Subgroups — C₅₃×#61285 #27268797

Order 13568.

1818 conjugacy classes of subgroups.

The subgroup lattice has 788 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×#3506	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3353	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3351	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3340	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3337	C₂	1	4	yes	maximal, complemented
8	C₅₃×#3335	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3097	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3096	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3057	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2912	C₂	1	2	yes	maximal, complemented
18	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#131×C₅₃	C₂²	1	2	yes	—
20	C₅₃×#559	—	2	1	no	—
21	C₅₃×#559	—	2	2	no	—
22	C₅₃×#557	—	2	1	no	—
23	C₅₃×#556	—	2	1	no	—
24	C₅₃×#556	—	2	2	no	—
25	C₅₃×#556	C₂²	1	2	yes	complemented
26	C₅₃×#555	C₂²	1	2	yes	—
27	C₅₃×#554	C₂²	1	2	yes	complemented
28	C₅₃×#553	C₂²	1	4	yes	—
29	C₅₃×#552	C₂²	1	4	yes	complemented
30	C₅₃×#550	—	2	1	no	—
31	C₅₃×#547	C₂²	1	2	yes	—
32	C₅₃×#539	—	2	2	no	—
33	C₅₃×#538	—	2	2	no	—
34	C₅₃×#536	C₂²	1	2	yes	—
35	C₅₃×#535	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	C₅₃×#525	—	2	2	no	—
41	C₅₃×#520	C₂²	1	2	yes	—
42	C₅₃×#520	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×#500	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#499	C₂²	1	2	yes	complemented
48	C₅₃×#499	C₂²	1	2	yes	complemented
49	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#485	C₂²	1	4	yes	complemented
52	C₅₃×#485	C₂²	1	4	yes	complemented
53	C₅₃×#484	C₂²	1	4	yes	complemented
54	C₅₃×#483	C₂²	1	4	yes	complemented
55	C₅₃×#482	C₂²	1	4	yes	—
56	C₅₃×#482	C₂²	1	4	yes	—
57	C₅₃×#481	C₂²	1	4	yes	—
58	C₅₃×#480	C₂²	1	4	yes	—
59	C₅₃×#479	C₂²	1	4	yes	complemented
60	C₅₃×#478	C₂²	1	4	yes	—
61	C₅₃×#477	C₂²	1	2	yes	complemented
62	C₅₃×#476	C₂²	1	2	yes	—
63	C₅₃×#475	C₂²	1	2	yes	complemented
64	C₅₃×#474	C₂²	1	2	yes	—
65	C₅₃×#468	C₂²	1	4	yes	—
66	C₅₃×#468	C₂²	1	4	yes	—
67	C₅₃×#465	C₂²	1	4	yes	—
68	C₅₃×#465	C₂²	1	4	yes	—
69	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
70	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
71	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
72	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
73	C₅₃×#436	C₂²	1	2	yes	complemented
74	C₅₃×#436	C₂²	1	2	yes	complemented
75	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
76	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
77	C₅₃×#428	C₂²	1	2	yes	—
78	C₅₃×#428	C₂²	1	2	yes	—
79	C₅₃×#428	C₂²	1	4	yes	complemented
80	C₅₃×#428	C₂²	1	4	yes	complemented
81	C₅₃×#427	C₂²	1	2	yes	—
82	C₅₃×#427	C₂²	1	2	yes	—
83	C₅₃×#427	C₂²	1	4	yes	complemented
84	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
85	C₂×#106×C₅₃	C₂²	1	4	yes	complemented
86	C₅₃×#423	C₂²	1	1	yes	characteristic
87	C₅₃×#419	C₂²	1	2	yes	—
88	C₅₃×#418	C₂²	1	2	yes	—
89	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
90	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
