Subgroups — C₅₃×#61283 #27268795

Order 13568.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3348	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3345	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3343	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3339	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3337	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#559	—	2	1	no	—
28	C₅₃×#559	—	2	1	no	—
29	C₅₃×#556	—	2	1	no	—
30	C₅₃×#555	C₂²	1	2	yes	—
31	C₅₃×#553	—	2	2	no	—
32	C₅₃×#553	—	2	2	no	—
33	C₅₃×#553	C₂²	1	2	yes	—
34	C₅₃×#553	C₂²	1	2	yes	—
35	C₅₃×#553	C₂²	1	2	yes	complemented
36	C₅₃×#553	C₂²	1	2	yes	complemented
37	C₅₃×#552	C₂²	1	2	yes	complemented
38	C₅₃×#552	C₂²	1	2	yes	complemented
39	C₅₃×#550	—	2	1	no	—
40	C₅₃×#547	C₂²	1	2	yes	—
41	C₅₃×#541	—	2	1	no	—
42	C₅₃×#540	—	2	1	no	—
43	C₅₃×#538	—	2	2	no	—
44	C₅₃×#537	C₂²	1	1	yes	characteristic
45	C₅₃×#537	C₂²	1	1	yes	characteristic
46	C₅₃×#535	C₂²	1	1	yes	characteristic
47	C₅₃×#535	C₂²	1	1	yes	characteristic
48	C₅₃×#533	C₂²	1	1	yes	characteristic
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₅₃×#529	—	2	1	no	—
51	C₅₃×#529	—	2	1	no	—
52	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
53	C₅₃×#525	—	2	2	no	—
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×#520	C₂²	1	1	yes	characteristic
58	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×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×#499	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	2	yes	complemented
65	C₅₃×#485	C₂²	1	2	yes	complemented
66	C₅₃×#484	C₂²	1	2	yes	complemented
67	C₅₃×#483	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	—
69	C₅₃×#482	C₂²	1	2	yes	—
70	C₅₃×#482	C₂²	1	2	yes	—
71	C₅₃×#482	C₂²	1	2	yes	—
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#481	C₂²	1	2	yes	—
75	C₅₃×#481	C₂²	1	2	yes	—
76	C₅₃×#481	C₂²	1	2	yes	complemented
77	C₅₃×#480	C₂²	1	2	yes	—
78	C₅₃×#480	C₂²	1	2	yes	—
79	C₅₃×#480	C₂²	1	2	yes	complemented
80	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	—
84	C₅₃×#478	C₂²	1	2	yes	—
85	C₅₃×#478	C₂²	1	2	yes	—
86	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#469	C₂²	1	2	yes	—
93	C₅₃×#469	C₂²	1	2	yes	—
94	C₅₃×#468	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	—
96	C₅₃×#466	C₂²	1	2	yes	—
97	C₅₃×#466	C₂²	1	2	yes	—
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	—
100	C₅₃×#442	C₂²	1	2	yes	—
101	C₅₃×#440	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
103	C₄×D₈×C₅₃	C₂²	1	2	yes	—
104	C₅₃×#436	C₂²	1	2	yes	complemented
105	C₅₃×#435	C₂²	1	2	yes	complemented
106	C₅₃×#435	C₂²	1	2	yes	complemented
107	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
108	C₅₃×#428	C₂²	1	1	yes	characteristic
109	C₅₃×#428	C₂²	1	1	yes	characteristic
110	C₅₃×#428	C₂²	1	1	yes	characteristic
111	C₅₃×#428	C₂²	1	1	yes	characteristic
112	C₅₃×#428	C₂²	1	1	yes	characteristic
113	C₅₃×#428	C₂²	1	2	yes	complemented
114	C₅₃×#428	C₂²	1	2	yes	complemented
115	C₅₃×#428	C₂²	1	2	yes	complemented
116	C₅₃×#428	C₂²	1	2	yes	complemented
117	C₅₃×#427	C₂²	1	1	yes	characteristic
118	C₅₃×#427	C₂²	1	1	yes	characteristic
119	C₅₃×#427	C₂²	1	2	yes	complemented
120	C₅₃×#427	C₂²	1	2	yes	complemented
121	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#107×C₅₃	C₂²	1	2	yes	complemented
