Subgroups — C₅₃×#61679 #27269191

Order 13568.

2224 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3319	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3303	C₂	1	2	yes	maximal, complemented
6	D₄×D₈×C₅₃	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3264	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3198	C₂	1	4	yes	maximal, complemented
12	C₅₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3008	C₂	1	4	yes	maximal, complemented
15	C₅₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	complemented
18	C₂²×D₈×C₅₃	C₂²	1	4	yes	complemented
19	C₅₃×H(3,𝔽₄)	—	2	2	no	—
20	C₅₃×#555	—	2	1	no	—
21	C₅₃×#555	C₂²	1	2	yes	complemented
22	C₅₃×#555	C₂²	1	2	yes	complemented
23	C₅₃×#547	—	2	1	no	—
24	C₅₃×#547	C₂²	1	2	yes	complemented
25	C₅₃×#546	—	2	2	no	—
26	C₅₃×#546	C₂²	1	4	yes	complemented
27	D₄²×C₅₃	—	2	1	no	—
28	D₄²×C₅₃	—	2	1	no	—
29	D₄²×C₅₃	C₂²	1	2	yes	complemented
30	D₄²×C₅₃	C₂²	1	2	yes	complemented
31	D₄²×C₅₃	C₂²	1	2	yes	complemented
32	C₅₃×#537	C₂²	1	2	yes	complemented
33	C₅₃×#535	—	2	2	no	—
34	C₅₃×#535	—	2	2	no	—
35	C₅₃×#535	C₂²	1	4	yes	complemented
36	C₅₃×#534	—	2	2	no	—
37	C₅₃×#532	C₂²	1	1	yes	characteristic
38	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×#121×C₅₃	—	2	2	no	—
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#496	C₂²	1	2	yes	complemented
44	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#489	C₂²	1	2	yes	complemented
47	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#485	C₂²	1	4	yes	complemented
50	C₅₃×#482	C₂²	1	4	yes	complemented
51	C₅₃×#481	C₂²	1	2	yes	complemented
52	C₅₃×#480	C₂²	1	2	yes	complemented
53	C₅₃×#476	C₂²	1	2	yes	complemented
54	C₅₃×#474	C₂²	1	2	yes	complemented
55	C₅₃×#469	C₂²	1	4	yes	complemented
56	C₅₃×#468	C₂²	1	4	yes	complemented
57	C₅₃×#466	C₂²	1	4	yes	complemented
58	C₅₃×#465	C₂²	1	4	yes	complemented
59	C₅₃×#463	C₂²	1	4	yes	complemented
60	C₅₃×#461	C₂²	1	2	yes	complemented
61	C₅₃×#459	C₂²	1	2	yes	complemented
62	C₅₃×#459	C₂²	1	2	yes	complemented
63	C₅₃×#459	C₂²	1	2	yes	complemented
64	C₅₃×#450	C₂²	1	4	yes	complemented
65	C₅₃×#449	C₂²	1	4	yes	complemented
66	C₅₃×#449	C₂²	1	4	yes	complemented
67	C₅₃×#449	C₂²	1	4	yes	complemented
68	C₅₃×#449	C₂²	1	4	yes	complemented
69	C₅₃×#447	C₂²	1	4	yes	complemented
70	C₅₃×#447	C₂²	1	2	yes	complemented
71	C₅₃×#447	C₂²	1	2	yes	complemented
72	C₅₃×#447	C₂²	1	4	yes	complemented
73	C₅₃×#447	C₂²	1	4	yes	complemented
74	C₅₃×#442	C₂²	1	4	yes	complemented
75	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
76	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
77	C₅₃×#436	C₂²	1	2	yes	complemented
78	C₅₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
80	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#418	C₂²	1	4	yes	complemented
83	C₅₃×#416	C₂²	1	4	yes	complemented
84	C₅₃×#408	C₂²	1	4	yes	complemented
85	H(5,𝔽₂)×C₅₃	—	4	8	no	—
86	C₂×#41×C₅₃	—	2	2	no	—
87	C₂×#41×C₅₃	—	2	1	no	—
88	C₂×#41×C₅₃	—	2	1	no	—
89	C₂×#41×C₅₃	C₂³	1	4	yes	—
90	C₂×#41×C₅₃	C₂³	1	2	yes	—
91	C₂×#41×C₅₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₅₃	—	2	4	no	—
93	C₂²×D₄×C₅₃	—	2	2	no	—
94	C₂²×D₄×C₅₃	—	2	2	no	—
95	C₂²×D₄×C₅₃	—	2	2	no	—
96	C₂²×D₄×C₅₃	—	2	2	no	—
97	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
