Subgroups — C₅₃×#60846 #27268358

Order 13568.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3233	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3232	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3231	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3228	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3160	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3131	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3091	C₂	1	4	yes	maximal, complemented
14	C₅₃×#3076	C₂	1	4	yes	maximal, complemented
15	C₂×C₅₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#533	—	2	1	no	—
17	C₅₃×#533	—	2	1	no	—
18	C₅₃×#533	—	2	1	no	—
19	C₅₃×#533	—	2	1	no	—
20	C₅₃×#533	C₂²	1	1	yes	characteristic
21	C₅₃×#533	C₂²	1	1	yes	characteristic
22	C₅₃×#533	C₂²	1	2	yes	—
23	C₅₃×#533	C₂²	1	2	yes	—
24	C₅₃×#533	C₂²	1	2	yes	—
25	C₅₃×#533	C₂²	1	2	yes	—
26	C₅₃×#533	C₂²	1	1	yes	characteristic
27	C₅₃×#532	C₂²	1	1	yes	characteristic
28	C₅₃×#532	C₂²	1	1	yes	characteristic
29	C₅₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#529	—	2	1	no	—
33	C₅₃×#529	—	2	1	no	—
34	C₅₃×#529	—	2	1	no	—
35	C₅₃×#529	—	2	1	no	—
36	C₅₃×#529	C₂²	1	2	yes	—
37	C₅₃×#529	C₂²	1	2	yes	—
38	C₂×#125×C₅₃	C₂²	1	2	yes	—
39	C₅₃×#525	—	2	1	no	—
40	C₅₃×#525	—	2	1	no	—
41	C₅₃×#525	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
43	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
44	C₄×#41×C₅₃	—	2	1	no	—
45	C₄×#41×C₅₃	—	2	1	no	—
46	C₄×#41×C₅₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₅₃	—	2	1	no	—
48	C₂×C₄×Q₈×C₅₃	—	2	1	no	—
49	C₂×#117×C₅₃	C₂²	1	2	yes	—
50	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#500	C₂²	1	2	yes	complemented
52	C₅₃×#500	C₂²	1	2	yes	complemented
53	C₅₃×#499	C₂²	1	8	yes	complemented
54	C₅₃×#498	C₂²	1	2	yes	complemented
55	C₅₃×#498	C₂²	1	2	yes	complemented
56	C₅₃×#488	C₂²	1	8	yes	complemented
57	C₅₃×#487	C₂²	1	2	yes	complemented
58	C₅₃×#487	C₂²	1	2	yes	complemented
59	C₅₃×#486	C₂²	1	2	yes	complemented
60	C₅₃×#486	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	8	yes	—
62	C₅₃×#484	C₂²	1	4	yes	—
63	C₅₃×#483	C₂²	1	4	yes	—
64	C₅₃×#482	C₂²	1	8	yes	—
65	C₅₃×#481	C₂²	1	4	yes	—
66	C₅₃×#480	C₂²	1	4	yes	—
67	C₅₃×#479	C₂²	1	8	yes	complemented
68	C₅₃×#478	C₂²	1	8	yes	complemented
69	C₅₃×#477	C₂²	1	4	yes	complemented
70	C₅₃×#476	C₂²	1	4	yes	complemented
71	C₅₃×#475	C₂²	1	4	yes	complemented
72	C₅₃×#474	C₂²	1	4	yes	complemented
73	C₅₃×#431	C₂²	1	1	yes	characteristic
74	C₅₃×#431	C₂²	1	1	yes	characteristic
75	C₅₃×#431	C₂²	1	2	yes	—
76	C₅₃×#431	C₂²	1	2	yes	—
77	C₅₃×#431	C₂²	1	2	yes	—
78	C₅₃×#427	C₂²	1	8	yes	—
79	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
80	C₅₃×#416	C₂²	1	8	yes	—
81	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
82	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
83	C₂×#41×C₅₃	—	2	1	no	—
84	C₂×#41×C₅₃	—	2	1	no	—
85	C₂×#41×C₅₃	C₂³	1	2	yes	—
86	C₂²×Q₈×C₅₃	—	2	1	no	—
87	C₂²×Q₈×C₅₃	—	2	1	no	—
88	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
