Subgroups — C₂×C₅₃×#2425 #27242179

Order 13568.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2425	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#95×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×#123×C₅₃	—	2	8	no	—
25	C₂×#123×C₅₃	—	2	8	no	—
26	C₂×#123×C₅₃	C₂²	1	8	yes	complemented
27	C₂×#123×C₅₃	C₂²	1	8	yes	complemented
28	C₂×#121×C₅₃	—	2	8	no	—
29	C₂×#121×C₅₃	C₂²	1	8	yes	—
30	C₂×C₄×D₄×C₅₃	—	2	8	no	—
31	C₂×C₄×D₄×C₅₃	C₂²	1	8	yes	complemented
32	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊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×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#398	C₂²	1	8	yes	complemented
53	C₅₃×#397	C₂²	1	8	yes	complemented
54	C₅₃×#396	C₂²	1	8	yes	complemented
55	C₅₃×#394	C₂²	1	8	yes	complemented
56	C₅₃×#389	C₂²	1	8	yes	complemented
57	C₅₃×#388	C₂²	1	8	yes	complemented
58	C₅₃×#386	C₂²	1	8	yes	complemented
59	C₅₃×#386	C₂²	1	8	yes	complemented
60	C₅₃×#385	C₂²	1	8	yes	complemented
61	C₅₃×#380	C₂²	1	8	yes	complemented
62	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
68	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
69	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
70	C₂×#95×C₅₃	C₂²	1	8	yes	complemented
71	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
72	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
73	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₅₃	—	2	4	no	—
75	C₂²×D₄×C₅₃	—	2	4	no	—
76	C₂²×D₄×C₅₃	—	2	4	no	—
77	C₂²×D₄×C₅₃	—	2	4	no	—
78	C₂²×D₄×C₅₃	—	2	4	no	—
79	C₂²×D₄×C₅₃	—	2	4	no	—
80	C₂²×D₄×C₅₃	—	2	4	no	—
81	C₂²×D₄×C₅₃	—	4	2	no	—
82	C₂²×D₄×C₅₃	D₄	1	8	yes	—
83	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
86	C₂³×C₄×C₅₃	—	2	4	no	—
87	C₂³×C₄×C₅₃	—	2	4	no	—
88	C₂³×C₄×C₅₃	—	2	4	no	—
89	C₂³×C₄×C₅₃	—	2	4	no	—
90	C₂³×C₄×C₅₃	—	2	4	no	—
91	C₂³×C₄×C₅₃	—	2	4	no	—
92	C₂³×C₄×C₅₃	—	2	4	no	—
93	C₂³×C₄×C₅₃	—	2	4	no	—
94	C₂³×C₄×C₅₃	—	2	4	no	—
95	C₂³×C₄×C₅₃	—	4	2	no	—
96	C₂³×C₄×C₅₃	—	4	2	no	—
97	C₂³×C₄×C₅₃	—	4	2	no	—
98	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
107	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
108	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
109	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	#123×C₅₃	—	2	32	no	—
115	#123×C₅₃	—	2	32	no	—
116	#121×C₅₃	—	2	32	no	—
117	C₄×D₄×C₅₃	—	2	32	no	—
118	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
119	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
120	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
121	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
122	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
123	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
124	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
125	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
138	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
139	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
140	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
141	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
144	C₂×C₂²⋊C₄×C₅₃	D₄	1	8	yes	complemented
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
156	C₂×C₄²×C₅₃	—	2	4	no	—
157	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
158	#95×C₅₃	C₂³	1	4	yes	—
159	#95×C₅₃	C₂³	1	4	yes	—
