Subgroups — C₅₃×#60819 #27268331

Order 13568.

2058 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3224	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3212	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3211	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₅₃×#559	—	2	2	no	—
31	C₅₃×#556	—	2	2	no	—
32	C₅₃×#551	—	2	4	no	—
33	C₅₃×#548	—	2	2	no	—
34	C₅₃×#546	—	2	4	no	—
35	C₅₃×#546	—	2	2	no	—
36	C₅₃×#542	C₂²	1	4	yes	complemented
37	C₅₃×#536	C₂²	1	1	yes	characteristic
38	C₅₃×#536	C₂²	1	1	yes	characteristic
39	C₅₃×#536	C₂²	1	2	yes	complemented
40	C₅₃×#535	C₂²	1	1	yes	characteristic
41	C₅₃×#535	C₂²	1	1	yes	characteristic
42	C₅₃×#535	C₂²	1	2	yes	complemented
43	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#532	C₂²	1	1	yes	characteristic
45	C₅₃×#532	C₂²	1	2	yes	complemented
46	C₅₃×#529	C₂²	1	4	yes	complemented
47	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
49	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
52	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
53	C₅₃×#497	C₂²	1	2	yes	complemented
54	C₅₃×#496	C₂²	1	2	yes	complemented
55	C₅₃×#495	C₂²	1	2	yes	complemented
56	C₅₃×#495	C₂²	1	4	yes	complemented
57	C₅₃×#495	C₂²	1	2	yes	complemented
58	C₅₃×#495	C₂²	1	4	yes	complemented
59	C₅₃×#489	C₂²	1	4	yes	complemented
60	C₅₃×#488	C₂²	1	2	yes	complemented
61	C₅₃×#488	C₂²	1	4	yes	complemented
62	C₅₃×#488	C₂²	1	2	yes	complemented
63	C₅₃×#487	C₂²	1	2	yes	complemented
64	C₅₃×#486	C₂²	1	2	yes	complemented
65	C₅₃×#464	C₂²	1	4	yes	complemented
66	C₅₃×#464	C₂²	1	4	yes	complemented
67	C₅₃×#463	C₂²	1	4	yes	complemented
68	C₅₃×#463	C₂²	1	4	yes	complemented
69	C₅₃×#462	C₂²	1	4	yes	complemented
70	C₅₃×#461	C₂²	1	4	yes	complemented
71	C₅₃×#460	C₂²	1	4	yes	complemented
72	C₅₃×#459	C₂²	1	4	yes	complemented
73	C₅₃×#452	C₂²	1	4	yes	complemented
74	C₅₃×#452	C₂²	1	4	yes	complemented
75	C₅₃×#451	C₂²	1	4	yes	complemented
76	C₅₃×#450	C₂²	1	4	yes	complemented
77	C₅₃×#449	C₂²	1	4	yes	—
78	C₅₃×#449	C₂²	1	4	yes	complemented
79	C₅₃×#448	C₂²	1	4	yes	complemented
80	C₅₃×#447	C₂²	1	4	yes	—
81	C₅₃×#433	C₂²	1	4	yes	complemented
82	C₅₃×#431	C₂²	1	4	yes	complemented
83	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#418	C₂²	1	1	yes	characteristic
88	C₅₃×#418	C₂²	1	1	yes	characteristic
89	C₅₃×#416	C₂²	1	1	yes	characteristic
90	C₅₃×#416	C₂²	1	1	yes	characteristic
91	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#408	C₂²	1	1	yes	characteristic
94	C₅₃×#408	C₂²	1	1	yes	characteristic
95	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
97	2₋¹⁺⁴×C₅₃	—	4	2	no	—
98	2₋¹⁺⁴×C₅₃	—	4	2	no	—
99	H(5,𝔽₂)×C₅₃	—	4	2	no	—
100	H(5,𝔽₂)×C₅₃	—	4	2	no	—
101	C₂×#41×C₅₃	—	2	1	no	—
102	C₂×#41×C₅₃	—	2	2	no	—
103	C₂×#41×C₅₃	—	2	1	no	—
104	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
105	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
106	C₂×#41×C₅₃	C₂³	1	2	yes	—
107	C₂×#41×C₅₃	C₂³	1	2	yes	—
108	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₅₃	—	2	1	no	—
110	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₅₃	—	2	2	no	—
114	C₂²×D₄×C₅₃	—	2	1	no	—
115	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
118	#137×C₅₃	—	4	2	no	—
119	#137×C₅₃	—	4	2	no	—
120	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
121	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
122	C₂×Q₁₆×C₅₃	—	4	2	no	—
123	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
124	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₅₃	—	4	2	no	—
127	C₂×SD₁₆×C₅₃	—	4	2	no	—
