Subgroups — C₅₃×#62097 #27269609

Order 13568.

1738 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3381	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3340	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3336	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3302	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3296	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3248	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3233	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3107	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₅₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#557	—	2	1	no	—
19	C₅₃×#557	C₂²	1	2	yes	complemented
20	C₅₃×#556	—	2	1	no	—
21	C₅₃×#556	C₂²	1	1	yes	characteristic
22	C₅₃×#556	C₂²	1	2	yes	complemented
23	C₅₃×#555	C₂²	1	1	yes	characteristic
24	C₅₃×#554	C₂²	1	1	yes	characteristic
25	C₅₃×#553	—	2	1	no	—
26	C₅₃×#552	—	2	1	no	—
27	C₅₃×#552	—	2	2	no	—
28	C₅₃×#552	C₂²	1	2	yes	—
29	C₅₃×#552	C₂²	1	4	yes	—
30	C₅₃×#551	—	2	2	no	—
31	C₅₃×#547	C₂²	1	1	yes	characteristic
32	C₅₃×#546	C₂²	1	2	yes	—
33	C₅₃×#541	—	2	2	no	—
34	C₅₃×#536	—	2	1	no	—
35	C₅₃×#533	C₂²	1	1	yes	characteristic
36	C₅₃×#533	C₂²	1	1	yes	characteristic
37	C₅₃×#533	C₂²	1	2	yes	complemented
38	C₅₃×#533	C₂²	1	2	yes	complemented
39	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#529	—	2	2	no	—
41	C₅₃×#529	C₂²	1	2	yes	—
42	C₅₃×#525	—	2	1	no	—
43	C₅₃×#519	—	2	1	no	—
44	C₄×#41×C₅₃	C₂²	1	2	yes	—
45	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#117×C₅₃	—	2	1	no	—
48	C₅₃×#499	C₂²	1	4	yes	complemented
49	C₅₃×#498	C₂²	1	2	yes	complemented
50	C₅₃×#488	C₂²	1	4	yes	—
51	C₅₃×#487	C₂²	1	2	yes	complemented
52	C₅₃×#485	C₂²	1	4	yes	complemented
53	C₅₃×#485	C₂²	1	4	yes	complemented
54	C₅₃×#483	C₂²	1	4	yes	—
55	C₅₃×#483	C₂²	1	2	yes	—
56	C₅₃×#482	C₂²	1	4	yes	—
57	C₅₃×#479	C₂²	1	4	yes	complemented
58	C₅₃×#479	C₂²	1	4	yes	complemented
59	C₅₃×#478	C₂²	1	4	yes	—
60	C₅₃×#477	C₂²	1	2	yes	complemented
61	C₅₃×#477	C₂²	1	2	yes	complemented
62	C₅₃×#476	C₂²	1	1	yes	characteristic
63	C₅₃×#476	C₂²	1	1	yes	characteristic
64	C₅₃×#475	C₂²	1	2	yes	complemented
65	C₅₃×#475	C₂²	1	2	yes	complemented
66	C₅₃×#474	C₂²	1	2	yes	—
67	C₅₃×#474	C₂²	1	2	yes	—
68	C₅₃×#474	C₂²	1	2	yes	—
69	C₅₃×#474	C₂²	1	2	yes	—
70	C₅₃×#467	C₂²	1	4	yes	—
71	C₅₃×#467	C₂²	1	4	yes	complemented
72	C₅₃×#465	C₂²	1	4	yes	—
73	C₅₃×#464	C₂²	1	4	yes	—
74	C₅₃×#462	C₂²	1	2	yes	complemented
75	C₅₃×#462	C₂²	1	2	yes	complemented
76	C₅₃×#461	C₂²	1	1	yes	characteristic
77	C₅₃×#461	C₂²	1	1	yes	characteristic
78	C₅₃×#452	C₂²	1	4	yes	—
79	C₅₃×#450	C₂²	1	2	yes	—
80	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
81	C₄×Q₁₆×C₅₃	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
85	C₈×D₄×C₅₃	C₂²	1	4	yes	—
86	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
