Subgroups — C₅₃×#60695 #27268207

Order 13568.

1978 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3460	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3179	C₂	1	4	yes	maximal, complemented
3	C₅₃×#3176	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3175	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3171	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3169	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3168	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	2	yes	maximal, complemented
15	C₄×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#131×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
19	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
23	C₅₃×#544	C₂²	1	2	yes	—
24	C₅₃×#542	—	2	2	no	—
25	C₅₃×#542	C₂²	1	4	yes	complemented
26	C₅₃×#540	—	2	2	no	—
27	C₅₃×#540	C₂²	1	4	yes	complemented
28	C₅₃×#538	—	2	4	no	—
29	C₅₃×#537	C₂²	1	2	yes	—
30	C₅₃×#535	C₂²	1	2	yes	—
31	C₅₃×#535	C₂²	1	2	yes	—
32	C₅₃×#532	—	2	2	no	—
33	C₅₃×#532	C₂²	1	4	yes	complemented
34	C₅₃×#529	—	2	2	no	—
35	C₅₃×#529	C₂²	1	4	yes	complemented
36	C₅₃×#525	—	2	4	no	—
37	C₄×#41×C₅₃	C₂²	1	2	yes	—
38	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
40	C₅₃×#501	C₂²	1	4	yes	complemented
41	C₅₃×#500	C₂²	1	2	yes	complemented
42	C₅₃×#499	C₂²	1	2	yes	complemented
43	C₅₃×#496	C₂²	1	4	yes	—
44	C₅₃×#495	C₂²	1	2	yes	—
45	C₅₃×#493	C₂²	1	2	yes	—
46	C₅₃×#490	C₂²	1	4	yes	complemented
47	C₅₃×#489	C₂²	1	4	yes	complemented
48	C₅₃×#488	C₂²	1	4	yes	complemented
49	C₅₃×#486	C₂²	1	4	yes	complemented
50	C₅₃×#469	C₂²	1	4	yes	—
51	C₅₃×#469	C₂²	1	4	yes	complemented
52	C₅₃×#468	C₂²	1	4	yes	complemented
53	C₅₃×#468	C₂²	1	4	yes	complemented
54	C₅₃×#467	C₂²	1	2	yes	complemented
55	C₅₃×#466	C₂²	1	2	yes	—
56	C₅₃×#466	C₂²	1	2	yes	—
57	C₅₃×#466	C₂²	1	2	yes	complemented
58	C₅₃×#466	C₂²	1	4	yes	complemented
59	C₅₃×#465	C₂²	1	4	yes	complemented
60	C₅₃×#442	C₂²	1	4	yes	complemented
61	C₅₃×#440	C₂²	1	4	yes	complemented
62	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
65	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
66	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
67	C₄×D₈×C₅₃	C₂²	1	2	yes	—
68	C₄×D₈×C₅₃	C₂²	1	2	yes	—
69	C₄×D₈×C₅₃	C₂²	1	2	yes	—
70	C₄×D₈×C₅₃	C₂²	1	2	yes	—
71	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₈×C₅₃	C₂²	1	4	yes	complemented
74	C₅₃×#428	C₂²	1	2	yes	—
75	C₅₃×#427	C₂²	1	1	yes	characteristic
76	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
77	C₅₃×#418	C₂²	1	2	yes	—
78	C₅₃×#417	C₂²	1	2	yes	—
79	C₅₃×#416	C₂²	1	2	yes	—
80	C₂×#102×C₅₃	C₂²	1	2	yes	—
81	C₅₃×#405	C₂²	1	1	yes	characteristic
82	C₅₃×#405	C₂²	1	1	yes	characteristic
83	C₅₃×#405	C₂²	1	2	yes	complemented
84	C₅₃×#405	C₂²	1	2	yes	complemented
85	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₅₃	C₂²	1	2	yes	complemented
87	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	complemented
89	C₂×#41×C₅₃	—	2	4	no	—
90	C₂×#41×C₅₃	C₂³	1	2	yes	—
