Subgroups — C₅₃×#61385 #27268897

Order 13568.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3504	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×#3389	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3386	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3384	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3381	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3380	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic
22	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic
23	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
25	C₅₃×#557	C₂²	1	2	yes	complemented
26	C₅₃×#557	C₂²	1	2	yes	complemented
27	C₅₃×#554	—	2	1	no	—
28	C₅₃×#554	—	2	1	no	—
29	C₅₃×#554	—	2	1	no	—
30	C₅₃×#554	—	2	2	no	—
31	C₅₃×#554	—	2	2	no	—
32	C₅₃×#554	C₂²	1	2	yes	—
33	C₅₃×#554	C₂²	1	2	yes	—
34	C₅₃×#554	C₂²	1	2	yes	—
35	C₅₃×#554	C₂²	1	2	yes	complemented
36	C₅₃×#554	C₂²	1	2	yes	complemented
37	D₄×Q₈×C₅₃	—	2	1	no	—
38	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
39	C₅₃×#544	—	2	1	no	—
40	C₅₃×#544	—	2	1	no	—
41	C₅₃×#544	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	1	yes	characteristic
43	C₅₃×#544	C₂²	1	1	yes	characteristic
44	C₅₃×#544	C₂²	1	1	yes	characteristic
45	C₅₃×#543	—	2	2	no	—
46	C₅₃×#533	—	2	1	no	—
47	C₅₃×#533	C₂²	1	1	yes	characteristic
48	C₅₃×#533	C₂²	1	1	yes	characteristic
49	C₂×#125×C₅₃	—	2	1	no	—
50	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
52	C₅₃×#520	C₂²	1	1	yes	characteristic
53	C₅₃×#520	C₂²	1	1	yes	characteristic
54	C₅₃×#518	C₂²	1	1	yes	characteristic
55	C₅₃×#518	C₂²	1	1	yes	characteristic
56	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
58	C₅₃×#501	C₂²	1	2	yes	complemented
59	C₅₃×#501	C₂²	1	2	yes	complemented
60	C₅₃×#501	C₂²	1	2	yes	complemented
61	C₅₃×#501	C₂²	1	2	yes	complemented
62	C₅₃×#501	C₂²	1	2	yes	complemented
63	C₅₃×#501	C₂²	1	2	yes	complemented
64	C₅₃×#500	C₂²	1	2	yes	complemented
65	C₅₃×#499	C₂²	1	2	yes	complemented
66	C₅₃×#499	C₂²	1	2	yes	complemented
67	C₅₃×#499	C₂²	1	2	yes	complemented
68	C₅₃×#499	C₂²	1	2	yes	complemented
69	C₅₃×#498	C₂²	1	2	yes	complemented
70	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#479	C₂²	1	2	yes	complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	—
75	C₅₃×#478	C₂²	1	2	yes	—
76	C₅₃×#478	C₂²	1	2	yes	—
77	C₅₃×#478	C₂²	1	2	yes	—
78	C₅₃×#478	C₂²	1	2	yes	—
79	C₅₃×#478	C₂²	1	2	yes	—
80	C₅₃×#478	C₂²	1	2	yes	—
81	C₅₃×#478	C₂²	1	2	yes	—
82	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#478	C₂²	1	2	yes	complemented
85	C₅₃×#478	C₂²	1	2	yes	complemented
86	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#477	C₂²	1	2	yes	complemented
88	C₅₃×#476	C₂²	1	2	yes	—
89	C₅₃×#476	C₂²	1	2	yes	—
90	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#476	C₂²	1	2	yes	complemented
92	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#475	C₂²	1	2	yes	complemented
94	C₅₃×#474	C₂²	1	2	yes	—
95	C₅₃×#474	C₂²	1	2	yes	—
96	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#474	C₂²	1	2	yes	complemented
98	C₅₃×#446	C₂²	1	2	yes	complemented
99	C₅₃×#446	C₂²	1	2	yes	complemented
100	C₅₃×#446	C₂²	1	2	yes	complemented
101	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
102	C₅₃×#442	C₂²	1	2	yes	—
103	C₅₃×#442	C₂²	1	2	yes	—
104	C₅₃×#442	C₂²	1	2	yes	—
105	C₅₃×#440	C₂²	1	2	yes	—
106	C₅₃×#440	C₂²	1	2	yes	—
107	C₅₃×#440	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
109	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
110	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
111	C₄×D₈×C₅₃	C₂²	1	2	yes	—
112	C₄×D₈×C₅₃	C₂²	1	2	yes	—
