Subgroups — C₅₃×#35025 #27242537

Order 13568.

2176 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2651	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2648	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2593	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2554	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2480	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2418	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2408	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#2321	C₂	1	2	yes	maximal, complemented
20	C₅₃×#2312	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
26	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#120×C₅₃	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#400	C₂²	1	2	yes	complemented
45	C₅₃×#399	C₂²	1	2	yes	complemented
46	C₅₃×#398	C₂²	1	2	yes	complemented
47	C₅₃×#398	C₂²	1	2	yes	complemented
48	C₅₃×#397	C₂²	1	2	yes	complemented
49	C₅₃×#397	C₂²	1	2	yes	complemented
50	C₅₃×#397	C₂²	1	2	yes	complemented
51	C₅₃×#397	C₂²	1	2	yes	complemented
52	C₅₃×#396	C₂²	1	2	yes	complemented
53	C₅₃×#396	C₂²	1	2	yes	complemented
54	C₅₃×#394	C₂²	1	2	yes	—
55	C₅₃×#394	C₂²	1	2	yes	—
56	C₅₃×#394	C₂²	1	2	yes	—
57	C₅₃×#394	C₂²	1	2	yes	complemented
58	C₅₃×#394	C₂²	1	2	yes	complemented
59	C₅₃×#392	C₂²	1	2	yes	—
60	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#390	C₂²	1	1	yes	characteristic
63	C₅₃×#390	C₂²	1	1	yes	characteristic
64	C₅₃×#390	C₂²	1	1	yes	characteristic
65	C₅₃×#390	C₂²	1	1	yes	characteristic
66	C₅₃×#390	C₂²	1	1	yes	characteristic
67	C₅₃×#390	C₂²	1	1	yes	characteristic
68	C₅₃×#390	C₂²	1	2	yes	—
69	C₅₃×#390	C₂²	1	1	yes	characteristic
70	C₅₃×#390	C₂²	1	1	yes	characteristic
71	C₅₃×#390	C₂²	1	2	yes	—
72	C₅₃×#390	C₂²	1	2	yes	complemented
73	C₅₃×#390	C₂²	1	2	yes	complemented
74	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#388	C₂²	1	2	yes	complemented
79	C₅₃×#388	C₂²	1	2	yes	complemented
80	C₅₃×#388	C₂²	1	2	yes	complemented
81	C₅₃×#388	C₂²	1	2	yes	complemented
82	C₅₃×#388	C₂²	1	2	yes	complemented
83	C₅₃×#388	C₂²	1	2	yes	complemented
84	C₅₃×#388	C₂²	1	2	yes	complemented
85	C₅₃×#388	C₂²	1	2	yes	complemented
86	C₅₃×#388	C₂²	1	2	yes	complemented
87	C₅₃×#388	C₂²	1	2	yes	complemented
88	C₅₃×#388	C₂²	1	2	yes	complemented
89	C₅₃×#388	C₂²	1	2	yes	complemented
90	C₅₃×#388	C₂²	1	2	yes	complemented
91	C₅₃×#388	C₂²	1	2	yes	complemented
92	C₅₃×#388	C₂²	1	2	yes	complemented
93	C₅₃×#388	C₂²	1	2	yes	complemented
94	C₅₃×#388	C₂²	1	2	yes	complemented
95	C₅₃×#387	C₂²	1	2	yes	complemented
96	C₅₃×#386	C₂²	1	2	yes	—
97	C₅₃×#386	C₂²	1	2	yes	complemented
98	C₅₃×#386	C₂²	1	2	yes	complemented
99	C₅₃×#386	C₂²	1	2	yes	complemented