91	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₅₃	—	2	2	no	—
94	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
95	#135×C₅₃	—	2	4	no	—
96	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
99	C₂×D₈×C₅₃	—	2	4	no	—
100	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×D₈×C₅₃	C₂³	1	2	yes	—
102	C₂×D₈×C₅₃	C₂³	1	4	yes	—
103	C₂×D₈×C₅₃	C₂³	1	2	yes	—
104	#131×C₅₃	—	2	4	no	—
105	#131×C₅₃	—	2	4	no	—
106	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
108	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
109	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
112	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₃	—	2	2	no	—
115	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
116	#127×C₅₃	—	2	2	no	—
117	#127×C₅₃	C₂³	1	4	yes	—
118	#126×C₅₃	—	2	4	no	—
119	#126×C₅₃	—	2	4	no	—
120	#125×C₅₃	—	2	2	no	—
121	#125×C₅₃	C₂³	1	4	yes	—
122	#124×C₅₃	—	2	4	no	—
123	#124×C₅₃	—	2	4	no	—
124	#124×C₅₃	—	2	2	no	—
125	#124×C₅₃	C₂³	1	4	yes	—
126	#123×C₅₃	—	2	4	no	—
127	#123×C₅₃	—	2	4	no	—
128	#123×C₅₃	—	2	4	no	—
129	#123×C₅₃	—	2	4	no	—
130	C₂²⋊Q₈×C₅₃	—	2	4	no	—
131	C₂²⋊Q₈×C₅₃	—	2	4	no	—
132	C₂²⋊Q₈×C₅₃	—	2	2	no	—
133	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
134	#121×C₅₃	—	2	2	no	—
135	#121×C₅₃	—	2	2	no	—
136	#121×C₅₃	—	2	4	no	—
137	#121×C₅₃	—	2	4	no	—
138	#121×C₅₃	—	2	4	no	—
139	#121×C₅₃	—	2	2	no	—
140	#121×C₅₃	—	2	4	no	—
141	#121×C₅₃	C₂³	1	4	yes	—
142	#121×C₅₃	C₂³	1	4	yes	—
143	#121×C₅₃	C₂³	1	4	yes	—
144	#120×C₅₃	—	2	4	no	—
145	#120×C₅₃	—	2	4	no	—
146	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
147	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
150	C₄×D₄×C₅₃	—	2	2	no	—
151	C₄×D₄×C₅₃	—	2	2	no	—
152	C₄×D₄×C₅₃	—	2	4	no	—
153	C₄×D₄×C₅₃	—	2	2	no	—
154	C₄×D₄×C₅₃	—	2	2	no	—
155	C₄×D₄×C₅₃	—	2	4	no	—
156	C₄×D₄×C₅₃	D₄	1	2	yes	—
157	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
158	C₄×D₄×C₅₃	D₄	1	2	yes	—
159	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
160	C₄×D₄×C₅₃	C₂³	1	4	yes	—
161	C₄×D₄×C₅₃	C₂³	1	4	yes	—
162	C₄×D₄×C₅₃	C₂³	1	2	yes	—
163	C₄×D₄×C₅₃	C₂³	1	2	yes	—
164	#117×C₅₃	—	2	2	no	—
165	#117×C₅₃	—	2	4	no	—
166	#117×C₅₃	C₂³	1	2	yes	—
167	#117×C₅₃	C₂³	1	1	yes	characteristic
168	#117×C₅₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
171	C₂×C₄²×C₅₃	—	2	2	no	—
172	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
174	#107×C₅₃	C₂³	1	1	yes	characteristic
175	#107×C₅₃	C₂³	1	2	yes	—
176	#107×C₅₃	C₂³	1	1	yes	characteristic
177	#107×C₅₃	C₂³	1	4	yes	—
178	#107×C₅₃	C₂³	1	2	yes	—
179	#106×C₅₃	C₂³	1	4	yes	—
180	#106×C₅₃	C₂³	1	2	yes	—
181	#103×C₅₃	C₂³	1	2	yes	—
182	#103×C₅₃	C₂³	1	4	yes	—
183	#103×C₅₃	C₂³	1	2	yes	—
184	#102×C₅₃	C₂³	1	2	yes	—
185	#102×C₅₃	C₂³	1	4	yes	—
186	#102×C₅₃	C₂³	1	4	yes	—
187	#102×C₅₃	C₂³	1	4	yes	—
188	#102×C₅₃	C₂³	1	4	yes	—
189	#102×C₅₃	C₂³	1	4	yes	—
190	#102×C₅₃	C₂³	1	2	yes	—
191	#97×C₅₃	C₂³	1	2	yes	—
192	#97×C₅₃	C₂³	1	2	yes	—
193	#97×C₅₃	C₂³	1	2	yes	—
194	C₄×C₈×C₅₃	C₂³	1	2	yes	—
