Subgroups — C₅₃×#24472 #27231984

Order 13568.

1372 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3068	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3021	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#453	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2901	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2050	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2048	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2008	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1906	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1903	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1903	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1861	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1795	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#585	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#577	—	2	2	no	—
19	C₅₃×#577	—	2	2	no	—
20	C₅₃×#576	—	2	2	no	—
21	C₅₃×#576	—	2	2	no	—
22	C₅₃×#575	—	2	2	no	—
23	C₅₃×#575	C₂²	1	1	yes	characteristic
24	C₅₃×#575	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#568	C₂²	1	1	yes	characteristic
32	C₅₃×#568	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
34	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#472	—	2	2	no	—
37	C₅₃×#471	—	2	2	no	—
38	C₅₃×#460	—	2	2	no	—
39	C₅₃×#459	—	2	2	no	—
40	C₅₃×#454	—	2	2	no	—
41	C₅₃×#453	—	2	2	no	—
42	C₅₃×#453	—	2	2	no	—
43	C₅₃×#453	—	2	2	no	—
44	C₅₃×#430	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#421	—	2	2	no	—
47	C₅₃×#421	C₂²	1	1	yes	characteristic
48	C₅₃×#421	C₂²	1	1	yes	characteristic
49	C₅₃×#421	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#421	C₂²	1	1	yes	characteristic, complemented
51	C₂×#104×C₅₃	—	2	2	no	—
52	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#413	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#413	C₂²	1	1	yes	characteristic, complemented
60	C₂×#100×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×#100×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#410	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#344	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#344	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#339	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#338	C₂²	1	1	yes	characteristic, complemented
67	2₋¹⁺⁴×C₅₃	—	2	1	no	—
68	2₋¹⁺⁴×C₅₃	—	2	1	no	—
69	2₋¹⁺⁴×C₅₃	D₄	1	2	yes	complemented
70	H(5,𝔽₂)×C₅₃	—	2	2	no	—
71	H(5,𝔽₂)×C₅₃	—	2	1	no	—
72	H(5,𝔽₂)×C₅₃	—	2	2	no	—
73	H(5,𝔽₂)×C₅₃	—	2	1	no	—
74	H(5,𝔽₂)×C₅₃	—	2	2	no	—
75	H(5,𝔽₂)×C₅₃	—	4	1	no	—
76	H(5,𝔽₂)×C₅₃	—	4	1	no	—
77	H(5,𝔽₂)×C₅₃	D₄	1	2	yes	complemented
78	C₂×#41×C₅₃	—	2	2	no	—
79	C₂×#41×C₅₃	—	2	2	no	—
80	C₂×#41×C₅₃	—	2	1	no	—
81	C₂×#41×C₅₃	—	2	1	no	—
82	C₂×#41×C₅₃	—	4	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	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₅₃	—	2	1	no	—
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	—	4	1	no	—
90	C₂²×D₄×C₅₃	—	4	1	no	—
91	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
93	#137×C₅₃	—	2	4	no	—
94	#137×C₅₃	—	2	1	no	—
95	#137×C₅₃	—	2	1	no	—
96	#137×C₅₃	—	2	1	no	—
97	#137×C₅₃	D₄	1	2	yes	complemented
98	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
99	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
