Subgroups — C₅₃×#22398 #27229910

Order 13568.

1630 conjugacy classes of subgroups.

The subgroup lattice has 990 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	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1780	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1779	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1750	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	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₅₃×#525	—	2	4	no	—
23	C₅₃×#525	—	2	4	no	—
24	C₂×#123×C₅₃	C₄	1	1	yes	characteristic
25	C₂×#123×C₅₃	C₄	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
28	C₂×#121×C₅₃	C₄	1	1	yes	characteristic
29	C₂×#121×C₅₃	C₄	1	1	yes	characteristic
30	C₂×#120×C₅₃	C₄	1	1	yes	characteristic
31	C₂×#120×C₅₃	C₄	1	1	yes	characteristic
32	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#435	—	2	4	no	—
38	C₈×D₄×C₅₃	—	2	4	no	—
39	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#408	—	2	4	no	—
42	C₂×C₂²⋊C₈×C₅₃	—	2	4	no	—
43	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×#41×C₅₃	—	2	2	no	—
67	C₂×#41×C₅₃	—	2	2	no	—
68	C₂×#41×C₅₃	—	2	2	no	—
69	C₂×#41×C₅₃	—	2	2	no	—
70	C₂×#41×C₅₃	—	4	1	no	—
71	C₂×#41×C₅₃	—	4	1	no	—
72	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₅₃	—	2	2	no	—
81	C₂³×C₄×C₅₃	—	2	2	no	—
82	C₂³×C₄×C₅₃	—	2	2	no	—
83	C₂³×C₄×C₅₃	—	2	2	no	—
84	C₂³×C₄×C₅₃	—	4	1	no	—
85	C₂³×C₄×C₅₃	—	4	1	no	—
86	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₅₃	—	2	2	no	—
95	C₂×M₁₆×C₅₃	—	2	2	no	—
96	C₂×M₁₆×C₅₃	—	4	1	no	—
97	C₂²×C₈×C₅₃	—	2	2	no	—
98	C₂²×C₈×C₅₃	—	2	2	no	—
99	C₂²×C₈×C₅₃	—	2	2	no	—
100	C₂²×C₈×C₅₃	—	2	2	no	—
101	C₂²×C₈×C₅₃	—	2	2	no	—
102	C₂²×C₈×C₅₃	—	2	2	no	—
103	C₂²×C₈×C₅₃	—	4	1	no	—
104	C₂²×C₈×C₅₃	—	4	1	no	—
105	C₂²×C₈×C₅₃	—	4	1	no	—
106	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
114	#123×C₅₃	—	2	4	no	—
115	#123×C₅₃	—	2	4	no	—
116	C₂²⋊Q₈×C₅₃	—	2	4	no	—
117	C₂²⋊Q₈×C₅₃	—	2	4	no	—
118	#121×C₅₃	—	2	4	no	—
119	#121×C₅₃	—	2	4	no	—
120	#120×C₅₃	—	2	4	no	—
121	#120×C₅₃	—	2	4	no	—
122	C₄×D₄×C₅₃	—	2	2	no	—
123	C₄×D₄×C₅₃	—	2	2	no	—
124	C₄×D₄×C₅₃	—	2	2	no	—
125	C₄×D₄×C₅₃	—	2	2	no	—
126	C₄×D₄×C₅₃	—	2	2	no	—
127	C₄×D₄×C₅₃	—	2	2	no	—
128	C₄×D₄×C₅₃	D₄	1	4	yes	—
129	C₄×D₄×C₅₃	D₄	1	4	yes	—
130	#117×C₅₃	—	2	2	no	—
131	#117×C₅₃	—	2	2	no	—
132	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
148	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
150	C₄⋊C₈×C₅₃	—	2	2	no	—
151	C₄⋊C₈×C₅₃	—	2	2	no	—
152	C₂²⋊C₈×C₅₃	—	2	2	no	—
153	C₂²⋊C₈×C₅₃	—	2	2	no	—
154	C₂²⋊C₈×C₅₃	—	2	2	no	—
155	C₂²⋊C₈×C₅₃	—	2	2	no	—
156	C₂²⋊C₈×C₅₃	—	2	2	no	—
157	C₂²⋊C₈×C₅₃	—	2	2	no	—
158	C₂²⋊C₈×C₅₃	—	2	2	no	—
159	C₂²⋊C₈×C₅₃	—	2	2	no	—
160	C₂²⋊C₈×C₅₃	—	2	2	no	—
161	C₂²⋊C₈×C₅₃	—	2	2	no	—
162	C₂²⋊C₈×C₅₃	—	2	2	no	—
163	C₂²⋊C₈×C₅₃	—	4	1	no	—
164	C₂²⋊C₈×C₅₃	—	4	1	no	—
165	C₂²⋊C₈×C₅₃	—	4	1	no	—
166	C₂²⋊C₈×C₅₃	—	4	1	no	—
167	C₂²⋊C₈×C₅₃	D₄	1	4	yes	complemented
168	#97×C₅₃	—	2	2	no	—
169	C₄×C₈×C₅₃	—	2	2	no	—
170	C₂⁴×C₅₃	—	2	2	no	—
171	C₂⁴×C₅₃	—	2	2	no	—
172	C₂⁴×C₅₃	—	2	2	no	—
173	C₂⁴×C₅₃	—	2	2	no	—
174	C₂⁴×C₅₃	—	2	2	no	—
175	C₂⁴×C₅₃	—	4	1	no	—
176	C₂⁴×C₅₃	—	4	1	no	—
177	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