89	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
92	C₄⋊Q₈×C₅₃	—	2	1	no	—
93	C₄⋊Q₈×C₅₃	—	2	1	no	—
94	C₄⋊Q₈×C₅₃	—	2	1	no	—
95	C₄⋊Q₈×C₅₃	—	2	1	no	—
96	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
101	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
103	#127×C₅₃	C₂³	1	1	yes	characteristic
104	#126×C₅₃	—	2	2	no	—
105	#126×C₅₃	—	2	2	no	—
106	#125×C₅₃	—	2	2	no	—
107	#125×C₅₃	—	2	2	no	—
108	#125×C₅₃	—	2	1	no	—
109	#125×C₅₃	—	2	1	no	—
110	#125×C₅₃	C₂³	1	4	yes	—
111	#125×C₅₃	C₂³	1	2	yes	—
112	#125×C₅₃	C₂³	1	4	yes	—
113	#124×C₅₃	—	2	1	no	—
114	#124×C₅₃	—	2	1	no	—
115	#124×C₅₃	C₂³	1	2	yes	—
116	#123×C₅₃	—	2	2	no	—
117	#123×C₅₃	—	2	2	no	—
118	#123×C₅₃	—	2	2	no	—
119	C₂²⋊Q₈×C₅₃	—	2	2	no	—
120	C₂²⋊Q₈×C₅₃	—	2	2	no	—
121	C₂²⋊Q₈×C₅₃	—	2	2	no	—
122	C₂²⋊Q₈×C₅₃	—	2	2	no	—
123	C₂²⋊Q₈×C₅₃	—	2	2	no	—
124	C₂²⋊Q₈×C₅₃	—	2	2	no	—
125	C₂²⋊Q₈×C₅₃	—	2	2	no	—
126	C₂²⋊Q₈×C₅₃	—	2	2	no	—
127	C₂²⋊Q₈×C₅₃	—	2	1	no	—
128	C₂²⋊Q₈×C₅₃	—	2	1	no	—
129	C₂²⋊Q₈×C₅₃	—	2	1	no	—
130	C₂²⋊Q₈×C₅₃	—	2	1	no	—
131	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
133	#121×C₅₃	—	2	1	no	—
134	#121×C₅₃	—	2	1	no	—
135	#121×C₅₃	—	2	1	no	—
136	#121×C₅₃	—	2	1	no	—
137	#121×C₅₃	C₂³	1	2	yes	—
138	#121×C₅₃	C₂³	1	2	yes	—
139	#120×C₅₃	—	2	2	no	—
140	C₄×Q₈×C₅₃	—	2	2	no	—
141	C₄×Q₈×C₅₃	—	2	2	no	—
142	C₄×Q₈×C₅₃	—	2	2	no	—
143	C₄×Q₈×C₅₃	—	2	2	no	—
144	C₄×Q₈×C₅₃	—	2	2	no	—
145	C₄×Q₈×C₅₃	—	2	2	no	—
146	C₄×Q₈×C₅₃	—	2	2	no	—
147	C₄×Q₈×C₅₃	—	2	2	no	—
148	C₄×Q₈×C₅₃	—	2	1	no	—
149	C₄×Q₈×C₅₃	—	2	1	no	—
150	C₄×Q₈×C₅₃	—	2	1	no	—
151	C₄×Q₈×C₅₃	—	2	1	no	—
152	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
154	C₄×D₄×C₅₃	—	2	1	no	—
155	C₄×D₄×C₅₃	—	2	1	no	—
156	C₄×D₄×C₅₃	—	2	1	no	—
157	C₄×D₄×C₅₃	—	2	1	no	—
158	C₄×D₄×C₅₃	—	2	2	no	—
159	C₄×D₄×C₅₃	—	2	2	no	—
160	C₄×D₄×C₅₃	—	2	2	no	—
161	C₄×D₄×C₅₃	—	2	2	no	—
162	C₄×D₄×C₅₃	—	2	2	no	—
163	C₄×D₄×C₅₃	—	2	2	no	—
164	C₄×D₄×C₅₃	C₂³	1	2	yes	—
165	C₄×D₄×C₅₃	C₂³	1	2	yes	—
166	#117×C₅₃	—	2	2	no	—
167	#117×C₅₃	—	2	2	no	—
168	#117×C₅₃	—	2	2	no	—
169	#117×C₅₃	—	2	2	no	—
170	#117×C₅₃	—	2	2	no	—
171	#117×C₅₃	—	2	1	no	—
172	#117×C₅₃	—	2	1	no	—
173	#117×C₅₃	C₂³	1	4	yes	—
174	#117×C₅₃	C₂³	1	4	yes	—
175	#117×C₅₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
177	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
178	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
179	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
183	C₂×C₄²×C₅₃	—	2	2	no	—
184	C₂×C₄²×C₅₃	—	2	2	no	—
185	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	#107×C₅₃	C₂³	1	8	yes	—
198	#107×C₅₃	C₂³	1	8	yes	—
199	#106×C₅₃	C₂³	1	8	yes	—
200	#106×C₅₃	C₂³	1	8	yes	—
201	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
202	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
203	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
204	#103×C₅₃	C₂³	1	8	yes	—
205	#103×C₅₃	C₂³	1	8	yes	—
206	#102×C₅₃	C₂³	1	8	yes	—
207	#102×C₅₃	C₂³	1	8	yes	—
208	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
209	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