99	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
100	C₂³×C₄×C₅₃	—	2	1	no	—
101	AGL(1,ℤ/8)×C₅₃	—	4	8	no	—
102	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
104	C₂×D₈×C₅₃	—	4	8	no	—
105	C₂×D₈×C₅₃	C₂³	1	2	yes	—
106	C₂×D₈×C₅₃	C₂³	1	4	yes	—
107	C₂×D₈×C₅₃	C₂³	1	2	yes	—
108	C₂×D₈×C₅₃	C₂³	1	4	yes	—
109	C₂×D₈×C₅₃	C₂³	1	4	yes	—
110	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
111	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
113	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
116	#127×C₅₃	—	2	4	no	—
117	#127×C₅₃	D₄	1	1	yes	characteristic
118	#127×C₅₃	C₂³	1	1	yes	characteristic
119	#127×C₅₃	C₂³	1	1	yes	characteristic
120	#127×C₅₃	C₂³	1	1	yes	characteristic
121	#124×C₅₃	—	2	4	no	—
122	#124×C₅₃	—	2	4	no	—
123	#124×C₅₃	—	2	1	no	—
124	#124×C₅₃	—	2	1	no	—
125	#124×C₅₃	—	2	4	no	—
126	#124×C₅₃	D₄	1	2	yes	—
127	#124×C₅₃	C₂³	1	2	yes	—
128	#123×C₅₃	—	2	4	no	—
129	#123×C₅₃	—	2	4	no	—
130	C₂²⋊Q₈×C₅₃	—	2	2	no	—
131	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
132	#121×C₅₃	—	2	2	no	—
133	#121×C₅₃	—	2	2	no	—
134	#121×C₅₃	—	2	2	no	—
135	#121×C₅₃	—	2	4	no	—
136	#121×C₅₃	—	2	4	no	—
137	#121×C₅₃	—	2	2	no	—
138	#121×C₅₃	—	2	2	no	—
139	#121×C₅₃	—	2	2	no	—
140	#121×C₅₃	—	2	2	no	—
141	#121×C₅₃	—	2	1	no	—
142	#121×C₅₃	—	2	1	no	—
143	#121×C₅₃	—	2	1	no	—
144	#121×C₅₃	—	2	1	no	—
145	#121×C₅₃	D₄	1	2	yes	—
146	#121×C₅₃	D₄	1	2	yes	—
147	#121×C₅₃	C₂³	1	2	yes	—
148	#121×C₅₃	C₂³	1	2	yes	—
149	#121×C₅₃	C₂³	1	4	yes	—
150	#121×C₅₃	C₂³	1	4	yes	—
151	#121×C₅₃	C₂³	1	4	yes	—
152	#120×C₅₃	—	2	4	no	—
153	#120×C₅₃	—	2	4	no	—
154	#120×C₅₃	—	2	4	no	—
155	#120×C₅₃	—	2	4	no	—
156	#120×C₅₃	—	2	4	no	—
157	#120×C₅₃	—	2	4	no	—
158	C₄×D₄×C₅₃	—	2	1	no	—
159	C₄×D₄×C₅₃	—	2	1	no	—
160	C₄×D₄×C₅₃	—	2	1	no	—
161	C₄×D₄×C₅₃	—	2	1	no	—
162	C₄×D₄×C₅₃	—	2	1	no	—
163	C₄×D₄×C₅₃	—	2	1	no	—
164	C₄×D₄×C₅₃	C₂³	1	2	yes	—
165	C₄×D₄×C₅₃	C₂³	1	2	yes	—
166	C₄×D₄×C₅₃	C₂³	1	2	yes	—
167	C₄×D₄×C₅₃	C₂³	1	2	yes	—
168	C₄×D₄×C₅₃	C₂³	1	2	yes	—
169	C₄×D₄×C₅₃	C₂³	1	2	yes	—
170	#117×C₅₃	—	2	2	no	—
171	#117×C₅₃	—	2	2	no	—
172	#117×C₅₃	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
174	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
176	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
177	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
178	#107×C₅₃	C₂³	1	2	yes	—
179	#107×C₅₃	C₂³	1	2	yes	—
180	#106×C₅₃	C₂³	1	4	yes	—
181	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
182	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
183	#103×C₅₃	C₂³	1	4	yes	—
184	#103×C₅₃	C₂³	1	4	yes	—
185	#102×C₅₃	C₂³	1	4	yes	—
186	#102×C₅₃	C₂³	1	4	yes	—
187	#102×C₅₃	C₂³	1	2	yes	—
188	#102×C₅₃	C₂³	1	4	yes	—
189	#102×C₅₃	C₂³	1	2	yes	—
190	#102×C₅₃	C₂³	1	2	yes	—
191	#102×C₅₃	C₂³	1	2	yes	—
192	#102×C₅₃	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
194	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
197	#97×C₅₃	C₂³	1	2	yes	—
198	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
200	C₂⁴×C₅₃	—	2	1	no	—
201	C₂⁴×C₅₃	—	2	4	no	—
202	C₂⁴×C₅₃	—	2	4	no	—
203	#41×C₅₃	—	2	8	no	—
204	#41×C₅₃	—	4	4	no	—
205	#41×C₅₃	—	4	4	no	—
206	#41×C₅₃	—	4	4	no	—
207	#41×C₅₃	—	4	8	no	—
208	#41×C₅₃	—	8	2	no	—
209	#41×C₅₃	—	8	2	no	—
210	C₂×Q₈×C₅₃	—	2	1	no	—
211	C₂×Q₈×C₅₃	—	2	1	no	—