123	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
124	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
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×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#408	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₅₃	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	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	—	2	1	no	—
141	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
142	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
143	C₂×D₈×C₅₃	C₂³	1	2	yes	—
144	#131×C₅₃	—	2	4	no	—
145	#131×C₅₃	—	2	4	no	—
146	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
155	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	#127×C₅₃	—	2	1	no	—
158	#127×C₅₃	—	2	1	no	—
159	#127×C₅₃	D₄	1	1	yes	characteristic
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	#126×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	1	no	—
169	#125×C₅₃	—	2	1	no	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#125×C₅₃	C₂³	1	1	yes	characteristic
172	#125×C₅₃	C₂³	1	1	yes	characteristic
173	#125×C₅₃	C₂³	1	2	yes	—
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	2	no	—
176	#124×C₅₃	—	2	1	no	—
177	#124×C₅₃	—	2	1	no	—
178	#124×C₅₃	D₄	1	1	yes	characteristic
179	#124×C₅₃	D₄	1	1	yes	characteristic
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	1	no	—
190	C₂²⋊Q₈×C₅₃	—	2	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	—	2	1	no	—
193	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
195	#121×C₅₃	—	2	2	no	—
196	#121×C₅₃	—	2	1	no	—
197	#121×C₅₃	—	2	1	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	D₄	1	2	yes	—
205	#121×C₅₃	D₄	1	2	yes	—
206	#121×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	C₂³	1	2	yes	—
208	#121×C₅₃	C₂³	1	2	yes	—
209	#121×C₅₃	C₂³	1	2	yes	—
210	#121×C₅₃	C₂³	1	2	yes	—
211	#121×C₅₃	C₂³	1	2	yes	—
212	#120×C₅₃	—	2	2	no	—
213	#120×C₅₃	—	2	2	no	—
214	C₄×Q₈×C₅₃	—	2	1	no	—
215	C₄×Q₈×C₅₃	—	2	1	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	—	2	1	no	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	—	2	1	no	—
220	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
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	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	2	no	—
247	#117×C₅₃	—	2	1	no	—
248	#117×C₅₃	C₂³	1	2	yes	—
249	#117×C₅₃	C₂³	1	2	yes	—
250	#117×C₅₃	C₂³	1	1	yes	characteristic
251	#117×C₅₃	C₂³	1	1	yes	characteristic
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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×C₄²×C₅₃	—	2	1	no	—
266	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
274	#107×C₅₃	C₂³	1	2	yes	—
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	1	yes	characteristic
277	#107×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	2	yes	—
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	2	yes	—
284	#106×C₅₃	C₂³	1	1	yes	characteristic
285	#106×C₅₃	C₂³	1	2	yes	—
286	#106×C₅₃	C₂³	1	1	yes	characteristic
287	#106×C₅₃	C₂³	1	1	yes	characteristic
288	#106×C₅₃	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×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	1	yes	characteristic
297	#103×C₅₃	C₂³	1	1	yes	characteristic
