Subgroups — C₅₃×#62114 #27269626

Order 13568.

1740 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3511	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3357	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3346	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3329	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3320	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3254	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3237	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3112	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3078	C₂	1	2	yes	maximal, complemented
16	C₂×C₅₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#557	—	2	1	no	—
20	C₅₃×#557	C₂²	1	1	yes	characteristic
21	C₅₃×#556	—	2	1	no	—
22	C₅₃×#555	C₂²	1	2	yes	—
23	C₅₃×#554	—	2	1	no	—
24	C₅₃×#554	—	2	2	no	—
25	C₅₃×#554	C₂²	1	2	yes	—
26	C₅₃×#554	C₂²	1	2	yes	—
27	C₅₃×#554	C₂²	1	1	yes	characteristic
28	C₅₃×#553	C₂²	1	4	yes	—
29	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#548	—	2	2	no	—
32	C₅₃×#547	—	2	1	no	—
33	C₅₃×#542	—	2	2	no	—
34	C₅₃×#537	—	2	1	no	—
35	C₅₃×#533	—	2	1	no	—
36	C₅₃×#533	—	2	2	no	—
37	C₅₃×#533	C₂²	1	1	yes	characteristic
38	C₅₃×#533	C₂²	1	2	yes	—
39	C₅₃×#533	C₂²	1	2	yes	—
40	C₅₃×#532	C₂²	1	1	yes	characteristic
41	C₅₃×#532	C₂²	1	2	yes	—
42	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#520	—	2	1	no	—
44	C₄×#41×C₅₃	—	2	1	no	—
45	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
48	C₅₃×#501	C₂²	1	4	yes	—
49	C₅₃×#500	C₂²	1	2	yes	—
50	C₅₃×#491	C₂²	1	4	yes	—
51	C₅₃×#487	C₂²	1	2	yes	—
52	C₅₃×#485	C₂²	1	4	yes	—
53	C₅₃×#485	C₂²	1	4	yes	—
54	C₅₃×#484	C₂²	1	4	yes	—
55	C₅₃×#481	C₂²	1	2	yes	—
56	C₅₃×#480	C₂²	1	4	yes	—
57	C₅₃×#479	C₂²	1	4	yes	—
58	C₅₃×#479	C₂²	1	4	yes	—
59	C₅₃×#477	C₂²	1	2	yes	—
60	C₅₃×#477	C₂²	1	2	yes	—
61	C₅₃×#477	C₂²	1	2	yes	—
62	C₅₃×#477	C₂²	1	2	yes	—
63	C₅₃×#477	C₂²	1	2	yes	—
64	C₅₃×#477	C₂²	1	2	yes	—
65	C₅₃×#476	C₂²	1	2	yes	—
66	C₅₃×#475	C₂²	1	1	yes	characteristic
67	C₅₃×#475	C₂²	1	2	yes	—
68	C₅₃×#475	C₂²	1	1	yes	characteristic
69	C₅₃×#474	C₂²	1	4	yes	—
70	C₅₃×#468	C₂²	1	4	yes	—
71	C₅₃×#468	C₂²	1	4	yes	—
72	C₅₃×#465	C₂²	1	4	yes	—
73	C₅₃×#461	C₂²	1	2	yes	—
74	C₅₃×#461	C₂²	1	4	yes	—
75	C₅₃×#460	C₂²	1	2	yes	—
76	C₅₃×#460	C₂²	1	1	yes	characteristic
77	C₅₃×#460	C₂²	1	1	yes	characteristic
78	C₅₃×#448	C₂²	1	2	yes	—
79	C₅₃×#448	C₂²	1	4	yes	—
80	C₅₃×#446	C₂²	1	2	yes	—
81	C₅₃×#440	C₂²	1	4	yes	—
82	C₅₃×#440	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
85	C₅₃×#436	C₂²	1	2	yes	—
86	C₅₃×#435	C₂²	1	4	yes	—
87	C₅₃×#432	C₂²	1	2	yes	—
88	C₅₃×#431	C₂²	1	1	yes	characteristic
89	C₅₃×#428	C₂²	1	4	yes	—
90	C₂×#107×C₅₃	C₂²	1	2	yes	—
91	C₅₃×#423	C₂²	1	2	yes	—
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
93	C₅₃×#419	C₂²	1	4	yes	—
94	C₂×#103×C₅₃	C₂²	1	2	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	—	2	2	no	—
97	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
98	C₂²×Q₈×C₅₃	—	2	1	no	—