160	#95×C₅₃	C₂³	1	4	yes	—
161	#95×C₅₃	C₂³	1	4	yes	—
162	#95×C₅₃	C₂³	1	4	yes	—
163	#95×C₅₃	C₂³	1	4	yes	—
164	#95×C₅₃	C₂³	1	4	yes	—
165	#95×C₅₃	C₂³	1	4	yes	—
166	C₂⁴×C₅₃	—	2	2	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	2	no	—
179	C₂⁴×C₅₃	—	2	2	no	—
180	C₂⁴×C₅₃	—	2	2	no	—
181	C₂⁴×C₅₃	—	2	2	no	—
182	C₂⁴×C₅₃	—	2	2	no	—
183	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
184	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
185	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
186	C₂⁴×C₅₃	#41	1	4	yes	—
187	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
188	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
189	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
190	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
191	C₂×D₄×C₅₃	—	2	32	no	—
192	C₂×D₄×C₅₃	—	2	8	no	—
193	C₂×D₄×C₅₃	—	2	8	no	—
194	C₂×D₄×C₅₃	—	2	8	no	—
195	C₂×D₄×C₅₃	—	2	8	no	—
196	C₂×D₄×C₅₃	—	2	8	no	—
197	C₂×D₄×C₅₃	—	2	8	no	—
198	C₂×D₄×C₅₃	—	2	8	no	—
199	C₂×D₄×C₅₃	—	4	4	no	—
200	C₂×D₄×C₅₃	—	4	16	no	—
201	C₂×D₄×C₅₃	—	4	16	no	—
202	C₂×D₄×C₅₃	C₂×D₄	1	16	yes	—
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	2	no	—
220	C₂²×C₄×C₅₃	—	2	2	no	—
221	C₂²×C₄×C₅₃	—	2	2	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
223	C₂²×C₄×C₅₃	—	2	8	no	—
224	C₂²×C₄×C₅₃	—	2	8	no	—
225	C₂²×C₄×C₅₃	—	2	8	no	—
226	C₂²×C₄×C₅₃	—	2	8	no	—
227	C₂²×C₄×C₅₃	—	2	2	no	—
228	C₂²×C₄×C₅₃	—	2	2	no	—
229	C₂²×C₄×C₅₃	—	2	8	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	2	no	—
234	C₂²×C₄×C₅₃	—	2	2	no	—
235	C₂²×C₄×C₅₃	—	2	2	no	—
236	C₂²×C₄×C₅₃	—	2	2	no	—
237	C₂²×C₄×C₅₃	—	2	2	no	—
238	C₂²×C₄×C₅₃	—	2	2	no	—
239	C₂²×C₄×C₅₃	—	2	8	no	—
240	C₂²×C₄×C₅₃	—	2	8	no	—
241	C₂²×C₄×C₅₃	—	2	8	no	—
242	C₂²×C₄×C₅₃	—	2	8	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	16	no	—
247	C₂²×C₄×C₅₃	—	4	16	no	—
248	C₂²×C₄×C₅₃	—	4	16	no	—
249	C₂²×C₄×C₅₃	—	4	16	no	—
250	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
252	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
253	C₂²×C₄×C₅₃	#41	1	4	yes	—
254	C₂²×C₄×C₅₃	#41	1	4	yes	—
255	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₅₃	—	2	8	no	—
268	C₄⋊C₄×C₅₃	—	2	8	no	—
269	C₄⋊C₄×C₅₃	—	2	8	no	—
270	C₄⋊C₄×C₅₃	—	2	8	no	—
271	C₄⋊C₄×C₅₃	—	2	8	no	—
272	C₄⋊C₄×C₅₃	—	2	8	no	—
273	C₄⋊C₄×C₅₃	—	2	8	no	—
274	C₄⋊C₄×C₅₃	—	4	4	no	—
275	C₂²⋊C₄×C₅₃	—	2	8	no	—
276	C₂²⋊C₄×C₅₃	—	2	8	no	—
277	C₂²⋊C₄×C₅₃	—	2	8	no	—
278	C₂²⋊C₄×C₅₃	—	2	8	no	—
279	C₂²⋊C₄×C₅₃	—	2	8	no	—
280	C₂²⋊C₄×C₅₃	—	2	8	no	—
281	C₂²⋊C₄×C₅₃	—	2	8	no	—
282	C₂²⋊C₄×C₅₃	—	2	8	no	—
283	C₂²⋊C₄×C₅₃	—	2	8	no	—
284	C₂²⋊C₄×C₅₃	—	4	4	no	—
285	C₂²⋊C₄×C₅₃	C₂×D₄	1	16	yes	complemented
286	C₄²×C₅₃	—	2	8	no	—
287	C₂³×C₅₃	—	2	8	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	2	no	—
294	C₂³×C₅₃	—	2	2	no	—
295	C₂³×C₅₃	—	2	2	no	—
296	C₂³×C₅₃	—	2	2	no	—
297	C₂³×C₅₃	—	2	8	no	—
298	C₂³×C₅₃	—	2	8	no	—
299	C₂³×C₅₃	—	2	8	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	—	2	2	no	—
307	C₂³×C₅₃	—	2	2	no	—
308	C₂³×C₅₃	—	2	2	no	—
309	C₂³×C₅₃	—	2	2	no	—
310	C₂³×C₅₃	—	2	2	no	—
311	C₂³×C₅₃	—	2	2	no	—
312	C₂³×C₅₃	—	2	2	no	—
313	C₂³×C₅₃	—	4	4	no	—
314	C₂³×C₅₃	—	4	4	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	—	4	4	no	—
322	C₂³×C₅₃	—	4	4	no	—
323	C₂³×C₅₃	—	4	4	no	—
324	C₂³×C₅₃	#121	1	16	yes	—
