Subgroups — C₅₃×#61326 #27268838

Order 13568.

1806 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3372	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3361	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3360	C₂	1	4	yes	maximal, complemented
8	C₅₃×#3359	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3137	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3084	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3042	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic
15	C₅₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#559	C₂²	1	2	yes	complemented
21	C₅₃×#557	C₂²	1	2	yes	complemented
22	C₅₃×#556	—	2	1	no	—
23	C₅₃×#556	C₂²	1	4	yes	complemented
24	C₅₃×#554	—	2	1	no	—
25	C₅₃×#554	—	2	1	no	—
26	C₅₃×#554	—	2	2	no	—
27	C₅₃×#554	C₂²	1	4	yes	—
28	C₅₃×#554	C₂²	1	2	yes	—
29	C₅₃×#552	—	2	2	no	—
30	D₄×Q₈×C₅₃	—	2	1	no	—
31	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
32	C₅₃×#544	C₂²	1	2	yes	—
33	C₅₃×#543	—	2	2	no	—
34	C₅₃×#539	—	2	2	no	—
35	C₅₃×#536	C₂²	1	2	yes	—
36	C₅₃×#533	C₂²	1	1	yes	characteristic
37	C₅₃×#533	C₂²	1	1	yes	characteristic
38	C₅₃×#532	C₂²	1	1	yes	characteristic
39	C₅₃×#529	—	2	2	no	—
40	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
41	C₅₃×#520	C₂²	1	2	yes	—
42	C₅₃×#518	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#491	C₂²	1	4	yes	complemented
46	C₅₃×#489	C₂²	1	4	yes	complemented
47	C₅₃×#488	C₂²	1	2	yes	complemented
48	C₅₃×#488	C₂²	1	4	yes	complemented
49	C₅₃×#488	C₂²	1	2	yes	complemented
50	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#487	C₂²	1	4	yes	complemented
52	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#479	C₂²	1	4	yes	complemented
56	C₅₃×#479	C₂²	1	4	yes	complemented
57	C₅₃×#478	C₂²	1	4	yes	complemented
58	C₅₃×#477	C₂²	1	2	yes	complemented
59	C₅₃×#476	C₂²	1	4	yes	complemented
60	C₅₃×#475	C₂²	1	2	yes	complemented
61	C₅₃×#475	C₂²	1	4	yes	complemented
62	C₅₃×#463	C₂²	1	4	yes	—
63	C₅₃×#463	C₂²	1	4	yes	—
64	C₅₃×#463	C₂²	1	4	yes	—
65	C₅₃×#461	C₂²	1	2	yes	—
66	C₅₃×#461	C₂²	1	4	yes	—
67	C₅₃×#461	C₂²	1	4	yes	—
68	C₅₃×#459	C₂²	1	2	yes	—
69	C₅₃×#446	C₂²	1	2	yes	complemented
70	C₅₃×#446	C₂²	1	2	yes	complemented
71	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
73	C₅₃×#442	C₂²	1	4	yes	—
74	C₅₃×#440	C₂²	1	4	yes	—
75	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
76	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
77	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
80	C₄×D₈×C₅₃	C₂²	1	4	yes	—
81	C₅₃×#428	C₂²	1	2	yes	—
82	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
83	C₅₃×#424	C₂²	1	2	yes	—
84	C₅₃×#423	C₂²	1	1	yes	characteristic
85	C₅₃×#419	C₂²	1	2	yes	—
86	C₅₃×#417	C₂²	1	2	yes	—
87	C₅₃×#416	C₂²	1	2	yes	—
88	C₅₃×#416	C₂²	1	2	yes	—
89	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
