Subgroups — C₂×C₅₃×#2480 #27242172

Order 13568.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2480	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#379	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅₃×#379	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×#126×C₅₃	—	2	8	no	—
21	C₂×#126×C₅₃	C₂²	1	8	yes	complemented
22	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊C₄×C₅₃	—	2	8	no	—
29	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	—
30	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#397	C₂²	1	8	yes	complemented
49	C₅₃×#397	C₂²	1	8	yes	complemented
50	C₅₃×#397	C₂²	1	8	yes	complemented
51	C₅₃×#396	C₂²	1	8	yes	complemented
52	C₅₃×#388	C₂²	1	8	yes	complemented
53	C₅₃×#388	C₂²	1	8	yes	complemented
54	C₅₃×#388	C₂²	1	8	yes	complemented
55	C₅₃×#385	C₂²	1	8	yes	complemented
56	C₅₃×#385	C₂²	1	8	yes	complemented
57	C₅₃×#380	C₂²	1	8	yes	complemented
58	C₅₃×#379	C₂²	1	8	yes	—
59	C₅₃×#379	C₂²	1	8	yes	—
60	C₄×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	complemented
61	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₅₃	—	2	4	no	—
70	C₂⁵×C₅₃	—	2	4	no	—
71	C₂⁵×C₅₃	—	2	4	no	—
72	C₂⁵×C₅₃	—	2	4	no	—
73	C₂⁵×C₅₃	—	2	4	no	—
74	C₂⁵×C₅₃	—	4	2	no	—
75	C₂⁵×C₅₃	—	4	2	no	—
76	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
77	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
78	C₂⁵×C₅₃	C₂³	1	4	yes	—
79	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₅₃	—	2	4	no	—
81	C₂³×C₄×C₅₃	—	2	4	no	—
82	C₂³×C₄×C₅₃	—	2	4	no	—
83	C₂³×C₄×C₅₃	—	2	4	no	—
84	C₂³×C₄×C₅₃	—	4	2	no	—
85	C₂³×C₄×C₅₃	—	4	2	no	—
86	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅₃	C₂³	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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
97	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	#126×C₅₃	—	2	32	no	—
101	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
102	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
103	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
104	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
105	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
106	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
107	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
108	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
109	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
110	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
111	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
112	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
113	C₂×C₂²⋊C₄×C₅₃	—	2	32	no	—
114	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
115	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
117	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
118	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
119	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
120	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
126	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
127	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
128	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
129	C₂×C₂²⋊C₄×C₅₃	D₄	1	8	yes	—
130	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
146	C₂×C₄²×C₅₃	—	2	4	no	—
147	C₂×C₄²×C₅₃	—	4	2	no	—
