Subgroups — C₅₃×#61647 #27269159

Order 13568.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3331	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3330	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3314	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3273	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3269	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3201	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
25	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
26	C₅₃×#562	—	2	2	no	—
27	C₅₃×#554	C₂²	1	2	yes	complemented
28	C₅₃×#548	C₂²	1	2	yes	complemented
29	C₅₃×#547	—	2	1	no	—
30	C₅₃×#547	—	2	1	no	—
31	C₅₃×#547	C₂²	1	2	yes	—
32	C₅₃×#547	C₂²	1	2	yes	complemented
33	C₅₃×#547	C₂²	1	2	yes	complemented
34	C₅₃×#546	—	2	1	no	—
35	C₅₃×#546	—	2	1	no	—
36	C₅₃×#546	—	2	2	no	—
37	C₅₃×#546	C₂²	1	2	yes	—
38	C₅₃×#546	C₂²	1	2	yes	complemented
39	C₅₃×#546	C₂²	1	2	yes	complemented
40	C₅₃×#543	—	2	1	no	—
41	C₅₃×#542	C₂²	1	2	yes	complemented
42	C₅₃×#539	—	2	1	no	—
43	C₅₃×#538	—	2	1	no	—
44	C₅₃×#537	—	2	1	no	—
45	C₅₃×#537	C₂²	1	2	yes	—
46	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#534	—	2	2	no	—
49	C₅₃×#525	C₂²	1	1	yes	characteristic
50	C₅₃×#525	C₂²	1	1	yes	characteristic
51	C₂×#123×C₅₃	—	2	2	no	—
52	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#497	C₂²	1	2	yes	complemented
56	C₅₃×#495	C₂²	1	2	yes	complemented
57	C₅₃×#489	C₂²	1	2	yes	complemented
58	C₅₃×#487	C₂²	1	2	yes	complemented
59	C₅₃×#485	C₂²	1	2	yes	complemented
60	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#484	C₂²	1	2	yes	complemented
62	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#483	C₂²	1	2	yes	complemented
64	C₅₃×#482	C₂²	1	2	yes	complemented
65	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#476	C₂²	1	2	yes	complemented
68	C₅₃×#474	C₂²	1	2	yes	complemented
69	C₅₃×#470	C₂²	1	2	yes	complemented
70	C₅₃×#470	C₂²	1	2	yes	complemented
71	C₅₃×#469	C₂²	1	2	yes	complemented
72	C₅₃×#468	C₂²	1	2	yes	complemented
73	C₅₃×#468	C₂²	1	2	yes	complemented
74	C₅₃×#468	C₂²	1	2	yes	complemented
75	C₅₃×#467	C₂²	1	2	yes	complemented
76	C₅₃×#465	C₂²	1	2	yes	complemented
77	C₅₃×#464	C₂²	1	2	yes	complemented
78	C₅₃×#463	C₂²	1	2	yes	complemented
79	C₅₃×#463	C₂²	1	2	yes	complemented
80	C₅₃×#463	C₂²	1	2	yes	complemented
81	C₅₃×#462	C₂²	1	2	yes	complemented
82	C₅₃×#461	C₂²	1	2	yes	complemented
83	C₅₃×#452	C₂²	1	2	yes	complemented
84	C₅₃×#452	C₂²	1	2	yes	complemented
85	C₅₃×#452	C₂²	1	2	yes	complemented
86	C₅₃×#452	C₂²	1	2	yes	complemented
87	C₅₃×#452	C₂²	1	2	yes	complemented
88	C₅₃×#452	C₂²	1	2	yes	complemented
89	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#451	C₂²	1	2	yes	complemented
91	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#450	C₂²	1	2	yes	complemented
93	C₅₃×#450	C₂²	1	2	yes	complemented
94	C₅₃×#449	C₂²	1	2	yes	—
95	C₅₃×#449	C₂²	1	2	yes	complemented
96	C₅₃×#449	C₂²	1	2	yes	complemented
97	C₅₃×#449	C₂²	1	2	yes	complemented
98	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#448	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	—
101	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#447	C₂²	1	2	yes	complemented
103	C₅₃×#442	C₂²	1	2	yes	complemented
104	C₅₃×#440	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
106	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
107	C₅₃×#436	C₂²	1	2	yes	complemented
108	C₅₃×#436	C₂²	1	2	yes	complemented
109	C₅₃×#435	C₂²	1	2	yes	complemented
110	C₅₃×#435	C₂²	1	2	yes	complemented
111	C₅₃×#433	C₂²	1	2	yes	complemented
112	C₅₃×#417	C₂²	1	2	yes	complemented
113	C₅₃×#417	C₂²	1	2	yes	complemented
114	C₅₃×#417	C₂²	1	2	yes	complemented
115	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
116	C₅₃×#408	C₂²	1	2	yes	complemented
117	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
119	H(5,𝔽₂)×C₅₃	—	4	4	no	—
120	C₂×#41×C₅₃	—	2	1	no	—
121	C₂×#41×C₅₃	—	2	2	no	—
122	C₂×#41×C₅₃	—	2	1	no	—
123	C₂×#41×C₅₃	—	2	1	no	—