90	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
91	C₅₃×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₅₃	C₂³	1	2	yes	—
94	C₂²×Q₈×C₅₃	—	2	2	no	—
95	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₃	—	2	1	no	—
98	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
99	C₂×SD₁₆×C₅₃	—	2	4	no	—
100	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
103	C₂×D₈×C₅₃	C₂³	1	4	yes	—
104	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₃	—	2	2	no	—
108	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
109	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
110	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
115	#127×C₅₃	C₂³	1	1	yes	characteristic
116	#126×C₅₃	—	2	4	no	—
117	#126×C₅₃	—	2	4	no	—
118	#125×C₅₃	—	2	2	no	—
119	#125×C₅₃	—	2	4	no	—
120	#125×C₅₃	—	2	2	no	—
121	#125×C₅₃	D₄	1	2	yes	—
122	#125×C₅₃	C₂³	1	2	yes	—
123	#125×C₅₃	C₂³	1	4	yes	—
124	#124×C₅₃	—	2	2	no	—
125	#124×C₅₃	C₂³	1	2	yes	—
126	#124×C₅₃	C₂³	1	4	yes	—
127	#123×C₅₃	—	2	4	no	—
128	#123×C₅₃	—	2	4	no	—
129	C₂²⋊Q₈×C₅₃	—	2	2	no	—
130	C₂²⋊Q₈×C₅₃	—	2	4	no	—
131	C₂²⋊Q₈×C₅₃	—	2	2	no	—
132	C₂²⋊Q₈×C₅₃	—	2	2	no	—
133	C₂²⋊Q₈×C₅₃	—	2	4	no	—
134	C₂²⋊Q₈×C₅₃	—	2	4	no	—
135	C₂²⋊Q₈×C₅₃	—	2	4	no	—
136	C₂²⋊Q₈×C₅₃	—	2	4	no	—
137	C₂²⋊Q₈×C₅₃	—	2	2	no	—
138	C₂²⋊Q₈×C₅₃	—	2	4	no	—
139	C₂²⋊Q₈×C₅₃	—	2	4	no	—
140	C₂²⋊Q₈×C₅₃	—	2	1	no	—
141	C₂²⋊Q₈×C₅₃	—	2	1	no	—
142	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
143	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
144	#121×C₅₃	—	2	1	no	—
145	#121×C₅₃	—	2	1	no	—
146	C₄×Q₈×C₅₃	—	2	1	no	—
147	C₄×Q₈×C₅₃	—	2	1	no	—
148	C₄×Q₈×C₅₃	—	2	1	no	—
149	C₄×Q₈×C₅₃	—	2	1	no	—
150	C₄×Q₈×C₅₃	—	2	2	no	—
151	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
156	C₄×D₄×C₅₃	—	2	2	no	—
157	C₄×D₄×C₅₃	—	2	2	no	—
158	C₄×D₄×C₅₃	—	2	2	no	—
159	C₄×D₄×C₅₃	—	2	4	no	—
160	C₄×D₄×C₅₃	—	2	1	no	—
161	C₄×D₄×C₅₃	—	2	1	no	—
162	C₄×D₄×C₅₃	—	2	1	no	—
163	C₄×D₄×C₅₃	—	2	1	no	—
164	C₄×D₄×C₅₃	C₂³	1	2	yes	—
165	C₄×D₄×C₅₃	C₂³	1	2	yes	—
166	C₄×D₄×C₅₃	C₂³	1	4	yes	—
167	C₄×D₄×C₅₃	C₂³	1	4	yes	—
168	C₄×D₄×C₅₃	C₂³	1	4	yes	—
169	#117×C₅₃	—	2	2	no	—
170	#117×C₅₃	—	2	4	no	—
171	#117×C₅₃	C₂³	1	2	yes	—
172	#117×C₅₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
174	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
175	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
176	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
180	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
181	C₂×C₄²×C₅₃	—	2	1	no	—
182	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
183	#107×C₅₃	C₂³	1	4	yes	—
184	#106×C₅₃	C₂³	1	2	yes	—
185	#106×C₅₃	C₂³	1	2	yes	—
186	#106×C₅₃	C₂³	1	4	yes	—
187	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
188	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
189	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