87	C₅₃×#431	C₂²	1	1	yes	characteristic
88	C₅₃×#431	C₂²	1	2	yes	complemented
89	C₅₃×#427	C₂²	1	4	yes	complemented
90	C₂×#107×C₅₃	C₂²	1	2	yes	—
91	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
93	C₅₃×#416	C₂²	1	4	yes	—
94	C₂×#102×C₅₃	C₂²	1	2	yes	—
95	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
96	C₂×#41×C₅₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₅₃	—	2	1	no	—
98	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅₃	—	2	1	no	—
100	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
104	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₅₃	—	2	1	no	—
106	C₄⋊Q₈×C₅₃	—	2	1	no	—
107	C₄⋊Q₈×C₅₃	—	2	2	no	—
108	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	#126×C₅₃	—	2	2	no	—
115	#126×C₅₃	—	2	2	no	—
116	#126×C₅₃	—	2	4	no	—
117	#126×C₅₃	—	2	4	no	—
118	#126×C₅₃	—	2	2	no	—
119	#125×C₅₃	—	2	2	no	—
120	#125×C₅₃	—	2	4	no	—
121	#125×C₅₃	—	2	4	no	—
122	#125×C₅₃	—	2	1	no	—
123	#125×C₅₃	—	2	1	no	—
124	#125×C₅₃	—	2	2	no	—
125	#125×C₅₃	C₂³	1	4	yes	—
126	#125×C₅₃	C₂³	1	2	yes	—
127	#124×C₅₃	—	2	2	no	—
128	#124×C₅₃	—	2	2	no	—
129	#124×C₅₃	C₂³	1	2	yes	—
130	#123×C₅₃	—	2	2	no	—
131	#123×C₅₃	—	2	2	no	—
132	#123×C₅₃	—	2	2	no	—
133	#123×C₅₃	—	2	4	no	—
134	#123×C₅₃	—	2	2	no	—
135	C₂²⋊Q₈×C₅₃	—	2	2	no	—
136	C₂²⋊Q₈×C₅₃	—	2	1	no	—
137	C₂²⋊Q₈×C₅₃	—	2	1	no	—
138	C₂²⋊Q₈×C₅₃	—	2	1	no	—
139	C₂²⋊Q₈×C₅₃	—	2	1	no	—
140	C₂²⋊Q₈×C₅₃	—	2	2	no	—
141	C₂²⋊Q₈×C₅₃	—	2	2	no	—
142	C₂²⋊Q₈×C₅₃	—	2	2	no	—
143	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
147	#121×C₅₃	—	2	2	no	—
148	#121×C₅₃	—	2	1	no	—
149	#121×C₅₃	—	2	1	no	—
150	#121×C₅₃	C₂³	1	2	yes	—
151	#120×C₅₃	—	2	2	no	—
152	C₄×Q₈×C₅₃	—	2	2	no	—
153	C₄×Q₈×C₅₃	—	2	2	no	—
154	C₄×Q₈×C₅₃	—	2	2	no	—
155	C₄×Q₈×C₅₃	—	2	2	no	—
156	C₄×Q₈×C₅₃	—	2	1	no	—
157	C₄×Q₈×C₅₃	—	2	1	no	—
158	C₄×Q₈×C₅₃	—	2	2	no	—
159	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
165	C₄×D₄×C₅₃	—	2	1	no	—
166	C₄×D₄×C₅₃	—	2	1	no	—
167	C₄×D₄×C₅₃	—	2	2	no	—
168	C₄×D₄×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	D₄	1	2	yes	—
171	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
172	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₅₃	C₂³	1	2	yes	—
177	C₄×D₄×C₅₃	C₂³	1	2	yes	—
178	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
179	#117×C₅₃	—	2	1	no	—
180	#117×C₅₃	—	2	1	no	—
181	#117×C₅₃	—	2	2	no	—
182	#117×C₅₃	—	2	4	no	—
183	#117×C₅₃	—	2	2	no	—
184	#117×C₅₃	—	2	2	no	—
185	#117×C₅₃	—	2	1	no	—
186	#117×C₅₃	—	2	1	no	—
187	#117×C₅₃	—	2	2	no	—
188	#117×C₅₃	D₄	1	1	yes	characteristic
189	#117×C₅₃	D₄	1	2	yes	—
190	#117×C₅₃	C₂³	1	2	yes	—
191	#117×C₅₃	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
199	C₂×C₄²×C₅₃	—	2	2	no	—
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
202	#107×C₅₃	C₂³	1	4	yes	—
203	#107×C₅₃	C₂³	1	4	yes	—
204	#107×C₅₃	C₂³	1	4	yes	—