100	AGL(1,ℤ/8)×C₅₃	—	2	4	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	—	2	2	no	—
105	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
106	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
107	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
108	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
109	AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
110	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
111	AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
112	AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
113	AGL(1,ℤ/8)×C₅₃	—	4	1	no	—
114	AGL(1,ℤ/8)×C₅₃	D₄	1	2	yes	complemented
115	#135×C₅₃	—	2	4	no	—
116	#135×C₅₃	—	2	4	no	—
117	#135×C₅₃	—	2	2	no	—
118	#135×C₅₃	—	2	2	no	—
119	C₂×SD₁₆×C₅₃	—	2	4	no	—
120	C₂×SD₁₆×C₅₃	—	2	1	no	—
121	C₂×SD₁₆×C₅₃	—	2	1	no	—
122	C₂×SD₁₆×C₅₃	—	2	1	no	—
123	C₂×SD₁₆×C₅₃	—	2	1	no	—
124	C₂×SD₁₆×C₅₃	D₄	1	2	yes	complemented
125	C₂×D₈×C₅₃	—	2	4	no	—
126	C₂×D₈×C₅₃	—	2	1	no	—
127	C₂×D₈×C₅₃	—	2	1	no	—
128	C₂×D₈×C₅₃	—	2	1	no	—
129	C₂×D₈×C₅₃	—	2	1	no	—
130	C₂×D₈×C₅₃	D₄	1	2	yes	complemented
131	#131×C₅₃	—	2	2	no	—
132	#131×C₅₃	—	2	2	no	—
133	#131×C₅₃	—	2	2	no	—
134	#131×C₅₃	—	4	1	no	—
135	C₂×M₁₆×C₅₃	—	2	2	no	—
136	C₂×M₁₆×C₅₃	—	2	2	no	—
137	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	#127×C₅₃	—	2	1	no	—
144	#127×C₅₃	—	2	1	no	—
145	#127×C₅₃	—	2	2	no	—
146	#127×C₅₃	—	2	1	no	—
147	#124×C₅₃	—	2	1	no	—
148	#121×C₅₃	—	4	1	no	—
149	#120×C₅₃	—	4	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	#117×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₅₃	—	2	1	no	—
157	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
158	#108×C₅₃	—	2	2	no	—
159	C₄⋊C₈×C₅₃	—	2	2	no	—
160	#104×C₅₃	—	2	2	no	—
161	#104×C₅₃	—	2	1	no	—
162	#104×C₅₃	—	2	1	no	—
163	#104×C₅₃	—	2	1	no	—
164	#104×C₅₃	—	2	1	no	—
165	#104×C₅₃	—	2	2	no	—
166	#104×C₅₃	—	2	2	no	—
167	#104×C₅₃	—	2	2	no	—
168	#104×C₅₃	D₄	1	2	yes	complemented
169	#104×C₅₃	D₄	1	2	yes	complemented
170	#102×C₅₃	—	2	2	no	—
171	#102×C₅₃	—	2	2	no	—
172	#102×C₅₃	—	4	1	no	—
173	#101×C₅₃	—	2	1	no	—
174	#101×C₅₃	—	2	1	no	—
175	#100×C₅₃	—	2	2	no	—
176	#100×C₅₃	—	2	2	no	—
177	#100×C₅₃	—	2	1	no	—
178	#100×C₅₃	—	2	1	no	—
179	#99×C₅₃	—	4	1	no	—
180	C₂⁴×C₅₃	—	2	1	no	—
181	C₂⁴×C₅₃	—	2	1	no	—
182	C₂⁴×C₅₃	—	4	1	no	—
183	#41×C₅₃	—	2	1	no	—
184	#41×C₅₃	—	2	1	no	—
185	#41×C₅₃	—	2	1	no	—
186	#41×C₅₃	—	2	1	no	—
187	#41×C₅₃	—	2	4	no	—
188	#41×C₅₃	—	2	2	no	—
189	#41×C₅₃	—	2	2	no	—
190	#41×C₅₃	—	2	2	no	—
191	#41×C₅₃	—	2	2	no	—
192	#41×C₅₃	—	2	1	no	—
193	#41×C₅₃	—	2	1	no	—
194	#41×C₅₃	—	2	1	no	—
195	#41×C₅₃	—	2	1	no	—
196	#41×C₅₃	—	2	1	no	—
197	#41×C₅₃	—	2	1	no	—
198	#41×C₅₃	—	2	1	no	—
199	#41×C₅₃	—	2	1	no	—
200	#41×C₅₃	—	4	2	no	—
201	#41×C₅₃	—	4	2	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	1	no	—
207	#41×C₅₃	—	4	1	no	—
208	#41×C₅₃	—	4	2	no	—
209	#41×C₅₃	C₂×D₄	1	2	yes	—
210	#41×C₅₃	C₂×D₄	1	2	yes	—
211	#41×C₅₃	C₂×D₄	1	2	yes	—
212	#41×C₅₃	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₅₃	—	2	2	no	—
214	C₂×Q₈×C₅₃	—	2	2	no	—
215	C₂×Q₈×C₅₃	—	4	1	no	—
216	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
217	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
218	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