99	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
104	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
105	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₅₃	—	2	1	no	—
107	C₄⋊Q₈×C₅₃	—	2	2	no	—
108	C₄⋊Q₈×C₅₃	—	2	1	no	—
109	C₄⋊Q₈×C₅₃	—	2	2	no	—
110	C₄⋊Q₈×C₅₃	—	2	1	no	—
111	C₄⋊Q₈×C₅₃	—	2	1	no	—
112	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
119	#127×C₅₃	C₂³	1	1	yes	characteristic
120	#126×C₅₃	—	2	4	no	—
121	#125×C₅₃	—	2	1	no	—
122	#125×C₅₃	—	2	2	no	—
123	#125×C₅₃	—	2	1	no	—
124	#125×C₅₃	—	2	2	no	—
125	#125×C₅₃	—	2	1	no	—
126	#125×C₅₃	—	2	2	no	—
127	#125×C₅₃	C₂³	1	4	yes	—
128	#124×C₅₃	—	2	4	no	—
129	#124×C₅₃	—	2	1	no	—
130	#124×C₅₃	—	2	2	no	—
131	#123×C₅₃	—	2	4	no	—
132	C₂²⋊Q₈×C₅₃	—	2	4	no	—
133	C₂²⋊Q₈×C₅₃	—	2	2	no	—
134	C₂²⋊Q₈×C₅₃	—	2	2	no	—
135	C₂²⋊Q₈×C₅₃	—	2	2	no	—
136	C₂²⋊Q₈×C₅₃	—	2	2	no	—
137	C₂²⋊Q₈×C₅₃	—	2	2	no	—
138	C₂²⋊Q₈×C₅₃	—	2	2	no	—
139	C₂²⋊Q₈×C₅₃	—	2	2	no	—
140	C₂²⋊Q₈×C₅₃	—	2	2	no	—
141	C₂²⋊Q₈×C₅₃	—	2	2	no	—
142	C₂²⋊Q₈×C₅₃	—	2	1	no	—
143	C₂²⋊Q₈×C₅₃	—	2	2	no	—
144	C₂²⋊Q₈×C₅₃	C₂³	1	2	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	4	no	—
149	#121×C₅₃	—	2	2	no	—
150	#121×C₅₃	—	2	1	no	—
151	#121×C₅₃	C₂³	1	2	yes	—
152	#121×C₅₃	C₂³	1	4	yes	—
153	C₄×Q₈×C₅₃	—	2	2	no	—
154	C₄×Q₈×C₅₃	—	2	1	no	—
155	C₄×Q₈×C₅₃	—	2	1	no	—
156	C₄×Q₈×C₅₃	—	2	2	no	—
157	C₄×Q₈×C₅₃	—	2	2	no	—
158	C₄×Q₈×C₅₃	—	2	2	no	—
159	C₄×Q₈×C₅₃	—	2	1	no	—
160	C₄×Q₈×C₅₃	—	2	2	no	—
161	C₄×Q₈×C₅₃	—	2	1	no	—
162	C₄×Q₈×C₅₃	—	2	1	no	—
163	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
172	C₄×D₄×C₅₃	—	2	4	no	—
173	C₄×D₄×C₅₃	—	2	2	no	—
174	C₄×D₄×C₅₃	—	2	1	no	—
175	C₄×D₄×C₅₃	—	2	2	no	—
176	C₄×D₄×C₅₃	—	2	1	no	—
177	C₄×D₄×C₅₃	—	2	2	no	—
178	C₄×D₄×C₅₃	—	2	1	no	—
179	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
180	C₄×D₄×C₅₃	D₄	1	2	yes	—
181	C₄×D₄×C₅₃	C₂³	1	4	yes	—
182	C₄×D₄×C₅₃	C₂³	1	2	yes	—
183	C₄×D₄×C₅₃	C₂³	1	2	yes	—
184	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
185	#117×C₅₃	—	2	2	no	—
186	#117×C₅₃	—	2	2	no	—
187	#117×C₅₃	—	2	1	no	—
188	#117×C₅₃	D₄	1	1	yes	characteristic
189	#117×C₅₃	D₄	1	2	yes	—
190	#117×C₅₃	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₅₃	—	2	2	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×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₃	—	2	2	no	—
199	C₂×C₄²×C₅₃	—	2	1	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	#107×C₅₃	C₂³	1	4	yes	—
206	#106×C₅₃	C₂³	1	2	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	4	yes	—
220	#103×C₅₃	C₂³	1	2	yes	—
221	#102×C₅₃	C₂³	1	2	yes	—
222	#102×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
226	#97×C₅₃	C₂³	1	4	yes	—
227	C₄×C₈×C₅₃	C₂³	1	2	yes	—
228	#41×C₅₃	—	2	4	no	—
229	#41×C₅₃	—	4	4	no	—
230	#41×C₅₃	—	8	4	no	—
231	C₂×Q₈×C₅₃	—	2	1	no	—
232	C₂×Q₈×C₅₃	—	2	2	no	—
233	C₂×Q₈×C₅₃	—	2	1	no	—
234	C₂×Q₈×C₅₃	—	2	2	no	—
235	C₂×Q₈×C₅₃	—	2	2	no	—
236	C₂×Q₈×C₅₃	—	2	1	no	—
237	C₂×Q₈×C₅₃	—	2	2	no	—
238	C₂×Q₈×C₅₃	—	2	2	no	—
239	C₂×Q₈×C₅₃	—	2	4	no	—
