Subgroups — C₅₃×#61271 #27268783

Order 13568.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3492	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3343	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3335	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2947	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	C₂×C₅₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×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	C₂²	1	2	yes	—
28	C₅₃×#554	—	2	1	no	—
29	C₅₃×#554	C₂²	1	2	yes	—
30	C₅₃×#554	C₂²	1	2	yes	—
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#553	C₂²	1	2	yes	—
33	C₅₃×#552	—	2	2	no	—
34	C₅₃×#552	—	2	1	no	—
35	C₅₃×#552	C₂²	1	2	yes	—
36	C₅₃×#552	C₂²	1	2	yes	—
37	C₅₃×#552	C₂²	1	2	yes	—
38	C₅₃×#551	—	2	2	no	—
39	C₅₃×#547	—	2	1	no	—
40	C₅₃×#547	C₂²	1	2	yes	—
41	C₅₃×#544	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	1	yes	characteristic
43	C₅₃×#542	—	2	1	no	—
44	C₅₃×#541	—	2	1	no	—
45	C₅₃×#539	—	2	2	no	—
46	C₅₃×#537	C₂²	1	1	yes	characteristic
47	C₅₃×#536	C₂²	1	1	yes	characteristic
48	C₅₃×#533	—	2	1	no	—
49	C₅₃×#529	—	2	1	no	—
50	C₅₃×#525	—	2	2	no	—
51	C₅₃×#525	C₂²	1	1	yes	characteristic
52	C₅₃×#525	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈×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×#519	C₂²	1	1	yes	characteristic
58	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#501	C₂²	1	2	yes	complemented
61	C₅₃×#501	C₂²	1	2	yes	complemented
62	C₅₃×#499	C₂²	1	2	yes	complemented
63	C₅₃×#498	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	1	yes	characteristic
65	C₅₃×#485	C₂²	1	1	yes	characteristic
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#485	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	2	yes	complemented
69	C₅₃×#484	C₂²	1	1	yes	characteristic
70	C₅₃×#484	C₂²	1	2	yes	complemented
71	C₅₃×#483	C₂²	1	2	yes	—
72	C₅₃×#483	C₂²	1	1	yes	characteristic
73	C₅₃×#483	C₂²	1	2	yes	—
74	C₅₃×#483	C₂²	1	2	yes	—
75	C₅₃×#483	C₂²	1	2	yes	—
76	C₅₃×#483	C₂²	1	2	yes	complemented
77	C₅₃×#483	C₂²	1	2	yes	complemented
78	C₅₃×#482	C₂²	1	1	yes	characteristic
79	C₅₃×#482	C₂²	1	1	yes	characteristic
80	C₅₃×#482	C₂²	1	2	yes	complemented
81	C₅₃×#481	C₂²	1	1	yes	characteristic
82	C₅₃×#481	C₂²	1	2	yes	complemented
83	C₅₃×#480	C₂²	1	1	yes	characteristic
84	C₅₃×#479	C₂²	1	2	yes	complemented
85	C₅₃×#479	C₂²	1	2	yes	complemented
86	C₅₃×#479	C₂²	1	2	yes	complemented
87	C₅₃×#478	C₂²	1	2	yes	complemented
88	C₅₃×#477	C₂²	1	2	yes	complemented
89	C₅₃×#476	C₂²	1	2	yes	complemented
90	C₅₃×#475	C₂²	1	2	yes	complemented
91	C₅₃×#475	C₂²	1	2	yes	complemented
92	C₅₃×#470	C₂²	1	2	yes	—
93	C₅₃×#470	C₂²	1	2	yes	complemented
94	C₅₃×#468	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	complemented
96	C₅₃×#467	C₂²	1	2	yes	—
97	C₅₃×#467	C₂²	1	2	yes	complemented
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#441	C₂²	1	2	yes	complemented
101	C₅₃×#440	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
104	C₅₃×#436	C₂²	1	2	yes	—
105	C₅₃×#435	C₂²	1	2	yes	—
106	C₅₃×#435	C₂²	1	2	yes	—
107	C₈×D₄×C₅₃	C₂²	1	2	yes	—
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	—
114	C₅₃×#428	C₂²	1	2	yes	—
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	C₂×#107×C₅₃	C₂²	1	2	yes	—