219	C₂×Q₈×C₅₃	#41	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	2	no	—
224	C₂×D₄×C₅₃	—	2	2	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	—	2	1	no	—
237	C₂×D₄×C₅₃	—	2	1	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	2	no	—
242	C₂×D₄×C₅₃	—	4	2	no	—
243	C₂×D₄×C₅₃	—	4	2	no	—
244	C₂×D₄×C₅₃	—	4	2	no	—
245	C₂×D₄×C₅₃	—	4	1	no	—
246	C₂×D₄×C₅₃	—	4	4	no	—
247	C₂×D₄×C₅₃	—	4	2	no	—
248	C₂×D₄×C₅₃	—	4	2	no	—
249	C₂×D₄×C₅₃	—	4	4	no	—
250	C₂×D₄×C₅₃	—	4	2	no	—
251	C₂×D₄×C₅₃	—	4	2	no	—
252	C₂×D₄×C₅₃	—	8	4	no	—
253	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₅₃	#41	1	1	yes	characteristic
258	C₂²×C₄×C₅₃	—	2	1	no	—
259	C₂²×C₄×C₅₃	—	2	1	no	—
260	C₂²×C₄×C₅₃	—	2	1	no	—
261	C₂²×C₄×C₅₃	—	2	1	no	—
262	C₂²×C₄×C₅₃	—	2	1	no	—
263	C₂²×C₄×C₅₃	—	4	1	no	—
264	C₂²×C₄×C₅₃	—	4	2	no	—
265	C₂²×C₄×C₅₃	—	4	1	no	—
266	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₅₃	—	2	2	no	—
268	Q₁₆×C₅₃	—	2	2	no	—
269	SD₁₆×C₅₃	—	2	4	no	—
270	SD₁₆×C₅₃	—	2	2	no	—
271	SD₁₆×C₅₃	—	2	2	no	—
272	SD₁₆×C₅₃	—	2	2	no	—
273	SD₁₆×C₅₃	—	2	4	no	—
274	SD₁₆×C₅₃	—	2	2	no	—
275	SD₁₆×C₅₃	—	4	2	no	—
276	SD₁₆×C₅₃	—	4	2	no	—
277	SD₁₆×C₅₃	—	4	2	no	—
278	D₈×C₅₃	—	2	4	no	—
279	D₈×C₅₃	—	2	2	no	—
280	D₈×C₅₃	—	2	2	no	—
281	D₈×C₅₃	—	2	4	no	—
282	D₈×C₅₃	—	4	2	no	—
283	D₈×C₅₃	—	4	2	no	—
284	D₈×C₅₃	—	4	2	no	—
285	M₁₆×C₅₃	—	2	4	no	—
286	M₁₆×C₅₃	—	2	1	no	—
287	M₁₆×C₅₃	—	2	1	no	—
288	M₁₆×C₅₃	—	2	1	no	—
289	M₁₆×C₅₃	—	2	1	no	—
290	M₁₆×C₅₃	—	2	1	no	—
291	M₁₆×C₅₃	—	2	1	no	—
292	M₁₆×C₅₃	—	2	1	no	—
293	M₁₆×C₅₃	—	2	1	no	—
294	M₁₆×C₅₃	—	2	1	no	—
295	M₁₆×C₅₃	—	2	1	no	—
296	M₁₆×C₅₃	—	4	2	no	—
297	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
298	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
299	C₂×C₈×C₅₃	—	2	4	no	—
300	C₂×C₈×C₅₃	—	2	1	no	—
301	C₂×C₈×C₅₃	—	2	1	no	—
302	C₂×C₈×C₅₃	—	2	1	no	—
303	C₂×C₈×C₅₃	—	2	1	no	—
304	C₂×C₈×C₅₃	—	2	1	no	—
305	C₂×C₈×C₅₃	—	4	2	no	—
306	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₅₃	—	2	1	no	—
308	C₄⋊C₄×C₅₃	—	2	1	no	—
309	C₄⋊C₄×C₅₃	—	4	1	no	—
310	C₂²⋊C₄×C₅₃	—	2	1	no	—
311	C₂²⋊C₄×C₅₃	—	2	1	no	—
312	C₂²⋊C₄×C₅₃	—	4	1	no	—
313	C₂²⋊C₄×C₅₃	—	4	2	no	—
314	C₄²×C₅₃	—	2	1	no	—
315	C₄²×C₅₃	—	2	1	no	—
316	C₄²×C₅₃	—	2	1	no	—
317	C₄²×C₅₃	—	4	1	no	—
318	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
320	C₂³×C₅₃	—	2	1	no	—
321	C₂³×C₅₃	—	2	1	no	—
322	C₂³×C₅₃	—	2	1	no	—
323	C₂³×C₅₃	—	2	2	no	—
324	C₂³×C₅₃	—	2	1	no	—
325	C₂³×C₅₃	—	4	2	no	—
326	C₂³×C₅₃	—	4	4	no	—
327	C₂³×C₅₃	—	4	1	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	2	no	—
333	C₂³×C₅₃	—	8	2	no	—
334	C₂³×C₅₃	—	16	2	no	—
335	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
336	Q₈×C₅₃	—	2	1	no	—
337	Q₈×C₅₃	—	2	1	no	—
338	Q₈×C₅₃	—	2	1	no	—
339	Q₈×C₅₃	—	2	1	no	—
340	Q₈×C₅₃	—	2	1	no	—
341	Q₈×C₅₃	—	2	1	no	—
342	Q₈×C₅₃	—	4	2	no	—
343	Q₈×C₅₃	#120	1	2	yes	—
344	Q₈×C₅₃	#121	1	2	yes	—
345	D₄×C₅₃	—	2	2	no	—
346	D₄×C₅₃	—	2	2	no	—
347	D₄×C₅₃	—	2	2	no	—
348	D₄×C₅₃	—	2	2	no	—
349	D₄×C₅₃	—	2	1	no	—
350	D₄×C₅₃	—	2	2	no	—
351	D₄×C₅₃	—	2	1	no	—
352	D₄×C₅₃	—	2	1	no	—
353	D₄×C₅₃	—	2	1	no	—
354	D₄×C₅₃	—	2	1	no	—
355	D₄×C₅₃	—	2	1	no	—
356	D₄×C₅₃	—	2	2	no	—
357	D₄×C₅₃	—	4	2	no	—
358	D₄×C₅₃	—	4	2	no	—
359	D₄×C₅₃	—	4	4	no	—
360	D₄×C₅₃	—	4	2	no	—
361	D₄×C₅₃	—	4	4	no	—
362	D₄×C₅₃	—	4	1	no	—
363	D₄×C₅₃	—	4	1	no	—
