Subgroups — C₅₃×#34082 #27241594

Order 13568.

2714 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2335	C₂	1	4	yes	maximal, complemented
3	C₅₃×#2333	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2332	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2329	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2325	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2321	C₂	1	4	yes	maximal, complemented
8	C₅₃×#2298	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2297	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2293	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2290	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2290	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×D₄×C₅₃	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#525	C₄	1	16	yes	complemented
19	C₂×#123×C₅₃	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×#120×C₅₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
28	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
32	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
33	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
36	C₅₃×#391	C₂²	1	4	yes	complemented
37	C₅₃×#390	C₂²	1	4	yes	—
38	C₅₃×#390	C₂²	1	4	yes	—
39	C₅₃×#389	C₂²	1	4	yes	complemented
40	C₅₃×#388	C₂²	1	4	yes	—
41	C₅₃×#388	C₂²	1	4	yes	—
42	C₅₃×#388	C₂²	1	4	yes	—
43	C₅₃×#388	C₂²	1	4	yes	—
44	C₅₃×#388	C₂²	1	4	yes	complemented
45	C₅₃×#388	C₂²	1	4	yes	complemented
46	C₅₃×#387	C₂²	1	4	yes	complemented
47	C₅₃×#387	C₂²	1	4	yes	complemented
48	C₅₃×#387	C₂²	1	4	yes	complemented
49	C₅₃×#387	C₂²	1	4	yes	complemented
50	C₅₃×#386	C₂²	1	4	yes	—
51	C₅₃×#386	C₂²	1	4	yes	—
52	C₅₃×#386	C₂²	1	4	yes	—
53	C₅₃×#386	C₂²	1	4	yes	complemented
54	C₅₃×#385	C₂²	1	4	yes	—
55	C₅₃×#385	C₂²	1	4	yes	complemented
56	C₅₃×#381	C₂²	1	2	yes	—
57	C₅₃×#380	C₂²	1	2	yes	—
58	C₅₃×#380	C₂²	1	2	yes	—
59	C₅₃×#379	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
61	C₄×C₄⋊C₄×C₅₃	C₂²	1	4	yes	complemented
62	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
68	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
69	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
72	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
73	C₅₃×#376	C₂²	1	2	yes	complemented
74	C₂×#95×C₅₃	C₂²	1	2	yes	—
75	C₄³×C₅₃	C₂²	1	2	yes	complemented
76	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
77	C₂×#41×C₅₃	—	4	2	no	—
78	C₂×#41×C₅₃	—	4	2	no	—
79	C₂×#41×C₅₃	C₂×C₄	1	8	yes	complemented
80	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅₃	—	4	2	no	—
86	C₂³×C₄×C₅₃	—	4	2	no	—
87	C₂³×C₄×C₅₃	C₂×C₄	1	8	yes	complemented
88	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
98	#123×C₅₃	C₂×C₄	1	16	yes	complemented
99	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
100	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
101	#121×C₅₃	C₂×C₄	1	8	yes	—
102	#121×C₅₃	C₂×C₄	1	8	yes	complemented
103	#120×C₅₃	C₂×C₄	1	16	yes	complemented
104	C₄×D₄×C₅₃	—	2	16	no	—
105	C₄×D₄×C₅₃	C₂×C₄	1	16	yes	complemented
106	C₄×D₄×C₅₃	C₂×C₄	1	16	yes	complemented
107	#117×C₅₃	—	4	2	no	—
108	#117×C₅₃	—	4	2	no	—
109	#117×C₅₃	—	4	4	no	—
110	#117×C₅₃	C₂×C₄	1	8	yes	complemented
111	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
121	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₅₃	—	4	2	no	—
136	C₂×C₄²×C₅₃	—	4	2	no	—
137	C₂×C₄²×C₅₃	—	4	4	no	—
138	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
