Subgroups — C₅₃×#24459 #27231971

Order 13568.

1362 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#576	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#455	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2003	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1792	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#576	—	2	4	no	—
19	C₅₃×#576	—	2	4	no	—
20	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
23	C₂×AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#135×C₅₃	—	2	1	no	—
27	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₈×C₅₃	—	2	1	no	—
30	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
34	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#471	—	2	4	no	—
37	C₅₃×#464	—	2	1	no	—
38	C₅₃×#463	—	2	1	no	—
39	C₅₃×#462	—	2	1	no	—
40	C₅₃×#461	—	2	1	no	—
41	C₅₃×#455	—	2	4	no	—
42	C₅₃×#452	—	2	1	no	—
43	C₅₃×#452	—	2	1	no	—
44	C₅₃×#450	—	2	1	no	—
45	C₅₃×#450	—	2	1	no	—
46	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
48	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#418	—	2	1	no	—
52	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#417	—	2	1	no	—
55	C₅₃×#417	C₂²	1	1	yes	characteristic
56	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#416	—	2	1	no	—
58	C₅₃×#416	C₂²	1	1	yes	characteristic
59	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×#102×C₅₃	—	2	1	no	—
61	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#101×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×#100×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#100×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#343	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#341	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#339	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
71	H(5,𝔽₂)×C₅₃	—	2	2	no	—
72	H(5,𝔽₂)×C₅₃	—	2	2	no	—
73	H(5,𝔽₂)×C₅₃	—	2	2	no	—
74	H(5,𝔽₂)×C₅₃	—	2	2	no	—
75	H(5,𝔽₂)×C₅₃	—	2	2	no	—
76	H(5,𝔽₂)×C₅₃	—	4	1	no	—
77	H(5,𝔽₂)×C₅₃	—	4	1	no	—
78	H(5,𝔽₂)×C₅₃	D₄	1	4	yes	—
79	C₂×#41×C₅₃	—	2	1	no	—
80	C₂×#41×C₅₃	—	2	1	no	—
81	C₂×#41×C₅₃	—	2	1	no	—
82	C₂×#41×C₅₃	—	2	1	no	—
83	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
84	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₅₃	—	2	1	no	—
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	—	2	1	no	—
90	C₂²×D₄×C₅₃	—	2	1	no	—
91	C₂²×D₄×C₅₃	—	4	1	no	—
92	C₂²×D₄×C₅₃	—	4	1	no	—
93	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
95	#137×C₅₃	—	2	2	no	—
96	#137×C₅₃	—	2	2	no	—
97	#137×C₅₃	—	2	2	no	—
98	#137×C₅₃	—	2	2	no	—
99	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
100	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
101	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
102	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
103	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
104	AGL(1,ℤ/8)×C₅₃	D₄	1	4	yes	—
105	#135×C₅₃	—	2	8	no	—
106	#135×C₅₃	—	2	2	no	—
107	#135×C₅₃	—	2	2	no	—
108	C₂×Q₁₆×C₅₃	—	2	1	no	—
109	C₂×Q₁₆×C₅₃	—	2	1	no	—
110	C₂×Q₁₆×C₅₃	D₄	1	1	yes	characteristic
111	C₂×SD₁₆×C₅₃	—	2	1	no	—
112	C₂×SD₁₆×C₅₃	—	2	1	no	—
113	C₂×SD₁₆×C₅₃	—	2	1	no	—
114	C₂×SD₁₆×C₅₃	—	2	1	no	—
115	C₂×SD₁₆×C₅₃	—	2	2	no	—
116	C₂×SD₁₆×C₅₃	—	2	1	no	—