212	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
214	C₂×D₄×C₅₃	—	2	4	no	—
215	C₂×D₄×C₅₃	—	2	8	no	—
216	C₂×D₄×C₅₃	—	2	4	no	—
217	C₂×D₄×C₅₃	—	2	2	no	—
218	C₂×D₄×C₅₃	—	2	4	no	—
219	C₂×D₄×C₅₃	—	2	4	no	—
220	C₂×D₄×C₅₃	—	2	4	no	—
221	C₂×D₄×C₅₃	—	2	2	no	—
222	C₂×D₄×C₅₃	—	2	2	no	—
223	C₂×D₄×C₅₃	—	2	1	no	—
224	C₂×D₄×C₅₃	—	2	1	no	—
225	C₂×D₄×C₅₃	—	2	1	no	—
226	C₂×D₄×C₅₃	—	2	1	no	—
227	C₂×D₄×C₅₃	—	2	4	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	4	no	—
232	C₂×D₄×C₅₃	—	4	4	no	—
233	C₂×D₄×C₅₃	—	4	4	no	—
234	C₂×D₄×C₅₃	—	4	4	no	—
235	C₂×D₄×C₅₃	—	4	8	no	—
236	C₂×D₄×C₅₃	—	4	16	no	—
237	C₂×D₄×C₅₃	—	8	4	no	—
238	C₂×D₄×C₅₃	—	8	4	no	—
239	C₂×D₄×C₅₃	—	8	4	no	—
240	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
243	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
244	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₃	—	2	1	no	—
249	C₂²×C₄×C₅₃	—	2	4	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	2	2	no	—
253	C₂²×C₄×C₅₃	—	2	2	no	—
254	C₂²×C₄×C₅₃	—	2	2	no	—
255	C₂²×C₄×C₅₃	—	8	2	no	—
256	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
260	SD₁₆×C₅₃	—	4	4	no	—
261	SD₁₆×C₅₃	—	4	4	no	—
262	D₈×C₅₃	—	2	4	no	—
263	D₈×C₅₃	—	2	8	no	—
264	D₈×C₅₃	—	2	4	no	—
265	D₈×C₅₃	—	4	4	no	—
266	D₈×C₅₃	—	4	4	no	—
267	M₁₆×C₅₃	—	4	4	no	—
268	C₂×C₈×C₅₃	—	4	4	no	—
269	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₄⋊C₄×C₅₃	—	2	4	no	—
274	C₄⋊C₄×C₅₃	—	2	1	no	—
275	C₄⋊C₄×C₅₃	—	2	1	no	—
276	C₄⋊C₄×C₅₃	—	2	1	no	—
277	C₄⋊C₄×C₅₃	—	2	1	no	—
278	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₅₃	—	2	4	no	—
284	C₂²⋊C₄×C₅₃	—	2	4	no	—
285	C₂²⋊C₄×C₅₃	—	2	2	no	—
286	C₂²⋊C₄×C₅₃	—	2	2	no	—
287	C₂²⋊C₄×C₅₃	—	2	2	no	—
288	C₂²⋊C₄×C₅₃	—	2	4	no	—
289	C₂²⋊C₄×C₅₃	—	2	4	no	—
290	C₂²⋊C₄×C₅₃	—	2	4	no	—
291	C₂²⋊C₄×C₅₃	—	2	2	no	—
292	C₂²⋊C₄×C₅₃	—	2	2	no	—
293	C₂²⋊C₄×C₅₃	—	2	2	no	—
294	C₂²⋊C₄×C₅₃	—	2	2	no	—
295	C₂²⋊C₄×C₅₃	—	2	2	no	—
296	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
298	C₄²×C₅₃	—	2	4	no	—
299	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂³×C₅₃	—	2	4	no	—
304	C₂³×C₅₃	—	2	2	no	—
305	C₂³×C₅₃	—	2	2	no	—
306	C₂³×C₅₃	—	2	2	no	—
307	C₂³×C₅₃	—	2	2	no	—
308	C₂³×C₅₃	—	4	8	no	—
309	C₂³×C₅₃	—	8	1	no	—
310	C₂³×C₅₃	—	8	1	no	—
311	C₂³×C₅₃	—	8	4	no	—
312	C₂³×C₅₃	—	8	4	no	—
313	C₂³×C₅₃	—	8	4	no	—
314	C₂³×C₅₃	—	8	4	no	—
315	C₂³×C₅₃	—	8	4	no	—
316	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
317	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
318	Q₈×C₅₃	—	2	4	no	—
319	Q₈×C₅₃	—	4	2	no	—
320	Q₈×C₅₃	—	8	1	no	—
321	Q₈×C₅₃	—	8	1	no	—
322	D₄×C₅₃	—	2	4	no	—
323	D₄×C₅₃	—	2	4	no	—
324	D₄×C₅₃	—	2	2	no	—
325	D₄×C₅₃	—	2	4	no	—
326	D₄×C₅₃	—	2	2	no	—
327	D₄×C₅₃	—	2	4	no	—
328	D₄×C₅₃	—	2	2	no	—
329	D₄×C₅₃	—	4	2	no	—
330	D₄×C₅₃	—	4	4	no	—
331	D₄×C₅₃	—	4	2	no	—
332	D₄×C₅₃	—	4	8	no	—
333	D₄×C₅₃	—	4	2	no	—
334	D₄×C₅₃	—	4	8	no	—
335	D₄×C₅₃	—	4	4	no	—
336	D₄×C₅₃	—	4	2	no	—
337	D₄×C₅₃	—	4	2	no	—
338	D₄×C₅₃	—	8	1	no	—
339	D₄×C₅₃	—	8	4	no	—
340	D₄×C₅₃	—	8	1	no	—
341	D₄×C₅₃	—	8	1	no	—
342	D₄×C₅₃	—	8	4	no	—
343	D₄×C₅₃	—	8	4	no	—
344	D₄×C₅₃	—	8	4	no	—
345	D₄×C₅₃	—	8	2	no	—
346	D₄×C₅₃	—	8	2	no	—
347	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	2	4	no	—
350	C₂×C₄×C₅₃	—	2	2	no	—
351	C₂×C₄×C₅₃	—	2	4	no	—
352	C₂×C₄×C₅₃	—	2	2	no	—
353	C₂×C₄×C₅₃	—	2	2	no	—
