Subgroups — C₅₃×#61331 #27268843

Order 13568.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3371	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3361	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3360	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#559	C₂²	1	2	yes	—
28	C₅₃×#559	C₂²	1	2	yes	—
29	C₅₃×#557	C₂²	1	2	yes	complemented
30	C₅₃×#557	C₂²	1	2	yes	complemented
31	C₅₃×#556	C₂²	1	2	yes	—
32	C₅₃×#556	C₂²	1	2	yes	—
33	C₅₃×#554	—	2	2	no	—
34	C₅₃×#554	—	2	2	no	—
35	C₅₃×#554	C₂²	1	2	yes	complemented
36	C₅₃×#554	C₂²	1	2	yes	complemented
37	C₅₃×#551	—	2	2	no	—
38	C₅₃×#551	—	2	2	no	—
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×#542	—	2	1	no	—
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#536	C₂²	1	1	yes	characteristic
46	C₅₃×#535	C₂²	1	1	yes	characteristic
47	C₅₃×#533	—	2	1	no	—
48	C₅₃×#533	C₂²	1	1	yes	characteristic
49	C₅₃×#529	—	2	1	no	—
50	C₅₃×#529	—	2	1	no	—
51	C₂×#125×C₅₃	—	2	1	no	—
52	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
54	C₅₃×#520	C₂²	1	1	yes	characteristic
55	C₅₃×#520	C₂²	1	1	yes	characteristic
56	C₅₃×#519	C₂²	1	1	yes	characteristic
57	C₅₃×#518	C₂²	1	1	yes	characteristic
58	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
59	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#491	C₂²	1	2	yes	complemented
61	C₅₃×#490	C₂²	1	2	yes	—
62	C₅₃×#489	C₂²	1	2	yes	—
63	C₅₃×#489	C₂²	1	2	yes	complemented
64	C₅₃×#488	C₂²	1	2	yes	—
65	C₅₃×#488	C₂²	1	2	yes	—
66	C₅₃×#488	C₂²	1	2	yes	—
67	C₅₃×#488	C₂²	1	2	yes	—
68	C₅₃×#488	C₂²	1	2	yes	—
69	C₅₃×#488	C₂²	1	2	yes	complemented
70	C₅₃×#487	C₂²	1	2	yes	complemented
71	C₅₃×#486	C₂²	1	2	yes	—
72	C₅₃×#479	C₂²	1	2	yes	complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#479	C₂²	1	2	yes	complemented
75	C₅₃×#479	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	2	yes	—
77	C₅₃×#478	C₂²	1	2	yes	—
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#477	C₂²	1	2	yes	complemented
81	C₅₃×#476	C₂²	1	2	yes	—
82	C₅₃×#475	C₂²	1	2	yes	complemented
83	C₅₃×#474	C₂²	1	2	yes	—
84	C₅₃×#464	C₂²	1	2	yes	—
85	C₅₃×#464	C₂²	1	2	yes	—
86	C₅₃×#464	C₂²	1	2	yes	—
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	—
89	C₅₃×#463	C₂²	1	2	yes	—
90	C₅₃×#463	C₂²	1	2	yes	—
91	C₅₃×#463	C₂²	1	2	yes	complemented
92	C₅₃×#462	C₂²	1	2	yes	complemented
93	C₅₃×#461	C₂²	1	2	yes	complemented
94	C₅₃×#460	C₂²	1	2	yes	—
95	C₅₃×#459	C₂²	1	2	yes	—
96	C₅₃×#446	C₂²	1	2	yes	complemented
97	C₅₃×#446	C₂²	1	2	yes	complemented
98	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
99	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
100	C₅₃×#442	C₂²	1	2	yes	—
101	C₅₃×#441	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	—
103	C₅₃×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
105	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
106	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
113	C₄×D₈×C₅₃	C₂²	1	2	yes	—
114	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#428	C₂²	1	1	yes	characteristic
117	C₅₃×#428	C₂²	1	1	yes	characteristic
118	C₅₃×#427	C₂²	1	1	yes	characteristic
119	C₅₃×#424	C₂²	1	1	yes	characteristic
120	C₅₃×#424	C₂²	1	1	yes	characteristic
121	C₅₃×#423	C₂²	1	1	yes	characteristic
