Subgroups — C₅₃×#61863 #27269375

Order 13568.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3380	C₂	1	2	yes	maximal, complemented
8	Q₈×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3361	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3243	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
21	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#562	—	2	2	no	—
25	C₅₃×#559	C₂²	1	2	yes	complemented
26	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#554	—	2	1	no	—
29	C₅₃×#554	—	2	2	no	—
30	C₅₃×#554	C₂²	1	1	yes	characteristic
31	C₅₃×#554	C₂²	1	2	yes	—
32	C₅₃×#554	C₂²	1	1	yes	characteristic
33	C₅₃×#554	C₂²	1	2	yes	—
34	C₅₃×#554	C₂²	1	2	yes	complemented
35	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₅₃	—	2	1	no	—
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#548	—	2	1	no	—
41	C₅₃×#547	—	2	1	no	—
42	C₅₃×#544	C₂²	1	2	yes	—
43	C₅₃×#543	—	2	2	no	—
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#542	C₂²	1	2	yes	—
46	C₅₃×#540	C₂²	1	2	yes	—
47	C₅₃×#539	—	2	2	no	—
48	C₅₃×#536	—	2	1	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₅₃×#532	C₂²	1	1	yes	characteristic
52	C₅₃×#529	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
55	C₅₃×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	complemented
58	C₅₃×#501	C₂²	1	2	yes	complemented
59	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#500	C₂²	1	2	yes	complemented
61	C₅₃×#499	C₂²	1	2	yes	complemented
62	C₅₃×#499	C₂²	1	2	yes	complemented
63	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#490	C₂²	1	2	yes	complemented
65	C₅₃×#489	C₂²	1	2	yes	complemented
66	C₅₃×#488	C₂²	1	2	yes	complemented
67	C₅₃×#488	C₂²	1	2	yes	complemented
68	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#486	C₂²	1	2	yes	complemented
71	C₅₃×#485	C₂²	1	2	yes	—
72	C₅₃×#484	C₂²	1	1	yes	characteristic
73	C₅₃×#482	C₂²	1	2	yes	—
74	C₅₃×#482	C₂²	1	2	yes	—
75	C₅₃×#482	C₂²	1	2	yes	—
76	C₅₃×#481	C₂²	1	1	yes	characteristic
77	C₅₃×#480	C₂²	1	2	yes	—
78	C₅₃×#479	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	1	yes	characteristic
80	C₅₃×#478	C₂²	1	1	yes	characteristic
81	C₅₃×#478	C₂²	1	2	yes	—
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	complemented
84	C₅₃×#478	C₂²	1	2	yes	complemented
85	C₅₃×#478	C₂²	1	2	yes	complemented
86	C₅₃×#478	C₂²	1	2	yes	complemented
87	C₅₃×#478	C₂²	1	2	yes	complemented
88	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#477	C₂²	1	2	yes	complemented
90	C₅₃×#476	C₂²	1	2	yes	—
91	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#476	C₂²	1	2	yes	complemented
93	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#474	C₂²	1	1	yes	characteristic
95	C₅₃×#474	C₂²	1	1	yes	characteristic
96	C₅₃×#474	C₂²	1	2	yes	—
97	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#474	C₂²	1	2	yes	complemented
99	C₅₃×#474	C₂²	1	2	yes	complemented
100	C₅₃×#463	C₂²	1	1	yes	characteristic
101	C₅₃×#463	C₂²	1	1	yes	characteristic
102	C₅₃×#463	C₂²	1	2	yes	—
103	C₅₃×#463	C₂²	1	2	yes	—
104	C₅₃×#459	C₂²	1	1	yes	characteristic
105	C₅₃×#459	C₂²	1	1	yes	characteristic
106	C₅₃×#459	C₂²	1	2	yes	—
107	C₅₃×#459	C₂²	1	2	yes	—
108	C₅₃×#450	C₂²	1	1	yes	characteristic
109	C₅₃×#447	C₂²	1	2	yes	—
110	C₅₃×#447	C₂²	1	1	yes	characteristic
111	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#446	C₂²	1	2	yes	complemented
