Subgroups — C₅₃×#61318 #27268830

Order 13568.

1880 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3370	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3366	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3361	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3142	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3080	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3036	C₂	1	2	yes	maximal, complemented
15	Q₈×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	2	yes	maximal, complemented
18	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
20	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
21	C₅₃×#559	C₂²	1	2	yes	complemented
22	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
23	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
24	C₅₃×#556	C₂²	1	2	yes	complemented
25	C₅₃×#554	—	2	1	no	—
26	C₅₃×#554	—	2	1	no	—
27	C₅₃×#554	—	2	2	no	—
28	C₅₃×#554	C₂²	1	2	yes	—
29	C₅₃×#554	C₂²	1	2	yes	—
30	C₅₃×#554	C₂²	1	4	yes	—
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#553	—	2	2	no	—
33	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#548	—	2	1	no	—
35	C₅₃×#532	C₂²	1	1	yes	characteristic
36	C₅₃×#532	C₂²	1	2	yes	—
37	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#529	—	2	2	no	—
39	C₅₃×#529	—	2	1	no	—
40	C₂×#125×C₅₃	C₂²	1	2	yes	—
41	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
42	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
43	C₄×#41×C₅₃	—	2	1	no	—
44	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
45	C₄×#41×C₅₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₅₃	—	2	1	no	—
50	C₅₃×#491	C₂²	1	4	yes	complemented
51	C₅₃×#490	C₂²	1	4	yes	complemented
52	C₅₃×#489	C₂²	1	4	yes	complemented
53	C₅₃×#488	C₂²	1	4	yes	complemented
54	C₅₃×#488	C₂²	1	4	yes	complemented
55	C₅₃×#487	C₂²	1	2	yes	complemented
56	C₅₃×#486	C₂²	1	2	yes	complemented
57	C₅₃×#479	C₂²	1	4	yes	complemented
58	C₅₃×#479	C₂²	1	4	yes	complemented
59	C₅₃×#478	C₂²	1	4	yes	complemented
60	C₅₃×#478	C₂²	1	4	yes	complemented
61	C₅₃×#477	C₂²	1	2	yes	complemented
62	C₅₃×#476	C₂²	1	2	yes	complemented
63	C₅₃×#475	C₂²	1	2	yes	complemented
64	C₅₃×#474	C₂²	1	2	yes	complemented
65	C₅₃×#463	C₂²	1	4	yes	—
66	C₅₃×#463	C₂²	1	4	yes	—
67	C₅₃×#463	C₂²	1	4	yes	—
68	C₅₃×#461	C₂²	1	2	yes	—
69	C₅₃×#461	C₂²	1	4	yes	—
70	C₅₃×#459	C₂²	1	2	yes	—
71	C₅₃×#459	C₂²	1	4	yes	—
72	C₅₃×#446	C₂²	1	2	yes	complemented
73	C₅₃×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
75	C₅₃×#442	C₂²	1	4	yes	—
76	C₅₃×#442	C₂²	1	2	yes	—
77	C₅₃×#440	C₂²	1	4	yes	—
78	C₅₃×#440	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
81	C₄×D₈×C₅₃	C₂²	1	2	yes	—
82	C₄×D₈×C₅₃	C₂²	1	4	yes	—
83	C₅₃×#428	C₂²	1	2	yes	—
84	C₅₃×#428	C₂²	1	1	yes	characteristic
85	C₅₃×#423	C₂²	1	1	yes	characteristic
86	C₅₃×#423	C₂²	1	2	yes	—
87	C₅₃×#418	C₂²	1	1	yes	characteristic
88	C₅₃×#417	C₂²	1	2	yes	—
89	C₅₃×#417	C₂²	1	1	yes	characteristic
90	C₅₃×#417	C₂²	1	2	yes	—
91	C₅₃×#417	C₂²	1	2	yes	—
92	C₅₃×#417	C₂²	1	2	yes	—
93	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