113	C₄×D₈×C₅₃	C₂²	1	2	yes	—
114	C₅₃×#428	C₂²	1	1	yes	characteristic
115	C₅₃×#428	C₂²	1	1	yes	characteristic
116	C₅₃×#428	C₂²	1	1	yes	characteristic
117	C₅₃×#428	C₂²	1	1	yes	characteristic
118	C₅₃×#428	C₂²	1	1	yes	characteristic
119	C₅₃×#427	C₂²	1	1	yes	characteristic
120	C₅₃×#427	C₂²	1	1	yes	characteristic
121	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
123	C₅₃×#424	C₂²	1	1	yes	characteristic
124	C₅₃×#424	C₂²	1	1	yes	characteristic
125	C₂×C₄⋊C₈×C₅₃	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×#405	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₅₃	—	2	2	no	—
137	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	—	2	1	no	—
139	AGL(1,ℤ/8)×C₅₃	Q₈	1	8	yes	complemented
140	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×D₈×C₅₃	C₂³	1	2	yes	—
142	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₄⋊Q₈×C₅₃	—	2	1	no	—
147	C₄⋊Q₈×C₅₃	—	2	1	no	—
148	C₄⋊Q₈×C₅₃	—	2	1	no	—
149	C₄⋊Q₈×C₅₃	—	2	1	no	—
150	C₄⋊Q₈×C₅₃	—	2	2	no	—
151	C₄⋊Q₈×C₅₃	—	2	2	no	—
152	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	D₄	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	2	yes	—
157	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	#125×C₅₃	—	2	1	no	—
161	#125×C₅₃	—	2	1	no	—
162	#125×C₅₃	—	2	2	no	—
163	#125×C₅₃	—	2	2	no	—
164	#125×C₅₃	—	2	2	no	—
165	#125×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	1	no	—
167	#125×C₅₃	—	2	1	no	—
168	#125×C₅₃	—	2	1	no	—
169	#125×C₅₃	—	2	1	no	—
170	#125×C₅₃	D₄	1	1	yes	characteristic
171	#125×C₅₃	D₄	1	1	yes	characteristic
172	#125×C₅₃	C₂³	1	2	yes	—
173	#125×C₅₃	C₂³	1	1	yes	characteristic
174	#125×C₅₃	C₂³	1	1	yes	characteristic
175	#125×C₅₃	C₂³	1	2	yes	—
176	#125×C₅₃	C₂³	1	2	yes	—
177	#125×C₅₃	C₂³	1	2	yes	—
178	#125×C₅₃	C₂³	1	2	yes	—
179	#125×C₅₃	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₅₃	—	2	2	no	—
181	C₂²⋊Q₈×C₅₃	—	2	2	no	—
182	C₂²⋊Q₈×C₅₃	—	2	2	no	—
183	C₂²⋊Q₈×C₅₃	—	2	2	no	—
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	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	2	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	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
205	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
206	C₄×Q₈×C₅₃	—	2	2	no	—
207	C₄×Q₈×C₅₃	—	2	2	no	—
208	C₄×Q₈×C₅₃	—	2	1	no	—
209	C₄×Q₈×C₅₃	—	2	1	no	—
210	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
216	C₄×D₄×C₅₃	—	2	1	no	—
217	C₄×D₄×C₅₃	—	2	1	no	—
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	1	no	—
223	C₄×D₄×C₅₃	—	2	1	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	1	no	—
226	C₄×D₄×C₅₃	C₂³	1	2	yes	—
227	C₄×D₄×C₅₃	C₂³	1	2	yes	—
228	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₅₃	C₂³	1	2	yes	—
236	#117×C₅₃	—	2	1	no	—
237	#117×C₅₃	—	2	1	no	—
238	#117×C₅₃	—	2	1	no	—
239	#117×C₅₃	C₂³	1	1	yes	characteristic
240	#117×C₅₃	C₂³	1	1	yes	characteristic
241	#117×C₅₃	C₂³	1	1	yes	characteristic
242	#117×C₅₃	C₂³	1	1	yes	characteristic
243	#117×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
247	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
248	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
250	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
251	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
252	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
260	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
261	#107×C₅₃	C₂³	1	2	yes	—
262	#107×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	1	yes	characteristic
269	#107×C₅₃	C₂³	1	2	yes	—
270	#107×C₅₃	C₂³	1	1	yes	characteristic
271	#107×C₅₃	C₂³	1	1	yes	characteristic