121	C₂×#106×C₅₃	C₂²	1	2	yes	—
122	C₂×#106×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×#419	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×#103×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#103×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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	—	2	1	no	—
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	#137×C₅₃	—	2	4	no	—
142	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×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	—	2	1	no	—
157	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
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	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	1	no	—
172	#125×C₅₃	C₂³	1	2	yes	—
173	#125×C₅₃	C₂³	1	2	yes	—
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	2	no	—
183	#123×C₅₃	—	2	1	no	—
184	#123×C₅₃	D₄	1	2	yes	—
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	1	no	—
193	C₂²⋊Q₈×C₅₃	—	2	1	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
196	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
197	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	1	no	—
207	#121×C₅₃	D₄	1	1	yes	characteristic
208	#121×C₅₃	D₄	1	1	yes	characteristic
209	#121×C₅₃	C₂³	1	1	yes	characteristic
210	#121×C₅₃	C₂³	1	1	yes	characteristic
211	#121×C₅₃	C₂³	1	2	yes	—
212	#120×C₅₃	—	2	1	no	—
213	#120×C₅₃	D₄	1	2	yes	—
214	C₄×Q₈×C₅₃	—	2	1	no	—
215	C₄×Q₈×C₅₃	—	2	1	no	—
216	C₄×Q₈×C₅₃	—	2	2	no	—
217	C₄×Q₈×C₅₃	—	2	1	no	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
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	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
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	2	no	—
240	#117×C₅₃	—	2	1	no	—
241	#117×C₅₃	—	2	1	no	—
242	#117×C₅₃	C₂³	1	1	yes	characteristic
243	#117×C₅₃	C₂³	1	1	yes	characteristic
244	#117×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
249	#117×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
251	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
252	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
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	2	yes	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
266	C₂×C₄²×C₅₃	—	2	1	no	—
267	#107×C₅₃	C₂³	1	1	yes	characteristic
268	#107×C₅₃	C₂³	1	1	yes	characteristic
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	2	yes	—
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	2	yes	—
274	#107×C₅₃	C₂³	1	2	yes	—
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#106×C₅₃	C₂³	1	1	yes	characteristic
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
288	#106×C₅₃	C₂³	1	1	yes	characteristic
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	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	2	yes	—
301	#103×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
313	#97×C₅₃	C₂³	1	2	yes	—
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	2	2	no	—
319	#41×C₅₃	—	2	2	no	—
320	#41×C₅₃	—	8	4	no	—
321	C₂×Q₈×C₅₃	—	2	1	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	2	2	no	—