100	C₅₃×#385	C₂²	1	2	yes	—
101	C₅₃×#385	C₂²	1	2	yes	—
102	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#380	C₂²	1	1	yes	characteristic
104	C₅₃×#380	C₂²	1	2	yes	—
105	C₅₃×#380	C₂²	1	2	yes	—
106	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#379	C₂²	1	2	yes	—
108	C₅₃×#379	C₂²	1	2	yes	—
109	C₅₃×#379	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄³×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂⁵×C₅₃	C₂³	1	2	yes	—
124	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₃	—	2	4	no	—
126	C₂²×D₄×C₅₃	—	4	2	no	—
127	C₂²×D₄×C₅₃	—	4	2	no	—
128	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
132	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	#126×C₅₃	—	4	4	no	—
142	#125×C₅₃	—	4	2	no	—
143	#124×C₅₃	—	4	2	no	—
144	#124×C₅₃	—	4	2	no	—
145	#123×C₅₃	—	4	4	no	—
146	C₂²⋊Q₈×C₅₃	—	2	4	no	—
147	C₂²⋊Q₈×C₅₃	—	4	2	no	—
148	#121×C₅₃	—	4	2	no	—
149	#121×C₅₃	—	4	2	no	—
150	#120×C₅₃	—	2	8	no	—
151	C₄×Q₈×C₅₃	—	4	2	no	—
152	C₄×D₄×C₅₃	—	2	4	no	—
153	C₄×D₄×C₅₃	—	2	4	no	—
154	C₄×D₄×C₅₃	—	2	4	no	—
155	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
175	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
176	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₅₃	—	4	2	no	—
209	C₂×C₄²×C₅₃	—	4	2	no	—
210	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
225	#95×C₅₃	C₂³	1	1	yes	characteristic
226	#95×C₅₃	C₂³	1	1	yes	characteristic
227	#95×C₅₃	C₂³	1	1	yes	characteristic
228	#95×C₅₃	C₂³	1	1	yes	characteristic
229	#95×C₅₃	C₂³	1	1	yes	characteristic
230	#95×C₅₃	C₂³	1	1	yes	characteristic
231	#95×C₅₃	C₂³	1	2	yes	—
232	#95×C₅₃	C₂³	1	2	yes	—
233	#95×C₅₃	C₂³	1	2	yes	—
234	#95×C₅₃	C₂³	1	2	yes	—
235	#95×C₅₃	C₂³	1	2	yes	—
236	#95×C₅₃	C₂³	1	2	yes	—
237	#95×C₅₃	C₂³	1	2	yes	—
238	#95×C₅₃	C₂³	1	2	yes	—
239	#95×C₅₃	C₂³	1	2	yes	—
240	#95×C₅₃	C₂³	1	2	yes	—
241	#95×C₅₃	C₂³	1	2	yes	—
242	#95×C₅₃	C₂³	1	2	yes	—
243	#95×C₅₃	C₂³	1	2	yes	—
244	C₂⁴×C₅₃	—	2	4	no	—
245	C₂⁴×C₅₃	—	2	4	no	—
246	C₂⁴×C₅₃	—	2	4	no	—
247	C₂⁴×C₅₃	—	4	2	no	—
248	C₂⁴×C₅₃	—	4	2	no	—
249	C₂⁴×C₅₃	—	4	2	no	—
250	C₂⁴×C₅₃	—	4	2	no	—
251	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
252	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
253	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₅₃	—	2	2	no	—
256	C₂×Q₈×C₅₃	—	2	2	no	—
257	C₂×Q₈×C₅₃	—	2	2	no	—
258	C₂×D₄×C₅₃	—	2	2	no	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	—	2	4	no	—
261	C₂×D₄×C₅₃	—	2	4	no	—
262	C₂×D₄×C₅₃	—	2	4	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	2	2	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	2	no	—
267	C₂×D₄×C₅₃	—	2	2	no	—
268	C₂×D₄×C₅₃	—	2	2	no	—
269	C₂×D₄×C₅₃	—	4	2	no	—
270	C₂×D₄×C₅₃	—	4	2	no	—