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	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	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	#97×C₅₃	C₂³	1	2	yes	—
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	1	no	—
316	#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	—	2	2	no	—
321	#41×C₅₃	—	2	2	no	—
322	#41×C₅₃	—	8	4	no	—
323	C₂×Q₈×C₅₃	—	2	1	no	—
324	C₂×Q₈×C₅₃	—	2	1	no	—
325	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₅₃	—	2	1	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	1	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
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	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	2	no	—
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	1	no	—
357	C₂²×C₄×C₅₃	—	2	2	no	—
358	C₂²×C₄×C₅₃	—	8	2	no	—
359	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	SD₁₆×C₅₃	—	2	4	no	—
365	D₈×C₅₃	—	2	4	no	—
366	M₁₆×C₅₃	—	2	2	no	—
367	M₁₆×C₅₃	—	2	4	no	—
368	M₁₆×C₅₃	—	2	4	no	—
369	M₁₆×C₅₃	#41	1	4	yes	complemented
370	C₂×C₈×C₅₃	—	2	2	no	—
371	C₂×C₈×C₅₃	—	2	2	no	—
372	C₂×C₈×C₅₃	—	2	4	no	—
373	C₂×C₈×C₅₃	—	2	4	no	—
374	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
375	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
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	1	no	—
385	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	1	no	—
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	—	2	1	no	—
400	C₄⋊C₄×C₅₃	—	2	1	no	—
401	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	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	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	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
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	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	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	1	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	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	—	2	1	no	—
443	C₄²×C₅₃	—	2	1	no	—
444	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂³×C₅₃	—	2	1	no	—
449	C₂³×C₅₃	—	2	2	no	—
450	C₂³×C₅₃	—	4	2	no	—
451	C₂³×C₅₃	—	8	1	no	—
452	C₂³×C₅₃	—	8	1	no	—
453	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
454	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
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	1	no	—
460	Q₈×C₅₃	—	4	2	no	—
461	Q₈×C₅₃	—	8	1	no	—
462	D₄×C₅₃	—	2	4	no	—
463	D₄×C₅₃	—	2	4	no	—
464	D₄×C₅₃	—	2	2	no	—
465	D₄×C₅₃	—	2	2	no	—
466	D₄×C₅₃	—	2	2	no	—
467	D₄×C₅₃	—	2	1	no	—
468	D₄×C₅₃	—	2	2	no	—
469	D₄×C₅₃	—	2	1	no	—
470	D₄×C₅₃	—	4	2	no	—
471	D₄×C₅₃	—	4	2	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	—	8	2	no	—
477	D₄×C₅₃	—	8	2	no	—
478	D₄×C₅₃	—	8	2	no	—
479	D₄×C₅₃	—	8	2	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	2	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	1	no	—
495	C₂×C₄×C₅₃	—	4	1	no	—
496	C₂×C₄×C₅₃	—	4	4	no	—
497	C₂×C₄×C₅₃	—	4	2	no	—
498	C₂×C₄×C₅₃	—	8	1	no	—
499	C₂×C₄×C₅₃	—	8	1	no	—
500	C₂×C₄×C₅₃	—	8	2	no	—
501	C₂×C₄×C₅₃	—	8	2	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	1	no	—
506	C₂×C₄×C₅₃	—	8	2	no	—
507	C₂×C₄×C₅₃	—	8	2	no	—
508	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
516	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
517	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