128	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
134	C₂×D₈×C₅₃	—	4	2	no	—
135	C₂×D₈×C₅₃	C₂³	1	4	yes	—
136	C₂×D₈×C₅₃	C₂³	1	2	yes	—
137	C₂×D₈×C₅₃	C₂³	1	2	yes	—
138	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₅₃	—	2	1	no	—
143	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
144	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
146	#127×C₅₃	—	2	1	no	—
147	#127×C₅₃	C₂³	1	1	yes	characteristic
148	#127×C₅₃	C₂³	1	2	yes	—
149	#126×C₅₃	—	2	4	no	—
150	#126×C₅₃	—	2	4	no	—
151	#125×C₅₃	C₂³	1	2	yes	—
152	#124×C₅₃	—	2	4	no	—
153	#124×C₅₃	—	2	2	no	—
154	#124×C₅₃	—	2	4	no	—
155	#124×C₅₃	—	2	2	no	—
156	#124×C₅₃	—	2	1	no	—
157	#124×C₅₃	—	2	1	no	—
158	#124×C₅₃	C₂³	1	2	yes	—
159	#124×C₅₃	C₂³	1	1	yes	characteristic
160	#124×C₅₃	C₂³	1	1	yes	characteristic
161	#124×C₅₃	C₂³	1	2	yes	—
162	#124×C₅₃	C₂³	1	2	yes	—
163	#124×C₅₃	C₂³	1	2	yes	—
164	#124×C₅₃	C₂³	1	2	yes	—
165	#124×C₅₃	C₂³	1	2	yes	—
166	#123×C₅₃	—	2	2	no	—
167	#123×C₅₃	—	2	4	no	—
168	#123×C₅₃	—	2	4	no	—
169	#123×C₅₃	—	2	2	no	—
170	#123×C₅₃	—	2	4	no	—
171	C₂²⋊Q₈×C₅₃	—	2	2	no	—
172	C₂²⋊Q₈×C₅₃	—	2	4	no	—
173	C₂²⋊Q₈×C₅₃	—	2	4	no	—
174	C₂²⋊Q₈×C₅₃	—	2	2	no	—
175	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
176	#121×C₅₃	—	2	2	no	—
177	#121×C₅₃	—	2	4	no	—
178	#121×C₅₃	—	2	2	no	—
179	#121×C₅₃	—	2	4	no	—
180	#121×C₅₃	C₂³	1	4	yes	—
181	#120×C₅₃	—	2	2	no	—
182	#120×C₅₃	—	2	4	no	—
183	#120×C₅₃	—	2	2	no	—
184	C₄×Q₈×C₅₃	—	2	2	no	—
185	C₄×Q₈×C₅₃	—	2	2	no	—
186	C₄×Q₈×C₅₃	D₄	1	2	yes	—
187	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
188	C₄×D₄×C₅₃	—	2	2	no	—
189	C₄×D₄×C₅₃	—	2	2	no	—
190	C₄×D₄×C₅₃	—	2	4	no	—
191	C₄×D₄×C₅₃	—	2	4	no	—
192	C₄×D₄×C₅₃	D₄	1	4	yes	—
193	C₄×D₄×C₅₃	D₄	1	2	yes	—
194	C₄×D₄×C₅₃	C₂³	1	4	yes	—
195	#117×C₅₃	—	2	2	no	—
196	#117×C₅₃	—	2	4	no	—
197	#117×C₅₃	C₂³	1	1	yes	characteristic
198	#117×C₅₃	C₂³	1	1	yes	characteristic
199	#117×C₅₃	C₂³	1	1	yes	characteristic
200	#117×C₅₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
204	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
205	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
207	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
208	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
209	#103×C₅₃	C₂³	1	2	yes	—
210	#103×C₅₃	C₂³	1	2	yes	—
211	#103×C₅₃	C₂³	1	2	yes	—
212	#103×C₅₃	C₂³	1	2	yes	—
213	#103×C₅₃	C₂³	1	4	yes	—
214	#103×C₅₃	C₂³	1	4	yes	—
215	#102×C₅₃	C₂³	1	2	yes	—
216	#102×C₅₃	C₂³	1	2	yes	—
217	#102×C₅₃	C₂³	1	2	yes	—
218	#102×C₅₃	C₂³	1	2	yes	—
219	#102×C₅₃	C₂³	1	4	yes	—
220	#102×C₅₃	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
223	#97×C₅₃	C₂³	1	2	yes	—
224	C₄×C₈×C₅₃	C₂³	1	2	yes	—
225	C₄×C₈×C₅₃	C₂³	1	2	yes	—
226	C₄×C₈×C₅₃	C₂³	1	2	yes	—
227	C₂⁴×C₅₃	—	2	1	no	—
228	C₂⁴×C₅₃	—	2	2	no	—
229	C₂⁴×C₅₃	—	2	1	no	—
230	#41×C₅₃	—	2	2	no	—
231	#41×C₅₃	—	2	2	no	—
232	#41×C₅₃	—	2	2	no	—
233	#41×C₅₃	—	2	2	no	—
234	#41×C₅₃	—	2	2	no	—
235	#41×C₅₃	—	2	2	no	—
236	#41×C₅₃	—	4	2	no	—
237	#41×C₅₃	—	4	2	no	—
238	#41×C₅₃	—	4	2	no	—
239	#41×C₅₃	—	4	2	no	—
240	#41×C₅₃	—	4	8	no	—
241	#41×C₅₃	—	4	4	no	—
242	#41×C₅₃	—	4	4	no	—
243	C₂×Q₈×C₅₃	—	2	1	no	—
244	C₂×Q₈×C₅₃	—	2	2	no	—
245	C₂×Q₈×C₅₃	—	2	1	no	—
246	C₂×Q₈×C₅₃	—	2	2	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	—	2	2	no	—
249	C₂×Q₈×C₅₃	—	2	2	no	—
250	C₂×Q₈×C₅₃	—	2	2	no	—
251	C₂×Q₈×C₅₃	—	4	2	no	—
252	C₂×Q₈×C₅₃	—	4	2	no	—
253	C₂×Q₈×C₅₃	—	4	4	no	—
254	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
255	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	—	2	1	no	—
261	C₂×D₄×C₅₃	—	2	2	no	—
262	C₂×D₄×C₅₃	—	2	1	no	—