91	C₅₃×#408	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₅₃	—	2	2	no	—
94	C₂×#41×C₅₃	C₂³	1	2	yes	—
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	C₂×SD₁₆×C₅₃	—	2	4	no	—
99	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
101	#131×C₅₃	—	2	8	no	—
102	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
103	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
104	C₂²×C₈×C₅₃	C₂³	1	4	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	C₂³	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	1	yes	characteristic
113	#127×C₅₃	—	2	2	no	—
114	#127×C₅₃	D₄	1	1	yes	characteristic
115	#126×C₅₃	—	2	4	no	—
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	C₂³	1	2	yes	—
121	#125×C₅₃	C₂³	1	2	yes	—
122	#124×C₅₃	—	2	4	no	—
123	#124×C₅₃	—	2	2	no	—
124	#124×C₅₃	—	2	2	no	—
125	#124×C₅₃	—	2	2	no	—
126	#124×C₅₃	D₄	1	2	yes	—
127	#123×C₅₃	—	2	4	no	—
128	#123×C₅₃	—	2	4	no	—
129	#123×C₅₃	—	2	4	no	—
130	#123×C₅₃	—	2	4	no	—
131	C₂²⋊Q₈×C₅₃	—	2	2	no	—
132	C₂²⋊Q₈×C₅₃	—	2	4	no	—
133	C₂²⋊Q₈×C₅₃	—	2	1	no	—
134	C₂²⋊Q₈×C₅₃	—	2	1	no	—
135	C₂²⋊Q₈×C₅₃	—	2	1	no	—
136	C₂²⋊Q₈×C₅₃	—	2	1	no	—
137	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
139	#121×C₅₃	—	2	2	no	—
140	#121×C₅₃	—	2	4	no	—
141	#121×C₅₃	D₄	1	2	yes	—
142	#121×C₅₃	D₄	1	2	yes	—
143	#121×C₅₃	C₂³	1	4	yes	—
144	#121×C₅₃	C₂³	1	4	yes	—
145	#120×C₅₃	—	2	4	no	—
146	C₄×Q₈×C₅₃	—	2	2	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	1	no	—
151	C₄×Q₈×C₅₃	—	2	1	no	—
152	C₄×Q₈×C₅₃	—	2	1	no	—
153	C₄×Q₈×C₅₃	—	2	2	no	—
154	C₄×Q₈×C₅₃	—	2	2	no	—
155	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
157	C₄×D₄×C₅₃	—	2	4	no	—
158	C₄×D₄×C₅₃	—	2	1	no	—
159	C₄×D₄×C₅₃	—	2	1	no	—
160	C₄×D₄×C₅₃	—	2	4	no	—
161	C₄×D₄×C₅₃	—	2	4	no	—
162	C₄×D₄×C₅₃	—	2	2	no	—
163	C₄×D₄×C₅₃	—	2	2	no	—
164	C₄×D₄×C₅₃	—	2	2	no	—
165	C₄×D₄×C₅₃	C₂³	1	2	yes	—
166	C₄×D₄×C₅₃	C₂³	1	2	yes	—
167	C₄×D₄×C₅₃	C₂³	1	2	yes	—
168	C₄×D₄×C₅₃	C₂³	1	2	yes	—
169	#117×C₅₃	—	2	2	no	—
170	#117×C₅₃	—	2	4	no	—
171	#117×C₅₃	C₂³	1	4	yes	—
172	#117×C₅₃	C₂³	1	2	yes	—
173	#117×C₅₃	C₂³	1	2	yes	—
174	#117×C₅₃	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
176	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
179	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
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	2	yes	—
184	#107×C₅₃	C₂³	1	4	yes	—
185	#107×C₅₃	C₂³	1	2	yes	—
186	#107×C₅₃	C₂³	1	2	yes	—
187	#107×C₅₃	C₂³	1	2	yes	—
188	#107×C₅₃	C₂³	1	4	yes	—
189	#106×C₅₃	C₂³	1	2	yes	—
190	#106×C₅₃	C₂³	1	4	yes	—
191	#106×C₅₃	C₂³	1	2	yes	—
192	#106×C₅₃	C₂³	1	2	yes	—
193	#106×C₅₃	C₂³	1	2	yes	—
194	#106×C₅₃	C₂³	1	2	yes	—
195	#106×C₅₃	C₂³	1	2	yes	—
196	#106×C₅₃	C₂³	1	4	yes	—
197	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
198	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
199	#103×C₅₃	C₂³	1	2	yes	—
200	#103×C₅₃	C₂³	1	2	yes	—
201	#103×C₅₃	C₂³	1	4	yes	—
202	#103×C₅₃	C₂³	1	4	yes	—
203	#102×C₅₃	C₂³	1	2	yes	—
204	#102×C₅₃	C₂³	1	2	yes	—
205	#102×C₅₃	C₂³	1	4	yes	—
206	#102×C₅₃	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
208	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
209	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