211	C₄×C₈×C₅₃	C₂³	1	2	yes	—
212	C₄×C₈×C₅₃	C₂³	1	2	yes	—
213	C₄×C₈×C₅₃	C₂³	1	4	yes	—
214	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
215	#41×C₅₃	—	2	8	no	—
216	#41×C₅₃	—	4	4	no	—
217	#41×C₅₃	—	4	4	no	—
218	C₂×Q₈×C₅₃	—	2	1	no	—
219	C₂×Q₈×C₅₃	—	2	1	no	—
220	C₂×Q₈×C₅₃	—	2	2	no	—
221	C₂×Q₈×C₅₃	—	2	2	no	—
222	C₂×Q₈×C₅₃	—	2	2	no	—
223	C₂×Q₈×C₅₃	—	2	2	no	—
224	C₂×Q₈×C₅₃	—	4	4	no	—
225	C₂×Q₈×C₅₃	—	4	4	no	—
226	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₅₃	—	2	2	no	—
228	C₂×D₄×C₅₃	—	2	2	no	—
229	C₂×D₄×C₅₃	—	2	2	no	—
230	C₂×D₄×C₅₃	—	2	1	no	—
231	C₂×D₄×C₅₃	—	2	1	no	—
232	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₅₃	—	2	4	no	—
234	C₂²×C₄×C₅₃	—	2	4	no	—
235	C₂²×C₄×C₅₃	—	2	2	no	—
236	C₂²×C₄×C₅₃	—	2	2	no	—
237	C₂²×C₄×C₅₃	—	2	2	no	—
238	C₂²×C₄×C₅₃	—	2	2	no	—
239	C₂²×C₄×C₅₃	—	2	2	no	—
240	C₂²×C₄×C₅₃	—	4	2	no	—
241	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₅₃	—	2	8	no	—
260	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
261	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
262	C₄⋊C₄×C₅₃	—	2	4	no	—
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	—	2	4	no	—
265	C₄⋊C₄×C₅₃	—	2	4	no	—
266	C₄⋊C₄×C₅₃	—	2	2	no	—
267	C₄⋊C₄×C₅₃	—	2	2	no	—
268	C₄⋊C₄×C₅₃	—	2	2	no	—
269	C₄⋊C₄×C₅₃	—	2	2	no	—
270	C₄⋊C₄×C₅₃	—	2	2	no	—
271	C₄⋊C₄×C₅₃	—	2	2	no	—
272	C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₄⋊C₄×C₅₃	—	2	1	no	—
274	C₄⋊C₄×C₅₃	—	2	1	no	—
275	C₄⋊C₄×C₅₃	—	2	1	no	—
276	C₄⋊C₄×C₅₃	—	2	2	no	—
277	C₄⋊C₄×C₅₃	—	2	2	no	—
278	C₄⋊C₄×C₅₃	—	2	2	no	—
279	C₄⋊C₄×C₅₃	—	2	2	no	—
280	C₄⋊C₄×C₅₃	—	2	2	no	—
281	C₄⋊C₄×C₅₃	—	2	2	no	—
282	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
283	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₅₃	—	2	4	no	—
287	C₂²⋊C₄×C₅₃	—	2	4	no	—
288	C₂²⋊C₄×C₅₃	—	2	2	no	—
289	C₂²⋊C₄×C₅₃	—	2	2	no	—
290	C₂²⋊C₄×C₅₃	—	2	2	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	—	2	2	no	—
297	C₄²×C₅₃	—	2	2	no	—
298	C₄²×C₅₃	—	2	2	no	—
299	C₄²×C₅₃	—	2	4	no	—
300	C₄²×C₅₃	—	2	2	no	—
301	C₄²×C₅₃	—	2	4	no	—
302	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
316	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
318	C₂³×C₅₃	—	2	2	no	—
319	C₂³×C₅₃	—	2	2	no	—
320	C₂³×C₅₃	—	2	2	no	—
321	C₂³×C₅₃	—	4	1	no	—
322	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
324	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₅₃	—	2	4	no	—
326	Q₈×C₅₃	—	4	4	no	—
327	Q₈×C₅₃	—	4	4	no	—
328	Q₈×C₅₃	—	4	4	no	—
329	Q₈×C₅₃	—	4	2	no	—
330	Q₈×C₅₃	—	4	4	no	—
331	Q₈×C₅₃	—	4	2	no	—
332	D₄×C₅₃	—	2	4	no	—
333	D₄×C₅₃	—	4	4	no	—
334	D₄×C₅₃	—	4	4	no	—
335	D₄×C₅₃	—	4	4	no	—
336	D₄×C₅₃	—	4	2	no	—
337	D₄×C₅₃	—	4	2	no	—
338	C₂×C₄×C₅₃	—	2	2	no	—
339	C₂×C₄×C₅₃	—	2	2	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	2	no	—
345	C₂×C₄×C₅₃	—	2	2	no	—
346	C₂×C₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	2	2	no	—
350	C₂×C₄×C₅₃	—	2	2	no	—
351	C₂×C₄×C₅₃	—	2	2	no	—
352	C₂×C₄×C₅₃	—	2	2	no	—
353	C₂×C₄×C₅₃	—	2	2	no	—
354	C₂×C₄×C₅₃	—	2	4	no	—