263	C₂×D₄×C₅₃	—	2	4	no	—
264	C₂×D₄×C₅₃	—	2	1	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	1	no	—
267	C₂×D₄×C₅₃	—	2	4	no	—
268	C₂×D₄×C₅₃	—	2	2	no	—
269	C₂×D₄×C₅₃	—	2	2	no	—
270	C₂×D₄×C₅₃	—	2	2	no	—
271	C₂×D₄×C₅₃	—	2	2	no	—
272	C₂×D₄×C₅₃	—	2	2	no	—
273	C₂×D₄×C₅₃	—	4	2	no	—
274	C₂×D₄×C₅₃	—	4	2	no	—
275	C₂×D₄×C₅₃	—	4	8	no	—
276	C₂×D₄×C₅₃	—	4	4	no	—
277	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
278	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
279	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
280	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
281	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅₃	—	2	1	no	—
284	C₂²×C₄×C₅₃	—	2	2	no	—
285	C₂²×C₄×C₅₃	—	2	1	no	—
286	C₂²×C₄×C₅₃	—	2	2	no	—
287	C₂²×C₄×C₅₃	—	2	1	no	—
288	C₂²×C₄×C₅₃	—	2	2	no	—
289	C₂²×C₄×C₅₃	—	2	1	no	—
290	C₂²×C₄×C₅₃	—	2	4	no	—
291	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	Q₁₆×C₅₃	—	4	4	no	—
296	Q₁₆×C₅₃	—	4	2	no	—
297	Q₁₆×C₅₃	—	4	2	no	—
298	SD₁₆×C₅₃	—	4	4	no	—
299	SD₁₆×C₅₃	—	4	4	no	—
300	SD₁₆×C₅₃	—	4	2	no	—
301	SD₁₆×C₅₃	—	4	2	no	—
302	SD₁₆×C₅₃	—	4	2	no	—
303	SD₁₆×C₅₃	—	4	2	no	—
304	D₈×C₅₃	—	4	4	no	—
305	D₈×C₅₃	—	4	2	no	—
306	D₈×C₅₃	—	4	2	no	—
307	M₁₆×C₅₃	—	2	2	no	—
308	M₁₆×C₅₃	—	2	2	no	—
309	C₂×C₈×C₅₃	—	2	2	no	—
310	C₂×C₈×C₅₃	—	2	2	no	—
311	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
312	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
313	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₅₃	—	2	2	no	—
316	C₄⋊C₄×C₅₃	—	2	4	no	—
317	C₄⋊C₄×C₅₃	—	2	4	no	—
318	C₄⋊C₄×C₅₃	—	2	2	no	—
319	C₄⋊C₄×C₅₃	—	2	4	no	—
320	C₄⋊C₄×C₅₃	—	2	2	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
323	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
324	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
326	C₂²⋊C₄×C₅₃	—	2	1	no	—
327	C₂²⋊C₄×C₅₃	—	2	1	no	—
328	C₂²⋊C₄×C₅₃	—	2	4	no	—
329	C₂²⋊C₄×C₅₃	—	2	4	no	—
330	C₂²⋊C₄×C₅₃	—	2	2	no	—
331	C₂²⋊C₄×C₅₃	—	2	4	no	—
332	C₂²⋊C₄×C₅₃	—	2	4	no	—
333	C₂²⋊C₄×C₅₃	—	2	4	no	—
334	C₂²⋊C₄×C₅₃	—	2	4	no	—
335	C₂²⋊C₄×C₅₃	—	2	4	no	—
336	C₂²⋊C₄×C₅₃	—	2	4	no	—
337	C₂²⋊C₄×C₅₃	—	2	4	no	—
338	C₂²⋊C₄×C₅₃	—	2	2	no	—
339	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
341	C₄²×C₅₃	—	2	4	no	—
342	C₄²×C₅₃	—	2	1	no	—
343	C₄²×C₅₃	—	2	1	no	—
344	C₄²×C₅₃	C₂×D₄	1	4	yes	—
345	C₄²×C₅₃	C₂×D₄	1	2	yes	—
346	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₅₃	C₂⁴	1	2	yes	—
349	C₂³×C₅₃	—	2	1	no	—
350	C₂³×C₅₃	—	2	2	no	—
351	C₂³×C₅₃	—	2	2	no	—
352	C₂³×C₅₃	—	2	1	no	—
353	C₂³×C₅₃	—	4	4	no	—
354	C₂³×C₅₃	—	4	2	no	—
355	C₂³×C₅₃	—	4	2	no	—
356	C₂³×C₅₃	—	8	2	no	—
357	C₂³×C₅₃	—	8	2	no	—
358	C₂³×C₅₃	—	8	4	no	—
359	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
360	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₅₃	—	2	2	no	—
362	Q₈×C₅₃	—	2	2	no	—
363	Q₈×C₅₃	—	2	2	no	—
364	Q₈×C₅₃	—	2	2	no	—
365	Q₈×C₅₃	—	2	2	no	—
366	Q₈×C₅₃	—	2	1	no	—
367	Q₈×C₅₃	—	2	1	no	—
368	Q₈×C₅₃	—	2	1	no	—
369	Q₈×C₅₃	—	2	1	no	—
370	Q₈×C₅₃	—	4	4	no	—
371	Q₈×C₅₃	—	4	2	no	—
372	Q₈×C₅₃	—	4	2	no	—
373	Q₈×C₅₃	—	8	2	no	—
374	D₄×C₅₃	—	2	4	no	—
375	D₄×C₅₃	—	2	2	no	—
376	D₄×C₅₃	—	2	2	no	—
377	D₄×C₅₃	—	2	2	no	—
378	D₄×C₅₃	—	2	2	no	—
379	D₄×C₅₃	—	2	2	no	—
380	D₄×C₅₃	—	2	1	no	—
381	D₄×C₅₃	—	2	1	no	—
382	D₄×C₅₃	—	2	1	no	—
383	D₄×C₅₃	—	2	1	no	—
384	D₄×C₅₃	—	4	4	no	—
385	D₄×C₅₃	—	4	4	no	—
386	D₄×C₅₃	—	4	4	no	—
387	D₄×C₅₃	—	4	2	no	—
388	D₄×C₅₃	—	4	2	no	—
389	D₄×C₅₃	—	4	2	no	—
390	D₄×C₅₃	—	4	2	no	—
391	D₄×C₅₃	—	8	4	no	—
392	D₄×C₅₃	—	8	2	no	—
393	D₄×C₅₃	—	8	4	no	—
394	C₂×C₄×C₅₃	—	2	2	no	—