178	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
179	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
180	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
181	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
182	#41×C₅₃	—	4	4	no	—
183	#41×C₅₃	—	4	4	no	—
184	#41×C₅₃	—	4	4	no	—
185	#41×C₅₃	—	4	4	no	—
186	C₂×Q₈×C₅₃	—	2	2	no	—
187	C₂×Q₈×C₅₃	—	2	2	no	—
188	C₂×Q₈×C₅₃	—	4	1	no	—
189	C₂×D₄×C₅₃	—	2	2	no	—
190	C₂×D₄×C₅₃	—	2	2	no	—
191	C₂×D₄×C₅₃	—	2	2	no	—
192	C₂×D₄×C₅₃	—	2	2	no	—
193	C₂×D₄×C₅₃	—	2	2	no	—
194	C₂×D₄×C₅₃	—	2	2	no	—
195	C₂×D₄×C₅₃	—	2	2	no	—
196	C₂×D₄×C₅₃	—	2	2	no	—
197	C₂×D₄×C₅₃	—	2	2	no	—
198	C₂×D₄×C₅₃	—	2	2	no	—
199	C₂×D₄×C₅₃	—	2	2	no	—
200	C₂×D₄×C₅₃	—	2	2	no	—
201	C₂×D₄×C₅₃	—	2	2	no	—
202	C₂×D₄×C₅₃	—	2	2	no	—
203	C₂×D₄×C₅₃	—	2	2	no	—
204	C₂×D₄×C₅₃	—	4	1	no	—
205	C₂×D₄×C₅₃	—	4	1	no	—
206	C₂×D₄×C₅₃	—	4	1	no	—
207	C₂×D₄×C₅₃	—	4	1	no	—
208	C₂×D₄×C₅₃	—	4	1	no	—
209	C₂×D₄×C₅₃	C₂²⋊C₄	1	4	yes	—
210	C₂²×C₄×C₅₃	—	2	1	no	—
211	C₂²×C₄×C₅₃	—	2	1	no	—
212	C₂²×C₄×C₅₃	—	2	1	no	—
213	C₂²×C₄×C₅₃	—	2	1	no	—
214	C₂²×C₄×C₅₃	—	2	1	no	—
215	C₂²×C₄×C₅₃	—	2	1	no	—
216	C₂²×C₄×C₅₃	—	2	1	no	—
217	C₂²×C₄×C₅₃	—	2	1	no	—
218	C₂²×C₄×C₅₃	—	2	1	no	—
219	C₂²×C₄×C₅₃	—	2	1	no	—
220	C₂²×C₄×C₅₃	—	2	1	no	—
221	C₂²×C₄×C₅₃	—	2	1	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
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	2	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	2	1	no	—
229	C₂²×C₄×C₅₃	—	2	1	no	—
230	C₂²×C₄×C₅₃	—	2	1	no	—
231	C₂²×C₄×C₅₃	—	2	1	no	—
232	C₂²×C₄×C₅₃	—	2	1	no	—
233	C₂²×C₄×C₅₃	—	2	1	no	—
234	C₂²×C₄×C₅₃	—	2	1	no	—
235	C₂²×C₄×C₅₃	—	2	1	no	—
236	C₂²×C₄×C₅₃	—	2	1	no	—
237	C₂²×C₄×C₅₃	—	2	1	no	—
238	C₂²×C₄×C₅₃	—	2	1	no	—
239	C₂²×C₄×C₅₃	—	2	1	no	—
240	C₂²×C₄×C₅₃	—	4	1	no	—
241	C₂²×C₄×C₅₃	—	4	1	no	—
242	C₂²×C₄×C₅₃	—	4	1	no	—
243	C₂²×C₄×C₅₃	—	4	4	no	—
244	C₂²×C₄×C₅₃	—	4	4	no	—
245	C₂²×C₄×C₅₃	—	4	4	no	—
246	C₂²×C₄×C₅₃	—	4	4	no	—
247	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
249	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
250	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
251	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
252	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
255	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
256	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₅₃	#41	1	2	yes	—
262	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	M₁₆×C₅₃	—	4	4	no	—
264	C₂×C₈×C₅₃	—	2	1	no	—
265	C₂×C₈×C₅₃	—	2	1	no	—
266	C₂×C₈×C₅₃	—	2	1	no	—
267	C₂×C₈×C₅₃	—	2	1	no	—
268	C₂×C₈×C₅₃	—	2	1	no	—
269	C₂×C₈×C₅₃	—	2	1	no	—
270	C₂×C₈×C₅₃	—	2	1	no	—
271	C₂×C₈×C₅₃	—	2	1	no	—
272	C₂×C₈×C₅₃	—	2	1	no	—
273	C₂×C₈×C₅₃	—	2	1	no	—
274	C₂×C₈×C₅₃	—	2	1	no	—
275	C₂×C₈×C₅₃	—	2	1	no	—
276	C₂×C₈×C₅₃	—	2	1	no	—
277	C₂×C₈×C₅₃	—	2	1	no	—
278	C₂×C₈×C₅₃	—	2	1	no	—
279	C₂×C₈×C₅₃	—	2	1	no	—
280	C₂×C₈×C₅₃	—	2	1	no	—
281	C₂×C₈×C₅₃	—	2	1	no	—
282	C₂×C₈×C₅₃	—	2	1	no	—
283	C₂×C₈×C₅₃	—	2	1	no	—
284	C₂×C₈×C₅₃	—	2	1	no	—
285	C₂×C₈×C₅₃	—	2	1	no	—
286	C₂×C₈×C₅₃	—	4	4	no	—
287	C₂×C₈×C₅₃	—	4	4	no	—
288	C₂×C₈×C₅₃	—	4	4	no	—
289	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
