Subgroups — C₅₃×#61274 #27268786

Order 13568.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3353	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3348	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3345	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3341	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3337	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#556	—	2	1	no	—
28	C₅₃×#556	C₂²	1	2	yes	complemented
29	C₅₃×#555	—	2	1	no	—
30	C₅₃×#555	C₂²	1	2	yes	—
31	C₅₃×#555	C₂²	1	2	yes	complemented
32	C₅₃×#553	—	2	1	no	—
33	C₅₃×#553	C₂²	1	2	yes	—
34	C₅₃×#553	C₂²	1	2	yes	—
35	C₅₃×#553	C₂²	1	2	yes	complemented
36	C₅₃×#552	—	2	1	no	—
37	C₅₃×#552	C₂²	1	2	yes	complemented
38	C₅₃×#551	—	2	2	no	—
39	C₅₃×#547	C₂²	1	2	yes	—
40	C₅₃×#546	—	2	2	no	—
41	C₅₃×#544	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	1	yes	characteristic
43	C₅₃×#542	—	2	1	no	—
44	C₅₃×#540	—	2	1	no	—
45	C₅₃×#538	—	2	2	no	—
46	C₅₃×#537	C₂²	1	1	yes	characteristic
47	C₅₃×#535	C₂²	1	1	yes	characteristic
48	C₅₃×#532	—	2	1	no	—
49	C₅₃×#529	—	2	2	no	—
50	C₅₃×#529	—	2	1	no	—
51	C₅₃×#525	C₂²	1	1	yes	characteristic
52	C₅₃×#525	C₂²	1	1	yes	characteristic
53	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
54	C₅₃×#520	C₂²	1	1	yes	characteristic
55	C₅₃×#520	C₂²	1	1	yes	characteristic
56	C₅₃×#520	C₂²	1	1	yes	characteristic
57	C₅₃×#518	C₂²	1	1	yes	characteristic
58	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#501	C₂²	1	2	yes	complemented
61	C₅₃×#501	C₂²	1	2	yes	complemented
62	C₅₃×#500	C₂²	1	2	yes	complemented
63	C₅₃×#499	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#484	C₂²	1	2	yes	complemented
68	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#482	C₂²	1	2	yes	—
71	C₅₃×#482	C₂²	1	2	yes	—
72	C₅₃×#482	C₂²	1	2	yes	—
73	C₅₃×#482	C₂²	1	2	yes	—
74	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#482	C₂²	1	2	yes	complemented
76	C₅₃×#482	C₂²	1	2	yes	complemented
77	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#482	C₂²	1	2	yes	complemented
79	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#481	C₂²	1	2	yes	complemented
81	C₅₃×#480	C₂²	1	2	yes	complemented
82	C₅₃×#480	C₂²	1	2	yes	complemented
83	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#479	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×#476	C₂²	1	2	yes	complemented
89	C₅₃×#476	C₂²	1	2	yes	complemented
90	C₅₃×#475	C₂²	1	2	yes	complemented
91	C₅₃×#474	C₂²	1	2	yes	complemented
92	C₅₃×#469	C₂²	1	2	yes	—
93	C₅₃×#469	C₂²	1	2	yes	complemented
94	C₅₃×#468	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	complemented
96	C₅₃×#466	C₂²	1	2	yes	—
97	C₅₃×#466	C₂²	1	2	yes	complemented
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#442	C₂²	1	2	yes	complemented
101	C₅₃×#440	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
103	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
104	C₅₃×#436	C₂²	1	2	yes	complemented
105	C₅₃×#435	C₂²	1	2	yes	complemented
106	C₅₃×#435	C₂²	1	2	yes	complemented
107	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
108	C₅₃×#428	C₂²	1	1	yes	characteristic
109	C₅₃×#428	C₂²	1	1	yes	characteristic
110	C₅₃×#428	C₂²	1	1	yes	characteristic
111	C₅₃×#428	C₂²	1	1	yes	characteristic
112	C₅₃×#428	C₂²	1	1	yes	characteristic
113	C₅₃×#428	C₂²	1	2	yes	complemented
114	C₅₃×#428	C₂²	1	2	yes	complemented
115	C₅₃×#428	C₂²	1	2	yes	complemented
116	C₅₃×#428	C₂²	1	2	yes	complemented
117	C₅₃×#427	C₂²	1	1	yes	characteristic
118	C₅₃×#427	C₂²	1	1	yes	characteristic
119	C₅₃×#427	C₂²	1	2	yes	complemented
120	C₅₃×#427	C₂²	1	2	yes	complemented
121	C₅₃×#427	C₂²	1	2	yes	complemented