395	C₂×C₄×C₅₃	—	2	2	no	—
396	C₂×C₄×C₅₃	—	2	1	no	—
397	C₂×C₄×C₅₃	—	2	2	no	—
398	C₂×C₄×C₅₃	—	2	1	no	—
399	C₂×C₄×C₅₃	—	2	2	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	2	no	—
402	C₂×C₄×C₅₃	—	4	4	no	—
403	C₂×C₄×C₅₃	—	4	2	no	—
404	C₂×C₄×C₅₃	—	4	4	no	—
405	C₂×C₄×C₅₃	—	4	4	no	—
406	C₂×C₄×C₅₃	—	4	4	no	—
407	C₂×C₄×C₅₃	—	4	2	no	—
408	C₂×C₄×C₅₃	—	4	2	no	—
409	C₂×C₄×C₅₃	—	4	2	no	—
410	C₂×C₄×C₅₃	—	4	2	no	—
411	C₂×C₄×C₅₃	—	8	4	no	—
412	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
414	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₅₃	—	2	2	no	—
421	C₈×C₅₃	—	2	2	no	—
422	C₈×C₅₃	—	2	2	no	—
423	C₈×C₅₃	—	2	2	no	—
424	#60819	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂²×C₅₃	—	2	2	no	—
426	C₂²×C₅₃	—	2	4	no	—
427	C₂²×C₅₃	—	2	2	no	—
428	C₂²×C₅₃	—	4	4	no	—
429	C₂²×C₅₃	—	4	2	no	—
430	C₂²×C₅₃	—	4	4	no	—
431	C₂²×C₅₃	—	4	2	no	—
432	C₂²×C₅₃	—	4	1	no	—
433	C₂²×C₅₃	—	4	2	no	—
434	C₂²×C₅₃	—	4	1	no	—
435	C₂²×C₅₃	—	4	2	no	—
436	C₂²×C₅₃	—	16	2	no	—
437	C₂²×C₅₃	—	16	2	no	—
438	C₂²×C₅₃	—	16	4	no	—
439	C₂²×C₅₃	#535	1	2	yes	—
440	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
441	C₄×C₅₃	—	2	2	no	—
442	C₄×C₅₃	—	2	4	no	—
443	C₄×C₅₃	—	2	2	no	—
444	C₄×C₅₃	—	2	2	no	—
445	C₄×C₅₃	—	4	2	no	—
446	C₄×C₅₃	—	4	2	no	—
447	C₄×C₅₃	—	4	1	no	—
448	C₄×C₅₃	—	4	2	no	—
449	C₄×C₅₃	—	4	1	no	—
450	C₄×C₅₃	—	4	2	no	—
451	C₄×C₅₃	#535	1	2	yes	—
452	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
454	#3510	C₂×C₅₃	1	1	yes	characteristic, complemented
455	#3500	C₂×C₅₃	1	1	yes	characteristic, complemented
456	#3225	C₂×C₅₃	1	4	yes	complemented
457	#3224	C₂×C₅₃	1	4	yes	complemented
458	#3212	C₂×C₅₃	1	4	yes	complemented
459	#3211	C₂×C₅₃	1	4	yes	complemented
460	#3153	C₂×C₅₃	1	1	yes	characteristic, complemented
461	C₂×#495	C₂×C₅₃	1	1	yes	characteristic, complemented
462	#3140	C₂×C₅₃	1	1	yes	characteristic, complemented
463	#3131	C₂×C₅₃	1	1	yes	characteristic, complemented
464	#3044	C₂×C₅₃	1	1	yes	characteristic, complemented
465	#3043	C₂×C₅₃	1	1	yes	characteristic, complemented
466	#3042	C₂×C₅₃	1	1	yes	characteristic, complemented
467	#3041	C₂×C₅₃	1	1	yes	characteristic, complemented
468	#3011	C₂×C₅₃	1	1	yes	characteristic, complemented
469	#3010	C₂×C₅₃	1	1	yes	characteristic, complemented
470	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
471	#3008	C₂×C₅₃	1	1	yes	characteristic, complemented
472	#2922	C₂×C₅₃	1	1	yes	characteristic, complemented
473	C₂×C₅₃	—	2	2	no	—
474	C₂×C₅₃	—	4	2	no	—
475	C₂×C₅₃	—	8	1	no	—
476	C₂×C₅₃	—	8	2	no	—
477	C₂×C₅₃	—	8	2	no	—
478	C₂×C₅₃	—	8	1	no	—
479	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
480	C₂×C₅₃	#3584	1	2	yes	—
481	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
482	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
483	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
484	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
485	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
486	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
487	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
488	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
489	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
490	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
491	#559	—	2	2	no	—
492	#556	—	2	2	no	—
493	#551	—	2	4	no	—
494	#548	—	2	2	no	—
495	#546	—	2	4	no	—
496	#546	—	2	2	no	—
497	#542	C₂²×C₅₃	1	4	yes	complemented
498	#536	C₂²×C₅₃	1	1	yes	characteristic
499	#536	C₂²×C₅₃	1	1	yes	characteristic
500	#536	C₂²×C₅₃	1	2	yes	complemented