113	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
114	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
117	C₅₃×#442	C₂²	1	2	yes	—
118	C₅₃×#442	C₂²	1	2	yes	—
119	C₅₃×#442	C₂²	1	2	yes	—
120	C₅₃×#440	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
124	C₄×D₈×C₅₃	C₂²	1	2	yes	—
125	C₄×D₈×C₅₃	C₂²	1	2	yes	—
126	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
127	C₄×D₈×C₅₃	C₂²	1	2	yes	—
128	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₅₃	C₂²	1	2	yes	—
130	C₄×D₈×C₅₃	C₂²	1	2	yes	—
131	C₅₃×#433	C₂²	1	2	yes	—
132	C₅₃×#433	C₂²	1	2	yes	—
133	C₅₃×#431	C₂²	1	1	yes	characteristic
134	C₅₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×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×D₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	—	2	1	no	—
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₅₃	C₂³	1	2	yes	—
145	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₅₃	C₂³	1	2	yes	—
147	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₄⋊Q₈×C₅₃	—	2	2	no	—
149	C₄⋊Q₈×C₅₃	—	2	1	no	—
150	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
151	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
158	#127×C₅₃	C₂³	1	1	yes	characteristic
159	#127×C₅₃	C₂³	1	2	yes	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	1	no	—
162	#125×C₅₃	—	2	2	no	—
163	#125×C₅₃	—	2	2	no	—
164	#125×C₅₃	D₄	1	2	yes	—
165	#125×C₅₃	C₂³	1	2	yes	—
166	#125×C₅₃	C₂³	1	2	yes	—
167	#125×C₅₃	C₂³	1	2	yes	—
168	#125×C₅₃	C₂³	1	1	yes	characteristic
169	#125×C₅₃	C₂³	1	2	yes	—
170	#124×C₅₃	—	2	2	no	—
171	#124×C₅₃	—	2	1	no	—
172	#124×C₅₃	—	2	1	no	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	C₂³	1	1	yes	characteristic
175	#124×C₅₃	C₂³	1	2	yes	—
176	#123×C₅₃	—	2	2	no	—
177	#123×C₅₃	—	2	2	no	—
178	#123×C₅₃	—	2	2	no	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	1	no	—
183	C₂²⋊Q₈×C₅₃	—	2	1	no	—
184	C₂²⋊Q₈×C₅₃	—	2	1	no	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	2	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	C₂³	1	1	yes	characteristic
217	#121×C₅₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	—	2	1	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
226	C₄×D₄×C₅₃	—	2	2	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	2	yes	—
247	#117×C₅₃	—	2	1	no	—
248	#117×C₅₃	C₂³	1	2	yes	—
249	#117×C₅₃	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
251	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
252	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
253	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
257	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
258	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
259	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
260	#107×C₅₃	C₂³	1	2	yes	—
261	#107×C₅₃	C₂³	1	2	yes	—
262	#107×C₅₃	C₂³	1	2	yes	—
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	1	yes	characteristic
268	#106×C₅₃	C₂³	1	2	yes	—
269	#106×C₅₃	C₂³	1	2	yes	—
270	#106×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	1	yes	characteristic
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	#103×C₅₃	C₂³	1	2	yes	—
283	#103×C₅₃	C₂³	1	2	yes	—
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	1	yes	characteristic
286	#102×C₅₃	C₂³	1	2	yes	—
287	#102×C₅₃	C₂³	1	1	yes	characteristic
288	#102×C₅₃	C₂³	1	2	yes	—