122	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
123	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
124	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
125	C₅₃×#424	C₂²	1	1	yes	characteristic
126	C₅₃×#418	C₂²	1	1	yes	characteristic
127	C₅₃×#417	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₅₃×#416	C₂²	1	1	yes	characteristic
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
134	C₅₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	—	2	2	no	—
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₅₃	—	2	1	no	—
139	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
142	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
143	C₂×D₈×C₅₃	C₂³	1	2	yes	—
144	#131×C₅₃	—	2	4	no	—
145	C₂×M₁₆×C₅₃	—	2	4	no	—
146	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₃	—	2	1	no	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
158	#127×C₅₃	—	2	1	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	2	no	—
162	#126×C₅₃	—	2	2	no	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#125×C₅₃	—	2	1	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	1	no	—
168	#125×C₅₃	C₂³	1	2	yes	—
169	#125×C₅₃	C₂³	1	2	yes	—
170	#124×C₅₃	—	2	2	no	—
171	#124×C₅₃	—	2	2	no	—
172	#124×C₅₃	—	2	2	no	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	—	2	1	no	—
175	#124×C₅₃	—	2	2	no	—
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	#123×C₅₃	D₄	1	2	yes	—
184	C₂²⋊Q₈×C₅₃	—	2	2	no	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	1	no	—
188	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
189	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
190	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
193	#121×C₅₃	—	2	2	no	—
194	#121×C₅₃	—	2	2	no	—
195	#121×C₅₃	—	2	1	no	—
196	#121×C₅₃	—	2	2	no	—
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	1	no	—
201	#121×C₅₃	—	2	1	no	—
202	#121×C₅₃	D₄	1	1	yes	characteristic
203	#121×C₅₃	D₄	1	1	yes	characteristic
204	#121×C₅₃	C₂³	1	2	yes	—
205	#121×C₅₃	C₂³	1	2	yes	—
206	#121×C₅₃	C₂³	1	1	yes	characteristic
207	#121×C₅₃	C₂³	1	1	yes	characteristic
208	#121×C₅₃	C₂³	1	2	yes	—
209	#121×C₅₃	C₂³	1	2	yes	—
210	#121×C₅₃	C₂³	1	2	yes	—
211	#120×C₅₃	—	2	1	no	—
212	#120×C₅₃	—	2	2	no	—
213	#120×C₅₃	D₄	1	2	yes	—
214	C₄×Q₈×C₅₃	—	2	2	no	—
215	C₄×Q₈×C₅₃	—	2	1	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
218	C₄×D₄×C₅₃	—	2	1	no	—
219	C₄×D₄×C₅₃	—	2	1	no	—
220	C₄×D₄×C₅₃	—	2	2	no	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	2	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	—	2	2	no	—
227	C₄×D₄×C₅₃	—	2	1	no	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	C₂³	1	2	yes	—
231	C₄×D₄×C₅₃	C₂³	1	2	yes	—
232	C₄×D₄×C₅₃	C₂³	1	2	yes	—
233	C₄×D₄×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	C₂³	1	2	yes	—
235	#117×C₅₃	—	2	1	no	—
236	#117×C₅₃	—	2	2	no	—
237	#117×C₅₃	—	2	2	no	—
238	#117×C₅₃	—	2	2	no	—
239	#117×C₅₃	—	2	1	no	—
240	#117×C₅₃	—	2	1	no	—
241	#117×C₅₃	—	2	1	no	—
242	#117×C₅₃	—	2	1	no	—
243	#117×C₅₃	C₂³	1	1	yes	characteristic
244	#117×C₅₃	C₂³	1	1	yes	characteristic
245	#117×C₅₃	C₂³	1	2	yes	—
246	#117×C₅₃	C₂³	1	1	yes	characteristic
247	#117×C₅₃	C₂³	1	1	yes	characteristic
248	#117×C₅₃	C₂³	1	2	yes	—
249	#117×C₅₃	C₂³	1	2	yes	—
250	#117×C₅₃	C₂³	1	1	yes	characteristic
251	#117×C₅₃	C₂³	1	2	yes	—
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
262	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
265	C₂×C₄²×C₅₃	—	2	1	no	—
266	C₂×C₄²×C₅₃	—	2	1	no	—
267	#107×C₅₃	C₂³	1	1	yes	characteristic
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	1	yes	characteristic
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	2	yes	—
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	2	yes	—