501	#535	C₂²×C₅₃	1	1	yes	characteristic
502	#535	C₂²×C₅₃	1	1	yes	characteristic
503	#535	C₂²×C₅₃	1	2	yes	complemented
504	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
505	#532	C₂²×C₅₃	1	1	yes	characteristic
506	#532	C₂²×C₅₃	1	2	yes	complemented
507	#529	C₂²×C₅₃	1	4	yes	complemented
508	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
509	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
510	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
511	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
512	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
513	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
514	#497	C₂²×C₅₃	1	2	yes	complemented
515	#496	C₂²×C₅₃	1	2	yes	complemented
516	#495	C₂²×C₅₃	1	4	yes	complemented
517	#495	C₂²×C₅₃	1	4	yes	complemented
518	#495	C₂²×C₅₃	1	2	yes	complemented
519	#495	C₂²×C₅₃	1	2	yes	complemented
520	#489	C₂²×C₅₃	1	4	yes	complemented
521	#488	C₂²×C₅₃	1	2	yes	complemented
522	#488	C₂²×C₅₃	1	2	yes	complemented
523	#488	C₂²×C₅₃	1	4	yes	complemented
524	#487	C₂²×C₅₃	1	2	yes	complemented
525	#486	C₂²×C₅₃	1	2	yes	complemented
526	#464	C₂²×C₅₃	1	4	yes	complemented
527	#464	C₂²×C₅₃	1	4	yes	complemented
528	#463	C₂²×C₅₃	1	4	yes	complemented
529	#463	C₂²×C₅₃	1	4	yes	complemented
530	#462	C₂²×C₅₃	1	4	yes	complemented
531	#461	C₂²×C₅₃	1	4	yes	complemented
532	#460	C₂²×C₅₃	1	4	yes	complemented
533	#459	C₂²×C₅₃	1	4	yes	complemented
534	#452	C₂²×C₅₃	1	4	yes	complemented
535	#452	C₂²×C₅₃	1	4	yes	complemented
536	#451	C₂²×C₅₃	1	4	yes	complemented
537	#450	C₂²×C₅₃	1	4	yes	complemented
538	#449	C₂²×C₅₃	1	4	yes	—
539	#449	C₂²×C₅₃	1	4	yes	complemented
540	#448	C₂²×C₅₃	1	4	yes	complemented
541	#447	C₂²×C₅₃	1	4	yes	—
542	#433	C₂²×C₅₃	1	4	yes	complemented
543	#431	C₂²×C₅₃	1	4	yes	complemented
544	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
545	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
546	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
547	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
548	#418	C₂²×C₅₃	1	1	yes	characteristic
549	#418	C₂²×C₅₃	1	1	yes	characteristic
550	#416	C₂²×C₅₃	1	1	yes	characteristic
551	#416	C₂²×C₅₃	1	1	yes	characteristic
552	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
553	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
554	#408	C₂²×C₅₃	1	1	yes	characteristic
555	#408	C₂²×C₅₃	1	1	yes	characteristic
556	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
557	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
558	C₅₃	#60819	1	1	yes	characteristic, direct product factor, Sylow
559	2₋¹⁺⁴	—	4	2	no	—
560	2₋¹⁺⁴	—	4	2	no	—
561	H(5,𝔽₂)	—	4	2	no	—
562	H(5,𝔽₂)	—	4	2	no	—
563	C₂×#41	—	2	1	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
567	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
568	C₂×#41	C₂³×C₅₃	1	2	yes	—
569	C₂×#41	C₂³×C₅₃	1	2	yes	—
570	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
571	C₂²×Q₈	—	2	1	no	—
572	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
573	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
580	#137	—	4	2	no	—
581	#137	—	4	2	no	—
582	AGL(1,ℤ/8)	—	4	2	no	—
583	AGL(1,ℤ/8)	—	4	2	no	—
584	C₂×Q₁₆	—	4	2	no	—
585	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
586	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
587	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
588	C₂×SD₁₆	—	4	2	no	—
589	C₂×SD₁₆	—	4	2	no	—
590	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
596	C₂×D₈	—	4	2	no	—
597	C₂×D₈	C₂³×C₅₃	1	4	yes	—