122	C₅₃×#419	C₂²	1	1	yes	characteristic
123	C₅₃×#418	C₂²	1	1	yes	characteristic
124	C₅₃×#417	C₂²	1	1	yes	characteristic
125	C₅₃×#417	C₂²	1	1	yes	characteristic
126	C₅₃×#416	C₂²	1	1	yes	characteristic
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
129	C₂×#103×C₅₃	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	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
139	#137×C₅₃	—	2	4	no	—
140	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
141	#135×C₅₃	—	2	4	no	—
142	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₅₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
157	C₄⋊Q₈×C₅₃	—	2	2	no	—
158	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
163	#127×C₅₃	C₂³	1	2	yes	—
164	#126×C₅₃	—	2	2	no	—
165	#126×C₅₃	—	2	2	no	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	1	no	—
169	#125×C₅₃	—	2	1	no	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	2	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	1	no	—
175	#125×C₅₃	—	2	1	no	—
176	#125×C₅₃	D₄	1	1	yes	characteristic
177	#125×C₅₃	D₄	1	1	yes	characteristic
178	#125×C₅₃	C₂³	1	2	yes	—
179	#125×C₅₃	C₂³	1	2	yes	—
180	#125×C₅₃	C₂³	1	2	yes	—
181	#125×C₅₃	C₂³	1	2	yes	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	—	2	2	no	—
186	#124×C₅₃	C₂³	1	2	yes	—
187	#124×C₅₃	C₂³	1	2	yes	—
188	#124×C₅₃	C₂³	1	2	yes	—
189	#124×C₅₃	C₂³	1	2	yes	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	1	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	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	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
208	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
209	#121×C₅₃	—	2	1	no	—
210	#121×C₅₃	—	2	1	no	—
211	#120×C₅₃	—	2	2	no	—
212	C₄×Q₈×C₅₃	—	2	1	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	—	2	2	no	—
215	C₄×Q₈×C₅₃	—	2	2	no	—
216	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	1	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	#117×C₅₃	—	2	1	no	—
245	#117×C₅₃	—	2	1	no	—
246	#117×C₅₃	—	2	2	no	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	—	2	2	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	—	2	1	no	—
251	#117×C₅₃	C₂³	1	1	yes	characteristic
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	#117×C₅₃	C₂³	1	1	yes	characteristic
254	#117×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
258	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
259	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
266	C₂×C₄²×C₅₃	—	2	1	no	—
267	C₂×C₄²×C₅₃	—	2	1	no	—
268	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	1	yes	characteristic
271	#107×C₅₃	C₂³	1	2	yes	—
272	#107×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	1	yes	characteristic
274	#106×C₅₃	C₂³	1	1	yes	characteristic
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	#103×C₅₃	C₂³	1	1	yes	characteristic
284	#103×C₅₃	C₂³	1	2	yes	—
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
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	#102×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#97×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂⁴×C₅₃	—	2	1	no	—
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	2	2	no	—