148	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
149	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
150	#95×C₅₃	C₂³	1	4	yes	complemented
151	#95×C₅₃	C₂³	1	4	yes	complemented
152	#95×C₅₃	C₂³	1	4	yes	complemented
153	#95×C₅₃	C₂³	1	4	yes	complemented
154	#95×C₅₃	C₂³	1	4	yes	complemented
155	#95×C₅₃	C₂³	1	4	yes	complemented
156	#95×C₅₃	C₂³	1	4	yes	complemented
157	#95×C₅₃	C₂³	1	4	yes	complemented
158	C₂⁴×C₅₃	—	2	2	no	—
159	C₂⁴×C₅₃	—	2	2	no	—
160	C₂⁴×C₅₃	—	2	2	no	—
161	C₂⁴×C₅₃	—	2	2	no	—
162	C₂⁴×C₅₃	—	2	32	no	—
163	C₂⁴×C₅₃	—	2	8	no	—
164	C₂⁴×C₅₃	—	2	2	no	—
165	C₂⁴×C₅₃	—	2	8	no	—
166	C₂⁴×C₅₃	—	2	8	no	—
167	C₂⁴×C₅₃	—	2	2	no	—
168	C₂⁴×C₅₃	—	2	2	no	—
169	C₂⁴×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	—	2	2	no	—
176	C₂⁴×C₅₃	—	2	2	no	—
177	C₂⁴×C₅₃	—	2	2	no	—
178	C₂⁴×C₅₃	—	2	8	no	—
179	C₂⁴×C₅₃	—	2	8	no	—
180	C₂⁴×C₅₃	—	4	4	no	—
181	C₂⁴×C₅₃	—	4	4	no	—
182	C₂⁴×C₅₃	—	4	16	no	—
183	C₂⁴×C₅₃	—	4	16	no	—
184	C₂⁴×C₅₃	—	4	16	no	—
185	C₂⁴×C₅₃	—	4	16	no	—
186	C₂⁴×C₅₃	—	4	16	no	—
187	C₂⁴×C₅₃	—	4	16	no	—
188	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
189	C₂⁴×C₅₃	#41	1	4	yes	—
190	C₂⁴×C₅₃	#41	1	4	yes	—
191	C₂⁴×C₅₃	#41	1	4	yes	—
192	C₂⁴×C₅₃	#41	1	4	yes	—
193	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
194	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
195	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
196	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₅₃	—	2	2	no	—
198	C₂²×C₄×C₅₃	—	2	2	no	—
199	C₂²×C₄×C₅₃	—	2	2	no	—
200	C₂²×C₄×C₅₃	—	2	2	no	—
201	C₂²×C₄×C₅₃	—	2	2	no	—
202	C₂²×C₄×C₅₃	—	2	2	no	—
203	C₂²×C₄×C₅₃	—	2	2	no	—
204	C₂²×C₄×C₅₃	—	2	2	no	—
205	C₂²×C₄×C₅₃	—	2	2	no	—
206	C₂²×C₄×C₅₃	—	2	2	no	—
207	C₂²×C₄×C₅₃	—	2	2	no	—
208	C₂²×C₄×C₅₃	—	2	2	no	—
209	C₂²×C₄×C₅₃	—	2	2	no	—
210	C₂²×C₄×C₅₃	—	2	2	no	—
211	C₂²×C₄×C₅₃	—	2	2	no	—
212	C₂²×C₄×C₅₃	—	2	2	no	—
213	C₂²×C₄×C₅₃	—	2	2	no	—
214	C₂²×C₄×C₅₃	—	2	2	no	—
215	C₂²×C₄×C₅₃	—	2	2	no	—
216	C₂²×C₄×C₅₃	—	2	2	no	—
217	C₂²×C₄×C₅₃	—	2	2	no	—
218	C₂²×C₄×C₅₃	—	2	2	no	—
219	C₂²×C₄×C₅₃	—	2	8	no	—
220	C₂²×C₄×C₅₃	—	2	8	no	—
221	C₂²×C₄×C₅₃	—	2	2	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	2	no	—
229	C₂²×C₄×C₅₃	—	2	2	no	—
230	C₂²×C₄×C₅₃	—	2	2	no	—
231	C₂²×C₄×C₅₃	—	2	2	no	—
232	C₂²×C₄×C₅₃	—	2	2	no	—
233	C₂²×C₄×C₅₃	—	2	8	no	—
234	C₂²×C₄×C₅₃	—	2	8	no	—
235	C₂²×C₄×C₅₃	—	4	4	no	—
236	C₂²×C₄×C₅₃	—	4	4	no	—
237	C₂²×C₄×C₅₃	—	4	16	no	—
238	C₂²×C₄×C₅₃	—	4	16	no	—
239	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₅₃	—	2	8	no	—
254	C₄⋊C₄×C₅₃	—	2	8	no	—
255	C₄⋊C₄×C₅₃	—	2	8	no	—
256	C₄⋊C₄×C₅₃	—	4	4	no	—
257	C₄⋊C₄×C₅₃	—	4	4	no	—
258	C₄⋊C₄×C₅₃	—	4	4	no	—
259	C₂²⋊C₄×C₅₃	—	2	8	no	—
260	C₂²⋊C₄×C₅₃	—	2	8	no	—
261	C₂²⋊C₄×C₅₃	—	2	8	no	—
262	C₂²⋊C₄×C₅₃	—	2	8	no	—
263	C₂²⋊C₄×C₅₃	—	2	8	no	—
264	C₂²⋊C₄×C₅₃	—	2	8	no	—
265	C₂²⋊C₄×C₅₃	—	2	8	no	—
266	C₂²⋊C₄×C₅₃	—	2	8	no	—
267	C₂²⋊C₄×C₅₃	—	2	8	no	—
268	C₂²⋊C₄×C₅₃	—	2	8	no	—
269	C₂²⋊C₄×C₅₃	—	2	8	no	—
270	C₂²⋊C₄×C₅₃	—	4	4	no	—
271	C₂²⋊C₄×C₅₃	—	4	4	no	—
272	C₂²⋊C₄×C₅₃	—	4	4	no	—
273	C₂²⋊C₄×C₅₃	—	4	4	no	—
274	C₂²⋊C₄×C₅₃	C₂×D₄	1	16	yes	—
275	C₄²×C₅₃	—	2	8	no	—
276	C₄²×C₅₃	—	4	4	no	—
277	C₂³×C₅₃	—	2	8	no	—
278	C₂³×C₅₃	—	2	8	no	—
279	C₂³×C₅₃	—	2	8	no	—
280	C₂³×C₅₃	—	2	8	no	—
281	C₂³×C₅₃	—	2	8	no	—
282	C₂³×C₅₃	—	2	8	no	—
283	C₂³×C₅₃	—	2	2	no	—
284	C₂³×C₅₃	—	2	2	no	—
285	C₂³×C₅₃	—	2	2	no	—