289	#102×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	1	yes	characteristic
296	#102×C₅₃	C₂³	1	1	yes	characteristic
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	#97×C₅₃	C₂³	1	2	yes	—
306	#97×C₅₃	C₂³	1	2	yes	—
307	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	C₂⁴×C₅₃	—	2	1	no	—
313	#41×C₅₃	—	8	2	no	—
314	#41×C₅₃	—	8	2	no	—
315	C₂×Q₈×C₅₃	—	2	1	no	—
316	C₂×Q₈×C₅₃	—	2	1	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	2	no	—
319	C₂×Q₈×C₅₃	—	2	2	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	8	2	no	—
322	C₂×Q₈×C₅₃	—	8	2	no	—
323	C₂×Q₈×C₅₃	—	8	2	no	—
324	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
338	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	1	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	—	2	2	no	—
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	2	no	—
354	C₂²×C₄×C₅₃	—	2	2	no	—
355	C₂²×C₄×C₅₃	—	8	2	no	—
356	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	SD₁₆×C₅₃	—	2	2	no	—
360	SD₁₆×C₅₃	—	2	2	no	—
361	D₈×C₅₃	—	2	4	no	—
362	D₈×C₅₃	—	2	2	no	—
363	D₈×C₅₃	—	2	4	no	—
364	D₈×C₅₃	—	2	2	no	—
365	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
367	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₅₃	—	2	1	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	1	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	—	2	2	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	1	no	—
384	C₄⋊C₄×C₅₃	—	2	1	no	—
385	C₄⋊C₄×C₅₃	—	2	1	no	—
386	C₄⋊C₄×C₅₃	—	2	2	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	1	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
430	C₄²×C₅₃	—	2	1	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	—	2	2	no	—
433	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₄²×C₅₃	C₂⁴	1	2	yes	—
438	C₄²×C₅₃	C₂⁴	1	2	yes	—
439	C₂³×C₅₃	—	2	4	no	—
440	C₂³×C₅₃	—	2	1	no	—
441	C₂³×C₅₃	—	2	1	no	—
442	C₂³×C₅₃	—	2	2	no	—
443	C₂³×C₅₃	—	2	1	no	—
444	C₂³×C₅₃	—	8	1	no	—
445	C₂³×C₅₃	—	8	1	no	—
446	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₅₃	—	2	2	no	—
448	Q₈×C₅₃	—	2	2	no	—
449	Q₈×C₅₃	—	2	1	no	—
450	Q₈×C₅₃	—	2	1	no	—
451	Q₈×C₅₃	—	4	2	no	—
452	Q₈×C₅₃	—	4	2	no	—
453	Q₈×C₅₃	—	4	2	no	—
454	Q₈×C₅₃	—	8	1	no	—
455	Q₈×C₅₃	—	8	2	no	—
456	Q₈×C₅₃	—	8	2	no	—
457	Q₈×C₅₃	—	8	2	no	—
458	D₄×C₅₃	—	2	4	no	—
459	D₄×C₅₃	—	2	1	no	—
460	D₄×C₅₃	—	2	1	no	—
461	D₄×C₅₃	—	2	2	no	—
462	D₄×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	1	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	4	2	no	—
466	D₄×C₅₃	—	8	1	no	—
467	D₄×C₅₃	—	8	2	no	—
468	D₄×C₅₃	—	8	2	no	—
469	D₄×C₅₃	—	8	1	no	—
470	D₄×C₅₃	—	8	2	no	—
471	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
472	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
473	C₂×C₄×C₅₃	—	2	2	no	—
474	C₂×C₄×C₅₃	—	2	1	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	2	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	4	1	no	—
485	C₂×C₄×C₅₃	—	4	2	no	—
486	C₂×C₄×C₅₃	—	4	2	no	—
487	C₂×C₄×C₅₃	—	4	2	no	—
488	C₂×C₄×C₅₃	—	8	2	no	—
489	C₂×C₄×C₅₃	—	8	2	no	—
490	C₂×C₄×C₅₃	—	8	2	no	—
491	C₂×C₄×C₅₃	—	8	1	no	—
492	C₂×C₄×C₅₃	—	8	1	no	—
493	C₂×C₄×C₅₃	—	8	2	no	—
494	C₂×C₄×C₅₃	—	8	2	no	—
495	C₂×C₄×C₅₃	—	8	2	no	—
496	C₂×C₄×C₅₃	—	8	2	no	—
497	C₂×C₄×C₅₃	—	8	2	no	—
498	C₂×C₄×C₅₃	—	8	1	no	—
499	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
509	C₈×C₅₃	—	2	2	no	—