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	#41×C₅₃	—	8	4	no	—
217	C₂×Q₈×C₅₃	—	2	1	no	—
218	C₂×Q₈×C₅₃	—	2	1	no	—
219	C₂×Q₈×C₅₃	—	2	1	no	—
220	C₂×Q₈×C₅₃	—	2	1	no	—
221	C₂×Q₈×C₅₃	—	2	1	no	—
222	C₂×Q₈×C₅₃	—	2	2	no	—
223	C₂×Q₈×C₅₃	—	2	2	no	—
224	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₅₃	—	2	4	no	—
227	C₂×D₄×C₅₃	—	2	4	no	—
228	C₂×D₄×C₅₃	—	2	1	no	—
229	C₂×D₄×C₅₃	—	2	2	no	—
230	C₂×D₄×C₅₃	—	2	2	no	—
231	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₃	—	2	1	no	—
237	C₂²×C₄×C₅₃	—	2	1	no	—
238	C₂²×C₄×C₅₃	—	2	1	no	—
239	C₂²×C₄×C₅₃	—	2	4	no	—
240	C₂²×C₄×C₅₃	—	2	4	no	—
241	C₂²×C₄×C₅₃	—	2	2	no	—
242	C₂²×C₄×C₅₃	—	2	2	no	—
243	C₂²×C₄×C₅₃	—	8	2	no	—
244	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₅₃	—	2	4	no	—
249	SD₁₆×C₅₃	—	2	4	no	—
250	M₁₆×C₅₃	—	2	4	no	—
251	M₁₆×C₅₃	—	2	8	no	—
252	C₂×C₈×C₅₃	—	2	2	no	—
253	C₂×C₈×C₅₃	—	2	8	no	—
254	C₂×C₈×C₅₃	#41	1	4	yes	complemented
255	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
258	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₄⋊C₄×C₅₃	—	2	2	no	—
261	C₄⋊C₄×C₅₃	—	2	2	no	—
262	C₄⋊C₄×C₅₃	—	2	1	no	—
263	C₄⋊C₄×C₅₃	—	2	1	no	—
264	C₄⋊C₄×C₅₃	—	2	4	no	—
265	C₄⋊C₄×C₅₃	—	2	4	no	—
266	C₄⋊C₄×C₅₃	—	2	1	no	—
267	C₄⋊C₄×C₅₃	—	2	2	no	—
268	C₄⋊C₄×C₅₃	—	2	4	no	—
269	C₄⋊C₄×C₅₃	—	2	2	no	—
270	C₄⋊C₄×C₅₃	—	2	1	no	—
271	C₄⋊C₄×C₅₃	—	2	2	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	2	yes	—
277	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₂²⋊C₄×C₅₃	—	2	4	no	—
285	C₂²⋊C₄×C₅₃	—	2	2	no	—
286	C₂²⋊C₄×C₅₃	—	2	4	no	—
287	C₂²⋊C₄×C₅₃	—	2	2	no	—
288	C₂²⋊C₄×C₅₃	—	2	4	no	—
289	C₂²⋊C₄×C₅₃	—	2	4	no	—
290	C₂²⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
296	C₄²×C₅₃	—	2	2	no	—
297	C₄²×C₅₃	—	2	2	no	—
298	C₄²×C₅₃	—	2	4	no	—
299	C₄²×C₅₃	—	2	4	no	—
300	C₄²×C₅₃	—	2	2	no	—
301	C₄²×C₅₃	—	2	2	no	—
302	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₂³×C₅₃	—	2	2	no	—
307	C₂³×C₅₃	—	4	2	no	—
308	C₂³×C₅₃	—	8	1	no	—
309	C₂³×C₅₃	—	8	1	no	—
310	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
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	—	4	2	no	—
316	Q₈×C₅₃	—	4	2	no	—
317	Q₈×C₅₃	—	4	2	no	—
318	Q₈×C₅₃	—	8	1	no	—
319	Q₈×C₅₃	—	8	1	no	—
320	D₄×C₅₃	—	2	8	no	—
321	D₄×C₅₃	—	2	4	no	—
322	D₄×C₅₃	—	2	4	no	—
323	D₄×C₅₃	—	2	2	no	—
324	D₄×C₅₃	—	2	2	no	—
325	D₄×C₅₃	—	4	2	no	—
326	D₄×C₅₃	—	4	2	no	—
327	D₄×C₅₃	—	8	4	no	—
328	D₄×C₅₃	—	8	4	no	—
329	C₂×C₄×C₅₃	—	2	2	no	—
330	C₂×C₄×C₅₃	—	2	4	no	—
331	C₂×C₄×C₅₃	—	2	4	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	—	2	2	no	—
338	C₂×C₄×C₅₃	—	2	2	no	—
339	C₂×C₄×C₅₃	—	4	1	no	—
340	C₂×C₄×C₅₃	—	4	2	no	—
341	C₂×C₄×C₅₃	—	4	4	no	—
342	C₂×C₄×C₅₃	—	8	2	no	—
343	C₂×C₄×C₅₃	—	8	1	no	—
344	C₂×C₄×C₅₃	—	8	4	no	—
345	C₂×C₄×C₅₃	—	8	1	no	—
346	C₂×C₄×C₅₃	—	8	4	no	—
347	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
354	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
355	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
356	C₈×C₅₃	—	2	4	no	—
357	C₈×C₅₃	—	2	1	no	—
358	C₈×C₅₃	—	2	1	no	—
359	C₈×C₅₃	C₂×#41	1	2	yes	—
360	C₈×C₅₃	C₂×#41	1	2	yes	—
361	#61285	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂²×C₅₃	—	2	1	no	—