325	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
326	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
327	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
328	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
329	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
330	C₂³×C₅₃	C₂×#41	1	4	yes	—
331	C₂³×C₅₃	C₂×#41	1	2	yes	—
332	C₂³×C₅₃	C₂×#41	1	2	yes	—
333	C₂³×C₅₃	C₂×#41	1	2	yes	—
334	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
336	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
337	D₄×C₅₃	—	2	32	no	—
338	D₄×C₅₃	—	4	16	no	—
339	D₄×C₅₃	—	4	16	no	—
340	C₂×C₄×C₅₃	—	2	8	no	—
341	C₂×C₄×C₅₃	—	2	8	no	—
342	C₂×C₄×C₅₃	—	2	8	no	—
343	C₂×C₄×C₅₃	—	2	8	no	—
344	C₂×C₄×C₅₃	—	2	8	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	—	2	2	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	—	4	16	no	—
377	C₂×C₄×C₅₃	—	4	16	no	—
378	C₂×C₄×C₅₃	—	4	16	no	—
379	C₂×C₄×C₅₃	—	4	16	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	—	4	4	no	—
384	C₂×C₄×C₅₃	—	4	4	no	—
385	C₂×C₄×C₅₃	—	4	4	no	—
386	C₂×C₄×C₅₃	—	4	4	no	—
387	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
389	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
390	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
391	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
392	C₂×#2425	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
393	C₂²×C₅₃	—	2	4	no	—
394	C₂²×C₅₃	—	2	32	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	—	2	4	no	—
400	C₂²×C₅₃	—	2	4	no	—
401	C₂²×C₅₃	—	2	4	no	—
402	C₂²×C₅₃	—	2	4	no	—
403	C₂²×C₅₃	—	4	2	no	—
404	C₂²×C₅₃	—	4	16	no	—
405	C₂²×C₅₃	—	4	2	no	—
406	C₂²×C₅₃	—	4	2	no	—
407	C₂²×C₅₃	—	4	2	no	—
408	C₂²×C₅₃	—	4	2	no	—
409	C₂²×C₅₃	—	4	2	no	—
410	C₂²×C₅₃	—	4	2	no	—
411	C₂²×C₅₃	—	4	2	no	—
412	C₂²×C₅₃	—	4	2	no	—
413	C₂²×C₅₃	—	4	2	no	—
414	C₂²×C₅₃	—	4	2	no	—
415	C₂²×C₅₃	—	8	8	no	—
416	C₂²×C₅₃	C₂×#121	1	8	yes	—
417	C₂²×C₅₃	C₂×#121	1	4	yes	—
418	C₂²×C₅₃	#529	1	4	yes	—
419	C₂²×C₅₃	#539	1	4	yes	—
420	C₂²×C₅₃	#546	1	4	yes	—
421	C₂²×C₅₃	#546	1	4	yes	—
422	C₂²×C₅₃	#547	1	4	yes	—
423	C₂²×C₅₃	#547	1	4	yes	—
424	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
425	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
426	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
427	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
428	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
431	C₄×C₅₃	—	2	4	no	—
432	C₄×C₅₃	—	2	4	no	—
433	C₄×C₅₃	—	2	4	no	—
434	C₄×C₅₃	—	2	4	no	—
435	C₄×C₅₃	—	2	4	no	—
436	C₄×C₅₃	—	4	2	no	—
437	C₄×C₅₃	—	4	2	no	—
438	C₄×C₅₃	—	4	2	no	—
439	C₄×C₅₃	—	4	2	no	—
440	C₄×C₅₃	—	4	2	no	—
441	C₄×C₅₃	—	4	2	no	—
442	C₄×C₅₃	—	4	2	no	—
443	C₂²×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
444	C₂²×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
445	C₂²×#121	C₂×C₅₃	1	1	yes	characteristic
446	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
447	#2425	C₂×C₅₃	1	16	yes	direct product factor
448	C₂×#398	C₂×C₅₃	1	1	yes	characteristic, complemented
449	C₂×#397	C₂×C₅₃	1	1	yes	characteristic, complemented
450	C₂×#396	C₂×C₅₃	1	1	yes	characteristic, complemented
451	C₂×#394	C₂×C₅₃	1	1	yes	characteristic, complemented
452	C₂×#389	C₂×C₅₃	1	1	yes	characteristic, complemented
453	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