97	C₂×#41×C₅₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₅₃	—	2	1	no	—
99	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅₃	—	2	1	no	—
102	C₂³×C₄×C₅₃	—	2	2	no	—
103	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
104	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
105	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
107	C₂×D₈×C₅₃	C₂³	1	2	yes	—
108	C₂×D₈×C₅₃	C₂³	1	4	yes	—
109	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
111	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₃	—	2	1	no	—
113	C₄⋊Q₈×C₅₃	—	2	1	no	—
114	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
118	#127×C₅₃	C₂³	1	1	yes	characteristic
119	#127×C₅₃	C₂³	1	2	yes	—
120	#126×C₅₃	—	2	2	no	—
121	#126×C₅₃	—	2	2	no	—
122	#126×C₅₃	—	2	2	no	—
123	#125×C₅₃	—	2	1	no	—
124	#125×C₅₃	—	2	2	no	—
125	#125×C₅₃	—	2	2	no	—
126	#125×C₅₃	—	2	2	no	—
127	#125×C₅₃	C₂³	1	4	yes	—
128	#125×C₅₃	C₂³	1	4	yes	—
129	#124×C₅₃	—	2	1	no	—
130	#124×C₅₃	—	2	2	no	—
131	#124×C₅₃	C₂³	1	2	yes	—
132	#124×C₅₃	C₂³	1	2	yes	—
133	#124×C₅₃	C₂³	1	2	yes	—
134	#123×C₅₃	—	2	2	no	—
135	#123×C₅₃	—	2	2	no	—
136	#123×C₅₃	—	2	2	no	—
137	C₂²⋊Q₈×C₅₃	—	2	4	no	—
138	C₂²⋊Q₈×C₅₃	—	2	4	no	—
139	C₂²⋊Q₈×C₅₃	—	2	4	no	—
140	C₂²⋊Q₈×C₅₃	—	2	4	no	—
141	C₂²⋊Q₈×C₅₃	—	2	2	no	—
142	C₂²⋊Q₈×C₅₃	—	2	2	no	—
143	C₂²⋊Q₈×C₅₃	—	2	4	no	—
144	C₂²⋊Q₈×C₅₃	—	2	1	no	—
145	C₂²⋊Q₈×C₅₃	—	2	2	no	—
146	#121×C₅₃	—	2	1	no	—
147	#121×C₅₃	—	2	2	no	—
148	#121×C₅₃	—	2	1	no	—
149	#121×C₅₃	—	2	2	no	—
150	#121×C₅₃	—	2	1	no	—
151	#121×C₅₃	—	2	2	no	—
152	C₄×Q₈×C₅₃	—	2	1	no	—
153	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
154	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
155	C₄×Q₈×C₅₃	D₄	1	2	yes	—
156	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
163	C₄×D₄×C₅₃	—	2	1	no	—
164	C₄×D₄×C₅₃	—	2	2	no	—
165	C₄×D₄×C₅₃	—	2	1	no	—
166	C₄×D₄×C₅₃	—	2	1	no	—
167	C₄×D₄×C₅₃	—	2	2	no	—
168	C₄×D₄×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	—	2	1	no	—
171	C₄×D₄×C₅₃	—	2	2	no	—
172	C₄×D₄×C₅₃	—	2	1	no	—
173	C₄×D₄×C₅₃	—	2	1	no	—
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	—	2	1	no	—
176	C₄×D₄×C₅₃	—	2	2	no	—
177	C₄×D₄×C₅₃	C₂³	1	2	yes	—
178	C₄×D₄×C₅₃	C₂³	1	4	yes	—
179	C₄×D₄×C₅₃	C₂³	1	4	yes	—
180	C₄×D₄×C₅₃	C₂³	1	2	yes	—
181	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₅₃	C₂³	1	2	yes	—
183	C₄×D₄×C₅₃	C₂³	1	2	yes	—
184	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
185	#117×C₅₃	—	2	1	no	—
186	#117×C₅₃	—	2	2	no	—
187	#117×C₅₃	—	2	2	no	—
188	#117×C₅₃	—	2	1	no	—
189	#117×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
191	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
193	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
196	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
198	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
202	C₂×C₄²×C₅₃	—	2	2	no	—
203	C₂×C₄²×C₅₃	—	2	1	no	—
204	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
206	#107×C₅₃	C₂³	1	4	yes	—
207	#107×C₅₃	C₂³	1	2	yes	—
208	#106×C₅₃	C₂³	1	4	yes	—
209	#106×C₅₃	C₂³	1	2	yes	—