355	C₂×C₄×C₅₃	—	2	4	no	—
356	C₂×C₄×C₅₃	—	4	1	no	—
357	C₂×C₄×C₅₃	—	4	1	no	—
358	C₂×C₄×C₅₃	—	4	1	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	—	4	4	no	—
363	C₂×C₄×C₅₃	—	4	4	no	—
364	C₂×C₄×C₅₃	#135	1	4	yes	—
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	1	yes	characteristic
368	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
377	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
378	C₈×C₅₃	—	2	4	no	—
379	C₈×C₅₃	—	2	4	no	—
380	#60846	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂²×C₅₃	—	2	1	no	—
382	C₂²×C₅₃	—	2	1	no	—
383	C₂²×C₅₃	—	2	1	no	—
384	C₂²×C₅₃	—	2	1	no	—
385	C₂²×C₅₃	—	2	1	no	—
386	C₂²×C₅₃	—	2	1	no	—
387	C₂²×C₅₃	—	2	1	no	—
388	C₂²×C₅₃	—	4	4	no	—
389	C₂²×C₅₃	—	4	2	no	—
390	C₂²×C₅₃	—	4	2	no	—
391	C₂²×C₅₃	—	4	2	no	—
392	C₂²×C₅₃	#536	1	2	yes	—
393	C₂²×C₅₃	C₂×#135	1	2	yes	—
394	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₅₃	—	2	1	no	—
396	C₄×C₅₃	—	2	1	no	—
397	C₄×C₅₃	—	2	1	no	—
398	C₄×C₅₃	—	2	1	no	—
399	C₄×C₅₃	—	2	1	no	—
400	C₄×C₅₃	—	2	1	no	—
401	C₄×C₅₃	—	2	1	no	—
402	C₄×C₅₃	—	4	2	no	—
403	C₄×C₅₃	—	4	2	no	—
404	C₄×C₅₃	—	4	4	no	—
405	C₄×C₅₃	—	4	2	no	—
406	C₄×C₅₃	—	4	4	no	—
407	C₄×C₅₃	#536	1	2	yes	—
408	C₄×C₅₃	C₂×#135	1	2	yes	—
409	C₄×C₅₃	C₂×#135	1	2	yes	—
410	C₄×C₅₃	#575	1	2	yes	—
411	C₄×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
412	#3444	C₂×C₅₃	1	1	yes	characteristic
413	C₂×#533	C₂×C₅₃	1	1	yes	characteristic, complemented
414	#3233	C₂×C₅₃	1	4	yes	complemented
415	#3232	C₂×C₅₃	1	4	yes	complemented
416	#3231	C₂×C₅₃	1	2	yes	complemented
417	#3230	C₂×C₅₃	1	1	yes	characteristic, complemented
418	#3229	C₂×C₅₃	1	1	yes	characteristic, complemented
419	#3228	C₂×C₅₃	1	2	yes	complemented
420	#3227	C₂×C₅₃	1	1	yes	characteristic, complemented
421	#3226	C₂×C₅₃	1	1	yes	characteristic, complemented
422	#3160	C₂×C₅₃	1	2	yes	complemented
423	#3131	C₂×C₅₃	1	2	yes	complemented
424	#3091	C₂×C₅₃	1	4	yes	complemented
425	#3076	C₂×C₅₃	1	4	yes	complemented
426	C₂×#431	C₂×C₅₃	1	1	yes	characteristic, complemented
427	C₂×C₅₃	—	2	2	no	—
428	C₂×C₅₃	—	2	2	no	—
429	C₂×C₅₃	—	4	1	no	—
430	C₂×C₅₃	—	8	2	no	—
431	C₂×C₅₃	C₂×#536	1	1	yes	characteristic
432	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
433	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
434	#533	—	2	1	no	—
435	#533	—	2	1	no	—
436	#533	—	2	1	no	—
437	#533	—	2	1	no	—
438	#533	C₂²×C₅₃	1	1	yes	characteristic
439	#533	C₂²×C₅₃	1	1	yes	characteristic
440	#533	C₂²×C₅₃	1	2	yes	—
441	#533	C₂²×C₅₃	1	2	yes	—
442	#533	C₂²×C₅₃	1	1	yes	characteristic
443	#533	C₂²×C₅₃	1	2	yes	—
444	#533	C₂²×C₅₃	1	2	yes	—
445	#532	C₂²×C₅₃	1	1	yes	characteristic
446	#532	C₂²×C₅₃	1	1	yes	characteristic
447	#532	C₂²×C₅₃	1	1	yes	characteristic
448	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
450	#529	—	2	1	no	—
451	#529	—	2	1	no	—
452	#529	—	2	1	no	—
453	#529	—	2	1	no	—
454	#529	C₂²×C₅₃	1	2	yes	—
455	#529	C₂²×C₅₃	1	2	yes	—
456	C₂×#125	C₂²×C₅₃	1	2	yes	—
457	#525	—	2	1	no	—
458	#525	—	2	1	no	—
459	#525	C₂²×C₅₃	1	2	yes	—