124	C₂×#41×C₅₃	—	4	4	no	—
125	C₂×#41×C₅₃	C₂³	1	2	yes	—
126	C₂×#41×C₅₃	C₂³	1	2	yes	—
127	C₂×#41×C₅₃	C₂³	1	2	yes	—
128	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
129	C₂×#41×C₅₃	C₂³	1	2	yes	—
130	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₃	—	2	1	no	—
134	C₂²×D₄×C₅₃	—	2	1	no	—
135	C₂²×D₄×C₅₃	—	2	2	no	—
136	C₂²×D₄×C₅₃	—	2	1	no	—
137	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	—	2	1	no	—
141	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	#137×C₅₃	—	4	4	no	—
143	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
144	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
145	#135×C₅₃	—	4	4	no	—
146	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×D₈×C₅₃	C₂³	1	2	yes	—
156	C₂×D₈×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	C₂³	1	2	yes	—
158	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₃	—	2	1	no	—
163	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
165	#126×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	2	no	—
167	#124×C₅₃	—	2	2	no	—
168	#124×C₅₃	—	2	2	no	—
169	#124×C₅₃	—	2	1	no	—
170	#124×C₅₃	C₂³	1	2	yes	—
171	#124×C₅₃	C₂³	1	2	yes	—
172	#123×C₅₃	—	2	2	no	—
173	#123×C₅₃	—	2	2	no	—
174	#123×C₅₃	—	2	2	no	—
175	#123×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	2	no	—
184	#123×C₅₃	—	2	1	no	—
185	#123×C₅₃	D₄	1	2	yes	—
186	C₂²⋊Q₈×C₅₃	—	2	1	no	—
187	C₂²⋊Q₈×C₅₃	—	2	1	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	1	no	—
196	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
197	C₂²⋊Q₈×C₅₃	D₄	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	1	yes	characteristic
201	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	D₄	1	1	yes	characteristic
217	#121×C₅₃	D₄	1	1	yes	characteristic
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	C₂³	1	1	yes	characteristic
221	#121×C₅₃	C₂³	1	1	yes	characteristic
222	#121×C₅₃	C₂³	1	2	yes	—
223	#120×C₅₃	—	2	1	no	—
224	#120×C₅₃	—	2	2	no	—
225	#120×C₅₃	—	2	2	no	—
226	#120×C₅₃	—	2	2	no	—
227	#120×C₅₃	D₄	1	2	yes	—
228	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	C₂³	1	2	yes	—
236	C₄×D₄×C₅₃	C₂³	1	2	yes	—
237	C₄×D₄×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	#117×C₅₃	C₂³	1	1	yes	characteristic
241	#117×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
243	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
244	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
248	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
249	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
250	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
251	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
252	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
254	#107×C₅₃	C₂³	1	2	yes	—
255	#107×C₅₃	C₂³	1	2	yes	—
256	#106×C₅₃	C₂³	1	2	yes	—
257	#106×C₅₃	C₂³	1	2	yes	—
258	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
259	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
260	#103×C₅₃	C₂³	1	2	yes	—
261	#103×C₅₃	C₂³	1	2	yes	—
262	#103×C₅₃	C₂³	1	2	yes	—
263	#103×C₅₃	C₂³	1	2	yes	—
264	#103×C₅₃	C₂³	1	2	yes	—
265	#103×C₅₃	C₂³	1	2	yes	—
266	#103×C₅₃	C₂³	1	2	yes	—
267	#103×C₅₃	C₂³	1	2	yes	—
268	#102×C₅₃	C₂³	1	2	yes	—
269	#102×C₅₃	C₂³	1	2	yes	—
270	#102×C₅₃	C₂³	1	2	yes	—
271	#102×C₅₃	C₂³	1	2	yes	—
272	#102×C₅₃	C₂³	1	2	yes	—
273	#102×C₅₃	C₂³	1	2	yes	—
274	#102×C₅₃	C₂³	1	2	yes	—
275	#102×C₅₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
284	#97×C₅₃	C₂³	1	2	yes	—
285	C₄×C₈×C₅₃	C₂³	1	2	yes	—
286	C₂⁴×C₅₃	—	2	1	no	—
287	C₂⁴×C₅₃	—	2	1	no	—
288	C₂⁴×C₅₃	—	2	2	no	—
289	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
290	#41×C₅₃	—	2	4	no	—
291	#41×C₅₃	—	2	4	no	—
292	#41×C₅₃	—	2	4	no	—
293	#41×C₅₃	—	4	2	no	—
294	#41×C₅₃	—	4	2	no	—
295	#41×C₅₃	—	4	2	no	—
296	#41×C₅₃	—	4	2	no	—
297	#41×C₅₃	—	4	2	no	—
298	#41×C₅₃	—	4	2	no	—
299	#41×C₅₃	—	4	2	no	—
300	#41×C₅₃	—	4	4	no	—
301	#41×C₅₃	—	4	4	no	—
302	#41×C₅₃	—	4	4	no	—
303	#41×C₅₃	—	8	4	no	—