454	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
455	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
456	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
457	C₂×#380	C₂×C₅₃	1	1	yes	characteristic, complemented
458	C₂²×#95	C₂×C₅₃	1	1	yes	characteristic, complemented
459	C₂×C₅₃	—	2	8	no	—
460	C₂×C₅₃	—	4	4	no	—
461	C₂×C₅₃	—	8	2	no	—
462	C₂×C₅₃	#2425	1	8	yes	direct product factor
463	C₂×C₅₃	C₂²×#121	1	1	yes	characteristic
464	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
465	C₂×C₅₃	C₂×#539	1	1	yes	characteristic
466	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
467	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
468	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
469	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
470	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
471	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
472	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
473	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
474	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
475	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
476	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
477	C₂×#123	—	2	8	no	—
478	C₂×#123	—	2	8	no	—
479	C₂×#123	C₂²×C₅₃	1	8	yes	complemented
480	C₂×#123	C₂²×C₅₃	1	8	yes	complemented
481	C₂×#121	—	2	8	no	—
482	C₂×#121	C₂²×C₅₃	1	8	yes	—
483	C₂×C₄×D₄	—	2	8	no	—
484	C₂×C₄×D₄	C₂²×C₅₃	1	8	yes	complemented
485	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
486	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
487	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
488	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
489	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
490	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
491	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
492	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
493	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
494	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
495	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
496	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
497	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
498	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
499	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
501	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
502	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
503	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
504	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
505	#398	C₂²×C₅₃	1	8	yes	complemented
506	#397	C₂²×C₅₃	1	8	yes	complemented
507	#396	C₂²×C₅₃	1	8	yes	complemented
508	#394	C₂²×C₅₃	1	8	yes	complemented
509	#389	C₂²×C₅₃	1	8	yes	complemented
510	#388	C₂²×C₅₃	1	8	yes	complemented
511	#386	C₂²×C₅₃	1	8	yes	complemented
512	#386	C₂²×C₅₃	1	8	yes	complemented
513	#385	C₂²×C₅₃	1	8	yes	complemented
514	#380	C₂²×C₅₃	1	8	yes	complemented
515	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
516	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
517	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
518	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
519	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