117	C₂×SD₁₆×C₅₃	—	2	1	no	—
118	C₂×SD₁₆×C₅₃	—	4	1	no	—
119	C₂×SD₁₆×C₅₃	D₄	1	1	yes	characteristic
120	C₂×SD₁₆×C₅₃	D₄	1	1	yes	characteristic
121	C₂×D₈×C₅₃	—	2	8	no	—
122	C₂×D₈×C₅₃	—	2	1	no	—
123	C₂×D₈×C₅₃	—	2	1	no	—
124	C₂×D₈×C₅₃	—	2	1	no	—
125	C₂×D₈×C₅₃	—	2	1	no	—
126	C₂×D₈×C₅₃	—	2	2	no	—
127	C₂×D₈×C₅₃	—	2	2	no	—
128	C₂×D₈×C₅₃	D₄	1	1	yes	characteristic
129	#131×C₅₃	—	2	2	no	—
130	#131×C₅₃	—	2	2	no	—
131	#131×C₅₃	—	2	2	no	—
132	#131×C₅₃	—	4	1	no	—
133	C₂×M₁₆×C₅₃	—	2	1	no	—
134	C₂×M₁₆×C₅₃	—	2	1	no	—
135	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₅₃	—	2	1	no	—
140	C₂²×C₈×C₅₃	—	2	1	no	—
141	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈×C₅₃	—	2	1	no	—
144	#124×C₅₃	—	2	2	no	—
145	#124×C₅₃	—	2	1	no	—
146	#124×C₅₃	—	4	1	no	—
147	#123×C₅₃	—	4	1	no	—
148	C₂²⋊Q₈×C₅₃	—	2	1	no	—
149	C₂²⋊Q₈×C₅₃	—	2	1	no	—
150	C₄×Q₈×C₅₃	—	2	1	no	—
151	C₄×D₄×C₅₃	—	2	1	no	—
152	C₄×D₄×C₅₃	—	4	1	no	—
153	#117×C₅₃	—	2	1	no	—
154	#117×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₅₃	—	4	1	no	—
158	C₂×C₂²⋊C₄×C₅₃	—	4	1	no	—
159	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
160	#108×C₅₃	—	2	2	no	—
161	C₄⋊C₈×C₅₃	—	2	1	no	—
162	C₄⋊C₈×C₅₃	—	2	1	no	—
163	#104×C₅₃	—	2	2	no	—
164	#104×C₅₃	—	2	2	no	—
165	#104×C₅₃	—	4	1	no	—
166	#103×C₅₃	—	2	1	no	—
167	#103×C₅₃	—	2	1	no	—
168	#103×C₅₃	—	2	1	no	—
169	#103×C₅₃	—	2	1	no	—
170	#103×C₅₃	D₄	1	1	yes	characteristic
171	#103×C₅₃	D₄	1	1	yes	characteristic
172	#102×C₅₃	—	2	1	no	—
173	#102×C₅₃	—	2	1	no	—
174	#102×C₅₃	—	2	1	no	—
175	#102×C₅₃	—	2	1	no	—
176	#102×C₅₃	—	2	1	no	—
177	#102×C₅₃	—	2	1	no	—
178	#102×C₅₃	—	2	1	no	—
179	#102×C₅₃	—	2	1	no	—
180	#102×C₅₃	D₄	1	1	yes	characteristic
181	#102×C₅₃	D₄	1	1	yes	characteristic
182	#101×C₅₃	—	2	2	no	—
183	#100×C₅₃	—	2	2	no	—
184	#100×C₅₃	—	2	2	no	—
185	C₂²⋊C₈×C₅₃	—	2	1	no	—
186	C₂²⋊C₈×C₅₃	—	2	1	no	—
187	C₂⁴×C₅₃	—	2	1	no	—
188	C₂⁴×C₅₃	—	2	1	no	—
189	C₂⁴×C₅₃	—	4	1	no	—
190	C₂⁴×C₅₃	—	4	1	no	—
191	#41×C₅₃	—	2	1	no	—
192	#41×C₅₃	—	2	1	no	—
193	#41×C₅₃	—	2	1	no	—
194	#41×C₅₃	—	2	1	no	—
195	#41×C₅₃	—	2	4	no	—
196	#41×C₅₃	—	2	4	no	—
197	#41×C₅₃	—	2	4	no	—
198	#41×C₅₃	—	2	1	no	—
199	#41×C₅₃	—	2	1	no	—
200	#41×C₅₃	—	2	1	no	—
201	#41×C₅₃	—	2	1	no	—
202	#41×C₅₃	—	4	2	no	—
203	#41×C₅₃	—	4	2	no	—
204	#41×C₅₃	—	4	2	no	—
205	#41×C₅₃	—	4	2	no	—
206	#41×C₅₃	—	4	2	no	—
207	#41×C₅₃	C₂×D₄	1	2	yes	—
208	#41×C₅₃	C₂×D₄	1	2	yes	—
209	#41×C₅₃	C₂×D₄	1	2	yes	—
210	#41×C₅₃	#41	1	2	yes	—
211	C₂×Q₈×C₅₃	—	2	1	no	—
212	C₂×Q₈×C₅₃	—	2	1	no	—
213	C₂×Q₈×C₅₃	—	2	1	no	—
214	C₂×Q₈×C₅₃	—	2	1	no	—
215	C₂×Q₈×C₅₃	—	2	1	no	—
216	C₂×Q₈×C₅₃	—	2	1	no	—
217	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
218	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
219	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
220	C₂×D₄×C₅₃	—	2	1	no	—
221	C₂×D₄×C₅₃	—	2	1	no	—
222	C₂×D₄×C₅₃	—	2	4	no	—
223	C₂×D₄×C₅₃	—	2	4	no	—
224	C₂×D₄×C₅₃	—	2	4	no	—
225	C₂×D₄×C₅₃	—	2	1	no	—
226	C₂×D₄×C₅₃	—	2	1	no	—
227	C₂×D₄×C₅₃	—	2	1	no	—
228	C₂×D₄×C₅₃	—	2	1	no	—
229	C₂×D₄×C₅₃	—	2	1	no	—
230	C₂×D₄×C₅₃	—	2	1	no	—
231	C₂×D₄×C₅₃	—	2	1	no	—
232	C₂×D₄×C₅₃	—	2	1	no	—
233	C₂×D₄×C₅₃	—	2	1	no	—
234	C₂×D₄×C₅₃	—	2	1	no	—
235	C₂×D₄×C₅₃	—	2	1	no	—
236	C₂×D₄×C₅₃	—	4	2	no	—