205	#106×C₅₃	C₂³	1	2	yes	—
206	#106×C₅₃	C₂³	1	4	yes	—
207	#106×C₅₃	C₂³	1	4	yes	—
208	#106×C₅₃	C₂³	1	2	yes	—
209	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
210	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
211	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
214	#103×C₅₃	C₂³	1	2	yes	—
215	#103×C₅₃	C₂³	1	4	yes	—
216	#103×C₅₃	C₂³	1	4	yes	—
217	#103×C₅₃	C₂³	1	4	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	2	yes	—
220	#102×C₅₃	C₂³	1	2	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
226	C₄×C₈×C₅₃	C₂³	1	2	yes	—
227	C₄×C₈×C₅₃	C₂³	1	4	yes	—
228	C₂⁴×C₅₃	—	2	1	no	—
229	#41×C₅₃	—	2	4	no	—
230	#41×C₅₃	—	2	4	no	—
231	#41×C₅₃	—	4	2	no	—
232	C₂×Q₈×C₅₃	—	2	1	no	—
233	C₂×Q₈×C₅₃	—	2	2	no	—
234	C₂×Q₈×C₅₃	—	2	2	no	—
235	C₂×Q₈×C₅₃	—	2	1	no	—
236	C₂×Q₈×C₅₃	—	4	4	no	—
237	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₅₃	—	2	2	no	—
241	C₂×D₄×C₅₃	—	2	2	no	—
242	C₂×D₄×C₅₃	—	2	2	no	—
243	C₂×D₄×C₅₃	—	2	1	no	—
244	C₂×D₄×C₅₃	—	4	1	no	—
245	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅₃	—	2	1	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	1	no	—
252	C₂²×C₄×C₅₃	—	2	2	no	—
253	C₂²×C₄×C₅₃	—	2	1	no	—
254	C₂²×C₄×C₅₃	—	2	1	no	—
255	C₂²×C₄×C₅₃	—	2	1	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	4	4	no	—
258	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
264	Q₁₆×C₅₃	—	4	4	no	—
265	SD₁₆×C₅₃	—	2	4	no	—
266	SD₁₆×C₅₃	—	4	2	no	—
267	C₂×C₈×C₅₃	—	4	4	no	—
268	C₂×C₈×C₅₃	—	4	2	no	—
269	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
271	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₄⋊C₄×C₅₃	—	2	1	no	—
274	C₄⋊C₄×C₅₃	—	2	2	no	—
275	C₄⋊C₄×C₅₃	—	2	2	no	—
276	C₄⋊C₄×C₅₃	—	2	2	no	—
277	C₄⋊C₄×C₅₃	—	2	2	no	—
278	C₄⋊C₄×C₅₃	—	2	1	no	—
279	C₄⋊C₄×C₅₃	—	2	2	no	—
280	C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₄⋊C₄×C₅₃	—	2	2	no	—
282	C₄⋊C₄×C₅₃	—	2	2	no	—
283	C₄⋊C₄×C₅₃	—	2	1	no	—
284	C₄⋊C₄×C₅₃	—	2	1	no	—
285	C₄⋊C₄×C₅₃	—	2	4	no	—
286	C₄⋊C₄×C₅₃	—	2	4	no	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	1	no	—
290	C₄⋊C₄×C₅₃	—	2	4	no	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	4	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₅₃	—	2	2	no	—
304	C₂²⋊C₄×C₅₃	—	2	2	no	—
305	C₂²⋊C₄×C₅₃	—	2	4	no	—
306	C₂²⋊C₄×C₅₃	—	2	2	no	—
307	C₂²⋊C₄×C₅₃	—	2	4	no	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₂²⋊C₄×C₅₃	—	2	1	no	—
310	C₂²⋊C₄×C₅₃	—	2	2	no	—
311	C₂²⋊C₄×C₅₃	—	2	2	no	—
312	C₂²⋊C₄×C₅₃	—	2	1	no	—
313	C₂²⋊C₄×C₅₃	—	2	1	no	—
314	C₂²⋊C₄×C₅₃	—	2	1	no	—
315	C₂²⋊C₄×C₅₃	—	2	2	no	—
316	C₂²⋊C₄×C₅₃	—	2	2	no	—
317	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
320	C₄²×C₅₃	—	2	2	no	—
321	C₄²×C₅₃	—	2	2	no	—
322	C₄²×C₅₃	—	2	2	no	—
323	C₄²×C₅₃	—	2	4	no	—
324	C₄²×C₅₃	—	2	4	no	—
325	C₄²×C₅₃	—	2	2	no	—
326	C₄²×C₅₃	C₂×D₄	1	2	yes	—
327	C₄²×C₅₃	C₂×D₄	1	2	yes	—