240	C₂×Q₈×C₅₃	—	4	1	no	—
241	C₂×Q₈×C₅₃	—	4	2	no	—
242	C₂×Q₈×C₅₃	—	8	2	no	—
243	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₅₃	—	2	2	no	—
248	C₂×D₄×C₅₃	—	2	4	no	—
249	C₂×D₄×C₅₃	—	2	1	no	—
250	C₂×D₄×C₅₃	—	2	1	no	—
251	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅₃	—	2	2	no	—
255	C₂²×C₄×C₅₃	—	2	1	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	1	no	—
258	C₂²×C₄×C₅₃	—	2	2	no	—
259	C₂²×C₄×C₅₃	—	2	2	no	—
260	C₂²×C₄×C₅₃	—	2	4	no	—
261	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
267	SD₁₆×C₅₃	—	2	4	no	—
268	SD₁₆×C₅₃	—	4	4	no	—
269	SD₁₆×C₅₃	—	4	2	no	—
270	M₁₆×C₅₃	—	4	4	no	—
271	C₂×C₈×C₅₃	—	4	2	no	—
272	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
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	4	no	—
279	C₄⋊C₄×C₅₃	—	2	2	no	—
280	C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₄⋊C₄×C₅₃	—	2	1	no	—
282	C₄⋊C₄×C₅₃	—	2	2	no	—
283	C₄⋊C₄×C₅₃	—	2	2	no	—
284	C₄⋊C₄×C₅₃	—	2	1	no	—
285	C₄⋊C₄×C₅₃	—	2	2	no	—
286	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
291	C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₄⋊C₄×C₅₃	—	2	4	no	—
294	C₄⋊C₄×C₅₃	—	2	2	no	—
295	C₄⋊C₄×C₅₃	—	2	1	no	—
296	C₄⋊C₄×C₅₃	—	2	2	no	—
297	C₄⋊C₄×C₅₃	—	2	2	no	—
298	C₄⋊C₄×C₅₃	—	2	2	no	—
299	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₂²⋊C₄×C₅₃	—	2	2	no	—
310	C₂²⋊C₄×C₅₃	—	2	2	no	—
311	C₂²⋊C₄×C₅₃	—	2	4	no	—
312	C₂²⋊C₄×C₅₃	—	2	4	no	—
313	C₂²⋊C₄×C₅₃	—	2	2	no	—
314	C₂²⋊C₄×C₅₃	—	2	4	no	—
315	C₂²⋊C₄×C₅₃	—	2	2	no	—
316	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
317	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
319	C₄²×C₅₃	—	2	1	no	—
320	C₄²×C₅₃	—	2	2	no	—
321	C₄²×C₅₃	—	2	1	no	—
322	C₄²×C₅₃	—	2	2	no	—
323	C₄²×C₅₃	—	2	1	no	—
324	C₄²×C₅₃	—	2	2	no	—
325	C₄²×C₅₃	—	2	1	no	—
326	C₄²×C₅₃	—	2	4	no	—
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	C₂×D₄	1	2	yes	—
331	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₅₃	C₂⁴	1	2	yes	—
333	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂³×C₅₃	—	2	2	no	—
335	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
336	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
337	Q₈×C₅₃	—	2	2	no	—
338	Q₈×C₅₃	—	2	1	no	—
339	Q₈×C₅₃	—	2	1	no	—
340	Q₈×C₅₃	—	2	2	no	—
341	Q₈×C₅₃	—	2	1	no	—
342	Q₈×C₅₃	—	2	2	no	—
343	Q₈×C₅₃	—	4	2	no	—
344	Q₈×C₅₃	—	4	4	no	—
345	Q₈×C₅₃	—	4	4	no	—
346	Q₈×C₅₃	—	4	2	no	—
347	Q₈×C₅₃	—	8	2	no	—
348	Q₈×C₅₃	—	8	1	no	—
349	Q₈×C₅₃	—	8	2	no	—
350	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
351	D₄×C₅₃	—	2	4	no	—
352	D₄×C₅₃	—	2	2	no	—
353	D₄×C₅₃	—	2	2	no	—
354	D₄×C₅₃	—	2	2	no	—
355	D₄×C₅₃	—	4	2	no	—
356	D₄×C₅₃	—	4	4	no	—
357	D₄×C₅₃	—	4	2	no	—
358	D₄×C₅₃	—	8	4	no	—
359	C₂×C₄×C₅₃	—	2	1	no	—
360	C₂×C₄×C₅₃	—	2	4	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	2	no	—
365	C₂×C₄×C₅₃	—	2	1	no	—
366	C₂×C₄×C₅₃	—	2	4	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	1	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	1	no	—