518	C₈×C₅₃	—	2	1	no	—
519	C₈×C₅₃	—	2	1	no	—
520	C₈×C₅₃	—	2	1	no	—
521	C₈×C₅₃	—	2	1	no	—
522	C₈×C₅₃	—	2	2	no	—
523	C₈×C₅₃	C₂×#41	1	4	yes	—
524	#61283	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
525	C₂²×C₅₃	—	2	1	no	—
526	C₂²×C₅₃	—	2	1	no	—
527	C₂²×C₅₃	—	2	2	no	—
528	C₂²×C₅₃	—	2	2	no	—
529	C₂²×C₅₃	—	2	2	no	—
530	C₂²×C₅₃	—	2	2	no	—
531	C₂²×C₅₃	—	2	2	no	—
532	C₂²×C₅₃	—	2	2	no	—
533	C₂²×C₅₃	—	4	1	no	—
534	C₂²×C₅₃	—	4	2	no	—
535	C₂²×C₅₃	—	4	2	no	—
536	C₂²×C₅₃	—	4	1	no	—
537	C₂²×C₅₃	—	4	1	no	—
538	C₂²×C₅₃	—	4	2	no	—
539	C₂²×C₅₃	—	8	4	no	—
540	C₂²×C₅₃	#547	1	2	yes	—
541	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
542	C₄×C₅₃	—	2	1	no	—
543	C₄×C₅₃	—	2	1	no	—
544	C₄×C₅₃	—	2	1	no	—
545	C₄×C₅₃	—	2	1	no	—
546	C₄×C₅₃	—	2	2	no	—
547	C₄×C₅₃	—	2	2	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	1	no	—
554	C₄×C₅₃	—	4	2	no	—
555	C₄×C₅₃	—	4	1	no	—
556	C₄×C₅₃	—	4	1	no	—
557	C₄×C₅₃	—	4	1	no	—
558	C₄×C₅₃	#547	1	2	yes	—
559	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
560	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	#3512	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#3506	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3355	C₂×C₅₃	1	2	yes	complemented
564	#3351	C₂×C₅₃	1	2	yes	complemented
565	#3348	C₂×C₅₃	1	2	yes	complemented
566	#3347	C₂×C₅₃	1	2	yes	complemented
567	#3345	C₂×C₅₃	1	2	yes	complemented
568	#3343	C₂×C₅₃	1	2	yes	complemented
569	#3339	C₂×C₅₃	1	2	yes	complemented
570	#3337	C₂×C₅₃	1	2	yes	complemented
571	#3166	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#3096	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
577	C₂×#478	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3062	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#3062	C₂×C₅₃	1	1	yes	characteristic, complemented
580	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#2935	C₂×C₅₃	1	1	yes	characteristic, complemented
582	#2913	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#2912	C₂×C₅₃	1	1	yes	characteristic, complemented
584	C₂×C₅₃	—	2	2	no	—
585	C₂×C₅₃	—	4	2	no	—
586	C₂×C₅₃	—	4	2	no	—
587	C₂×C₅₃	—	8	1	no	—
588	C₂×C₅₃	—	8	2	no	—
589	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
590	C₂×C₅₃	#3584	1	1	yes	characteristic
591	C₂×C₅₃	#3585	1	1	yes	characteristic
592	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
593	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
594	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
595	#559	—	2	1	no	—
596	#559	—	2	1	no	—
597	#556	—	2	1	no	—
598	#555	C₂²×C₅₃	1	2	yes	—
599	#553	—	2	2	no	—
600	#553	—	2	2	no	—
601	#553	C₂²×C₅₃	1	2	yes	—
602	#553	C₂²×C₅₃	1	2	yes	—
603	#553	C₂²×C₅₃	1	2	yes	complemented
604	#553	C₂²×C₅₃	1	2	yes	complemented
605	#552	C₂²×C₅₃	1	2	yes	complemented
606	#552	C₂²×C₅₃	1	2	yes	complemented
607	#550	—	2	1	no	—
608	#547	C₂²×C₅₃	1	2	yes	—
609	#541	—	2	1	no	—
610	#540	—	2	1	no	—
611	#538	—	2	2	no	—
612	#537	C₂²×C₅₃	1	1	yes	characteristic
613	#537	C₂²×C₅₃	1	1	yes	characteristic
614	#535	C₂²×C₅₃	1	1	yes	characteristic
615	#535	C₂²×C₅₃	1	1	yes	characteristic
616	#533	C₂²×C₅₃	1	1	yes	characteristic
617	#532	C₂²×C₅₃	1	1	yes	characteristic
618	#529	—	2	1	no	—
619	#529	—	2	1	no	—
620	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