276	#107×C₅₃	C₂³	1	2	yes	—
277	#107×C₅₃	C₂³	1	2	yes	—
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	1	yes	characteristic
280	#106×C₅₃	C₂³	1	2	yes	—
281	#106×C₅₃	C₂³	1	2	yes	—
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	1	yes	characteristic
284	#106×C₅₃	C₂³	1	2	yes	—
285	#106×C₅₃	C₂³	1	2	yes	—
286	#106×C₅₃	C₂³	1	2	yes	—
287	#106×C₅₃	C₂³	1	1	yes	characteristic
288	#106×C₅₃	C₂³	1	2	yes	—
289	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	#97×C₅₃	C₂³	1	2	yes	—
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	1	no	—
316	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
317	#41×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	2	2	no	—
319	#41×C₅₃	—	2	2	no	—
320	#41×C₅₃	—	2	2	no	—
321	#41×C₅₃	—	8	4	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₅₃	—	2	1	no	—
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	1	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	2	no	—
333	C₂×D₄×C₅₃	—	2	2	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	—	8	2	no	—
338	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₅₃	—	2	2	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	1	no	—
347	C₂²×C₄×C₅₃	—	2	1	no	—
348	C₂²×C₄×C₅₃	—	2	1	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	1	no	—
354	C₂²×C₄×C₅₃	—	2	2	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	SD₁₆×C₅₃	—	2	4	no	—
365	D₈×C₅₃	—	2	4	no	—
366	M₁₆×C₅₃	—	2	2	no	—
367	M₁₆×C₅₃	—	2	4	no	—
368	M₁₆×C₅₃	—	2	4	no	—
369	M₁₆×C₅₃	#41	1	4	yes	complemented
370	C₂×C₈×C₅₃	—	2	2	no	—
371	C₂×C₈×C₅₃	—	2	2	no	—
372	C₂×C₈×C₅₃	—	2	4	no	—
373	C₂×C₈×C₅₃	—	2	4	no	—
374	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
379	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	2	no	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	1	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	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
437	C₄²×C₅₃	—	2	1	no	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	—	2	1	no	—
440	C₄²×C₅₃	—	2	1	no	—
441	C₄²×C₅₃	—	2	2	no	—
442	C₄²×C₅₃	—	2	1	no	—
443	C₄²×C₅₃	—	2	2	no	—
444	C₄²×C₅₃	—	2	2	no	—
445	C₄²×C₅₃	—	2	2	no	—
446	C₄²×C₅₃	—	2	1	no	—
447	C₄²×C₅₃	C₂⁴	1	2	yes	—
448	C₂³×C₅₃	—	2	2	no	—
449	C₂³×C₅₃	—	2	1	no	—
450	C₂³×C₅₃	—	2	2	no	—
451	C₂³×C₅₃	—	4	1	no	—
452	C₂³×C₅₃	—	4	1	no	—
453	C₂³×C₅₃	—	4	2	no	—
454	C₂³×C₅₃	—	8	1	no	—
455	C₂³×C₅₃	—	8	1	no	—
456	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
457	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
458	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₅₃	—	2	2	no	—
461	Q₈×C₅₃	—	2	1	no	—
462	Q₈×C₅₃	—	2	1	no	—
463	Q₈×C₅₃	—	8	2	no	—
464	Q₈×C₅₃	—	8	2	no	—
465	D₄×C₅₃	—	2	4	no	—
466	D₄×C₅₃	—	2	2	no	—
467	D₄×C₅₃	—	2	2	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	2	2	no	—
470	D₄×C₅₃	—	2	1	no	—
471	D₄×C₅₃	—	4	2	no	—
472	D₄×C₅₃	—	4	2	no	—
473	D₄×C₅₃	—	4	4	no	—
474	D₄×C₅₃	—	4	2	no	—
475	D₄×C₅₃	—	4	2	no	—
476	D₄×C₅₃	—	8	1	no	—
477	D₄×C₅₃	—	8	2	no	—
478	D₄×C₅₃	—	8	2	no	—
479	D₄×C₅₃	—	8	1	no	—
480	D₄×C₅₃	—	8	2	no	—
481	D₄×C₅₃	—	8	2	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	2	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	1	no	—
490	C₂×C₄×C₅₃	—	2	2	no	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	2	1	no	—
493	C₂×C₄×C₅₃	—	2	2	no	—
494	C₂×C₄×C₅₃	—	2	2	no	—
495	C₂×C₄×C₅₃	—	2	1	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	2	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	4	2	no	—
502	C₂×C₄×C₅₃	—	4	2	no	—
503	C₂×C₄×C₅₃	—	8	2	no	—
504	C₂×C₄×C₅₃	—	8	2	no	—
505	C₂×C₄×C₅₃	—	8	2	no	—
506	C₂×C₄×C₅₃	—	8	1	no	—
507	C₂×C₄×C₅₃	—	8	2	no	—
508	C₂×C₄×C₅₃	—	8	1	no	—