272	#106×C₅₃	C₂³	1	1	yes	characteristic
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	2	yes	—
279	#106×C₅₃	C₂³	1	2	yes	—
280	#106×C₅₃	C₂³	1	2	yes	—
281	#106×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
288	C₄⋊C₈×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	#97×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	#97×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	C₄×C₈×C₅₃	C₂³	1	2	yes	—
313	C₂⁴×C₅₃	—	2	1	no	—
314	#41×C₅₃	—	2	2	no	—
315	#41×C₅₃	C₂×Q₈	1	4	yes	complemented
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	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	8	4	no	—
323	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₅₃	—	2	1	no	—
327	C₂×D₄×C₅₃	—	2	1	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	C₂×Q₈	1	4	yes	—
330	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅₃	—	2	1	no	—
333	C₂²×C₄×C₅₃	—	2	1	no	—
334	C₂²×C₄×C₅₃	—	2	1	no	—
335	C₂²×C₄×C₅₃	—	2	1	no	—
336	C₂²×C₄×C₅₃	—	2	2	no	—
337	C₂²×C₄×C₅₃	—	2	1	no	—
338	C₂²×C₄×C₅₃	—	2	1	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	2	no	—
341	C₂²×C₄×C₅₃	—	2	2	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	2	no	—
344	C₂²×C₄×C₅₃	—	2	2	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	8	2	no	—
347	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
350	SD₁₆×C₅₃	C₂×Q₈	1	8	yes	complemented
351	D₈×C₅₃	C₂×Q₈	1	8	yes	complemented
352	M₁₆×C₅₃	—	2	2	no	—
353	M₁₆×C₅₃	C₂×Q₈	1	4	yes	complemented
354	C₂×C₈×C₅₃	—	2	2	no	—
355	C₂×C₈×C₅₃	—	2	2	no	—
356	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₅₃	—	2	1	no	—
363	C₄⋊C₄×C₅₃	—	2	1	no	—
364	C₄⋊C₄×C₅₃	—	2	1	no	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	1	no	—
368	C₄⋊C₄×C₅₃	—	2	1	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	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	2	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	1	no	—
387	C₄⋊C₄×C₅₃	—	2	1	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	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	2	yes	—
406	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	—	2	1	no	—
427	C₄²×C₅₃	—	2	1	no	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	—	2	2	no	—
430	C₄²×C₅₃	—	2	1	no	—
431	C₄²×C₅₃	—	2	1	no	—
432	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₅₃	C₂⁴	1	2	yes	—
436	C₄²×C₅₃	C₂⁴	1	2	yes	—
437	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂³×C₅₃	—	2	1	no	—
439	C₂³×C₅₃	—	2	2	no	—
440	C₂³×C₅₃	—	2	4	no	—
441	C₂³×C₅₃	—	8	1	no	—
442	C₂³×C₅₃	—	8	1	no	—
443	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
444	Q₈×C₅₃	—	2	1	no	—
445	Q₈×C₅₃	—	4	2	no	—
446	Q₈×C₅₃	—	4	2	no	—
447	Q₈×C₅₃	—	4	2	no	—
448	Q₈×C₅₃	—	8	1	no	—
449	Q₈×C₅₃	—	8	2	no	—
450	Q₈×C₅₃	—	8	2	no	—
451	Q₈×C₅₃	—	8	2	no	—
452	Q₈×C₅₃	—	8	2	no	—
453	Q₈×C₅₃	C₂²×Q₈	1	2	yes	—
454	D₄×C₅₃	—	2	4	no	—
455	D₄×C₅₃	—	2	4	no	—
456	D₄×C₅₃	—	2	2	no	—
457	D₄×C₅₃	—	2	1	no	—
458	D₄×C₅₃	C₂²×Q₈	1	4	yes	—
459	D₄×C₅₃	C₂²×Q₈	1	2	yes	—
460	C₂×C₄×C₅₃	—	2	1	no	—
461	C₂×C₄×C₅₃	—	2	4	no	—
462	C₂×C₄×C₅₃	—	2	2	no	—
463	C₂×C₄×C₅₃	—	2	1	no	—
464	C₂×C₄×C₅₃	—	2	1	no	—
465	C₂×C₄×C₅₃	—	2	1	no	—
466	C₂×C₄×C₅₃	—	2	1	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	2	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	1	no	—
471	C₂×C₄×C₅₃	—	4	1	no	—
472	C₂×C₄×C₅₃	—	4	1	no	—
473	C₂×C₄×C₅₃	—	4	4	no	—
474	C₂×C₄×C₅₃	—	8	1	no	—
475	C₂×C₄×C₅₃	—	8	2	no	—
476	C₂×C₄×C₅₃	—	8	2	no	—
477	C₂×C₄×C₅₃	—	8	2	no	—
478	C₂×C₄×C₅₃	—	8	1	no	—
479	C₂×C₄×C₅₃	—	8	2	no	—
480	C₂×C₄×C₅₃	—	8	2	no	—
481	C₂×C₄×C₅₃	—	8	2	no	—
482	C₂×C₄×C₅₃	—	8	2	no	—
483	C₂×C₄×C₅₃	—	8	1	no	—
484	C₂×C₄×C₅₃	—	8	1	no	—