460	C₂×C₂²⋊Q₈	—	2	1	no	—
461	C₂×C₂²⋊Q₈	—	2	1	no	—
462	C₄×#41	—	2	1	no	—
463	C₄×#41	—	2	1	no	—
464	C₄×#41	C₂²×C₅₃	1	2	yes	—
465	C₂×C₄×Q₈	—	2	1	no	—
466	C₂×C₄×Q₈	—	2	1	no	—
467	C₂×#117	C₂²×C₅₃	1	2	yes	—
468	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
469	#500	C₂²×C₅₃	1	2	yes	complemented
470	#500	C₂²×C₅₃	1	2	yes	complemented
471	#499	C₂²×C₅₃	1	8	yes	complemented
472	#498	C₂²×C₅₃	1	2	yes	complemented
473	#498	C₂²×C₅₃	1	2	yes	complemented
474	#488	C₂²×C₅₃	1	8	yes	complemented
475	#487	C₂²×C₅₃	1	2	yes	complemented
476	#487	C₂²×C₅₃	1	2	yes	complemented
477	#486	C₂²×C₅₃	1	2	yes	complemented
478	#486	C₂²×C₅₃	1	2	yes	complemented
479	#485	C₂²×C₅₃	1	8	yes	—
480	#484	C₂²×C₅₃	1	4	yes	—
481	#483	C₂²×C₅₃	1	4	yes	—
482	#482	C₂²×C₅₃	1	8	yes	—
483	#481	C₂²×C₅₃	1	4	yes	—
484	#480	C₂²×C₅₃	1	4	yes	—
485	#479	C₂²×C₅₃	1	8	yes	complemented
486	#478	C₂²×C₅₃	1	8	yes	complemented
487	#477	C₂²×C₅₃	1	4	yes	complemented
488	#476	C₂²×C₅₃	1	4	yes	complemented
489	#475	C₂²×C₅₃	1	4	yes	complemented
490	#474	C₂²×C₅₃	1	4	yes	complemented
491	#431	C₂²×C₅₃	1	1	yes	characteristic
492	#431	C₂²×C₅₃	1	1	yes	characteristic
493	#431	C₂²×C₅₃	1	2	yes	—
494	#431	C₂²×C₅₃	1	2	yes	—
495	#431	C₂²×C₅₃	1	2	yes	—
496	#427	C₂²×C₅₃	1	8	yes	—
497	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
498	#416	C₂²×C₅₃	1	8	yes	—
499	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
500	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	—
501	C₅₃	#60846	1	1	yes	characteristic, direct product factor, Sylow
502	C₂×#41	—	2	1	no	—
503	C₂×#41	—	2	1	no	—
504	C₂×#41	C₂³×C₅₃	1	2	yes	—
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
508	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
517	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
522	#127	C₂³×C₅₃	1	1	yes	characteristic
523	#126	—	2	2	no	—
524	#126	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	—	2	2	no	—
527	#125	—	2	1	no	—
528	#125	—	2	1	no	—
529	#125	C₂³×C₅₃	1	4	yes	—
530	#125	C₂³×C₅₃	1	4	yes	—
531	#125	C₂³×C₅₃	1	2	yes	—
532	#124	—	2	1	no	—
533	#124	—	2	1	no	—
534	#124	C₂³×C₅₃	1	2	yes	—
535	#123	—	2	2	no	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
551	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
552	#121	—	2	1	no	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	C₂³×C₅₃	1	2	yes	—
557	#121	C₂³×C₅₃	1	2	yes	—
558	#120	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
572	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	C₂³×C₅₃	1	2	yes	—
584	C₄×D₄	C₂³×C₅₃	1	2	yes	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	—	2	1	no	—
588	#117	—	2	1	no	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	C₂³×C₅₃	1	4	yes	—
593	#117	C₂³×C₅₃	1	4	yes	—
594	#117	C₂³×C₅₃	1	2	yes	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	—	2	2	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
601	C₂×C₂²⋊C₄	—	2	2	no	—
602	C₂×C₄²	—	2	2	no	—
603	C₂×C₄²	—	2	2	no	—
604	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