304	C₂×Q₈×C₅₃	—	2	1	no	—
305	C₂×Q₈×C₅₃	—	2	1	no	—
306	C₂×Q₈×C₅₃	—	2	2	no	—
307	C₂×Q₈×C₅₃	—	4	2	no	—
308	C₂×Q₈×C₅₃	—	4	2	no	—
309	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
311	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
313	C₂×D₄×C₅₃	—	2	4	no	—
314	C₂×D₄×C₅₃	—	2	4	no	—
315	C₂×D₄×C₅₃	—	2	2	no	—
316	C₂×D₄×C₅₃	—	2	2	no	—
317	C₂×D₄×C₅₃	—	2	2	no	—
318	C₂×D₄×C₅₃	—	2	1	no	—
319	C₂×D₄×C₅₃	—	2	2	no	—
320	C₂×D₄×C₅₃	—	2	1	no	—
321	C₂×D₄×C₅₃	—	2	1	no	—
322	C₂×D₄×C₅₃	—	2	2	no	—
323	C₂×D₄×C₅₃	—	2	2	no	—
324	C₂×D₄×C₅₃	—	2	2	no	—
325	C₂×D₄×C₅₃	—	2	1	no	—
326	C₂×D₄×C₅₃	—	2	2	no	—
327	C₂×D₄×C₅₃	—	2	1	no	—
328	C₂×D₄×C₅₃	—	4	2	no	—
329	C₂×D₄×C₅₃	—	4	2	no	—
330	C₂×D₄×C₅₃	—	4	4	no	—
331	C₂×D₄×C₅₃	—	4	4	no	—
332	C₂×D₄×C₅₃	—	4	8	no	—
333	C₂×D₄×C₅₃	—	8	2	no	—
334	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
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	2	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	—	2	2	no	—
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	—	2	1	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	2	no	—
354	C₂²×C₄×C₅₃	—	4	2	no	—
355	C₂²×C₄×C₅₃	—	4	4	no	—
356	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	Q₁₆×C₅₃	—	4	2	no	—
364	Q₁₆×C₅₃	—	4	2	no	—
365	Q₁₆×C₅₃	—	4	2	no	—
366	SD₁₆×C₅₃	—	2	4	no	—
367	SD₁₆×C₅₃	—	2	4	no	—
368	SD₁₆×C₅₃	—	4	2	no	—
369	SD₁₆×C₅₃	—	4	2	no	—
370	SD₁₆×C₅₃	—	4	2	no	—
371	SD₁₆×C₅₃	—	4	2	no	—
372	D₈×C₅₃	—	2	4	no	—
373	D₈×C₅₃	—	2	4	no	—
374	D₈×C₅₃	—	4	2	no	—
375	M₁₆×C₅₃	—	4	2	no	—
376	M₁₆×C₅₃	—	4	2	no	—
377	M₁₆×C₅₃	—	4	2	no	—
378	C₂×C₈×C₅₃	—	4	2	no	—
379	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
380	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
381	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
382	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
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	2	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	2	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	2	no	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₅₃	—	2	1	no	—
406	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
430	C₄²×C₅₃	—	2	1	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	C₂⁴	1	2	yes	—
433	C₂³×C₅₃	—	2	4	no	—
434	C₂³×C₅₃	—	2	2	no	—
435	C₂³×C₅₃	—	2	2	no	—
436	C₂³×C₅₃	—	2	1	no	—
437	C₂³×C₅₃	—	4	1	no	—
438	C₂³×C₅₃	—	4	1	no	—
439	C₂³×C₅₃	—	4	1	no	—
440	C₂³×C₅₃	—	4	4	no	—
441	C₂³×C₅₃	—	4	2	no	—
442	C₂³×C₅₃	—	8	1	no	—
443	C₂³×C₅₃	—	8	1	no	—
444	C₂³×C₅₃	—	8	1	no	—
445	C₂³×C₅₃	—	8	1	no	—
446	C₂³×C₅₃	—	8	2	no	—
447	C₂³×C₅₃	—	8	2	no	—
448	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
449	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
452	Q₈×C₅₃	—	2	2	no	—
453	Q₈×C₅₃	—	2	2	no	—
454	Q₈×C₅₃	—	2	2	no	—
455	Q₈×C₅₃	—	2	2	no	—
456	Q₈×C₅₃	—	2	2	no	—
457	Q₈×C₅₃	—	4	1	no	—
458	Q₈×C₅₃	—	4	2	no	—
459	Q₈×C₅₃	—	8	1	no	—
460	Q₈×C₅₃	—	8	2	no	—
461	D₄×C₅₃	—	2	4	no	—
462	D₄×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	2	no	—
464	D₄×C₅₃	—	2	2	no	—
465	D₄×C₅₃	—	2	2	no	—
466	D₄×C₅₃	—	4	1	no	—
467	D₄×C₅₃	—	4	2	no	—
468	D₄×C₅₃	—	4	2	no	—
469	D₄×C₅₃	—	4	2	no	—
470	D₄×C₅₃	—	4	4	no	—
471	D₄×C₅₃	—	4	4	no	—
472	D₄×C₅₃	—	4	4	no	—
473	D₄×C₅₃	—	4	4	no	—
474	D₄×C₅₃	—	4	2	no	—
475	D₄×C₅₃	—	4	4	no	—
476	D₄×C₅₃	—	8	1	no	—
477	D₄×C₅₃	—	8	1	no	—
478	D₄×C₅₃	—	8	1	no	—
479	D₄×C₅₃	—	8	2	no	—
480	D₄×C₅₃	—	8	2	no	—
481	D₄×C₅₃	—	8	2	no	—
482	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
483	C₂×C₄×C₅₃	—	2	2	no	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	2	no	—
486	C₂×C₄×C₅₃	—	2	2	no	—
487	C₂×C₄×C₅₃	—	2	2	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	2	no	—
492	C₂×C₄×C₅₃	—	2	2	no	—
493	C₂×C₄×C₅₃	—	2	1	no	—
494	C₂×C₄×C₅₃	—	2	1	no	—
495	C₂×C₄×C₅₃	—	4	1	no	—
496	C₂×C₄×C₅₃	—	4	1	no	—
497	C₂×C₄×C₅₃	—	4	1	no	—
498	C₂×C₄×C₅₃	—	4	4	no	—
499	C₂×C₄×C₅₃	—	4	4	no	—
500	C₂×C₄×C₅₃	—	4	4	no	—
501	C₂×C₄×C₅₃	—	4	2	no	—
502	C₂×C₄×C₅₃	—	4	2	no	—
503	C₂×C₄×C₅₃	—	4	2	no	—