485	C₂×C₄×C₅₃	—	8	1	no	—
486	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
496	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
497	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
498	C₈×C₅₃	—	2	1	no	—
499	C₈×C₅₃	—	2	1	no	—
500	C₈×C₅₃	—	2	1	no	—
501	C₈×C₅₃	—	2	1	no	—
502	C₈×C₅₃	—	2	2	no	—
503	C₈×C₅₃	C₂²×Q₈	1	4	yes	—
504	#61385	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂²×C₅₃	—	2	1	no	—
506	C₂²×C₅₃	—	2	1	no	—
507	C₂²×C₅₃	—	2	2	no	—
508	C₂²×C₅₃	—	2	4	no	—
509	C₂²×C₅₃	—	4	1	no	—
510	C₂²×C₅₃	—	4	2	no	—
511	C₂²×C₅₃	—	4	2	no	—
512	C₂²×C₅₃	—	4	1	no	—
513	C₂²×C₅₃	—	8	4	no	—
514	C₂²×C₅₃	D₄×Q₈	1	2	yes	—
515	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₅₃	—	2	1	no	—
517	C₄×C₅₃	—	2	1	no	—
518	C₄×C₅₃	—	2	2	no	—
519	C₄×C₅₃	—	2	2	no	—
520	C₄×C₅₃	—	2	1	no	—
521	C₄×C₅₃	—	2	1	no	—
522	C₄×C₅₃	—	2	2	no	—
523	C₄×C₅₃	—	2	2	no	—
524	C₄×C₅₃	—	2	2	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	1	no	—
527	C₄×C₅₃	—	4	2	no	—
528	C₄×C₅₃	—	4	1	no	—
529	C₄×C₅₃	—	4	2	no	—
530	C₄×C₅₃	—	4	1	no	—
531	C₄×C₅₃	—	4	1	no	—
532	C₄×C₅₃	—	4	2	no	—
533	C₄×C₅₃	—	4	1	no	—
534	C₄×C₅₃	D₄×Q₈	1	2	yes	—
535	C₄×C₅₃	C₂³×Q₈	1	1	yes	characteristic
536	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	#3504	C₂×C₅₃	1	1	yes	characteristic, complemented
538	#3501	C₂×C₅₃	1	1	yes	characteristic, complemented
539	#3389	C₂×C₅₃	1	2	yes	complemented
540	#3389	C₂×C₅₃	1	2	yes	complemented
541	#3388	C₂×C₅₃	1	2	yes	complemented
542	#3388	C₂×C₅₃	1	2	yes	complemented
543	#3386	C₂×C₅₃	1	2	yes	complemented
544	#3384	C₂×C₅₃	1	2	yes	complemented
545	#3381	C₂×C₅₃	1	2	yes	complemented
546	#3380	C₂×C₅₃	1	2	yes	complemented
547	#3166	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#3164	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3163	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3083	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
555	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#2962	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#2946	C₂×C₅₃	1	1	yes	characteristic
558	#2946	C₂×C₅₃	1	1	yes	characteristic
559	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic
560	C₂×C₅₃	—	2	2	no	—
561	C₂×C₅₃	—	4	2	no	—
562	C₂×C₅₃	—	4	4	no	—
563	C₂×C₅₃	C₂×D₄×Q₈	1	1	yes	characteristic
564	C₂×C₅₃	#3584	1	1	yes	characteristic
565	C₂×C₅₃	#3585	1	1	yes	characteristic
566	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
567	#557	C₂²×C₅₃	1	2	yes	complemented
568	#557	C₂²×C₅₃	1	2	yes	complemented
569	#554	—	2	1	no	—
570	#554	—	2	1	no	—
571	#554	—	2	1	no	—
572	#554	—	2	2	no	—
573	#554	—	2	2	no	—
574	#554	C₂²×C₅₃	1	2	yes	—
575	#554	C₂²×C₅₃	1	2	yes	—
576	#554	C₂²×C₅₃	1	2	yes	—
577	#554	C₂²×C₅₃	1	2	yes	complemented
578	#554	C₂²×C₅₃	1	2	yes	complemented
579	D₄×Q₈	—	2	1	no	—
580	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
581	#544	—	2	1	no	—
582	#544	—	2	1	no	—
583	#544	C₂²×C₅₃	1	1	yes	characteristic
584	#544	C₂²×C₅₃	1	1	yes	characteristic
585	#544	C₂²×C₅₃	1	1	yes	characteristic
586	#544	C₂²×C₅₃	1	1	yes	characteristic
587	#543	—	2	2	no	—
588	#533	—	2	1	no	—
589	#533	C₂²×C₅₃	1	1	yes	characteristic
590	#533	C₂²×C₅₃	1	1	yes	characteristic
591	C₂×#125	—	2	1	no	—
592	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
593	C₂×C₂²⋊Q₈	—	2	2	no	—
594	#520	C₂²×C₅₃	1	1	yes	characteristic
595	#520	C₂²×C₅₃	1	1	yes	characteristic
596	#518	C₂²×C₅₃	1	1	yes	characteristic
597	#518	C₂²×C₅₃	1	1	yes	characteristic
598	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
599	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
600	#501	C₂²×C₅₃	1	2	yes	complemented