364	D₄×C₅₃	—	4	1	no	—
365	D₄×C₅₃	—	4	1	no	—
366	D₄×C₅₃	—	4	1	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	—	8	4	no	—
373	D₄×C₅₃	—	8	4	no	—
374	D₄×C₅₃	—	16	2	no	—
375	D₄×C₅₃	#120	1	2	yes	—
376	D₄×C₅₃	#121	1	2	yes	—
377	C₂×C₄×C₅₃	—	2	1	no	—
378	C₂×C₄×C₅₃	—	2	1	no	—
379	C₂×C₄×C₅₃	—	2	1	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	2	1	no	—
385	C₂×C₄×C₅₃	—	2	1	no	—
386	C₂×C₄×C₅₃	—	2	1	no	—
387	C₂×C₄×C₅₃	—	4	2	no	—
388	C₂×C₄×C₅₃	—	4	2	no	—
389	C₂×C₄×C₅₃	—	4	2	no	—
390	C₂×C₄×C₅₃	—	4	2	no	—
391	C₂×C₄×C₅₃	—	4	4	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	—	4	1	no	—
396	C₂×C₄×C₅₃	—	4	1	no	—
397	C₂×C₄×C₅₃	—	4	1	no	—
398	C₂×C₄×C₅₃	—	8	2	no	—
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
404	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
405	C₈×C₅₃	—	2	2	no	—
406	C₈×C₅₃	—	2	2	no	—
407	C₈×C₅₃	—	2	2	no	—
408	C₈×C₅₃	—	4	1	no	—
409	C₈×C₅₃	—	4	1	no	—
410	C₈×C₅₃	—	4	1	no	—
411	#24472	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂²×C₅₃	—	2	2	no	—
413	C₂²×C₅₃	—	2	2	no	—
414	C₂²×C₅₃	—	4	1	no	—
415	C₂²×C₅₃	—	4	1	no	—
416	C₂²×C₅₃	—	4	2	no	—
417	C₂²×C₅₃	—	4	1	no	—
418	C₂²×C₅₃	—	8	1	no	—
419	C₂²×C₅₃	—	8	1	no	—
420	C₂²×C₅₃	—	8	2	no	—
421	C₂²×C₅₃	—	8	1	no	—
422	C₂²×C₅₃	—	8	1	no	—
423	C₂²×C₅₃	—	8	2	no	—
424	C₂²×C₅₃	—	8	2	no	—
425	C₂²×C₅₃	—	8	2	no	—
426	C₂²×C₅₃	—	8	1	no	—
427	C₂²×C₅₃	—	16	1	no	—
428	C₂²×C₅₃	—	16	1	no	—
429	C₂²×C₅₃	—	16	2	no	—
430	C₂²×C₅₃	—	16	4	no	—
431	C₂²×C₅₃	#534	1	1	yes	characteristic
432	C₂²×C₅₃	D₄²	1	1	yes	characteristic
433	C₂²×C₅₃	#546	1	1	yes	characteristic
434	C₄×C₅₃	—	2	2	no	—
435	C₄×C₅₃	—	2	2	no	—
436	C₄×C₅₃	—	2	2	no	—
437	C₄×C₅₃	—	4	1	no	—
438	C₄×C₅₃	—	4	1	no	—
439	C₄×C₅₃	—	4	1	no	—
440	C₄×C₅₃	—	8	1	no	—
441	C₄×C₅₃	—	8	1	no	—
442	C₄×C₅₃	C₂×#120	1	1	yes	characteristic
443	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
444	C₄×C₅₃	D₄²	1	1	yes	characteristic
445	C₄×C₅₃	#546	1	1	yes	characteristic
446	#3585	C₂×C₅₃	1	1	yes	characteristic, complemented
447	#3068	C₂×C₅₃	1	1	yes	characteristic, complemented
448	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
449	#3021	C₂×C₅₃	1	1	yes	characteristic, complemented
450	C₂×#453	C₂×C₅₃	1	1	yes	characteristic, complemented
451	#2901	C₂×C₅₃	1	1	yes	characteristic, complemented
452	#2050	C₂×C₅₃	1	1	yes	characteristic, complemented
453	#2048	C₂×C₅₃	1	1	yes	characteristic, complemented
454	#2008	C₂×C₅₃	1	1	yes	characteristic, complemented
455	#2002	C₂×C₅₃	1	1	yes	characteristic, complemented
456	#1906	C₂×C₅₃	1	1	yes	characteristic, complemented
457	#1903	C₂×C₅₃	1	1	yes	characteristic, complemented
458	#1903	C₂×C₅₃	1	1	yes	characteristic, complemented
459	#1861	C₂×C₅₃	1	1	yes	characteristic, complemented
460	#1795	C₂×C₅₃	1	1	yes	characteristic, complemented
461	C₂×C₅₃	—	2	1	no	—
462	C₂×C₅₃	—	2	1	no	—
463	C₂×C₅₃	—	2	1	no	—
464	C₂×C₅₃	—	4	2	no	—
465	C₂×C₅₃	—	4	2	no	—
466	C₂×C₅₃	—	8	2	no	—
467	C₂×C₅₃	—	8	1	no	—
468	C₂×C₅₃	—	8	1	no	—
469	C₂×C₅₃	—	16	1	no	—
470	C₂×C₅₃	#2410	1	1	yes	characteristic
471	#585	C₂²×C₅₃	1	1	yes	characteristic
472	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
473	#577	—	2	2	no	—
474	#577	—	2	2	no	—
475	#576	—	2	2	no	—
476	#576	—	2	2	no	—
477	#575	—	2	2	no	—
478	#575	C₂²×C₅₃	1	1	yes	characteristic