363	C₂²×C₅₃	—	2	1	no	—
364	C₂²×C₅₃	—	2	4	no	—
365	C₂²×C₅₃	—	2	4	no	—
366	C₂²×C₅₃	—	2	4	no	—
367	C₂²×C₅₃	—	4	2	no	—
368	C₂²×C₅₃	—	4	2	no	—
369	C₂²×C₅₃	—	4	2	no	—
370	C₂²×C₅₃	—	8	4	no	—
371	C₂²×C₅₃	#547	1	2	yes	—
372	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₅₃	—	2	1	no	—
374	C₄×C₅₃	—	2	1	no	—
375	C₄×C₅₃	—	2	4	no	—
376	C₄×C₅₃	—	2	1	no	—
377	C₄×C₅₃	—	4	2	no	—
378	C₄×C₅₃	—	4	2	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	#547	1	2	yes	—
385	C₄×C₅₃	#577	1	2	yes	—
386	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
387	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
388	#3507	C₂×C₅₃	1	1	yes	characteristic, complemented
389	#3506	C₂×C₅₃	1	1	yes	characteristic
390	#3357	C₂×C₅₃	1	2	yes	complemented
391	#3353	C₂×C₅₃	1	2	yes	complemented
392	#3351	C₂×C₅₃	1	4	yes	complemented
393	#3340	C₂×C₅₃	1	2	yes	complemented
394	#3337	C₂×C₅₃	1	4	yes	complemented
395	#3335	C₂×C₅₃	1	2	yes	complemented
396	#3160	C₂×C₅₃	1	1	yes	characteristic, complemented
397	#3097	C₂×C₅₃	1	2	yes	complemented
398	#3096	C₂×C₅₃	1	2	yes	complemented
399	#3078	C₂×C₅₃	1	1	yes	characteristic, complemented
400	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
401	#3057	C₂×C₅₃	1	2	yes	complemented
402	C₂×C₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
403	#2931	C₂×C₅₃	1	1	yes	characteristic, complemented
404	#2912	C₂×C₅₃	1	2	yes	complemented
405	C₂×C₅₃	—	2	2	no	—
406	C₂×C₅₃	—	4	4	no	—
407	C₂×C₅₃	—	8	2	no	—
408	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
409	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
410	C₂×C₅₃	#3584	1	1	yes	characteristic
411	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
412	C₂×#131	C₂²×C₅₃	1	2	yes	—
413	#559	—	2	1	no	—
414	#559	—	2	2	no	—
415	#557	—	2	1	no	—
416	#556	—	2	1	no	—
417	#556	—	2	2	no	—
418	#556	C₂²×C₅₃	1	2	yes	complemented
419	#555	C₂²×C₅₃	1	2	yes	—
420	#554	C₂²×C₅₃	1	2	yes	complemented
421	#553	C₂²×C₅₃	1	4	yes	—
422	#552	C₂²×C₅₃	1	4	yes	complemented
423	#550	—	2	1	no	—
424	#547	C₂²×C₅₃	1	2	yes	—
425	#539	—	2	2	no	—
426	#538	—	2	2	no	—
427	#536	C₂²×C₅₃	1	2	yes	—
428	#535	C₂²×C₅₃	1	2	yes	—
429	#533	C₂²×C₅₃	1	1	yes	characteristic
430	#533	C₂²×C₅₃	1	1	yes	characteristic
431	#532	C₂²×C₅₃	1	1	yes	characteristic
432	#529	—	2	2	no	—
433	#525	—	2	2	no	—
434	#520	C₂²×C₅₃	1	2	yes	—
435	#520	C₂²×C₅₃	1	2	yes	—
436	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
438	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
439	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
440	#499	C₂²×C₅₃	1	2	yes	complemented
441	#499	C₂²×C₅₃	1	2	yes	complemented
442	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
443	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
444	#485	C₂²×C₅₃	1	4	yes	complemented
445	#485	C₂²×C₅₃	1	4	yes	complemented
446	#484	C₂²×C₅₃	1	4	yes	complemented
447	#483	C₂²×C₅₃	1	4	yes	complemented
448	#482	C₂²×C₅₃	1	4	yes	—
449	#482	C₂²×C₅₃	1	4	yes	—
450	#481	C₂²×C₅₃	1	4	yes	—
451	#480	C₂²×C₅₃	1	4	yes	—
452	#479	C₂²×C₅₃	1	4	yes	complemented
453	#478	C₂²×C₅₃	1	4	yes	—
454	#477	C₂²×C₅₃	1	2	yes	complemented