237	C₂×D₄×C₅₃	—	4	2	no	—
238	C₂×D₄×C₅₃	—	4	2	no	—
239	C₂×D₄×C₅₃	—	4	1	no	—
240	C₂×D₄×C₅₃	—	4	1	no	—
241	C₂×D₄×C₅₃	—	4	1	no	—
242	C₂×D₄×C₅₃	—	4	1	no	—
243	C₂×D₄×C₅₃	—	4	4	no	—
244	C₂×D₄×C₅₃	—	4	2	no	—
245	C₂×D₄×C₅₃	—	4	4	no	—
246	C₂×D₄×C₅₃	—	4	4	no	—
247	C₂×D₄×C₅₃	—	4	4	no	—
248	C₂×D₄×C₅₃	—	4	2	no	—
249	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₅₃	—	2	1	no	—
255	C₂²×C₄×C₅₃	—	2	1	no	—
256	C₂²×C₄×C₅₃	—	2	1	no	—
257	C₂²×C₄×C₅₃	—	2	1	no	—
258	C₂²×C₄×C₅₃	—	2	1	no	—
259	C₂²×C₄×C₅₃	—	2	1	no	—
260	C₂²×C₄×C₅₃	—	4	1	no	—
261	C₂²×C₄×C₅₃	—	4	1	no	—
262	C₂²×C₄×C₅₃	—	4	1	no	—
263	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₅₃	—	2	2	no	—
265	Q₁₆×C₅₃	—	4	2	no	—
266	Q₁₆×C₅₃	—	4	2	no	—
267	SD₁₆×C₅₃	—	2	4	no	—
268	SD₁₆×C₅₃	—	2	4	no	—
269	SD₁₆×C₅₃	—	2	2	no	—
270	SD₁₆×C₅₃	—	2	2	no	—
271	SD₁₆×C₅₃	—	4	2	no	—
272	SD₁₆×C₅₃	—	4	2	no	—
273	SD₁₆×C₅₃	—	4	2	no	—
274	SD₁₆×C₅₃	—	4	2	no	—
275	D₈×C₅₃	—	2	4	no	—
276	D₈×C₅₃	—	2	4	no	—
277	D₈×C₅₃	—	2	4	no	—
278	D₈×C₅₃	—	2	2	no	—
279	D₈×C₅₃	—	2	4	no	—
280	M₁₆×C₅₃	—	2	4	no	—
281	M₁₆×C₅₃	—	2	1	no	—
282	M₁₆×C₅₃	—	2	1	no	—
283	M₁₆×C₅₃	—	2	1	no	—
284	M₁₆×C₅₃	—	2	1	no	—
285	M₁₆×C₅₃	—	2	1	no	—
286	M₁₆×C₅₃	—	2	1	no	—
287	M₁₆×C₅₃	—	2	1	no	—
288	M₁₆×C₅₃	—	4	2	no	—
289	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
290	C₂×C₈×C₅₃	—	2	4	no	—
291	C₂×C₈×C₅₃	—	2	1	no	—
292	C₂×C₈×C₅₃	—	2	1	no	—
293	C₂×C₈×C₅₃	—	2	1	no	—
294	C₂×C₈×C₅₃	—	2	1	no	—
295	C₂×C₈×C₅₃	—	2	1	no	—
296	C₂×C₈×C₅₃	—	2	1	no	—
297	C₂×C₈×C₅₃	—	2	1	no	—
298	C₂×C₈×C₅₃	—	2	1	no	—
299	C₂×C₈×C₅₃	—	4	2	no	—
300	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
302	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₅₃	—	2	1	no	—
305	C₄⋊C₄×C₅₃	—	2	1	no	—
306	C₄⋊C₄×C₅₃	—	4	1	no	—
307	C₄⋊C₄×C₅₃	—	4	1	no	—
308	C₄⋊C₄×C₅₃	—	4	1	no	—
309	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
311	C₂²⋊C₄×C₅₃	—	2	1	no	—
312	C₂²⋊C₄×C₅₃	—	4	1	no	—
313	C₂²⋊C₄×C₅₃	—	4	1	no	—
314	C₂²⋊C₄×C₅₃	—	4	1	no	—
315	C₂²⋊C₄×C₅₃	—	4	4	no	—
316	C₂²⋊C₄×C₅₃	—	8	2	no	—
317	C₄²×C₅₃	—	2	1	no	—
318	C₄²×C₅₃	—	2	1	no	—
319	C₄²×C₅₃	—	2	1	no	—
320	C₄²×C₅₃	—	4	1	no	—
321	C₂³×C₅₃	—	2	1	no	—
322	C₂³×C₅₃	—	2	1	no	—
323	C₂³×C₅₃	—	2	1	no	—
324	C₂³×C₅₃	—	2	2	no	—
325	C₂³×C₅₃	—	2	2	no	—
326	C₂³×C₅₃	—	4	4	no	—
327	C₂³×C₅₃	—	4	4	no	—
328	C₂³×C₅₃	—	4	1	no	—
329	C₂³×C₅₃	—	4	1	no	—
330	C₂³×C₅₃	—	4	1	no	—
331	C₂³×C₅₃	—	4	1	no	—
332	C₂³×C₅₃	—	8	1	no	—
333	C₂³×C₅₃	—	8	1	no	—
334	C₂³×C₅₃	—	8	1	no	—
335	C₂³×C₅₃	—	8	1	no	—
336	C₂³×C₅₃	—	16	1	no	—
337	C₂³×C₅₃	—	16	1	no	—
338	C₂³×C₅₃	—	16	1	no	—
339	C₂³×C₅₃	—	16	1	no	—
340	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
341	Q₈×C₅₃	—	2	1	no	—
342	Q₈×C₅₃	—	2	1	no	—
343	Q₈×C₅₃	—	2	1	no	—
344	Q₈×C₅₃	—	2	1	no	—
345	Q₈×C₅₃	—	4	1	no	—
346	Q₈×C₅₃	—	4	1	no	—
347	Q₈×C₅₃	—	4	1	no	—
348	Q₈×C₅₃	—	4	1	no	—
349	Q₈×C₅₃	#120	1	2	yes	—
350	Q₈×C₅₃	#121	1	2	yes	—
351	D₄×C₅₃	—	2	2	no	—
352	D₄×C₅₃	—	2	2	no	—
353	D₄×C₅₃	—	2	2	no	—
354	D₄×C₅₃	—	2	2	no	—
355	D₄×C₅₃	—	2	1	no	—
356	D₄×C₅₃	—	2	2	no	—
357	D₄×C₅₃	—	2	2	no	—
358	D₄×C₅₃	—	2	2	no	—
359	D₄×C₅₃	—	2	1	no	—
360	D₄×C₅₃	—	2	2	no	—
361	D₄×C₅₃	—	2	1	no	—
362	D₄×C₅₃	—	2	1	no	—
363	D₄×C₅₃	—	4	4	no	—
364	D₄×C₅₃	—	4	4	no	—
365	D₄×C₅₃	—	4	4	no	—