509	C₂×C₄×C₅₃	—	8	1	no	—
510	C₂×C₄×C₅₃	—	8	1	no	—
511	C₂×C₄×C₅₃	—	8	2	no	—
512	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
519	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
520	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
521	C₈×C₅₃	—	2	1	no	—
522	C₈×C₅₃	—	2	1	no	—
523	C₈×C₅₃	—	2	2	no	—
524	C₈×C₅₃	—	2	1	no	—
525	C₈×C₅₃	—	2	1	no	—
526	C₈×C₅₃	C₂×#41	1	4	yes	—
527	#61274	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
528	C₂²×C₅₃	—	2	1	no	—
529	C₂²×C₅₃	—	2	1	no	—
530	C₂²×C₅₃	—	2	2	no	—
531	C₂²×C₅₃	—	2	1	no	—
532	C₂²×C₅₃	—	2	1	no	—
533	C₂²×C₅₃	—	2	1	no	—
534	C₂²×C₅₃	—	2	2	no	—
535	C₂²×C₅₃	—	2	1	no	—
536	C₂²×C₅₃	—	2	1	no	—
537	C₂²×C₅₃	—	2	1	no	—
538	C₂²×C₅₃	—	2	2	no	—
539	C₂²×C₅₃	—	4	1	no	—
540	C₂²×C₅₃	—	4	2	no	—
541	C₂²×C₅₃	—	4	2	no	—
542	C₂²×C₅₃	—	4	1	no	—
543	C₂²×C₅₃	—	4	1	no	—
544	C₂²×C₅₃	—	4	2	no	—
545	C₂²×C₅₃	—	8	2	no	—
546	C₂²×C₅₃	—	16	2	no	—
547	C₂²×C₅₃	#547	1	2	yes	—
548	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₅₃	—	2	2	no	—
550	C₄×C₅₃	—	2	2	no	—
551	C₄×C₅₃	—	2	1	no	—
552	C₄×C₅₃	—	2	1	no	—
553	C₄×C₅₃	—	2	2	no	—
554	C₄×C₅₃	—	4	1	no	—
555	C₄×C₅₃	—	4	2	no	—
556	C₄×C₅₃	—	4	1	no	—
557	C₄×C₅₃	—	4	1	no	—
558	C₄×C₅₃	—	4	1	no	—
559	C₄×C₅₃	—	4	1	no	—
560	C₄×C₅₃	—	4	2	no	—
561	C₄×C₅₃	—	4	2	no	—
562	C₄×C₅₃	—	4	1	no	—
563	C₄×C₅₃	—	4	1	no	—
564	C₄×C₅₃	#547	1	2	yes	—
565	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
566	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
567	#3494	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#3493	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3355	C₂×C₅₃	1	2	yes	complemented
570	#3353	C₂×C₅₃	1	2	yes	complemented
571	#3350	C₂×C₅₃	1	2	yes	complemented
572	#3348	C₂×C₅₃	1	2	yes	complemented
573	#3347	C₂×C₅₃	1	2	yes	complemented
574	#3345	C₂×C₅₃	1	2	yes	complemented
575	#3341	C₂×C₅₃	1	2	yes	complemented
576	#3337	C₂×C₅₃	1	2	yes	complemented
577	#3164	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
581	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
582	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
584	#3062	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3055	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#2933	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#2912	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#2911	C₂×C₅₃	1	1	yes	characteristic, complemented
590	C₂×C₅₃	—	2	2	no	—
591	C₂×C₅₃	—	4	2	no	—
592	C₂×C₅₃	—	4	1	no	—
593	C₂×C₅₃	—	4	1	no	—
594	C₂×C₅₃	—	8	1	no	—
595	C₂×C₅₃	—	8	2	no	—
596	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
597	C₂×C₅₃	#3584	1	1	yes	characteristic
598	C₂×C₅₃	#3585	1	1	yes	characteristic
599	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
600	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
601	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
602	#556	—	2	1	no	—
603	#556	C₂²×C₅₃	1	2	yes	complemented
604	#555	—	2	1	no	—
605	#555	C₂²×C₅₃	1	2	yes	—
606	#555	C₂²×C₅₃	1	2	yes	complemented
607	#553	—	2	1	no	—
608	#553	C₂²×C₅₃	1	2	yes	—
609	#553	C₂²×C₅₃	1	2	yes	—
610	#553	C₂²×C₅₃	1	2	yes	complemented
611	#552	—	2	1	no	—
612	#552	C₂²×C₅₃	1	2	yes	complemented
613	#551	—	2	2	no	—
614	#547	C₂²×C₅₃	1	2	yes	—
615	#546	—	2	2	no	—
616	#544	C₂²×C₅₃	1	1	yes	characteristic
617	#544	C₂²×C₅₃	1	1	yes	characteristic
618	#542	—	2	1	no	—
619	#540	—	2	1	no	—
620	#538	—	2	2	no	—
621	#537	C₂²×C₅₃	1	1	yes	characteristic
622	#535	C₂²×C₅₃	1	1	yes	characteristic
623	#532	—	2	1	no	—
624	#529	—	2	2	no	—
625	#529	—	2	1	no	—
626	#525	C₂²×C₅₃	1	1	yes	characteristic
627	#525	C₂²×C₅₃	1	1	yes	characteristic
628	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