210	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
211	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
214	#103×C₅₃	C₂³	1	4	yes	—
215	#103×C₅₃	C₂³	1	4	yes	—
216	#103×C₅₃	C₂³	1	2	yes	—
217	#103×C₅₃	C₂³	1	4	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#102×C₅₃	C₂³	1	4	yes	—
220	#102×C₅₃	C₂³	1	4	yes	—
221	#102×C₅₃	C₂³	1	2	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	#102×C₅₃	C₂³	1	2	yes	—
225	#102×C₅₃	C₂³	1	2	yes	—
226	#97×C₅₃	C₂³	1	2	yes	—
227	#97×C₅₃	C₂³	1	4	yes	—
228	C₄×C₈×C₅₃	C₂³	1	2	yes	—
229	C₄×C₈×C₅₃	C₂³	1	4	yes	—
230	C₂⁴×C₅₃	—	2	1	no	—
231	#41×C₅₃	—	2	2	no	—
232	#41×C₅₃	—	2	4	no	—
233	#41×C₅₃	—	2	2	no	—
234	#41×C₅₃	—	2	4	no	—
235	#41×C₅₃	—	4	4	no	—
236	C₂×Q₈×C₅₃	—	2	2	no	—
237	C₂×Q₈×C₅₃	—	2	2	no	—
238	C₂×Q₈×C₅₃	—	4	2	no	—
239	C₂×Q₈×C₅₃	—	8	2	no	—
240	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
243	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₅₃	—	2	1	no	—
246	C₂×D₄×C₅₃	—	2	2	no	—
247	C₂×D₄×C₅₃	—	2	1	no	—
248	C₂×D₄×C₅₃	—	2	2	no	—
249	C₂×D₄×C₅₃	—	2	1	no	—
250	C₂×D₄×C₅₃	—	2	2	no	—
251	C₂×D₄×C₅₃	—	2	1	no	—
252	C₂×D₄×C₅₃	—	2	2	no	—
253	C₂×D₄×C₅₃	#41	1	4	yes	complemented
254	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₃	—	2	1	no	—
258	C₂²×C₄×C₅₃	—	2	2	no	—
259	C₂²×C₄×C₅₃	—	2	2	no	—
260	C₂²×C₄×C₅₃	—	2	1	no	—
261	C₂²×C₄×C₅₃	—	2	2	no	—
262	C₂²×C₄×C₅₃	—	2	1	no	—
263	C₂²×C₄×C₅₃	—	2	2	no	—
264	C₂²×C₄×C₅₃	—	2	2	no	—
265	C₂²×C₄×C₅₃	—	2	2	no	—
266	C₂²×C₄×C₅₃	—	2	1	no	—
267	C₂²×C₄×C₅₃	—	2	4	no	—
268	C₂²×C₄×C₅₃	—	2	4	no	—
269	C₂²×C₄×C₅₃	—	4	4	no	—
270	C₂²×C₄×C₅₃	—	8	4	no	—
271	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
276	SD₁₆×C₅₃	—	2	8	no	—
277	SD₁₆×C₅₃	—	2	4	no	—
278	D₈×C₅₃	—	2	4	no	—
279	D₈×C₅₃	—	2	8	no	—
280	M₁₆×C₅₃	—	2	2	no	—
281	M₁₆×C₅₃	—	2	4	no	—
282	M₁₆×C₅₃	—	2	2	no	—
283	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
286	C₄⋊C₄×C₅₃	—	2	4	no	—
287	C₄⋊C₄×C₅₃	—	2	4	no	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	4	no	—
291	C₄⋊C₄×C₅₃	—	2	4	no	—
292	C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	2	no	—
295	C₄⋊C₄×C₅₃	—	2	1	no	—
296	C₄⋊C₄×C₅₃	—	2	1	no	—
297	C₄⋊C₄×C₅₃	—	2	2	no	—
298	C₄⋊C₄×C₅₃	—	2	2	no	—
299	C₄⋊C₄×C₅₃	—	2	1	no	—
300	C₄⋊C₄×C₅₃	—	2	2	no	—
301	C₄⋊C₄×C₅₃	—	2	1	no	—
302	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
313	C₂²⋊C₄×C₅₃	—	2	1	no	—
314	C₂²⋊C₄×C₅₃	—	2	4	no	—
315	C₂²⋊C₄×C₅₃	—	2	4	no	—
316	C₂²⋊C₄×C₅₃	—	2	2	no	—
317	C₂²⋊C₄×C₅₃	—	2	2	no	—
318	C₂²⋊C₄×C₅₃	—	2	2	no	—
319	C₂²⋊C₄×C₅₃	—	2	2	no	—
320	C₂²⋊C₄×C₅₃	—	2	2	no	—
321	C₂²⋊C₄×C₅₃	—	2	2	no	—
322	C₂²⋊C₄×C₅₃	—	2	1	no	—
323	C₂²⋊C₄×C₅₃	—	2	1	no	—
324	C₂²⋊C₄×C₅₃	—	2	2	no	—
325	C₂²⋊C₄×C₅₃	—	2	2	no	—
326	C₂²⋊C₄×C₅₃	—	2	2	no	—
327	C₂²⋊C₄×C₅₃	—	2	2	no	—
328	C₄²×C₅₃	—	2	1	no	—
329	C₄²×C₅₃	—	2	2	no	—
330	C₄²×C₅₃	—	2	1	no	—
331	C₄²×C₅₃	—	2	2	no	—
332	C₄²×C₅₃	—	2	1	no	—
333	C₄²×C₅₃	C₂×D₄	1	2	yes	—
334	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₅₃	C₂×D₄	1	2	yes	—
336	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₅₃	C₂⁴	1	2	yes	—