286	C₂³×C₅₃	—	2	2	no	—
287	C₂³×C₅₃	—	2	32	no	—
288	C₂³×C₅₃	—	2	8	no	—
289	C₂³×C₅₃	—	2	8	no	—
290	C₂³×C₅₃	—	2	8	no	—
291	C₂³×C₅₃	—	2	8	no	—
292	C₂³×C₅₃	—	2	8	no	—
293	C₂³×C₅₃	—	2	8	no	—
294	C₂³×C₅₃	—	2	2	no	—
295	C₂³×C₅₃	—	2	2	no	—
296	C₂³×C₅₃	—	2	2	no	—
297	C₂³×C₅₃	—	2	2	no	—
298	C₂³×C₅₃	—	2	2	no	—
299	C₂³×C₅₃	—	2	2	no	—
300	C₂³×C₅₃	—	2	2	no	—
301	C₂³×C₅₃	—	2	2	no	—
302	C₂³×C₅₃	—	2	2	no	—
303	C₂³×C₅₃	—	2	2	no	—
304	C₂³×C₅₃	—	2	2	no	—
305	C₂³×C₅₃	—	2	2	no	—
306	C₂³×C₅₃	—	4	16	no	—
307	C₂³×C₅₃	—	4	16	no	—
308	C₂³×C₅₃	—	4	16	no	—
309	C₂³×C₅₃	—	4	16	no	—
310	C₂³×C₅₃	—	4	16	no	—
311	C₂³×C₅₃	—	4	128	no	—
312	C₂³×C₅₃	—	4	4	no	—
313	C₂³×C₅₃	—	4	4	no	—
314	C₂³×C₅₃	—	4	16	no	—
315	C₂³×C₅₃	—	4	4	no	—
316	C₂³×C₅₃	—	4	4	no	—
317	C₂³×C₅₃	—	4	4	no	—
318	C₂³×C₅₃	—	4	4	no	—
319	C₂³×C₅₃	—	4	4	no	—
320	C₂³×C₅₃	—	4	4	no	—
321	C₂³×C₅₃	#126	1	16	yes	complemented
322	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
323	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
324	C₂³×C₅₃	C₂×#41	1	4	yes	—
325	C₂³×C₅₃	C₂×#41	1	4	yes	—
326	C₂³×C₅₃	C₂×#41	1	4	yes	—
327	C₂³×C₅₃	C₂×#41	1	4	yes	—
328	C₂³×C₅₃	C₂×#41	1	2	yes	—
329	C₂³×C₅₃	C₂×#41	1	2	yes	—
330	C₂³×C₅₃	C₂×#41	1	2	yes	—
331	C₂³×C₅₃	C₂×#41	1	2	yes	—
332	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
333	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
334	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
335	C₂×C₄×C₅₃	—	2	8	no	—
336	C₂×C₄×C₅₃	—	2	8	no	—
337	C₂×C₄×C₅₃	—	2	2	no	—
338	C₂×C₄×C₅₃	—	2	2	no	—
339	C₂×C₄×C₅₃	—	2	2	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	2	no	—
345	C₂×C₄×C₅₃	—	2	2	no	—
346	C₂×C₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	2	2	no	—
350	C₂×C₄×C₅₃	—	2	2	no	—
351	C₂×C₄×C₅₃	—	2	2	no	—
352	C₂×C₄×C₅₃	—	2	2	no	—
353	C₂×C₄×C₅₃	—	2	2	no	—
354	C₂×C₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	2	no	—
357	C₂×C₄×C₅₃	—	2	2	no	—
358	C₂×C₄×C₅₃	—	2	2	no	—
359	C₂×C₄×C₅₃	—	2	2	no	—
360	C₂×C₄×C₅₃	—	2	2	no	—
361	C₂×C₄×C₅₃	—	2	2	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	4	16	no	—
372	C₂×C₄×C₅₃	—	4	16	no	—
373	C₂×C₄×C₅₃	—	4	4	no	—
374	C₂×C₄×C₅₃	—	4	4	no	—
375	C₂×C₄×C₅₃	—	4	4	no	—
376	C₂×C₄×C₅₃	—	4	4	no	—
377	C₂×C₄×C₅₃	—	4	4	no	—
378	C₂×C₄×C₅₃	—	4	4	no	—
379	C₂×C₄×C₅₃	—	4	4	no	—
380	C₂×C₄×C₅₃	—	4	4	no	—
381	C₂×C₄×C₅₃	—	4	4	no	—
382	C₂×C₄×C₅₃	—	4	4	no	—
383	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
384	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
385	C₂×#2480	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
386	C₂²×C₅₃	—	2	4	no	—
387	C₂²×C₅₃	—	2	4	no	—
388	C₂²×C₅₃	—	2	4	no	—
389	C₂²×C₅₃	—	2	4	no	—
390	C₂²×C₅₃	—	2	4	no	—
391	C₂²×C₅₃	—	2	4	no	—
392	C₂²×C₅₃	—	2	32	no	—
393	C₂²×C₅₃	—	2	4	no	—
394	C₂²×C₅₃	—	2	4	no	—
395	C₂²×C₅₃	—	2	4	no	—
396	C₂²×C₅₃	—	2	4	no	—
397	C₂²×C₅₃	—	2	4	no	—
398	C₂²×C₅₃	—	2	4	no	—
399	C₂²×C₅₃	—	4	64	no	—
400	C₂²×C₅₃	—	4	2	no	—
401	C₂²×C₅₃	—	4	2	no	—
402	C₂²×C₅₃	—	4	2	no	—
403	C₂²×C₅₃	—	4	2	no	—
404	C₂²×C₅₃	—	4	2	no	—
405	C₂²×C₅₃	—	4	2	no	—
406	C₂²×C₅₃	—	4	2	no	—
407	C₂²×C₅₃	—	4	2	no	—
408	C₂²×C₅₃	—	4	16	no	—
409	C₂²×C₅₃	—	4	16	no	—
410	C₂²×C₅₃	#525	1	4	yes	—
411	C₂²×C₅₃	C₂×#126	1	4	yes	—
412	C₂²×C₅₃	C₂×#126	1	8	yes	complemented
413	C₂²×C₅₃	#538	1	4	yes	—
414	C₂²×C₅₃	#546	1	4	yes	—
415	C₂²×C₅₃	#546	1	4	yes	—