504	C₂×C₄×C₅₃	—	8	2	no	—
505	C₂×C₄×C₅₃	—	8	2	no	—
506	C₂×C₄×C₅₃	—	8	2	no	—
507	C₂×C₄×C₅₃	—	8	2	no	—
508	C₂×C₄×C₅₃	—	8	1	no	—
509	C₂×C₄×C₅₃	—	8	1	no	—
510	C₂×C₄×C₅₃	—	8	2	no	—
511	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
518	C₈×C₅₃	—	2	2	no	—
519	C₈×C₅₃	—	2	2	no	—
520	C₈×C₅₃	—	2	2	no	—
521	C₈×C₅₃	—	2	2	no	—
522	#61647	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
523	C₂²×C₅₃	—	2	1	no	—
524	C₂²×C₅₃	—	2	2	no	—
525	C₂²×C₅₃	—	2	1	no	—
526	C₂²×C₅₃	—	2	1	no	—
527	C₂²×C₅₃	—	2	1	no	—
528	C₂²×C₅₃	—	2	2	no	—
529	C₂²×C₅₃	—	2	1	no	—
530	C₂²×C₅₃	—	2	1	no	—
531	C₂²×C₅₃	—	2	1	no	—
532	C₂²×C₅₃	—	2	1	no	—
533	C₂²×C₅₃	—	2	1	no	—
534	C₂²×C₅₃	—	2	2	no	—
535	C₂²×C₅₃	—	2	4	no	—
536	C₂²×C₅₃	—	4	2	no	—
537	C₂²×C₅₃	—	4	2	no	—
538	C₂²×C₅₃	—	4	2	no	—
539	C₂²×C₅₃	—	4	1	no	—
540	C₂²×C₅₃	—	4	1	no	—
541	C₂²×C₅₃	—	4	2	no	—
542	C₂²×C₅₃	—	4	1	no	—
543	C₂²×C₅₃	—	4	2	no	—
544	C₂²×C₅₃	—	8	4	no	—
545	C₂²×C₅₃	—	8	2	no	—
546	C₂²×C₅₃	—	16	4	no	—
547	C₂²×C₅₃	—	16	2	no	—
548	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₅₃	—	2	2	no	—
550	C₄×C₅₃	—	2	2	no	—
551	C₄×C₅₃	—	2	1	no	—
552	C₄×C₅₃	—	2	1	no	—
553	C₄×C₅₃	—	2	1	no	—
554	C₄×C₅₃	—	2	2	no	—
555	C₄×C₅₃	—	4	2	no	—
556	C₄×C₅₃	—	4	2	no	—
557	C₄×C₅₃	—	4	1	no	—
558	C₄×C₅₃	—	4	1	no	—
559	C₄×C₅₃	—	4	1	no	—
560	C₄×C₅₃	—	4	2	no	—
561	C₄×C₅₃	—	4	2	no	—
562	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
563	#3536	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3485	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3331	C₂×C₅₃	1	2	yes	complemented
566	#3330	C₂×C₅₃	1	2	yes	complemented
567	#3314	C₂×C₅₃	1	2	yes	complemented
568	#3306	C₂×C₅₃	1	2	yes	complemented
569	#3275	C₂×C₅₃	1	2	yes	complemented
570	#3273	C₂×C₅₃	1	2	yes	complemented
571	#3269	C₂×C₅₃	1	2	yes	complemented
572	#3267	C₂×C₅₃	1	2	yes	complemented
573	#3225	C₂×C₅₃	1	2	yes	complemented
574	#3201	C₂×C₅₃	1	2	yes	complemented
575	#3196	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3194	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3118	C₂×C₅₃	1	2	yes	complemented
578	#3012	C₂×C₅₃	1	2	yes	complemented
579	#3007	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#2978	C₂×C₅₃	1	1	yes	characteristic, complemented
582	C₂×C₅₃	—	4	1	no	—
583	C₂×C₅₃	—	4	1	no	—
584	C₂×C₅₃	—	4	1	no	—
585	C₂×C₅₃	—	4	2	no	—
586	C₂×C₅₃	—	4	4	no	—
587	C₂×C₅₃	—	8	2	no	—
588	C₂×C₅₃	—	8	1	no	—
589	C₂×C₅₃	#3484	1	1	yes	characteristic
590	C₂×C₅₃	#3585	1	1	yes	characteristic
591	C₂×C₅₃	#3586	1	1	yes	characteristic
592	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic, complemented
593	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
594	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
595	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
596	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
597	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
598	#562	—	2	2	no	—
599	#554	C₂²×C₅₃	1	2	yes	complemented
600	#548	C₂²×C₅₃	1	2	yes	complemented
601	#547	—	2	1	no	—
602	#547	—	2	1	no	—
603	#547	C₂²×C₅₃	1	2	yes	—
604	#547	C₂²×C₅₃	1	2	yes	complemented
605	#547	C₂²×C₅₃	1	2	yes	complemented
606	#546	—	2	1	no	—
607	#546	—	2	1	no	—
608	#546	—	2	2	no	—
609	#546	C₂²×C₅₃	1	2	yes	—
610	#546	C₂²×C₅₃	1	2	yes	complemented
611	#546	C₂²×C₅₃	1	2	yes	complemented
612	#543	—	2	1	no	—
613	#542	C₂²×C₅₃	1	2	yes	complemented
614	#539	—	2	1	no	—
615	#538	—	2	1	no	—
616	#537	—	2	1	no	—
617	#537	C₂²×C₅₃	1	2	yes	—
618	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
619	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
620	#534	—	2	2	no	—
621	#525	C₂²×C₅₃	1	1	yes	characteristic
622	#525	C₂²×C₅₃	1	1	yes	characteristic
623	C₂×#123	—	2	2	no	—
624	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
625	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
626	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
627	#497	C₂²×C₅₃	1	2	yes	complemented
628	#495	C₂²×C₅₃	1	2	yes	complemented
629	#489	C₂²×C₅₃	1	2	yes	complemented