325	C₂×Q₈×C₅₃	—	2	2	no	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₅₃	—	2	1	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	1	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	—	2	1	no	—
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	—	2	2	no	—
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	8	2	no	—
353	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	Q₁₆×C₅₃	—	2	4	no	—
361	SD₁₆×C₅₃	—	2	4	no	—
362	M₁₆×C₅₃	—	2	2	no	—
363	M₁₆×C₅₃	—	2	4	no	—
364	M₁₆×C₅₃	—	2	4	no	—
365	M₁₆×C₅₃	#41	1	4	yes	complemented
366	C₂×C₈×C₅₃	—	2	2	no	—
367	C₂×C₈×C₅₃	—	2	2	no	—
368	C₂×C₈×C₅₃	—	2	4	no	—
369	C₂×C₈×C₅₃	—	2	4	no	—
370	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
375	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	2	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	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	—	2	2	no	—
397	C₄⋊C₄×C₅₃	—	2	2	no	—
398	C₄⋊C₄×C₅₃	—	2	2	no	—
399	C₄⋊C₄×C₅₃	—	2	1	no	—
400	C₄⋊C₄×C₅₃	—	2	2	no	—
401	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	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	1	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	1	no	—
439	C₄²×C₅₃	—	2	1	no	—
440	C₄²×C₅₃	—	2	1	no	—
441	C₄²×C₅₃	—	2	2	no	—
442	C₄²×C₅₃	—	2	2	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	2	no	—
450	C₂³×C₅₃	—	2	1	no	—
451	C₂³×C₅₃	—	4	1	no	—
452	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
454	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
455	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
456	Q₈×C₅₃	—	2	2	no	—
457	Q₈×C₅₃	—	2	2	no	—
458	Q₈×C₅₃	—	2	1	no	—
459	Q₈×C₅₃	—	2	2	no	—
460	Q₈×C₅₃	—	2	1	no	—
461	Q₈×C₅₃	—	4	2	no	—
462	Q₈×C₅₃	—	8	2	no	—
463	Q₈×C₅₃	—	8	2	no	—
464	D₄×C₅₃	—	2	4	no	—
465	D₄×C₅₃	—	2	4	no	—
466	D₄×C₅₃	—	2	2	no	—
467	D₄×C₅₃	—	2	1	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	4	2	no	—
470	D₄×C₅₃	—	4	2	no	—
471	D₄×C₅₃	—	4	2	no	—
472	D₄×C₅₃	—	4	2	no	—
473	D₄×C₅₃	—	8	2	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	2	2	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	1	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	1	no	—
494	C₂×C₄×C₅₃	—	4	2	no	—
495	C₂×C₄×C₅₃	—	4	2	no	—
496	C₂×C₄×C₅₃	—	4	4	no	—
497	C₂×C₄×C₅₃	—	4	2	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	2	no	—
500	C₂×C₄×C₅₃	—	8	1	no	—
501	C₂×C₄×C₅₃	—	8	1	no	—
502	C₂×C₄×C₅₃	—	8	1	no	—
503	C₂×C₄×C₅₃	—	8	2	no	—
504	C₂×C₄×C₅₃	—	8	1	no	—
505	C₂×C₄×C₅₃	—	8	2	no	—
506	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
513	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
514	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
515	C₈×C₅₃	—	2	1	no	—
516	C₈×C₅₃	—	2	1	no	—
517	C₈×C₅₃	—	2	2	no	—
518	C₈×C₅₃	—	2	1	no	—
519	C₈×C₅₃	—	2	1	no	—
520	C₈×C₅₃	C₂×#41	1	4	yes	—
521	#61271	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
522	C₂²×C₅₃	—	2	1	no	—
523	C₂²×C₅₃	—	2	1	no	—
524	C₂²×C₅₃	—	2	1	no	—
525	C₂²×C₅₃	—	2	1	no	—
526	C₂²×C₅₃	—	2	2	no	—
527	C₂²×C₅₃	—	2	1	no	—
528	C₂²×C₅₃	—	2	1	no	—
529	C₂²×C₅₃	—	2	2	no	—
530	C₂²×C₅₃	—	2	1	no	—
531	C₂²×C₅₃	—	2	2	no	—
532	C₂²×C₅₃	—	4	4	no	—
533	C₂²×C₅₃	—	4	1	no	—
534	C₂²×C₅₃	—	4	1	no	—
535	C₂²×C₅₃	—	4	1	no	—
536	C₂²×C₅₃	#547	1	2	yes	—
537	C₂²×C₅₃	#577	1	2	yes	—
538	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₅₃	—	2	2	no	—