598	C₂×D₈	C₂³×C₅₃	1	2	yes	—
599	C₂×D₈	C₂³×C₅₃	1	2	yes	—
600	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
601	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
602	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
603	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
604	C₄⋊Q₈	—	2	1	no	—
605	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
606	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
607	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
608	#127	—	2	1	no	—
609	#127	C₂³×C₅₃	1	1	yes	characteristic
610	#127	C₂³×C₅₃	1	2	yes	—
611	#126	—	2	4	no	—
612	#126	—	2	4	no	—
613	#125	C₂³×C₅₃	1	2	yes	—
614	#124	—	2	1	no	—
615	#124	—	2	1	no	—
616	#124	—	2	4	no	—
617	#124	—	2	2	no	—
618	#124	—	2	4	no	—
619	#124	—	2	2	no	—
620	#124	C₂³×C₅₃	1	2	yes	—
621	#124	C₂³×C₅₃	1	2	yes	—
622	#124	C₂³×C₅₃	1	1	yes	characteristic
623	#124	C₂³×C₅₃	1	2	yes	—
624	#124	C₂³×C₅₃	1	2	yes	—
625	#124	C₂³×C₅₃	1	2	yes	—
626	#124	C₂³×C₅₃	1	2	yes	—
627	#124	C₂³×C₅₃	1	1	yes	characteristic
628	#123	—	2	2	no	—
629	#123	—	2	4	no	—
630	#123	—	2	2	no	—
631	#123	—	2	4	no	—
632	#123	—	2	4	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	4	no	—
636	C₂²⋊Q₈	—	2	4	no	—
637	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
638	#121	—	2	2	no	—
639	#121	—	2	4	no	—
640	#121	—	2	2	no	—
641	#121	—	2	4	no	—
642	#121	C₂³×C₅₃	1	4	yes	—
643	#120	—	2	2	no	—
644	#120	—	2	2	no	—
645	#120	—	2	4	no	—
646	C₄×Q₈	—	2	2	no	—
647	C₄×Q₈	—	2	2	no	—
648	C₄×Q₈	D₄×C₅₃	1	2	yes	—
649	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
650	C₄×D₄	—	2	4	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	D₄×C₅₃	1	4	yes	—
655	C₄×D₄	D₄×C₅₃	1	2	yes	—
656	C₄×D₄	C₂³×C₅₃	1	4	yes	—
657	#117	—	2	2	no	—
658	#117	—	2	4	no	—
659	#117	C₂³×C₅₃	1	1	yes	characteristic
660	#117	C₂³×C₅₃	1	1	yes	characteristic
661	#117	C₂³×C₅₃	1	1	yes	characteristic
662	#117	C₂³×C₅₃	1	2	yes	—
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₂²⋊C₄	—	2	4	no	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
670	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
671	#103	C₂³×C₅₃	1	2	yes	—
672	#103	C₂³×C₅₃	1	2	yes	—
673	#103	C₂³×C₅₃	1	2	yes	—
674	#103	C₂³×C₅₃	1	2	yes	—
675	#103	C₂³×C₅₃	1	4	yes	—
676	#103	C₂³×C₅₃	1	4	yes	—
677	#102	C₂³×C₅₃	1	2	yes	—
678	#102	C₂³×C₅₃	1	2	yes	—
679	#102	C₂³×C₅₃	1	2	yes	—
680	#102	C₂³×C₅₃	1	2	yes	—
681	#102	C₂³×C₅₃	1	4	yes	—
682	#102	C₂³×C₅₃	1	4	yes	—
683	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
684	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
685	#97	C₂³×C₅₃	1	2	yes	—
686	C₄×C₈	C₂³×C₅₃	1	2	yes	—
687	C₄×C₈	C₂³×C₅₃	1	2	yes	—
688	C₄×C₈	C₂³×C₅₃	1	2	yes	—
689	C₂⁴	—	2	1	no	—
690	C₂⁴	—	2	2	no	—
691	C₂⁴	—	2	1	no	—
692	#41	—	2	2	no	—
693	#41	—	2	2	no	—
694	#41	—	2	2	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	2	no	—
698	#41	—	4	2	no	—
699	#41	—	4	2	no	—
700	#41	—	4	2	no	—
701	#41	—	4	2	no	—
702	#41	—	4	8	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×Q₈	—	4	4	no	—
716	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
717	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
718	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
719	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
720	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	8	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
740	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
741	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
742	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