629	#520	C₂²×C₅₃	1	1	yes	characteristic
630	#520	C₂²×C₅₃	1	1	yes	characteristic
631	#520	C₂²×C₅₃	1	1	yes	characteristic
632	#518	C₂²×C₅₃	1	1	yes	characteristic
633	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
634	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
635	#501	C₂²×C₅₃	1	2	yes	complemented
636	#501	C₂²×C₅₃	1	2	yes	complemented
637	#500	C₂²×C₅₃	1	2	yes	complemented
638	#499	C₂²×C₅₃	1	2	yes	complemented
639	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
640	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	#485	C₂²×C₅₃	1	2	yes	complemented
642	#484	C₂²×C₅₃	1	2	yes	complemented
643	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#482	C₂²×C₅₃	1	2	yes	—
646	#482	C₂²×C₅₃	1	2	yes	—
647	#482	C₂²×C₅₃	1	2	yes	—
648	#482	C₂²×C₅₃	1	2	yes	—
649	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
650	#482	C₂²×C₅₃	1	2	yes	complemented
651	#482	C₂²×C₅₃	1	2	yes	complemented
652	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#482	C₂²×C₅₃	1	2	yes	complemented
654	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#481	C₂²×C₅₃	1	2	yes	complemented
656	#480	C₂²×C₅₃	1	2	yes	complemented
657	#480	C₂²×C₅₃	1	2	yes	complemented
658	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#479	C₂²×C₅₃	1	2	yes	complemented
660	#478	C₂²×C₅₃	1	2	yes	complemented
661	#478	C₂²×C₅₃	1	2	yes	complemented
662	#478	C₂²×C₅₃	1	2	yes	complemented
663	#476	C₂²×C₅₃	1	2	yes	complemented
664	#476	C₂²×C₅₃	1	2	yes	complemented
665	#475	C₂²×C₅₃	1	2	yes	complemented
666	#474	C₂²×C₅₃	1	2	yes	complemented
667	#469	C₂²×C₅₃	1	2	yes	—
668	#469	C₂²×C₅₃	1	2	yes	complemented
669	#468	C₂²×C₅₃	1	2	yes	—
670	#468	C₂²×C₅₃	1	2	yes	complemented
671	#466	C₂²×C₅₃	1	2	yes	—
672	#466	C₂²×C₅₃	1	2	yes	complemented
673	#465	C₂²×C₅₃	1	2	yes	—
674	#465	C₂²×C₅₃	1	2	yes	complemented
675	#442	C₂²×C₅₃	1	2	yes	complemented
676	#440	C₂²×C₅₃	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
678	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
679	#436	C₂²×C₅₃	1	2	yes	complemented
680	#435	C₂²×C₅₃	1	2	yes	complemented
681	#435	C₂²×C₅₃	1	2	yes	complemented
682	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
683	#428	C₂²×C₅₃	1	1	yes	characteristic
684	#428	C₂²×C₅₃	1	1	yes	characteristic
685	#428	C₂²×C₅₃	1	1	yes	characteristic
686	#428	C₂²×C₅₃	1	1	yes	characteristic
687	#428	C₂²×C₅₃	1	1	yes	characteristic
688	#428	C₂²×C₅₃	1	2	yes	complemented
689	#428	C₂²×C₅₃	1	2	yes	complemented
690	#428	C₂²×C₅₃	1	2	yes	complemented
691	#428	C₂²×C₅₃	1	2	yes	complemented
692	#427	C₂²×C₅₃	1	1	yes	characteristic
693	#427	C₂²×C₅₃	1	1	yes	characteristic
694	#427	C₂²×C₅₃	1	2	yes	complemented
695	#427	C₂²×C₅₃	1	2	yes	complemented
696	#427	C₂²×C₅₃	1	2	yes	complemented
697	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
698	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
699	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
700	#424	C₂²×C₅₃	1	1	yes	characteristic
701	#418	C₂²×C₅₃	1	1	yes	characteristic
702	#417	C₂²×C₅₃	1	1	yes	characteristic
703	#416	C₂²×C₅₃	1	1	yes	characteristic
704	#416	C₂²×C₅₃	1	1	yes	characteristic
705	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
706	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
707	#408	C₂²×C₅₃	1	1	yes	characteristic
708	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
709	#405	C₂²×C₅₃	1	1	yes	characteristic
710	C₅₃	#61274	1	1	yes	characteristic, direct product factor, Sylow
711	C₂×#41	—	2	2	no	—
712	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
713	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
714	C₂²×D₄	—	2	1	no	—