271	C₂×D₄×C₅₃	—	4	16	no	—
272	C₂×D₄×C₅₃	—	4	2	no	—
273	C₂×D₄×C₅₃	—	4	2	no	—
274	C₂×D₄×C₅₃	—	4	2	no	—
275	C₂×D₄×C₅₃	—	4	2	no	—
276	C₂×D₄×C₅₃	#41	1	4	yes	—
277	C₂²×C₄×C₅₃	—	2	2	no	—
278	C₂²×C₄×C₅₃	—	2	2	no	—
279	C₂²×C₄×C₅₃	—	2	2	no	—
280	C₂²×C₄×C₅₃	—	2	2	no	—
281	C₂²×C₄×C₅₃	—	2	4	no	—
282	C₂²×C₄×C₅₃	—	2	2	no	—
283	C₂²×C₄×C₅₃	—	2	2	no	—
284	C₂²×C₄×C₅₃	—	2	2	no	—
285	C₂²×C₄×C₅₃	—	2	2	no	—
286	C₂²×C₄×C₅₃	—	2	2	no	—
287	C₂²×C₄×C₅₃	—	2	2	no	—
288	C₂²×C₄×C₅₃	—	4	1	no	—
289	C₂²×C₄×C₅₃	—	4	1	no	—
290	C₂²×C₄×C₅₃	—	4	1	no	—
291	C₂²×C₄×C₅₃	—	4	1	no	—
292	C₂²×C₄×C₅₃	—	4	1	no	—
293	C₂²×C₄×C₅₃	—	4	1	no	—
294	C₂²×C₄×C₅₃	—	4	2	no	—
295	C₂²×C₄×C₅₃	—	4	2	no	—
296	C₂²×C₄×C₅₃	#41	1	4	yes	—
297	C₂²×C₄×C₅₃	#41	1	4	yes	—
298	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₅₃	—	2	2	no	—
318	C₄⋊C₄×C₅₃	—	2	2	no	—
319	C₄⋊C₄×C₅₃	—	2	2	no	—
320	C₄⋊C₄×C₅₃	—	2	4	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	2	no	—
323	C₄⋊C₄×C₅₃	—	2	2	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	4	no	—
327	C₄⋊C₄×C₅₃	—	4	2	no	—
328	C₄⋊C₄×C₅₃	—	4	2	no	—
329	C₄⋊C₄×C₅₃	—	4	2	no	—
330	C₄⋊C₄×C₅₃	—	4	2	no	—
331	C₄⋊C₄×C₅₃	—	4	2	no	—
332	C₄⋊C₄×C₅₃	—	4	2	no	—
333	C₄⋊C₄×C₅₃	—	4	2	no	—
334	C₄⋊C₄×C₅₃	—	4	2	no	—
335	C₂²⋊C₄×C₅₃	—	2	2	no	—
336	C₂²⋊C₄×C₅₃	—	2	2	no	—
337	C₂²⋊C₄×C₅₃	—	2	2	no	—
338	C₂²⋊C₄×C₅₃	—	2	2	no	—
339	C₂²⋊C₄×C₅₃	—	2	4	no	—
340	C₂²⋊C₄×C₅₃	—	2	4	no	—
341	C₂²⋊C₄×C₅₃	—	2	4	no	—
342	C₂²⋊C₄×C₅₃	—	2	4	no	—
343	C₂²⋊C₄×C₅₃	—	2	4	no	—
344	C₂²⋊C₄×C₅₃	—	2	4	no	—
345	C₂²⋊C₄×C₅₃	—	2	2	no	—
346	C₂²⋊C₄×C₅₃	—	2	2	no	—
347	C₂²⋊C₄×C₅₃	—	2	4	no	—
348	C₂²⋊C₄×C₅₃	—	2	4	no	—
349	C₂²⋊C₄×C₅₃	—	2	4	no	—
350	C₂²⋊C₄×C₅₃	—	2	4	no	—
351	C₂²⋊C₄×C₅₃	—	4	2	no	—
352	C₂²⋊C₄×C₅₃	—	4	2	no	—
353	C₂²⋊C₄×C₅₃	—	4	2	no	—
354	C₂²⋊C₄×C₅₃	—	4	2	no	—
355	C₂²⋊C₄×C₅₃	—	4	2	no	—
356	C₂²⋊C₄×C₅₃	—	4	2	no	—
357	C₂²⋊C₄×C₅₃	—	4	2	no	—
358	C₂²⋊C₄×C₅₃	—	4	2	no	—
359	C₂²⋊C₄×C₅₃	—	4	2	no	—
360	C₂²⋊C₄×C₅₃	—	4	2	no	—
361	C₂²⋊C₄×C₅₃	—	4	2	no	—
362	C₂²⋊C₄×C₅₃	—	4	2	no	—
363	C₂²⋊C₄×C₅₃	—	4	2	no	—
364	C₂²⋊C₄×C₅₃	—	4	2	no	—
365	C₂²⋊C₄×C₅₃	—	4	2	no	—
366	C₂²⋊C₄×C₅₃	—	4	2	no	—
367	C₄²×C₅₃	—	2	2	no	—
368	C₄²×C₅₃	—	2	2	no	—
369	C₄²×C₅₃	—	2	2	no	—
370	C₄²×C₅₃	—	2	2	no	—
371	C₄²×C₅₃	—	2	2	no	—
372	C₄²×C₅₃	—	2	2	no	—
373	C₄²×C₅₃	—	2	2	no	—
374	C₄²×C₅₃	—	2	2	no	—
375	C₄²×C₅₃	—	4	1	no	—
376	C₄²×C₅₃	—	4	1	no	—
377	C₄²×C₅₃	—	4	1	no	—
378	C₄²×C₅₃	—	4	1	no	—
379	C₄²×C₅₃	—	4	1	no	—
380	C₄²×C₅₃	—	4	2	no	—
381	C₄²×C₅₃	—	4	2	no	—
382	C₂³×C₅₃	—	2	1	no	—
383	C₂³×C₅₃	—	2	1	no	—
384	C₂³×C₅₃	—	2	1	no	—
385	C₂³×C₅₃	—	2	1	no	—
386	C₂³×C₅₃	—	2	1	no	—
387	C₂³×C₅₃	—	2	1	no	—
388	C₂³×C₅₃	—	2	1	no	—
389	C₂³×C₅₃	—	2	1	no	—
390	C₂³×C₅₃	—	2	1	no	—
391	C₂³×C₅₃	—	2	1	no	—