510	C₈×C₅₃	—	2	1	no	—
511	C₈×C₅₃	—	2	1	no	—
512	C₈×C₅₃	—	2	2	no	—
513	C₈×C₅₃	—	2	1	no	—
514	C₈×C₅₃	—	2	1	no	—
515	#61863	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂²×C₅₃	—	2	1	no	—
517	C₂²×C₅₃	—	2	1	no	—
518	C₂²×C₅₃	—	2	2	no	—
519	C₂²×C₅₃	—	2	2	no	—
520	C₂²×C₅₃	—	2	1	no	—
521	C₂²×C₅₃	—	4	1	no	—
522	C₂²×C₅₃	—	4	1	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	—	4	1	no	—
525	C₂²×C₅₃	—	4	2	no	—
526	C₂²×C₅₃	—	4	1	no	—
527	C₂²×C₅₃	—	4	2	no	—
528	C₂²×C₅₃	—	4	1	no	—
529	C₂²×C₅₃	—	4	1	no	—
530	C₂²×C₅₃	—	4	2	no	—
531	C₂²×C₅₃	—	8	4	no	—
532	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₅₃	—	2	1	no	—
534	C₄×C₅₃	—	2	1	no	—
535	C₄×C₅₃	—	2	2	no	—
536	C₄×C₅₃	—	2	2	no	—
537	C₄×C₅₃	—	2	1	no	—
538	C₄×C₅₃	—	2	1	no	—
539	C₄×C₅₃	—	2	2	no	—
540	C₄×C₅₃	—	2	2	no	—
541	C₄×C₅₃	—	4	1	no	—
542	C₄×C₅₃	—	4	2	no	—
543	C₄×C₅₃	—	4	1	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	1	no	—
546	C₄×C₅₃	—	4	1	no	—
547	C₄×C₅₃	—	4	2	no	—
548	C₄×C₅₃	—	4	2	no	—
549	C₄×C₅₃	#576	1	2	yes	—
550	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
551	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
552	#3554	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#3501	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3389	C₂×C₅₃	1	2	yes	complemented
555	#3386	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#3381	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3380	C₂×C₅₃	1	2	yes	complemented
559	Q₈×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3370	C₂×C₅₃	1	2	yes	complemented
562	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3361	C₂×C₅₃	1	2	yes	complemented
565	#3358	C₂×C₅₃	1	1	yes	characteristic, complemented
566	#3243	C₂×C₅₃	1	2	yes	complemented
567	#3241	C₂×C₅₃	1	2	yes	complemented
568	#3233	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3228	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3122	C₂×C₅₃	1	2	yes	complemented
571	#3118	C₂×C₅₃	1	2	yes	complemented
572	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#2986	C₂×C₅₃	1	1	yes	characteristic, complemented
575	C₂×C₅₃	—	4	1	no	—
576	C₂×C₅₃	—	4	2	no	—
577	C₂×C₅₃	—	4	2	no	—
578	C₂×C₅₃	—	8	2	no	—
579	C₂×C₅₃	—	8	1	no	—
580	C₂×C₅₃	#3486	1	1	yes	characteristic
581	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
582	C₂×C₅₃	#3584	1	1	yes	characteristic
583	#562	—	2	2	no	—
584	#559	C₂²×C₅₃	1	2	yes	complemented
585	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
586	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
587	#554	—	2	1	no	—
588	#554	—	2	2	no	—
589	#554	C₂²×C₅₃	1	1	yes	characteristic
590	#554	C₂²×C₅₃	1	2	yes	—
591	#554	C₂²×C₅₃	1	1	yes	characteristic
592	#554	C₂²×C₅₃	1	2	yes	—
593	#554	C₂²×C₅₃	1	2	yes	complemented
594	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
595	D₄×Q₈	—	2	1	no	—
596	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
597	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
598	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
599	#548	—	2	1	no	—
600	#547	—	2	1	no	—
601	#544	C₂²×C₅₃	1	2	yes	—
602	#543	—	2	2	no	—
603	#542	—	2	1	no	—
604	#542	C₂²×C₅₃	1	2	yes	—
605	#540	C₂²×C₅₃	1	2	yes	—
606	#539	—	2	2	no	—
607	#536	—	2	1	no	—
608	#533	C₂²×C₅₃	1	1	yes	characteristic
609	#533	C₂²×C₅₃	1	1	yes	characteristic
610	#532	C₂²×C₅₃	1	1	yes	characteristic