520	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
521	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
522	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
523	C₂×#95	C₂²×C₅₃	1	8	yes	complemented
524	C₅₃	C₂×#2425	1	1	yes	characteristic, direct product factor, Sylow
525	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
526	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
527	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
528	C₂²×D₄	—	2	4	no	—
529	C₂²×D₄	—	2	4	no	—
530	C₂²×D₄	—	2	4	no	—
531	C₂²×D₄	—	2	4	no	—
532	C₂²×D₄	—	2	4	no	—
533	C₂²×D₄	—	2	4	no	—
534	C₂²×D₄	—	2	4	no	—
535	C₂²×D₄	—	4	2	no	—
536	C₂²×D₄	D₄×C₅₃	1	8	yes	—
537	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
538	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
539	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
540	C₂³×C₄	—	2	4	no	—
541	C₂³×C₄	—	2	4	no	—
542	C₂³×C₄	—	2	4	no	—
543	C₂³×C₄	—	2	4	no	—
544	C₂³×C₄	—	2	4	no	—
545	C₂³×C₄	—	2	4	no	—
546	C₂³×C₄	—	2	4	no	—
547	C₂³×C₄	—	2	4	no	—
548	C₂³×C₄	—	2	4	no	—
549	C₂³×C₄	—	4	2	no	—
550	C₂³×C₄	—	4	2	no	—
551	C₂³×C₄	—	4	2	no	—
552	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
560	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
561	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
562	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
563	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
568	#123	—	2	32	no	—
569	#123	—	2	32	no	—
570	#121	—	2	32	no	—
571	C₄×D₄	—	2	32	no	—
572	C₂×C₄⋊C₄	—	2	4	no	—
573	C₂×C₄⋊C₄	—	2	4	no	—
574	C₂×C₄⋊C₄	—	2	4	no	—
575	C₂×C₄⋊C₄	—	2	4	no	—
576	C₂×C₄⋊C₄	—	2	4	no	—
577	C₂×C₄⋊C₄	—	2	4	no	—
578	C₂×C₄⋊C₄	—	2	4	no	—
579	C₂×C₄⋊C₄	—	4	2	no	—
580	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
582	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₂²⋊C₄	—	2	4	no	—
590	C₂×C₂²⋊C₄	—	2	4	no	—
591	C₂×C₂²⋊C₄	—	2	4	no	—
592	C₂×C₂²⋊C₄	—	2	4	no	—
593	C₂×C₂²⋊C₄	—	2	4	no	—
594	C₂×C₂²⋊C₄	—	2	4	no	—
595	C₂×C₂²⋊C₄	—	2	4	no	—
596	C₂×C₂²⋊C₄	—	2	4	no	—
597	C₂×C₂²⋊C₄	—	4	2	no	—
598	C₂×C₂²⋊C₄	D₄×C₅₃	1	8	yes	complemented
599	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
610	C₂×C₄²	—	2	4	no	—
611	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
612	#95	C₂³×C₅₃	1	4	yes	—
613	#95	C₂³×C₅₃	1	4	yes	—
614	#95	C₂³×C₅₃	1	4	yes	—
615	#95	C₂³×C₅₃	1	4	yes	—
616	#95	C₂³×C₅₃	1	4	yes	—
617	#95	C₂³×C₅₃	1	4	yes	—
618	#95	C₂³×C₅₃	1	4	yes	—
619	#95	C₂³×C₅₃	1	4	yes	—
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	2	no	—
627	C₂⁴	—	2	2	no	—
628	C₂⁴	—	2	2	no	—
629	C₂⁴	—	2	2	no	—
630	C₂⁴	—	2	2	no	—
631	C₂⁴	—	2	2	no	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	2	no	—
635	C₂⁴	—	2	2	no	—
636	C₂⁴	—	2	2	no	—
637	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
638	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
639	C₂⁴	C₂×D₄×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	C₂×D₄	—	2	32	no	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	8	no	—
649	C₂×D₄	—	2	8	no	—
650	C₂×D₄	—	2	8	no	—
651	C₂×D₄	—	2	8	no	—
652	C₂×D₄	—	2	8	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	16	no	—
655	C₂×D₄	—	4	16	no	—
656	C₂×D₄	C₂×D₄×C₅₃	1	16	yes	—
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	2	no	—
668	C₂²×C₄	—	2	2	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	8	no	—