392	C₂³×C₅₃	—	2	2	no	—
393	C₂³×C₅₃	—	2	2	no	—
394	C₂³×C₅₃	—	2	2	no	—
395	C₂³×C₅₃	—	2	2	no	—
396	C₂³×C₅₃	—	2	2	no	—
397	C₂³×C₅₃	—	2	2	no	—
398	C₂³×C₅₃	—	2	2	no	—
399	C₂³×C₅₃	—	2	2	no	—
400	C₂³×C₅₃	—	2	2	no	—
401	C₂³×C₅₃	—	2	2	no	—
402	C₂³×C₅₃	—	2	2	no	—
403	C₂³×C₅₃	—	2	2	no	—
404	C₂³×C₅₃	—	2	2	no	—
405	C₂³×C₅₃	—	2	2	no	—
406	C₂³×C₅₃	—	4	8	no	—
407	C₂³×C₅₃	—	4	8	no	—
408	C₂³×C₅₃	—	4	8	no	—
409	C₂³×C₅₃	—	8	4	no	—
410	C₂³×C₅₃	—	8	4	no	—
411	C₂³×C₅₃	—	8	4	no	—
412	C₂³×C₅₃	—	8	4	no	—
413	C₂³×C₅₃	C₂×#41	1	2	yes	—
414	C₂³×C₅₃	C₂×#41	1	2	yes	—
415	C₂³×C₅₃	C₂×#41	1	2	yes	—
416	C₂³×C₅₃	C₂×#41	1	2	yes	—
417	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
418	Q₈×C₅₃	—	4	4	no	—
419	D₄×C₅₃	—	2	8	no	—
420	D₄×C₅₃	—	4	8	no	—
421	D₄×C₅₃	—	4	4	no	—
422	D₄×C₅₃	—	4	4	no	—
423	D₄×C₅₃	—	8	4	no	—
424	D₄×C₅₃	—	8	4	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	1	no	—
427	C₂×C₄×C₅₃	—	2	1	no	—
428	C₂×C₄×C₅₃	—	2	1	no	—
429	C₂×C₄×C₅₃	—	2	1	no	—
430	C₂×C₄×C₅₃	—	2	1	no	—
431	C₂×C₄×C₅₃	—	2	1	no	—
432	C₂×C₄×C₅₃	—	2	1	no	—
433	C₂×C₄×C₅₃	—	2	1	no	—
434	C₂×C₄×C₅₃	—	2	1	no	—
435	C₂×C₄×C₅₃	—	2	8	no	—
436	C₂×C₄×C₅₃	—	2	2	no	—
437	C₂×C₄×C₅₃	—	2	2	no	—
438	C₂×C₄×C₅₃	—	2	1	no	—
439	C₂×C₄×C₅₃	—	2	1	no	—
440	C₂×C₄×C₅₃	—	2	1	no	—
441	C₂×C₄×C₅₃	—	2	1	no	—
442	C₂×C₄×C₅₃	—	2	2	no	—
443	C₂×C₄×C₅₃	—	2	2	no	—
444	C₂×C₄×C₅₃	—	2	2	no	—
445	C₂×C₄×C₅₃	—	2	1	no	—
446	C₂×C₄×C₅₃	—	2	1	no	—
447	C₂×C₄×C₅₃	—	2	1	no	—
448	C₂×C₄×C₅₃	—	2	2	no	—
449	C₂×C₄×C₅₃	—	2	1	no	—
450	C₂×C₄×C₅₃	—	2	1	no	—
451	C₂×C₄×C₅₃	—	2	1	no	—
452	C₂×C₄×C₅₃	—	2	1	no	—
453	C₂×C₄×C₅₃	—	2	1	no	—
454	C₂×C₄×C₅₃	—	2	1	no	—
455	C₂×C₄×C₅₃	—	2	1	no	—
456	C₂×C₄×C₅₃	—	2	2	no	—
457	C₂×C₄×C₅₃	—	2	2	no	—
458	C₂×C₄×C₅₃	—	2	2	no	—
459	C₂×C₄×C₅₃	—	2	2	no	—
460	C₂×C₄×C₅₃	—	2	2	no	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	2	2	no	—
463	C₂×C₄×C₅₃	—	2	2	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	1	no	—
466	C₂×C₄×C₅₃	—	2	1	no	—
467	C₂×C₄×C₅₃	—	2	1	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	1	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	1	no	—
473	C₂×C₄×C₅₃	—	2	2	no	—
474	C₂×C₄×C₅₃	—	2	1	no	—
475	C₂×C₄×C₅₃	—	4	4	no	—
476	C₂×C₄×C₅₃	—	4	4	no	—
477	C₂×C₄×C₅₃	—	4	4	no	—
478	C₂×C₄×C₅₃	—	4	4	no	—
479	C₂×C₄×C₅₃	—	4	4	no	—
480	C₂×C₄×C₅₃	—	8	4	no	—
481	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
482	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
483	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
484	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
485	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
486	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
487	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