319	#41×C₅₃	#41	1	4	yes	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	2	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	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
338	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	1	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	1	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	2	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	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	C₂⁴	1	1	yes	characteristic
356	Q₁₆×C₅₃	—	2	2	no	—
357	Q₁₆×C₅₃	—	2	4	no	—
358	SD₁₆×C₅₃	—	2	2	no	—
359	SD₁₆×C₅₃	—	2	4	no	—
360	SD₁₆×C₅₃	—	2	2	no	—
361	SD₁₆×C₅₃	—	2	4	no	—
362	D₈×C₅₃	—	2	2	no	—
363	D₈×C₅₃	—	2	4	no	—
364	M₁₆×C₅₃	—	2	2	no	—
365	M₁₆×C₅₃	—	2	2	no	—
366	C₂×C₈×C₅₃	—	2	2	no	—
367	C₂×C₈×C₅₃	—	2	2	no	—
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
373	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
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	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	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	1	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	2	no	—
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	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	1	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	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
432	C₄²×C₅₃	—	2	1	no	—
433	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	—	2	1	no	—
435	C₄²×C₅₃	—	2	1	no	—
436	C₄²×C₅₃	—	2	1	no	—
437	C₄²×C₅₃	—	2	1	no	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	—	2	2	no	—
440	C₄²×C₅₃	—	2	2	no	—
441	C₄²×C₅₃	—	2	2	no	—
442	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₄²×C₅₃	C₂⁴	1	2	yes	—
447	C₄²×C₅₃	C₂⁴	1	2	yes	—
448	C₂³×C₅₃	—	2	1	no	—
449	C₂³×C₅₃	—	2	1	no	—
450	C₂³×C₅₃	—	2	2	no	—
451	C₂³×C₅₃	—	4	2	no	—
452	C₂³×C₅₃	—	8	1	no	—
453	C₂³×C₅₃	—	8	1	no	—
454	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₅₃	—	2	1	no	—
456	Q₈×C₅₃	—	2	2	no	—
457	Q₈×C₅₃	—	2	1	no	—
458	Q₈×C₅₃	—	2	2	no	—
459	Q₈×C₅₃	—	2	1	no	—
460	Q₈×C₅₃	—	4	2	no	—
461	Q₈×C₅₃	—	4	2	no	—
462	Q₈×C₅₃	—	4	2	no	—
463	Q₈×C₅₃	—	8	2	no	—
464	Q₈×C₅₃	—	8	2	no	—
465	Q₈×C₅₃	C₂×#41	1	2	yes	—
466	D₄×C₅₃	—	2	4	no	—
467	D₄×C₅₃	—	2	2	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	2	1	no	—
470	D₄×C₅₃	—	2	2	no	—
471	D₄×C₅₃	—	2	1	no	—
472	D₄×C₅₃	—	4	2	no	—
473	D₄×C₅₃	—	4	2	no	—
474	D₄×C₅₃	—	8	2	no	—
475	D₄×C₅₃	—	8	2	no	—
476	D₄×C₅₃	C₂×#41	1	2	yes	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	4	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	2	no	—
487	C₂×C₄×C₅₃	—	4	1	no	—
488	C₂×C₄×C₅₃	—	4	1	no	—
489	C₂×C₄×C₅₃	—	4	2	no	—
490	C₂×C₄×C₅₃	—	4	2	no	—
491	C₂×C₄×C₅₃	—	8	1	no	—
492	C₂×C₄×C₅₃	—	8	1	no	—
493	C₂×C₄×C₅₃	—	8	1	no	—
494	C₂×C₄×C₅₃	—	8	1	no	—
495	C₂×C₄×C₅₃	—	8	2	no	—
496	C₂×C₄×C₅₃	—	8	2	no	—
497	C₂×C₄×C₅₃	—	8	2	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	1	no	—
500	C₂×C₄×C₅₃	—	8	1	no	—
501	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
511	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
512	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
513	C₈×C₅₃	—	2	1	no	—
514	C₈×C₅₃	—	2	1	no	—
515	C₈×C₅₃	—	2	2	no	—
516	C₈×C₅₃	—	2	2	no	—
517	C₈×C₅₃	—	2	1	no	—
518	C₈×C₅₃	—	2	1	no	—