354	C₂×C₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	4	1	no	—
357	C₂×C₄×C₅₃	—	4	8	no	—
358	C₂×C₄×C₅₃	—	4	4	no	—
359	C₂×C₄×C₅₃	—	4	4	no	—
360	C₂×C₄×C₅₃	—	4	4	no	—
361	C₂×C₄×C₅₃	—	4	4	no	—
362	C₂×C₄×C₅₃	—	8	2	no	—
363	C₂×C₄×C₅₃	—	8	1	no	—
364	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₅₃	C₂²×D₄	1	4	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	C₂⁵	1	1	yes	characteristic
371	C₈×C₅₃	—	2	2	no	—
372	C₈×C₅₃	—	2	4	no	—
373	C₈×C₅₃	—	2	2	no	—
374	#61679	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂²×C₅₃	—	2	1	no	—
376	C₂²×C₅₃	—	2	4	no	—
377	C₂²×C₅₃	—	2	1	no	—
378	C₂²×C₅₃	—	2	4	no	—
379	C₂²×C₅₃	—	2	4	no	—
380	C₂²×C₅₃	—	2	1	no	—
381	C₂²×C₅₃	—	2	4	no	—
382	C₂²×C₅₃	—	4	2	no	—
383	C₂²×C₅₃	—	4	2	no	—
384	C₂²×C₅₃	—	4	2	no	—
385	C₂²×C₅₃	—	4	2	no	—
386	C₂²×C₅₃	—	4	2	no	—
387	C₂²×C₅₃	—	4	2	no	—
388	C₂²×C₅₃	—	4	2	no	—
389	C₂²×C₅₃	—	4	2	no	—
390	C₂²×C₅₃	—	4	2	no	—
391	C₂²×C₅₃	—	4	2	no	—
392	C₂²×C₅₃	—	4	2	no	—
393	C₂²×C₅₃	—	8	4	no	—
394	C₂²×C₅₃	—	16	8	no	—
395	C₂²×C₅₃	—	16	8	no	—
396	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
397	C₄×C₅₃	—	2	1	no	—
398	C₄×C₅₃	—	2	1	no	—
399	C₄×C₅₃	—	2	1	no	—
400	C₄×C₅₃	—	2	4	no	—
401	C₄×C₅₃	—	2	1	no	—
402	C₄×C₅₃	—	4	2	no	—
403	C₄×C₅₃	—	4	2	no	—
404	C₄×C₅₃	—	4	2	no	—
405	C₄×C₅₃	—	4	2	no	—
406	C₄×C₅₃	#576	1	2	yes	—
407	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
408	#3549	C₂×C₅₃	1	1	yes	characteristic, complemented
409	#3496	C₂×C₅₃	1	1	yes	characteristic, complemented
410	#3325	C₂×C₅₃	1	2	yes	complemented
411	#3319	C₂×C₅₃	1	4	yes	complemented
412	#3303	C₂×C₅₃	1	2	yes	complemented
413	D₄×D₈	C₂×C₅₃	1	2	yes	complemented
414	#3272	C₂×C₅₃	1	2	yes	complemented
415	#3264	C₂×C₅₃	1	4	yes	complemented
416	#3214	C₂×C₅₃	1	1	yes	characteristic, complemented
417	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
418	#3198	C₂×C₅₃	1	4	yes	complemented
419	#3109	C₂×C₅₃	1	1	yes	characteristic, complemented
420	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
421	#3008	C₂×C₅₃	1	4	yes	complemented
422	#2981	C₂×C₅₃	1	1	yes	characteristic, complemented
423	C₂×C₅₃	—	4	1	no	—
424	C₂×C₅₃	—	4	4	no	—
425	C₂×C₅₃	—	4	4	no	—
426	C₂×C₅₃	—	8	2	no	—
427	C₂×C₅₃	—	8	2	no	—
428	C₂×C₅₃	—	8	2	no	—
429	C₂×C₅₃	#3484	1	1	yes	characteristic
430	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
431	C₂×C₅₃	#3585	1	1	yes	characteristic
432	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	complemented
433	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	4	yes	complemented
434	C₂²×D₈	C₂²×C₅₃	1	4	yes	complemented
435	H(3,𝔽₄)	—	2	2	no	—
436	#555	—	2	1	no	—
437	#555	C₂²×C₅₃	1	2	yes	complemented
438	#555	C₂²×C₅₃	1	2	yes	complemented
439	#547	—	2	1	no	—
440	#547	C₂²×C₅₃	1	2	yes	complemented
441	#546	—	2	2	no	—
442	#546	C₂²×C₅₃	1	4	yes	complemented
443	D₄²	—	2	1	no	—
444	D₄²	—	2	1	no	—
445	D₄²	C₂²×C₅₃	1	2	yes	complemented
446	D₄²	C₂²×C₅₃	1	2	yes	complemented
447	D₄²	C₂²×C₅₃	1	2	yes	complemented
448	#537	C₂²×C₅₃	1	2	yes	complemented
449	#535	—	2	2	no	—
450	#535	—	2	2	no	—
451	#535	C₂²×C₅₃	1	4	yes	complemented
452	#534	—	2	2	no	—
453	#532	C₂²×C₅₃	1	1	yes	characteristic
454	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
455	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
456	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