479	#575	C₂²×C₅₃	1	1	yes	characteristic
480	C₂×AGL(1,ℤ/8)	—	2	2	no	—
481	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
482	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
483	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
484	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
485	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
486	#568	C₂²×C₅₃	1	1	yes	characteristic
487	#568	C₂²×C₅₃	1	1	yes	characteristic, complemented
488	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
489	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
490	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
491	#472	—	2	2	no	—
492	#471	—	2	2	no	—
493	#460	—	2	2	no	—
494	#459	—	2	2	no	—
495	#454	—	2	2	no	—
496	#453	—	2	2	no	—
497	#453	—	2	2	no	—
498	#453	—	2	2	no	—
499	#430	C₂²×C₅₃	1	1	yes	characteristic, complemented
500	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
501	#421	—	2	2	no	—
502	#421	C₂²×C₅₃	1	1	yes	characteristic
503	#421	C₂²×C₅₃	1	1	yes	characteristic
504	#421	C₂²×C₅₃	1	1	yes	characteristic, complemented
505	#421	C₂²×C₅₃	1	1	yes	characteristic, complemented
506	C₂×#104	—	2	2	no	—
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	C₂²×C₅₃	1	1	yes	characteristic, complemented
511	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
512	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
513	#413	C₂²×C₅₃	1	1	yes	characteristic, complemented
514	#413	C₂²×C₅₃	1	1	yes	characteristic, complemented
515	C₂×#100	C₂²×C₅₃	1	1	yes	characteristic, complemented
516	C₂×#100	C₂²×C₅₃	1	1	yes	characteristic, complemented
517	#410	C₂²×C₅₃	1	1	yes	characteristic, complemented
518	#344	C₂²×C₅₃	1	1	yes	characteristic, complemented
519	#344	C₂²×C₅₃	1	1	yes	characteristic, complemented
520	#339	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	#338	C₂²×C₅₃	1	1	yes	characteristic, complemented
522	C₅₃	#24472	1	1	yes	characteristic, direct product factor, Sylow
523	2₋¹⁺⁴	—	2	1	no	—
524	2₋¹⁺⁴	—	2	1	no	—
525	2₋¹⁺⁴	D₄×C₅₃	1	2	yes	complemented
526	H(5,𝔽₂)	—	2	2	no	—
527	H(5,𝔽₂)	—	2	1	no	—
528	H(5,𝔽₂)	—	2	2	no	—
529	H(5,𝔽₂)	—	2	1	no	—
530	H(5,𝔽₂)	—	2	2	no	—
531	H(5,𝔽₂)	—	4	1	no	—
532	H(5,𝔽₂)	—	4	1	no	—
533	H(5,𝔽₂)	D₄×C₅₃	1	2	yes	complemented
534	C₂×#41	—	2	2	no	—
535	C₂×#41	—	2	2	no	—
536	C₂×#41	—	2	1	no	—
537	C₂×#41	—	2	1	no	—
538	C₂×#41	—	4	1	no	—
539	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
540	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
541	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
542	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
543	C₂²×D₄	—	2	1	no	—
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	—	4	1	no	—
546	C₂²×D₄	—	4	1	no	—
547	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
549	#137	—	2	4	no	—
550	#137	—	2	1	no	—
551	#137	—	2	1	no	—
552	#137	—	2	1	no	—
553	#137	D₄×C₅₃	1	2	yes	complemented
554	AGL(1,ℤ/8)	—	2	4	no	—
555	AGL(1,ℤ/8)	—	2	4	no	—
556	AGL(1,ℤ/8)	—	2	4	no	—
557	AGL(1,ℤ/8)	—	2	2	no	—
558	AGL(1,ℤ/8)	—	2	2	no	—
559	AGL(1,ℤ/8)	—	2	1	no	—
560	AGL(1,ℤ/8)	—	2	2	no	—
561	AGL(1,ℤ/8)	—	2	1	no	—
562	AGL(1,ℤ/8)	—	2	1	no	—
563	AGL(1,ℤ/8)	—	2	2	no	—
564	AGL(1,ℤ/8)	—	2	2	no	—
565	AGL(1,ℤ/8)	—	2	2	no	—
566	AGL(1,ℤ/8)	—	2	2	no	—
567	AGL(1,ℤ/8)	—	2	2	no	—