190	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
191	#103×C₅₃	C₂³	1	2	yes	—
192	#103×C₅₃	C₂³	1	2	yes	—
193	#103×C₅₃	C₂³	1	2	yes	—
194	#103×C₅₃	C₂³	1	2	yes	—
195	#103×C₅₃	C₂³	1	2	yes	—
196	#103×C₅₃	C₂³	1	4	yes	—
197	#103×C₅₃	C₂³	1	4	yes	—
198	#103×C₅₃	C₂³	1	4	yes	—
199	#103×C₅₃	C₂³	1	2	yes	—
200	#102×C₅₃	C₂³	1	2	yes	—
201	#102×C₅₃	C₂³	1	2	yes	—
202	#102×C₅₃	C₂³	1	2	yes	—
203	#102×C₅₃	C₂³	1	2	yes	—
204	#102×C₅₃	C₂³	1	4	yes	—
205	#102×C₅₃	C₂³	1	2	yes	—
206	#102×C₅₃	C₂³	1	2	yes	—
207	#97×C₅₃	C₂³	1	4	yes	—
208	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₅₃	C₂³	1	4	yes	—
211	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
213	C₂⁴×C₅₃	—	2	1	no	—
214	#41×C₅₃	—	2	4	no	—
215	#41×C₅₃	—	2	4	no	—
216	C₂×Q₈×C₅₃	—	2	1	no	—
217	C₂×Q₈×C₅₃	—	2	1	no	—
218	C₂×Q₈×C₅₃	—	2	1	no	—
219	C₂×Q₈×C₅₃	—	2	4	no	—
220	C₂×Q₈×C₅₃	—	2	2	no	—
221	C₂×Q₈×C₅₃	—	2	2	no	—
222	C₂×Q₈×C₅₃	—	8	4	no	—
223	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₅₃	—	2	2	no	—
228	C₂×D₄×C₅₃	—	2	1	no	—
229	C₂×D₄×C₅₃	—	2	1	no	—
230	C₂×D₄×C₅₃	—	2	1	no	—
231	C₂×D₄×C₅₃	—	2	2	no	—
232	C₂×D₄×C₅₃	#41	1	4	yes	—
233	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅₃	—	2	1	no	—
236	C₂²×C₄×C₅₃	—	2	1	no	—
237	C₂²×C₄×C₅₃	—	2	1	no	—
238	C₂²×C₄×C₅₃	—	2	2	no	—
239	C₂²×C₄×C₅₃	—	2	2	no	—
240	C₂²×C₄×C₅₃	—	2	4	no	—
241	C₂²×C₄×C₅₃	—	2	4	no	—
242	C₂²×C₄×C₅₃	—	2	2	no	—
243	C₂²×C₄×C₅₃	—	2	4	no	—
244	C₂²×C₄×C₅₃	—	8	2	no	—
245	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₅₃	—	2	4	no	—
249	SD₁₆×C₅₃	—	2	4	no	—
250	SD₁₆×C₅₃	—	2	8	no	—
251	D₈×C₅₃	—	2	8	no	—
252	M₁₆×C₅₃	—	2	4	no	—
253	C₂×C₈×C₅₃	—	2	2	no	—
254	C₂×C₈×C₅₃	—	2	2	no	—
255	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
260	C₄⋊C₄×C₅₃	—	2	1	no	—
261	C₄⋊C₄×C₅₃	—	2	2	no	—
262	C₄⋊C₄×C₅₃	—	2	1	no	—
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	—	2	2	no	—
265	C₄⋊C₄×C₅₃	—	2	2	no	—
266	C₄⋊C₄×C₅₃	—	2	4	no	—
267	C₄⋊C₄×C₅₃	—	2	4	no	—
268	C₄⋊C₄×C₅₃	—	2	4	no	—
269	C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₄⋊C₄×C₅₃	—	2	4	no	—
271	C₄⋊C₄×C₅₃	—	2	1	no	—
272	C₄⋊C₄×C₅₃	—	2	1	no	—
273	C₄⋊C₄×C₅₃	—	2	2	no	—
274	C₄⋊C₄×C₅₃	—	2	1	no	—
275	C₄⋊C₄×C₅₃	—	2	4	no	—
276	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₅₃	—	2	2	no	—
287	C₂²⋊C₄×C₅₃	—	2	2	no	—
288	C₂²⋊C₄×C₅₃	—	2	2	no	—
289	C₂²⋊C₄×C₅₃	—	2	4	no	—
290	C₂²⋊C₄×C₅₃	—	2	4	no	—
291	C₂²⋊C₄×C₅₃	—	2	2	no	—
292	C₂²⋊C₄×C₅₃	—	2	4	no	—
293	C₂²⋊C₄×C₅₃	—	2	4	no	—
294	C₂²⋊C₄×C₅₃	—	2	2	no	—
295	C₂²⋊C₄×C₅₃	—	2	4	no	—
296	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
297	C₄²×C₅₃	—	2	2	no	—
298	C₄²×C₅₃	—	2	2	no	—
299	C₄²×C₅₃	—	2	4	no	—
300	C₄²×C₅₃	—	2	2	no	—
301	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₄²×C₅₃	C₂⁴	1	4	yes	—
306	C₂³×C₅₃	—	2	2	no	—
307	C₂³×C₅₃	—	2	4	no	—
308	C₂³×C₅₃	—	2	2	no	—
309	C₂³×C₅₃	—	8	1	no	—
310	C₂³×C₅₃	—	8	1	no	—