611	#529	C₂²×C₅₃	1	1	yes	characteristic
612	C₂×C₂²⋊Q₈	—	2	1	no	—
613	C₂×C₂²⋊Q₈	—	2	1	no	—
614	#518	C₂²×C₅₃	1	2	yes	—
615	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
616	#501	C₂²×C₅₃	1	2	yes	complemented
617	#501	C₂²×C₅₃	1	2	yes	complemented
618	#500	C₂²×C₅₃	1	2	yes	complemented
619	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
620	#499	C₂²×C₅₃	1	2	yes	complemented
621	#499	C₂²×C₅₃	1	2	yes	complemented
622	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
623	#490	C₂²×C₅₃	1	2	yes	complemented
624	#489	C₂²×C₅₃	1	2	yes	complemented
625	#488	C₂²×C₅₃	1	2	yes	complemented
626	#488	C₂²×C₅₃	1	2	yes	complemented
627	#486	C₂²×C₅₃	1	2	yes	complemented
628	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
629	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
630	#485	C₂²×C₅₃	1	2	yes	—
631	#484	C₂²×C₅₃	1	1	yes	characteristic
632	#482	C₂²×C₅₃	1	2	yes	—
633	#482	C₂²×C₅₃	1	2	yes	—
634	#482	C₂²×C₅₃	1	2	yes	—
635	#481	C₂²×C₅₃	1	1	yes	characteristic
636	#480	C₂²×C₅₃	1	2	yes	—
637	#479	C₂²×C₅₃	1	2	yes	complemented
638	#478	C₂²×C₅₃	1	1	yes	characteristic
639	#478	C₂²×C₅₃	1	1	yes	characteristic
640	#478	C₂²×C₅₃	1	2	yes	—
641	#478	C₂²×C₅₃	1	2	yes	—
642	#478	C₂²×C₅₃	1	2	yes	complemented
643	#478	C₂²×C₅₃	1	2	yes	complemented
644	#478	C₂²×C₅₃	1	2	yes	complemented
645	#478	C₂²×C₅₃	1	2	yes	complemented
646	#478	C₂²×C₅₃	1	2	yes	complemented
647	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	#477	C₂²×C₅₃	1	2	yes	complemented
649	#476	C₂²×C₅₃	1	2	yes	—
650	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#476	C₂²×C₅₃	1	2	yes	complemented
652	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#474	C₂²×C₅₃	1	1	yes	characteristic
654	#474	C₂²×C₅₃	1	1	yes	characteristic
655	#474	C₂²×C₅₃	1	2	yes	—
656	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#474	C₂²×C₅₃	1	2	yes	complemented
658	#474	C₂²×C₅₃	1	2	yes	complemented
659	#463	C₂²×C₅₃	1	1	yes	characteristic
660	#463	C₂²×C₅₃	1	1	yes	characteristic
661	#463	C₂²×C₅₃	1	2	yes	—
662	#463	C₂²×C₅₃	1	2	yes	—
663	#459	C₂²×C₅₃	1	1	yes	characteristic
664	#459	C₂²×C₅₃	1	1	yes	characteristic
665	#459	C₂²×C₅₃	1	2	yes	—
666	#459	C₂²×C₅₃	1	2	yes	—
667	#450	C₂²×C₅₃	1	1	yes	characteristic
668	#447	C₂²×C₅₃	1	2	yes	—
669	#447	C₂²×C₅₃	1	1	yes	characteristic
670	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#446	C₂²×C₅₃	1	2	yes	complemented
672	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
676	#442	C₂²×C₅₃	1	2	yes	—
677	#442	C₂²×C₅₃	1	2	yes	—
678	#442	C₂²×C₅₃	1	2	yes	—
679	#440	C₂²×C₅₃	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
683	C₄×D₈	C₂²×C₅₃	1	2	yes	—
684	C₄×D₈	C₂²×C₅₃	1	2	yes	—
685	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
686	C₄×D₈	C₂²×C₅₃	1	2	yes	—
687	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
688	C₄×D₈	C₂²×C₅₃	1	2	yes	—
689	C₄×D₈	C₂²×C₅₃	1	2	yes	—
690	#433	C₂²×C₅₃	1	2	yes	—
691	#433	C₂²×C₅₃	1	2	yes	—
692	#431	C₂²×C₅₃	1	1	yes	characteristic
693	#431	C₂²×C₅₃	1	1	yes	characteristic
694	C₅₃	#61863	1	1	yes	characteristic, direct product factor, Sylow
695	C₂×#41	—	2	1	no	—
696	C₂×#41	—	2	1	no	—
697	C₂²×Q₈	—	2	1	no	—
698	C₂²×Q₈	—	2	1	no	—
699	C₂²×Q₈	—	2	1	no	—
700	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
701	C₂³×C₄	—	2	1	no	—
702	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×D₈	C₂³×C₅₃	1	2	yes	—