540	C₄×C₅₃	—	2	1	no	—
541	C₄×C₅₃	—	2	1	no	—
542	C₄×C₅₃	—	2	2	no	—
543	C₄×C₅₃	—	2	2	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	2	no	—
546	C₄×C₅₃	—	4	1	no	—
547	C₄×C₅₃	—	4	1	no	—
548	C₄×C₅₃	—	4	1	no	—
549	C₄×C₅₃	—	4	2	no	—
550	C₄×C₅₃	—	4	1	no	—
551	C₄×C₅₃	—	4	1	no	—
552	C₄×C₅₃	—	4	2	no	—
553	C₄×C₅₃	—	4	2	no	—
554	C₄×C₅₃	—	4	1	no	—
555	C₄×C₅₃	#547	1	2	yes	—
556	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
557	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
558	#3495	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3492	C₂×C₅₃	1	1	yes	characteristic
560	#3356	C₂×C₅₃	1	2	yes	complemented
561	#3351	C₂×C₅₃	1	2	yes	complemented
562	#3350	C₂×C₅₃	1	2	yes	complemented
563	#3344	C₂×C₅₃	1	2	yes	complemented
564	#3344	C₂×C₅₃	1	2	yes	complemented
565	#3343	C₂×C₅₃	1	2	yes	complemented
566	#3336	C₂×C₅₃	1	2	yes	complemented
567	#3335	C₂×C₅₃	1	2	yes	complemented
568	#3163	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
572	C₂×#483	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3082	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#3063	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3056	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#2947	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#2933	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#2912	C₂×C₅₃	1	1	yes	characteristic, complemented
580	C₂×#428	C₂×C₅₃	1	1	yes	characteristic, complemented
581	C₂×C₅₃	—	2	2	no	—
582	C₂×C₅₃	—	2	2	no	—
583	C₂×C₅₃	—	4	2	no	—
584	C₂×C₅₃	—	4	1	no	—
585	C₂×C₅₃	—	8	1	no	—
586	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
587	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
588	C₂×C₅₃	#3586	1	1	yes	characteristic
589	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
590	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
591	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
592	#556	C₂²×C₅₃	1	2	yes	—
593	#554	—	2	1	no	—
594	#554	C₂²×C₅₃	1	2	yes	—
595	#554	C₂²×C₅₃	1	2	yes	—
596	#553	—	2	1	no	—
597	#553	C₂²×C₅₃	1	2	yes	—
598	#552	—	2	2	no	—
599	#552	—	2	1	no	—
600	#552	C₂²×C₅₃	1	2	yes	—
601	#552	C₂²×C₅₃	1	2	yes	—
602	#552	C₂²×C₅₃	1	2	yes	—
603	#551	—	2	2	no	—
604	#547	—	2	1	no	—
605	#547	C₂²×C₅₃	1	2	yes	—
606	#544	C₂²×C₅₃	1	1	yes	characteristic
607	#544	C₂²×C₅₃	1	1	yes	characteristic
608	#542	—	2	1	no	—
609	#541	—	2	1	no	—
610	#539	—	2	2	no	—
611	#537	C₂²×C₅₃	1	1	yes	characteristic
612	#536	C₂²×C₅₃	1	1	yes	characteristic
613	#533	—	2	1	no	—
614	#529	—	2	1	no	—
615	#525	—	2	2	no	—
616	#525	C₂²×C₅₃	1	1	yes	characteristic
617	#525	C₂²×C₅₃	1	1	yes	characteristic
618	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
619	#520	C₂²×C₅₃	1	1	yes	characteristic
620	#520	C₂²×C₅₃	1	1	yes	characteristic
621	#520	C₂²×C₅₃	1	1	yes	characteristic
622	#519	C₂²×C₅₃	1	1	yes	characteristic
623	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
624	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
625	#501	C₂²×C₅₃	1	2	yes	complemented
626	#501	C₂²×C₅₃	1	2	yes	complemented
627	#499	C₂²×C₅₃	1	2	yes	complemented
628	#498	C₂²×C₅₃	1	2	yes	complemented
629	#485	C₂²×C₅₃	1	1	yes	characteristic
630	#485	C₂²×C₅₃	1	1	yes	characteristic