601	#501	C₂²×C₅₃	1	2	yes	complemented
602	#501	C₂²×C₅₃	1	2	yes	complemented
603	#501	C₂²×C₅₃	1	2	yes	complemented
604	#501	C₂²×C₅₃	1	2	yes	complemented
605	#501	C₂²×C₅₃	1	2	yes	complemented
606	#500	C₂²×C₅₃	1	2	yes	complemented
607	#499	C₂²×C₅₃	1	2	yes	complemented
608	#499	C₂²×C₅₃	1	2	yes	complemented
609	#499	C₂²×C₅₃	1	2	yes	complemented
610	#499	C₂²×C₅₃	1	2	yes	complemented
611	#498	C₂²×C₅₃	1	2	yes	complemented
612	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
613	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	#479	C₂²×C₅₃	1	2	yes	complemented
615	#479	C₂²×C₅₃	1	2	yes	complemented
616	#478	C₂²×C₅₃	1	2	yes	—
617	#478	C₂²×C₅₃	1	2	yes	—
618	#478	C₂²×C₅₃	1	2	yes	—
619	#478	C₂²×C₅₃	1	2	yes	—
620	#478	C₂²×C₅₃	1	2	yes	—
621	#478	C₂²×C₅₃	1	2	yes	—
622	#478	C₂²×C₅₃	1	2	yes	—
623	#478	C₂²×C₅₃	1	2	yes	—
624	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
625	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
626	#478	C₂²×C₅₃	1	2	yes	complemented
627	#478	C₂²×C₅₃	1	2	yes	complemented
628	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
629	#477	C₂²×C₅₃	1	2	yes	complemented
630	#476	C₂²×C₅₃	1	2	yes	—
631	#476	C₂²×C₅₃	1	2	yes	—
632	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#476	C₂²×C₅₃	1	2	yes	complemented
634	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	#475	C₂²×C₅₃	1	2	yes	complemented
636	#474	C₂²×C₅₃	1	2	yes	—
637	#474	C₂²×C₅₃	1	2	yes	—
638	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#474	C₂²×C₅₃	1	2	yes	complemented
640	#446	C₂²×C₅₃	1	2	yes	complemented
641	#446	C₂²×C₅₃	1	2	yes	complemented
642	#446	C₂²×C₅₃	1	2	yes	complemented
643	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
644	#442	C₂²×C₅₃	1	2	yes	—
645	#442	C₂²×C₅₃	1	2	yes	—
646	#442	C₂²×C₅₃	1	2	yes	—
647	#440	C₂²×C₅₃	1	2	yes	—
648	#440	C₂²×C₅₃	1	2	yes	—
649	#440	C₂²×C₅₃	1	2	yes	—
650	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
651	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
652	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
653	C₄×D₈	C₂²×C₅₃	1	2	yes	—
654	C₄×D₈	C₂²×C₅₃	1	2	yes	—
655	C₄×D₈	C₂²×C₅₃	1	2	yes	—
656	#428	C₂²×C₅₃	1	1	yes	characteristic
657	#428	C₂²×C₅₃	1	1	yes	characteristic
658	#428	C₂²×C₅₃	1	1	yes	characteristic
659	#428	C₂²×C₅₃	1	1	yes	characteristic
660	#428	C₂²×C₅₃	1	1	yes	characteristic
661	#427	C₂²×C₅₃	1	1	yes	characteristic
662	#427	C₂²×C₅₃	1	1	yes	characteristic
663	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
664	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
665	#424	C₂²×C₅₃	1	1	yes	characteristic
666	#424	C₂²×C₅₃	1	1	yes	characteristic
667	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
668	#418	C₂²×C₅₃	1	1	yes	characteristic
669	#417	C₂²×C₅₃	1	1	yes	characteristic
670	#416	C₂²×C₅₃	1	1	yes	characteristic
671	#416	C₂²×C₅₃	1	1	yes	characteristic
672	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
673	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
674	#405	C₂²×C₅₃	1	1	yes	characteristic
675	#405	C₂²×C₅₃	1	1	yes	characteristic
676	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
677	C₅₃	#61385	1	1	yes	characteristic, direct product factor, Sylow
678	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
679	C₂²×Q₈	—	2	2	no	—
680	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
681	C₂³×C₄	—	2	1	no	—
682	AGL(1,ℤ/8)	Q₈×C₅₃	1	8	yes	complemented
683	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
684	C₂×D₈	C₂³×C₅₃	1	2	yes	—
685	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
687	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