290	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	2	no	—
295	C₄⋊C₄×C₅₃	—	2	2	no	—
296	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
297	C₂²⋊C₄×C₅₃	—	2	2	no	—
298	C₂²⋊C₄×C₅₃	—	2	2	no	—
299	C₂²⋊C₄×C₅₃	—	2	2	no	—
300	C₂²⋊C₄×C₅₃	—	2	2	no	—
301	C₂²⋊C₄×C₅₃	—	2	2	no	—
302	C₂²⋊C₄×C₅₃	—	2	2	no	—
303	C₂²⋊C₄×C₅₃	—	2	2	no	—
304	C₂²⋊C₄×C₅₃	—	2	2	no	—
305	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
306	C₂²⋊C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
307	C₄²×C₅₃	—	2	1	no	—
308	C₄²×C₅₃	—	2	1	no	—
309	C₄²×C₅₃	C₂×D₄	1	2	yes	—
310	C₄²×C₅₃	C₂×D₄	1	2	yes	—
311	C₂³×C₅₃	—	2	1	no	—
312	C₂³×C₅₃	—	2	1	no	—
313	C₂³×C₅₃	—	2	1	no	—
314	C₂³×C₅₃	—	2	1	no	—
315	C₂³×C₅₃	—	2	8	no	—
316	C₂³×C₅₃	—	2	1	no	—
317	C₂³×C₅₃	—	2	1	no	—
318	C₂³×C₅₃	—	2	1	no	—
319	C₂³×C₅₃	—	2	1	no	—
320	C₂³×C₅₃	—	2	1	no	—
321	C₂³×C₅₃	—	2	1	no	—
322	C₂³×C₅₃	—	2	1	no	—
323	C₂³×C₅₃	—	2	1	no	—
324	C₂³×C₅₃	—	2	1	no	—
325	C₂³×C₅₃	—	2	1	no	—
326	C₂³×C₅₃	—	2	1	no	—
327	C₂³×C₅₃	—	2	1	no	—
328	C₂³×C₅₃	—	2	1	no	—
329	C₂³×C₅₃	—	2	1	no	—
330	C₂³×C₅₃	—	2	1	no	—
331	C₂³×C₅₃	—	2	1	no	—
332	C₂³×C₅₃	—	2	1	no	—
333	C₂³×C₅₃	—	2	1	no	—
334	C₂³×C₅₃	—	2	1	no	—
335	C₂³×C₅₃	—	2	1	no	—
336	C₂³×C₅₃	—	2	1	no	—
337	C₂³×C₅₃	—	2	1	no	—
338	C₂³×C₅₃	—	2	1	no	—
339	C₂³×C₅₃	—	2	1	no	—
340	C₂³×C₅₃	—	2	1	no	—
341	C₂³×C₅₃	—	4	4	no	—
342	C₂³×C₅₃	—	4	4	no	—
343	C₂³×C₅₃	—	4	4	no	—
344	C₂³×C₅₃	—	4	4	no	—
345	C₂³×C₅₃	—	4	4	no	—
346	C₂³×C₅₃	—	4	4	no	—
347	C₂³×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂³×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
349	C₂³×C₅₃	C₄×D₄	1	2	yes	—
350	C₂³×C₅₃	#131	1	2	yes	—
351	C₂³×C₅₃	#131	1	2	yes	—
352	C₂³×C₅₃	#131	1	2	yes	—
353	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
354	Q₈×C₅₃	—	4	4	no	—
355	D₄×C₅₃	—	2	8	no	—
356	D₄×C₅₃	—	4	4	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	4	no	—
359	D₄×C₅₃	—	4	4	no	—
360	D₄×C₅₃	—	4	4	no	—
361	D₄×C₅₃	—	4	4	no	—
362	C₂×C₄×C₅₃	—	2	1	no	—
363	C₂×C₄×C₅₃	—	2	1	no	—
364	C₂×C₄×C₅₃	—	2	1	no	—
365	C₂×C₄×C₅₃	—	2	1	no	—
366	C₂×C₄×C₅₃	—	2	1	no	—
367	C₂×C₄×C₅₃	—	2	1	no	—
368	C₂×C₄×C₅₃	—	2	1	no	—
369	C₂×C₄×C₅₃	—	2	1	no	—
370	C₂×C₄×C₅₃	—	2	1	no	—
371	C₂×C₄×C₅₃	—	2	1	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	2	1	no	—
385	C₂×C₄×C₅₃	—	2	1	no	—
386	C₂×C₄×C₅₃	—	2	1	no	—
387	C₂×C₄×C₅₃	—	2	1	no	—
388	C₂×C₄×C₅₃	—	2	1	no	—
389	C₂×C₄×C₅₃	—	2	1	no	—
390	C₂×C₄×C₅₃	—	2	1	no	—
391	C₂×C₄×C₅₃	—	2	1	no	—
392	C₂×C₄×C₅₃	—	2	1	no	—
393	C₂×C₄×C₅₃	—	2	1	no	—
394	C₂×C₄×C₅₃	—	2	1	no	—
395	C₂×C₄×C₅₃	—	2	1	no	—
396	C₂×C₄×C₅₃	—	4	4	no	—
397	C₂×C₄×C₅₃	—	4	4	no	—
398	C₂×C₄×C₅₃	—	4	4	no	—
399	C₂×C₄×C₅₃	—	4	1	no	—
400	C₂×C₄×C₅₃	—	4	1	no	—
401	C₂×C₄×C₅₃	—	4	1	no	—
402	C₂×C₄×C₅₃	—	4	1	no	—
403	C₂×C₄×C₅₃	—	4	1	no	—
404	C₂×C₄×C₅₃	—	4	1	no	—
405	C₂×C₄×C₅₃	—	4	1	no	—
406	C₂×C₄×C₅₃	—	4	1	no	—
407	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
408	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
409	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
410	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
411	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
412	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