457	C₂×#121	—	2	2	no	—
458	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
459	#496	C₂²×C₅₃	1	2	yes	complemented
460	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
461	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
462	#489	C₂²×C₅₃	1	2	yes	complemented
463	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
464	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
465	#485	C₂²×C₅₃	1	4	yes	complemented
466	#482	C₂²×C₅₃	1	4	yes	complemented
467	#481	C₂²×C₅₃	1	2	yes	complemented
468	#480	C₂²×C₅₃	1	2	yes	complemented
469	#476	C₂²×C₅₃	1	2	yes	complemented
470	#474	C₂²×C₅₃	1	2	yes	complemented
471	#469	C₂²×C₅₃	1	4	yes	complemented
472	#468	C₂²×C₅₃	1	4	yes	complemented
473	#466	C₂²×C₅₃	1	4	yes	complemented
474	#465	C₂²×C₅₃	1	4	yes	complemented
475	#463	C₂²×C₅₃	1	4	yes	complemented
476	#461	C₂²×C₅₃	1	2	yes	complemented
477	#459	C₂²×C₅₃	1	2	yes	complemented
478	#459	C₂²×C₅₃	1	2	yes	complemented
479	#459	C₂²×C₅₃	1	2	yes	complemented
480	#450	C₂²×C₅₃	1	4	yes	complemented
481	#449	C₂²×C₅₃	1	4	yes	complemented
482	#449	C₂²×C₅₃	1	4	yes	complemented
483	#449	C₂²×C₅₃	1	4	yes	complemented
484	#449	C₂²×C₅₃	1	4	yes	complemented
485	#447	C₂²×C₅₃	1	2	yes	complemented
486	#447	C₂²×C₅₃	1	2	yes	complemented
487	#447	C₂²×C₅₃	1	4	yes	complemented
488	#447	C₂²×C₅₃	1	4	yes	complemented
489	#447	C₂²×C₅₃	1	4	yes	complemented
490	#442	C₂²×C₅₃	1	4	yes	complemented
491	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
492	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
493	#436	C₂²×C₅₃	1	2	yes	complemented
494	#435	C₂²×C₅₃	1	4	yes	complemented
495	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
496	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
497	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
498	#418	C₂²×C₅₃	1	4	yes	complemented
499	#416	C₂²×C₅₃	1	4	yes	complemented
500	#408	C₂²×C₅₃	1	4	yes	complemented
501	C₅₃	#61679	1	1	yes	characteristic, direct product factor, Sylow
502	H(5,𝔽₂)	—	4	8	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	—	2	1	no	—
505	C₂×#41	—	2	1	no	—
506	C₂×#41	C₂³×C₅₃	1	4	yes	—
507	C₂×#41	C₂³×C₅₃	1	2	yes	—
508	C₂×#41	C₂³×C₅₃	1	2	yes	—
509	C₂²×D₄	—	2	4	no	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	—	2	2	no	—
512	C₂²×D₄	—	2	2	no	—
513	C₂²×D₄	—	2	2	no	—
514	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
516	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
517	C₂³×C₄	—	2	1	no	—
518	AGL(1,ℤ/8)	—	4	8	no	—
519	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
520	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
521	C₂×D₈	—	4	8	no	—
522	C₂×D₈	C₂³×C₅₃	1	2	yes	—
523	C₂×D₈	C₂³×C₅₃	1	4	yes	—
524	C₂×D₈	C₂³×C₅₃	1	2	yes	—
525	C₂×D₈	C₂³×C₅₃	1	4	yes	—
526	C₂×D₈	C₂³×C₅₃	1	4	yes	—
527	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
528	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
529	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
533	#127	—	2	4	no	—
534	#127	D₄×C₅₃	1	1	yes	characteristic
535	#127	C₂³×C₅₃	1	1	yes	characteristic
536	#127	C₂³×C₅₃	1	1	yes	characteristic
537	#127	C₂³×C₅₃	1	1	yes	characteristic
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#124	—	2	4	no	—
541	#124	—	2	1	no	—
542	#124	—	2	1	no	—