195	C₄×C₈×C₅₃	C₂³	1	2	yes	—
196	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₅₃	C₂³	1	2	yes	—
201	C₂⁴×C₅₃	—	2	2	no	—
202	#41×C₅₃	—	2	2	no	—
203	#41×C₅₃	—	2	2	no	—
204	#41×C₅₃	—	2	4	no	—
205	#41×C₅₃	—	2	4	no	—
206	#41×C₅₃	—	8	8	no	—
207	C₂×Q₈×C₅₃	—	2	4	no	—
208	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₅₃	—	2	2	no	—
211	C₂×D₄×C₅₃	—	2	4	no	—
212	C₂×D₄×C₅₃	—	2	4	no	—
213	C₂×D₄×C₅₃	—	2	4	no	—
214	C₂×D₄×C₅₃	—	2	2	no	—
215	C₂×D₄×C₅₃	—	2	4	no	—
216	C₂×D₄×C₅₃	—	2	4	no	—
217	C₂×D₄×C₅₃	—	2	4	no	—
218	C₂×D₄×C₅₃	—	2	4	no	—
219	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
222	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₃	—	2	2	no	—
224	C₂²×C₄×C₅₃	—	2	2	no	—
225	C₂²×C₄×C₅₃	—	2	2	no	—
226	C₂²×C₄×C₅₃	—	2	4	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	2	4	no	—
229	C₂²×C₄×C₅₃	—	8	4	no	—
230	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₅₃	—	2	2	no	—
237	SD₁₆×C₅₃	—	2	4	no	—
238	SD₁₆×C₅₃	—	2	8	no	—
239	D₈×C₅₃	—	2	4	no	—
240	D₈×C₅₃	—	2	4	no	—
241	D₈×C₅₃	—	2	2	no	—
242	D₈×C₅₃	—	2	8	no	—
243	M₁₆×C₅₃	—	2	2	no	—
244	M₁₆×C₅₃	—	2	4	no	—
245	M₁₆×C₅₃	—	2	4	no	—
246	M₁₆×C₅₃	#41	1	4	yes	complemented
247	C₂×C₈×C₅₃	—	2	2	no	—
248	C₂×C₈×C₅₃	—	2	4	no	—
249	C₂×C₈×C₅₃	—	2	4	no	—
250	C₂×C₈×C₅₃	#41	1	4	yes	complemented
251	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
253	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
256	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₅₃	—	2	2	no	—
258	C₄⋊C₄×C₅₃	—	2	2	no	—
259	C₄⋊C₄×C₅₃	—	2	2	no	—
260	C₄⋊C₄×C₅₃	—	2	4	no	—
261	C₄⋊C₄×C₅₃	—	2	4	no	—
262	C₄⋊C₄×C₅₃	—	2	4	no	—
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
267	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
270	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂²⋊C₄×C₅₃	—	2	4	no	—
273	C₂²⋊C₄×C₅₃	—	2	4	no	—
274	C₂²⋊C₄×C₅₃	—	2	4	no	—
275	C₂²⋊C₄×C₅₃	—	2	2	no	—
276	C₂²⋊C₄×C₅₃	—	2	2	no	—
277	C₂²⋊C₄×C₅₃	—	2	4	no	—
278	C₂²⋊C₄×C₅₃	—	2	4	no	—
279	C₂²⋊C₄×C₅₃	—	2	4	no	—
280	C₂²⋊C₄×C₅₃	—	2	4	no	—
281	C₂²⋊C₄×C₅₃	—	2	4	no	—
282	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
285	C₄²×C₅₃	—	2	2	no	—
286	C₄²×C₅₃	—	2	2	no	—
287	C₄²×C₅₃	—	2	2	no	—
288	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₅₃	C₂×D₄	1	2	yes	—
290	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₅₃	C₂×D₄	1	2	yes	—
292	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
293	C₄²×C₅₃	C₂⁴	1	2	yes	—
294	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂³×C₅₃	—	2	2	no	—
296	C₂³×C₅₃	—	2	4	no	—
297	C₂³×C₅₃	—	4	4	no	—
298	C₂³×C₅₃	—	8	2	no	—
299	C₂³×C₅₃	—	8	2	no	—
300	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
301	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₅₃	—	2	2	no	—
303	Q₈×C₅₃	—	2	2	no	—
304	Q₈×C₅₃	—	2	2	no	—
305	Q₈×C₅₃	—	8	4	no	—
306	D₄×C₅₃	—	2	4	no	—
307	D₄×C₅₃	—	2	2	no	—
308	D₄×C₅₃	—	2	4	no	—
309	D₄×C₅₃	—	2	4	no	—
310	D₄×C₅₃	—	2	2	no	—
311	D₄×C₅₃	—	2	2	no	—
312	D₄×C₅₃	—	4	4	no	—
313	D₄×C₅₃	—	4	4	no	—