519	#61331	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
520	C₂²×C₅₃	—	2	1	no	—
521	C₂²×C₅₃	—	2	1	no	—
522	C₂²×C₅₃	—	2	2	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	—	4	1	no	—
525	C₂²×C₅₃	—	4	1	no	—
526	C₂²×C₅₃	—	4	1	no	—
527	C₂²×C₅₃	—	4	2	no	—
528	C₂²×C₅₃	—	4	2	no	—
529	C₂²×C₅₃	—	4	1	no	—
530	C₂²×C₅₃	—	4	2	no	—
531	C₂²×C₅₃	—	16	2	no	—
532	C₂²×C₅₃	#548	1	2	yes	—
533	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
534	C₄×C₅₃	—	2	1	no	—
535	C₄×C₅₃	—	2	1	no	—
536	C₄×C₅₃	—	2	1	no	—
537	C₄×C₅₃	—	2	1	no	—
538	C₄×C₅₃	—	2	2	no	—
539	C₄×C₅₃	—	2	2	no	—
540	C₄×C₅₃	—	2	2	no	—
541	C₄×C₅₃	—	2	2	no	—
542	C₄×C₅₃	—	2	2	no	—
543	C₄×C₅₃	—	4	1	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	2	no	—
546	C₄×C₅₃	—	4	2	no	—
547	C₄×C₅₃	—	4	1	no	—
548	C₄×C₅₃	—	4	1	no	—
549	C₄×C₅₃	—	4	1	no	—
550	C₄×C₅₃	—	4	2	no	—
551	C₄×C₅₃	#548	1	2	yes	—
552	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
553	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	#3510	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3504	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3377	C₂×C₅₃	1	2	yes	complemented
557	#3376	C₂×C₅₃	1	2	yes	complemented
558	#3371	C₂×C₅₃	1	2	yes	complemented
559	#3370	C₂×C₅₃	1	2	yes	complemented
560	#3365	C₂×C₅₃	1	2	yes	complemented
561	#3364	C₂×C₅₃	1	2	yes	complemented
562	#3361	C₂×C₅₃	1	2	yes	complemented
563	#3360	C₂×C₅₃	1	2	yes	complemented
564	#3137	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
566	C₂×#488	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3082	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3045	C₂×C₅₃	1	1	yes	characteristic
572	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#2960	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#2947	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
576	C₄×#135	C₂×C₅₃	1	1	yes	characteristic, complemented
577	C₂×C₅₃	—	2	2	no	—
578	C₂×C₅₃	—	4	2	no	—
579	C₂×C₅₃	—	8	1	no	—
580	C₂×C₅₃	—	8	2	no	—
581	C₂×C₅₃	C₂×#548	1	1	yes	characteristic
582	C₂×C₅₃	#3584	1	1	yes	characteristic
583	C₂×C₅₃	#3584	1	1	yes	characteristic
584	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
585	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
586	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
587	#559	C₂²×C₅₃	1	2	yes	—
588	#559	C₂²×C₅₃	1	2	yes	—
589	#557	C₂²×C₅₃	1	2	yes	complemented
590	#557	C₂²×C₅₃	1	2	yes	complemented
591	#556	C₂²×C₅₃	1	2	yes	—
592	#556	C₂²×C₅₃	1	2	yes	—
593	#554	—	2	2	no	—
594	#554	—	2	2	no	—
595	#554	C₂²×C₅₃	1	2	yes	complemented
596	#554	C₂²×C₅₃	1	2	yes	complemented
597	#551	—	2	2	no	—
598	#551	—	2	2	no	—
599	#544	—	2	1	no	—
600	#544	—	2	1	no	—
601	#544	C₂²×C₅₃	1	1	yes	characteristic
602	#544	C₂²×C₅₃	1	1	yes	characteristic
603	#542	—	2	1	no	—
604	#542	—	2	1	no	—
605	#536	C₂²×C₅₃	1	1	yes	characteristic
606	#535	C₂²×C₅₃	1	1	yes	characteristic
607	#533	—	2	1	no	—
608	#533	C₂²×C₅₃	1	1	yes	characteristic
609	#529	—	2	1	no	—
610	#529	—	2	1	no	—
611	C₂×#125	—	2	1	no	—
612	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
613	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
614	#520	C₂²×C₅₃	1	1	yes	characteristic
615	#520	C₂²×C₅₃	1	1	yes	characteristic
616	#519	C₂²×C₅₃	1	1	yes	characteristic