631	#485	C₂²×C₅₃	1	2	yes	complemented
632	#485	C₂²×C₅₃	1	2	yes	complemented
633	#485	C₂²×C₅₃	1	2	yes	complemented
634	#484	C₂²×C₅₃	1	1	yes	characteristic
635	#484	C₂²×C₅₃	1	2	yes	complemented
636	#483	C₂²×C₅₃	1	2	yes	—
637	#483	C₂²×C₅₃	1	1	yes	characteristic
638	#483	C₂²×C₅₃	1	2	yes	—
639	#483	C₂²×C₅₃	1	2	yes	—
640	#483	C₂²×C₅₃	1	2	yes	—
641	#483	C₂²×C₅₃	1	2	yes	complemented
642	#483	C₂²×C₅₃	1	2	yes	complemented
643	#482	C₂²×C₅₃	1	1	yes	characteristic
644	#482	C₂²×C₅₃	1	1	yes	characteristic
645	#482	C₂²×C₅₃	1	2	yes	complemented
646	#481	C₂²×C₅₃	1	1	yes	characteristic
647	#481	C₂²×C₅₃	1	2	yes	complemented
648	#480	C₂²×C₅₃	1	1	yes	characteristic
649	#479	C₂²×C₅₃	1	2	yes	complemented
650	#479	C₂²×C₅₃	1	2	yes	complemented
651	#479	C₂²×C₅₃	1	2	yes	complemented
652	#478	C₂²×C₅₃	1	2	yes	complemented
653	#477	C₂²×C₅₃	1	2	yes	complemented
654	#476	C₂²×C₅₃	1	2	yes	complemented
655	#475	C₂²×C₅₃	1	2	yes	complemented
656	#475	C₂²×C₅₃	1	2	yes	complemented
657	#470	C₂²×C₅₃	1	2	yes	—
658	#470	C₂²×C₅₃	1	2	yes	complemented
659	#468	C₂²×C₅₃	1	2	yes	—
660	#468	C₂²×C₅₃	1	2	yes	complemented
661	#467	C₂²×C₅₃	1	2	yes	—
662	#467	C₂²×C₅₃	1	2	yes	complemented
663	#465	C₂²×C₅₃	1	2	yes	—
664	#465	C₂²×C₅₃	1	2	yes	complemented
665	#441	C₂²×C₅₃	1	2	yes	complemented
666	#440	C₂²×C₅₃	1	2	yes	complemented
667	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
668	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
669	#436	C₂²×C₅₃	1	2	yes	—
670	#435	C₂²×C₅₃	1	2	yes	—
671	#435	C₂²×C₅₃	1	2	yes	—
672	C₈×D₄	C₂²×C₅₃	1	2	yes	—
673	#428	C₂²×C₅₃	1	1	yes	characteristic
674	#428	C₂²×C₅₃	1	1	yes	characteristic
675	#428	C₂²×C₅₃	1	2	yes	—
676	#428	C₂²×C₅₃	1	2	yes	—
677	#428	C₂²×C₅₃	1	1	yes	characteristic
678	#428	C₂²×C₅₃	1	1	yes	characteristic
679	#428	C₂²×C₅₃	1	1	yes	characteristic
680	#428	C₂²×C₅₃	1	2	yes	complemented
681	#428	C₂²×C₅₃	1	2	yes	complemented
682	#427	C₂²×C₅₃	1	1	yes	characteristic
683	#427	C₂²×C₅₃	1	1	yes	characteristic
684	#427	C₂²×C₅₃	1	2	yes	complemented
685	C₂×#107	C₂²×C₅₃	1	2	yes	—
686	C₂×#106	C₂²×C₅₃	1	2	yes	—
687	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
688	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
689	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
690	#424	C₂²×C₅₃	1	1	yes	characteristic
691	#419	C₂²×C₅₃	1	1	yes	characteristic
692	#417	C₂²×C₅₃	1	1	yes	characteristic
693	#416	C₂²×C₅₃	1	1	yes	characteristic
694	#416	C₂²×C₅₃	1	1	yes	characteristic
695	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
696	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
697	#408	C₂²×C₅₃	1	1	yes	characteristic
698	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
699	#405	C₂²×C₅₃	1	1	yes	characteristic
700	C₅₃	#61271	1	1	yes	characteristic, direct product factor, Sylow
701	C₂×#41	—	2	2	no	—
702	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
704	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
705	C₂³×C₄	—	2	1	no	—
706	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
707	#137	—	2	4	no	—
708	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
710	#131	—	2	4	no	—
711	C₂×M₁₆	—	2	4	no	—
712	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