416	C₂²×C₅₃	#551	1	4	yes	—
417	C₂²×C₅₃	#551	1	4	yes	—
418	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
419	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
420	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
421	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
422	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
423	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₄×C₅₃	—	2	4	no	—
426	C₄×C₅₃	—	2	4	no	—
427	C₄×C₅₃	—	4	2	no	—
428	C₄×C₅₃	—	4	2	no	—
429	C₄×C₅₃	—	4	2	no	—
430	C₄×C₅₃	—	4	2	no	—
431	C₄×C₅₃	—	4	2	no	—
432	C₄×C₅₃	—	4	2	no	—
433	C₄×C₅₃	—	4	2	no	—
434	C₄×C₅₃	—	4	2	no	—
435	C₄×C₅₃	—	4	2	no	—
436	C₄×C₅₃	—	4	2	no	—
437	C₂²×#126	C₂×C₅₃	1	1	yes	characteristic, complemented
438	C₂³×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic
439	#2480	C₂×C₅₃	1	16	yes	direct product factor
440	C₂×#397	C₂×C₅₃	1	1	yes	characteristic, complemented
441	C₂×#397	C₂×C₅₃	1	1	yes	characteristic, complemented
442	C₂×#397	C₂×C₅₃	1	1	yes	characteristic, complemented
443	C₂×#396	C₂×C₅₃	1	1	yes	characteristic, complemented
444	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
445	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
446	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
447	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
448	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
449	C₂×#380	C₂×C₅₃	1	1	yes	characteristic, complemented
450	C₂×#379	C₂×C₅₃	1	1	yes	characteristic
451	C₂×#379	C₂×C₅₃	1	1	yes	characteristic
452	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
453	C₂×C₅₃	—	2	8	no	—
454	C₂×C₅₃	—	4	4	no	—
455	C₂×C₅₃	—	4	4	no	—
456	C₂×C₅₃	#2480	1	8	yes	direct product factor
457	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
458	C₂×C₅₃	C₂²×#126	1	1	yes	characteristic
459	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
460	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
461	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
462	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
463	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
464	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
465	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
466	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
467	C₂×#126	—	2	8	no	—
468	C₂×#126	C₂²×C₅₃	1	8	yes	complemented
469	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
470	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
471	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
472	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
473	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
474	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
475	C₂²×C₂²⋊C₄	—	2	8	no	—
476	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
477	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
478	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
480	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
481	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
482	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	—
483	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
484	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
485	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
486	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