314	D₄×C₅₃	—	8	4	no	—
315	D₄×C₅₃	—	8	4	no	—
316	D₄×C₅₃	—	8	4	no	—
317	D₄×C₅₃	—	8	4	no	—
318	D₄×C₅₃	—	8	4	no	—
319	C₂×C₄×C₅₃	—	2	2	no	—
320	C₂×C₄×C₅₃	—	2	4	no	—
321	C₂×C₄×C₅₃	—	2	2	no	—
322	C₂×C₄×C₅₃	—	2	2	no	—
323	C₂×C₄×C₅₃	—	2	4	no	—
324	C₂×C₄×C₅₃	—	2	2	no	—
325	C₂×C₄×C₅₃	—	2	2	no	—
326	C₂×C₄×C₅₃	—	2	2	no	—
327	C₂×C₄×C₅₃	—	4	1	no	—
328	C₂×C₄×C₅₃	—	4	2	no	—
329	C₂×C₄×C₅₃	—	4	4	no	—
330	C₂×C₄×C₅₃	—	4	8	no	—
331	C₂×C₄×C₅₃	—	4	4	no	—
332	C₂×C₄×C₅₃	—	8	2	no	—
333	C₂×C₄×C₅₃	—	8	4	no	—
334	C₂×C₄×C₅₃	—	8	2	no	—
335	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
344	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
345	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
346	C₈×C₅₃	—	2	1	no	—
347	C₈×C₅₃	—	2	1	no	—
348	C₈×C₅₃	—	2	2	no	—
349	C₈×C₅₃	C₂×#41	1	2	yes	—
350	C₈×C₅₃	C₂×#41	1	4	yes	—
351	C₈×C₅₃	C₂×#41	1	2	yes	—
352	#60695	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂²×C₅₃	—	2	1	no	—
354	C₂²×C₅₃	—	2	1	no	—
355	C₂²×C₅₃	—	2	2	no	—
356	C₂²×C₅₃	—	2	2	no	—
357	C₂²×C₅₃	—	2	2	no	—
358	C₂²×C₅₃	—	4	2	no	—
359	C₂²×C₅₃	—	4	4	no	—
360	C₂²×C₅₃	—	4	2	no	—
361	C₂²×C₅₃	—	4	4	no	—
362	C₂²×C₅₃	—	4	4	no	—
363	C₂²×C₅₃	—	4	2	no	—
364	C₂²×C₅₃	—	8	8	no	—
365	C₂²×C₅₃	#532	1	2	yes	—
366	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₅₃	—	2	1	no	—
368	C₄×C₅₃	—	2	1	no	—
369	C₄×C₅₃	—	2	2	no	—
370	C₄×C₅₃	—	2	2	no	—
371	C₄×C₅₃	—	2	1	no	—
372	C₄×C₅₃	—	2	2	no	—
373	C₄×C₅₃	—	4	2	no	—
374	C₄×C₅₃	—	4	2	no	—
375	C₄×C₅₃	—	4	4	no	—
376	C₄×C₅₃	—	4	2	no	—
377	C₄×C₅₃	#532	1	2	yes	—
378	C₄×C₅₃	#576	1	2	yes	—
379	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
380	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
381	#3460	C₂×C₅₃	1	2	yes	complemented
382	#3179	C₂×C₅₃	1	4	yes	complemented
383	#3176	C₂×C₅₃	1	2	yes	complemented
384	#3175	C₂×C₅₃	1	2	yes	complemented
385	#3171	C₂×C₅₃	1	4	yes	complemented
386	#3169	C₂×C₅₃	1	2	yes	complemented
387	#3168	C₂×C₅₃	1	2	yes	complemented
388	#3164	C₂×C₅₃	1	1	yes	characteristic, complemented
389	#3155	C₂×C₅₃	1	1	yes	characteristic, complemented
390	#3136	C₂×C₅₃	1	2	yes	complemented
391	#3062	C₂×C₅₃	1	2	yes	complemented
392	#3061	C₂×C₅₃	1	1	yes	characteristic, complemented
393	#3058	C₂×C₅₃	1	1	yes	characteristic, complemented
394	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	2	yes	complemented
395	C₄×#135	C₂×C₅₃	1	1	yes	characteristic, complemented
396	C₂×C₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
397	C₄×#131	C₂×C₅₃	1	1	yes	characteristic, complemented
398	C₂×C₅₃	—	2	2	no	—
399	C₂×C₅₃	—	4	2	no	—
400	C₂×C₅₃	—	8	2	no	—
401	C₂×C₅₃	—	8	4	no	—
402	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
403	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
404	C₂×C₅₃	#3584	1	1	yes	characteristic
405	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
406	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
407	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
409	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