141	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
143	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
147	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
148	#95×C₅₃	C₂³	1	4	yes	—
149	#95×C₅₃	C₂³	1	4	yes	—
150	#95×C₅₃	C₂³	1	4	yes	—
151	#95×C₅₃	C₂³	1	4	yes	—
152	#95×C₅₃	C₂³	1	4	yes	—
153	#95×C₅₃	C₂³	1	4	yes	—
154	#95×C₅₃	C₂³	1	4	yes	—
155	#95×C₅₃	C₂³	1	4	yes	—
156	#95×C₅₃	C₂³	1	4	yes	—
157	#95×C₅₃	C₂³	1	4	yes	—
158	C₂⁴×C₅₃	—	2	4	no	—
159	C₂⁴×C₅₃	—	4	1	no	—
160	C₂⁴×C₅₃	—	4	1	no	—
161	C₂⁴×C₅₃	—	4	2	no	—
162	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
163	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
166	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
167	#41×C₅₃	—	4	16	no	—
168	C₂×Q₈×C₅₃	—	4	1	no	—
169	C₂×Q₈×C₅₃	—	4	1	no	—
170	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
171	C₂×D₄×C₅₃	—	2	8	no	—
172	C₂×D₄×C₅₃	—	4	4	no	—
173	C₂×D₄×C₅₃	—	4	1	no	—
174	C₂×D₄×C₅₃	—	4	1	no	—
175	C₂×D₄×C₅₃	—	4	2	no	—
176	C₂×D₄×C₅₃	—	4	2	no	—
177	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
178	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
179	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
180	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₅₃	—	2	2	no	—
182	C₂²×C₄×C₅₃	—	2	2	no	—
183	C₂²×C₄×C₅₃	—	2	4	no	—
184	C₂²×C₄×C₅₃	—	2	2	no	—
185	C₂²×C₄×C₅₃	—	2	2	no	—
186	C₂²×C₄×C₅₃	—	2	4	no	—
187	C₂²×C₄×C₅₃	—	2	2	no	—
188	C₂²×C₄×C₅₃	—	2	2	no	—
189	C₂²×C₄×C₅₃	—	2	4	no	—
190	C₂²×C₄×C₅₃	—	2	8	no	—
191	C₂²×C₄×C₅₃	—	4	16	no	—
192	C₂²×C₄×C₅₃	—	4	2	no	—
193	C₂²×C₄×C₅₃	—	4	4	no	—
194	C₂²×C₄×C₅₃	—	4	2	no	—
195	C₂²×C₄×C₅₃	—	4	1	no	—
196	C₂²×C₄×C₅₃	—	4	1	no	—
197	C₂²×C₄×C₅₃	—	4	1	no	—
198	C₂²×C₄×C₅₃	—	4	1	no	—
199	C₂²×C₄×C₅₃	—	4	1	no	—
200	C₂²×C₄×C₅₃	—	4	1	no	—
201	C₂²×C₄×C₅₃	—	4	2	no	—
202	C₂²×C₄×C₅₃	—	4	4	no	—
203	C₂²×C₄×C₅₃	—	4	2	no	—
204	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
206	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
207	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
208	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
209	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
210	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
211	C₂²×C₄×C₅₃	#41	1	8	yes	complemented
212	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₄⋊C₄×C₅₃	—	2	8	no	—
224	C₄⋊C₄×C₅₃	—	4	4	no	—
225	C₄⋊C₄×C₅₃	—	4	2	no	—
226	C₄⋊C₄×C₅₃	—	4	2	no	—
227	C₄⋊C₄×C₅₃	—	4	4	no	—
228	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
229	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
230	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
231	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
232	C₂²⋊C₄×C₅₃	—	2	8	no	—
233	C₂²⋊C₄×C₅₃	—	2	8	no	—
234	C₂²⋊C₄×C₅₃	—	2	8	no	—
235	C₂²⋊C₄×C₅₃	—	2	8	no	—
236	C₂²⋊C₄×C₅₃	—	4	4	no	—
237	C₂²⋊C₄×C₅₃	—	4	4	no	—
238	C₂²⋊C₄×C₅₃	—	4	2	no	—
239	C₂²⋊C₄×C₅₃	—	4	4	no	—
240	C₂²⋊C₄×C₅₃	—	4	2	no	—
241	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
242	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
243	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
244	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
245	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
246	C₄²×C₅₃	—	2	8	no	—
247	C₄²×C₅₃	—	2	4	no	—
248	C₄²×C₅₃	—	2	4	no	—
249	C₄²×C₅₃	—	2	4	no	—
250	C₄²×C₅₃	—	2	4	no	—
251	C₄²×C₅₃	—	4	2	no	—
252	C₄²×C₅₃	—	4	2	no	—
253	C₄²×C₅₃	—	4	4	no	—