743	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
754	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
757	Q₁₆	—	4	4	no	—
758	Q₁₆	—	4	2	no	—
759	Q₁₆	—	4	2	no	—
760	SD₁₆	—	4	4	no	—
761	SD₁₆	—	4	4	no	—
762	SD₁₆	—	4	2	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	D₈	—	4	4	no	—
767	D₈	—	4	2	no	—
768	D₈	—	4	2	no	—
769	M₁₆	—	2	2	no	—
770	M₁₆	—	2	2	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	—	2	2	no	—
773	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
774	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
775	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
776	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
785	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
786	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	1	no	—
805	C₄²	—	2	1	no	—
806	C₄²	C₂×D₄×C₅₃	1	4	yes	—
807	C₄²	C₂×D₄×C₅₃	1	2	yes	—
808	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
809	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
810	C₄²	C₂⁴×C₅₃	1	2	yes	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	—	8	4	no	—
821	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
822	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	2	1	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	2	1	no	—
831	Q₈	—	2	1	no	—
832	Q₈	—	4	4	no	—
833	Q₈	—	4	2	no	—
834	Q₈	—	4	2	no	—
835	Q₈	—	8	2	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	1	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	4	2	no	—
852	D₄	—	4	2	no	—
853	D₄	—	8	4	no	—
854	D₄	—	8	2	no	—
855	D₄	—	8	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
875	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
879	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
880	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
881	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
882	C₈	—	2	2	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₈	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	16	2	no	—
898	C₂²	—	16	2	no	—
899	C₂²	—	16	4	no	—
900	C₂²	C₅₃×#535	1	2	yes	—
901	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	C₅₃×#535	1	2	yes	—
913	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
914	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
915	C₂	—	2	2	no	—
916	C₂	—	4	2	no	—
917	C₂	—	8	2	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	—	8	1	no	—
921	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
922	C₂	C₅₃×#3584	1	2	yes	—

	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3510	C₂	semidirect
2. C₅₃×#3500	C₂	semidirect
3. C₅₃×#3225	C₂	semidirect
4. C₅₃×#3224	C₂	semidirect
5. C₅₃×#3212	C₂	semidirect
6. C₅₃×#3211	C₂	semidirect
7. C₅₃×#3153	C₂	semidirect
8. C₂×C₅₃×#495	C₂	semidirect
9. C₅₃×#3140	C₂	semidirect
10. C₅₃×#3131	C₂	semidirect
11. C₅₃×#3044	C₂	semidirect
12. C₅₃×#3043	C₂	semidirect
13. C₅₃×#3042	C₂	semidirect
14. C₅₃×#3041	C₂	semidirect
15. C₅₃×#3011	C₂	semidirect
16. C₅₃×#3010	C₂	semidirect
17. C₅₃×#3009	C₂	semidirect
18. C₅₃×#3008	C₂	semidirect
19. C₅₃×#2922	C₂	semidirect
23. C₂×#137×C₅₃	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
26. C₂²×Q₁₆×C₅₃	C₂²	semidirect
28. C₂²×SD₁₆×C₅₃	C₂²	semidirect
36. C₅₃×#542	C₂²	semidirect
39. C₅₃×#536	C₂²	semidirect
42. C₅₃×#535	C₂²	semidirect
43. C₅₃×#533	C₂²	semidirect
45. C₅₃×#532	C₂²	semidirect
46. C₅₃×#529	C₂²	semidirect
48. C₂×#124×C₅₃	C₂²	semidirect
49. C₂×#124×C₅₃	C₂²	semidirect
50. C₅₃×#519	C₂²	semidirect
51. C₅₃×#518	C₂²	semidirect
53. C₅₃×#497	C₂²	semidirect
54. C₅₃×#496	C₂²	semidirect