605	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
606	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
607	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
608	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
609	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
616	#107	C₂³×C₅₃	1	8	yes	—
617	#107	C₂³×C₅₃	1	8	yes	—
618	#106	C₂³×C₅₃	1	8	yes	—
619	#106	C₂³×C₅₃	1	8	yes	—
620	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
621	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
622	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
623	#103	C₂³×C₅₃	1	8	yes	—
624	#103	C₂³×C₅₃	1	8	yes	—
625	#102	C₂³×C₅₃	1	8	yes	—
626	#102	C₂³×C₅₃	1	8	yes	—
627	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
628	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
629	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
630	C₄×C₈	C₂³×C₅₃	1	2	yes	—
631	C₄×C₈	C₂³×C₅₃	1	2	yes	—
632	C₄×C₈	C₂³×C₅₃	1	4	yes	—
633	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
634	#41	—	2	8	no	—
635	#41	—	4	4	no	—
636	#41	—	4	4	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	4	4	no	—
644	C₂×Q₈	—	4	4	no	—
645	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
678	C₂×C₈	—	2	8	no	—
679	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
680	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	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	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
702	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
703	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	4	no	—
721	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
722	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
723	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
724	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
726	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
727	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
728	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
729	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
730	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
733	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
734	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
735	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
736	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	4	1	no	—
741	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
742	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
743	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
744	Q₈	—	2	4	no	—
745	Q₈	—	4	4	no	—
746	Q₈	—	4	4	no	—
747	Q₈	—	4	4	no	—
748	Q₈	—	4	2	no	—
749	Q₈	—	4	4	no	—
750	Q₈	—	4	2	no	—
751	D₄	—	2	4	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	4	no	—
755	D₄	—	4	2	no	—
756	D₄	—	4	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	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	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	#135×C₅₃	1	4	yes	—