678	C₂²×C₄	—	2	8	no	—
679	C₂²×C₄	—	2	8	no	—
680	C₂²×C₄	—	2	8	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	8	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	8	no	—
694	C₂²×C₄	—	2	8	no	—
695	C₂²×C₄	—	2	8	no	—
696	C₂²×C₄	—	2	8	no	—
697	C₂²×C₄	—	4	4	no	—
698	C₂²×C₄	—	4	4	no	—
699	C₂²×C₄	—	4	4	no	—
700	C₂²×C₄	—	4	16	no	—
701	C₂²×C₄	—	4	16	no	—
702	C₂²×C₄	—	4	16	no	—
703	C₂²×C₄	—	4	16	no	—
704	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
705	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
706	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
707	C₂²×C₄	#41×C₅₃	1	4	yes	—
708	C₂²×C₄	#41×C₅₃	1	4	yes	—
709	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
721	C₄⋊C₄	—	2	8	no	—
722	C₄⋊C₄	—	2	8	no	—
723	C₄⋊C₄	—	2	8	no	—
724	C₄⋊C₄	—	2	8	no	—
725	C₄⋊C₄	—	2	8	no	—
726	C₄⋊C₄	—	2	8	no	—
727	C₄⋊C₄	—	2	8	no	—
728	C₄⋊C₄	—	4	4	no	—
729	C₂²⋊C₄	—	2	8	no	—
730	C₂²⋊C₄	—	2	8	no	—
731	C₂²⋊C₄	—	2	8	no	—
732	C₂²⋊C₄	—	2	8	no	—
733	C₂²⋊C₄	—	2	8	no	—
734	C₂²⋊C₄	—	2	8	no	—
735	C₂²⋊C₄	—	2	8	no	—
736	C₂²⋊C₄	—	2	8	no	—
737	C₂²⋊C₄	—	2	8	no	—
738	C₂²⋊C₄	—	4	4	no	—
739	C₂²⋊C₄	C₂×D₄×C₅₃	1	16	yes	complemented
740	C₄²	—	2	8	no	—
741	C₂³	—	2	8	no	—
742	C₂³	—	2	8	no	—
743	C₂³	—	2	8	no	—
744	C₂³	—	2	8	no	—
745	C₂³	—	2	8	no	—
746	C₂³	—	2	8	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	8	no	—
752	C₂³	—	2	8	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	4	4	no	—
772	C₂³	—	4	4	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	4	no	—
778	C₂³	#121×C₅₃	1	16	yes	—
779	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
780	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
781	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
782	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
783	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
784	C₂³	C₂×#41×C₅₃	1	4	yes	—
785	C₂³	C₂×#41×C₅₃	1	2	yes	—
786	C₂³	C₂×#41×C₅₃	1	2	yes	—
787	C₂³	C₂×#41×C₅₃	1	2	yes	—
788	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
789	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
790	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
791	D₄	—	2	32	no	—
792	D₄	—	4	16	no	—
793	D₄	—	4	16	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	8	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	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	4	16	no	—
831	C₂×C₄	—	4	16	no	—
832	C₂×C₄	—	4	16	no	—
833	C₂×C₄	—	4	16	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
842	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
843	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
844	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
845	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
846	C₂²	—	2	32	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	16	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	8	8	no	—
869	C₂²	C₂×#121×C₅₃	1	8	yes	—
870	C₂²	C₂×#121×C₅₃	1	4	yes	—
871	C₂²	C₅₃×#529	1	4	yes	—
872	C₂²	C₅₃×#539	1	4	yes	—
873	C₂²	C₅₃×#546	1	4	yes	—
874	C₂²	C₅₃×#546	1	4	yes	—
875	C₂²	C₅₃×#547	1	4	yes	—
876	C₂²	C₅₃×#547	1	4	yes	—
877	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
878	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
879	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