689	C₄⋊Q₈	—	2	2	no	—
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
696	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
703	#125	—	2	1	no	—
704	#125	—	2	1	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	1	no	—
710	#125	—	2	1	no	—
711	#125	—	2	1	no	—
712	#125	—	2	1	no	—
713	#125	D₄×C₅₃	1	1	yes	characteristic
714	#125	D₄×C₅₃	1	1	yes	characteristic
715	#125	C₂³×C₅₃	1	2	yes	—
716	#125	C₂³×C₅₃	1	2	yes	—
717	#125	C₂³×C₅₃	1	1	yes	characteristic
718	#125	C₂³×C₅₃	1	1	yes	characteristic
719	#125	C₂³×C₅₃	1	2	yes	—
720	#125	C₂³×C₅₃	1	2	yes	—
721	#125	C₂³×C₅₃	1	2	yes	—
722	#125	C₂³×C₅₃	1	2	yes	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	1	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
748	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
756	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
757	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
758	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	C₂³×C₅₃	1	2	yes	—
770	C₄×D₄	C₂³×C₅₃	1	2	yes	—
771	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₅₃	1	2	yes	—
774	C₄×D₄	C₂³×C₅₃	1	2	yes	—
775	C₄×D₄	C₂³×C₅₃	1	2	yes	—
776	C₄×D₄	C₂³×C₅₃	1	2	yes	—
777	C₄×D₄	C₂³×C₅₃	1	2	yes	—
778	C₄×D₄	C₂³×C₅₃	1	2	yes	—
779	#117	—	2	1	no	—
780	#117	—	2	1	no	—
781	#117	—	2	1	no	—
782	#117	C₂³×C₅₃	1	1	yes	characteristic
783	#117	C₂³×C₅₃	1	1	yes	characteristic
784	#117	C₂³×C₅₃	1	1	yes	characteristic
785	#117	C₂³×C₅₃	1	1	yes	characteristic
786	#117	C₂³×C₅₃	1	1	yes	characteristic
787	C₂×C₄⋊C₄	—	2	1	no	—
788	C₂×C₄⋊C₄	—	2	1	no	—
789	C₂×C₄⋊C₄	—	2	1	no	—
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	—	2	2	no	—
792	C₂×C₄⋊C₄	—	2	2	no	—
793	C₂×C₄⋊C₄	—	2	2	no	—
794	C₂×C₄⋊C₄	—	2	2	no	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	—	2	1	no	—
800	C₂×C₂²⋊C₄	—	2	2	no	—
801	C₂×C₂²⋊C₄	—	2	2	no	—
802	C₂×C₄²	—	2	1	no	—
803	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
804	#107	C₂³×C₅₃	1	2	yes	—
805	#107	C₂³×C₅₃	1	2	yes	—
806	#107	C₂³×C₅₃	1	1	yes	characteristic
807	#107	C₂³×C₅₃	1	1	yes	characteristic
808	#107	C₂³×C₅₃	1	1	yes	characteristic
809	#107	C₂³×C₅₃	1	1	yes	characteristic
810	#107	C₂³×C₅₃	1	2	yes	—
811	#107	C₂³×C₅₃	1	2	yes	—
812	#107	C₂³×C₅₃	1	2	yes	—
813	#107	C₂³×C₅₃	1	2	yes	—
814	#107	C₂³×C₅₃	1	2	yes	—
815	#106	C₂³×C₅₃	1	2	yes	—
816	#106	C₂³×C₅₃	1	2	yes	—
817	#106	C₂³×C₅₃	1	1	yes	characteristic
818	#106	C₂³×C₅₃	1	1	yes	characteristic
819	#106	C₂³×C₅₃	1	1	yes	characteristic
820	#106	C₂³×C₅₃	1	1	yes	characteristic
821	#106	C₂³×C₅₃	1	2	yes	—
822	#106	C₂³×C₅₃	1	2	yes	—
823	#106	C₂³×C₅₃	1	2	yes	—
824	#106	C₂³×C₅₃	1	2	yes	—
825	#106	C₂³×C₅₃	1	2	yes	—
826	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
832	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
833	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
834	#103	C₂³×C₅₃	1	1	yes	characteristic
835	#103	C₂³×C₅₃	1	1	yes	characteristic
836	#103	C₂³×C₅₃	1	1	yes	characteristic
837	#103	C₂³×C₅₃	1	1	yes	characteristic
838	#103	C₂³×C₅₃	1	2	yes	—
839	#102	C₂³×C₅₃	1	2	yes	—
840	#102	C₂³×C₅₃	1	2	yes	—
841	#102	C₂³×C₅₃	1	2	yes	—
842	#102	C₂³×C₅₃	1	2	yes	—
843	#102	C₂³×C₅₃	1	1	yes	characteristic
844	#102	C₂³×C₅₃	1	1	yes	characteristic
845	#102	C₂³×C₅₃	1	1	yes	characteristic
846	#102	C₂³×C₅₃	1	1	yes	characteristic
847	#102	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	2	yes	—
849	#102	C₂³×C₅₃	1	2	yes	—
850	#97	C₂³×C₅₃	1	2	yes	—
851	#97	C₂³×C₅₃	1	2	yes	—
852	#97	C₂³×C₅₃	1	2	yes	—
853	C₄×C₈	C₂³×C₅₃	1	2	yes	—
854	C₄×C₈	C₂³×C₅₃	1	2	yes	—
855	C₄×C₈	C₂³×C₅₃	1	2	yes	—
856	C₂⁴	—	2	1	no	—