416	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
418	C₈×C₅₃	—	2	2	no	—
419	C₈×C₅₃	—	2	2	no	—
420	C₈×C₅₃	—	4	1	no	—
421	C₈×C₅₃	—	4	1	no	—
422	C₈×C₅₃	—	4	1	no	—
423	C₈×C₅₃	—	4	1	no	—
424	C₈×C₅₃	—	4	1	no	—
425	C₈×C₅₃	—	4	1	no	—
426	#22398	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂²×C₅₃	—	2	2	no	—
428	C₂²×C₅₃	—	2	2	no	—
429	C₂²×C₅₃	—	2	2	no	—
430	C₂²×C₅₃	—	2	2	no	—
431	C₂²×C₅₃	—	2	2	no	—
432	C₂²×C₅₃	—	2	2	no	—
433	C₂²×C₅₃	—	2	2	no	—
434	C₂²×C₅₃	—	2	2	no	—
435	C₂²×C₅₃	—	2	2	no	—
436	C₂²×C₅₃	—	2	2	no	—
437	C₂²×C₅₃	—	2	2	no	—
438	C₂²×C₅₃	—	2	2	no	—
439	C₂²×C₅₃	—	2	2	no	—
440	C₂²×C₅₃	—	2	2	no	—
441	C₂²×C₅₃	—	2	2	no	—
442	C₂²×C₅₃	—	4	16	no	—
443	C₂²×C₅₃	—	4	1	no	—
444	C₂²×C₅₃	—	4	1	no	—
445	C₂²×C₅₃	—	4	1	no	—
446	C₂²×C₅₃	—	4	1	no	—
447	C₂²×C₅₃	—	4	1	no	—
448	C₂²×C₅₃	—	4	1	no	—
449	C₂²×C₅₃	—	4	1	no	—
450	C₂²×C₅₃	—	4	1	no	—
451	C₂²×C₅₃	—	4	1	no	—
452	C₂²×C₅₃	—	4	1	no	—
453	C₂²×C₅₃	—	4	1	no	—
454	C₂²×C₅₃	—	4	1	no	—
455	C₂²×C₅₃	—	4	1	no	—
456	C₂²×C₅₃	—	4	1	no	—
457	C₂²×C₅₃	—	4	1	no	—
458	C₂²×C₅₃	—	4	1	no	—
459	C₂²×C₅₃	—	4	1	no	—
460	C₂²×C₅₃	—	4	1	no	—
461	C₂²×C₅₃	—	4	1	no	—
462	C₂²×C₅₃	#408	1	4	yes	complemented
463	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
465	C₂²×C₅₃	#518	1	1	yes	characteristic
466	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
467	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
468	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
469	C₂²×C₅₃	#568	1	1	yes	characteristic
470	C₄×C₅₃	—	2	2	no	—
471	C₄×C₅₃	—	2	2	no	—
472	C₄×C₅₃	—	2	2	no	—
473	C₄×C₅₃	—	2	2	no	—
474	C₄×C₅₃	—	2	2	no	—
475	C₄×C₅₃	—	4	1	no	—
476	C₄×C₅₃	—	4	1	no	—
477	C₄×C₅₃	—	4	1	no	—
478	C₄×C₅₃	—	4	1	no	—
479	C₄×C₅₃	D₄²	1	1	yes	characteristic
480	C₄×C₅₃	D₄²	1	1	yes	characteristic
481	C₄×C₅₃	#546	1	1	yes	characteristic
482	C₄×C₅₃	#546	1	1	yes	characteristic
483	C₂×#525	C₂×C₅₃	1	1	yes	characteristic
484	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
485	C₂×C₈×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
486	C₂×#408	C₂×C₅₃	1	1	yes	characteristic, complemented
487	C₂²×C₂²⋊C₈	C₂×C₅₃	1	1	yes	characteristic, complemented
488	#1955	C₂×C₅₃	1	1	yes	characteristic, complemented
489	#1954	C₂×C₅₃	1	1	yes	characteristic, complemented
490	#1870	C₂×C₅₃	1	1	yes	characteristic, complemented
491	#1869	C₂×C₅₃	1	1	yes	characteristic, complemented
492	#1869	C₂×C₅₃	1	1	yes	characteristic, complemented
493	#1869	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#1798	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#1780	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#1779	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#1750	C₂×C₅₃	1	1	yes	characteristic, complemented
498	C₂×C₅₃	—	2	4	no	—
499	C₂×C₅₃	—	4	2	no	—
500	C₂×C₅₃	—	4	2	no	—
501	C₂×C₅₃	—	4	2	no	—
502	C₂×C₅₃	—	8	1	no	—
503	C₂×C₅₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
504	C₂×C₅₃	C₂×#408	1	1	yes	characteristic
505	C₂×C₅₃	#2880	1	1	yes	characteristic
506	C₂×C₅₃	#2929	1	1	yes	characteristic
507	C₂×C₅₃	#2933	1	1	yes	characteristic
508	C₂×C₅₃	#2976	1	1	yes	characteristic
509	C₂×C₅₃	#2977	1	1	yes	characteristic