568	AGL(1,ℤ/8)	—	2	2	no	—
569	AGL(1,ℤ/8)	—	4	1	no	—
570	AGL(1,ℤ/8)	D₄×C₅₃	1	2	yes	complemented
571	#135	—	2	4	no	—
572	#135	—	2	4	no	—
573	#135	—	2	2	no	—
574	#135	—	2	2	no	—
575	C₂×SD₁₆	—	2	4	no	—
576	C₂×SD₁₆	—	2	1	no	—
577	C₂×SD₁₆	—	2	1	no	—
578	C₂×SD₁₆	—	2	1	no	—
579	C₂×SD₁₆	—	2	1	no	—
580	C₂×SD₁₆	D₄×C₅₃	1	2	yes	complemented
581	C₂×D₈	—	2	4	no	—
582	C₂×D₈	—	2	1	no	—
583	C₂×D₈	—	2	1	no	—
584	C₂×D₈	—	2	1	no	—
585	C₂×D₈	—	2	1	no	—
586	C₂×D₈	D₄×C₅₃	1	2	yes	complemented
587	#131	—	2	2	no	—
588	#131	—	2	2	no	—
589	#131	—	2	2	no	—
590	#131	—	4	1	no	—
591	C₂×M₁₆	—	2	2	no	—
592	C₂×M₁₆	—	2	2	no	—
593	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
594	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
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	#127	—	2	2	no	—
600	#127	—	2	1	no	—
601	#127	—	2	1	no	—
602	#127	—	2	1	no	—
603	#124	—	2	1	no	—
604	#121	—	4	1	no	—
605	#120	—	4	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	4	1	no	—
609	#117	—	2	1	no	—
610	#117	C₂³×C₅₃	1	1	yes	characteristic
611	#117	C₂³×C₅₃	1	1	yes	characteristic
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
614	#108	—	2	2	no	—
615	C₄⋊C₈	—	2	2	no	—
616	#104	—	2	2	no	—
617	#104	—	2	2	no	—
618	#104	—	2	2	no	—
619	#104	—	2	2	no	—
620	#104	—	2	1	no	—
621	#104	—	2	1	no	—
622	#104	—	2	1	no	—
623	#104	—	2	1	no	—
624	#104	D₄×C₅₃	1	2	yes	complemented
625	#104	D₄×C₅₃	1	2	yes	complemented
626	#102	—	2	2	no	—
627	#102	—	2	2	no	—
628	#102	—	4	1	no	—
629	#101	—	2	1	no	—
630	#101	—	2	1	no	—
631	#100	—	2	1	no	—
632	#100	—	2	1	no	—
633	#100	—	2	2	no	—
634	#100	—	2	2	no	—
635	#99	—	4	1	no	—
636	C₂⁴	—	2	1	no	—
637	C₂⁴	—	2	1	no	—
638	C₂⁴	—	4	1	no	—
639	#41	—	2	1	no	—
640	#41	—	2	1	no	—
641	#41	—	2	1	no	—
642	#41	—	2	1	no	—
643	#41	—	2	4	no	—
644	#41	—	2	2	no	—
645	#41	—	2	2	no	—
646	#41	—	2	2	no	—
647	#41	—	2	2	no	—
648	#41	—	2	1	no	—
649	#41	—	2	1	no	—
650	#41	—	2	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	1	no	—
656	#41	—	4	2	no	—
657	#41	—	4	2	no	—
658	#41	—	4	2	no	—
659	#41	—	4	2	no	—
660	#41	—	4	2	no	—
661	#41	—	4	2	no	—
662	#41	—	4	1	no	—
663	#41	—	4	1	no	—
664	#41	—	4	2	no	—
665	#41	C₂×D₄×C₅₃	1	2	yes	—
666	#41	C₂×D₄×C₅₃	1	2	yes	—
667	#41	C₂×D₄×C₅₃	1	2	yes	—
668	#41	C₂×D₄×C₅₃	1	2	yes	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	4	1	no	—
672	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
673	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
674	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
675	C₂×Q₈	#41×C₅₃	1	1	yes	characteristic
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	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	—	4	2	no	—
695	C₂×D₄	—	4	1	no	—
696	C₂×D₄	—	4	1	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	1	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	8	4	no	—
709	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
710	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
711	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
712	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
713	C₂×D₄	#41×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	—	4	1	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	1	no	—
722	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