621	#525	—	2	2	no	—
622	#520	C₂²×C₅₃	1	1	yes	characteristic
623	#520	C₂²×C₅₃	1	1	yes	characteristic
624	#520	C₂²×C₅₃	1	1	yes	characteristic
625	#520	C₂²×C₅₃	1	1	yes	characteristic
626	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
627	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
628	#501	C₂²×C₅₃	1	2	yes	complemented
629	#501	C₂²×C₅₃	1	2	yes	complemented
630	#499	C₂²×C₅₃	1	2	yes	complemented
631	#499	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	2	yes	complemented
635	#483	C₂²×C₅₃	1	2	yes	complemented
636	#482	C₂²×C₅₃	1	2	yes	—
637	#482	C₂²×C₅₃	1	2	yes	—
638	#482	C₂²×C₅₃	1	2	yes	—
639	#482	C₂²×C₅₃	1	2	yes	—
640	#482	C₂²×C₅₃	1	2	yes	complemented
641	#482	C₂²×C₅₃	1	2	yes	complemented
642	#481	C₂²×C₅₃	1	2	yes	—
643	#481	C₂²×C₅₃	1	2	yes	—
644	#481	C₂²×C₅₃	1	2	yes	complemented
645	#480	C₂²×C₅₃	1	2	yes	—
646	#480	C₂²×C₅₃	1	2	yes	—
647	#480	C₂²×C₅₃	1	2	yes	complemented
648	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
650	#478	C₂²×C₅₃	1	2	yes	—
651	#478	C₂²×C₅₃	1	2	yes	—
652	#478	C₂²×C₅₃	1	2	yes	—
653	#478	C₂²×C₅₃	1	2	yes	—
654	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	#469	C₂²×C₅₃	1	2	yes	—
661	#469	C₂²×C₅₃	1	2	yes	—
662	#468	C₂²×C₅₃	1	2	yes	—
663	#468	C₂²×C₅₃	1	2	yes	—
664	#466	C₂²×C₅₃	1	2	yes	—
665	#466	C₂²×C₅₃	1	2	yes	—
666	#465	C₂²×C₅₃	1	2	yes	—
667	#465	C₂²×C₅₃	1	2	yes	—
668	#442	C₂²×C₅₃	1	2	yes	—
669	#440	C₂²×C₅₃	1	2	yes	—
670	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
671	C₄×D₈	C₂²×C₅₃	1	2	yes	—
672	#436	C₂²×C₅₃	1	2	yes	complemented
673	#435	C₂²×C₅₃	1	2	yes	complemented
674	#435	C₂²×C₅₃	1	2	yes	complemented
675	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
676	#428	C₂²×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
681	#428	C₂²×C₅₃	1	2	yes	complemented
682	#428	C₂²×C₅₃	1	2	yes	complemented
683	#428	C₂²×C₅₃	1	2	yes	complemented
684	#428	C₂²×C₅₃	1	2	yes	complemented
685	#427	C₂²×C₅₃	1	1	yes	characteristic
686	#427	C₂²×C₅₃	1	1	yes	characteristic
687	#427	C₂²×C₅₃	1	2	yes	complemented
688	#427	C₂²×C₅₃	1	2	yes	complemented
689	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
690	C₂×#107	C₂²×C₅₃	1	2	yes	complemented
691	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
692	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
693	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
694	#418	C₂²×C₅₃	1	1	yes	characteristic
695	#417	C₂²×C₅₃	1	1	yes	characteristic
696	#416	C₂²×C₅₃	1	1	yes	characteristic
697	#416	C₂²×C₅₃	1	1	yes	characteristic
698	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
699	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
700	#408	C₂²×C₅₃	1	1	yes	characteristic
701	#408	C₂²×C₅₃	1	1	yes	characteristic
702	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
703	C₅₃	#61283	1	1	yes	characteristic, direct product factor, Sylow
704	C₂×#41	—	2	2	no	—
705	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
708	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
709	C₂³×C₄	—	2	1	no	—
710	AGL(1,ℤ/8)	—	2	4	no	—
711	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
712	C₂×D₈	C₂³×C₅₃	1	2	yes	—
713	#131	—	2	4	no	—
714	#131	—	2	4	no	—
715	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
716	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