488	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
489	#35025	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
490	C₂²×C₅₃	—	2	2	no	—
491	C₂²×C₅₃	—	2	2	no	—
492	C₂²×C₅₃	—	2	2	no	—
493	C₂²×C₅₃	—	2	2	no	—
494	C₂²×C₅₃	—	2	2	no	—
495	C₂²×C₅₃	—	2	2	no	—
496	C₂²×C₅₃	—	2	2	no	—
497	C₂²×C₅₃	—	2	2	no	—
498	C₂²×C₅₃	—	2	2	no	—
499	C₂²×C₅₃	—	4	1	no	—
500	C₂²×C₅₃	—	4	1	no	—
501	C₂²×C₅₃	—	4	1	no	—
502	C₂²×C₅₃	—	4	1	no	—
503	C₂²×C₅₃	—	4	2	no	—
504	C₂²×C₅₃	—	4	2	no	—
505	C₂²×C₅₃	—	4	2	no	—
506	C₂²×C₅₃	—	4	2	no	—
507	C₂²×C₅₃	—	4	2	no	—
508	C₂²×C₅₃	—	4	2	no	—
509	C₂²×C₅₃	—	4	2	no	—
510	C₂²×C₅₃	—	4	2	no	—
511	C₂²×C₅₃	—	4	2	no	—
512	C₂²×C₅₃	—	4	2	no	—
513	C₂²×C₅₃	—	4	2	no	—
514	C₂²×C₅₃	—	4	2	no	—
515	C₂²×C₅₃	—	4	2	no	—
516	C₂²×C₅₃	—	4	2	no	—
517	C₂²×C₅₃	—	8	16	no	—
518	C₂²×C₅₃	#529	1	4	yes	—
519	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
520	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
521	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂²×C₅₃	#585	1	1	yes	characteristic
526	C₄×C₅₃	—	2	2	no	—
527	C₄×C₅₃	—	2	2	no	—
528	C₄×C₅₃	—	2	2	no	—
529	C₄×C₅₃	—	2	2	no	—
530	C₄×C₅₃	—	2	2	no	—
531	C₄×C₅₃	—	4	1	no	—
532	C₄×C₅₃	—	4	2	no	—
533	C₄×C₅₃	—	4	1	no	—
534	C₄×C₅₃	—	4	2	no	—
535	C₄×C₅₃	—	4	1	no	—
536	C₄×C₅₃	—	4	1	no	—
537	C₄×C₅₃	—	4	2	no	—
538	C₄×C₅₃	—	4	2	no	—
539	C₄×C₅₃	—	4	1	no	—
540	C₄×C₅₃	—	4	2	no	—
541	C₄×C₅₃	—	4	1	no	—
542	C₄×C₅₃	—	4	1	no	—
543	C₄×C₅₃	—	4	2	no	—
544	C₄×C₅₃	#538	1	4	yes	—
545	#2861	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#2860	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#2854	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#2850	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#2651	C₂×C₅₃	1	2	yes	complemented
550	#2648	C₂×C₅₃	1	2	yes	complemented
551	#2593	C₂×C₅₃	1	2	yes	complemented
552	#2554	C₂×C₅₃	1	2	yes	complemented
553	#2513	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#2490	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#2480	C₂×C₅₃	1	2	yes	complemented
556	#2448	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#2442	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#2435	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#2426	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#2418	C₂×C₅₃	1	2	yes	complemented
561	#2417	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#2408	C₂×C₅₃	1	1	yes	characteristic
563	#2321	C₂×C₅₃	1	2	yes	complemented
564	#2312	C₂×C₅₃	1	2	yes	complemented
565	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
566	C₂×#390	C₂×C₅₃	1	1	yes	characteristic, complemented
567	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
568	C₂×C₅₃	—	2	4	no	—