705	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×D₈	C₂³×C₅₃	1	2	yes	—
707	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	2	2	no	—
710	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
711	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
713	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
714	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
716	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
718	#127	C₂³×C₅₃	1	1	yes	characteristic
719	#127	C₂³×C₅₃	1	2	yes	—
720	#126	—	2	2	no	—
721	#126	—	2	1	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	D₄×C₅₃	1	2	yes	—
725	#125	C₂³×C₅₃	1	1	yes	characteristic
726	#125	C₂³×C₅₃	1	2	yes	—
727	#125	C₂³×C₅₃	1	2	yes	—
728	#125	C₂³×C₅₃	1	2	yes	—
729	#125	C₂³×C₅₃	1	2	yes	—
730	#124	—	2	1	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	1	no	—
734	#124	C₂³×C₅₃	1	1	yes	characteristic
735	#124	C₂³×C₅₃	1	2	yes	—
736	#123	—	2	1	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
768	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
769	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	C₂³×C₅₃	1	1	yes	characteristic
777	#121	C₂³×C₅₃	1	2	yes	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
783	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₅₃	1	2	yes	—
799	C₄×D₄	C₂³×C₅₃	1	2	yes	—
800	C₄×D₄	C₂³×C₅₃	1	2	yes	—
801	C₄×D₄	C₂³×C₅₃	1	2	yes	—
802	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₅₃	1	2	yes	—
804	C₄×D₄	C₂³×C₅₃	1	2	yes	—
805	C₄×D₄	C₂³×C₅₃	1	2	yes	—
806	C₄×D₄	C₂³×C₅₃	1	2	yes	—
807	#117	—	2	1	no	—
808	#117	C₂³×C₅₃	1	2	yes	—
809	#117	C₂³×C₅₃	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	2	no	—
811	C₂×C₄⋊C₄	—	2	2	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	2	no	—
815	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	2	2	no	—
818	C₂×C₂²⋊C₄	—	2	2	no	—
819	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
820	#107	C₂³×C₅₃	1	2	yes	—
821	#107	C₂³×C₅₃	1	2	yes	—
822	#107	C₂³×C₅₃	1	2	yes	—
823	#107	C₂³×C₅₃	1	1	yes	characteristic
824	#107	C₂³×C₅₃	1	2	yes	—
825	#107	C₂³×C₅₃	1	2	yes	—
826	#107	C₂³×C₅₃	1	1	yes	characteristic
827	#107	C₂³×C₅₃	1	2	yes	—
828	#106	C₂³×C₅₃	1	2	yes	—
829	#106	C₂³×C₅₃	1	1	yes	characteristic
830	#106	C₂³×C₅₃	1	1	yes	characteristic
831	#106	C₂³×C₅₃	1	2	yes	—
832	#106	C₂³×C₅₃	1	2	yes	—
833	#106	C₂³×C₅₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
840	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
841	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
842	#103	C₂³×C₅₃	1	1	yes	characteristic
843	#103	C₂³×C₅₃	1	2	yes	—
844	#103	C₂³×C₅₃	1	1	yes	characteristic
845	#103	C₂³×C₅₃	1	2	yes	—
846	#102	C₂³×C₅₃	1	1	yes	characteristic
847	#102	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	1	yes	characteristic
849	#102	C₂³×C₅₃	1	2	yes	—
850	#102	C₂³×C₅₃	1	1	yes	characteristic
851	#102	C₂³×C₅₃	1	2	yes	—
852	#102	C₂³×C₅₃	1	2	yes	—
853	#102	C₂³×C₅₃	1	2	yes	—
854	#102	C₂³×C₅₃	1	2	yes	—
855	#102	C₂³×C₅₃	1	1	yes	characteristic
856	#102	C₂³×C₅₃	1	2	yes	—
857	#102	C₂³×C₅₃	1	1	yes	characteristic
858	#102	C₂³×C₅₃	1	1	yes	characteristic
859	#102	C₂³×C₅₃	1	2	yes	—
860	#102	C₂³×C₅₃	1	2	yes	—
861	#102	C₂³×C₅₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
865	#97	C₂³×C₅₃	1	2	yes	—
866	#97	C₂³×C₅₃	1	2	yes	—