715	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
716	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
717	AGL(1,ℤ/8)	—	2	4	no	—
718	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
719	C₂×D₈	C₂³×C₅₃	1	2	yes	—
720	#131	—	2	4	no	—
721	C₂×M₁₆	—	2	4	no	—
722	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
723	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
724	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
725	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
726	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
727	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
729	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
733	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
734	#127	—	2	1	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#125	—	2	1	no	—
742	#125	—	2	2	no	—
743	#125	—	2	1	no	—
744	#125	C₂³×C₅₃	1	2	yes	—
745	#125	C₂³×C₅₃	1	2	yes	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	1	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	D₄×C₅₃	1	2	yes	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
765	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	D₄×C₅₃	1	1	yes	characteristic
779	#121	D₄×C₅₃	1	1	yes	characteristic
780	#121	C₂³×C₅₃	1	2	yes	—
781	#121	C₂³×C₅₃	1	2	yes	—
782	#121	C₂³×C₅₃	1	1	yes	characteristic
783	#121	C₂³×C₅₃	1	1	yes	characteristic
784	#121	C₂³×C₅₃	1	2	yes	—
785	#121	C₂³×C₅₃	1	2	yes	—
786	#121	C₂³×C₅₃	1	2	yes	—
787	#120	—	2	1	no	—
788	#120	—	2	2	no	—
789	#120	D₄×C₅₃	1	2	yes	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	C₂³×C₅₃	1	2	yes	—
807	C₄×D₄	C₂³×C₅₃	1	2	yes	—
808	C₄×D₄	C₂³×C₅₃	1	2	yes	—
809	C₄×D₄	C₂³×C₅₃	1	2	yes	—
810	C₄×D₄	C₂³×C₅₃	1	2	yes	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	—	2	2	no	—
819	#117	C₂³×C₅₃	1	1	yes	characteristic
820	#117	C₂³×C₅₃	1	1	yes	characteristic
821	#117	C₂³×C₅₃	1	2	yes	—
822	#117	C₂³×C₅₃	1	1	yes	characteristic
823	#117	C₂³×C₅₃	1	2	yes	—
824	#117	C₂³×C₅₃	1	1	yes	characteristic
825	#117	C₂³×C₅₃	1	1	yes	characteristic
826	#117	C₂³×C₅₃	1	2	yes	—
827	#117	C₂³×C₅₃	1	2	yes	—
828	#117	C₂³×C₅₃	1	1	yes	characteristic
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
831	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
832	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
836	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
837	C₂×C₂²⋊C₄	—	2	1	no	—
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	2	1	no	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	—	2	1	no	—
843	#107	C₂³×C₅₃	1	2	yes	—
844	#107	C₂³×C₅₃	1	2	yes	—
845	#107	C₂³×C₅₃	1	1	yes	characteristic
846	#107	C₂³×C₅₃	1	1	yes	characteristic
847	#107	C₂³×C₅₃	1	1	yes	characteristic
848	#107	C₂³×C₅₃	1	1	yes	characteristic
849	#107	C₂³×C₅₃	1	2	yes	—
850	#107	C₂³×C₅₃	1	2	yes	—
851	#107	C₂³×C₅₃	1	2	yes	—
852	#107	C₂³×C₅₃	1	2	yes	—
853	#107	C₂³×C₅₃	1	2	yes	—
854	#106	C₂³×C₅₃	1	2	yes	—
855	#106	C₂³×C₅₃	1	2	yes	—
856	#106	C₂³×C₅₃	1	1	yes	characteristic
857	#106	C₂³×C₅₃	1	2	yes	—
858	#106	C₂³×C₅₃	1	2	yes	—
859	#106	C₂³×C₅₃	1	1	yes	characteristic
860	#106	C₂³×C₅₃	1	1	yes	characteristic
861	#106	C₂³×C₅₃	1	1	yes	characteristic
862	#106	C₂³×C₅₃	1	2	yes	—
863	#106	C₂³×C₅₃	1	2	yes	—
864	#106	C₂³×C₅₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
866	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
867	#103	C₂³×C₅₃	1	1	yes	characteristic
868	#103	C₂³×C₅₃	1	1	yes	characteristic
869	#103	C₂³×C₅₃	1	1	yes	characteristic
870	#103	C₂³×C₅₃	1	1	yes	characteristic
871	#103	C₂³×C₅₃	1	2	yes	—
872	#102	C₂³×C₅₃	1	2	yes	—
873	#102	C₂³×C₅₃	1	2	yes	—
874	#102	C₂³×C₅₃	1	2	yes	—
875	#102	C₂³×C₅₃	1	2	yes	—