617	#518	C₂²×C₅₃	1	1	yes	characteristic
618	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
619	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
620	#491	C₂²×C₅₃	1	2	yes	complemented
621	#490	C₂²×C₅₃	1	2	yes	—
622	#489	C₂²×C₅₃	1	2	yes	—
623	#489	C₂²×C₅₃	1	2	yes	complemented
624	#488	C₂²×C₅₃	1	2	yes	—
625	#488	C₂²×C₅₃	1	2	yes	—
626	#488	C₂²×C₅₃	1	2	yes	—
627	#488	C₂²×C₅₃	1	2	yes	—
628	#488	C₂²×C₅₃	1	2	yes	—
629	#488	C₂²×C₅₃	1	2	yes	complemented
630	#487	C₂²×C₅₃	1	2	yes	complemented
631	#486	C₂²×C₅₃	1	2	yes	—
632	#479	C₂²×C₅₃	1	2	yes	complemented
633	#479	C₂²×C₅₃	1	2	yes	complemented
634	#479	C₂²×C₅₃	1	2	yes	complemented
635	#479	C₂²×C₅₃	1	2	yes	complemented
636	#478	C₂²×C₅₃	1	2	yes	—
637	#478	C₂²×C₅₃	1	2	yes	—
638	#478	C₂²×C₅₃	1	2	yes	complemented
639	#478	C₂²×C₅₃	1	2	yes	complemented
640	#477	C₂²×C₅₃	1	2	yes	complemented
641	#476	C₂²×C₅₃	1	2	yes	—
642	#475	C₂²×C₅₃	1	2	yes	complemented
643	#474	C₂²×C₅₃	1	2	yes	—
644	#464	C₂²×C₅₃	1	2	yes	—
645	#464	C₂²×C₅₃	1	2	yes	—
646	#464	C₂²×C₅₃	1	2	yes	—
647	#464	C₂²×C₅₃	1	2	yes	complemented
648	#463	C₂²×C₅₃	1	2	yes	—
649	#463	C₂²×C₅₃	1	2	yes	—
650	#463	C₂²×C₅₃	1	2	yes	—
651	#463	C₂²×C₅₃	1	2	yes	complemented
652	#462	C₂²×C₅₃	1	2	yes	complemented
653	#461	C₂²×C₅₃	1	2	yes	complemented
654	#460	C₂²×C₅₃	1	2	yes	—
655	#459	C₂²×C₅₃	1	2	yes	—
656	#446	C₂²×C₅₃	1	2	yes	complemented
657	#446	C₂²×C₅₃	1	2	yes	complemented
658	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
659	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
660	#442	C₂²×C₅₃	1	2	yes	—
661	#441	C₂²×C₅₃	1	2	yes	complemented
662	#440	C₂²×C₅₃	1	2	yes	—
663	#440	C₂²×C₅₃	1	2	yes	complemented
664	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
666	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
668	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
670	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	C₄×D₈	C₂²×C₅₃	1	2	yes	—
674	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#428	C₂²×C₅₃	1	1	yes	characteristic
677	#428	C₂²×C₅₃	1	1	yes	characteristic
678	#427	C₂²×C₅₃	1	1	yes	characteristic
679	#424	C₂²×C₅₃	1	1	yes	characteristic
680	#424	C₂²×C₅₃	1	1	yes	characteristic
681	#423	C₂²×C₅₃	1	1	yes	characteristic
682	#419	C₂²×C₅₃	1	1	yes	characteristic
683	#418	C₂²×C₅₃	1	1	yes	characteristic
684	#417	C₂²×C₅₃	1	1	yes	characteristic
685	#417	C₂²×C₅₃	1	1	yes	characteristic
686	#416	C₂²×C₅₃	1	1	yes	characteristic
687	#416	C₂²×C₅₃	1	1	yes	characteristic
688	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
689	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
690	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
691	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
692	#405	C₂²×C₅₃	1	1	yes	characteristic
693	#405	C₂²×C₅₃	1	1	yes	characteristic
694	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
695	C₅₃	#61331	1	1	yes	characteristic, direct product factor, Sylow
696	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
697	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
698	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
699	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
700	#137	—	2	4	no	—
701	AGL(1,ℤ/8)	—	2	4	no	—