254	C₄²×C₅₃	—	4	4	no	—
255	C₄²×C₅₃	C₂²×C₄	1	8	yes	—
256	C₂³×C₅₃	—	2	1	no	—
257	C₂³×C₅₃	—	2	1	no	—
258	C₂³×C₅₃	—	2	2	no	—
259	C₂³×C₅₃	—	2	8	no	—
260	C₂³×C₅₃	—	2	4	no	—
261	C₂³×C₅₃	—	2	2	no	—
262	C₂³×C₅₃	—	2	2	no	—
263	C₂³×C₅₃	—	2	2	no	—
264	C₂³×C₅₃	—	2	1	no	—
265	C₂³×C₅₃	—	2	1	no	—
266	C₂³×C₅₃	—	2	1	no	—
267	C₂³×C₅₃	—	2	1	no	—
268	C₂³×C₅₃	—	2	2	no	—
269	C₂³×C₅₃	—	2	4	no	—
270	C₂³×C₅₃	—	2	2	no	—
271	C₂³×C₅₃	—	2	2	no	—
272	C₂³×C₅₃	—	4	4	no	—
273	C₂³×C₅₃	—	4	4	no	—
274	C₂³×C₅₃	—	4	8	no	—
275	C₂³×C₅₃	—	4	8	no	—
276	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
277	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
278	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
279	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
280	C₂³×C₅₃	C₂×#41	1	4	yes	—
281	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
282	Q₈×C₅₃	—	4	4	no	—
283	D₄×C₅₃	—	2	16	no	—
284	D₄×C₅₃	—	4	8	no	—
285	D₄×C₅₃	—	4	4	no	—
286	D₄×C₅₃	—	4	8	no	—
287	C₂×C₄×C₅₃	—	2	4	no	—
288	C₂×C₄×C₅₃	—	2	1	no	—
289	C₂×C₄×C₅₃	—	2	1	no	—
290	C₂×C₄×C₅₃	—	2	1	no	—
291	C₂×C₄×C₅₃	—	2	1	no	—
292	C₂×C₄×C₅₃	—	2	1	no	—
293	C₂×C₄×C₅₃	—	2	1	no	—
294	C₂×C₄×C₅₃	—	2	2	no	—
295	C₂×C₄×C₅₃	—	2	2	no	—
296	C₂×C₄×C₅₃	—	2	4	no	—
297	C₂×C₄×C₅₃	—	2	4	no	—
298	C₂×C₄×C₅₃	—	2	4	no	—
299	C₂×C₄×C₅₃	—	2	8	no	—
300	C₂×C₄×C₅₃	—	2	8	no	—
301	C₂×C₄×C₅₃	—	2	8	no	—
302	C₂×C₄×C₅₃	—	2	16	no	—
303	C₂×C₄×C₅₃	—	2	4	no	—
304	C₂×C₄×C₅₃	—	2	4	no	—
305	C₂×C₄×C₅₃	—	2	4	no	—
306	C₂×C₄×C₅₃	—	2	4	no	—
307	C₂×C₄×C₅₃	—	2	4	no	—
308	C₂×C₄×C₅₃	—	2	4	no	—
309	C₂×C₄×C₅₃	—	2	4	no	—
310	C₂×C₄×C₅₃	—	2	4	no	—
311	C₂×C₄×C₅₃	—	2	4	no	—
312	C₂×C₄×C₅₃	—	4	4	no	—
313	C₂×C₄×C₅₃	—	4	4	no	—
314	C₂×C₄×C₅₃	—	4	4	no	—
315	C₂×C₄×C₅₃	—	4	8	no	—
316	C₂×C₄×C₅₃	—	4	16	no	—
317	C₂×C₄×C₅₃	—	4	8	no	—
318	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
319	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
320	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
321	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
322	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
323	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
324	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
325	C₂×C₄×C₅₃	C₂×#41	1	8	yes	—
326	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
327	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
328	#34082	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂²×C₅₃	—	2	2	no	—
330	C₂²×C₅₃	—	2	2	no	—
331	C₂²×C₅₃	—	2	4	no	—
332	C₂²×C₅₃	—	2	4	no	—
333	C₂²×C₅₃	—	2	4	no	—
334	C₂²×C₅₃	—	2	2	no	—
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	2	4	no	—
339	C₂²×C₅₃	—	2	2	no	—
340	C₂²×C₅₃	—	2	4	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	4	16	no	—
343	C₂²×C₅₃	—	4	4	no	—
344	C₂²×C₅₃	—	4	2	no	—
345	C₂²×C₅₃	—	4	2	no	—
346	C₂²×C₅₃	—	4	4	no	—
347	C₂²×C₅₃	—	4	2	no	—
348	C₂²×C₅₃	—	4	2	no	—
349	C₂²×C₅₃	C₄×#41	1	4	yes	—
350	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
351	C₂²×C₅₃	C₂²×#41	1	2	yes	—
352	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₅₃	#585	1	2	yes	—
355	C₄×C₅₃	—	2	4	no	—
356	C₄×C₅₃	—	2	2	no	—
357	C₄×C₅₃	—	2	2	no	—
358	C₄×C₅₃	—	2	2	no	—
359	C₄×C₅₃	—	2	4	no	—
360	C₄×C₅₃	—	2	4	no	—
361	C₄×C₅₃	—	2	8	no	—
362	C₄×C₅₃	—	4	4	no	—
363	C₄×C₅₃	—	4	4	no	—
364	C₄×C₅₃	—	4	4	no	—
365	C₄×C₅₃	#518	1	4	yes	—
366	C₂×#525	C₂×C₅₃	1	1	yes	characteristic
367	#2335	C₂×C₅₃	1	4	yes	complemented