630	#487	C₂²×C₅₃	1	2	yes	complemented
631	#485	C₂²×C₅₃	1	2	yes	complemented
632	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#484	C₂²×C₅₃	1	2	yes	complemented
634	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	#483	C₂²×C₅₃	1	2	yes	complemented
636	#482	C₂²×C₅₃	1	2	yes	complemented
637	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
638	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#476	C₂²×C₅₃	1	2	yes	complemented
640	#474	C₂²×C₅₃	1	2	yes	complemented
641	#470	C₂²×C₅₃	1	2	yes	complemented
642	#470	C₂²×C₅₃	1	2	yes	complemented
643	#469	C₂²×C₅₃	1	2	yes	complemented
644	#468	C₂²×C₅₃	1	2	yes	complemented
645	#468	C₂²×C₅₃	1	2	yes	complemented
646	#468	C₂²×C₅₃	1	2	yes	complemented
647	#467	C₂²×C₅₃	1	2	yes	complemented
648	#465	C₂²×C₅₃	1	2	yes	complemented
649	#464	C₂²×C₅₃	1	2	yes	complemented
650	#463	C₂²×C₅₃	1	2	yes	complemented
651	#463	C₂²×C₅₃	1	2	yes	complemented
652	#463	C₂²×C₅₃	1	2	yes	complemented
653	#462	C₂²×C₅₃	1	2	yes	complemented
654	#461	C₂²×C₅₃	1	2	yes	complemented
655	#452	C₂²×C₅₃	1	2	yes	complemented
656	#452	C₂²×C₅₃	1	2	yes	complemented
657	#452	C₂²×C₅₃	1	2	yes	complemented
658	#452	C₂²×C₅₃	1	2	yes	complemented
659	#452	C₂²×C₅₃	1	2	yes	complemented
660	#452	C₂²×C₅₃	1	2	yes	complemented
661	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#451	C₂²×C₅₃	1	2	yes	complemented
663	#450	C₂²×C₅₃	1	2	yes	complemented
664	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#450	C₂²×C₅₃	1	2	yes	complemented
666	#449	C₂²×C₅₃	1	2	yes	—
667	#449	C₂²×C₅₃	1	2	yes	complemented
668	#449	C₂²×C₅₃	1	2	yes	complemented
669	#449	C₂²×C₅₃	1	2	yes	complemented
670	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#448	C₂²×C₅₃	1	2	yes	complemented
672	#447	C₂²×C₅₃	1	2	yes	—
673	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#447	C₂²×C₅₃	1	2	yes	complemented
675	#442	C₂²×C₅₃	1	2	yes	complemented
676	#440	C₂²×C₅₃	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
678	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
679	#436	C₂²×C₅₃	1	2	yes	complemented
680	#436	C₂²×C₅₃	1	2	yes	complemented
681	#435	C₂²×C₅₃	1	2	yes	complemented
682	#435	C₂²×C₅₃	1	2	yes	complemented
683	#433	C₂²×C₅₃	1	2	yes	complemented
684	#417	C₂²×C₅₃	1	2	yes	complemented
685	#417	C₂²×C₅₃	1	2	yes	complemented
686	#417	C₂²×C₅₃	1	2	yes	complemented
687	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
688	#408	C₂²×C₅₃	1	2	yes	complemented
689	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	C₅₃	#61647	1	1	yes	characteristic, direct product factor, Sylow
692	H(5,𝔽₂)	—	4	4	no	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	—	2	2	no	—
695	C₂×#41	—	2	1	no	—
696	C₂×#41	—	2	1	no	—
697	C₂×#41	—	4	4	no	—
698	C₂×#41	C₂³×C₅₃	1	2	yes	—
699	C₂×#41	C₂³×C₅₃	1	2	yes	—
700	C₂×#41	C₂³×C₅₃	1	2	yes	—
701	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
702	C₂×#41	C₂³×C₅₃	1	2	yes	—
703	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
704	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
706	C₂²×D₄	—	2	1	no	—
707	C₂²×D₄	—	2	1	no	—
708	C₂²×D₄	—	2	2	no	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
712	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
715	#137	—	4	4	no	—
716	AGL(1,ℤ/8)	—	4	4	no	—
717	AGL(1,ℤ/8)	—	4	4	no	—
718	#135	—	4	4	no	—
719	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
720	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
728	C₂×D₈	C₂³×C₅₃	1	2	yes	—
729	C₂×D₈	C₂³×C₅₃	1	2	yes	—
730	C₂×D₈	C₂³×C₅₃	1	2	yes	—
731	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
732	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
733	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
734	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
737	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
738	#126	—	2	2	no	—
739	#125	—	2	2	no	—
740	#124	—	2	1	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	C₂³×C₅₃	1	2	yes	—