723	Q₁₆	—	2	2	no	—
724	Q₁₆	—	2	2	no	—
725	SD₁₆	—	2	4	no	—
726	SD₁₆	—	2	2	no	—
727	SD₁₆	—	2	2	no	—
728	SD₁₆	—	2	2	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	2	2	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	—	4	2	no	—
733	SD₁₆	—	4	2	no	—
734	D₈	—	2	4	no	—
735	D₈	—	2	2	no	—
736	D₈	—	2	2	no	—
737	D₈	—	2	4	no	—
738	D₈	—	4	2	no	—
739	D₈	—	4	2	no	—
740	D₈	—	4	2	no	—
741	M₁₆	—	2	4	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	—	2	1	no	—
749	M₁₆	—	2	1	no	—
750	M₁₆	—	2	1	no	—
751	M₁₆	—	2	1	no	—
752	M₁₆	—	4	2	no	—
753	M₁₆	C₂×D₄×C₅₃	1	2	yes	—
754	M₁₆	C₂×D₄×C₅₃	1	2	yes	—
755	C₂×C₈	—	2	4	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	2	1	no	—
761	C₂×C₈	—	4	2	no	—
762	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	4	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	4	1	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	4	1	no	—
774	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	8	2	no	—
789	C₂³	—	8	2	no	—
790	C₂³	—	16	2	no	—
791	C₂³	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
792	Q₈	—	2	1	no	—
793	Q₈	—	2	1	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	1	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	4	2	no	—
799	Q₈	#120×C₅₃	1	2	yes	—
800	Q₈	#121×C₅₃	1	2	yes	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	1	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	1	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	1	no	—
812	D₄	—	2	2	no	—
813	D₄	—	4	2	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	1	no	—
819	D₄	—	4	1	no	—
820	D₄	—	4	1	no	—
821	D₄	—	4	1	no	—
822	D₄	—	4	1	no	—
823	D₄	—	4	1	no	—
824	D₄	—	4	1	no	—
825	D₄	—	4	1	no	—
826	D₄	—	4	1	no	—
827	D₄	—	4	1	no	—
828	D₄	—	8	4	no	—
829	D₄	—	8	4	no	—
830	D₄	—	16	2	no	—
831	D₄	#120×C₅₃	1	2	yes	—
832	D₄	#121×C₅₃	1	2	yes	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	4	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	—	8	2	no	—
855	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
859	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
860	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
861	C₈	—	2	2	no	—
862	C₈	—	2	2	no	—
863	C₈	—	2	2	no	—
864	C₈	—	4	1	no	—
865	C₈	—	4	1	no	—
866	C₈	—	4	1	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	8	1	no	—
874	C₂²	—	8	1	no	—
875	C₂²	—	8	2	no	—
876	C₂²	—	8	1	no	—
877	C₂²	—	8	1	no	—
878	C₂²	—	8	2	no	—
879	C₂²	—	8	2	no	—
880	C₂²	—	8	2	no	—
881	C₂²	—	8	1	no	—
882	C₂²	—	16	1	no	—
883	C₂²	—	16	1	no	—
884	C₂²	—	16	2	no	—
885	C₂²	—	16	4	no	—
886	C₂²	C₅₃×#534	1	1	yes	characteristic
887	C₂²	D₄²×C₅₃	1	1	yes	characteristic
888	C₂²	C₅₃×#546	1	1	yes	characteristic
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	8	1	no	—
896	C₄	—	8	1	no	—
897	C₄	C₂×#120×C₅₃	1	1	yes	characteristic
898	C₄	C₂×#121×C₅₃	1	1	yes	characteristic
899	C₄	D₄²×C₅₃	1	1	yes	characteristic
900	C₄	C₅₃×#546	1	1	yes	characteristic
901	C₂	—	2	1	no	—
902	C₂	—	2	1	no	—
903	C₂	—	2	1	no	—
904	C₂	—	4	2	no	—
905	C₂	—	4	2	no	—
906	C₂	—	8	2	no	—
907	C₂	—	8	1	no	—
908	C₂	—	8	1	no	—
909	C₂	—	16	1	no	—
910	C₂	C₅₃×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₃	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₃ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3585	C₂	semidirect