368	#2333	C₂×C₅₃	1	2	yes	complemented
369	#2332	C₂×C₅₃	1	2	yes	complemented
370	#2329	C₂×C₅₃	1	2	yes	complemented
371	#2325	C₂×C₅₃	1	2	yes	complemented
372	#2321	C₂×C₅₃	1	4	yes	complemented
373	#2298	C₂×C₅₃	1	2	yes	complemented
374	#2297	C₂×C₅₃	1	2	yes	complemented
375	#2293	C₂×C₅₃	1	2	yes	complemented
376	#2290	C₂×C₅₃	1	2	yes	complemented
377	#2290	C₂×C₅₃	1	2	yes	complemented
378	#2280	C₂×C₅₃	1	1	yes	characteristic, complemented
379	C₄²×D₄	C₂×C₅₃	1	2	yes	complemented
380	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
381	C₂×C₅₃	—	2	4	no	—
382	C₂×C₅₃	—	4	4	no	—
383	C₂×C₅₃	—	4	2	no	—
384	C₂×C₅₃	—	4	2	no	—
385	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
386	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
387	C₂×C₅₃	#3428	1	1	yes	characteristic
388	C₂×C₅₃	#3459	1	2	yes	—
389	C₂×C₅₃	#3460	1	2	yes	—
390	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
391	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
392	#525	C₄×C₅₃	1	16	yes	complemented
393	C₂×#123	C₂²×C₅₃	1	2	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
396	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
397	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
398	C₂×#120	C₂²×C₅₃	1	2	yes	—
399	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
400	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
402	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
403	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
404	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
405	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
406	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
407	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
408	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
409	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
410	#391	C₂²×C₅₃	1	4	yes	complemented
411	#390	C₂²×C₅₃	1	4	yes	—
412	#390	C₂²×C₅₃	1	4	yes	—
413	#389	C₂²×C₅₃	1	4	yes	complemented
414	#388	C₂²×C₅₃	1	4	yes	—
415	#388	C₂²×C₅₃	1	4	yes	—
416	#388	C₂²×C₅₃	1	4	yes	—
417	#388	C₂²×C₅₃	1	4	yes	—
418	#388	C₂²×C₅₃	1	4	yes	complemented
419	#388	C₂²×C₅₃	1	4	yes	complemented
420	#387	C₂²×C₅₃	1	4	yes	complemented
421	#387	C₂²×C₅₃	1	4	yes	complemented
422	#387	C₂²×C₅₃	1	4	yes	complemented
423	#387	C₂²×C₅₃	1	4	yes	complemented
424	#386	C₂²×C₅₃	1	4	yes	—
425	#386	C₂²×C₅₃	1	4	yes	—
426	#386	C₂²×C₅₃	1	4	yes	—
427	#386	C₂²×C₅₃	1	4	yes	complemented
428	#385	C₂²×C₅₃	1	4	yes	—
429	#385	C₂²×C₅₃	1	4	yes	complemented
430	#381	C₂²×C₅₃	1	2	yes	—
431	#380	C₂²×C₅₃	1	2	yes	—
432	#380	C₂²×C₅₃	1	2	yes	—
433	#379	C₂²×C₅₃	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₅₃	1	4	yes	complemented
435	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
436	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
437	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
441	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
445	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
446	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
447	#376	C₂²×C₅₃	1	2	yes	complemented
448	C₂×#95	C₂²×C₅₃	1	2	yes	—
449	C₄³	C₂²×C₅₃	1	2	yes	complemented
450	C₅₃	#34082	1	1	yes	characteristic, direct product factor, Sylow
451	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
452	C₂×#41	—	4	2	no	—
453	C₂×#41	—	4	2	no	—
454	C₂×#41	C₂×C₄×C₅₃	1	8	yes	complemented
455	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