857	#41	—	2	2	no	—
858	#41	C₂×Q₈×C₅₃	1	4	yes	complemented
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	8	4	no	—
866	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
867	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
868	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	C₂×Q₈×C₅₃	1	4	yes	—
873	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
874	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	8	2	no	—
890	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
891	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
893	SD₁₆	C₂×Q₈×C₅₃	1	8	yes	complemented
894	D₈	C₂×Q₈×C₅₃	1	8	yes	complemented
895	M₁₆	—	2	2	no	—
896	M₁₆	C₂×Q₈×C₅₃	1	4	yes	complemented
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
902	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
935	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
967	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
976	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
977	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
978	C₄²	C₂⁴×C₅₃	1	2	yes	—
979	C₄²	C₂⁴×C₅₃	1	2	yes	—
980	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
981	C₂³	—	2	1	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	4	no	—
984	C₂³	—	8	1	no	—
985	C₂³	—	8	1	no	—
986	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
987	Q₈	—	2	1	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	4	2	no	—
991	Q₈	—	8	1	no	—
992	Q₈	—	8	2	no	—
993	Q₈	—	8	2	no	—
994	Q₈	—	8	2	no	—
995	Q₈	—	8	2	no	—
996	Q₈	C₂²×Q₈×C₅₃	1	2	yes	—
997	D₄	—	2	4	no	—
998	D₄	—	2	4	no	—
999	D₄	—	2	2	no	—
1000	D₄	—	2	1	no	—
1001	D₄	C₂²×Q₈×C₅₃	1	2	yes	—
1002	D₄	C₂²×Q₈×C₅₃	1	4	yes	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	4	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	4	1	no	—
1015	C₂×C₄	—	4	1	no	—
1016	C₂×C₄	—	4	4	no	—
1017	C₂×C₄	—	8	1	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	2	no	—
1021	C₂×C₄	—	8	1	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	2	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	—	8	1	no	—
1028	C₂×C₄	—	8	1	no	—
1029	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1030	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1031	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1035	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1036	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1038	C₂×C₄	C₂²×Q₈×C₅₃	1	2	yes	—
1039	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1040	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	2	no	—
1046	C₈	C₂²×Q₈×C₅₃	1	4	yes	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	8	4	no	—
1056	C₂²	D₄×Q₈×C₅₃	1	2	yes	—
1057	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	D₄×Q₈×C₅₃	1	2	yes	—
1077	C₄	C₂³×Q₈×C₅₃	1	1	yes	characteristic
1078	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1079	C₂	—	2	2	no	—
1080	C₂	—	4	4	no	—
1081	C₂	—	4	2	no	—
1082	C₂	C₂×D₄×Q₈×C₅₃	1	1	yes	characteristic
1083	C₂	C₅₃×#3584	1	1	yes	characteristic
1084	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	C₂×AGL(1,ℤ/8)×C₅₃	C₂²
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×#3504	C₂	semidirect
2. C₅₃×#3501	C₂	semidirect
3. C₅₃×#3389	C₂	semidirect
4. C₅₃×#3389	C₂	semidirect
5. C₅₃×#3388	C₂	semidirect
6. C₅₃×#3388	C₂	semidirect
7. C₅₃×#3386	C₂	semidirect
8. C₅₃×#3384	C₂	semidirect
9. C₅₃×#3381	C₂	semidirect
10. C₅₃×#3380	C₂	semidirect
11. C₅₃×#3166	C₂	semidirect
12. C₅₃×#3164	C₂	semidirect
13. C₅₃×#3163	C₂	semidirect
14. C₅₃×#3084	C₂	semidirect
15. C₅₃×#3083	C₂	semidirect
16. C₅₃×#3081	C₂	semidirect
17. C₅₃×#3081	C₂	semidirect