328	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₅₃	C₂⁴	1	2	yes	—
332	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂³×C₅₃	—	2	1	no	—
334	C₂³×C₅₃	—	2	1	no	—
335	C₂³×C₅₃	—	4	2	no	—
336	C₂³×C₅₃	—	4	2	no	—
337	C₂³×C₅₃	—	8	1	no	—
338	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₅₃	—	2	2	no	—
341	Q₈×C₅₃	—	2	2	no	—
342	Q₈×C₅₃	—	2	2	no	—
343	Q₈×C₅₃	—	2	2	no	—
344	Q₈×C₅₃	—	2	2	no	—
345	Q₈×C₅₃	—	4	2	no	—
346	Q₈×C₅₃	—	4	4	no	—
347	Q₈×C₅₃	—	4	4	no	—
348	Q₈×C₅₃	—	8	1	no	—
349	D₄×C₅₃	—	2	4	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	—	4	2	no	—
355	D₄×C₅₃	—	4	4	no	—
356	D₄×C₅₃	—	8	2	no	—
357	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
358	C₂×C₄×C₅₃	—	2	4	no	—
359	C₂×C₄×C₅₃	—	2	1	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	1	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	1	no	—
364	C₂×C₄×C₅₃	—	2	1	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	4	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	4	2	no	—
371	C₂×C₄×C₅₃	—	4	1	no	—
372	C₂×C₄×C₅₃	—	4	4	no	—
373	C₂×C₄×C₅₃	—	4	2	no	—
374	C₂×C₄×C₅₃	—	4	4	no	—
375	C₂×C₄×C₅₃	—	4	2	no	—
376	C₂×C₄×C₅₃	—	4	2	no	—
377	C₂×C₄×C₅₃	—	4	2	no	—
378	C₂×C₄×C₅₃	—	4	2	no	—
379	C₂×C₄×C₅₃	—	8	2	no	—
380	C₂×C₄×C₅₃	#135	1	4	yes	—
381	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
390	C₈×C₅₃	—	2	2	no	—
391	C₈×C₅₃	—	2	2	no	—
392	C₈×C₅₃	—	2	4	no	—
393	#62097	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂²×C₅₃	—	2	1	no	—
395	C₂²×C₅₃	—	2	1	no	—
396	C₂²×C₅₃	—	2	2	no	—
397	C₂²×C₅₃	—	2	2	no	—
398	C₂²×C₅₃	—	2	2	no	—
399	C₂²×C₅₃	—	2	2	no	—
400	C₂²×C₅₃	—	4	1	no	—
401	C₂²×C₅₃	—	4	1	no	—
402	C₂²×C₅₃	—	4	1	no	—
403	C₂²×C₅₃	—	4	1	no	—
404	C₂²×C₅₃	—	4	1	no	—
405	C₂²×C₅₃	—	8	4	no	—
406	C₂²×C₅₃	C₂×#135	1	2	yes	—
407	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
408	C₄×C₅₃	—	2	1	no	—
409	C₄×C₅₃	—	2	2	no	—
410	C₄×C₅₃	—	2	1	no	—
411	C₄×C₅₃	—	2	2	no	—
412	C₄×C₅₃	—	2	1	no	—
413	C₄×C₅₃	—	2	2	no	—
414	C₄×C₅₃	—	4	2	no	—
415	C₄×C₅₃	—	4	2	no	—
416	C₄×C₅₃	—	4	2	no	—
417	C₄×C₅₃	—	4	2	no	—
418	C₄×C₅₃	—	4	1	no	—
419	C₄×C₅₃	—	4	1	no	—
420	C₄×C₅₃	—	4	4	no	—
421	C₄×C₅₃	C₂×#135	1	2	yes	—
422	C₄×C₅₃	C₂×#135	1	2	yes	—
423	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
424	C₄×C₅₃	#585	1	1	yes	characteristic
425	#3509	C₂×C₅₃	1	1	yes	characteristic, complemented
426	#3475	C₂×C₅₃	1	1	yes	characteristic
427	#3381	C₂×C₅₃	1	2	yes	complemented
428	#3364	C₂×C₅₃	1	2	yes	complemented
429	#3340	C₂×C₅₃	1	2	yes	complemented
430	#3336	C₂×C₅₃	1	4	yes	complemented
431	#3302	C₂×C₅₃	1	2	yes	complemented
432	#3296	C₂×C₅₃	1	4	yes	complemented
433	#3249	C₂×C₅₃	1	1	yes	characteristic, complemented
434	#3248	C₂×C₅₃	1	2	yes	complemented
435	#3233	C₂×C₅₃	1	2	yes	complemented
436	#3229	C₂×C₅₃	1	1	yes	characteristic, complemented