311	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₅₃	—	2	4	no	—
313	Q₈×C₅₃	—	2	2	no	—
314	Q₈×C₅₃	—	2	2	no	—
315	Q₈×C₅₃	—	2	2	no	—
316	Q₈×C₅₃	—	2	2	no	—
317	Q₈×C₅₃	—	4	2	no	—
318	Q₈×C₅₃	—	4	2	no	—
319	Q₈×C₅₃	—	4	2	no	—
320	Q₈×C₅₃	—	8	1	no	—
321	Q₈×C₅₃	—	8	4	no	—
322	D₄×C₅₃	—	2	4	no	—
323	D₄×C₅₃	—	2	2	no	—
324	D₄×C₅₃	—	2	2	no	—
325	D₄×C₅₃	—	2	2	no	—
326	D₄×C₅₃	—	4	4	no	—
327	D₄×C₅₃	—	4	2	no	—
328	D₄×C₅₃	—	8	1	no	—
329	D₄×C₅₃	C₂×#41	1	4	yes	—
330	C₂×C₄×C₅₃	—	2	2	no	—
331	C₂×C₄×C₅₃	—	2	2	no	—
332	C₂×C₄×C₅₃	—	2	2	no	—
333	C₂×C₄×C₅₃	—	2	2	no	—
334	C₂×C₄×C₅₃	—	2	2	no	—
335	C₂×C₄×C₅₃	—	2	2	no	—
336	C₂×C₄×C₅₃	—	2	2	no	—
337	C₂×C₄×C₅₃	—	4	1	no	—
338	C₂×C₄×C₅₃	—	4	2	no	—
339	C₂×C₄×C₅₃	—	4	4	no	—
340	C₂×C₄×C₅₃	—	4	4	no	—
341	C₂×C₄×C₅₃	—	8	4	no	—
342	C₂×C₄×C₅₃	—	8	4	no	—
343	C₂×C₄×C₅₃	—	8	2	no	—
344	C₂×C₄×C₅₃	—	8	4	no	—
345	C₂×C₄×C₅₃	—	8	1	no	—
346	C₂×C₄×C₅₃	—	8	1	no	—
347	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
355	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
356	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
357	C₈×C₅₃	—	2	1	no	—
358	C₈×C₅₃	—	2	1	no	—
359	C₈×C₅₃	—	2	4	no	—
360	C₈×C₅₃	—	2	1	no	—
361	C₈×C₅₃	—	2	1	no	—
362	#61326	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
363	C₂²×C₅₃	—	2	1	no	—
364	C₂²×C₅₃	—	2	1	no	—
365	C₂²×C₅₃	—	2	4	no	—
366	C₂²×C₅₃	—	4	2	no	—
367	C₂²×C₅₃	—	4	2	no	—
368	C₂²×C₅₃	—	4	2	no	—
369	C₂²×C₅₃	—	4	2	no	—
370	C₂²×C₅₃	—	4	2	no	—
371	C₂²×C₅₃	—	8	4	no	—
372	C₂²×C₅₃	#548	1	2	yes	—
373	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₅₃	—	2	1	no	—
375	C₄×C₅₃	—	2	1	no	—
376	C₄×C₅₃	—	2	4	no	—
377	C₄×C₅₃	—	2	1	no	—
378	C₄×C₅₃	—	2	4	no	—
379	C₄×C₅₃	—	4	2	no	—
380	C₄×C₅₃	—	4	2	no	—
381	C₄×C₅₃	—	4	2	no	—
382	C₄×C₅₃	—	4	2	no	—
383	C₄×C₅₃	—	4	2	no	—
384	C₄×C₅₃	—	4	2	no	—
385	C₄×C₅₃	#548	1	2	yes	—
386	C₄×C₅₃	#577	1	2	yes	—
387	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
388	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
389	#3507	C₂×C₅₃	1	1	yes	characteristic, complemented
390	#3501	C₂×C₅₃	1	1	yes	characteristic, complemented
391	#3376	C₂×C₅₃	1	4	yes	complemented
392	#3373	C₂×C₅₃	1	2	yes	complemented
393	#3372	C₂×C₅₃	1	2	yes	complemented
394	#3361	C₂×C₅₃	1	2	yes	complemented
395	#3360	C₂×C₅₃	1	4	yes	complemented
396	#3359	C₂×C₅₃	1	2	yes	complemented
397	#3137	C₂×C₅₃	1	2	yes	complemented
398	#3131	C₂×C₅₃	1	1	yes	characteristic, complemented
399	#3084	C₂×C₅₃	1	2	yes	complemented
400	#3078	C₂×C₅₃	1	1	yes	characteristic, complemented
401	#3042	C₂×C₅₃	1	2	yes	complemented
402	#3036	C₂×C₅₃	1	1	yes	characteristic
403	#2960	C₂×C₅₃	1	1	yes	characteristic, complemented
404	#2946	C₂×C₅₃	1	2	yes	complemented
405	C₂×C₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
406	C₂×C₅₃	—	2	2	no	—
407	C₂×C₅₃	—	4	4	no	—
408	C₂×C₅₃	—	8	2	no	—
409	C₂×C₅₃	C₂×#548	1	1	yes	characteristic