510	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
511	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
512	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
513	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
514	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
515	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
516	#525	—	2	4	no	—
517	#525	—	2	4	no	—
518	C₂×#123	C₄×C₅₃	1	1	yes	characteristic
519	C₂×#123	C₄×C₅₃	1	1	yes	characteristic
520	C₂×C₂²⋊Q₈	C₄×C₅₃	1	1	yes	characteristic
521	C₂×C₂²⋊Q₈	C₄×C₅₃	1	1	yes	characteristic
522	C₂×#121	C₄×C₅₃	1	1	yes	characteristic
523	C₂×#121	C₄×C₅₃	1	1	yes	characteristic
524	C₂×#120	C₄×C₅₃	1	1	yes	characteristic
525	C₂×#120	C₄×C₅₃	1	1	yes	characteristic
526	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
527	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
528	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
529	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
530	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
531	#435	—	2	4	no	—
532	C₈×D₄	—	2	4	no	—
533	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
534	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
535	#408	—	2	4	no	—
536	C₂×C₂²⋊C₈	—	2	4	no	—
537	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
543	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
544	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
548	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
549	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
550	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
551	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
552	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
553	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
554	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
555	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
556	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
557	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
558	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
559	C₅₃	#22398	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁵	C₂×C₄×C₅₃	1	1	yes	characteristic
561	C₂×#41	—	2	2	no	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	—	2	2	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	4	1	no	—
566	C₂×#41	—	4	1	no	—
567	C₂²×Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
568	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
569	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
570	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
571	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
572	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
573	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
574	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
575	C₂³×C₄	—	2	2	no	—
576	C₂³×C₄	—	2	2	no	—
577	C₂³×C₄	—	2	2	no	—
578	C₂³×C₄	—	2	2	no	—
579	C₂³×C₄	—	4	1	no	—
580	C₂³×C₄	—	4	1	no	—
581	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
582	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
583	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