437	#3107	C₂×C₅₃	1	2	yes	complemented
438	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
439	#3076	C₂×C₅₃	1	2	yes	complemented
440	C₂×#474	C₂×C₅₃	1	1	yes	characteristic, complemented
441	#2988	C₂×C₅₃	1	1	yes	characteristic, complemented
442	C₂×C₅₃	—	2	2	no	—
443	C₂×C₅₃	—	4	2	no	—
444	C₂×C₅₃	—	4	2	no	—
445	C₂×C₅₃	—	8	1	no	—
446	C₂×C₅₃	#3489	1	1	yes	characteristic
447	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
448	C₂×C₅₃	#3586	1	1	yes	characteristic
449	#557	—	2	1	no	—
450	#557	C₂²×C₅₃	1	2	yes	complemented
451	#556	—	2	1	no	—
452	#556	C₂²×C₅₃	1	1	yes	characteristic
453	#556	C₂²×C₅₃	1	2	yes	complemented
454	#555	C₂²×C₅₃	1	1	yes	characteristic
455	#554	C₂²×C₅₃	1	1	yes	characteristic
456	#553	—	2	1	no	—
457	#552	—	2	1	no	—
458	#552	—	2	2	no	—
459	#552	C₂²×C₅₃	1	2	yes	—
460	#552	C₂²×C₅₃	1	4	yes	—
461	#551	—	2	2	no	—
462	#547	C₂²×C₅₃	1	1	yes	characteristic
463	#546	C₂²×C₅₃	1	2	yes	—
464	#541	—	2	2	no	—
465	#536	—	2	1	no	—
466	#533	C₂²×C₅₃	1	1	yes	characteristic
467	#533	C₂²×C₅₃	1	1	yes	characteristic
468	#533	C₂²×C₅₃	1	2	yes	complemented
469	#533	C₂²×C₅₃	1	2	yes	complemented
470	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
471	#529	—	2	2	no	—
472	#529	C₂²×C₅₃	1	2	yes	—
473	#525	—	2	1	no	—
474	#519	—	2	1	no	—
475	C₄×#41	C₂²×C₅₃	1	2	yes	—
476	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
477	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
478	C₂×#117	—	2	1	no	—
479	#499	C₂²×C₅₃	1	4	yes	complemented
480	#498	C₂²×C₅₃	1	2	yes	complemented
481	#488	C₂²×C₅₃	1	4	yes	—
482	#487	C₂²×C₅₃	1	2	yes	complemented
483	#485	C₂²×C₅₃	1	4	yes	complemented
484	#485	C₂²×C₅₃	1	4	yes	complemented
485	#483	C₂²×C₅₃	1	2	yes	—
486	#483	C₂²×C₅₃	1	4	yes	—
487	#482	C₂²×C₅₃	1	4	yes	—
488	#479	C₂²×C₅₃	1	4	yes	complemented
489	#479	C₂²×C₅₃	1	4	yes	complemented
490	#478	C₂²×C₅₃	1	4	yes	—
491	#477	C₂²×C₅₃	1	2	yes	complemented
492	#477	C₂²×C₅₃	1	2	yes	complemented
493	#476	C₂²×C₅₃	1	1	yes	characteristic
494	#476	C₂²×C₅₃	1	1	yes	characteristic
495	#475	C₂²×C₅₃	1	2	yes	complemented
496	#475	C₂²×C₅₃	1	2	yes	complemented
497	#474	C₂²×C₅₃	1	2	yes	—
498	#474	C₂²×C₅₃	1	2	yes	—
499	#474	C₂²×C₅₃	1	2	yes	—
500	#474	C₂²×C₅₃	1	2	yes	—
501	#467	C₂²×C₅₃	1	4	yes	—
502	#467	C₂²×C₅₃	1	4	yes	complemented
503	#465	C₂²×C₅₃	1	4	yes	—
504	#464	C₂²×C₅₃	1	4	yes	—
505	#462	C₂²×C₅₃	1	2	yes	complemented
506	#462	C₂²×C₅₃	1	2	yes	complemented
507	#461	C₂²×C₅₃	1	1	yes	characteristic
508	#461	C₂²×C₅₃	1	1	yes	characteristic
509	#452	C₂²×C₅₃	1	4	yes	—
510	#450	C₂²×C₅₃	1	2	yes	—
511	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
512	C₄×Q₁₆	C₂²×C₅₃	1	4	yes	complemented
513	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
514	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
515	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