410	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
411	C₂×C₅₃	#3584	1	1	yes	characteristic
412	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
413	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
414	#559	C₂²×C₅₃	1	2	yes	complemented
415	#557	C₂²×C₅₃	1	2	yes	complemented
416	#556	—	2	1	no	—
417	#556	C₂²×C₅₃	1	4	yes	complemented
418	#554	—	2	1	no	—
419	#554	—	2	1	no	—
420	#554	—	2	2	no	—
421	#554	C₂²×C₅₃	1	4	yes	—
422	#554	C₂²×C₅₃	1	2	yes	—
423	#552	—	2	2	no	—
424	D₄×Q₈	—	2	1	no	—
425	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
426	#544	C₂²×C₅₃	1	2	yes	—
427	#543	—	2	2	no	—
428	#539	—	2	2	no	—
429	#536	C₂²×C₅₃	1	2	yes	—
430	#533	C₂²×C₅₃	1	1	yes	characteristic
431	#533	C₂²×C₅₃	1	1	yes	characteristic
432	#532	C₂²×C₅₃	1	1	yes	characteristic
433	#529	—	2	2	no	—
434	C₂×C₂²⋊Q₈	—	2	2	no	—
435	#520	C₂²×C₅₃	1	2	yes	—
436	#518	C₂²×C₅₃	1	2	yes	—
437	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
439	#491	C₂²×C₅₃	1	4	yes	complemented
440	#489	C₂²×C₅₃	1	4	yes	complemented
441	#488	C₂²×C₅₃	1	2	yes	complemented
442	#488	C₂²×C₅₃	1	4	yes	complemented
443	#488	C₂²×C₅₃	1	2	yes	complemented
444	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
445	#487	C₂²×C₅₃	1	4	yes	complemented
446	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
447	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
448	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
449	#479	C₂²×C₅₃	1	4	yes	complemented
450	#479	C₂²×C₅₃	1	4	yes	complemented
451	#478	C₂²×C₅₃	1	4	yes	complemented
452	#477	C₂²×C₅₃	1	2	yes	complemented
453	#476	C₂²×C₅₃	1	4	yes	complemented
454	#475	C₂²×C₅₃	1	2	yes	complemented
455	#475	C₂²×C₅₃	1	4	yes	complemented
456	#463	C₂²×C₅₃	1	4	yes	—
457	#463	C₂²×C₅₃	1	4	yes	—
458	#463	C₂²×C₅₃	1	4	yes	—
459	#461	C₂²×C₅₃	1	2	yes	—
460	#461	C₂²×C₅₃	1	4	yes	—
461	#461	C₂²×C₅₃	1	4	yes	—
462	#459	C₂²×C₅₃	1	2	yes	—
463	#446	C₂²×C₅₃	1	2	yes	complemented
464	#446	C₂²×C₅₃	1	2	yes	complemented
465	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
466	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
467	#442	C₂²×C₅₃	1	4	yes	—
468	#440	C₂²×C₅₃	1	4	yes	—
469	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
470	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
471	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
472	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
473	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
474	C₄×D₈	C₂²×C₅₃	1	4	yes	—
475	#428	C₂²×C₅₃	1	2	yes	—
476	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
477	#424	C₂²×C₅₃	1	2	yes	—
478	#423	C₂²×C₅₃	1	1	yes	characteristic
479	#419	C₂²×C₅₃	1	2	yes	—
480	#417	C₂²×C₅₃	1	2	yes	—
481	#416	C₂²×C₅₃	1	2	yes	—
482	#416	C₂²×C₅₃	1	2	yes	—
483	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
484	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