457	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
458	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
459	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
460	C₂³×C₄	—	4	2	no	—
461	C₂³×C₄	—	4	2	no	—
462	C₂³×C₄	C₂×C₄×C₅₃	1	8	yes	complemented
463	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
466	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
468	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
469	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
473	#123	C₂×C₄×C₅₃	1	16	yes	complemented
474	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
475	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
476	#121	C₂×C₄×C₅₃	1	8	yes	—
477	#121	C₂×C₄×C₅₃	1	8	yes	complemented
478	#120	C₂×C₄×C₅₃	1	16	yes	complemented
479	C₄×D₄	—	2	16	no	—
480	C₄×D₄	C₂×C₄×C₅₃	1	16	yes	complemented
481	C₄×D₄	C₂×C₄×C₅₃	1	16	yes	complemented
482	#117	—	4	2	no	—
483	#117	—	4	2	no	—
484	#117	—	4	4	no	—
485	#117	C₂×C₄×C₅₃	1	8	yes	complemented
486	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
495	C₂×C₂²⋊C₄	—	2	8	no	—
496	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
510	C₂×C₄²	—	4	2	no	—
511	C₂×C₄²	—	4	2	no	—
512	C₂×C₄²	—	4	4	no	—
513	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
514	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
515	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
516	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
517	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
518	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
519	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
520	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
521	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
522	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
523	#95	C₂³×C₅₃	1	4	yes	—
524	#95	C₂³×C₅₃	1	4	yes	—
525	#95	C₂³×C₅₃	1	4	yes	—
526	#95	C₂³×C₅₃	1	4	yes	—
527	#95	C₂³×C₅₃	1	4	yes	—
528	#95	C₂³×C₅₃	1	4	yes	—
529	#95	C₂³×C₅₃	1	4	yes	—
530	#95	C₂³×C₅₃	1	4	yes	—
531	#95	C₂³×C₅₃	1	4	yes	—
532	#95	C₂³×C₅₃	1	4	yes	—
533	C₂⁴	—	2	4	no	—
534	C₂⁴	—	4	1	no	—
535	C₂⁴	—	4	1	no	—
536	C₂⁴	—	4	2	no	—
537	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
538	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
539	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
540	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
541	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
542	#41	—	4	16	no	—
543	C₂×Q₈	—	4	1	no	—
544	C₂×Q₈	—	4	1	no	—
545	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
546	C₂×D₄	—	2	8	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	4	1	no	—
551	C₂×D₄	—	4	1	no	—
552	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
553	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
554	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
555	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	8	no	—
566	C₂²×C₄	—	4	16	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	1	no	—
571	C₂²×C₄	—	4	1	no	—
572	C₂²×C₄	—	4	1	no	—
573	C₂²×C₄	—	4	1	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
580	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
581	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
582	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
583	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
584	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