744	#124	C₂³×C₅₃	1	2	yes	—
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	—	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	#123	—	2	2	no	—
758	#123	D₄×C₅₃	1	2	yes	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
769	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
770	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	D₄×C₅₃	1	1	yes	characteristic
790	#121	D₄×C₅₃	1	1	yes	characteristic
791	#121	C₂³×C₅₃	1	2	yes	—
792	#121	C₂³×C₅₃	1	2	yes	—
793	#121	C₂³×C₅₃	1	1	yes	characteristic
794	#121	C₂³×C₅₃	1	1	yes	characteristic
795	#121	C₂³×C₅₃	1	2	yes	—
796	#120	—	2	1	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	#120	D₄×C₅₃	1	2	yes	—
801	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	C₂³×C₅₃	1	2	yes	—
809	C₄×D₄	C₂³×C₅₃	1	2	yes	—
810	C₄×D₄	C₂³×C₅₃	1	2	yes	—
811	C₄×D₄	C₂³×C₅₃	1	2	yes	—
812	C₄×D₄	C₂³×C₅₃	1	2	yes	—
813	#117	C₂³×C₅₃	1	1	yes	characteristic
814	#117	C₂³×C₅₃	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	—	2	2	no	—
818	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
821	C₂×C₂²⋊C₄	—	2	1	no	—
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	#107	C₂³×C₅₃	1	2	yes	—
828	#107	C₂³×C₅₃	1	2	yes	—
829	#106	C₂³×C₅₃	1	2	yes	—
830	#106	C₂³×C₅₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
832	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
833	#103	C₂³×C₅₃	1	2	yes	—
834	#103	C₂³×C₅₃	1	2	yes	—
835	#103	C₂³×C₅₃	1	2	yes	—
836	#103	C₂³×C₅₃	1	2	yes	—
837	#103	C₂³×C₅₃	1	2	yes	—
838	#103	C₂³×C₅₃	1	2	yes	—
839	#103	C₂³×C₅₃	1	2	yes	—
840	#103	C₂³×C₅₃	1	2	yes	—
841	#102	C₂³×C₅₃	1	2	yes	—
842	#102	C₂³×C₅₃	1	2	yes	—
843	#102	C₂³×C₅₃	1	2	yes	—
844	#102	C₂³×C₅₃	1	2	yes	—
845	#102	C₂³×C₅₃	1	2	yes	—
846	#102	C₂³×C₅₃	1	2	yes	—
847	#102	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
857	#97	C₂³×C₅₃	1	2	yes	—
858	C₄×C₈	C₂³×C₅₃	1	2	yes	—
859	C₂⁴	—	2	1	no	—
860	C₂⁴	—	2	1	no	—
861	C₂⁴	—	2	2	no	—
862	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
863	#41	—	2	4	no	—
864	#41	—	2	4	no	—
865	#41	—	2	4	no	—
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	#41	—	4	2	no	—
869	#41	—	4	2	no	—
870	#41	—	4	2	no	—
871	#41	—	4	2	no	—
872	#41	—	4	2	no	—
873	#41	—	4	4	no	—
874	#41	—	4	4	no	—
875	#41	—	4	4	no	—
876	#41	—	8	4	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	4	2	no	—
881	C₂×Q₈	—	4	2	no	—
882	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
884	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	4	no	—
904	C₂×D₄	—	4	4	no	—
905	C₂×D₄	—	4	8	no	—
906	C₂×D₄	—	8	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	2	yes	—
910	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
911	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
912	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
913	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
914	C₂²×C₄	—	2	1	no	—
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	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	4	2	no	—
928	C₂²×C₄	—	4	4	no	—
929	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
936	Q₁₆	—	4	2	no	—
937	Q₁₆	—	4	2	no	—
938	Q₁₆	—	4	2	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	4	2	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	D₈	—	2	4	no	—
946	D₈	—	2	4	no	—
947	D₈	—	4	2	no	—
948	M₁₆	—	4	2	no	—
949	M₁₆	—	4	2	no	—
950	M₁₆	—	4	2	no	—
951	C₂×C₈	—	4	2	no	—
952	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
953	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
954	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
955	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
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	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	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	2	no	—
993	C₂²⋊C₄	—	2	2	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	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	2	no	—
1005	C₄²	C₂⁴×C₅₃	1	2	yes	—