338	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₅₃	C₂⁴	1	2	yes	—
341	C₂³×C₅₃	—	2	4	no	—
342	C₂³×C₅₃	—	2	2	no	—
343	C₂³×C₅₃	—	2	2	no	—
344	C₂³×C₅₃	—	2	1	no	—
345	C₂³×C₅₃	—	4	2	no	—
346	C₂³×C₅₃	—	4	2	no	—
347	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₅₃	—	2	2	no	—
349	Q₈×C₅₃	—	2	2	no	—
350	Q₈×C₅₃	—	2	2	no	—
351	Q₈×C₅₃	—	2	1	no	—
352	Q₈×C₅₃	—	2	2	no	—
353	Q₈×C₅₃	—	2	1	no	—
354	Q₈×C₅₃	—	4	2	no	—
355	Q₈×C₅₃	—	8	2	no	—
356	Q₈×C₅₃	—	8	2	no	—
357	D₄×C₅₃	—	2	4	no	—
358	D₄×C₅₃	—	2	2	no	—
359	D₄×C₅₃	—	2	1	no	—
360	D₄×C₅₃	—	2	2	no	—
361	D₄×C₅₃	—	2	2	no	—
362	D₄×C₅₃	—	2	1	no	—
363	D₄×C₅₃	—	4	4	no	—
364	D₄×C₅₃	—	4	2	no	—
365	D₄×C₅₃	—	4	4	no	—
366	D₄×C₅₃	—	4	2	no	—
367	D₄×C₅₃	—	8	2	no	—
368	D₄×C₅₃	—	8	1	no	—
369	D₄×C₅₃	C₂×#41	1	4	yes	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	4	no	—
372	C₂×C₄×C₅₃	—	2	1	no	—
373	C₂×C₄×C₅₃	—	2	1	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	1	no	—
377	C₂×C₄×C₅₃	—	4	2	no	—
378	C₂×C₄×C₅₃	—	4	2	no	—
379	C₂×C₄×C₅₃	—	4	1	no	—
380	C₂×C₄×C₅₃	—	4	4	no	—
381	C₂×C₄×C₅₃	—	4	4	no	—
382	C₂×C₄×C₅₃	—	4	2	no	—
383	C₂×C₄×C₅₃	—	4	4	no	—
384	C₂×C₄×C₅₃	—	4	4	no	—
385	C₂×C₄×C₅₃	—	4	2	no	—
386	C₂×C₄×C₅₃	—	4	4	no	—
387	C₂×C₄×C₅₃	—	4	2	no	—
388	C₂×C₄×C₅₃	—	8	2	no	—
389	C₂×C₄×C₅₃	—	8	1	no	—
390	C₂×C₄×C₅₃	—	8	4	no	—
391	C₂×C₄×C₅₃	—	8	4	no	—
392	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
402	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
403	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
404	C₈×C₅₃	—	2	2	no	—
405	C₈×C₅₃	—	2	4	no	—
406	C₈×C₅₃	—	2	2	no	—
407	#61318	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
408	C₂²×C₅₃	—	2	1	no	—
409	C₂²×C₅₃	—	2	1	no	—
410	C₂²×C₅₃	—	2	4	no	—
411	C₂²×C₅₃	—	4	8	no	—
412	C₂²×C₅₃	—	4	2	no	—
413	C₂²×C₅₃	—	4	2	no	—
414	C₂²×C₅₃	—	4	2	no	—
415	C₂²×C₅₃	—	4	1	no	—
416	C₂²×C₅₃	—	4	2	no	—
417	C₂²×C₅₃	—	4	1	no	—
418	C₂²×C₅₃	—	4	2	no	—
419	C₂²×C₅₃	—	4	1	no	—
420	C₂²×C₅₃	#548	1	2	yes	—
421	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₅₃	—	2	2	no	—
423	C₄×C₅₃	—	2	2	no	—
424	C₄×C₅₃	—	2	1	no	—
425	C₄×C₅₃	—	2	1	no	—
426	C₄×C₅₃	—	2	1	no	—
427	C₄×C₅₃	—	2	2	no	—
428	C₄×C₅₃	—	2	2	no	—
429	C₄×C₅₃	—	4	4	no	—
430	C₄×C₅₃	—	4	1	no	—
431	C₄×C₅₃	—	4	2	no	—
432	C₄×C₅₃	—	4	1	no	—
433	C₄×C₅₃	—	4	1	no	—
434	C₄×C₅₃	—	4	2	no	—
435	C₄×C₅₃	#548	1	2	yes	—
436	C₄×C₅₃	#575	1	2	yes	—
437	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
438	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
439	#3480	C₂×C₅₃	1	1	yes	characteristic, complemented
440	C₂×#554	C₂×C₅₃	1	1	yes	characteristic, complemented
441	#3376	C₂×C₅₃	1	4	yes	complemented
442	#3372	C₂×C₅₃	1	2	yes	complemented
443	#3370	C₂×C₅₃	1	4	yes	complemented
444	#3366	C₂×C₅₃	1	2	yes	complemented
445	#3361	C₂×C₅₃	1	2	yes	complemented
446	#3360	C₂×C₅₃	1	2	yes	complemented
447	#3142	C₂×C₅₃	1	2	yes	complemented
448	#3141	C₂×C₅₃	1	1	yes	characteristic, complemented
449	#3080	C₂×C₅₃	1	2	yes	complemented
450	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
451	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