585	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
586	C₂²×C₄	#41×C₅₃	1	8	yes	complemented
587	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
588	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
589	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
590	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
597	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	—	4	4	no	—
602	C₄⋊C₄	—	4	4	no	—
603	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
604	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
605	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
606	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	4	2	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
617	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
618	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
619	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
620	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
621	C₄²	—	2	8	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	4	2	no	—
627	C₄²	—	4	4	no	—
628	C₄²	—	4	2	no	—
629	C₄²	—	4	4	no	—
630	C₄²	C₂²×C₄×C₅₃	1	8	yes	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	8	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	8	no	—
650	C₂³	—	4	8	no	—
651	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
652	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
653	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
654	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
655	C₂³	C₂×#41×C₅₃	1	4	yes	—
656	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
657	Q₈	—	4	4	no	—
658	D₄	—	2	16	no	—
659	D₄	—	4	8	no	—
660	D₄	—	4	4	no	—
661	D₄	—	4	8	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	8	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	8	no	—
677	C₂×C₄	—	2	16	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	8	no	—
691	C₂×C₄	—	4	16	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
694	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
695	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
696	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
697	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
698	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
699	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
700	C₂×C₄	C₂×#41×C₅₃	1	8	yes	—
701	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
702	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	16	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	4	no	—
723	C₂²	C₄×#41×C₅₃	1	4	yes	—
724	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
725	C₂²	C₂²×#41×C₅₃	1	2	yes	—
726	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
727	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
728	C₂²	C₅₃×#585	1	2	yes	—
729	C₄	—	2	8	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	4	no	—
736	C₄	—	4	4	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	4	no	—
739	C₄	C₅₃×#518	1	4	yes	—
740	C₂	—	2	4	no	—
741	C₂	—	4	2	no	—
742	C₂	—	4	2	no	—
743	C₂	—	4	4	no	—
744	C₂	C₂×C₄×#41×C₅₃	1	1	yes	characteristic
745	C₂	C₂×C₅₃×#518	1	1	yes	characteristic
746	C₂	C₅₃×#3428	1	1	yes	characteristic
747	C₂	C₅₃×#3459	1	2	yes	—
748	C₂	C₅₃×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂×C₅₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2335	C₂	semidirect
3. C₅₃×#2333	C₂	semidirect