713	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
714	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
715	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
716	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
717	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
718	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
719	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	1	no	—
738	#125	C₂³×C₅₃	1	2	yes	—
739	#125	C₂³×C₅₃	1	2	yes	—
740	#124	—	2	1	no	—
741	#124	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	D₄×C₅₃	1	2	yes	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	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	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
762	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	D₄×C₅₃	1	1	yes	characteristic
774	#121	D₄×C₅₃	1	1	yes	characteristic
775	#121	C₂³×C₅₃	1	1	yes	characteristic
776	#121	C₂³×C₅₃	1	1	yes	characteristic
777	#121	C₂³×C₅₃	1	2	yes	—
778	#120	—	2	1	no	—
779	#120	D₄×C₅₃	1	2	yes	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	2	no	—
785	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
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	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	2	no	—
808	#117	C₂³×C₅₃	1	1	yes	characteristic
809	#117	C₂³×C₅₃	1	1	yes	characteristic
810	#117	C₂³×C₅₃	1	1	yes	characteristic
811	#117	C₂³×C₅₃	1	1	yes	characteristic
812	#117	C₂³×C₅₃	1	1	yes	characteristic
813	#117	C₂³×C₅₃	1	2	yes	—
814	#117	C₂³×C₅₃	1	2	yes	—
815	#117	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	—	2	1	no	—
821	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
822	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
824	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
825	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
829	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₄²	—	2	1	no	—
833	#107	C₂³×C₅₃	1	2	yes	—
834	#107	C₂³×C₅₃	1	2	yes	—
835	#107	C₂³×C₅₃	1	2	yes	—
836	#107	C₂³×C₅₃	1	2	yes	—
837	#107	C₂³×C₅₃	1	1	yes	characteristic
838	#107	C₂³×C₅₃	1	1	yes	characteristic
839	#107	C₂³×C₅₃	1	1	yes	characteristic
840	#107	C₂³×C₅₃	1	1	yes	characteristic
841	#107	C₂³×C₅₃	1	2	yes	—
842	#106	C₂³×C₅₃	1	2	yes	—
843	#106	C₂³×C₅₃	1	2	yes	—
844	#106	C₂³×C₅₃	1	2	yes	—
845	#106	C₂³×C₅₃	1	2	yes	—
846	#106	C₂³×C₅₃	1	2	yes	—
847	#106	C₂³×C₅₃	1	2	yes	—
848	#106	C₂³×C₅₃	1	2	yes	—
849	#106	C₂³×C₅₃	1	2	yes	—
850	#106	C₂³×C₅₃	1	1	yes	characteristic
851	#106	C₂³×C₅₃	1	2	yes	—
852	#106	C₂³×C₅₃	1	1	yes	characteristic
853	#106	C₂³×C₅₃	1	1	yes	characteristic
854	#106	C₂³×C₅₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
857	#103	C₂³×C₅₃	1	2	yes	—
858	#103	C₂³×C₅₃	1	2	yes	—
859	#103	C₂³×C₅₃	1	2	yes	—
860	#103	C₂³×C₅₃	1	2	yes	—
861	#103	C₂³×C₅₃	1	1	yes	characteristic
862	#103	C₂³×C₅₃	1	1	yes	characteristic
863	#103	C₂³×C₅₃	1	1	yes	characteristic
864	#103	C₂³×C₅₃	1	1	yes	characteristic
865	#103	C₂³×C₅₃	1	2	yes	—
866	#103	C₂³×C₅₃	1	2	yes	—
867	#103	C₂³×C₅₃	1	2	yes	—
868	#102	C₂³×C₅₃	1	1	yes	characteristic
869	#102	C₂³×C₅₃	1	1	yes	characteristic
870	#102	C₂³×C₅₃	1	1	yes	characteristic
871	#102	C₂³×C₅₃	1	1	yes	characteristic