410	#544	C₂²×C₅₃	1	2	yes	—
411	#542	—	2	2	no	—
412	#542	C₂²×C₅₃	1	4	yes	complemented
413	#540	—	2	2	no	—
414	#540	C₂²×C₅₃	1	4	yes	complemented
415	#538	—	2	4	no	—
416	#537	C₂²×C₅₃	1	2	yes	—
417	#535	C₂²×C₅₃	1	2	yes	—
418	#535	C₂²×C₅₃	1	2	yes	—
419	#532	—	2	2	no	—
420	#532	C₂²×C₅₃	1	4	yes	complemented
421	#529	—	2	2	no	—
422	#529	C₂²×C₅₃	1	4	yes	complemented
423	#525	—	2	4	no	—
424	C₄×#41	C₂²×C₅₃	1	2	yes	—
425	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
427	#501	C₂²×C₅₃	1	4	yes	complemented
428	#500	C₂²×C₅₃	1	2	yes	complemented
429	#499	C₂²×C₅₃	1	2	yes	complemented
430	#496	C₂²×C₅₃	1	4	yes	—
431	#495	C₂²×C₅₃	1	2	yes	—
432	#493	C₂²×C₅₃	1	2	yes	—
433	#490	C₂²×C₅₃	1	4	yes	complemented
434	#489	C₂²×C₅₃	1	4	yes	complemented
435	#488	C₂²×C₅₃	1	4	yes	complemented
436	#486	C₂²×C₅₃	1	4	yes	complemented
437	#469	C₂²×C₅₃	1	4	yes	—
438	#469	C₂²×C₅₃	1	4	yes	complemented
439	#468	C₂²×C₅₃	1	4	yes	complemented
440	#468	C₂²×C₅₃	1	4	yes	complemented
441	#467	C₂²×C₅₃	1	2	yes	complemented
442	#466	C₂²×C₅₃	1	2	yes	—
443	#466	C₂²×C₅₃	1	2	yes	—
444	#466	C₂²×C₅₃	1	2	yes	complemented
445	#466	C₂²×C₅₃	1	4	yes	complemented
446	#465	C₂²×C₅₃	1	4	yes	complemented
447	#442	C₂²×C₅₃	1	4	yes	complemented
448	#440	C₂²×C₅₃	1	4	yes	complemented
449	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
450	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
451	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
452	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
453	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
454	C₄×D₈	C₂²×C₅₃	1	2	yes	—
455	C₄×D₈	C₂²×C₅₃	1	2	yes	—
456	C₄×D₈	C₂²×C₅₃	1	2	yes	—
457	C₄×D₈	C₂²×C₅₃	1	2	yes	—
458	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
459	C₄×D₈	C₂²×C₅₃	1	4	yes	complemented
460	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
461	#428	C₂²×C₅₃	1	2	yes	—
462	#427	C₂²×C₅₃	1	1	yes	characteristic
463	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
464	#418	C₂²×C₅₃	1	2	yes	—
465	#417	C₂²×C₅₃	1	2	yes	—
466	#416	C₂²×C₅₃	1	2	yes	—
467	C₂×#102	C₂²×C₅₃	1	2	yes	—
468	#405	C₂²×C₅₃	1	1	yes	characteristic
469	#405	C₂²×C₅₃	1	1	yes	characteristic
470	#405	C₂²×C₅₃	1	2	yes	complemented
471	#405	C₂²×C₅₃	1	2	yes	complemented
472	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
473	C₄×M₁₆	C₂²×C₅₃	1	2	yes	complemented
474	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
475	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	complemented
476	C₅₃	#60695	1	1	yes	characteristic, direct product factor, Sylow
477	C₂×#41	—	2	4	no	—
478	C₂×#41	C₂³×C₅₃	1	2	yes	—
479	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
480	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
481	C₂³×C₄	—	2	2	no	—
482	AGL(1,ℤ/8)	—	2	8	no	—
483	#135	—	2	4	no	—
484	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
485	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
486	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