372	C₂×C₄×C₅₃	—	4	1	no	—
373	C₂×C₄×C₅₃	—	4	2	no	—
374	C₂×C₄×C₅₃	—	4	2	no	—
375	C₂×C₄×C₅₃	—	4	4	no	—
376	C₂×C₄×C₅₃	—	4	4	no	—
377	C₂×C₄×C₅₃	—	8	4	no	—
378	C₂×C₄×C₅₃	—	8	1	no	—
379	C₂×C₄×C₅₃	—	8	2	no	—
380	C₂×C₄×C₅₃	—	8	2	no	—
381	C₂×C₄×C₅₃	#137	1	4	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	2	yes	—
387	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
391	C₈×C₅₃	—	2	2	no	—
392	C₈×C₅₃	—	2	4	no	—
393	C₈×C₅₃	—	2	2	no	—
394	#62114	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂²×C₅₃	—	2	1	no	—
396	C₂²×C₅₃	—	2	1	no	—
397	C₂²×C₅₃	—	2	2	no	—
398	C₂²×C₅₃	—	2	2	no	—
399	C₂²×C₅₃	—	2	2	no	—
400	C₂²×C₅₃	—	4	2	no	—
401	C₂²×C₅₃	—	4	2	no	—
402	C₂²×C₅₃	—	4	2	no	—
403	C₂²×C₅₃	C₂×#137	1	2	yes	—
404	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
405	C₄×C₅₃	—	2	1	no	—
406	C₄×C₅₃	—	2	2	no	—
407	C₄×C₅₃	—	2	1	no	—
408	C₄×C₅₃	—	2	1	no	—
409	C₄×C₅₃	—	2	2	no	—
410	C₄×C₅₃	—	2	2	no	—
411	C₄×C₅₃	—	2	2	no	—
412	C₄×C₅₃	—	4	1	no	—
413	C₄×C₅₃	—	4	4	no	—
414	C₄×C₅₃	—	4	1	no	—
415	C₄×C₅₃	—	4	2	no	—
416	C₄×C₅₃	—	4	1	no	—
417	C₄×C₅₃	—	4	2	no	—
418	C₄×C₅₃	—	4	2	no	—
419	C₄×C₅₃	C₂×#137	1	2	yes	—
420	C₄×C₅₃	C₂×#137	1	2	yes	—
421	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
422	C₄×C₅₃	#585	1	1	yes	characteristic
423	#3511	C₂×C₅₃	1	1	yes	characteristic
424	Q₈×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
425	#3385	C₂×C₅₃	1	2	yes	complemented
426	#3372	C₂×C₅₃	1	2	yes	complemented
427	#3357	C₂×C₅₃	1	2	yes	complemented
428	#3346	C₂×C₅₃	1	4	yes	complemented
429	#3329	C₂×C₅₃	1	2	yes	complemented
430	#3320	C₂×C₅₃	1	4	yes	complemented
431	#3254	C₂×C₅₃	1	2	yes	complemented
432	#3246	C₂×C₅₃	1	1	yes	characteristic, complemented
433	#3237	C₂×C₅₃	1	2	yes	complemented
434	#3230	C₂×C₅₃	1	1	yes	characteristic, complemented
435	#3112	C₂×C₅₃	1	2	yes	complemented
436	#3103	C₂×C₅₃	1	1	yes	characteristic, complemented
437	#3078	C₂×C₅₃	1	2	yes	complemented
438	C₂×#477	C₂×C₅₃	1	1	yes	characteristic, complemented
439	#2989	C₂×C₅₃	1	1	yes	characteristic, complemented
440	C₂×C₅₃	—	2	2	no	—
441	C₂×C₅₃	—	4	2	no	—
442	C₂×C₅₃	—	8	2	no	—
443	C₂×C₅₃	#3489	1	1	yes	characteristic
444	C₂×C₅₃	C₂²×#137	1	1	yes	characteristic
445	C₂×C₅₃	#3585	1	1	yes	characteristic
446	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
447	#557	—	2	1	no	—
448	#557	C₂²×C₅₃	1	1	yes	characteristic
449	#556	—	2	1	no	—
450	#555	C₂²×C₅₃	1	2	yes	—
451	#554	—	2	1	no	—
452	#554	—	2	2	no	—
453	#554	C₂²×C₅₃	1	2	yes	—
454	#554	C₂²×C₅₃	1	2	yes	—
455	#554	C₂²×C₅₃	1	1	yes	characteristic
456	#553	C₂²×C₅₃	1	4	yes	—
457	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
458	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
459	#548	—	2	2	no	—
460	#547	—	2	1	no	—
461	#542	—	2	2	no	—
462	#537	—	2	1	no	—
463	#533	—	2	1	no	—
464	#533	—	2	2	no	—
465	#533	C₂²×C₅₃	1	1	yes	characteristic
466	#533	C₂²×C₅₃	1	2	yes	—
467	#533	C₂²×C₅₃	1	2	yes	—
468	#532	C₂²×C₅₃	1	1	yes	characteristic