543	#124	D₄×C₅₃	1	2	yes	—
544	#124	C₂³×C₅₃	1	2	yes	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
549	#121	—	2	4	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	2	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	1	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	2	no	—
561	#121	—	2	4	no	—
562	#121	D₄×C₅₃	1	2	yes	—
563	#121	D₄×C₅₃	1	2	yes	—
564	#121	C₂³×C₅₃	1	2	yes	—
565	#121	C₂³×C₅₃	1	2	yes	—
566	#121	C₂³×C₅₃	1	4	yes	—
567	#121	C₂³×C₅₃	1	4	yes	—
568	#121	C₂³×C₅₃	1	4	yes	—
569	#120	—	2	4	no	—
570	#120	—	2	4	no	—
571	#120	—	2	4	no	—
572	#120	—	2	4	no	—
573	#120	—	2	4	no	—
574	#120	—	2	4	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	C₂³×C₅₃	1	2	yes	—
582	C₄×D₄	C₂³×C₅₃	1	2	yes	—
583	C₄×D₄	C₂³×C₅₃	1	2	yes	—
584	C₄×D₄	C₂³×C₅₃	1	2	yes	—
585	C₄×D₄	C₂³×C₅₃	1	2	yes	—
586	C₄×D₄	C₂³×C₅₃	1	2	yes	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	C₂³×C₅₃	1	4	yes	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	4	no	—
594	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
595	#107	C₂³×C₅₃	1	2	yes	—
596	#107	C₂³×C₅₃	1	2	yes	—
597	#106	C₂³×C₅₃	1	4	yes	—
598	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
599	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
600	#103	C₂³×C₅₃	1	4	yes	—
601	#103	C₂³×C₅₃	1	4	yes	—
602	#102	C₂³×C₅₃	1	2	yes	—
603	#102	C₂³×C₅₃	1	4	yes	—
604	#102	C₂³×C₅₃	1	2	yes	—
605	#102	C₂³×C₅₃	1	4	yes	—
606	#102	C₂³×C₅₃	1	4	yes	—
607	#102	C₂³×C₅₃	1	2	yes	—
608	#102	C₂³×C₅₃	1	2	yes	—
609	#102	C₂³×C₅₃	1	4	yes	—
610	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
611	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
612	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
613	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
614	#97	C₂³×C₅₃	1	2	yes	—
615	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
616	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
617	C₂⁴	—	2	1	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	2	4	no	—
620	#41	—	2	8	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	4	8	no	—
625	#41	—	8	2	no	—
626	#41	—	8	2	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	8	no	—
653	C₂×D₄	—	4	16	no	—
654	C₂×D₄	—	8	4	no	—
655	C₂×D₄	—	8	4	no	—
656	C₂×D₄	—	8	4	no	—
657	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
658	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
659	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
660	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
661	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
662	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
663	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
664	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
677	SD₁₆	—	4	4	no	—
678	SD₁₆	—	4	4	no	—
679	D₈	—	2	4	no	—
680	D₈	—	2	8	no	—
681	D₈	—	2	4	no	—
682	D₈	—	4	4	no	—
683	D₈	—	4	4	no	—
684	M₁₆	—	4	4	no	—
685	C₂×C₈	—	4	4	no	—
686	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
687	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
688	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
696	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
714	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
715	C₄²	—	2	4	no	—
716	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