516	C₈×D₄	C₂²×C₅₃	1	4	yes	—
517	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
518	#431	C₂²×C₅₃	1	1	yes	characteristic
519	#431	C₂²×C₅₃	1	2	yes	complemented
520	#427	C₂²×C₅₃	1	4	yes	complemented
521	C₂×#107	C₂²×C₅₃	1	2	yes	—
522	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
523	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
524	#416	C₂²×C₅₃	1	4	yes	—
525	C₂×#102	C₂²×C₅₃	1	2	yes	—
526	C₅₃	#62097	1	1	yes	characteristic, direct product factor, Sylow
527	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
528	C₂×#41	C₂³×C₅₃	1	2	yes	—
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
531	C₂³×C₄	—	2	1	no	—
532	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
534	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
535	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
536	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#126	—	2	4	no	—
549	#126	—	2	4	no	—
550	#126	—	2	2	no	—
551	#125	—	2	2	no	—
552	#125	—	2	4	no	—
553	#125	—	2	4	no	—
554	#125	—	2	1	no	—
555	#125	—	2	1	no	—
556	#125	—	2	2	no	—
557	#125	C₂³×C₅₃	1	2	yes	—
558	#125	C₂³×C₅₃	1	4	yes	—
559	#124	—	2	2	no	—
560	#124	—	2	2	no	—
561	#124	C₂³×C₅₃	1	2	yes	—
562	#123	—	2	2	no	—
563	#123	—	2	4	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
576	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
578	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	2	no	—
582	#121	C₂³×C₅₃	1	2	yes	—
583	#120	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
593	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
594	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
596	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	D₄×C₅₃	1	2	yes	—
603	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₅₃	1	2	yes	—
609	C₄×D₄	C₂³×C₅₃	1	2	yes	—
610	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
611	#117	—	2	1	no	—
612	#117	—	2	1	no	—
613	#117	—	2	2	no	—
614	#117	—	2	1	no	—
615	#117	—	2	1	no	—
616	#117	—	2	2	no	—
617	#117	—	2	4	no	—
618	#117	—	2	2	no	—
619	#117	—	2	2	no	—
620	#117	D₄×C₅₃	1	1	yes	characteristic
621	#117	D₄×C₅₃	1	2	yes	—
622	#117	C₂³×C₅₃	1	2	yes	—
623	#117	C₂³×C₅₃	1	4	yes	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₄²	—	2	2	no	—
632	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
634	#107	C₂³×C₅₃	1	4	yes	—
635	#107	C₂³×C₅₃	1	4	yes	—
636	#107	C₂³×C₅₃	1	4	yes	—
637	#106	C₂³×C₅₃	1	2	yes	—
638	#106	C₂³×C₅₃	1	4	yes	—
639	#106	C₂³×C₅₃	1	4	yes	—
640	#106	C₂³×C₅₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
642	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
643	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
644	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
645	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
646	#103	C₂³×C₅₃	1	4	yes	—
647	#103	C₂³×C₅₃	1	4	yes	—