867	C₄×C₈	C₂³×C₅₃	1	2	yes	—
868	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₅₃	1	2	yes	—
871	C₄×C₈	C₂³×C₅₃	1	2	yes	—
872	C₂⁴	—	2	1	no	—
873	#41	—	8	2	no	—
874	#41	—	8	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	8	2	no	—
882	C₂×Q₈	—	8	2	no	—
883	C₂×Q₈	—	8	2	no	—
884	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
885	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
886	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
899	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
919	SD₁₆	—	2	2	no	—
920	SD₁₆	—	2	2	no	—
921	D₈	—	2	4	no	—
922	D₈	—	2	2	no	—
923	D₈	—	2	4	no	—
924	D₈	—	2	2	no	—
925	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
927	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
930	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
952	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
953	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
959	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
995	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
997	C₄²	C₂⁴×C₅₃	1	2	yes	—
998	C₄²	C₂⁴×C₅₃	1	2	yes	—
999	C₂³	—	2	4	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	8	1	no	—
1005	C₂³	—	8	1	no	—
1006	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	4	2	no	—
1014	Q₈	—	8	1	no	—
1015	Q₈	—	8	2	no	—
1016	Q₈	—	8	2	no	—
1017	Q₈	—	8	2	no	—
1018	D₄	—	2	4	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	4	2	no	—
1026	D₄	—	8	1	no	—
1027	D₄	—	8	2	no	—
1028	D₄	—	8	2	no	—
1029	D₄	—	8	1	no	—
1030	D₄	—	8	2	no	—
1031	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1032	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	1	no	—
1052	C₂×C₄	—	8	1	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1060	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1064	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1068	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1069	C₈	—	2	2	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	8	4	no	—
1091	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	C₅₃×#576	1	2	yes	—
1109	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1110	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1111	C₂	—	4	1	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	4	2	no	—
1114	C₂	—	8	1	no	—
1115	C₂	—	8	2	no	—
1116	C₂	C₅₃×#3486	1	1	yes	characteristic
1117	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1118	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3554	C₂	semidirect
2. C₅₃×#3501	C₂	semidirect
3. C₅₃×#3389	C₂	semidirect
4. C₅₃×#3386	C₂	semidirect
5. C₅₃×#3384	C₂	semidirect
6. C₅₃×#3381	C₂	semidirect
7. C₅₃×#3380	C₂	semidirect
8. Q₈×D₈×C₅₃	C₂	semidirect
9. C₅₃×#3373	C₂	semidirect
10. C₅₃×#3370	C₂	semidirect
11. C₅₃×#3366	C₂	semidirect
12. C₅₃×#3361	C₂	semidirect
13. C₅₃×#3361	C₂	semidirect
14. C₅₃×#3358	C₂	semidirect
15. C₅₃×#3243	C₂	semidirect
16. C₅₃×#3241	C₂	semidirect
17. C₅₃×#3233	C₂	semidirect
18. C₅₃×#3228	C₂	semidirect
19. C₅₃×#3122	C₂	semidirect
20. C₅₃×#3118	C₂	semidirect
21. C₅₃×#3105	C₂	semidirect
22. C₅₃×#3100	C₂	semidirect
23. C₅₃×#2986	C₂	semidirect
25. C₅₃×#559	C₂²	semidirect
26. C₅₃×#559	C₂²	semidirect
27. C₅₃×#557	C₂²	semidirect
34. C₅₃×#554	C₂²	semidirect
35. C₅₃×#550	C₂²	semidirect
39. D₄×Q₈×C₅₃	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#501	C₂²	semidirect