702	#135	—	2	4	no	—
703	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
709	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
710	C₂×D₈	C₂³×C₅₃	1	2	yes	—
711	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
712	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
713	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
714	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	2	2	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
720	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
722	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
724	#127	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	#125	—	2	1	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	D₄×C₅₃	1	1	yes	characteristic
738	#125	D₄×C₅₃	1	1	yes	characteristic
739	#125	C₂³×C₅₃	1	2	yes	—
740	#125	C₂³×C₅₃	1	2	yes	—
741	#125	C₂³×C₅₃	1	2	yes	—
742	#125	C₂³×C₅₃	1	2	yes	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	—	2	1	no	—
747	#124	C₂³×C₅₃	1	2	yes	—
748	#124	C₂³×C₅₃	1	2	yes	—
749	#124	C₂³×C₅₃	1	2	yes	—
750	#124	C₂³×C₅₃	1	2	yes	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	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	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
769	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
770	#121	—	2	1	no	—
771	#121	—	2	1	no	—
772	#120	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
782	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
783	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₅₃	1	2	yes	—
802	C₄×D₄	C₂³×C₅₃	1	2	yes	—
803	C₄×D₄	C₂³×C₅₃	1	2	yes	—
804	C₄×D₄	C₂³×C₅₃	1	2	yes	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	2	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	1	no	—
812	#117	C₂³×C₅₃	1	1	yes	characteristic
813	#117	C₂³×C₅₃	1	1	yes	characteristic
814	#117	C₂³×C₅₃	1	1	yes	characteristic
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	2	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₄²	—	2	1	no	—
828	C₂×C₄²	—	2	1	no	—
829	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
830	#107	C₂³×C₅₃	1	1	yes	characteristic
831	#107	C₂³×C₅₃	1	1	yes	characteristic
832	#107	C₂³×C₅₃	1	2	yes	—
833	#107	C₂³×C₅₃	1	2	yes	—
834	#106	C₂³×C₅₃	1	1	yes	characteristic
835	#106	C₂³×C₅₃	1	1	yes	characteristic
836	#106	C₂³×C₅₃	1	2	yes	—
837	#106	C₂³×C₅₃	1	2	yes	—
838	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
840	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
841	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
842	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
843	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
844	#103	C₂³×C₅₃	1	2	yes	—
845	#103	C₂³×C₅₃	1	2	yes	—
846	#103	C₂³×C₅₃	1	2	yes	—
847	#103	C₂³×C₅₃	1	2	yes	—
848	#103	C₂³×C₅₃	1	1	yes	characteristic
849	#103	C₂³×C₅₃	1	1	yes	characteristic
850	#103	C₂³×C₅₃	1	1	yes	characteristic
851	#103	C₂³×C₅₃	1	1	yes	characteristic
852	#103	C₂³×C₅₃	1	2	yes	—
853	#103	C₂³×C₅₃	1	2	yes	—
854	#103	C₂³×C₅₃	1	2	yes	—
855	#103	C₂³×C₅₃	1	2	yes	—
856	#102	C₂³×C₅₃	1	2	yes	—
857	#102	C₂³×C₅₃	1	2	yes	—
858	#102	C₂³×C₅₃	1	2	yes	—
859	#102	C₂³×C₅₃	1	2	yes	—
860	#102	C₂³×C₅₃	1	1	yes	characteristic
861	#102	C₂³×C₅₃	1	1	yes	characteristic