18. C₅₃×#3076	C₂	semidirect
19. C₂×C₅₃×#478	C₂	semidirect
20. C₅₃×#2962	C₂	semidirect
25. C₅₃×#557	C₂²	semidirect
26. C₅₃×#557	C₂²	semidirect
35. C₅₃×#554	C₂²	semidirect
36. C₅₃×#554	C₂²	semidirect
58. C₅₃×#501	C₂²	semidirect
59. C₅₃×#501	C₂²	semidirect
60. C₅₃×#501	C₂²	semidirect
61. C₅₃×#501	C₂²	semidirect
62. C₅₃×#501	C₂²	semidirect
63. C₅₃×#501	C₂²	semidirect
64. C₅₃×#500	C₂²	semidirect
65. C₅₃×#499	C₂²	semidirect
66. C₅₃×#499	C₂²	semidirect
67. C₅₃×#499	C₂²	semidirect
68. C₅₃×#499	C₂²	semidirect
69. C₅₃×#498	C₂²	semidirect
70. C₅₃×#479	C₂²	semidirect
71. C₅₃×#479	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
82. C₅₃×#478	C₂²	semidirect
83. C₅₃×#478	C₂²	semidirect
84. C₅₃×#478	C₂²	semidirect
85. C₅₃×#478	C₂²	semidirect
86. C₅₃×#477	C₂²	semidirect
87. C₅₃×#477	C₂²	semidirect
90. C₅₃×#476	C₂²	semidirect
91. C₅₃×#476	C₂²	semidirect
92. C₅₃×#475	C₂²	semidirect
93. C₅₃×#475	C₂²	semidirect
96. C₅₃×#474	C₂²	semidirect
97. C₅₃×#474	C₂²	semidirect
98. C₅₃×#446	C₂²	semidirect
99. C₅₃×#446	C₂²	semidirect
100. C₅₃×#446	C₂²	semidirect
101. C₈×Q₈×C₅₃	C₂²	semidirect
139. AGL(1,ℤ/8)×C₅₃	Q₈	semidirect
315. #41×C₅₃	C₂×Q₈	semidirect
350. SD₁₆×C₅₃	C₂×Q₈	semidirect
351. D₈×C₅₃	C₂×Q₈	semidirect
353. M₁₆×C₅₃	C₂×Q₈	semidirect
504. #61385	C₅₃	direct (N × H)
537. #3504	C₂×C₅₃	semidirect
538. #3501	C₂×C₅₃	semidirect
539. #3389	C₂×C₅₃	semidirect
540. #3389	C₂×C₅₃	semidirect
541. #3388	C₂×C₅₃	semidirect
542. #3388	C₂×C₅₃	semidirect
543. #3386	C₂×C₅₃	semidirect
544. #3384	C₂×C₅₃	semidirect
545. #3381	C₂×C₅₃	semidirect
546. #3380	C₂×C₅₃	semidirect
547. #3166	C₂×C₅₃	semidirect
548. #3164	C₂×C₅₃	semidirect
549. #3163	C₂×C₅₃	semidirect
550. #3084	C₂×C₅₃	semidirect
551. #3083	C₂×C₅₃	semidirect
552. #3081	C₂×C₅₃	semidirect
553. #3081	C₂×C₅₃	semidirect
554. #3076	C₂×C₅₃	semidirect
555. C₂×#478	C₂×C₅₃	semidirect
556. #2962	C₂×C₅₃	semidirect
567. #557	C₂²×C₅₃	semidirect
568. #557	C₂²×C₅₃	semidirect
577. #554	C₂²×C₅₃	semidirect
578. #554	C₂²×C₅₃	semidirect
600. #501	C₂²×C₅₃	semidirect
601. #501	C₂²×C₅₃	semidirect
602. #501	C₂²×C₅₃	semidirect
603. #501	C₂²×C₅₃	semidirect
604. #501	C₂²×C₅₃	semidirect
605. #501	C₂²×C₅₃	semidirect
606. #500	C₂²×C₅₃	semidirect
607. #499	C₂²×C₅₃	semidirect
608. #499	C₂²×C₅₃	semidirect
609. #499	C₂²×C₅₃	semidirect
610. #499	C₂²×C₅₃	semidirect
611. #498	C₂²×C₅₃	semidirect
612. #479	C₂²×C₅₃	semidirect
613. #479	C₂²×C₅₃	semidirect
614. #479	C₂²×C₅₃	semidirect
615. #479	C₂²×C₅₃	semidirect
624. #478	C₂²×C₅₃	semidirect
625. #478	C₂²×C₅₃	semidirect
626. #478	C₂²×C₅₃	semidirect
627. #478	C₂²×C₅₃	semidirect
628. #477	C₂²×C₅₃	semidirect
629. #477	C₂²×C₅₃	semidirect
632. #476	C₂²×C₅₃	semidirect
633. #476	C₂²×C₅₃	semidirect
634. #475	C₂²×C₅₃	semidirect
635. #475	C₂²×C₅₃	semidirect
638. #474	C₂²×C₅₃	semidirect
639. #474	C₂²×C₅₃	semidirect
640. #446	C₂²×C₅₃	semidirect
641. #446	C₂²×C₅₃	semidirect
642. #446	C₂²×C₅₃	semidirect
643. C₈×Q₈	C₂²×C₅₃	semidirect
677. C₅₃	#61385	direct (N × H)
682. AGL(1,ℤ/8)	Q₈×C₅₃	semidirect
858. #41	C₂×Q₈×C₅₃	semidirect
893. SD₁₆	C₂×Q₈×C₅₃	semidirect
894. D₈	C₂×Q₈×C₅₃	semidirect
896. M₁₆	C₂×Q₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3504	2
C₅₃×#3501	2
C₅₃×#3389	2
C₅₃×#3388	2
C₅₃×#3386	2
C₅₃×#3384	2
C₅₃×#3381	2
C₅₃×#3380	2
C₅₃×#3166	2
C₅₃×#3164	2
C₅₃×#3163	2
C₅₃×#3084	2
C₅₃×#3083	2
C₅₃×#3081	2
C₅₃×#3076	2
C₂×C₅₃×#478	2
C₅₃×#2962	2
C₅₃×#2946	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61385	53

Subgroups — C53×#61385 #27268897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61385 #27268897