589	C₂×M₁₆	—	2	2	no	—
590	C₂×M₁₆	—	2	2	no	—
591	C₂×M₁₆	—	4	1	no	—
592	C₂²×C₈	—	2	2	no	—
593	C₂²×C₈	—	2	2	no	—
594	C₂²×C₈	—	2	2	no	—
595	C₂²×C₈	—	2	2	no	—
596	C₂²×C₈	—	2	2	no	—
597	C₂²×C₈	—	2	2	no	—
598	C₂²×C₈	—	4	1	no	—
599	C₂²×C₈	—	4	1	no	—
600	C₂²×C₈	—	4	1	no	—
601	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
602	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
603	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
604	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
605	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
606	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
607	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
608	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
609	#123	—	2	4	no	—
610	#123	—	2	4	no	—
611	C₂²⋊Q₈	—	2	4	no	—
612	C₂²⋊Q₈	—	2	4	no	—
613	#121	—	2	4	no	—
614	#121	—	2	4	no	—
615	#120	—	2	4	no	—
616	#120	—	2	4	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	D₄×C₅₃	1	4	yes	—
624	C₄×D₄	D₄×C₅₃	1	4	yes	—
625	#117	—	2	2	no	—
626	#117	—	2	2	no	—
627	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
645	C₄⋊C₈	—	2	2	no	—
646	C₄⋊C₈	—	2	2	no	—
647	C₂²⋊C₈	—	2	2	no	—
648	C₂²⋊C₈	—	2	2	no	—
649	C₂²⋊C₈	—	2	2	no	—
650	C₂²⋊C₈	—	2	2	no	—
651	C₂²⋊C₈	—	2	2	no	—
652	C₂²⋊C₈	—	2	2	no	—
653	C₂²⋊C₈	—	2	2	no	—
654	C₂²⋊C₈	—	2	2	no	—
655	C₂²⋊C₈	—	2	2	no	—
656	C₂²⋊C₈	—	2	2	no	—
657	C₂²⋊C₈	—	2	2	no	—
658	C₂²⋊C₈	—	4	1	no	—
659	C₂²⋊C₈	—	4	1	no	—
660	C₂²⋊C₈	—	4	1	no	—
661	C₂²⋊C₈	—	4	1	no	—
662	C₂²⋊C₈	D₄×C₅₃	1	4	yes	complemented
663	#97	—	2	2	no	—
664	C₄×C₈	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	2	2	no	—
667	C₂⁴	—	2	2	no	—
668	C₂⁴	—	2	2	no	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	4	1	no	—
671	C₂⁴	—	4	1	no	—
672	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
673	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
674	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
675	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
676	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	4	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	4	1	no	—
700	C₂×D₄	—	4	1	no	—
701	C₂×D₄	—	4	1	no	—
702	C₂×D₄	—	4	1	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	C₂²⋊C₄×C₅₃	1	4	yes	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	1	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	—	4	4	no	—
741	C₂²×C₄	—	4	4	no	—
742	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
743	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
744	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
745	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
746	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
747	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
748	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
749	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
750	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
751	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
752	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
753	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