485	#405	C₂²×C₅₃	1	2	yes	—
486	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
487	C₅₃	#61326	1	1	yes	characteristic, direct product factor, Sylow
488	C₂×#41	C₂³×C₅₃	1	2	yes	—
489	C₂²×Q₈	—	2	2	no	—
490	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
492	C₂³×C₄	—	2	1	no	—
493	AGL(1,ℤ/8)	—	2	8	no	—
494	C₂×SD₁₆	—	2	4	no	—
495	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
497	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
498	C₂×D₈	C₂³×C₅₃	1	4	yes	—
499	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
500	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
502	C₄⋊Q₈	—	2	2	no	—
503	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
504	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
507	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
510	#127	C₂³×C₅₃	1	1	yes	characteristic
511	#126	—	2	4	no	—
512	#126	—	2	4	no	—
513	#125	—	2	2	no	—
514	#125	—	2	4	no	—
515	#125	—	2	2	no	—
516	#125	D₄×C₅₃	1	2	yes	—
517	#125	C₂³×C₅₃	1	2	yes	—
518	#125	C₂³×C₅₃	1	4	yes	—
519	#124	—	2	2	no	—
520	#124	C₂³×C₅₃	1	2	yes	—
521	#124	C₂³×C₅₃	1	4	yes	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
538	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
548	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
549	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
550	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	4	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	C₂³×C₅₃	1	2	yes	—
560	C₄×D₄	C₂³×C₅₃	1	2	yes	—
561	C₄×D₄	C₂³×C₅₃	1	4	yes	—
562	C₄×D₄	C₂³×C₅₃	1	4	yes	—
563	C₄×D₄	C₂³×C₅₃	1	4	yes	—
564	#117	—	2	2	no	—
565	#117	—	2	4	no	—
566	#117	C₂³×C₅₃	1	2	yes	—
567	#117	C₂³×C₅₃	1	2	yes	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	2	no	—
570	C₂×C₄⋊C₄	—	2	4	no	—
571	C₂×C₄⋊C₄	—	2	2	no	—
572	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	4	no	—
576	C₂×C₄²	—	2	1	no	—
577	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
578	#107	C₂³×C₅₃	1	4	yes	—
579	#106	C₂³×C₅₃	1	2	yes	—
580	#106	C₂³×C₅₃	1	2	yes	—
581	#106	C₂³×C₅₃	1	4	yes	—
582	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
583	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
584	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
585	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
586	#103	C₂³×C₅₃	1	2	yes	—
587	#103	C₂³×C₅₃	1	2	yes	—
588	#103	C₂³×C₅₃	1	2	yes	—
589	#103	C₂³×C₅₃	1	2	yes	—
590	#103	C₂³×C₅₃	1	2	yes	—
591	#103	C₂³×C₅₃	1	2	yes	—
592	#103	C₂³×C₅₃	1	4	yes	—
593	#103	C₂³×C₅₃	1	4	yes	—
594	#103	C₂³×C₅₃	1	4	yes	—
595	#102	C₂³×C₅₃	1	2	yes	—
596	#102	C₂³×C₅₃	1	2	yes	—
597	#102	C₂³×C₅₃	1	2	yes	—
598	#102	C₂³×C₅₃	1	2	yes	—
599	#102	C₂³×C₅₃	1	2	yes	—
600	#102	C₂³×C₅₃	1	2	yes	—
601	#102	C₂³×C₅₃	1	4	yes	—
602	#97	C₂³×C₅₃	1	4	yes	—
603	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