487	C₂×D₈	—	2	4	no	—
488	C₂×D₈	C₂³×C₅₃	1	2	yes	—
489	C₂×D₈	C₂³×C₅₃	1	2	yes	—
490	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
491	C₂×D₈	C₂³×C₅₃	1	4	yes	—
492	#131	—	2	4	no	—
493	#131	—	2	4	no	—
494	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
495	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
496	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
497	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
500	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
501	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
502	C₄⋊Q₈	—	2	2	no	—
503	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
504	#127	—	2	2	no	—
505	#127	C₂³×C₅₃	1	4	yes	—
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#125	—	2	2	no	—
509	#125	C₂³×C₅₃	1	4	yes	—
510	#124	—	2	2	no	—
511	#124	—	2	4	no	—
512	#124	—	2	4	no	—
513	#124	C₂³×C₅₃	1	4	yes	—
514	#123	—	2	4	no	—
515	#123	—	2	4	no	—
516	#123	—	2	4	no	—
517	#123	—	2	4	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
522	#121	—	2	4	no	—
523	#121	—	2	2	no	—
524	#121	—	2	4	no	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#121	C₂³×C₅₃	1	4	yes	—
530	#121	C₂³×C₅₃	1	4	yes	—
531	#121	C₂³×C₅₃	1	4	yes	—
532	#120	—	2	4	no	—
533	#120	—	2	4	no	—
534	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
535	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
536	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
537	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	D₄×C₅₃	1	2	yes	—
545	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
546	C₄×D₄	D₄×C₅₃	1	2	yes	—
547	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
548	C₄×D₄	C₂³×C₅₃	1	4	yes	—
549	C₄×D₄	C₂³×C₅₃	1	4	yes	—
550	C₄×D₄	C₂³×C₅₃	1	2	yes	—
551	C₄×D₄	C₂³×C₅₃	1	2	yes	—
552	#117	—	2	2	no	—
553	#117	—	2	4	no	—
554	#117	C₂³×C₅₃	1	2	yes	—
555	#117	C₂³×C₅₃	1	1	yes	characteristic
556	#117	C₂³×C₅₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
558	C₂×C₂²⋊C₄	—	2	2	no	—
559	C₂×C₄²	—	2	2	no	—
560	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
562	#107	C₂³×C₅₃	1	2	yes	—
563	#107	C₂³×C₅₃	1	2	yes	—
564	#107	C₂³×C₅₃	1	1	yes	characteristic
565	#107	C₂³×C₅₃	1	1	yes	characteristic
566	#107	C₂³×C₅₃	1	4	yes	—
567	#106	C₂³×C₅₃	1	2	yes	—
568	#106	C₂³×C₅₃	1	4	yes	—
569	#103	C₂³×C₅₃	1	2	yes	—
570	#103	C₂³×C₅₃	1	2	yes	—
571	#103	C₂³×C₅₃	1	4	yes	—
572	#102	C₂³×C₅₃	1	4	yes	—
573	#102	C₂³×C₅₃	1	4	yes	—
574	#102	C₂³×C₅₃	1	2	yes	—
575	#102	C₂³×C₅₃	1	2	yes	—
576	#102	C₂³×C₅₃	1	4	yes	—
577	#102	C₂³×C₅₃	1	4	yes	—
578	#102	C₂³×C₅₃	1	4	yes	—
579	#97	C₂³×C₅₃	1	2	yes	—
580	#97	C₂³×C₅₃	1	2	yes	—
581	#97	C₂³×C₅₃	1	2	yes	—
582	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
583	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
584	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
586	C₄×C₈	C₂³×C₅₃	1	2	yes	—
587	C₄×C₈	C₂³×C₅₃	1	2	yes	—
588	C₄×C₈	C₂³×C₅₃	1	2	yes	—
589	C₂⁴	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	—	8	8	no	—