872	#102	C₂³×C₅₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
879	#97	C₂³×C₅₃	1	2	yes	—
880	C₄×C₈	C₂³×C₅₃	1	2	yes	—
881	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	#41	—	2	2	no	—
885	#41	—	2	2	no	—
886	#41	—	8	4	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	2	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
900	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
901	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
902	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
903	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	8	2	no	—
919	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
921	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
926	Q₁₆	—	2	4	no	—
927	SD₁₆	—	2	4	no	—
928	M₁₆	—	2	2	no	—
929	M₁₆	—	2	4	no	—
930	M₁₆	—	2	4	no	—
931	M₁₆	#41×C₅₃	1	4	yes	complemented
932	C₂×C₈	—	2	2	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	2	4	no	—
935	C₂×C₈	—	2	4	no	—
936	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
941	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×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	1	yes	characteristic
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₅₃	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	C₂⁴×C₅₃	1	2	yes	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1019	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1020	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1021	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	2	no	—
1030	D₄	—	2	4	no	—
1031	D₄	—	2	4	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	8	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	4	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	1	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1078	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1079	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1080	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	2	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	C₂×#41×C₅₃	1	4	yes	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	4	4	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	C₅₃×#547	1	2	yes	—
1102	C₂²	C₅₃×#577	1	2	yes	—
1103	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	C₅₃×#547	1	2	yes	—
1121	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1122	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1123	C₂	—	2	2	no	—
1124	C₂	—	2	2	no	—
1125	C₂	—	4	1	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	8	1	no	—
1128	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
1129	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1130	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3492	C₂
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×#3495	C₂	semidirect
3. C₅₃×#3356	C₂	semidirect
4. C₅₃×#3351	C₂	semidirect
5. C₅₃×#3350	C₂	semidirect
6. C₅₃×#3344	C₂	semidirect
7. C₅₃×#3344	C₂	semidirect
8. C₅₃×#3343	C₂	semidirect
9. C₅₃×#3336	C₂	semidirect
10. C₅₃×#3335	C₂	semidirect
11. C₅₃×#3163	C₂	semidirect
12. C₅₃×#3099	C₂	semidirect
13. C₅₃×#3097	C₂	semidirect
14. C₅₃×#3091	C₂	semidirect
15. C₂×C₅₃×#483	C₂	semidirect
16. C₅₃×#3084	C₂	semidirect
17. C₅₃×#3082	C₂	semidirect
18. C₅₃×#3063	C₂	semidirect