366	D₄×C₅₃	—	4	4	no	—
367	D₄×C₅₃	—	4	1	no	—
368	D₄×C₅₃	—	4	1	no	—
369	D₄×C₅₃	—	4	1	no	—
370	D₄×C₅₃	—	4	1	no	—
371	D₄×C₅₃	—	4	1	no	—
372	D₄×C₅₃	—	4	1	no	—
373	D₄×C₅₃	#120	1	2	yes	—
374	D₄×C₅₃	#121	1	2	yes	—
375	C₂×C₄×C₅₃	—	2	1	no	—
376	C₂×C₄×C₅₃	—	2	1	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	1	no	—
382	C₂×C₄×C₅₃	—	2	1	no	—
383	C₂×C₄×C₅₃	—	2	1	no	—
384	C₂×C₄×C₅₃	—	4	4	no	—
385	C₂×C₄×C₅₃	—	4	4	no	—
386	C₂×C₄×C₅₃	—	4	1	no	—
387	C₂×C₄×C₅₃	—	4	1	no	—
388	C₂×C₄×C₅₃	—	4	1	no	—
389	C₂×C₄×C₅₃	—	4	1	no	—
390	C₂×C₄×C₅₃	—	4	1	no	—
391	C₂×C₄×C₅₃	—	4	1	no	—
392	C₂×C₄×C₅₃	—	4	1	no	—
393	C₂×C₄×C₅₃	—	4	1	no	—
394	C₂×C₄×C₅₃	—	4	1	no	—
395	C₂×C₄×C₅₃	—	8	1	no	—
396	C₂×C₄×C₅₃	—	16	1	no	—
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
402	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
403	C₈×C₅₃	—	2	1	no	—
404	C₈×C₅₃	—	2	2	no	—
405	C₈×C₅₃	—	2	1	no	—
406	C₈×C₅₃	—	2	1	no	—
407	C₈×C₅₃	—	2	1	no	—
408	C₈×C₅₃	—	4	1	no	—
409	C₈×C₅₃	—	4	1	no	—
410	C₈×C₅₃	—	4	1	no	—
411	#24459	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂²×C₅₃	—	2	1	no	—
413	C₂²×C₅₃	—	2	1	no	—
414	C₂²×C₅₃	—	2	2	no	—
415	C₂²×C₅₃	—	2	2	no	—
416	C₂²×C₅₃	—	4	1	no	—
417	C₂²×C₅₃	—	4	1	no	—
418	C₂²×C₅₃	—	4	1	no	—
419	C₂²×C₅₃	—	4	1	no	—
420	C₂²×C₅₃	—	4	1	no	—
421	C₂²×C₅₃	—	4	2	no	—
422	C₂²×C₅₃	—	4	2	no	—
423	C₂²×C₅₃	—	4	1	no	—
424	C₂²×C₅₃	—	4	1	no	—
425	C₂²×C₅₃	—	8	2	no	—
426	C₂²×C₅₃	—	8	2	no	—
427	C₂²×C₅₃	—	8	1	no	—
428	C₂²×C₅₃	—	8	1	no	—
429	C₂²×C₅₃	—	8	1	no	—
430	C₂²×C₅₃	—	8	1	no	—
431	C₂²×C₅₃	—	16	1	no	—
432	C₂²×C₅₃	—	16	1	no	—
433	C₂²×C₅₃	—	16	4	no	—
434	C₂²×C₅₃	—	16	4	no	—
435	C₂²×C₅₃	#534	1	1	yes	characteristic
436	C₂²×C₅₃	D₄²	1	1	yes	characteristic
437	C₂²×C₅₃	#546	1	1	yes	characteristic
438	C₄×C₅₃	—	2	2	no	—
439	C₄×C₅₃	—	2	2	no	—
440	C₄×C₅₃	—	4	1	no	—
441	C₄×C₅₃	—	4	1	no	—
442	C₄×C₅₃	—	4	1	no	—
443	C₄×C₅₃	—	8	1	no	—
444	C₄×C₅₃	—	8	1	no	—
445	C₄×C₅₃	—	8	1	no	—
446	C₄×C₅₃	C₂×#120	1	1	yes	characteristic
447	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
448	C₄×C₅₃	D₄²	1	1	yes	characteristic
449	C₄×C₅₃	#546	1	1	yes	characteristic
450	C₂×#576	C₂×C₅₃	1	1	yes	characteristic
451	C₂×#471	C₂×C₅₃	1	1	yes	characteristic, complemented
452	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
453	C₂×#455	C₂×C₅₃	1	1	yes	characteristic, complemented
454	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
455	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
456	#2051	C₂×C₅₃	1	1	yes	characteristic, complemented
457	#2045	C₂×C₅₃	1	1	yes	characteristic, complemented
458	#2012	C₂×C₅₃	1	1	yes	characteristic, complemented
459	#2003	C₂×C₅₃	1	1	yes	characteristic, complemented
460	#1908	C₂×C₅₃	1	1	yes	characteristic, complemented
461	#1883	C₂×C₅₃	1	1	yes	characteristic, complemented
462	#1876	C₂×C₅₃	1	1	yes	characteristic, complemented
463	#1866	C₂×C₅₃	1	1	yes	characteristic, complemented
464	#1792	C₂×C₅₃	1	1	yes	characteristic, complemented
465	C₂×C₅₃	—	2	1	no	—
466	C₂×C₅₃	—	2	1	no	—
467	C₂×C₅₃	—	4	2	no	—
468	C₂×C₅₃	—	4	2	no	—
469	C₂×C₅₃	—	8	1	no	—
470	C₂×C₅₃	—	8	2	no	—
471	C₂×C₅₃	—	8	2	no	—
472	C₂×C₅₃	#2410	1	1	yes	characteristic
473	C₂×C₅₃	#3288	1	1	yes	characteristic
474	C₂×C₅₃	#3290	1	1	yes	characteristic