1006	C₂³	—	2	4	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	1	no	—
1012	C₂³	—	4	1	no	—
1013	C₂³	—	4	4	no	—
1014	C₂³	—	4	2	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	1	no	—
1018	C₂³	—	8	1	no	—
1019	C₂³	—	8	2	no	—
1020	C₂³	—	8	2	no	—
1021	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1022	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
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	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	4	1	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	—	8	1	no	—
1033	Q₈	—	8	2	no	—
1034	D₄	—	2	4	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	1	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	4	no	—
1049	D₄	—	8	1	no	—
1050	D₄	—	8	1	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	4	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1090	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1091	C₈	—	2	2	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	2	no	—
1094	C₈	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	4	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	8	4	no	—
1117	C₂²	—	8	2	no	—
1118	C₂²	—	16	4	no	—
1119	C₂²	—	16	2	no	—
1120	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1135	C₂	—	4	1	no	—
1136	C₂	—	4	1	no	—
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	4	4	no	—
1140	C₂	—	8	1	no	—
1141	C₂	—	8	2	no	—
1142	C₂	C₅₃×#3484	1	1	yes	characteristic
1143	C₂	C₅₃×#3585	1	1	yes	characteristic
1144	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3536	C₂	semidirect
2. C₅₃×#3485	C₂	semidirect
3. C₅₃×#3331	C₂	semidirect
4. C₅₃×#3330	C₂	semidirect
5. C₅₃×#3314	C₂	semidirect
6. C₅₃×#3306	C₂	semidirect
7. C₅₃×#3275	C₂	semidirect
8. C₅₃×#3273	C₂	semidirect
9. C₅₃×#3269	C₂	semidirect
10. C₅₃×#3267	C₂	semidirect
11. C₅₃×#3225	C₂	semidirect
12. C₅₃×#3201	C₂	semidirect
13. C₅₃×#3196	C₂	semidirect
14. C₅₃×#3194	C₂	semidirect
15. C₅₃×#3118	C₂	semidirect
16. C₅₃×#3012	C₂	semidirect
17. C₅₃×#3007	C₂	semidirect
18. C₅₃×#3006	C₂	semidirect
19. C₅₃×#2978	C₂	semidirect
20. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
22. C₂×#137×C₅₃	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
25. C₂×#135×C₅₃	C₂²	semidirect
27. C₅₃×#554	C₂²	semidirect
28. C₅₃×#548	C₂²	semidirect
32. C₅₃×#547	C₂²	semidirect
33. C₅₃×#547	C₂²	semidirect
38. C₅₃×#546	C₂²	semidirect
39. C₅₃×#546	C₂²	semidirect
41. C₅₃×#542	C₂²	semidirect
46. C₅₃×#536	C₂²	semidirect
47. C₅₃×#536	C₂²	semidirect
52. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
53. C₂×#121×C₅₃	C₂²	semidirect
54. C₅₃×#518	C₂²	semidirect
55. C₅₃×#497	C₂²	semidirect
56. C₅₃×#495	C₂²	semidirect
57. C₅₃×#489	C₂²	semidirect
58. C₅₃×#487	C₂²	semidirect
59. C₅₃×#485	C₂²	semidirect
60. C₅₃×#484	C₂²	semidirect
61. C₅₃×#484	C₂²	semidirect
62. C₅₃×#483	C₂²	semidirect
63. C₅₃×#483	C₂²	semidirect
64. C₅₃×#482	C₂²	semidirect
65. C₅₃×#481	C₂²	semidirect
66. C₅₃×#480	C₂²	semidirect
67. C₅₃×#476	C₂²	semidirect
68. C₅₃×#474	C₂²	semidirect
69. C₅₃×#470	C₂²	semidirect
70. C₅₃×#470	C₂²	semidirect
71. C₅₃×#469	C₂²	semidirect
72. C₅₃×#468	C₂²	semidirect
73. C₅₃×#468	C₂²	semidirect
74. C₅₃×#468	C₂²	semidirect
75. C₅₃×#467	C₂²	semidirect
76. C₅₃×#465	C₂²	semidirect
77. C₅₃×#464	C₂²	semidirect
78. C₅₃×#463	C₂²	semidirect
79. C₅₃×#463	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#462	C₂²	semidirect
82. C₅₃×#461	C₂²	semidirect
83. C₅₃×#452	C₂²	semidirect
84. C₅₃×#452	C₂²	semidirect
85. C₅₃×#452	C₂²	semidirect
86. C₅₃×#452	C₂²	semidirect
87. C₅₃×#452	C₂²	semidirect
88. C₅₃×#452	C₂²	semidirect
89. C₅₃×#451	C₂²	semidirect
90. C₅₃×#451	C₂²	semidirect
91. C₅₃×#450	C₂²	semidirect
92. C₅₃×#450	C₂²	semidirect
93. C₅₃×#450	C₂²	semidirect
95. C₅₃×#449	C₂²	semidirect
96. C₅₃×#449	C₂²	semidirect
97. C₅₃×#449	C₂²	semidirect
98. C₅₃×#448	C₂²	semidirect
99. C₅₃×#448	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₅₃×#447	C₂²	semidirect
103. C₅₃×#442	C₂²	semidirect