487	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
488	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
489	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
490	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
491	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
492	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
493	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
494	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
495	#397	C₂²×C₅₃	1	8	yes	complemented
496	#397	C₂²×C₅₃	1	8	yes	complemented
497	#397	C₂²×C₅₃	1	8	yes	complemented
498	#396	C₂²×C₅₃	1	8	yes	complemented
499	#388	C₂²×C₅₃	1	8	yes	complemented
500	#388	C₂²×C₅₃	1	8	yes	complemented
501	#388	C₂²×C₅₃	1	8	yes	complemented
502	#385	C₂²×C₅₃	1	8	yes	complemented
503	#385	C₂²×C₅₃	1	8	yes	complemented
504	#380	C₂²×C₅₃	1	8	yes	complemented
505	#379	C₂²×C₅₃	1	8	yes	—
506	#379	C₂²×C₅₃	1	8	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	complemented
508	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
509	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
510	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
511	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
512	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
513	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
514	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
515	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
516	C₅₃	C₂×#2480	1	1	yes	characteristic, direct product factor, Sylow
517	C₂⁵	—	2	4	no	—
518	C₂⁵	—	2	4	no	—
519	C₂⁵	—	2	4	no	—
520	C₂⁵	—	2	4	no	—
521	C₂⁵	—	2	4	no	—
522	C₂⁵	—	4	2	no	—
523	C₂⁵	—	4	2	no	—
524	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
525	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
526	C₂⁵	C₂³×C₅₃	1	4	yes	—
527	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
528	C₂³×C₄	—	2	4	no	—
529	C₂³×C₄	—	2	4	no	—
530	C₂³×C₄	—	2	4	no	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	—	4	2	no	—
533	C₂³×C₄	—	4	2	no	—
534	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
545	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
546	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
548	#126	—	2	32	no	—
549	C₂×C₄⋊C₄	—	2	4	no	—
550	C₂×C₄⋊C₄	—	2	4	no	—
551	C₂×C₄⋊C₄	—	2	4	no	—
552	C₂×C₄⋊C₄	—	4	2	no	—
553	C₂×C₄⋊C₄	—	4	2	no	—
554	C₂×C₄⋊C₄	—	4	2	no	—
555	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
556	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
557	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
558	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
559	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
560	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
561	C₂×C₂²⋊C₄	—	2	4	no	—
562	C₂×C₂²⋊C₄	—	2	4	no	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
570	C₂×C₂²⋊C₄	—	2	4	no	—
571	C₂×C₂²⋊C₄	—	2	4	no	—
572	C₂×C₂²⋊C₄	—	2	32	no	—
573	C₂×C₂²⋊C₄	—	4	2	no	—
574	C₂×C₂²⋊C₄	—	4	2	no	—
575	C₂×C₂²⋊C₄	—	4	2	no	—
576	C₂×C₂²⋊C₄	—	4	2	no	—
577	C₂×C₂²⋊C₄	D₄×C₅₃	1	8	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
594	C₂×C₄²	—	2	4	no	—
595	C₂×C₄²	—	4	2	no	—
596	C₂×C₄²	C₂³×C₅₃	1	4	yes	complemented
597	C₂×C₄²	C₂³×C₅₃	1	4	yes	complemented
598	#95	C₂³×C₅₃	1	4	yes	complemented
599	#95	C₂³×C₅₃	1	4	yes	complemented