475	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
476	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
477	#576	—	2	4	no	—
478	#576	—	2	4	no	—
479	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
480	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
481	C₂×AGL(1,ℤ/8)	—	2	1	no	—
482	C₂×AGL(1,ℤ/8)	—	2	1	no	—
483	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
484	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
485	C₂×#135	—	2	1	no	—
486	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
487	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
488	C₂²×D₈	—	2	1	no	—
489	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
490	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
491	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
492	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
493	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
494	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
495	#471	—	2	4	no	—
496	#464	—	2	1	no	—
497	#463	—	2	1	no	—
498	#462	—	2	1	no	—
499	#461	—	2	1	no	—
500	#455	—	2	4	no	—
501	#452	—	2	1	no	—
502	#452	—	2	1	no	—
503	#450	—	2	1	no	—
504	#450	—	2	1	no	—
505	C₂×#108	C₂²×C₅₃	1	1	yes	characteristic, complemented
506	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	C₂×#104	C₂²×C₅₃	1	1	yes	characteristic
508	C₂×#104	C₂²×C₅₃	1	1	yes	characteristic, complemented
509	C₂×#104	C₂²×C₅₃	1	1	yes	characteristic, complemented
510	#418	—	2	1	no	—
511	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
512	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
513	#417	—	2	1	no	—
514	#417	C₂²×C₅₃	1	1	yes	characteristic
515	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
516	#416	—	2	1	no	—
517	#416	C₂²×C₅₃	1	1	yes	characteristic
518	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
519	C₂×#102	—	2	1	no	—
520	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	C₂×#101	C₂²×C₅₃	1	1	yes	characteristic, complemented
522	C₂×#100	C₂²×C₅₃	1	1	yes	characteristic, complemented
523	C₂×#100	C₂²×C₅₃	1	1	yes	characteristic, complemented
524	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
525	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
526	#343	C₂²×C₅₃	1	1	yes	characteristic, complemented
527	#341	C₂²×C₅₃	1	1	yes	characteristic, complemented
528	#339	C₂²×C₅₃	1	1	yes	characteristic, complemented
529	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
530	C₅₃	#24459	1	1	yes	characteristic, direct product factor, Sylow
531	H(5,𝔽₂)	—	2	2	no	—
532	H(5,𝔽₂)	—	2	2	no	—
533	H(5,𝔽₂)	—	2	2	no	—
534	H(5,𝔽₂)	—	2	2	no	—
535	H(5,𝔽₂)	—	2	2	no	—
536	H(5,𝔽₂)	—	4	1	no	—
537	H(5,𝔽₂)	—	4	1	no	—
538	H(5,𝔽₂)	D₄×C₅₃	1	4	yes	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	2	1	no	—
542	C₂×#41	—	2	1	no	—
543	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
544	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
545	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	4	1	no	—
552	C₂²×D₄	—	4	1	no	—
553	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
555	#137	—	2	2	no	—
556	#137	—	2	2	no	—
557	#137	—	2	2	no	—
558	#137	—	2	2	no	—
559	AGL(1,ℤ/8)	—	2	8	no	—
560	AGL(1,ℤ/8)	—	2	8	no	—