452	#3036	C₂×C₅₃	1	2	yes	complemented
453	Q₈×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
454	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
455	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	2	yes	complemented
456	C₂×C₅₃	—	2	2	no	—
457	C₂×C₅₃	—	4	4	no	—
458	C₂×C₅₃	—	8	2	no	—
459	C₂×C₅₃	—	8	1	no	—
460	C₂×C₅₃	C₂×#548	1	1	yes	characteristic
461	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
462	C₂×C₅₃	#3585	1	1	yes	characteristic
463	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
464	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
465	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
466	#559	C₂²×C₅₃	1	2	yes	complemented
467	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
468	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
469	#556	C₂²×C₅₃	1	2	yes	complemented
470	#554	—	2	1	no	—
471	#554	—	2	1	no	—
472	#554	—	2	2	no	—
473	#554	C₂²×C₅₃	1	2	yes	—
474	#554	C₂²×C₅₃	1	2	yes	—
475	#554	C₂²×C₅₃	1	4	yes	—
476	#553	—	2	1	no	—
477	#553	—	2	2	no	—
478	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
479	#548	—	2	1	no	—
480	#532	C₂²×C₅₃	1	1	yes	characteristic
481	#532	C₂²×C₅₃	1	2	yes	—
482	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
483	#529	—	2	2	no	—
484	#529	—	2	1	no	—
485	C₂×#125	C₂²×C₅₃	1	2	yes	—
486	C₂×C₂²⋊Q₈	—	2	1	no	—
487	C₂×C₂²⋊Q₈	—	2	2	no	—
488	C₄×#41	—	2	1	no	—
489	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
490	C₄×#41	C₂²×C₅₃	1	2	yes	—
491	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
493	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
494	C₂²×C₄⋊C₄	—	2	1	no	—
495	#491	C₂²×C₅₃	1	4	yes	complemented
496	#490	C₂²×C₅₃	1	4	yes	complemented
497	#489	C₂²×C₅₃	1	4	yes	complemented
498	#488	C₂²×C₅₃	1	4	yes	complemented
499	#488	C₂²×C₅₃	1	4	yes	complemented
500	#487	C₂²×C₅₃	1	2	yes	complemented
501	#486	C₂²×C₅₃	1	2	yes	complemented
502	#479	C₂²×C₅₃	1	4	yes	complemented
503	#479	C₂²×C₅₃	1	4	yes	complemented
504	#478	C₂²×C₅₃	1	4	yes	complemented
505	#478	C₂²×C₅₃	1	4	yes	complemented
506	#477	C₂²×C₅₃	1	2	yes	complemented
507	#476	C₂²×C₅₃	1	2	yes	complemented
508	#475	C₂²×C₅₃	1	2	yes	complemented
509	#474	C₂²×C₅₃	1	2	yes	complemented
510	#463	C₂²×C₅₃	1	4	yes	—
511	#463	C₂²×C₅₃	1	4	yes	—
512	#463	C₂²×C₅₃	1	4	yes	—
513	#461	C₂²×C₅₃	1	2	yes	—
514	#461	C₂²×C₅₃	1	4	yes	—
515	#459	C₂²×C₅₃	1	2	yes	—
516	#459	C₂²×C₅₃	1	4	yes	—
517	#446	C₂²×C₅₃	1	2	yes	complemented
518	#446	C₂²×C₅₃	1	4	yes	complemented
519	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
520	#442	C₂²×C₅₃	1	4	yes	—
521	#442	C₂²×C₅₃	1	2	yes	—
522	#440	C₂²×C₅₃	1	4	yes	—
523	#440	C₂²×C₅₃	1	2	yes	—
524	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
525	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
526	C₄×D₈	C₂²×C₅₃	1	2	yes	—
527	C₄×D₈	C₂²×C₅₃	1	4	yes	—
528	#428	C₂²×C₅₃	1	2	yes	—
529	#428	C₂²×C₅₃	1	1	yes	characteristic
530	#423	C₂²×C₅₃	1	1	yes	characteristic
531	#423	C₂²×C₅₃	1	2	yes	—
532	#418	C₂²×C₅₃	1	1	yes	characteristic
533	#417	C₂²×C₅₃	1	2	yes	—
534	#417	C₂²×C₅₃	1	2	yes	—