59. C₅₃×#500	C₂²	semidirect
60. C₅₃×#500	C₂²	semidirect
61. C₅₃×#499	C₂²	semidirect
62. C₅₃×#499	C₂²	semidirect
63. C₅₃×#498	C₂²	semidirect
64. C₅₃×#490	C₂²	semidirect
65. C₅₃×#489	C₂²	semidirect
66. C₅₃×#488	C₂²	semidirect
67. C₅₃×#488	C₂²	semidirect
68. C₅₃×#486	C₂²	semidirect
69. C₅₃×#486	C₂²	semidirect
70. C₅₃×#486	C₂²	semidirect
78. C₅₃×#479	C₂²	semidirect
83. C₅₃×#478	C₂²	semidirect
84. C₅₃×#478	C₂²	semidirect
85. C₅₃×#478	C₂²	semidirect
86. C₅₃×#478	C₂²	semidirect
87. C₅₃×#478	C₂²	semidirect
88. C₅₃×#477	C₂²	semidirect
89. C₅₃×#477	C₂²	semidirect
91. C₅₃×#476	C₂²	semidirect
92. C₅₃×#476	C₂²	semidirect
93. C₅₃×#475	C₂²	semidirect
97. C₅₃×#474	C₂²	semidirect
98. C₅₃×#474	C₂²	semidirect
99. C₅₃×#474	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₅₃×#446	C₂²	semidirect
113. C₅₃×#446	C₂²	semidirect
114. C₈×Q₈×C₅₃	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
116. C₈×Q₈×C₅₃	C₂²	semidirect
515. #61863	C₅₃	direct (N × H)
552. #3554	C₂×C₅₃	semidirect
553. #3501	C₂×C₅₃	semidirect
554. #3389	C₂×C₅₃	semidirect
555. #3386	C₂×C₅₃	semidirect
556. #3384	C₂×C₅₃	semidirect
557. #3381	C₂×C₅₃	semidirect
558. #3380	C₂×C₅₃	semidirect
559. Q₈×D₈	C₂×C₅₃	semidirect
560. #3373	C₂×C₅₃	semidirect
561. #3370	C₂×C₅₃	semidirect
562. #3366	C₂×C₅₃	semidirect
563. #3361	C₂×C₅₃	semidirect
564. #3361	C₂×C₅₃	semidirect
565. #3358	C₂×C₅₃	semidirect
566. #3243	C₂×C₅₃	semidirect
567. #3241	C₂×C₅₃	semidirect
568. #3233	C₂×C₅₃	semidirect
569. #3228	C₂×C₅₃	semidirect
570. #3122	C₂×C₅₃	semidirect
571. #3118	C₂×C₅₃	semidirect
572. #3105	C₂×C₅₃	semidirect
573. #3100	C₂×C₅₃	semidirect
574. #2986	C₂×C₅₃	semidirect
584. #559	C₂²×C₅₃	semidirect
585. #559	C₂²×C₅₃	semidirect
586. #557	C₂²×C₅₃	semidirect
593. #554	C₂²×C₅₃	semidirect
594. #550	C₂²×C₅₃	semidirect
598. D₄×Q₈	C₂²×C₅₃	semidirect
616. #501	C₂²×C₅₃	semidirect
617. #501	C₂²×C₅₃	semidirect
618. #500	C₂²×C₅₃	semidirect
619. #500	C₂²×C₅₃	semidirect
620. #499	C₂²×C₅₃	semidirect
621. #499	C₂²×C₅₃	semidirect
622. #498	C₂²×C₅₃	semidirect
623. #490	C₂²×C₅₃	semidirect
624. #489	C₂²×C₅₃	semidirect
625. #488	C₂²×C₅₃	semidirect
626. #488	C₂²×C₅₃	semidirect
627. #486	C₂²×C₅₃	semidirect
628. #486	C₂²×C₅₃	semidirect
629. #486	C₂²×C₅₃	semidirect
637. #479	C₂²×C₅₃	semidirect
642. #478	C₂²×C₅₃	semidirect
643. #478	C₂²×C₅₃	semidirect
644. #478	C₂²×C₅₃	semidirect
645. #478	C₂²×C₅₃	semidirect
646. #478	C₂²×C₅₃	semidirect
647. #477	C₂²×C₅₃	semidirect
648. #477	C₂²×C₅₃	semidirect
650. #476	C₂²×C₅₃	semidirect
651. #476	C₂²×C₅₃	semidirect
652. #475	C₂²×C₅₃	semidirect
656. #474	C₂²×C₅₃	semidirect
657. #474	C₂²×C₅₃	semidirect
658. #474	C₂²×C₅₃	semidirect
670. #446	C₂²×C₅₃	semidirect
671. #446	C₂²×C₅₃	semidirect
672. #446	C₂²×C₅₃	semidirect
673. C₈×Q₈	C₂²×C₅₃	semidirect
674. C₈×Q₈	C₂²×C₅₃	semidirect
675. C₈×Q₈	C₂²×C₅₃	semidirect
694. C₅₃	#61863	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×#3554	2
C₅₃×#3501	2
C₅₃×#3389	2
C₅₃×#3386	2
C₅₃×#3384	2
C₅₃×#3381	2
C₅₃×#3380	2
Q₈×D₈×C₅₃	2
C₅₃×#3373	2
C₅₃×#3370	2
C₅₃×#3366	2
C₅₃×#3361	2
C₅₃×#3358	2
C₅₃×#3243	2
C₅₃×#3241	2
C₅₃×#3233	2
C₅₃×#3228	2
C₅₃×#3122	2
C₅₃×#3118	2
C₅₃×#3105	2
C₅₃×#3100	2
C₅₃×#2986	2
#61863	53

Subgroups — C53×#61863 #27269375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61863 #27269375