876	#102	C₂³×C₅₃	1	1	yes	characteristic
877	#102	C₂³×C₅₃	1	1	yes	characteristic
878	#102	C₂³×C₅₃	1	1	yes	characteristic
879	#102	C₂³×C₅₃	1	1	yes	characteristic
880	#102	C₂³×C₅₃	1	2	yes	—
881	#102	C₂³×C₅₃	1	2	yes	—
882	#102	C₂³×C₅₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
889	#97	C₂³×C₅₃	1	2	yes	—
890	C₄×C₈	C₂³×C₅₃	1	2	yes	—
891	C₂⁴	—	2	1	no	—
892	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	8	4	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	8	2	no	—
914	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
918	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
935	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
940	SD₁₆	—	2	4	no	—
941	D₈	—	2	4	no	—
942	M₁₆	—	2	2	no	—
943	M₁₆	—	2	4	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	#41×C₅₃	1	4	yes	complemented
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	2	4	no	—
949	C₂×C₈	—	2	4	no	—
950	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
955	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	C₂⁴×C₅₃	1	2	yes	—
1024	C₂³	—	2	2	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	1	no	—
1032	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1033	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1034	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1035	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	8	2	no	—
1040	Q₈	—	8	2	no	—
1041	D₄	—	2	4	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	1	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	1	no	—
1085	C₂×C₄	—	8	1	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1094	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1095	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1096	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	C₂×#41×C₅₃	1	4	yes	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	8	2	no	—
1121	C₂²	—	16	2	no	—
1122	C₂²	C₅₃×#547	1	2	yes	—
1123	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₅₃×#547	1	2	yes	—
1140	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1141	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1142	C₂	—	2	2	no	—
1143	C₂	—	4	1	no	—
1144	C₂	—	4	1	no	—
1145	C₂	—	4	2	no	—
1146	C₂	—	8	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
1149	C₂	C₅₃×#3584	1	1	yes	characteristic
1150	C₂	C₅₃×#3585	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3494	C₂	semidirect
2. C₅₃×#3493	C₂	semidirect
3. C₅₃×#3355	C₂	semidirect
4. C₅₃×#3353	C₂	semidirect
5. C₅₃×#3350	C₂	semidirect
6. C₅₃×#3348	C₂	semidirect
7. C₅₃×#3347	C₂	semidirect
8. C₅₃×#3345	C₂	semidirect
9. C₅₃×#3341	C₂	semidirect
10. C₅₃×#3337	C₂	semidirect
11. C₅₃×#3164	C₂	semidirect
12. C₅₃×#3098	C₂	semidirect
13. C₅₃×#3096	C₂	semidirect
14. C₅₃×#3091	C₂	semidirect
15. C₂×C₅₃×#482	C₂	semidirect
16. C₅₃×#3084	C₂	semidirect
17. C₅₃×#3081	C₂	semidirect
18. C₅₃×#3062	C₂	semidirect
19. C₅₃×#3055	C₂	semidirect
20. C₅₃×#2946	C₂	semidirect
21. C₅₃×#2933	C₂	semidirect
22. C₅₃×#2912	C₂	semidirect
23. C₅₃×#2911	C₂	semidirect
28. C₅₃×#556	C₂²	semidirect
31. C₅₃×#555	C₂²	semidirect
35. C₅₃×#553	C₂²	semidirect
37. C₅₃×#552	C₂²	semidirect
60. C₅₃×#501	C₂²	semidirect
61. C₅₃×#501	C₂²	semidirect
62. C₅₃×#500	C₂²	semidirect
63. C₅₃×#499	C₂²	semidirect
64. C₅₃×#485	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#484	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
74. C₅₃×#482	C₂²	semidirect
75. C₅₃×#482	C₂²	semidirect
76. C₅₃×#482	C₂²	semidirect
77. C₅₃×#482	C₂²	semidirect
78. C₅₃×#482	C₂²	semidirect
79. C₅₃×#481	C₂²	semidirect
80. C₅₃×#481	C₂²	semidirect
81. C₅₃×#480	C₂²	semidirect
82. C₅₃×#480	C₂²	semidirect