104. C₅₃×#440	C₂²	semidirect
105. C₄×SD₁₆×C₅₃	C₂²	semidirect
106. C₄×D₈×C₅₃	C₂²	semidirect
107. C₅₃×#436	C₂²	semidirect
108. C₅₃×#436	C₂²	semidirect
109. C₅₃×#435	C₂²	semidirect
110. C₅₃×#435	C₂²	semidirect
111. C₅₃×#433	C₂²	semidirect
112. C₅₃×#417	C₂²	semidirect
113. C₅₃×#417	C₂²	semidirect
114. C₅₃×#417	C₂²	semidirect
115. C₂×#102×C₅₃	C₂²	semidirect
116. C₅₃×#408	C₂²	semidirect
117. C₅₃×#407	C₂²	semidirect
118. C₅₃×#407	C₂²	semidirect
522. #61647	C₅₃	direct (N × H)
563. #3536	C₂×C₅₃	semidirect
564. #3485	C₂×C₅₃	semidirect
565. #3331	C₂×C₅₃	semidirect
566. #3330	C₂×C₅₃	semidirect
567. #3314	C₂×C₅₃	semidirect
568. #3306	C₂×C₅₃	semidirect
569. #3275	C₂×C₅₃	semidirect
570. #3273	C₂×C₅₃	semidirect
571. #3269	C₂×C₅₃	semidirect
572. #3267	C₂×C₅₃	semidirect
573. #3225	C₂×C₅₃	semidirect
574. #3201	C₂×C₅₃	semidirect
575. #3196	C₂×C₅₃	semidirect
576. #3194	C₂×C₅₃	semidirect
577. #3118	C₂×C₅₃	semidirect
578. #3012	C₂×C₅₃	semidirect
579. #3007	C₂×C₅₃	semidirect
580. #3006	C₂×C₅₃	semidirect
581. #2978	C₂×C₅₃	semidirect
592. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
594. C₂×#137	C₂²×C₅₃	semidirect
595. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
596. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
597. C₂×#135	C₂²×C₅₃	semidirect
599. #554	C₂²×C₅₃	semidirect
600. #548	C₂²×C₅₃	semidirect
604. #547	C₂²×C₅₃	semidirect
605. #547	C₂²×C₅₃	semidirect
610. #546	C₂²×C₅₃	semidirect
611. #546	C₂²×C₅₃	semidirect
613. #542	C₂²×C₅₃	semidirect
618. #536	C₂²×C₅₃	semidirect
619. #536	C₂²×C₅₃	semidirect
624. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
625. C₂×#121	C₂²×C₅₃	semidirect
626. #518	C₂²×C₅₃	semidirect
627. #497	C₂²×C₅₃	semidirect
628. #495	C₂²×C₅₃	semidirect
629. #489	C₂²×C₅₃	semidirect
630. #487	C₂²×C₅₃	semidirect
631. #485	C₂²×C₅₃	semidirect
632. #484	C₂²×C₅₃	semidirect
633. #484	C₂²×C₅₃	semidirect
634. #483	C₂²×C₅₃	semidirect
635. #483	C₂²×C₅₃	semidirect
636. #482	C₂²×C₅₃	semidirect
637. #481	C₂²×C₅₃	semidirect
638. #480	C₂²×C₅₃	semidirect
639. #476	C₂²×C₅₃	semidirect
640. #474	C₂²×C₅₃	semidirect
641. #470	C₂²×C₅₃	semidirect
642. #470	C₂²×C₅₃	semidirect
643. #469	C₂²×C₅₃	semidirect
644. #468	C₂²×C₅₃	semidirect
645. #468	C₂²×C₅₃	semidirect
646. #468	C₂²×C₅₃	semidirect
647. #467	C₂²×C₅₃	semidirect
648. #465	C₂²×C₅₃	semidirect
649. #464	C₂²×C₅₃	semidirect
650. #463	C₂²×C₅₃	semidirect
651. #463	C₂²×C₅₃	semidirect
652. #463	C₂²×C₅₃	semidirect
653. #462	C₂²×C₅₃	semidirect
654. #461	C₂²×C₅₃	semidirect
655. #452	C₂²×C₅₃	semidirect
656. #452	C₂²×C₅₃	semidirect
657. #452	C₂²×C₅₃	semidirect
658. #452	C₂²×C₅₃	semidirect
659. #452	C₂²×C₅₃	semidirect
660. #452	C₂²×C₅₃	semidirect
661. #451	C₂²×C₅₃	semidirect
662. #451	C₂²×C₅₃	semidirect
663. #450	C₂²×C₅₃	semidirect
664. #450	C₂²×C₅₃	semidirect
665. #450	C₂²×C₅₃	semidirect
667. #449	C₂²×C₅₃	semidirect
668. #449	C₂²×C₅₃	semidirect
669. #449	C₂²×C₅₃	semidirect
670. #448	C₂²×C₅₃	semidirect
671. #448	C₂²×C₅₃	semidirect
673. #447	C₂²×C₅₃	semidirect
674. #447	C₂²×C₅₃	semidirect
675. #442	C₂²×C₅₃	semidirect
676. #440	C₂²×C₅₃	semidirect
677. C₄×SD₁₆	C₂²×C₅₃	semidirect
678. C₄×D₈	C₂²×C₅₃	semidirect
679. #436	C₂²×C₅₃	semidirect
680. #436	C₂²×C₅₃	semidirect
681. #435	C₂²×C₅₃	semidirect
682. #435	C₂²×C₅₃	semidirect
683. #433	C₂²×C₅₃	semidirect
684. #417	C₂²×C₅₃	semidirect
685. #417	C₂²×C₅₃	semidirect
686. #417	C₂²×C₅₃	semidirect
687. C₂×#102	C₂²×C₅₃	semidirect
688. #408	C₂²×C₅₃	semidirect
689. #407	C₂²×C₅₃	semidirect
690. #407	C₂²×C₅₃	semidirect
691. C₅₃	#61647	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×#3536	2
C₅₃×#3485	2
C₅₃×#3331	2
C₅₃×#3330	2
C₅₃×#3314	2
C₅₃×#3306	2
C₅₃×#3275	2
C₅₃×#3273	2
C₅₃×#3269	2
C₅₃×#3267	2
C₅₃×#3225	2
C₅₃×#3201	2
C₅₃×#3196	2
C₅₃×#3194	2
C₅₃×#3118	2
C₅₃×#3012	2
C₅₃×#3007	2
C₅₃×#3006	2
C₅₃×#2978	2
#61647	53

Subgroups — C53×#61647 #27269159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61647 #27269159