469	#532	C₂²×C₅₃	1	2	yes	—
470	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
471	#520	—	2	1	no	—
472	C₄×#41	—	2	1	no	—
473	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
474	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
475	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
476	#501	C₂²×C₅₃	1	4	yes	—
477	#500	C₂²×C₅₃	1	2	yes	—
478	#491	C₂²×C₅₃	1	4	yes	—
479	#487	C₂²×C₅₃	1	2	yes	—
480	#485	C₂²×C₅₃	1	4	yes	—
481	#485	C₂²×C₅₃	1	4	yes	—
482	#484	C₂²×C₅₃	1	4	yes	—
483	#481	C₂²×C₅₃	1	2	yes	—
484	#480	C₂²×C₅₃	1	4	yes	—
485	#479	C₂²×C₅₃	1	4	yes	—
486	#479	C₂²×C₅₃	1	4	yes	—
487	#477	C₂²×C₅₃	1	2	yes	—
488	#477	C₂²×C₅₃	1	2	yes	—
489	#477	C₂²×C₅₃	1	2	yes	—
490	#477	C₂²×C₅₃	1	2	yes	—
491	#477	C₂²×C₅₃	1	2	yes	—
492	#477	C₂²×C₅₃	1	2	yes	—
493	#476	C₂²×C₅₃	1	2	yes	—
494	#475	C₂²×C₅₃	1	1	yes	characteristic
495	#475	C₂²×C₅₃	1	2	yes	—
496	#475	C₂²×C₅₃	1	1	yes	characteristic
497	#474	C₂²×C₅₃	1	4	yes	—
498	#468	C₂²×C₅₃	1	4	yes	—
499	#468	C₂²×C₅₃	1	4	yes	—
500	#465	C₂²×C₅₃	1	4	yes	—
501	#461	C₂²×C₅₃	1	2	yes	—
502	#461	C₂²×C₅₃	1	4	yes	—
503	#460	C₂²×C₅₃	1	1	yes	characteristic
504	#460	C₂²×C₅₃	1	1	yes	characteristic
505	#460	C₂²×C₅₃	1	2	yes	—
506	#448	C₂²×C₅₃	1	4	yes	—
507	#448	C₂²×C₅₃	1	2	yes	—
508	#446	C₂²×C₅₃	1	2	yes	—
509	#440	C₂²×C₅₃	1	4	yes	—
510	#440	C₂²×C₅₃	1	4	yes	—
511	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
512	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
513	#436	C₂²×C₅₃	1	2	yes	—
514	#435	C₂²×C₅₃	1	4	yes	—
515	#432	C₂²×C₅₃	1	2	yes	—
516	#431	C₂²×C₅₃	1	1	yes	characteristic
517	#428	C₂²×C₅₃	1	4	yes	—
518	C₂×#107	C₂²×C₅₃	1	2	yes	—
519	#423	C₂²×C₅₃	1	2	yes	—
520	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
521	#419	C₂²×C₅₃	1	4	yes	—
522	C₂×#103	C₂²×C₅₃	1	2	yes	—
523	C₅₃	#62114	1	1	yes	characteristic, direct product factor, Sylow
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	2	no	—
526	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
529	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
530	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
533	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
534	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	1	no	—
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	2	yes	—
545	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
548	#127	C₂³×C₅₃	1	1	yes	characteristic
549	#126	—	2	4	no	—
550	#125	—	2	1	no	—
551	#125	—	2	2	no	—
552	#125	—	2	1	no	—
553	#125	—	2	2	no	—
554	#125	—	2	1	no	—
555	#125	—	2	2	no	—
556	#125	C₂³×C₅₃	1	4	yes	—
557	#124	—	2	4	no	—
558	#124	—	2	1	no	—
559	#124	—	2	2	no	—
560	#123	—	2	4	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
575	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
576	#121	—	2	2	no	—
577	#121	—	2	4	no	—
578	#121	—	2	2	no	—
579	#121	—	2	1	no	—
580	#121	C₂³×C₅₃	1	2	yes	—
581	#121	C₂³×C₅₃	1	4	yes	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