83. C₅₃×#480	C₂²	semidirect
84. C₅₃×#479	C₂²	semidirect
85. C₅₃×#478	C₂²	semidirect
86. C₅₃×#478	C₂²	semidirect
87. C₅₃×#478	C₂²	semidirect
88. C₅₃×#476	C₂²	semidirect
89. C₅₃×#476	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
91. C₅₃×#474	C₂²	semidirect
93. C₅₃×#469	C₂²	semidirect
95. C₅₃×#468	C₂²	semidirect
97. C₅₃×#466	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
100. C₅₃×#442	C₂²	semidirect
101. C₅₃×#440	C₂²	semidirect
102. C₄×SD₁₆×C₅₃	C₂²	semidirect
103. C₄×D₈×C₅₃	C₂²	semidirect
104. C₅₃×#436	C₂²	semidirect
105. C₅₃×#435	C₂²	semidirect
106. C₅₃×#435	C₂²	semidirect
107. C₈×D₄×C₅₃	C₂²	semidirect
113. C₅₃×#428	C₂²	semidirect
114. C₅₃×#428	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
119. C₅₃×#427	C₂²	semidirect
120. C₅₃×#427	C₂²	semidirect
121. C₅₃×#427	C₂²	semidirect
124. C₂×#106×C₅₃	C₂²	semidirect
369. M₁₆×C₅₃	#41	semidirect
527. #61274	C₅₃	direct (N × H)
567. #3494	C₂×C₅₃	semidirect
568. #3493	C₂×C₅₃	semidirect
569. #3355	C₂×C₅₃	semidirect
570. #3353	C₂×C₅₃	semidirect
571. #3350	C₂×C₅₃	semidirect
572. #3348	C₂×C₅₃	semidirect
573. #3347	C₂×C₅₃	semidirect
574. #3345	C₂×C₅₃	semidirect
575. #3341	C₂×C₅₃	semidirect
576. #3337	C₂×C₅₃	semidirect
577. #3164	C₂×C₅₃	semidirect
578. #3098	C₂×C₅₃	semidirect
579. #3096	C₂×C₅₃	semidirect
580. #3091	C₂×C₅₃	semidirect
581. C₂×#482	C₂×C₅₃	semidirect
582. #3084	C₂×C₅₃	semidirect
583. #3081	C₂×C₅₃	semidirect
584. #3062	C₂×C₅₃	semidirect
585. #3055	C₂×C₅₃	semidirect
586. #2946	C₂×C₅₃	semidirect
587. #2933	C₂×C₅₃	semidirect
588. #2912	C₂×C₅₃	semidirect
589. #2911	C₂×C₅₃	semidirect
603. #556	C₂²×C₅₃	semidirect
606. #555	C₂²×C₅₃	semidirect
610. #553	C₂²×C₅₃	semidirect
612. #552	C₂²×C₅₃	semidirect
635. #501	C₂²×C₅₃	semidirect
636. #501	C₂²×C₅₃	semidirect
637. #500	C₂²×C₅₃	semidirect
638. #499	C₂²×C₅₃	semidirect
639. #485	C₂²×C₅₃	semidirect
640. #485	C₂²×C₅₃	semidirect
641. #485	C₂²×C₅₃	semidirect
642. #484	C₂²×C₅₃	semidirect
643. #484	C₂²×C₅₃	semidirect
644. #483	C₂²×C₅₃	semidirect
649. #482	C₂²×C₅₃	semidirect
650. #482	C₂²×C₅₃	semidirect
651. #482	C₂²×C₅₃	semidirect
652. #482	C₂²×C₅₃	semidirect
653. #482	C₂²×C₅₃	semidirect
654. #481	C₂²×C₅₃	semidirect
655. #481	C₂²×C₅₃	semidirect
656. #480	C₂²×C₅₃	semidirect
657. #480	C₂²×C₅₃	semidirect
658. #480	C₂²×C₅₃	semidirect
659. #479	C₂²×C₅₃	semidirect
660. #478	C₂²×C₅₃	semidirect
661. #478	C₂²×C₅₃	semidirect
662. #478	C₂²×C₅₃	semidirect
663. #476	C₂²×C₅₃	semidirect
664. #476	C₂²×C₅₃	semidirect
665. #475	C₂²×C₅₃	semidirect
666. #474	C₂²×C₅₃	semidirect
668. #469	C₂²×C₅₃	semidirect
670. #468	C₂²×C₅₃	semidirect
672. #466	C₂²×C₅₃	semidirect
674. #465	C₂²×C₅₃	semidirect
675. #442	C₂²×C₅₃	semidirect
676. #440	C₂²×C₅₃	semidirect
677. C₄×SD₁₆	C₂²×C₅₃	semidirect
678. C₄×D₈	C₂²×C₅₃	semidirect
679. #436	C₂²×C₅₃	semidirect
680. #435	C₂²×C₅₃	semidirect
681. #435	C₂²×C₅₃	semidirect
682. C₈×D₄	C₂²×C₅₃	semidirect
688. #428	C₂²×C₅₃	semidirect
689. #428	C₂²×C₅₃	semidirect
690. #428	C₂²×C₅₃	semidirect
691. #428	C₂²×C₅₃	semidirect
694. #427	C₂²×C₅₃	semidirect
695. #427	C₂²×C₅₃	semidirect
696. #427	C₂²×C₅₃	semidirect
699. C₂×#106	C₂²×C₅₃	semidirect
710. C₅₃	#61274	direct (N × H)
945. M₁₆	#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3494	2
C₅₃×#3493	2
C₅₃×#3355	2
C₅₃×#3353	2
C₅₃×#3350	2
C₅₃×#3348	2
C₅₃×#3347	2
C₅₃×#3345	2
C₅₃×#3341	2
C₅₃×#3337	2
C₅₃×#3164	2
C₅₃×#3098	2
C₅₃×#3096	2
C₅₃×#3091	2
C₂×C₅₃×#482	2
C₅₃×#3084	2
C₅₃×#3081	2
C₅₃×#3062	2
C₅₃×#3055	2
C₅₃×#2946	2
C₅₃×#2933	2
C₅₃×#2912	2
C₅₃×#2911	2
#61274	53

Subgroups — C53×#61274 #27268786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61274 #27268786