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	C₂²×D₄×C₅₃	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
795	C₂×C₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
796	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
797	C₈	—	2	4	no	—
798	C₈	—	2	4	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	C₅₃×#536	1	2	yes	—
811	C₂²	C₂×#135×C₅₃	1	2	yes	—
812	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	4	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	4	no	—
825	C₄	C₅₃×#536	1	2	yes	—
826	C₄	C₂×#135×C₅₃	1	2	yes	—
827	C₄	C₂×#135×C₅₃	1	2	yes	—
828	C₄	C₅₃×#575	1	2	yes	—
829	C₄	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×C₅₃×#536	1	1	yes	characteristic
835	C₂	C₂²×#135×C₅₃	1	1	yes	characteristic
836	C₂	C₂×C₅₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
prime radical	C₅₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#533	C₂	semidirect
3. C₅₃×#3233	C₂	semidirect
4. C₅₃×#3232	C₂	semidirect
5. C₅₃×#3231	C₂	semidirect
6. C₅₃×#3230	C₂	semidirect
7. C₅₃×#3229	C₂	semidirect
8. C₅₃×#3228	C₂	semidirect
9. C₅₃×#3227	C₂	semidirect
10. C₅₃×#3226	C₂	semidirect
11. C₅₃×#3160	C₂	semidirect
12. C₅₃×#3131	C₂	semidirect
13. C₅₃×#3091	C₂	semidirect
14. C₅₃×#3076	C₂	semidirect
15. C₂×C₅₃×#431	C₂	semidirect
51. C₅₃×#500	C₂²	semidirect
52. C₅₃×#500	C₂²	semidirect
53. C₅₃×#499	C₂²	semidirect
54. C₅₃×#498	C₂²	semidirect
55. C₅₃×#498	C₂²	semidirect
56. C₅₃×#488	C₂²	semidirect
57. C₅₃×#487	C₂²	semidirect
58. C₅₃×#487	C₂²	semidirect
59. C₅₃×#486	C₂²	semidirect
60. C₅₃×#486	C₂²	semidirect
67. C₅₃×#479	C₂²	semidirect
68. C₅₃×#478	C₂²	semidirect
69. C₅₃×#477	C₂²	semidirect
70. C₅₃×#476	C₂²	semidirect
71. C₅₃×#475	C₂²	semidirect
72. C₅₃×#474	C₂²	semidirect
380. #60846	C₅₃	direct (N × H)
413. C₂×#533	C₂×C₅₃	semidirect
414. #3233	C₂×C₅₃	semidirect
415. #3232	C₂×C₅₃	semidirect
416. #3231	C₂×C₅₃	semidirect
417. #3230	C₂×C₅₃	semidirect
418. #3229	C₂×C₅₃	semidirect
419. #3228	C₂×C₅₃	semidirect
420. #3227	C₂×C₅₃	semidirect
421. #3226	C₂×C₅₃	semidirect
422. #3160	C₂×C₅₃	semidirect
423. #3131	C₂×C₅₃	semidirect
424. #3091	C₂×C₅₃	semidirect
425. #3076	C₂×C₅₃	semidirect
426. C₂×#431	C₂×C₅₃	semidirect
469. #500	C₂²×C₅₃	semidirect
470. #500	C₂²×C₅₃	semidirect
471. #499	C₂²×C₅₃	semidirect
472. #498	C₂²×C₅₃	semidirect
473. #498	C₂²×C₅₃	semidirect
474. #488	C₂²×C₅₃	semidirect
475. #487	C₂²×C₅₃	semidirect
476. #487	C₂²×C₅₃	semidirect
477. #486	C₂²×C₅₃	semidirect
478. #486	C₂²×C₅₃	semidirect
485. #479	C₂²×C₅₃	semidirect
486. #478	C₂²×C₅₃	semidirect
487. #477	C₂²×C₅₃	semidirect
488. #476	C₂²×C₅₃	semidirect
489. #475	C₂²×C₅₃	semidirect
490. #474	C₂²×C₅₃	semidirect
501. C₅₃	#60846	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×#3444	2
C₂×C₅₃×#533	2
C₅₃×#3233	2
C₅₃×#3232	2
C₅₃×#3231	2
C₅₃×#3230	2
C₅₃×#3229	2
C₅₃×#3228	2
C₅₃×#3227	2
C₅₃×#3226	2
C₅₃×#3160	2
C₅₃×#3131	2
C₅₃×#3091	2
C₅₃×#3076	2
C₂×C₅₃×#431	2
#60846	53

Subgroups — C53×#60846 #27268358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60846 #27268358