4. C₅₃×#2332	C₂	semidirect
5. C₅₃×#2329	C₂	semidirect
6. C₅₃×#2325	C₂	semidirect
7. C₅₃×#2321	C₂	semidirect
8. C₅₃×#2298	C₂	semidirect
9. C₅₃×#2297	C₂	semidirect
10. C₅₃×#2293	C₂	semidirect
11. C₅₃×#2290	C₂	semidirect
12. C₅₃×#2290	C₂	semidirect
13. C₅₃×#2280	C₂	semidirect
14. C₄²×D₄×C₅₃	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
18. C₅₃×#525	C₄	semidirect
31. C₂×#117×C₅₃	C₂²	semidirect
35. C₂²×C₄²×C₅₃	C₂²	semidirect
36. C₅₃×#391	C₂²	semidirect
39. C₅₃×#389	C₂²	semidirect
44. C₅₃×#388	C₂²	semidirect
45. C₅₃×#388	C₂²	semidirect
46. C₅₃×#387	C₂²	semidirect
47. C₅₃×#387	C₂²	semidirect
48. C₅₃×#387	C₂²	semidirect
49. C₅₃×#387	C₂²	semidirect
53. C₅₃×#386	C₂²	semidirect
55. C₅₃×#385	C₂²	semidirect
60. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
61. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
62. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
73. C₅₃×#376	C₂²	semidirect
75. C₄³×C₅₃	C₂²	semidirect
79. C₂×#41×C₅₃	C₂×C₄	semidirect
87. C₂³×C₄×C₅₃	C₂×C₄	semidirect
98. #123×C₅₃	C₂×C₄	semidirect
99. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
100. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
102. #121×C₅₃	C₂×C₄	semidirect
103. #120×C₅₃	C₂×C₄	semidirect
105. C₄×D₄×C₅₃	C₂×C₄	semidirect
106. C₄×D₄×C₅₃	C₂×C₄	semidirect
110. #117×C₅₃	C₂×C₄	semidirect
211. C₂²×C₄×C₅₃	#41	semidirect
328. #34082	C₅₃	direct (N × H)
367. #2335	C₂×C₅₃	semidirect
368. #2333	C₂×C₅₃	semidirect
369. #2332	C₂×C₅₃	semidirect
370. #2329	C₂×C₅₃	semidirect
371. #2325	C₂×C₅₃	semidirect
372. #2321	C₂×C₅₃	semidirect
373. #2298	C₂×C₅₃	semidirect
374. #2297	C₂×C₅₃	semidirect
375. #2293	C₂×C₅₃	semidirect
376. #2290	C₂×C₅₃	semidirect
377. #2290	C₂×C₅₃	semidirect
378. #2280	C₂×C₅₃	semidirect
379. C₄²×D₄	C₂×C₅₃	semidirect
380. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
392. #525	C₄×C₅₃	semidirect
405. C₂×#117	C₂²×C₅₃	semidirect
409. C₂²×C₄²	C₂²×C₅₃	semidirect
410. #391	C₂²×C₅₃	semidirect
413. #389	C₂²×C₅₃	semidirect
418. #388	C₂²×C₅₃	semidirect
419. #388	C₂²×C₅₃	semidirect
420. #387	C₂²×C₅₃	semidirect
421. #387	C₂²×C₅₃	semidirect
422. #387	C₂²×C₅₃	semidirect
423. #387	C₂²×C₅₃	semidirect
427. #386	C₂²×C₅₃	semidirect
429. #385	C₂²×C₅₃	semidirect
434. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
435. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
436. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
445. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
446. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
447. #376	C₂²×C₅₃	semidirect
449. C₄³	C₂²×C₅₃	semidirect
450. C₅₃	#34082	direct (N × H)
454. C₂×#41	C₂×C₄×C₅₃	semidirect
462. C₂³×C₄	C₂×C₄×C₅₃	semidirect
473. #123	C₂×C₄×C₅₃	semidirect
474. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
475. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
477. #121	C₂×C₄×C₅₃	semidirect
478. #120	C₂×C₄×C₅₃	semidirect
480. C₄×D₄	C₂×C₄×C₅₃	semidirect
481. C₄×D₄	C₂×C₄×C₅₃	semidirect
485. #117	C₂×C₄×C₅₃	semidirect
586. C₂²×C₄	#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₃×#525	2
C₅₃×#2335	2
C₅₃×#2333	2
C₅₃×#2332	2
C₅₃×#2329	2
C₅₃×#2325	2
C₅₃×#2321	2
C₅₃×#2298	2
C₅₃×#2297	2
C₅₃×#2293	2
C₅₃×#2290	2
C₅₃×#2280	2
C₄²×D₄×C₅₃	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#34082	53

Subgroups — C53×#34082 #27241594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34082 #27241594