19. C₅₃×#3056	C₂	semidirect
20. C₅₃×#2947	C₂	semidirect
21. C₅₃×#2933	C₂	semidirect
22. C₅₃×#2912	C₂	semidirect
23. C₂×C₅₃×#428	C₂	semidirect
60. C₅₃×#501	C₂²	semidirect
61. C₅₃×#501	C₂²	semidirect
62. C₅₃×#499	C₂²	semidirect
63. C₅₃×#498	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
70. C₅₃×#484	C₂²	semidirect
76. C₅₃×#483	C₂²	semidirect
77. C₅₃×#483	C₂²	semidirect
80. C₅₃×#482	C₂²	semidirect
82. C₅₃×#481	C₂²	semidirect
84. C₅₃×#479	C₂²	semidirect
85. C₅₃×#479	C₂²	semidirect
86. C₅₃×#479	C₂²	semidirect
87. C₅₃×#478	C₂²	semidirect
88. C₅₃×#477	C₂²	semidirect
89. C₅₃×#476	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
91. C₅₃×#475	C₂²	semidirect
93. C₅₃×#470	C₂²	semidirect
95. C₅₃×#468	C₂²	semidirect
97. C₅₃×#467	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
100. C₅₃×#441	C₂²	semidirect
101. C₅₃×#440	C₂²	semidirect
102. C₄×Q₁₆×C₅₃	C₂²	semidirect
103. C₄×SD₁₆×C₅₃	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
119. C₅₃×#427	C₂²	semidirect
124. C₂×#106×C₅₃	C₂²	semidirect
365. M₁₆×C₅₃	#41	semidirect
521. #61271	C₅₃	direct (N × H)
558. #3495	C₂×C₅₃	semidirect
560. #3356	C₂×C₅₃	semidirect
561. #3351	C₂×C₅₃	semidirect
562. #3350	C₂×C₅₃	semidirect
563. #3344	C₂×C₅₃	semidirect
564. #3344	C₂×C₅₃	semidirect
565. #3343	C₂×C₅₃	semidirect
566. #3336	C₂×C₅₃	semidirect
567. #3335	C₂×C₅₃	semidirect
568. #3163	C₂×C₅₃	semidirect
569. #3099	C₂×C₅₃	semidirect
570. #3097	C₂×C₅₃	semidirect
571. #3091	C₂×C₅₃	semidirect
572. C₂×#483	C₂×C₅₃	semidirect
573. #3084	C₂×C₅₃	semidirect
574. #3082	C₂×C₅₃	semidirect
575. #3063	C₂×C₅₃	semidirect
576. #3056	C₂×C₅₃	semidirect
577. #2947	C₂×C₅₃	semidirect
578. #2933	C₂×C₅₃	semidirect
579. #2912	C₂×C₅₃	semidirect
580. C₂×#428	C₂×C₅₃	semidirect
625. #501	C₂²×C₅₃	semidirect
626. #501	C₂²×C₅₃	semidirect
627. #499	C₂²×C₅₃	semidirect
628. #498	C₂²×C₅₃	semidirect
631. #485	C₂²×C₅₃	semidirect
632. #485	C₂²×C₅₃	semidirect
633. #485	C₂²×C₅₃	semidirect
635. #484	C₂²×C₅₃	semidirect
641. #483	C₂²×C₅₃	semidirect
642. #483	C₂²×C₅₃	semidirect
645. #482	C₂²×C₅₃	semidirect
647. #481	C₂²×C₅₃	semidirect
649. #479	C₂²×C₅₃	semidirect
650. #479	C₂²×C₅₃	semidirect
651. #479	C₂²×C₅₃	semidirect
652. #478	C₂²×C₅₃	semidirect
653. #477	C₂²×C₅₃	semidirect
654. #476	C₂²×C₅₃	semidirect
655. #475	C₂²×C₅₃	semidirect
656. #475	C₂²×C₅₃	semidirect
658. #470	C₂²×C₅₃	semidirect
660. #468	C₂²×C₅₃	semidirect
662. #467	C₂²×C₅₃	semidirect
664. #465	C₂²×C₅₃	semidirect
665. #441	C₂²×C₅₃	semidirect
666. #440	C₂²×C₅₃	semidirect
667. C₄×Q₁₆	C₂²×C₅₃	semidirect
668. C₄×SD₁₆	C₂²×C₅₃	semidirect
680. #428	C₂²×C₅₃	semidirect
681. #428	C₂²×C₅₃	semidirect
684. #427	C₂²×C₅₃	semidirect
689. C₂×#106	C₂²×C₅₃	semidirect
700. C₅₃	#61271	direct (N × H)
931. 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×#3495	2
C₅₃×#3492	2
C₅₃×#3356	2
C₅₃×#3351	2
C₅₃×#3350	2
C₅₃×#3344	2
C₅₃×#3343	2
C₅₃×#3336	2
C₅₃×#3335	2
C₅₃×#3163	2
C₅₃×#3099	2
C₅₃×#3097	2
C₅₃×#3091	2
C₂×C₅₃×#483	2
C₅₃×#3084	2
C₅₃×#3082	2
C₅₃×#3063	2
C₅₃×#3056	2
C₅₃×#2947	2
C₅₃×#2933	2
C₅₃×#2912	2
C₂×C₅₃×#428	2
#61271	53

Subgroups — C53×#61271 #27268783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61271 #27268783