569	C₂×C₅₃	—	4	2	no	—
570	C₂×C₅₃	—	8	2	no	—
571	C₂×C₅₃	—	8	2	no	—
572	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
573	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
574	C₂×C₅₃	#3460	1	1	yes	characteristic
575	C₂×C₅₃	#3505	1	1	yes	characteristic
576	C₂×C₅₃	#3508	1	1	yes	characteristic
577	C₂×C₅₃	#3514	1	1	yes	characteristic
578	C₂×C₅₃	#3519	1	1	yes	characteristic
579	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
580	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
581	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
582	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
583	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
584	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
585	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
586	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
587	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
588	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
589	C₂×#120	C₂²×C₅₃	1	2	yes	—
590	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
591	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
593	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
594	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
595	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
596	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
597	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
598	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
599	#400	C₂²×C₅₃	1	2	yes	complemented
600	#399	C₂²×C₅₃	1	2	yes	complemented
601	#398	C₂²×C₅₃	1	2	yes	complemented
602	#398	C₂²×C₅₃	1	2	yes	complemented
603	#397	C₂²×C₅₃	1	2	yes	complemented
604	#397	C₂²×C₅₃	1	2	yes	complemented
605	#397	C₂²×C₅₃	1	2	yes	complemented
606	#397	C₂²×C₅₃	1	2	yes	complemented
607	#396	C₂²×C₅₃	1	2	yes	complemented
608	#396	C₂²×C₅₃	1	2	yes	complemented
609	#394	C₂²×C₅₃	1	2	yes	—
610	#394	C₂²×C₅₃	1	2	yes	—
611	#394	C₂²×C₅₃	1	2	yes	—
612	#394	C₂²×C₅₃	1	2	yes	complemented
613	#394	C₂²×C₅₃	1	2	yes	complemented
614	#392	C₂²×C₅₃	1	2	yes	—
615	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
616	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
617	#390	C₂²×C₅₃	1	2	yes	—
618	#390	C₂²×C₅₃	1	1	yes	characteristic
619	#390	C₂²×C₅₃	1	1	yes	characteristic
620	#390	C₂²×C₅₃	1	1	yes	characteristic
621	#390	C₂²×C₅₃	1	1	yes	characteristic
622	#390	C₂²×C₅₃	1	1	yes	characteristic
623	#390	C₂²×C₅₃	1	1	yes	characteristic
624	#390	C₂²×C₅₃	1	2	yes	—
625	#390	C₂²×C₅₃	1	1	yes	characteristic
626	#390	C₂²×C₅₃	1	1	yes	characteristic
627	#390	C₂²×C₅₃	1	2	yes	complemented
628	#390	C₂²×C₅₃	1	2	yes	complemented