595	C₂×Q₈	—	2	4	no	—
596	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
597	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
608	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
609	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
610	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	8	4	no	—
618	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
620	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
624	Q₁₆	—	2	2	no	—
625	SD₁₆	—	2	4	no	—
626	SD₁₆	—	2	8	no	—
627	D₈	—	2	4	no	—
628	D₈	—	2	4	no	—
629	D₈	—	2	2	no	—
630	D₈	—	2	8	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	—	2	4	no	—
634	M₁₆	#41×C₅₃	1	4	yes	complemented
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	#41×C₅₃	1	4	yes	complemented
639	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
642	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
643	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
644	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
653	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
655	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
658	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
678	C₄²	C₂×D₄×C₅₃	1	2	yes	—
679	C₄²	C₂×D₄×C₅₃	1	2	yes	—
680	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
681	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
682	C₄²	C₂⁴×C₅₃	1	2	yes	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	2	no	—
688	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
689	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	8	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	D₄	—	8	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
732	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
733	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂×#41×C₅₃	1	2	yes	—
738	C₈	C₂×#41×C₅₃	1	4	yes	—
739	C₈	C₂×#41×C₅₃	1	2	yes	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	8	8	no	—
752	C₂²	C₅₃×#532	1	2	yes	—
753	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₅₃×#532	1	2	yes	—
765	C₄	C₅₃×#576	1	2	yes	—
766	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
767	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	2	no	—
770	C₂	—	8	4	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
773	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
774	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3460	C₂	semidirect
2. C₅₃×#3179	C₂	semidirect
3. C₅₃×#3176	C₂	semidirect
4. C₅₃×#3175	C₂	semidirect
5. C₅₃×#3171	C₂	semidirect
6. C₅₃×#3169	C₂	semidirect
7. C₅₃×#3168	C₂	semidirect
8. C₅₃×#3164	C₂	semidirect
9. C₅₃×#3155	C₂	semidirect
10. C₅₃×#3136	C₂	semidirect
11. C₅₃×#3062	C₂	semidirect
12. C₅₃×#3061	C₂	semidirect
13. C₅₃×#3058	C₂	semidirect
14. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
15. C₄×#135×C₅₃	C₂	semidirect
16. C₂×C₄×D₈×C₅₃	C₂	semidirect
17. C₄×#131×C₅₃	C₂	semidirect
25. C₅₃×#542	C₂²	semidirect