648	#103	C₂³×C₅₃	1	2	yes	—
649	#103	C₂³×C₅₃	1	2	yes	—
650	#103	C₂³×C₅₃	1	4	yes	—
651	#103	C₂³×C₅₃	1	4	yes	—
652	#102	C₂³×C₅₃	1	4	yes	—
653	#102	C₂³×C₅₃	1	4	yes	—
654	#102	C₂³×C₅₃	1	2	yes	—
655	#102	C₂³×C₅₃	1	2	yes	—
656	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
658	C₄×C₈	C₂³×C₅₃	1	2	yes	—
659	C₄×C₈	C₂³×C₅₃	1	4	yes	—
660	C₂⁴	—	2	1	no	—
661	#41	—	2	4	no	—
662	#41	—	2	4	no	—
663	#41	—	4	2	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
670	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	4	1	no	—
677	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
678	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
679	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
680	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	4	4	no	—
690	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
693	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
696	Q₁₆	—	4	4	no	—
697	SD₁₆	—	2	4	no	—
698	SD₁₆	—	4	2	no	—
699	C₂×C₈	—	4	4	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
702	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
703	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
731	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
750	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
751	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	2	no	—
758	C₄²	C₂×D₄×C₅₃	1	2	yes	—
759	C₄²	C₂×D₄×C₅₃	1	2	yes	—
760	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
763	C₄²	C₂⁴×C₅₃	1	2	yes	—
764	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	8	1	no	—
770	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
771	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	4	2	no	—
778	Q₈	—	4	4	no	—
779	Q₈	—	4	4	no	—
780	Q₈	—	8	1	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	1	no	—
784	D₄	—	2	1	no	—
785	D₄	—	2	1	no	—
786	D₄	—	4	2	no	—
787	D₄	—	4	4	no	—
788	D₄	—	8	2	no	—
789	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	8	2	no	—
812	C₂×C₄	#135×C₅₃	1	4	yes	—
813	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
821	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
822	C₈	—	2	2	no	—
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	8	4	no	—
837	C₂²	C₂×#135×C₅₃	1	2	yes	—
838	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
839	C₄	—	2	2	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	C₂×#135×C₅₃	1	2	yes	—
853	C₄	C₂×#135×C₅₃	1	2	yes	—
854	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
855	C₄	C₅₃×#585	1	1	yes	characteristic
856	C₂	—	2	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	4	2	no	—
859	C₂	—	8	1	no	—
860	C₂	C₅₃×#3489	1	1	yes	characteristic
861	C₂	C₂²×#135×C₅₃	1	1	yes	characteristic
862	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3475	C₂
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×#3509	C₂	semidirect