561	AGL(1,ℤ/8)	—	2	2	no	—
562	AGL(1,ℤ/8)	—	2	2	no	—
563	AGL(1,ℤ/8)	—	2	2	no	—
564	AGL(1,ℤ/8)	D₄×C₅₃	1	4	yes	—
565	#135	—	2	8	no	—
566	#135	—	2	2	no	—
567	#135	—	2	2	no	—
568	C₂×Q₁₆	—	2	1	no	—
569	C₂×Q₁₆	—	2	1	no	—
570	C₂×Q₁₆	D₄×C₅₃	1	1	yes	characteristic
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	—	2	2	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	1	no	—
576	C₂×SD₁₆	—	2	1	no	—
577	C₂×SD₁₆	—	2	1	no	—
578	C₂×SD₁₆	—	4	1	no	—
579	C₂×SD₁₆	D₄×C₅₃	1	1	yes	characteristic
580	C₂×SD₁₆	D₄×C₅₃	1	1	yes	characteristic
581	C₂×D₈	—	2	8	no	—
582	C₂×D₈	—	2	1	no	—
583	C₂×D₈	—	2	1	no	—
584	C₂×D₈	—	2	2	no	—
585	C₂×D₈	—	2	2	no	—
586	C₂×D₈	—	2	1	no	—
587	C₂×D₈	—	2	1	no	—
588	C₂×D₈	D₄×C₅₃	1	1	yes	characteristic
589	#131	—	2	2	no	—
590	#131	—	2	2	no	—
591	#131	—	2	2	no	—
592	#131	—	4	1	no	—
593	C₂×M₁₆	—	2	1	no	—
594	C₂×M₁₆	—	2	1	no	—
595	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
596	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
597	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
598	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
599	C₂²×C₈	—	2	1	no	—
600	C₂²×C₈	—	2	1	no	—
601	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
602	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
603	C₄⋊Q₈	—	2	1	no	—
604	#124	—	2	2	no	—
605	#124	—	2	1	no	—
606	#124	—	4	1	no	—
607	#123	—	4	1	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	4	1	no	—
613	#117	—	2	1	no	—
614	#117	C₂³×C₅₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	—	4	1	no	—
618	C₂×C₂²⋊C₄	—	4	1	no	—
619	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
620	#108	—	2	2	no	—
621	C₄⋊C₈	—	2	1	no	—
622	C₄⋊C₈	—	2	1	no	—
623	#104	—	2	2	no	—
624	#104	—	2	2	no	—
625	#104	—	4	1	no	—
626	#103	—	2	1	no	—
627	#103	—	2	1	no	—
628	#103	—	2	1	no	—
629	#103	—	2	1	no	—
630	#103	D₄×C₅₃	1	1	yes	characteristic
631	#103	D₄×C₅₃	1	1	yes	characteristic
632	#102	—	2	1	no	—
633	#102	—	2	1	no	—
634	#102	—	2	1	no	—
635	#102	—	2	1	no	—
636	#102	—	2	1	no	—
637	#102	—	2	1	no	—
638	#102	—	2	1	no	—
639	#102	—	2	1	no	—
640	#102	D₄×C₅₃	1	1	yes	characteristic
641	#102	D₄×C₅₃	1	1	yes	characteristic
642	#101	—	2	2	no	—
643	#100	—	2	2	no	—
644	#100	—	2	2	no	—
645	C₂²⋊C₈	—	2	1	no	—
646	C₂²⋊C₈	—	2	1	no	—
647	C₂⁴	—	2	1	no	—
648	C₂⁴	—	2	1	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	—	4	1	no	—
651	#41	—	2	1	no	—
652	#41	—	2	1	no	—
653	#41	—	2	1	no	—
654	#41	—	2	1	no	—
655	#41	—	2	4	no	—
656	#41	—	2	4	no	—
657	#41	—	2	4	no	—
658	#41	—	2	1	no	—
659	#41	—	2	1	no	—
660	#41	—	2	1	no	—
661	#41	—	2	1	no	—
662	#41	—	4	2	no	—
663	#41	—	4	2	no	—
664	#41	—	4	2	no	—
665	#41	—	4	2	no	—
666	#41	—	4	2	no	—
667	#41	C₂×D₄×C₅₃	1	2	yes	—
668	#41	C₂×D₄×C₅₃	1	2	yes	—
669	#41	C₂×D₄×C₅₃	1	2	yes	—
670	#41	#41×C₅₃	1	2	yes	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
679	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	1	no	—
700	C₂×D₄	—	4	1	no	—
701	C₂×D₄	—	4	1	no	—
702	C₂×D₄	—	4	1	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
710	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
711	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
712	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
