₃	semidirect
478. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
480. C₂×C₄×C₈	C₂²×C₅₃	semidirect
481. #332	C₂²×C₅₃	semidirect
482. #332	C₂²×C₅₃	semidirect
483. #331	C₂²×C₅₃	semidirect
484. #331	C₂²×C₅₃	semidirect
485. Q₈⋊C₈	C₂²×C₅₃	semidirect
486. Q₈⋊C₈	C₂²×C₅₃	semidirect
489. D₄⋊C₈	C₂²×C₅₃	semidirect
490. D₄⋊C₈	C₂²×C₅₃	semidirect
491. D₄⋊C₈	C₂²×C₅₃	semidirect
492. D₄⋊C₈	C₂²×C₅₃	semidirect
493. C₅₃	#18516	direct (N × H)
615. #41	D₈×C₅₃	semidirect
759. D₄	#135×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₅₃	2
C₅₃×#3169	2
C₅₃×#3100	2
C₅₃×#3035	2
C₅₃×#1649	2
C₅₃×#1647	2
C₅₃×#1641	2
C₅₃×#1639	2
C₅₃×#1627	2
C₅₃×#1625	2
C₅₃×#1621	2
C₅₃×#1619	2
C₅₃×#1540	2
C₅₃×#1476	2
C₂×C₅₃×D₄⋊C₈	2
#18516	53

Subgroups — C53×#18516 #27226028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#18516 #27226028