862	#102	C₂³×C₅₃	1	1	yes	characteristic
863	#102	C₂³×C₅₃	1	1	yes	characteristic
864	#102	C₂³×C₅₃	1	2	yes	—
865	#102	C₂³×C₅₃	1	2	yes	—
866	#102	C₂³×C₅₃	1	2	yes	—
867	#102	C₂³×C₅₃	1	2	yes	—
868	#97	C₂³×C₅₃	1	2	yes	—
869	#97	C₂³×C₅₃	1	2	yes	—
870	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₅₃	1	2	yes	—
875	C₄×C₈	C₂³×C₅₃	1	2	yes	—
876	C₂⁴	—	2	1	no	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	—	2	2	no	—
880	#41	#41×C₅₃	1	4	yes	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
887	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
899	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
915	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
917	Q₁₆	—	2	2	no	—
918	Q₁₆	—	2	4	no	—
919	SD₁₆	—	2	2	no	—
920	SD₁₆	—	2	4	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	2	4	no	—
923	D₈	—	2	2	no	—
924	D₈	—	2	4	no	—
925	M₁₆	—	2	2	no	—
926	M₁₆	—	2	2	no	—
927	C₂×C₈	—	2	2	no	—
928	C₂×C₈	—	2	2	no	—
929	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
934	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	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	C₂×D₄×C₅₃	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1004	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₅₃	1	2	yes	—
1008	C₄²	C₂⁴×C₅₃	1	2	yes	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	8	1	no	—
1014	C₂³	—	8	1	no	—
1015	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	C₂×#41×C₅₃	1	2	yes	—
1027	D₄	—	2	4	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	C₂×#41×C₅₃	1	2	yes	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	4	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	8	1	no	—
1053	C₂×C₄	—	8	1	no	—
1054	C₂×C₄	—	8	1	no	—
1055	C₂×C₄	—	8	1	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1064	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1071	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1072	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1073	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	16	2	no	—
1092	C₂²	C₅₃×#548	1	2	yes	—
1093	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1094	C₄	—	2	2	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	C₅₃×#548	1	2	yes	—
1112	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1113	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1114	C₂	—	2	2	no	—
1115	C₂	—	4	2	no	—
1116	C₂	—	8	2	no	—
1117	C₂	—	8	1	no	—
1118	C₂	C₂×C₅₃×#548	1	1	yes	characteristic
1119	C₂	C₅₃×#3584	1	1	yes	characteristic
1120	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3045	C₂
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×#3510	C₂	semidirect
2. C₅₃×#3504	C₂	semidirect
3. C₅₃×#3377	C₂	semidirect
4. C₅₃×#3376	C₂	semidirect
5. C₅₃×#3371	C₂	semidirect
6. C₅₃×#3370	C₂	semidirect
7. C₅₃×#3365	C₂	semidirect
8. C₅₃×#3364	C₂	semidirect
9. C₅₃×#3361	C₂	semidirect
10. C₅₃×#3360	C₂	semidirect
11. C₅₃×#3137	C₂	semidirect
12. C₅₃×#3136	C₂	semidirect
13. C₂×C₅₃×#488	C₂	semidirect
14. C₅₃×#3082	C₂	semidirect
15. C₅₃×#3081	C₂	semidirect
16. C₅₃×#3080	C₂	semidirect
17. C₅₃×#3046	C₂	semidirect
19. C₅₃×#3040	C₂	semidirect
20. C₅₃×#2960	C₂	semidirect
21. C₅₃×#2947	C₂	semidirect
22. C₅₃×#2946	C₂	semidirect
23. C₄×#135×C₅₃	C₂	semidirect