455	#476	C₂²×C₅₃	1	2	yes	—
456	#475	C₂²×C₅₃	1	2	yes	complemented
457	#474	C₂²×C₅₃	1	2	yes	—
458	#468	C₂²×C₅₃	1	4	yes	—
459	#468	C₂²×C₅₃	1	4	yes	—
460	#465	C₂²×C₅₃	1	4	yes	—
461	#465	C₂²×C₅₃	1	4	yes	—
462	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
463	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
464	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
465	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
466	#436	C₂²×C₅₃	1	2	yes	complemented
467	#436	C₂²×C₅₃	1	2	yes	complemented
468	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
469	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
470	#428	C₂²×C₅₃	1	2	yes	—
471	#428	C₂²×C₅₃	1	2	yes	—
472	#428	C₂²×C₅₃	1	4	yes	complemented
473	#428	C₂²×C₅₃	1	4	yes	complemented
474	#427	C₂²×C₅₃	1	2	yes	—
475	#427	C₂²×C₅₃	1	2	yes	—
476	#427	C₂²×C₅₃	1	4	yes	complemented
477	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
478	C₂×#106	C₂²×C₅₃	1	4	yes	complemented
479	#423	C₂²×C₅₃	1	1	yes	characteristic
480	#419	C₂²×C₅₃	1	2	yes	—
481	#418	C₂²×C₅₃	1	2	yes	—
482	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
483	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
484	#408	C₂²×C₅₃	1	2	yes	—
485	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
486	C₅₃	#61285	1	1	yes	characteristic, direct product factor, Sylow
487	C₂×#41	—	2	2	no	—
488	C₂×#41	C₂³×C₅₃	1	2	yes	—
489	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
491	C₂³×C₄	—	2	1	no	—
492	C₂×SD₁₆	—	2	4	no	—
493	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
495	#131	—	2	8	no	—
496	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
497	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
498	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
499	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
501	C₄⋊Q₈	—	2	2	no	—
502	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
507	#127	—	2	2	no	—
508	#127	D₄×C₅₃	1	1	yes	characteristic
509	#126	—	2	4	no	—
510	#126	—	2	4	no	—
511	#126	—	2	4	no	—
512	#125	—	2	2	no	—
513	#125	—	2	4	no	—
514	#125	C₂³×C₅₃	1	2	yes	—
515	#125	C₂³×C₅₃	1	2	yes	—
516	#124	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	—	2	2	no	—
519	#124	—	2	4	no	—
520	#124	D₄×C₅₃	1	2	yes	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	1	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	C₂³×C₅₃	1	4	yes	—
532	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
533	#121	—	2	2	no	—
534	#121	—	2	4	no	—
535	#121	D₄×C₅₃	1	2	yes	—
536	#121	D₄×C₅₃	1	2	yes	—
537	#121	C₂³×C₅₃	1	4	yes	—
538	#121	C₂³×C₅₃	1	4	yes	—
539	#120	—	2	4	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
550	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	4	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	4	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	2	yes	—
562	C₄×D₄	C₂³×C₅₃	1	2	yes	—
563	#117	—	2	2	no	—
564	#117	—	2	4	no	—
565	#117	C₂³×C₅₃	1	2	yes	—
566	#117	C₂³×C₅₃	1	2	yes	—
567	#117	C₂³×C₅₃	1	4	yes	—
568	#117	C₂³×C₅₃	1	4	yes	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
577	#107	C₂³×C₅₃	1	2	yes	—
578	#107	C₂³×C₅₃	1	2	yes	—
579	#107	C₂³×C₅₃	1	2	yes	—