535	#417	C₂²×C₅₃	1	2	yes	—
536	#417	C₂²×C₅₃	1	2	yes	—
537	#417	C₂²×C₅₃	1	1	yes	characteristic
538	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
539	C₄×M₁₆	C₂²×C₅₃	1	2	yes	—
540	C₅₃	#61318	1	1	yes	characteristic, direct product factor, Sylow
541	C₂×#41	—	2	1	no	—
542	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
543	C₂×#41	C₂³×C₅₃	1	2	yes	—
544	C₂²×Q₈	—	2	1	no	—
545	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂³×C₄	—	2	1	no	—
548	C₂³×C₄	—	2	2	no	—
549	AGL(1,ℤ/8)	—	2	4	no	—
550	AGL(1,ℤ/8)	—	2	8	no	—
551	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
552	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
553	C₂×D₈	C₂³×C₅₃	1	2	yes	—
554	C₂×D₈	C₂³×C₅₃	1	4	yes	—
555	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
556	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
557	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
564	#127	C₂³×C₅₃	1	1	yes	characteristic
565	#127	C₂³×C₅₃	1	2	yes	—
566	#126	—	2	2	no	—
567	#126	—	2	2	no	—
568	#126	—	2	2	no	—
569	#125	—	2	1	no	—
570	#125	—	2	2	no	—
571	#125	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	C₂³×C₅₃	1	4	yes	—
574	#125	C₂³×C₅₃	1	4	yes	—
575	#124	—	2	1	no	—
576	#124	—	2	2	no	—
577	#124	C₂³×C₅₃	1	2	yes	—
578	#124	C₂³×C₅₃	1	2	yes	—
579	#124	C₂³×C₅₃	1	2	yes	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	—	2	4	no	—
592	#121	—	2	1	no	—
593	#121	—	2	2	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	—	2	1	no	—
597	#121	—	2	2	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
600	C₄×Q₈	D₄×C₅₃	1	2	yes	—
601	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
603	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	C₂³×C₅₃	1	2	yes	—
624	C₄×D₄	C₂³×C₅₃	1	4	yes	—
625	C₄×D₄	C₂³×C₅₃	1	4	yes	—
626	C₄×D₄	C₂³×C₅₃	1	2	yes	—
627	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₅₃	1	2	yes	—
629	C₄×D₄	C₂³×C₅₃	1	2	yes	—
630	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
631	#117	—	2	1	no	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	—	2	1	no	—
635	#117	C₂³×C₅₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	2	no	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	2	no	—
641	C₂×C₄⋊C₄	—	2	4	no	—
642	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	2	no	—
648	C₂×C₄²	—	2	2	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
651	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
652	#107	C₂³×C₅₃	1	4	yes	—
653	#107	C₂³×C₅₃	1	2	yes	—
654	#106	C₂³×C₅₃	1	4	yes	—
655	#106	C₂³×C₅₃	1	2	yes	—
656	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
657	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
658	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
659	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
660	#103	C₂³×C₅₃	1	4	yes	—
661	#103	C₂³×C₅₃	1	2	yes	—
662	#103	C₂³×C₅₃	1	4	yes	—
663	#103	C₂³×C₅₃	1	4	yes	—
664	#103	C₂³×C₅₃	1	4	yes	—
665	#102	C₂³×C₅₃	1	4	yes	—
666	#102	C₂³×C₅₃	1	2	yes	—
667	#102	C₂³×C₅₃	1	4	yes	—
668	#102	C₂³×C₅₃	1	4	yes	—
669	#102	C₂³×C₅₃	1	4	yes	—
670	#102	C₂³×C₅₃	1	2	yes	—