55. C₅₃×#495	C₂²	semidirect
56. C₅₃×#495	C₂²	semidirect
57. C₅₃×#495	C₂²	semidirect
58. C₅₃×#495	C₂²	semidirect
59. C₅₃×#489	C₂²	semidirect
60. C₅₃×#488	C₂²	semidirect
61. C₅₃×#488	C₂²	semidirect
62. C₅₃×#488	C₂²	semidirect
63. C₅₃×#487	C₂²	semidirect
64. C₅₃×#486	C₂²	semidirect
65. C₅₃×#464	C₂²	semidirect
66. C₅₃×#464	C₂²	semidirect
67. C₅₃×#463	C₂²	semidirect
68. C₅₃×#463	C₂²	semidirect
69. C₅₃×#462	C₂²	semidirect
70. C₅₃×#461	C₂²	semidirect
71. C₅₃×#460	C₂²	semidirect
72. C₅₃×#459	C₂²	semidirect
73. C₅₃×#452	C₂²	semidirect
74. C₅₃×#452	C₂²	semidirect
75. C₅₃×#451	C₂²	semidirect
76. C₅₃×#450	C₂²	semidirect
78. C₅₃×#449	C₂²	semidirect
79. C₅₃×#448	C₂²	semidirect
81. C₅₃×#433	C₂²	semidirect
82. C₅₃×#431	C₂²	semidirect
83. C₅₃×#424	C₂²	semidirect
84. C₅₃×#424	C₂²	semidirect
85. C₅₃×#419	C₂²	semidirect
86. C₅₃×#419	C₂²	semidirect
91. C₅₃×#416	C₂²	semidirect
92. C₅₃×#416	C₂²	semidirect
95. C₄×M₁₆×C₅₃	C₂²	semidirect
96. C₂×C₄×C₈×C₅₃	C₂²	semidirect
424. #60819	C₅₃	direct (N × H)
454. #3510	C₂×C₅₃	semidirect
455. #3500	C₂×C₅₃	semidirect
456. #3225	C₂×C₅₃	semidirect
457. #3224	C₂×C₅₃	semidirect
458. #3212	C₂×C₅₃	semidirect
459. #3211	C₂×C₅₃	semidirect
460. #3153	C₂×C₅₃	semidirect
461. C₂×#495	C₂×C₅₃	semidirect
462. #3140	C₂×C₅₃	semidirect
463. #3131	C₂×C₅₃	semidirect
464. #3044	C₂×C₅₃	semidirect
465. #3043	C₂×C₅₃	semidirect
466. #3042	C₂×C₅₃	semidirect
467. #3041	C₂×C₅₃	semidirect
468. #3011	C₂×C₅₃	semidirect
469. #3010	C₂×C₅₃	semidirect
470. #3009	C₂×C₅₃	semidirect
471. #3008	C₂×C₅₃	semidirect
472. #2922	C₂×C₅₃	semidirect
484. C₂×#137	C₂²×C₅₃	semidirect
486. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
487. C₂²×Q₁₆	C₂²×C₅₃	semidirect
489. C₂²×SD₁₆	C₂²×C₅₃	semidirect
497. #542	C₂²×C₅₃	semidirect
500. #536	C₂²×C₅₃	semidirect
503. #535	C₂²×C₅₃	semidirect
504. #533	C₂²×C₅₃	semidirect
506. #532	C₂²×C₅₃	semidirect
507. #529	C₂²×C₅₃	semidirect
509. C₂×#124	C₂²×C₅₃	semidirect
510. C₂×#124	C₂²×C₅₃	semidirect
511. #519	C₂²×C₅₃	semidirect
512. #518	C₂²×C₅₃	semidirect
514. #497	C₂²×C₅₃	semidirect
515. #496	C₂²×C₅₃	semidirect
516. #495	C₂²×C₅₃	semidirect
517. #495	C₂²×C₅₃	semidirect
518. #495	C₂²×C₅₃	semidirect
519. #495	C₂²×C₅₃	semidirect
520. #489	C₂²×C₅₃	semidirect
521. #488	C₂²×C₅₃	semidirect
522. #488	C₂²×C₅₃	semidirect
523. #488	C₂²×C₅₃	semidirect
524. #487	C₂²×C₅₃	semidirect
525. #486	C₂²×C₅₃	semidirect
526. #464	C₂²×C₅₃	semidirect
527. #464	C₂²×C₅₃	semidirect
528. #463	C₂²×C₅₃	semidirect
529. #463	C₂²×C₅₃	semidirect
530. #462	C₂²×C₅₃	semidirect
531. #461	C₂²×C₅₃	semidirect
532. #460	C₂²×C₅₃	semidirect
533. #459	C₂²×C₅₃	semidirect
534. #452	C₂²×C₅₃	semidirect
535. #452	C₂²×C₅₃	semidirect
536. #451	C₂²×C₅₃	semidirect
537. #450	C₂²×C₅₃	semidirect
539. #449	C₂²×C₅₃	semidirect
540. #448	C₂²×C₅₃	semidirect
542. #433	C₂²×C₅₃	semidirect
543. #431	C₂²×C₅₃	semidirect
544. #424	C₂²×C₅₃	semidirect
545. #424	C₂²×C₅₃	semidirect
546. #419	C₂²×C₅₃	semidirect
547. #419	C₂²×C₅₃	semidirect
552. #416	C₂²×C₅₃	semidirect
553. #416	C₂²×C₅₃	semidirect
556. C₄×M₁₆	C₂²×C₅₃	semidirect
557. C₂×C₄×C₈	C₂²×C₅₃	semidirect
558. C₅₃	#60819	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×#3510	2
C₅₃×#3500	2
C₅₃×#3225	2
C₅₃×#3224	2
C₅₃×#3212	2
C₅₃×#3211	2
C₅₃×#3153	2
C₂×C₅₃×#495	2
C₅₃×#3140	2
C₅₃×#3131	2
C₅₃×#3044	2
C₅₃×#3043	2
C₅₃×#3042	2
C₅₃×#3041	2
C₅₃×#3011	2
C₅₃×#3010	2
C₅₃×#3009	2
C₅₃×#3008	2
C₅₃×#2922	2
#60819	53

Subgroups — C53×#60819 #27268331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60819 #27268331