580	#107	C₂³×C₅₃	1	2	yes	—
581	#107	C₂³×C₅₃	1	4	yes	—
582	#107	C₂³×C₅₃	1	4	yes	—
583	#106	C₂³×C₅₃	1	2	yes	—
584	#106	C₂³×C₅₃	1	2	yes	—
585	#106	C₂³×C₅₃	1	2	yes	—
586	#106	C₂³×C₅₃	1	4	yes	—
587	#106	C₂³×C₅₃	1	4	yes	—
588	#106	C₂³×C₅₃	1	2	yes	—
589	#106	C₂³×C₅₃	1	2	yes	—
590	#106	C₂³×C₅₃	1	2	yes	—
591	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
592	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
593	#103	C₂³×C₅₃	1	2	yes	—
594	#103	C₂³×C₅₃	1	2	yes	—
595	#103	C₂³×C₅₃	1	4	yes	—
596	#103	C₂³×C₅₃	1	4	yes	—
597	#102	C₂³×C₅₃	1	2	yes	—
598	#102	C₂³×C₅₃	1	2	yes	—
599	#102	C₂³×C₅₃	1	4	yes	—
600	#102	C₂³×C₅₃	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
602	C₂²⋊C₈	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	C₂⁴	—	2	1	no	—
608	#41	—	2	4	no	—
609	#41	—	2	4	no	—
610	#41	—	8	4	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
627	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
628	C₂×D₄	C₂×D₄×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	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	8	2	no	—
638	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
641	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
642	SD₁₆	—	2	4	no	—
643	SD₁₆	—	2	4	no	—
644	M₁₆	—	2	4	no	—
645	M₁₆	—	2	8	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	8	no	—
648	C₂×C₈	#41×C₅₃	1	4	yes	complemented
649	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
650	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
652	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
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	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
689	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	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	C₂³	—	2	2	no	—
701	C₂³	—	4	2	no	—
702	C₂³	—	8	1	no	—
703	C₂³	—	8	1	no	—
704	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
705	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
706	Q₈	—	2	4	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	8	1	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	8	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	4	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	8	4	no	—
722	D₄	—	8	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	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	—	2	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	8	2	no	—
737	C₂×C₄	—	8	1	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
743	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
748	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
749	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
750	C₈	—	2	4	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	C₂×#41×C₅₃	1	2	yes	—
754	C₈	C₂×#41×C₅₃	1	2	yes	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	8	4	no	—
764	C₂²	C₅₃×#547	1	2	yes	—
765	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
766	C₄	—	2	4	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₅₃×#547	1	2	yes	—
778	C₄	C₅₃×#577	1	2	yes	—
779	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