880	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
881	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
882	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
883	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
884	C₄	—	2	4	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₂	—	2	8	no	—
897	C₂	—	4	4	no	—
898	C₂	—	8	2	no	—
899	C₂	C₅₃×#2425	1	8	yes	direct product factor
900	C₂	C₂²×#121×C₅₃	1	1	yes	characteristic
901	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
902	C₂	C₂×C₅₃×#539	1	1	yes	characteristic
903	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
904	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
905	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
906	C₂	C₂×C₅₃×#547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂²×#121×C₅₃	C₂
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×#123×C₅₃	C₂	semidirect
2. C₂²×#123×C₅₃	C₂	semidirect
4. C₂²×C₄×D₄×C₅₃	C₂	semidirect
5. C₅₃×#2425	C₂	direct (N × H)
6. C₂×C₅₃×#398	C₂	semidirect
7. C₂×C₅₃×#397	C₂	semidirect
8. C₂×C₅₃×#396	C₂	semidirect
9. C₂×C₅₃×#394	C₂	semidirect
10. C₂×C₅₃×#389	C₂	semidirect
11. C₂×C₅₃×#388	C₂	semidirect
12. C₂×C₅₃×#386	C₂	semidirect
13. C₂×C₅₃×#386	C₂	semidirect
14. C₂×C₅₃×#385	C₂	semidirect
15. C₂×C₅₃×#380	C₂	semidirect
16. C₂²×#95×C₅₃	C₂	semidirect
26. C₂×#123×C₅₃	C₂²	semidirect
27. C₂×#123×C₅₃	C₂²	semidirect
31. C₂×C₄×D₄×C₅₃	C₂²	semidirect
52. C₅₃×#398	C₂²	semidirect
53. C₅₃×#397	C₂²	semidirect
54. C₅₃×#396	C₂²	semidirect
55. C₅₃×#394	C₂²	semidirect
56. C₅₃×#389	C₂²	semidirect
57. C₅₃×#388	C₂²	semidirect
58. C₅₃×#386	C₂²	semidirect
59. C₅₃×#386	C₂²	semidirect
60. C₅₃×#385	C₂²	semidirect
61. C₅₃×#380	C₂²	semidirect
70. C₂×#95×C₅₃	C₂²	semidirect
144. C₂×C₂²⋊C₄×C₅₃	D₄	semidirect
285. C₂²⋊C₄×C₅₃	C₂×D₄	semidirect
392. C₂×#2425	C₅₃	direct (N × H)
443. C₂²×#123	C₂×C₅₃	semidirect
444. C₂²×#123	C₂×C₅₃	semidirect
446. C₂²×C₄×D₄	C₂×C₅₃	semidirect
447. #2425	C₂×C₅₃	direct (N × H)
448. C₂×#398	C₂×C₅₃	semidirect
449. C₂×#397	C₂×C₅₃	semidirect
450. C₂×#396	C₂×C₅₃	semidirect
451. C₂×#394	C₂×C₅₃	semidirect
452. C₂×#389	C₂×C₅₃	semidirect
453. C₂×#388	C₂×C₅₃	semidirect
454. C₂×#386	C₂×C₅₃	semidirect
455. C₂×#386	C₂×C₅₃	semidirect
456. C₂×#385	C₂×C₅₃	semidirect
457. C₂×#380	C₂×C₅₃	semidirect
458. C₂²×#95	C₂×C₅₃	semidirect
462. C₂×C₅₃	#2425	direct (N × H)
479. C₂×#123	C₂²×C₅₃	semidirect
480. C₂×#123	C₂²×C₅₃	semidirect
484. C₂×C₄×D₄	C₂²×C₅₃	semidirect
505. #398	C₂²×C₅₃	semidirect
506. #397	C₂²×C₅₃	semidirect
507. #396	C₂²×C₅₃	semidirect
508. #394	C₂²×C₅₃	semidirect
509. #389	C₂²×C₅₃	semidirect
510. #388	C₂²×C₅₃	semidirect
511. #386	C₂²×C₅₃	semidirect
512. #386	C₂²×C₅₃	semidirect
513. #385	C₂²×C₅₃	semidirect
514. #380	C₂²×C₅₃	semidirect
523. C₂×#95	C₂²×C₅₃	semidirect
524. C₅₃	C₂×#2425	direct (N × H)
598. C₂×C₂²⋊C₄	D₄×C₅₃	semidirect
739. C₂²⋊C₄	C₂×D₄×C₅₃	semidirect
899. C₂	C₅₃×#2425	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×#123×C₅₃	2
C₂²×#121×C₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₅₃×#2425	2
C₂×C₅₃×#398	2
C₂×C₅₃×#397	2
C₂×C₅₃×#396	2
C₂×C₅₃×#394	2
C₂×C₅₃×#389	2
C₂×C₅₃×#388	2
C₂×C₅₃×#386	2
C₂×C₅₃×#385	2
C₂×C₅₃×#380	2
C₂²×#95×C₅₃	2
C₂×#2425	53

Subgroups — C2×C53×#2425 #27242179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2425 #27242179