713	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	—	4	1	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
724	Q₁₆	—	2	2	no	—
725	Q₁₆	—	4	2	no	—
726	Q₁₆	—	4	2	no	—
727	SD₁₆	—	2	4	no	—
728	SD₁₆	—	2	4	no	—
729	SD₁₆	—	2	2	no	—
730	SD₁₆	—	2	2	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	—	4	2	no	—
733	SD₁₆	—	4	2	no	—
734	SD₁₆	—	4	2	no	—
735	D₈	—	2	4	no	—
736	D₈	—	2	4	no	—
737	D₈	—	2	4	no	—
738	D₈	—	2	2	no	—
739	D₈	—	2	4	no	—
740	M₁₆	—	2	4	no	—
741	M₁₆	—	2	1	no	—
742	M₁₆	—	2	1	no	—
743	M₁₆	—	2	1	no	—
744	M₁₆	—	2	1	no	—
745	M₁₆	—	2	1	no	—
746	M₁₆	—	2	1	no	—
747	M₁₆	—	2	1	no	—
748	M₁₆	—	4	2	no	—
749	M₁₆	C₂×D₄×C₅₃	1	2	yes	—
750	C₂×C₈	—	2	4	no	—
751	C₂×C₈	—	2	1	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	1	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	4	2	no	—
760	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
761	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
762	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
763	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	1	no	—
768	C₄⋊C₄	—	4	1	no	—
769	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	1	no	—
774	C₂²⋊C₄	—	4	1	no	—
775	C₂²⋊C₄	—	4	4	no	—
776	C₂²⋊C₄	—	8	2	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	2	1	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	4	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	4	4	no	—
787	C₂³	—	4	4	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	8	1	no	—
793	C₂³	—	8	1	no	—
794	C₂³	—	8	1	no	—
795	C₂³	—	8	1	no	—
796	C₂³	—	16	1	no	—
797	C₂³	—	16	1	no	—
798	C₂³	—	16	1	no	—
799	C₂³	—	16	1	no	—
800	C₂³	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
801	Q₈	—	2	1	no	—
802	Q₈	—	2	1	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	2	1	no	—
805	Q₈	—	4	1	no	—
806	Q₈	—	4	1	no	—
807	Q₈	—	4	1	no	—
808	Q₈	—	4	1	no	—
809	Q₈	#120×C₅₃	1	2	yes	—
810	Q₈	#121×C₅₃	1	2	yes	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	2	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	1	no	—
818	D₄	—	2	2	no	—
819	D₄	—	2	1	no	—
820	D₄	—	2	2	no	—
821	D₄	—	2	1	no	—
822	D₄	—	2	1	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	4	no	—
825	D₄	—	4	4	no	—
826	D₄	—	4	4	no	—
827	D₄	—	4	1	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	1	no	—
833	D₄	#120×C₅₃	1	2	yes	—
834	D₄	#121×C₅₃	1	2	yes	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	8	1	no	—
856	C₂×C₄	—	16	1	no	—
857	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
861	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
862	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
863	C₈	—	2	1	no	—
864	C₈	—	2	2	no	—
865	C₈	—	2	1	no	—
866	C₈	—	2	1	no	—
867	C₈	—	2	1	no	—
868	C₈	—	4	1	no	—
869	C₈	—	4	1	no	—
870	C₈	—	4	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	8	2	no	—
885	C₂²	—	8	2	no	—
886	C₂²	—	8	1	no	—
887	C₂²	—	8	1	no	—
888	C₂²	—	8	1	no	—
889	C₂²	—	8	1	no	—
890	C₂²	—	16	1	no	—
891	C₂²	—	16	1	no	—
892	C₂²	—	16	4	no	—
893	C₂²	—	16	4	no	—
894	C₂²	C₅₃×#534	1	1	yes	characteristic
895	C₂²	D₄²×C₅₃	1	1	yes	characteristic
896	C₂²	C₅₃×#546	1	1	yes	characteristic
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	8	1	no	—
903	C₄	—	8	1	no	—
904	C₄	—	8	1	no	—