754	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
756	C₂²×C₄	#41×C₅₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
758	M₁₆	—	4	4	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	2	1	no	—
761	C₂×C₈	—	2	1	no	—
762	C₂×C₈	—	2	1	no	—
763	C₂×C₈	—	2	1	no	—
764	C₂×C₈	—	2	1	no	—
765	C₂×C₈	—	2	1	no	—
766	C₂×C₈	—	2	1	no	—
767	C₂×C₈	—	2	1	no	—
768	C₂×C₈	—	2	1	no	—
769	C₂×C₈	—	2	1	no	—
770	C₂×C₈	—	2	1	no	—
771	C₂×C₈	—	2	1	no	—
772	C₂×C₈	—	2	1	no	—
773	C₂×C₈	—	2	1	no	—
774	C₂×C₈	—	2	1	no	—
775	C₂×C₈	—	2	1	no	—
776	C₂×C₈	—	2	1	no	—
777	C₂×C₈	—	2	1	no	—
778	C₂×C₈	—	2	1	no	—
779	C₂×C₈	—	2	1	no	—
780	C₂×C₈	—	2	1	no	—
781	C₂×C₈	—	4	4	no	—
782	C₂×C₈	—	4	4	no	—
783	C₂×C₈	—	4	4	no	—
784	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
785	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	4	yes	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	4	yes	—
801	C₂²⋊C₄	C₂²⋊C₄×C₅₃	1	4	yes	—
802	C₄²	—	2	1	no	—
803	C₄²	—	2	1	no	—
804	C₄²	C₂×D₄×C₅₃	1	2	yes	—
805	C₄²	C₂×D₄×C₅₃	1	2	yes	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	8	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	4	4	no	—
841	C₂³	—	4	4	no	—
842	C₂³	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
843	C₂³	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
844	C₂³	C₄×D₄×C₅₃	1	2	yes	—
845	C₂³	#131×C₅₃	1	2	yes	—
846	C₂³	#131×C₅₃	1	2	yes	—
847	C₂³	#131×C₅₃	1	2	yes	—
848	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
849	Q₈	—	4	4	no	—
850	D₄	—	2	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	4	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	4	no	—
856	D₄	—	4	4	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	1	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	1	no	—
900	C₂×C₄	—	4	1	no	—
901	C₂×C₄	—	4	1	no	—
902	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
903	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
904	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
905	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
906	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
907	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
909	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
910	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
911	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
912	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
913	C₈	—	2	2	no	—
914	C₈	—	2	2	no	—
915	C₈	—	4	1	no	—
916	C₈	—	4	1	no	—
917	C₈	—	4	1	no	—
918	C₈	—	4	1	no	—
919	C₈	—	4	1	no	—
920	C₈	—	4	1	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	4	16	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	C₅₃×#408	1	4	yes	complemented
957	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
958	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
959	C₂²	C₅₃×#518	1	1	yes	characteristic
960	C₂²	C₂×#131×C₅₃	1	1	yes	characteristic
961	C₂²	C₂×#131×C₅₃	1	1	yes	characteristic
962	C₂²	C₂×#131×C₅₃	1	1	yes	characteristic
963	C₂²	C₅₃×#568	1	1	yes	characteristic
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	1	no	—
973	C₄	D₄²×C₅₃	1	1	yes	characteristic
974	C₄	D₄²×C₅₃	1	1	yes	characteristic