600	#95	C₂³×C₅₃	1	4	yes	complemented
601	#95	C₂³×C₅₃	1	4	yes	complemented
602	#95	C₂³×C₅₃	1	4	yes	complemented
603	#95	C₂³×C₅₃	1	4	yes	complemented
604	#95	C₂³×C₅₃	1	4	yes	complemented
605	#95	C₂³×C₅₃	1	4	yes	complemented
606	C₂⁴	—	2	2	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	32	no	—
611	C₂⁴	—	2	8	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	8	no	—
614	C₂⁴	—	2	8	no	—
615	C₂⁴	—	2	2	no	—
616	C₂⁴	—	2	2	no	—
617	C₂⁴	—	2	2	no	—
618	C₂⁴	—	2	2	no	—
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	—	2	2	no	—
622	C₂⁴	—	2	2	no	—
623	C₂⁴	—	2	2	no	—
624	C₂⁴	—	2	2	no	—
625	C₂⁴	—	2	2	no	—
626	C₂⁴	—	2	8	no	—
627	C₂⁴	—	2	8	no	—
628	C₂⁴	—	4	4	no	—
629	C₂⁴	—	4	4	no	—
630	C₂⁴	—	4	16	no	—
631	C₂⁴	—	4	16	no	—
632	C₂⁴	—	4	16	no	—
633	C₂⁴	—	4	16	no	—
634	C₂⁴	—	4	16	no	—
635	C₂⁴	—	4	16	no	—
636	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
637	C₂⁴	#41×C₅₃	1	4	yes	—
638	C₂⁴	#41×C₅₃	1	4	yes	—
639	C₂⁴	#41×C₅₃	1	4	yes	—
640	C₂⁴	#41×C₅₃	1	4	yes	—
641	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
642	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
643	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
644	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	8	no	—
668	C₂²×C₄	—	2	8	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	8	no	—
682	C₂²×C₄	—	2	8	no	—
683	C₂²×C₄	—	4	4	no	—
684	C₂²×C₄	—	4	4	no	—
685	C₂²×C₄	—	4	16	no	—
686	C₂²×C₄	—	4	16	no	—
687	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
688	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
689	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
701	C₄⋊C₄	—	2	8	no	—
702	C₄⋊C₄	—	2	8	no	—
703	C₄⋊C₄	—	2	8	no	—
704	C₄⋊C₄	—	4	4	no	—
705	C₄⋊C₄	—	4	4	no	—
706	C₄⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	2	8	no	—
708	C₂²⋊C₄	—	2	8	no	—
709	C₂²⋊C₄	—	2	8	no	—
710	C₂²⋊C₄	—	2	8	no	—
711	C₂²⋊C₄	—	2	8	no	—
712	C₂²⋊C₄	—	2	8	no	—
713	C₂²⋊C₄	—	2	8	no	—
714	C₂²⋊C₄	—	2	8	no	—
715	C₂²⋊C₄	—	2	8	no	—
716	C₂²⋊C₄	—	2	8	no	—
717	C₂²⋊C₄	—	2	8	no	—
718	C₂²⋊C₄	—	4	4	no	—
719	C₂²⋊C₄	—	4	4	no	—
720	C₂²⋊C₄	—	4	4	no	—
721	C₂²⋊C₄	—	4	4	no	—
722	C₂²⋊C₄	C₂×D₄×C₅₃	1	16	yes	—
723	C₄²	—	2	8	no	—
724	C₄²	—	4	4	no	—
725	C₂³	—	2	8	no	—
726	C₂³	—	2	8	no	—
727	C₂³	—	2	8	no	—
728	C₂³	—	2	8	no	—
729	C₂³	—	2	8	no	—
730	C₂³	—	2	8	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	32	no	—
736	C₂³	—	2	8	no	—
737	C₂³	—	2	8	no	—
738	C₂³	—	2	8	no	—
739	C₂³	—	2	8	no	—
740	C₂³	—	2	8	no	—
741	C₂³	—	2	8	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	4	16	no	—
755	C₂³	—	4	16	no	—
756	C₂³	—	4	16	no	—
757	C₂³	—	4	16	no	—
758	C₂³	—	4	16	no	—
759	C₂³	—	4	128	no	—
760	C₂³	—	4	4	no	—
761	C₂³	—	4	4	no	—
762	C₂³	—	4	16	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	4	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	4	no	—
769	C₂³	#126×C₅₃	1	16	yes	complemented
770	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
771	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
772	C₂³	C₂×#41×C₅₃	1	4	yes	—
773	C₂³	C₂×#41×C₅₃	1	4	yes	—
774	C₂³	C₂×#41×C₅₃	1	4	yes	—
775	C₂³	C₂×#41×C₅₃	1	4	yes	—
776	C₂³	C₂×#41×C₅₃	1	2	yes	—
777	C₂³	C₂×#41×C₅₃	1	2	yes	—
778	C₂³	C₂×#41×C₅₃	1	2	yes	—
779	C₂³	C₂×#41×C₅₃	1	2	yes	—
780	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