717	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
718	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
719	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
722	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
723	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
726	#127	—	2	1	no	—
727	#127	—	2	1	no	—
728	#127	D₄×C₅₃	1	1	yes	characteristic
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	1	no	—
738	#125	—	2	1	no	—
739	#125	C₂³×C₅₃	1	2	yes	—
740	#125	C₂³×C₅₃	1	2	yes	—
741	#125	C₂³×C₅₃	1	1	yes	characteristic
742	#125	C₂³×C₅₃	1	1	yes	characteristic
743	#124	—	2	1	no	—
744	#124	—	2	1	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	D₄×C₅₃	1	1	yes	characteristic
748	#124	D₄×C₅₃	1	1	yes	characteristic
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
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	#123	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
764	#121	—	2	2	no	—
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	D₄×C₅₃	1	2	yes	—
774	#121	D₄×C₅₃	1	2	yes	—
775	#121	C₂³×C₅₃	1	2	yes	—
776	#121	C₂³×C₅₃	1	2	yes	—
777	#121	C₂³×C₅₃	1	2	yes	—
778	#121	C₂³×C₅₃	1	2	yes	—
779	#121	C₂³×C₅₃	1	2	yes	—
780	#121	C₂³×C₅₃	1	2	yes	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	C₂³×C₅₃	1	2	yes	—
808	C₄×D₄	C₂³×C₅₃	1	2	yes	—
809	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₅₃	1	2	yes	—
812	C₄×D₄	C₂³×C₅₃	1	2	yes	—
813	#117	—	2	2	no	—
814	#117	—	2	2	no	—
815	#117	—	2	2	no	—
816	#117	—	2	1	no	—
817	#117	C₂³×C₅₃	1	1	yes	characteristic
818	#117	C₂³×C₅₃	1	1	yes	characteristic
819	#117	C₂³×C₅₃	1	1	yes	characteristic
820	#117	C₂³×C₅₃	1	2	yes	—
821	#117	C₂³×C₅₃	1	2	yes	—
822	#117	C₂³×C₅₃	1	2	yes	—
823	#117	C₂³×C₅₃	1	2	yes	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
830	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
832	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
833	C₂×C₂²⋊C₄	—	2	1	no	—
834	C₂×C₄²	—	2	1	no	—
835	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
836	#107	C₂³×C₅₃	1	2	yes	—
837	#107	C₂³×C₅₃	1	2	yes	—
838	#107	C₂³×C₅₃	1	1	yes	characteristic
839	#107	C₂³×C₅₃	1	2	yes	—
840	#107	C₂³×C₅₃	1	2	yes	—
841	#107	C₂³×C₅₃	1	1	yes	characteristic
842	#107	C₂³×C₅₃	1	1	yes	characteristic
843	#107	C₂³×C₅₃	1	1	yes	characteristic
844	#107	C₂³×C₅₃	1	2	yes	—
845	#107	C₂³×C₅₃	1	2	yes	—
846	#107	C₂³×C₅₃	1	2	yes	—
847	#106	C₂³×C₅₃	1	2	yes	—
848	#106	C₂³×C₅₃	1	2	yes	—
849	#106	C₂³×C₅₃	1	1	yes	characteristic
850	#106	C₂³×C₅₃	1	2	yes	—
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	#106	C₂³×C₅₃	1	2	yes	—
856	#106	C₂³×C₅₃	1	2	yes	—
857	#106	C₂³×C₅₃	1	2	yes	—
858	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
861	C₄⋊C₈	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	1	yes	characteristic
866	#103	C₂³×C₅₃	1	2	yes	—
867	#102	C₂³×C₅₃	1	2	yes	—
868	#102	C₂³×C₅₃	1	2	yes	—
869	#102	C₂³×C₅₃	1	2	yes	—
870	#102	C₂³×C₅₃	1	2	yes	—
871	#102	C₂³×C₅₃	1	1	yes	characteristic
872	#102	C₂³×C₅₃	1	1	yes	characteristic
873	#102	C₂³×C₅₃	1	1	yes	characteristic
874	#102	C₂³×C₅₃	1	1	yes	characteristic
875	#102	C₂³×C₅₃	1	2	yes	—
876	#102	C₂³×C₅₃	1	2	yes	—
877	#102	C₂³×C₅₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
882	#97	C₂³×C₅₃	1	2	yes	—
883	C₄×C₈	C₂³×C₅₃	1	2	yes	—
884	C₂⁴	—	2	1	no	—