975	C₄	C₅₃×#546	1	1	yes	characteristic
976	C₄	C₅₃×#546	1	1	yes	characteristic
977	C₂	—	2	4	no	—
978	C₂	—	4	2	no	—
979	C₂	—	4	2	no	—
980	C₂	—	4	2	no	—
981	C₂	—	8	1	no	—
982	C₂	D₄×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
983	C₂	C₂×C₅₃×#408	1	1	yes	characteristic
984	C₂	C₅₃×#2880	1	1	yes	characteristic
985	C₂	C₅₃×#2929	1	1	yes	characteristic
986	C₂	C₅₃×#2933	1	1	yes	characteristic
987	C₂	C₅₃×#2976	1	1	yes	characteristic
988	C₂	C₅₃×#2977	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#435	C₂	semidirect
3. C₂×C₈×D₄×C₅₃	C₂	semidirect
4. C₂×C₅₃×#408	C₂	semidirect
5. C₂²×C₂²⋊C₈×C₅₃	C₂	semidirect
6. C₅₃×#1955	C₂	semidirect
7. C₅₃×#1954	C₂	semidirect
8. C₅₃×#1870	C₂	semidirect
9. C₅₃×#1869	C₂	semidirect
10. C₅₃×#1869	C₂	semidirect
11. C₅₃×#1869	C₂	semidirect
12. C₅₃×#1798	C₂	semidirect
13. C₅₃×#1780	C₂	semidirect
14. C₅₃×#1779	C₂	semidirect
15. C₅₃×#1750	C₂	semidirect
18. C₂²×M₁₆×C₅₃	C₂²	semidirect
21. C₂³×C₈×C₅₃	C₂²	semidirect
39. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
40. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
55. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
56. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
57. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
58. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
59. C₂×#97×C₅₃	C₂²	semidirect
60. C₂×C₄×C₈×C₅₃	C₂²	semidirect
61. C₅₃×#336	C₂²	semidirect
62. C₅₃×#336	C₂²	semidirect
63. C₅₃×#336	C₂²	semidirect
64. C₅₃×#336	C₂²	semidirect
167. C₂²⋊C₈×C₅₃	D₄	semidirect
426. #22398	C₅₃	direct (N × H)
462. C₂²×C₅₃	#408	semidirect
484. C₂×#435	C₂×C₅₃	semidirect
485. C₂×C₈×D₄	C₂×C₅₃	semidirect
486. C₂×#408	C₂×C₅₃	semidirect
487. C₂²×C₂²⋊C₈	C₂×C₅₃	semidirect
488. #1955	C₂×C₅₃	semidirect
489. #1954	C₂×C₅₃	semidirect
490. #1870	C₂×C₅₃	semidirect
491. #1869	C₂×C₅₃	semidirect
492. #1869	C₂×C₅₃	semidirect
493. #1869	C₂×C₅₃	semidirect
494. #1798	C₂×C₅₃	semidirect
495. #1780	C₂×C₅₃	semidirect
496. #1779	C₂×C₅₃	semidirect
497. #1750	C₂×C₅₃	semidirect
512. C₂²×M₁₆	C₂²×C₅₃	semidirect
515. C₂³×C₈	C₂²×C₅₃	semidirect
533. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
534. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
547. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
548. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
549. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
550. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
551. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
552. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
553. C₂×#97	C₂²×C₅₃	semidirect
554. C₂×C₄×C₈	C₂²×C₅₃	semidirect
555. #336	C₂²×C₅₃	semidirect
556. #336	C₂²×C₅₃	semidirect
557. #336	C₂²×C₅₃	semidirect
558. #336	C₂²×C₅₃	semidirect
559. C₅₃	#22398	direct (N × H)
662. C₂²⋊C₈	D₄×C₅₃	semidirect
956. C₂²	C₅₃×#408	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
C₂×C₅₃×#435	2
C₂×C₈×D₄×C₅₃	2
C₂×C₅₃×#408	2
C₂²×C₂²⋊C₈×C₅₃	2
C₅₃×#1955	2
C₅₃×#1954	2
C₅₃×#1870	2
C₅₃×#1869	2
C₅₃×#1798	2
C₅₃×#1780	2
C₅₃×#1779	2
C₅₃×#1750	2
#22398	53

Subgroups — C53×#22398 #27229910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22398 #27229910