905	C₄	C₂×#120×C₅₃	1	1	yes	characteristic
906	C₄	C₂×#121×C₅₃	1	1	yes	characteristic
907	C₄	D₄²×C₅₃	1	1	yes	characteristic
908	C₄	C₅₃×#546	1	1	yes	characteristic
909	C₂	—	2	1	no	—
910	C₂	—	2	1	no	—
911	C₂	—	4	2	no	—
912	C₂	—	4	2	no	—
913	C₂	—	8	1	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	C₅₃×#2410	1	1	yes	characteristic
917	C₂	C₅₃×#3288	1	1	yes	characteristic
918	C₂	C₅₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×C₅₃×#576	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#471	C₂	semidirect
3. C₅₃×#3046	C₂	semidirect
4. C₂×C₅₃×#455	C₂	semidirect
5. C₅₃×#3009	C₂	semidirect
6. C₅₃×#2897	C₂	semidirect
7. C₅₃×#2051	C₂	semidirect
8. C₅₃×#2045	C₂	semidirect
9. C₅₃×#2012	C₂	semidirect
10. C₅₃×#2003	C₂	semidirect
11. C₅₃×#1908	C₂	semidirect
12. C₅₃×#1883	C₂	semidirect
13. C₅₃×#1876	C₂	semidirect
14. C₅₃×#1866	C₂	semidirect
15. C₅₃×#1792	C₂	semidirect
21. C₂×#137×C₅₃	C₂²	semidirect
28. C₂²×SD₁₆×C₅₃	C₂²	semidirect
32. C₂×#131×C₅₃	C₂²	semidirect
33. C₅₃×#536	C₂²	semidirect
34. C₂×#124×C₅₃	C₂²	semidirect
35. C₅₃×#520	C₂²	semidirect
46. C₂×#108×C₅₃	C₂²	semidirect
47. C₅₃×#424	C₂²	semidirect
49. C₂×#104×C₅₃	C₂²	semidirect
50. C₂×#104×C₅₃	C₂²	semidirect
52. C₅₃×#418	C₂²	semidirect
53. C₅₃×#418	C₂²	semidirect
56. C₅₃×#417	C₂²	semidirect
59. C₂×#103×C₅₃	C₂²	semidirect
61. C₂×#102×C₅₃	C₂²	semidirect
62. C₂×#101×C₅₃	C₂²	semidirect
63. C₂×#100×C₅₃	C₂²	semidirect
64. C₂×#100×C₅₃	C₂²	semidirect
65. C₅₃×#408	C₂²	semidirect
66. C₅₃×#390	C₂²	semidirect
67. C₅₃×#343	C₂²	semidirect
68. C₅₃×#341	C₂²	semidirect
69. C₅₃×#339	C₂²	semidirect
70. C₅₃×#336	C₂²	semidirect
411. #24459	C₅₃	direct (N × H)
451. C₂×#471	C₂×C₅₃	semidirect
452. #3046	C₂×C₅₃	semidirect
453. C₂×#455	C₂×C₅₃	semidirect
454. #3009	C₂×C₅₃	semidirect
455. #2897	C₂×C₅₃	semidirect
456. #2051	C₂×C₅₃	semidirect
457. #2045	C₂×C₅₃	semidirect
458. #2012	C₂×C₅₃	semidirect
459. #2003	C₂×C₅₃	semidirect
460. #1908	C₂×C₅₃	semidirect
461. #1883	C₂×C₅₃	semidirect
462. #1876	C₂×C₅₃	semidirect
463. #1866	C₂×C₅₃	semidirect
464. #1792	C₂×C₅₃	semidirect
480. C₂×#137	C₂²×C₅₃	semidirect
487. C₂²×SD₁₆	C₂²×C₅₃	semidirect
491. C₂×#131	C₂²×C₅₃	semidirect
492. #536	C₂²×C₅₃	semidirect
493. C₂×#124	C₂²×C₅₃	semidirect
494. #520	C₂²×C₅₃	semidirect
505. C₂×#108	C₂²×C₅₃	semidirect
506. #424	C₂²×C₅₃	semidirect
508. C₂×#104	C₂²×C₅₃	semidirect
509. C₂×#104	C₂²×C₅₃	semidirect
511. #418	C₂²×C₅₃	semidirect
512. #418	C₂²×C₅₃	semidirect
515. #417	C₂²×C₅₃	semidirect
518. C₂×#103	C₂²×C₅₃	semidirect
520. C₂×#102	C₂²×C₅₃	semidirect
521. C₂×#101	C₂²×C₅₃	semidirect
522. C₂×#100	C₂²×C₅₃	semidirect
523. C₂×#100	C₂²×C₅₃	semidirect
524. #408	C₂²×C₅₃	semidirect
525. #390	C₂²×C₅₃	semidirect
526. #343	C₂²×C₅₃	semidirect
527. #341	C₂²×C₅₃	semidirect
528. #339	C₂²×C₅₃	semidirect
529. #336	C₂²×C₅₃	semidirect
530. C₅₃	#24459	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#576	2
C₂×C₅₃×#471	2
C₅₃×#3046	2
C₂×C₅₃×#455	2
C₅₃×#3009	2
C₅₃×#2897	2
C₅₃×#2051	2
C₅₃×#2045	2
C₅₃×#2012	2
C₅₃×#2003	2
C₅₃×#1908	2
C₅₃×#1883	2
C₅₃×#1876	2
C₅₃×#1866	2
C₅₃×#1792	2
#24459	53

Subgroups — C53×#24459 #27231971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#24459 #27231971