671	#102	C₂³×C₅₃	1	2	yes	—
672	#97	C₂³×C₅₃	1	2	yes	—
673	#97	C₂³×C₅₃	1	4	yes	—
674	C₄×C₈	C₂³×C₅₃	1	2	yes	—
675	C₄×C₈	C₂³×C₅₃	1	4	yes	—
676	C₂⁴	—	2	1	no	—
677	#41	—	2	2	no	—
678	#41	—	2	4	no	—
679	#41	—	2	2	no	—
680	#41	—	2	4	no	—
681	#41	—	4	4	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	8	2	no	—
686	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
687	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
688	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
689	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
690	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	#41×C₅₃	1	4	yes	complemented
700	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
701	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
702	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	4	4	no	—
716	C₂²×C₄	—	8	4	no	—
717	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
722	SD₁₆	—	2	8	no	—
723	SD₁₆	—	2	4	no	—
724	D₈	—	2	4	no	—
725	D₈	—	2	8	no	—
726	M₁₆	—	2	2	no	—
727	M₁₆	—	2	4	no	—
728	M₁₆	—	2	2	no	—
729	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
751	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
752	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
753	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
754	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
757	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	1	no	—
779	C₄²	C₂×D₄×C₅₃	1	2	yes	—
780	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₅₃	1	2	yes	—
782	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₅₃	1	2	yes	—
784	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
786	C₄²	C₂⁴×C₅₃	1	2	yes	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
794	Q₈	—	2	2	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	1	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	2	no	—
802	Q₈	—	8	2	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	1	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	1	no	—
815	D₄	C₂×#41×C₅₃	1	4	yes	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	2	no	—
835	C₂×C₄	—	8	1	no	—
836	C₂×C₄	—	8	4	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
841	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
847	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
848	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
849	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	8	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	1	no	—
865	C₂²	C₅₃×#548	1	2	yes	—
866	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
867	C₄	—	2	1	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	4	no	—
879	C₄	—	4	1	no	—
880	C₄	C₅₃×#548	1	2	yes	—
881	C₄	C₅₃×#575	1	2	yes	—
882	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
883	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
884	C₂	—	2	2	no	—
885	C₂	—	4	4	no	—
886	C₂	—	8	2	no	—
887	C₂	—	8	1	no	—
888	C₂	C₂×C₅₃×#548	1	1	yes	characteristic
889	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