27. C₅₃×#540	C₂²	semidirect
33. C₅₃×#532	C₂²	semidirect
35. C₅₃×#529	C₂²	semidirect
40. C₅₃×#501	C₂²	semidirect
41. C₅₃×#500	C₂²	semidirect
42. C₅₃×#499	C₂²	semidirect
46. C₅₃×#490	C₂²	semidirect
47. C₅₃×#489	C₂²	semidirect
48. C₅₃×#488	C₂²	semidirect
49. C₅₃×#486	C₂²	semidirect
51. C₅₃×#469	C₂²	semidirect
52. C₅₃×#468	C₂²	semidirect
53. C₅₃×#468	C₂²	semidirect
54. C₅₃×#467	C₂²	semidirect
57. C₅₃×#466	C₂²	semidirect
58. C₅₃×#466	C₂²	semidirect
59. C₅₃×#465	C₂²	semidirect
60. C₅₃×#442	C₂²	semidirect
61. C₅₃×#440	C₂²	semidirect
62. C₄×Q₁₆×C₅₃	C₂²	semidirect
63. C₄×Q₁₆×C₅₃	C₂²	semidirect
64. C₄×SD₁₆×C₅₃	C₂²	semidirect
65. C₄×SD₁₆×C₅₃	C₂²	semidirect
66. C₄×SD₁₆×C₅₃	C₂²	semidirect
71. C₄×D₈×C₅₃	C₂²	semidirect
72. C₄×D₈×C₅₃	C₂²	semidirect
73. C₄×D₈×C₅₃	C₂²	semidirect
83. C₅₃×#405	C₂²	semidirect
84. C₅₃×#405	C₂²	semidirect
86. C₄×M₁₆×C₅₃	C₂²	semidirect
88. C₂×C₄×C₈×C₅₃	C₂²	semidirect
246. M₁₆×C₅₃	#41	semidirect
250. C₂×C₈×C₅₃	#41	semidirect
352. #60695	C₅₃	direct (N × H)
381. #3460	C₂×C₅₃	semidirect
382. #3179	C₂×C₅₃	semidirect
383. #3176	C₂×C₅₃	semidirect
384. #3175	C₂×C₅₃	semidirect
385. #3171	C₂×C₅₃	semidirect
386. #3169	C₂×C₅₃	semidirect
387. #3168	C₂×C₅₃	semidirect
388. #3164	C₂×C₅₃	semidirect
389. #3155	C₂×C₅₃	semidirect
390. #3136	C₂×C₅₃	semidirect
391. #3062	C₂×C₅₃	semidirect
392. #3061	C₂×C₅₃	semidirect
393. #3058	C₂×C₅₃	semidirect
394. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
395. C₄×#135	C₂×C₅₃	semidirect
396. C₂×C₄×D₈	C₂×C₅₃	semidirect
397. C₄×#131	C₂×C₅₃	semidirect
412. #542	C₂²×C₅₃	semidirect
414. #540	C₂²×C₅₃	semidirect
420. #532	C₂²×C₅₃	semidirect
422. #529	C₂²×C₅₃	semidirect
427. #501	C₂²×C₅₃	semidirect
428. #500	C₂²×C₅₃	semidirect
429. #499	C₂²×C₅₃	semidirect
433. #490	C₂²×C₅₃	semidirect
434. #489	C₂²×C₅₃	semidirect
435. #488	C₂²×C₅₃	semidirect
436. #486	C₂²×C₅₃	semidirect
438. #469	C₂²×C₅₃	semidirect
439. #468	C₂²×C₅₃	semidirect
440. #468	C₂²×C₅₃	semidirect
441. #467	C₂²×C₅₃	semidirect
444. #466	C₂²×C₅₃	semidirect
445. #466	C₂²×C₅₃	semidirect
446. #465	C₂²×C₅₃	semidirect
447. #442	C₂²×C₅₃	semidirect
448. #440	C₂²×C₅₃	semidirect
449. C₄×Q₁₆	C₂²×C₅₃	semidirect
450. C₄×Q₁₆	C₂²×C₅₃	semidirect
451. C₄×SD₁₆	C₂²×C₅₃	semidirect
452. C₄×SD₁₆	C₂²×C₅₃	semidirect
453. C₄×SD₁₆	C₂²×C₅₃	semidirect
458. C₄×D₈	C₂²×C₅₃	semidirect
459. C₄×D₈	C₂²×C₅₃	semidirect
460. C₄×D₈	C₂²×C₅₃	semidirect
470. #405	C₂²×C₅₃	semidirect
471. #405	C₂²×C₅₃	semidirect
473. C₄×M₁₆	C₂²×C₅₃	semidirect
475. C₂×C₄×C₈	C₂²×C₅₃	semidirect
476. C₅₃	#60695	direct (N × H)
634. M₁₆	#41×C₅₃	semidirect
638. 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×#3460	2
C₅₃×#3179	2
C₅₃×#3176	2
C₅₃×#3175	2
C₅₃×#3171	2
C₅₃×#3169	2
C₅₃×#3168	2
C₅₃×#3164	2
C₅₃×#3155	2
C₅₃×#3136	2
C₅₃×#3062	2
C₅₃×#3061	2
C₅₃×#3058	2
C₄×AGL(1,ℤ/8)×C₅₃	2
C₄×#135×C₅₃	2
C₂×C₄×D₈×C₅₃	2
C₄×#131×C₅₃	2
#60695	53

Subgroups — C53×#60695 #27268207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60695 #27268207