781	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
782	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
783	C₂×C₄	—	2	8	no	—
784	C₂×C₄	—	2	8	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	4	16	no	—
820	C₂×C₄	—	4	16	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
832	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	32	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	4	64	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	16	no	—
854	C₂²	—	4	16	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	C₅₃×#525	1	4	yes	—
858	C₂²	C₂×#126×C₅₃	1	4	yes	—
859	C₂²	C₂×#126×C₅₃	1	8	yes	complemented
860	C₂²	C₅₃×#538	1	4	yes	—
861	C₂²	C₅₃×#546	1	4	yes	—
862	C₂²	C₅₃×#546	1	4	yes	—
863	C₂²	C₅₃×#551	1	4	yes	—
864	C₂²	C₅₃×#551	1	4	yes	—
865	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
866	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
867	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
868	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
869	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
870	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
871	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
872	C₄	—	2	4	no	—
873	C₄	—	2	4	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₂	—	2	8	no	—
885	C₂	—	4	4	no	—
886	C₂	—	4	4	no	—
887	C₂	C₅₃×#2480	1	8	yes	direct product factor
888	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
889	C₂	C₂²×#126×C₅₃	1	1	yes	characteristic
890	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
891	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
892	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
893	C₂	C₂×C₅₃×#551	1	1	yes	characteristic
894	C₂	C₂×C₅₃×#551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂⁶×C₅₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#126×C₅₃	C₂	semidirect
3. C₅₃×#2480	C₂	direct (N × H)
4. C₂×C₅₃×#397	C₂	semidirect
5. C₂×C₅₃×#397	C₂	semidirect
6. C₂×C₅₃×#397	C₂	semidirect
7. C₂×C₅₃×#396	C₂	semidirect
8. C₂×C₅₃×#388	C₂	semidirect
9. C₂×C₅₃×#388	C₂	semidirect
10. C₂×C₅₃×#388	C₂	semidirect
11. C₂×C₅₃×#385	C₂	semidirect
12. C₂×C₅₃×#385	C₂	semidirect
13. C₂×C₅₃×#380	C₂	semidirect
16. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
21. C₂×#126×C₅₃	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
23. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
25. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
26. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
27. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
46. C₂²×C₄²×C₅₃	C₂²	semidirect
47. C₂²×C₄²×C₅₃	C₂²	semidirect
48. C₅₃×#397	C₂²	semidirect
49. C₅₃×#397	C₂²	semidirect
50. C₅₃×#397	C₂²	semidirect
51. C₅₃×#396	C₂²	semidirect
52. C₅₃×#388	C₂²	semidirect
53. C₅₃×#388	C₂²	semidirect
54. C₅₃×#388	C₂²	semidirect
55. C₅₃×#385	C₂²	semidirect
56. C₅₃×#385	C₂²	semidirect
57. C₅₃×#380	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
61. C₂×#95×C₅₃	C₂²	semidirect
62. C₂×#95×C₅₃	C₂²	semidirect
63. C₂×#95×C₅₃	C₂²	semidirect
64. C₂×#95×C₅₃	C₂²	semidirect
65. C₂×#95×C₅₃	C₂²	semidirect
66. C₂×#95×C₅₃	C₂²	semidirect
67. C₂×#95×C₅₃	C₂²	semidirect
68. C₂×#95×C₅₃	C₂²	semidirect
107. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
108. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
109. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
110. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
111. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
112. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
148. C₂×C₄²×C₅₃	C₂³	semidirect
149. C₂×C₄²×C₅₃	C₂³	semidirect
150. #95×C₅₃	C₂³	semidirect
151. #95×C₅₃	C₂³	semidirect
152. #95×C₅₃	C₂³	semidirect
153. #95×C₅₃	C₂³	semidirect
154. #95×C₅₃	C₂³	semidirect
155. #95×C₅₃	C₂³	semidirect
156. #95×C₅₃	C₂³	semidirect
157. #95×C₅₃	C₂³	semidirect
321. C₂³×C₅₃	#126	semidirect
385. C₂×#2480	C₅₃	direct (N × H)
412. C₂²×C₅₃	C₂×#126	semidirect
437. C₂²×#126	C₂×C₅₃	semidirect
439. #2480	C₂×C₅₃	direct (N × H)
440. C₂×#397	C₂×C₅₃	semidirect
441. C₂×#397	C₂×C₅₃	semidirect
442. C₂×#397	C₂×C₅₃	semidirect
443. C₂×#396	C₂×C₅₃	semidirect
444. C₂×#388	C₂×C₅₃	semidirect
445. C₂×#388	C₂×C₅₃	semidirect
446. C₂×#388	C₂×C₅₃	semidirect
447. C₂×#385	C₂×C₅₃	semidirect
448. C₂×#385	C₂×C₅₃	semidirect
449. C₂×#380	C₂×C₅₃	semidirect
452. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
456. C₂×C₅₃	#2480	direct (N × H)
468. C₂×#126	C₂²×C₅₃	semidirect
469. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
470. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
471. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
472. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
473. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
474. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
493. C₂²×C₄²	C₂²×C₅₃	semidirect
494. C₂²×C₄²	C₂²×C₅₃	semidirect
495. #397	C₂²×C₅₃	semidirect
496. #397	C₂²×C₅₃	semidirect
497. #397	C₂²×C₅₃	semidirect
498. #396	C₂²×C₅₃	semidirect
499. #388	C₂²×C₅₃	semidirect
500. #388	C₂²×C₅₃	semidirect
501. #388	C₂²×C₅₃	semidirect
502. #385	C₂²×C₅₃	semidirect
503. #385	C₂²×C₅₃	semidirect
504. #380	C₂²×C₅₃	semidirect
507. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
508. C₂×#95	C₂²×C₅₃	semidirect
509. C₂×#95	C₂²×C₅₃	semidirect
510. C₂×#95	C₂²×C₅₃	semidirect
511. C₂×#95	C₂²×C₅₃	semidirect
512. C₂×#95	C₂²×C₅₃	semidirect
513. C₂×#95	C₂²×C₅₃	semidirect
514. C₂×#95	C₂²×C₅₃	semidirect
515. C₂×#95	C₂²×C₅₃	semidirect
516. C₅₃	C₂×#2480	direct (N × H)
555. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
556. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
557. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
558. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
559. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
560. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
596. C₂×C₄²	C₂³×C₅₃	semidirect
597. C₂×C₄²	C₂³×C₅₃	semidirect
598. #95	C₂³×C₅₃	semidirect
599. #95	C₂³×C₅₃	semidirect
600. #95	C₂³×C₅₃	semidirect
601. #95	C₂³×C₅₃	semidirect
602. #95	C₂³×C₅₃	semidirect
603. #95	C₂³×C₅₃	semidirect
604. #95	C₂³×C₅₃	semidirect
605. #95	C₂³×C₅₃	semidirect
769. C₂³	#126×C₅₃	semidirect
859. C₂²	C₂×#126×C₅₃	semidirect
887. C₂	C₅₃×#2480	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#126×C₅₃	2
C₂³×C₂²⋊C₄×C₅₃	2
C₅₃×#2480	2
C₂×C₅₃×#397	2
C₂×C₅₃×#396	2
C₂×C₅₃×#388	2
C₂×C₅₃×#385	2
C₂×C₅₃×#380	2
C₂×C₅₃×#379	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
C₂×#2480	53

Subgroups — C2×C53×#2480 #27242172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2480 #27242172