2. C₅₃×#3068	C₂	semidirect
3. C₅₃×#3038	C₂	semidirect
4. C₅₃×#3021	C₂	semidirect
5. C₂×C₅₃×#453	C₂	semidirect
6. C₅₃×#2901	C₂	semidirect
7. C₅₃×#2050	C₂	semidirect
8. C₅₃×#2048	C₂	semidirect
9. C₅₃×#2008	C₂	semidirect
10. C₅₃×#2002	C₂	semidirect
11. C₅₃×#1906	C₂	semidirect
12. C₅₃×#1903	C₂	semidirect
13. C₅₃×#1903	C₂	semidirect
14. C₅₃×#1861	C₂	semidirect
15. C₅₃×#1795	C₂	semidirect
29. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
30. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
32. C₅₃×#568	C₂²	semidirect
33. C₅₃×#535	C₂²	semidirect
34. C₂×#127×C₅₃	C₂²	semidirect
35. C₄×#41×C₅₃	C₂²	semidirect
44. C₅₃×#430	C₂²	semidirect
45. C₅₃×#423	C₂²	semidirect
49. C₅₃×#421	C₂²	semidirect
50. C₅₃×#421	C₂²	semidirect
53. C₂×#104×C₅₃	C₂²	semidirect
54. C₂×#104×C₅₃	C₂²	semidirect
55. C₅₃×#418	C₂²	semidirect
56. C₅₃×#418	C₂²	semidirect
57. C₅₃×#418	C₂²	semidirect
58. C₅₃×#413	C₂²	semidirect
59. C₅₃×#413	C₂²	semidirect
60. C₂×#100×C₅₃	C₂²	semidirect
61. C₂×#100×C₅₃	C₂²	semidirect
62. C₅₃×#410	C₂²	semidirect
63. C₅₃×#344	C₂²	semidirect
64. C₅₃×#344	C₂²	semidirect
65. C₅₃×#339	C₂²	semidirect
66. C₅₃×#338	C₂²	semidirect
69. 2₋¹⁺⁴×C₅₃	D₄	semidirect
77. H(5,𝔽₂)×C₅₃	D₄	semidirect
97. #137×C₅₃	D₄	semidirect
114. AGL(1,ℤ/8)×C₅₃	D₄	semidirect
124. C₂×SD₁₆×C₅₃	D₄	semidirect
130. C₂×D₈×C₅₃	D₄	semidirect
168. #104×C₅₃	D₄	semidirect
169. #104×C₅₃	D₄	semidirect
411. #24472	C₅₃	direct (N × H)
446. #3585	C₂×C₅₃	semidirect
447. #3068	C₂×C₅₃	semidirect
448. #3038	C₂×C₅₃	semidirect
449. #3021	C₂×C₅₃	semidirect
450. C₂×#453	C₂×C₅₃	semidirect
451. #2901	C₂×C₅₃	semidirect
452. #2050	C₂×C₅₃	semidirect
453. #2048	C₂×C₅₃	semidirect
454. #2008	C₂×C₅₃	semidirect
455. #2002	C₂×C₅₃	semidirect
456. #1906	C₂×C₅₃	semidirect
457. #1903	C₂×C₅₃	semidirect
458. #1903	C₂×C₅₃	semidirect
459. #1861	C₂×C₅₃	semidirect
460. #1795	C₂×C₅₃	semidirect
484. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
485. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
487. #568	C₂²×C₅₃	semidirect
488. #535	C₂²×C₅₃	semidirect
489. C₂×#127	C₂²×C₅₃	semidirect
490. C₄×#41	C₂²×C₅₃	semidirect
499. #430	C₂²×C₅₃	semidirect
500. #423	C₂²×C₅₃	semidirect
504. #421	C₂²×C₅₃	semidirect
505. #421	C₂²×C₅₃	semidirect
508. C₂×#104	C₂²×C₅₃	semidirect
509. C₂×#104	C₂²×C₅₃	semidirect
510. #418	C₂²×C₅₃	semidirect
511. #418	C₂²×C₅₃	semidirect
512. #418	C₂²×C₅₃	semidirect
513. #413	C₂²×C₅₃	semidirect
514. #413	C₂²×C₅₃	semidirect
515. C₂×#100	C₂²×C₅₃	semidirect
516. C₂×#100	C₂²×C₅₃	semidirect
517. #410	C₂²×C₅₃	semidirect
518. #344	C₂²×C₅₃	semidirect
519. #344	C₂²×C₅₃	semidirect
520. #339	C₂²×C₅₃	semidirect
521. #338	C₂²×C₅₃	semidirect
522. C₅₃	#24472	direct (N × H)
525. 2₋¹⁺⁴	D₄×C₅₃	semidirect
533. H(5,𝔽₂)	D₄×C₅₃	semidirect
553. #137	D₄×C₅₃	semidirect
570. AGL(1,ℤ/8)	D₄×C₅₃	semidirect
580. C₂×SD₁₆	D₄×C₅₃	semidirect
586. C₂×D₈	D₄×C₅₃	semidirect
624. #104	D₄×C₅₃	semidirect
625. #104	D₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3585	2
C₅₃×#3068	2
C₅₃×#3038	2
C₅₃×#3021	2
C₂×C₅₃×#453	2
C₅₃×#2901	2
C₅₃×#2050	2
C₅₃×#2048	2
C₅₃×#2008	2
C₅₃×#2002	2
C₅₃×#1906	2
C₅₃×#1903	2
C₅₃×#1861	2
C₅₃×#1795	2
#24472	53

Subgroups — C53×#24472 #27231984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#24472 #27231984