29. C₅₃×#557	C₂²	semidirect
30. C₅₃×#557	C₂²	semidirect
35. C₅₃×#554	C₂²	semidirect
36. C₅₃×#554	C₂²	semidirect
60. C₅₃×#491	C₂²	semidirect
63. C₅₃×#489	C₂²	semidirect
69. C₅₃×#488	C₂²	semidirect
70. C₅₃×#487	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
74. C₅₃×#479	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#477	C₂²	semidirect
82. C₅₃×#475	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#462	C₂²	semidirect
93. C₅₃×#461	C₂²	semidirect
96. C₅₃×#446	C₂²	semidirect
97. C₅₃×#446	C₂²	semidirect
98. C₈×Q₈×C₅₃	C₂²	semidirect
99. C₈×Q₈×C₅₃	C₂²	semidirect
101. C₅₃×#441	C₂²	semidirect
103. C₅₃×#440	C₂²	semidirect
104. C₄×Q₁₆×C₅₃	C₂²	semidirect
105. C₄×Q₁₆×C₅₃	C₂²	semidirect
106. C₄×Q₁₆×C₅₃	C₂²	semidirect
108. C₄×SD₁₆×C₅₃	C₂²	semidirect
109. C₄×SD₁₆×C₅₃	C₂²	semidirect
110. C₄×SD₁₆×C₅₃	C₂²	semidirect
111. C₄×SD₁₆×C₅₃	C₂²	semidirect
112. C₄×SD₁₆×C₅₃	C₂²	semidirect
114. C₄×D₈×C₅₃	C₂²	semidirect
115. C₄×D₈×C₅₃	C₂²	semidirect
519. #61331	C₅₃	direct (N × H)
554. #3510	C₂×C₅₃	semidirect
555. #3504	C₂×C₅₃	semidirect
556. #3377	C₂×C₅₃	semidirect
557. #3376	C₂×C₅₃	semidirect
558. #3371	C₂×C₅₃	semidirect
559. #3370	C₂×C₅₃	semidirect
560. #3365	C₂×C₅₃	semidirect
561. #3364	C₂×C₅₃	semidirect
562. #3361	C₂×C₅₃	semidirect
563. #3360	C₂×C₅₃	semidirect
564. #3137	C₂×C₅₃	semidirect
565. #3136	C₂×C₅₃	semidirect
566. C₂×#488	C₂×C₅₃	semidirect
567. #3082	C₂×C₅₃	semidirect
568. #3081	C₂×C₅₃	semidirect
569. #3080	C₂×C₅₃	semidirect
570. #3046	C₂×C₅₃	semidirect
572. #3040	C₂×C₅₃	semidirect
573. #2960	C₂×C₅₃	semidirect
574. #2947	C₂×C₅₃	semidirect
575. #2946	C₂×C₅₃	semidirect
576. C₄×#135	C₂×C₅₃	semidirect
589. #557	C₂²×C₅₃	semidirect
590. #557	C₂²×C₅₃	semidirect
595. #554	C₂²×C₅₃	semidirect
596. #554	C₂²×C₅₃	semidirect
620. #491	C₂²×C₅₃	semidirect
623. #489	C₂²×C₅₃	semidirect
629. #488	C₂²×C₅₃	semidirect
630. #487	C₂²×C₅₃	semidirect
632. #479	C₂²×C₅₃	semidirect
633. #479	C₂²×C₅₃	semidirect
634. #479	C₂²×C₅₃	semidirect
635. #479	C₂²×C₅₃	semidirect
638. #478	C₂²×C₅₃	semidirect
639. #478	C₂²×C₅₃	semidirect
640. #477	C₂²×C₅₃	semidirect
642. #475	C₂²×C₅₃	semidirect
647. #464	C₂²×C₅₃	semidirect
651. #463	C₂²×C₅₃	semidirect
652. #462	C₂²×C₅₃	semidirect
653. #461	C₂²×C₅₃	semidirect
656. #446	C₂²×C₅₃	semidirect
657. #446	C₂²×C₅₃	semidirect
658. C₈×Q₈	C₂²×C₅₃	semidirect
659. C₈×Q₈	C₂²×C₅₃	semidirect
661. #441	C₂²×C₅₃	semidirect
663. #440	C₂²×C₅₃	semidirect
664. C₄×Q₁₆	C₂²×C₅₃	semidirect
665. C₄×Q₁₆	C₂²×C₅₃	semidirect
666. C₄×Q₁₆	C₂²×C₅₃	semidirect
668. C₄×SD₁₆	C₂²×C₅₃	semidirect
669. C₄×SD₁₆	C₂²×C₅₃	semidirect
670. C₄×SD₁₆	C₂²×C₅₃	semidirect
671. C₄×SD₁₆	C₂²×C₅₃	semidirect
672. C₄×SD₁₆	C₂²×C₅₃	semidirect
674. C₄×D₈	C₂²×C₅₃	semidirect
675. C₄×D₈	C₂²×C₅₃	semidirect
695. C₅₃	#61331	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3510	2
C₅₃×#3504	2
C₅₃×#3377	2
C₅₃×#3376	2
C₅₃×#3371	2
C₅₃×#3370	2
C₅₃×#3365	2
C₅₃×#3364	2
C₅₃×#3361	2
C₅₃×#3360	2
C₅₃×#3137	2
C₅₃×#3136	2
C₂×C₅₃×#488	2
C₅₃×#3082	2
C₅₃×#3081	2
C₅₃×#3080	2
C₅₃×#3046	2
C₅₃×#3045	2
C₅₃×#3040	2
C₅₃×#2960	2
C₅₃×#2947	2
C₅₃×#2946	2
C₄×#135×C₅₃	2
#61331	53

Subgroups — C53×#61331 #27268843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61331 #27268843