890	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 ◁ C₂×C₄×Q₈×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3480	C₂	semidirect
2. C₂×C₅₃×#554	C₂	semidirect
3. C₅₃×#3376	C₂	semidirect
4. C₅₃×#3372	C₂	semidirect
5. C₅₃×#3370	C₂	semidirect
6. C₅₃×#3366	C₂	semidirect
7. C₅₃×#3361	C₂	semidirect
8. C₅₃×#3360	C₂	semidirect
9. C₅₃×#3142	C₂	semidirect
10. C₅₃×#3141	C₂	semidirect
11. C₅₃×#3080	C₂	semidirect
12. C₅₃×#3079	C₂	semidirect
13. C₅₃×#3036	C₂	semidirect
14. C₅₃×#3036	C₂	semidirect
15. Q₈×M₁₆×C₅₃	C₂	semidirect
16. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
20. C₅₃×#559	C₂²	semidirect
21. C₅₃×#559	C₂²	semidirect
22. C₅₃×#557	C₂²	semidirect
23. C₅₃×#556	C₂²	semidirect
24. C₅₃×#556	C₂²	semidirect
33. C₅₃×#550	C₂²	semidirect
50. C₅₃×#491	C₂²	semidirect
51. C₅₃×#490	C₂²	semidirect
52. C₅₃×#489	C₂²	semidirect
53. C₅₃×#488	C₂²	semidirect
54. C₅₃×#488	C₂²	semidirect
55. C₅₃×#487	C₂²	semidirect
56. C₅₃×#486	C₂²	semidirect
57. C₅₃×#479	C₂²	semidirect
58. C₅₃×#479	C₂²	semidirect
59. C₅₃×#478	C₂²	semidirect
60. C₅₃×#478	C₂²	semidirect
61. C₅₃×#477	C₂²	semidirect
62. C₅₃×#476	C₂²	semidirect
63. C₅₃×#475	C₂²	semidirect
64. C₅₃×#474	C₂²	semidirect
72. C₅₃×#446	C₂²	semidirect
73. C₅₃×#446	C₂²	semidirect
74. C₈×Q₈×C₅₃	C₂²	semidirect
253. C₂×D₄×C₅₃	#41	semidirect
407. #61318	C₅₃	direct (N × H)
439. #3480	C₂×C₅₃	semidirect
440. C₂×#554	C₂×C₅₃	semidirect
441. #3376	C₂×C₅₃	semidirect
442. #3372	C₂×C₅₃	semidirect
443. #3370	C₂×C₅₃	semidirect
444. #3366	C₂×C₅₃	semidirect
445. #3361	C₂×C₅₃	semidirect
446. #3360	C₂×C₅₃	semidirect
447. #3142	C₂×C₅₃	semidirect
448. #3141	C₂×C₅₃	semidirect
449. #3080	C₂×C₅₃	semidirect
450. #3079	C₂×C₅₃	semidirect
451. #3036	C₂×C₅₃	semidirect
452. #3036	C₂×C₅₃	semidirect
453. Q₈×M₁₆	C₂×C₅₃	semidirect
454. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
455. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
465. #559	C₂²×C₅₃	semidirect
466. #559	C₂²×C₅₃	semidirect
467. #557	C₂²×C₅₃	semidirect
468. #556	C₂²×C₅₃	semidirect
469. #556	C₂²×C₅₃	semidirect
478. #550	C₂²×C₅₃	semidirect
495. #491	C₂²×C₅₃	semidirect
496. #490	C₂²×C₅₃	semidirect
497. #489	C₂²×C₅₃	semidirect
498. #488	C₂²×C₅₃	semidirect
499. #488	C₂²×C₅₃	semidirect
500. #487	C₂²×C₅₃	semidirect
501. #486	C₂²×C₅₃	semidirect
502. #479	C₂²×C₅₃	semidirect
503. #479	C₂²×C₅₃	semidirect
504. #478	C₂²×C₅₃	semidirect
505. #478	C₂²×C₅₃	semidirect
506. #477	C₂²×C₅₃	semidirect
507. #476	C₂²×C₅₃	semidirect
508. #475	C₂²×C₅₃	semidirect
509. #474	C₂²×C₅₃	semidirect
517. #446	C₂²×C₅₃	semidirect
518. #446	C₂²×C₅₃	semidirect
519. C₈×Q₈	C₂²×C₅₃	semidirect
540. C₅₃	#61318	direct (N × H)
699. C₂×D₄	#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×#3480	2
C₂×C₅₃×#554	2
C₅₃×#3376	2
C₅₃×#3372	2
C₅₃×#3370	2
C₅₃×#3366	2
C₅₃×#3361	2
C₅₃×#3360	2
C₅₃×#3142	2
C₅₃×#3141	2
C₅₃×#3080	2
C₅₃×#3079	2
C₅₃×#3036	2
Q₈×M₁₆×C₅₃	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61318	53

Subgroups — C53×#61318 #27268830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61318 #27268830