604	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
605	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
607	C₄×C₈	C₂³×C₅₃	1	4	yes	—
608	C₂⁴	—	2	1	no	—
609	#41	—	2	4	no	—
610	#41	—	2	4	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	8	4	no	—
618	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
619	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	#41×C₅₃	1	4	yes	—
628	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
629	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	8	2	no	—
640	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
643	SD₁₆	—	2	4	no	—
644	SD₁₆	—	2	4	no	—
645	SD₁₆	—	2	8	no	—
646	D₈	—	2	8	no	—
647	M₁₆	—	2	4	no	—
648	C₂×C₈	—	2	2	no	—
649	C₂×C₈	—	2	2	no	—
650	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
672	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
673	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
676	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
697	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
698	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
699	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
700	C₄²	C₂⁴×C₅₃	1	4	yes	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	8	1	no	—
705	C₂³	—	8	1	no	—
706	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	2	2	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	4	2	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	4	2	no	—
715	Q₈	—	8	1	no	—
716	Q₈	—	8	4	no	—
717	D₄	—	2	4	no	—
718	D₄	—	2	2	no	—
719	D₄	—	2	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	1	no	—
724	D₄	C₂×#41×C₅₃	1	4	yes	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	2	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	1	no	—
742	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
744	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
747	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
749	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
750	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
751	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
752	C₈	—	2	1	no	—
753	C₈	—	2	1	no	—
754	C₈	—	2	4	no	—
755	C₈	—	2	1	no	—
756	C₈	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	8	4	no	—
766	C₂²	C₅₃×#548	1	2	yes	—
767	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
768	C₄	—	2	1	no	—
769	C₄	—	2	4	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	4	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	C₅₃×#548	1	2	yes	—
780	C₄	C₅₃×#577	1	2	yes	—
781	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
782	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
783	C₂	—	2	2	no	—
784	C₂	—	4	4	no	—
785	C₂	—	8	2	no	—
786	C₂	C₂×C₅₃×#548	1	1	yes	characteristic
787	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