718	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
719	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
720	C₂³	—	2	4	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	4	no	—
729	C₂³	—	8	4	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
734	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
735	Q₈	—	2	4	no	—
736	Q₈	—	4	2	no	—
737	Q₈	—	8	1	no	—
738	Q₈	—	8	1	no	—
739	D₄	—	2	4	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	2	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	4	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	8	1	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	1	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	4	no	—
762	D₄	—	8	2	no	—
763	D₄	—	8	2	no	—
764	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	8	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	2	no	—
780	C₂×C₄	—	8	1	no	—
781	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
782	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
787	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
788	C₈	—	2	2	no	—
789	C₈	—	2	4	no	—
790	C₈	—	2	2	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	8	4	no	—
810	C₂²	—	16	8	no	—
811	C₂²	—	16	8	no	—
812	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	4	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	C₅₃×#576	1	2	yes	—
823	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
824	C₂	—	4	1	no	—
825	C₂	—	4	4	no	—
826	C₂	—	4	4	no	—
827	C₂	—	8	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	2	no	—
830	C₂	C₅₃×#3484	1	1	yes	characteristic
831	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
832	C₂	C₅₃×#3585	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 ◁ C₅₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3549	C₂	semidirect
2. C₅₃×#3496	C₂	semidirect
3. C₅₃×#3325	C₂	semidirect
4. C₅₃×#3319	C₂	semidirect
5. C₅₃×#3303	C₂	semidirect
6. D₄×D₈×C₅₃	C₂	semidirect
7. C₅₃×#3272	C₂	semidirect
8. C₅₃×#3264	C₂	semidirect
9. C₅₃×#3214	C₂	semidirect
10. C₅₃×#3207	C₂	semidirect
11. C₅₃×#3198	C₂	semidirect
12. C₅₃×#3109	C₂	semidirect
13. C₅₃×#3100	C₂	semidirect
14. C₅₃×#3008	C₂	semidirect
15. C₅₃×#2981	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
17. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
18. C₂²×D₈×C₅₃	C₂²	semidirect
21. C₅₃×#555	C₂²	semidirect
22. C₅₃×#555	C₂²	semidirect
24. C₅₃×#547	C₂²	semidirect
26. C₅₃×#546	C₂²	semidirect
29. D₄²×C₅₃	C₂²	semidirect
30. D₄²×C₅₃	C₂²	semidirect
31. D₄²×C₅₃	C₂²	semidirect
32. C₅₃×#537	C₂²	semidirect
35. C₅₃×#535	C₂²	semidirect
38. C₅₃×#532	C₂²	semidirect
39. C₅₃×#532	C₂²	semidirect
40. C₅₃×#532	C₂²	semidirect
42. C₂×C₄×D₄×C₅₃	C₂²	semidirect
43. C₅₃×#496	C₂²	semidirect
44. C₅₃×#493	C₂²	semidirect
45. C₅₃×#492	C₂²	semidirect
46. C₅₃×#489	C₂²	semidirect
47. C₅₃×#487	C₂²	semidirect
48. C₅₃×#486	C₂²	semidirect
49. C₅₃×#485	C₂²	semidirect
50. C₅₃×#482	C₂²	semidirect
51. C₅₃×#481	C₂²	semidirect
52. C₅₃×#480	C₂²	semidirect
53. C₅₃×#476	C₂²	semidirect
54. C₅₃×#474	C₂²	semidirect
55. C₅₃×#469	C₂²	semidirect
56. C₅₃×#468	C₂²	semidirect
57. C₅₃×#466	C₂²	semidirect
58. C₅₃×#465	C₂²	semidirect
59. C₅₃×#463	C₂²	semidirect
60. C₅₃×#461	C₂²	semidirect
61. C₅₃×#459	C₂²	semidirect
62. C₅₃×#459	C₂²	semidirect