885	#41	—	2	2	no	—
886	#41	—	2	2	no	—
887	#41	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	2	2	no	—
891	#41	—	8	4	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
895	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
908	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
909	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
910	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
912	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
913	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
914	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	8	2	no	—
928	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
929	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
933	SD₁₆	—	2	4	no	—
934	D₈	—	2	4	no	—
935	M₁₆	—	2	2	no	—
936	M₁₆	—	2	4	no	—
937	M₁₆	—	2	4	no	—
938	M₁₆	#41×C₅₃	1	4	yes	complemented
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	2	4	no	—
942	C₂×C₈	—	2	4	no	—
943	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
944	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	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	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
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	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1014	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	4	2	no	—
1020	C₂³	—	8	1	no	—
1021	C₂³	—	8	1	no	—
1022	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1023	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1024	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	8	1	no	—
1031	D₄	—	2	4	no	—
1032	D₄	—	2	4	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	—	8	1	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1084	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1085	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1086	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	C₂×#41×C₅₃	1	4	yes	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	8	4	no	—
1108	C₂²	C₅₃×#547	1	2	yes	—
1109	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1110	C₄	—	2	2	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	C₅₃×#547	1	2	yes	—
1127	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1128	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1129	C₂	—	2	2	no	—
1130	C₂	—	4	2	no	—
1131	C₂	—	4	2	no	—
1132	C₂	—	8	2	no	—
1133	C₂	—	8	1	no	—
1134	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
1135	C₂	C₅₃×#3584	1	1	yes	characteristic
1136	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3512	C₂	semidirect
2. C₅₃×#3506	C₂	semidirect
3. C₅₃×#3355	C₂	semidirect
4. C₅₃×#3351	C₂	semidirect
5. C₅₃×#3348	C₂	semidirect
6. C₅₃×#3347	C₂	semidirect
7. C₅₃×#3345	C₂	semidirect
8. C₅₃×#3343	C₂	semidirect
9. C₅₃×#3339	C₂	semidirect
10. C₅₃×#3337	C₂	semidirect
11. C₅₃×#3166	C₂	semidirect
12. C₅₃×#3099	C₂	semidirect
13. C₅₃×#3098	C₂	semidirect
14. C₅₃×#3096	C₂	semidirect
15. C₅₃×#3096	C₂	semidirect
16. C₅₃×#3076	C₂	semidirect
17. C₂×C₅₃×#478	C₂	semidirect
18. C₅₃×#3062	C₂	semidirect
19. C₅₃×#3062	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
21. C₅₃×#2935	C₂	semidirect
22. C₅₃×#2913	C₂	semidirect
23. C₅₃×#2912	C₂	semidirect
35. C₅₃×#553	C₂²	semidirect
36. C₅₃×#553	C₂²	semidirect