788	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×#3036	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×#3507	C₂	semidirect
2. C₅₃×#3501	C₂	semidirect
3. C₅₃×#3376	C₂	semidirect
4. C₅₃×#3373	C₂	semidirect
5. C₅₃×#3372	C₂	semidirect
6. C₅₃×#3361	C₂	semidirect
7. C₅₃×#3360	C₂	semidirect
8. C₅₃×#3359	C₂	semidirect
9. C₅₃×#3137	C₂	semidirect
10. C₅₃×#3131	C₂	semidirect
11. C₅₃×#3084	C₂	semidirect
12. C₅₃×#3078	C₂	semidirect
13. C₅₃×#3042	C₂	semidirect
15. C₅₃×#2960	C₂	semidirect
16. C₅₃×#2946	C₂	semidirect
17. C₂×C₄×SD₁₆×C₅₃	C₂	semidirect
20. C₅₃×#559	C₂²	semidirect
21. C₅₃×#557	C₂²	semidirect
23. C₅₃×#556	C₂²	semidirect
45. C₅₃×#491	C₂²	semidirect
46. C₅₃×#489	C₂²	semidirect
47. C₅₃×#488	C₂²	semidirect
48. C₅₃×#488	C₂²	semidirect
49. C₅₃×#488	C₂²	semidirect
50. C₅₃×#487	C₂²	semidirect
51. C₅₃×#487	C₂²	semidirect
52. C₅₃×#487	C₂²	semidirect
53. C₅₃×#486	C₂²	semidirect
54. C₅₃×#486	C₂²	semidirect
55. C₅₃×#479	C₂²	semidirect
56. C₅₃×#479	C₂²	semidirect
57. C₅₃×#478	C₂²	semidirect
58. C₅₃×#477	C₂²	semidirect
59. C₅₃×#476	C₂²	semidirect
60. C₅₃×#475	C₂²	semidirect
61. C₅₃×#475	C₂²	semidirect
69. C₅₃×#446	C₂²	semidirect
70. C₅₃×#446	C₂²	semidirect
71. C₈×Q₈×C₅₃	C₂²	semidirect
72. C₈×Q₈×C₅₃	C₂²	semidirect
362. #61326	C₅₃	direct (N × H)
389. #3507	C₂×C₅₃	semidirect
390. #3501	C₂×C₅₃	semidirect
391. #3376	C₂×C₅₃	semidirect
392. #3373	C₂×C₅₃	semidirect
393. #3372	C₂×C₅₃	semidirect
394. #3361	C₂×C₅₃	semidirect
395. #3360	C₂×C₅₃	semidirect
396. #3359	C₂×C₅₃	semidirect
397. #3137	C₂×C₅₃	semidirect
398. #3131	C₂×C₅₃	semidirect
399. #3084	C₂×C₅₃	semidirect
400. #3078	C₂×C₅₃	semidirect
401. #3042	C₂×C₅₃	semidirect
403. #2960	C₂×C₅₃	semidirect
404. #2946	C₂×C₅₃	semidirect
405. C₂×C₄×SD₁₆	C₂×C₅₃	semidirect
414. #559	C₂²×C₅₃	semidirect
415. #557	C₂²×C₅₃	semidirect
417. #556	C₂²×C₅₃	semidirect
439. #491	C₂²×C₅₃	semidirect
440. #489	C₂²×C₅₃	semidirect
441. #488	C₂²×C₅₃	semidirect
442. #488	C₂²×C₅₃	semidirect
443. #488	C₂²×C₅₃	semidirect
444. #487	C₂²×C₅₃	semidirect
445. #487	C₂²×C₅₃	semidirect
446. #487	C₂²×C₅₃	semidirect
447. #486	C₂²×C₅₃	semidirect
448. #486	C₂²×C₅₃	semidirect
449. #479	C₂²×C₅₃	semidirect
450. #479	C₂²×C₅₃	semidirect
451. #478	C₂²×C₅₃	semidirect
452. #477	C₂²×C₅₃	semidirect
453. #476	C₂²×C₅₃	semidirect
454. #475	C₂²×C₅₃	semidirect
455. #475	C₂²×C₅₃	semidirect
463. #446	C₂²×C₅₃	semidirect
464. #446	C₂²×C₅₃	semidirect
465. C₈×Q₈	C₂²×C₅₃	semidirect
466. C₈×Q₈	C₂²×C₅₃	semidirect
487. C₅₃	#61326	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×#3507	2
C₅₃×#3501	2
C₅₃×#3376	2
C₅₃×#3373	2
C₅₃×#3372	2
C₅₃×#3361	2
C₅₃×#3360	2
C₅₃×#3359	2
C₅₃×#3137	2
C₅₃×#3131	2
C₅₃×#3084	2
C₅₃×#3078	2
C₅₃×#3042	2
C₅₃×#3036	2
C₅₃×#2960	2
C₅₃×#2946	2
C₂×C₄×SD₁₆×C₅₃	2
#61326	53

Subgroups — C53×#61326 #27268838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61326 #27268838