596	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
600	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
609	C₄×D₄	D₄×C₅₃	1	2	yes	—
610	C₄×D₄	C₂³×C₅₃	1	4	yes	—
611	C₄×D₄	C₂³×C₅₃	1	2	yes	—
612	C₄×D₄	C₂³×C₅₃	1	2	yes	—
613	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
614	#117	—	2	2	no	—
615	#117	—	2	1	no	—
616	#117	—	2	2	no	—
617	#117	D₄×C₅₃	1	1	yes	characteristic
618	#117	D₄×C₅₃	1	2	yes	—
619	#117	C₂³×C₅₃	1	4	yes	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
627	C₂×C₄²	—	2	2	no	—
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
631	#107	C₂³×C₅₃	1	4	yes	—
632	#107	C₂³×C₅₃	1	4	yes	—
633	#107	C₂³×C₅₃	1	4	yes	—
634	#107	C₂³×C₅₃	1	4	yes	—
635	#106	C₂³×C₅₃	1	2	yes	—
636	#106	C₂³×C₅₃	1	4	yes	—
637	#106	C₂³×C₅₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
640	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
641	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
642	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
643	#103	C₂³×C₅₃	1	4	yes	—
644	#103	C₂³×C₅₃	1	4	yes	—
645	#103	C₂³×C₅₃	1	2	yes	—
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	4	yes	—
650	#102	C₂³×C₅₃	1	2	yes	—
651	#102	C₂³×C₅₃	1	2	yes	—
652	#102	C₂³×C₅₃	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
654	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
655	#97	C₂³×C₅₃	1	4	yes	—
656	C₄×C₈	C₂³×C₅₃	1	2	yes	—
657	#41	—	2	4	no	—
658	#41	—	4	4	no	—
659	#41	—	8	4	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	4	1	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	8	2	no	—
672	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
673	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
674	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
681	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
682	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	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	SD₁₆	—	2	4	no	—
697	SD₁₆	—	4	4	no	—
698	SD₁₆	—	4	2	no	—
699	M₁₆	—	4	4	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
702	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
703	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	1	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	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
731	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
747	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	1	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	4	no	—
756	C₄²	C₂×D₄×C₅₃	1	2	yes	—
757	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
758	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
759	C₄²	C₂×D₄×C₅₃	1	2	yes	—
760	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
761	C₄²	C₂⁴×C₅₃	1	2	yes	—
762	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
763	C₂³	—	2	2	no	—
764	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
765	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