780	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
781	C₂	—	2	2	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
785	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
786	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×#3506	C₂
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×#3507	C₂	semidirect
3. C₅₃×#3357	C₂	semidirect
4. C₅₃×#3353	C₂	semidirect
5. C₅₃×#3351	C₂	semidirect
6. C₅₃×#3340	C₂	semidirect
7. C₅₃×#3337	C₂	semidirect
8. C₅₃×#3335	C₂	semidirect
9. C₅₃×#3160	C₂	semidirect
10. C₅₃×#3097	C₂	semidirect
11. C₅₃×#3096	C₂	semidirect
12. C₅₃×#3078	C₂	semidirect
13. C₅₃×#3077	C₂	semidirect
14. C₅₃×#3057	C₂	semidirect
15. C₂×C₄×SD₁₆×C₅₃	C₂	semidirect
16. C₅₃×#2931	C₂	semidirect
17. C₅₃×#2912	C₂	semidirect
25. C₅₃×#556	C₂²	semidirect
27. C₅₃×#554	C₂²	semidirect
29. C₅₃×#552	C₂²	semidirect
45. C₅₃×#500	C₂²	semidirect
46. C₅₃×#500	C₂²	semidirect
47. C₅₃×#499	C₂²	semidirect
48. C₅₃×#499	C₂²	semidirect
49. C₅₃×#498	C₂²	semidirect
50. C₅₃×#498	C₂²	semidirect
51. C₅₃×#485	C₂²	semidirect
52. C₅₃×#485	C₂²	semidirect
53. C₅₃×#484	C₂²	semidirect
54. C₅₃×#483	C₂²	semidirect
59. C₅₃×#479	C₂²	semidirect
61. C₅₃×#477	C₂²	semidirect
63. C₅₃×#475	C₂²	semidirect
73. C₅₃×#436	C₂²	semidirect
74. C₅₃×#436	C₂²	semidirect
75. C₈×D₄×C₅₃	C₂²	semidirect
76. C₈×D₄×C₅₃	C₂²	semidirect
79. C₅₃×#428	C₂²	semidirect
80. C₅₃×#428	C₂²	semidirect
83. C₅₃×#427	C₂²	semidirect
85. C₂×#106×C₅₃	C₂²	semidirect
254. C₂×C₈×C₅₃	#41	semidirect
361. #61285	C₅₃	direct (N × H)
388. #3507	C₂×C₅₃	semidirect
390. #3357	C₂×C₅₃	semidirect
391. #3353	C₂×C₅₃	semidirect
392. #3351	C₂×C₅₃	semidirect
393. #3340	C₂×C₅₃	semidirect
394. #3337	C₂×C₅₃	semidirect
395. #3335	C₂×C₅₃	semidirect
396. #3160	C₂×C₅₃	semidirect
397. #3097	C₂×C₅₃	semidirect
398. #3096	C₂×C₅₃	semidirect
399. #3078	C₂×C₅₃	semidirect
400. #3077	C₂×C₅₃	semidirect
401. #3057	C₂×C₅₃	semidirect
402. C₂×C₄×SD₁₆	C₂×C₅₃	semidirect
403. #2931	C₂×C₅₃	semidirect
404. #2912	C₂×C₅₃	semidirect
418. #556	C₂²×C₅₃	semidirect
420. #554	C₂²×C₅₃	semidirect
422. #552	C₂²×C₅₃	semidirect
438. #500	C₂²×C₅₃	semidirect
439. #500	C₂²×C₅₃	semidirect
440. #499	C₂²×C₅₃	semidirect
441. #499	C₂²×C₅₃	semidirect
442. #498	C₂²×C₅₃	semidirect
443. #498	C₂²×C₅₃	semidirect
444. #485	C₂²×C₅₃	semidirect
445. #485	C₂²×C₅₃	semidirect
446. #484	C₂²×C₅₃	semidirect
447. #483	C₂²×C₅₃	semidirect
452. #479	C₂²×C₅₃	semidirect
454. #477	C₂²×C₅₃	semidirect
456. #475	C₂²×C₅₃	semidirect
466. #436	C₂²×C₅₃	semidirect
467. #436	C₂²×C₅₃	semidirect
468. C₈×D₄	C₂²×C₅₃	semidirect
469. C₈×D₄	C₂²×C₅₃	semidirect
472. #428	C₂²×C₅₃	semidirect
473. #428	C₂²×C₅₃	semidirect
476. #427	C₂²×C₅₃	semidirect
478. C₂×#106	C₂²×C₅₃	semidirect
486. C₅₃	#61285	direct (N × H)
648. C₂×C₈	#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×#3507	2
C₅₃×#3506	2
C₅₃×#3357	2
C₅₃×#3353	2
C₅₃×#3351	2
C₅₃×#3340	2
C₅₃×#3337	2
C₅₃×#3335	2
C₅₃×#3160	2
C₅₃×#3097	2
C₅₃×#3096	2
C₅₃×#3078	2
C₅₃×#3077	2
C₅₃×#3057	2
C₂×C₄×SD₁₆×C₅₃	2
C₅₃×#2931	2
C₅₃×#2912	2
#61285	53

Subgroups — C53×#61285 #27268797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61285 #27268797