3. C₅₃×#3381	C₂	semidirect
4. C₅₃×#3364	C₂	semidirect
5. C₅₃×#3340	C₂	semidirect
6. C₅₃×#3336	C₂	semidirect
7. C₅₃×#3302	C₂	semidirect
8. C₅₃×#3296	C₂	semidirect
9. C₅₃×#3249	C₂	semidirect
10. C₅₃×#3248	C₂	semidirect
11. C₅₃×#3233	C₂	semidirect
12. C₅₃×#3229	C₂	semidirect
13. C₅₃×#3107	C₂	semidirect
14. C₅₃×#3101	C₂	semidirect
15. C₅₃×#3076	C₂	semidirect
16. C₂×C₅₃×#474	C₂	semidirect
17. C₅₃×#2988	C₂	semidirect
19. C₅₃×#557	C₂²	semidirect
22. C₅₃×#556	C₂²	semidirect
37. C₅₃×#533	C₂²	semidirect
38. C₅₃×#533	C₂²	semidirect
48. C₅₃×#499	C₂²	semidirect
49. C₅₃×#498	C₂²	semidirect
51. C₅₃×#487	C₂²	semidirect
52. C₅₃×#485	C₂²	semidirect
53. C₅₃×#485	C₂²	semidirect
57. C₅₃×#479	C₂²	semidirect
58. C₅₃×#479	C₂²	semidirect
60. C₅₃×#477	C₂²	semidirect
61. C₅₃×#477	C₂²	semidirect
64. C₅₃×#475	C₂²	semidirect
65. C₅₃×#475	C₂²	semidirect
71. C₅₃×#467	C₂²	semidirect
74. C₅₃×#462	C₂²	semidirect
75. C₅₃×#462	C₂²	semidirect
80. C₈×Q₈×C₅₃	C₂²	semidirect
81. C₄×Q₁₆×C₅₃	C₂²	semidirect
86. C₈×D₄×C₅₃	C₂²	semidirect
88. C₅₃×#431	C₂²	semidirect
89. C₅₃×#427	C₂²	semidirect
92. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
393. #62097	C₅₃	direct (N × H)
425. #3509	C₂×C₅₃	semidirect
427. #3381	C₂×C₅₃	semidirect
428. #3364	C₂×C₅₃	semidirect
429. #3340	C₂×C₅₃	semidirect
430. #3336	C₂×C₅₃	semidirect
431. #3302	C₂×C₅₃	semidirect
432. #3296	C₂×C₅₃	semidirect
433. #3249	C₂×C₅₃	semidirect
434. #3248	C₂×C₅₃	semidirect
435. #3233	C₂×C₅₃	semidirect
436. #3229	C₂×C₅₃	semidirect
437. #3107	C₂×C₅₃	semidirect
438. #3101	C₂×C₅₃	semidirect
439. #3076	C₂×C₅₃	semidirect
440. C₂×#474	C₂×C₅₃	semidirect
441. #2988	C₂×C₅₃	semidirect
450. #557	C₂²×C₅₃	semidirect
453. #556	C₂²×C₅₃	semidirect
468. #533	C₂²×C₅₃	semidirect
469. #533	C₂²×C₅₃	semidirect
479. #499	C₂²×C₅₃	semidirect
480. #498	C₂²×C₅₃	semidirect
482. #487	C₂²×C₅₃	semidirect
483. #485	C₂²×C₅₃	semidirect
484. #485	C₂²×C₅₃	semidirect
488. #479	C₂²×C₅₃	semidirect
489. #479	C₂²×C₅₃	semidirect
491. #477	C₂²×C₅₃	semidirect
492. #477	C₂²×C₅₃	semidirect
495. #475	C₂²×C₅₃	semidirect
496. #475	C₂²×C₅₃	semidirect
502. #467	C₂²×C₅₃	semidirect
505. #462	C₂²×C₅₃	semidirect
506. #462	C₂²×C₅₃	semidirect
511. C₈×Q₈	C₂²×C₅₃	semidirect
512. C₄×Q₁₆	C₂²×C₅₃	semidirect
517. C₈×D₄	C₂²×C₅₃	semidirect
519. #431	C₂²×C₅₃	semidirect
520. #427	C₂²×C₅₃	semidirect
523. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
526. C₅₃	#62097	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×#3509	2
C₅₃×#3475	2
C₅₃×#3381	2
C₅₃×#3364	2
C₅₃×#3340	2
C₅₃×#3336	2
C₅₃×#3302	2
C₅₃×#3296	2
C₅₃×#3249	2
C₅₃×#3248	2
C₅₃×#3233	2
C₅₃×#3229	2
C₅₃×#3107	2
C₅₃×#3101	2
C₅₃×#3076	2
C₂×C₅₃×#474	2
C₅₃×#2988	2
#62097	53

Subgroups — C53×#62097 #27269609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62097 #27269609