37. C₅₃×#552	C₂²	semidirect
38. C₅₃×#552	C₂²	semidirect
60. C₅₃×#501	C₂²	semidirect
61. C₅₃×#501	C₂²	semidirect
62. C₅₃×#499	C₂²	semidirect
63. C₅₃×#499	C₂²	semidirect
64. C₅₃×#485	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#484	C₂²	semidirect
67. C₅₃×#483	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
76. C₅₃×#481	C₂²	semidirect
79. C₅₃×#480	C₂²	semidirect
80. C₅₃×#479	C₂²	semidirect
81. C₅₃×#479	C₂²	semidirect
86. C₅₃×#478	C₂²	semidirect
87. C₅₃×#478	C₂²	semidirect
88. C₅₃×#477	C₂²	semidirect
89. C₅₃×#476	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
91. C₅₃×#474	C₂²	semidirect
104. C₅₃×#436	C₂²	semidirect
105. C₅₃×#435	C₂²	semidirect
106. C₅₃×#435	C₂²	semidirect
107. C₈×D₄×C₅₃	C₂²	semidirect
113. C₅₃×#428	C₂²	semidirect
114. C₅₃×#428	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
119. C₅₃×#427	C₂²	semidirect
120. C₅₃×#427	C₂²	semidirect
122. C₂×#107×C₅₃	C₂²	semidirect
124. C₂×#106×C₅₃	C₂²	semidirect
369. M₁₆×C₅₃	#41	semidirect
524. #61283	C₅₃	direct (N × H)
561. #3512	C₂×C₅₃	semidirect
562. #3506	C₂×C₅₃	semidirect
563. #3355	C₂×C₅₃	semidirect
564. #3351	C₂×C₅₃	semidirect
565. #3348	C₂×C₅₃	semidirect
566. #3347	C₂×C₅₃	semidirect
567. #3345	C₂×C₅₃	semidirect
568. #3343	C₂×C₅₃	semidirect
569. #3339	C₂×C₅₃	semidirect
570. #3337	C₂×C₅₃	semidirect
571. #3166	C₂×C₅₃	semidirect
572. #3099	C₂×C₅₃	semidirect
573. #3098	C₂×C₅₃	semidirect
574. #3096	C₂×C₅₃	semidirect
575. #3096	C₂×C₅₃	semidirect
576. #3076	C₂×C₅₃	semidirect
577. C₂×#478	C₂×C₅₃	semidirect
578. #3062	C₂×C₅₃	semidirect
579. #3062	C₂×C₅₃	semidirect
580. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
581. #2935	C₂×C₅₃	semidirect
582. #2913	C₂×C₅₃	semidirect
583. #2912	C₂×C₅₃	semidirect
603. #553	C₂²×C₅₃	semidirect
604. #553	C₂²×C₅₃	semidirect
605. #552	C₂²×C₅₃	semidirect
606. #552	C₂²×C₅₃	semidirect
628. #501	C₂²×C₅₃	semidirect
629. #501	C₂²×C₅₃	semidirect
630. #499	C₂²×C₅₃	semidirect
631. #499	C₂²×C₅₃	semidirect
632. #485	C₂²×C₅₃	semidirect
633. #485	C₂²×C₅₃	semidirect
634. #484	C₂²×C₅₃	semidirect
635. #483	C₂²×C₅₃	semidirect
640. #482	C₂²×C₅₃	semidirect
641. #482	C₂²×C₅₃	semidirect
644. #481	C₂²×C₅₃	semidirect
647. #480	C₂²×C₅₃	semidirect
648. #479	C₂²×C₅₃	semidirect
649. #479	C₂²×C₅₃	semidirect
654. #478	C₂²×C₅₃	semidirect
655. #478	C₂²×C₅₃	semidirect
656. #477	C₂²×C₅₃	semidirect
657. #476	C₂²×C₅₃	semidirect
658. #475	C₂²×C₅₃	semidirect
659. #474	C₂²×C₅₃	semidirect
672. #436	C₂²×C₅₃	semidirect
673. #435	C₂²×C₅₃	semidirect
674. #435	C₂²×C₅₃	semidirect
675. C₈×D₄	C₂²×C₅₃	semidirect
681. #428	C₂²×C₅₃	semidirect
682. #428	C₂²×C₅₃	semidirect
683. #428	C₂²×C₅₃	semidirect
684. #428	C₂²×C₅₃	semidirect
687. #427	C₂²×C₅₃	semidirect
688. #427	C₂²×C₅₃	semidirect
690. C₂×#107	C₂²×C₅₃	semidirect
692. C₂×#106	C₂²×C₅₃	semidirect
703. C₅₃	#61283	direct (N × H)
938. 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×#3512	2
C₅₃×#3506	2
C₅₃×#3355	2
C₅₃×#3351	2
C₅₃×#3348	2
C₅₃×#3347	2
C₅₃×#3345	2
C₅₃×#3343	2
C₅₃×#3339	2
C₅₃×#3337	2
C₅₃×#3166	2
C₅₃×#3099	2
C₅₃×#3098	2
C₅₃×#3096	2
C₅₃×#3076	2
C₂×C₅₃×#478	2
C₅₃×#3062	2
C₄×AGL(1,ℤ/8)×C₅₃	2
C₅₃×#2935	2
C₅₃×#2913	2
C₅₃×#2912	2
#61283	53

Subgroups — C53×#61283 #27268795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61283 #27268795