766	Q₈	—	2	2	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	2	1	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	1	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	4	4	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	8	2	no	—
777	Q₈	—	8	1	no	—
778	Q₈	—	8	2	no	—
779	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
780	D₄	—	2	4	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	2	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	2	no	—
787	D₄	—	8	4	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	1	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	#137×C₅₃	1	4	yes	—
811	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
812	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
813	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
819	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	2	4	no	—
822	C₈	—	2	2	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	C₂×#137×C₅₃	1	2	yes	—
832	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
833	C₄	—	2	1	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	1	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	4	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	2	no	—
847	C₄	C₂×#137×C₅₃	1	2	yes	—
848	C₄	C₂×#137×C₅₃	1	2	yes	—
849	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
850	C₄	C₅₃×#585	1	1	yes	characteristic
851	C₂	—	2	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	8	2	no	—
854	C₂	C₅₃×#3489	1	1	yes	characteristic
855	C₂	C₂²×#137×C₅₃	1	1	yes	characteristic
856	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3511	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
2. Q₈×#41×C₅₃	C₂	semidirect
3. C₅₃×#3385	C₂	semidirect
4. C₅₃×#3372	C₂	semidirect
5. C₅₃×#3357	C₂	semidirect
6. C₅₃×#3346	C₂	semidirect
7. C₅₃×#3329	C₂	semidirect
8. C₅₃×#3320	C₂	semidirect
9. C₅₃×#3254	C₂	semidirect
10. C₅₃×#3246	C₂	semidirect
11. C₅₃×#3237	C₂	semidirect
12. C₅₃×#3230	C₂	semidirect
13. C₅₃×#3112	C₂	semidirect
14. C₅₃×#3103	C₂	semidirect
15. C₅₃×#3078	C₂	semidirect
16. C₂×C₅₃×#477	C₂	semidirect
17. C₅₃×#2989	C₂	semidirect
394. #62114	C₅₃	direct (N × H)
424. Q₈×#41	C₂×C₅₃	semidirect
425. #3385	C₂×C₅₃	semidirect
426. #3372	C₂×C₅₃	semidirect
427. #3357	C₂×C₅₃	semidirect
428. #3346	C₂×C₅₃	semidirect
429. #3329	C₂×C₅₃	semidirect
430. #3320	C₂×C₅₃	semidirect
431. #3254	C₂×C₅₃	semidirect
432. #3246	C₂×C₅₃	semidirect
433. #3237	C₂×C₅₃	semidirect
434. #3230	C₂×C₅₃	semidirect
435. #3112	C₂×C₅₃	semidirect
436. #3103	C₂×C₅₃	semidirect
437. #3078	C₂×C₅₃	semidirect
438. C₂×#477	C₂×C₅₃	semidirect
439. #2989	C₂×C₅₃	semidirect
523. C₅₃	#62114	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×#3511	2
Q₈×#41×C₅₃	2
C₅₃×#3385	2
C₅₃×#3372	2
C₅₃×#3357	2
C₅₃×#3346	2
C₅₃×#3329	2
C₅₃×#3320	2
C₅₃×#3254	2
C₅₃×#3246	2
C₅₃×#3237	2
C₅₃×#3230	2
C₅₃×#3112	2
C₅₃×#3103	2
C₅₃×#3078	2
C₂×C₅₃×#477	2
C₅₃×#2989	2
#62114	53

Subgroups — C53×#62114 #27269626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62114 #27269626