63. C₅₃×#459	C₂²	semidirect
64. C₅₃×#450	C₂²	semidirect
65. C₅₃×#449	C₂²	semidirect
66. C₅₃×#449	C₂²	semidirect
67. C₅₃×#449	C₂²	semidirect
68. C₅₃×#449	C₂²	semidirect
69. C₅₃×#447	C₂²	semidirect
70. C₅₃×#447	C₂²	semidirect
71. C₅₃×#447	C₂²	semidirect
72. C₅₃×#447	C₂²	semidirect
73. C₅₃×#447	C₂²	semidirect
74. C₅₃×#442	C₂²	semidirect
75. C₄×D₈×C₅₃	C₂²	semidirect
76. C₄×D₈×C₅₃	C₂²	semidirect
77. C₅₃×#436	C₂²	semidirect
78. C₅₃×#435	C₂²	semidirect
79. C₈×D₄×C₅₃	C₂²	semidirect
80. C₅₃×#432	C₂²	semidirect
81. C₅₃×#431	C₂²	semidirect
82. C₅₃×#418	C₂²	semidirect
83. C₅₃×#416	C₂²	semidirect
84. C₅₃×#408	C₂²	semidirect
374. #61679	C₅₃	direct (N × H)
408. #3549	C₂×C₅₃	semidirect
409. #3496	C₂×C₅₃	semidirect
410. #3325	C₂×C₅₃	semidirect
411. #3319	C₂×C₅₃	semidirect
412. #3303	C₂×C₅₃	semidirect
413. D₄×D₈	C₂×C₅₃	semidirect
414. #3272	C₂×C₅₃	semidirect
415. #3264	C₂×C₅₃	semidirect
416. #3214	C₂×C₅₃	semidirect
417. #3207	C₂×C₅₃	semidirect
418. #3198	C₂×C₅₃	semidirect
419. #3109	C₂×C₅₃	semidirect
420. #3100	C₂×C₅₃	semidirect
421. #3008	C₂×C₅₃	semidirect
422. #2981	C₂×C₅₃	semidirect
432. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
433. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
434. C₂²×D₈	C₂²×C₅₃	semidirect
437. #555	C₂²×C₅₃	semidirect
438. #555	C₂²×C₅₃	semidirect
440. #547	C₂²×C₅₃	semidirect
442. #546	C₂²×C₅₃	semidirect
445. D₄²	C₂²×C₅₃	semidirect
446. D₄²	C₂²×C₅₃	semidirect
447. D₄²	C₂²×C₅₃	semidirect
448. #537	C₂²×C₅₃	semidirect
451. #535	C₂²×C₅₃	semidirect
454. #532	C₂²×C₅₃	semidirect
455. #532	C₂²×C₅₃	semidirect
456. #532	C₂²×C₅₃	semidirect
458. C₂×C₄×D₄	C₂²×C₅₃	semidirect
459. #496	C₂²×C₅₃	semidirect
460. #493	C₂²×C₅₃	semidirect
461. #492	C₂²×C₅₃	semidirect
462. #489	C₂²×C₅₃	semidirect
463. #487	C₂²×C₅₃	semidirect
464. #486	C₂²×C₅₃	semidirect
465. #485	C₂²×C₅₃	semidirect
466. #482	C₂²×C₅₃	semidirect
467. #481	C₂²×C₅₃	semidirect
468. #480	C₂²×C₅₃	semidirect
469. #476	C₂²×C₅₃	semidirect
470. #474	C₂²×C₅₃	semidirect
471. #469	C₂²×C₅₃	semidirect
472. #468	C₂²×C₅₃	semidirect
473. #466	C₂²×C₅₃	semidirect
474. #465	C₂²×C₅₃	semidirect
475. #463	C₂²×C₅₃	semidirect
476. #461	C₂²×C₅₃	semidirect
477. #459	C₂²×C₅₃	semidirect
478. #459	C₂²×C₅₃	semidirect
479. #459	C₂²×C₅₃	semidirect
480. #450	C₂²×C₅₃	semidirect
481. #449	C₂²×C₅₃	semidirect
482. #449	C₂²×C₅₃	semidirect
483. #449	C₂²×C₅₃	semidirect
484. #449	C₂²×C₅₃	semidirect
485. #447	C₂²×C₅₃	semidirect
486. #447	C₂²×C₅₃	semidirect
487. #447	C₂²×C₅₃	semidirect
488. #447	C₂²×C₅₃	semidirect
489. #447	C₂²×C₅₃	semidirect
490. #442	C₂²×C₅₃	semidirect
491. C₄×D₈	C₂²×C₅₃	semidirect
492. C₄×D₈	C₂²×C₅₃	semidirect
493. #436	C₂²×C₅₃	semidirect
494. #435	C₂²×C₅₃	semidirect
495. C₈×D₄	C₂²×C₅₃	semidirect
496. #432	C₂²×C₅₃	semidirect
497. #431	C₂²×C₅₃	semidirect
498. #418	C₂²×C₅₃	semidirect
499. #416	C₂²×C₅₃	semidirect
500. #408	C₂²×C₅₃	semidirect
501. C₅₃	#61679	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3549	2
C₅₃×#3496	2
C₅₃×#3325	2
C₅₃×#3319	2
C₅₃×#3303	2
D₄×D₈×C₅₃	2
C₅₃×#3272	2
C₅₃×#3264	2
C₅₃×#3214	2
C₅₃×#3207	2
C₅₃×#3198	2
C₅₃×#3109	2
C₅₃×#3100	2
C₅₃×#3008	2
C₅₃×#2981	2
#61679	53

Subgroups — C53×#61679 #27269191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61679 #27269191