629	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
630	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
631	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
632	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#388	C₂²×C₅₃	1	2	yes	complemented
634	#388	C₂²×C₅₃	1	2	yes	complemented
635	#388	C₂²×C₅₃	1	2	yes	complemented
636	#388	C₂²×C₅₃	1	2	yes	complemented
637	#388	C₂²×C₅₃	1	2	yes	complemented
638	#388	C₂²×C₅₃	1	2	yes	complemented
639	#388	C₂²×C₅₃	1	2	yes	complemented
640	#388	C₂²×C₅₃	1	2	yes	complemented
641	#388	C₂²×C₅₃	1	2	yes	complemented
642	#388	C₂²×C₅₃	1	2	yes	complemented
643	#388	C₂²×C₅₃	1	2	yes	complemented
644	#388	C₂²×C₅₃	1	2	yes	complemented
645	#388	C₂²×C₅₃	1	2	yes	complemented
646	#388	C₂²×C₅₃	1	2	yes	complemented
647	#388	C₂²×C₅₃	1	2	yes	complemented
648	#388	C₂²×C₅₃	1	2	yes	complemented
649	#388	C₂²×C₅₃	1	2	yes	complemented
650	#387	C₂²×C₅₃	1	2	yes	complemented
651	#386	C₂²×C₅₃	1	2	yes	—
652	#386	C₂²×C₅₃	1	2	yes	complemented
653	#386	C₂²×C₅₃	1	2	yes	complemented
654	#386	C₂²×C₅₃	1	2	yes	complemented
655	#385	C₂²×C₅₃	1	2	yes	—
656	#385	C₂²×C₅₃	1	2	yes	—
657	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#380	C₂²×C₅₃	1	2	yes	—
659	#380	C₂²×C₅₃	1	2	yes	—
660	#380	C₂²×C₅₃	1	1	yes	characteristic
661	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
662	#379	C₂²×C₅₃	1	2	yes	—
663	#379	C₂²×C₅₃	1	2	yes	—
664	#379	C₂²×C₅₃	1	2	yes	—
665	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
666	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
667	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
671	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
672	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
673	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
674	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	C₄³	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	C₅₃	#35025	1	1	yes	characteristic, direct product factor, Sylow
679	C₂⁵	C₂³×C₅₃	1	2	yes	—
680	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
681	C₂²×D₄	—	2	4	no	—
682	C₂²×D₄	—	4	2	no	—
683	C₂²×D₄	—	4	2	no	—
684	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
685	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
687	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
688	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
689	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
690	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
695	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
697	#126	—	4	4	no	—
698	#125	—	4	2	no	—
699	#124	—	4	2	no	—
700	#124	—	4	2	no	—
701	#123	—	4	4	no	—
702	C₂²⋊Q₈	—	2	4	no	—
703	C₂²⋊Q₈	—	4	2	no	—
704	#121	—	4	2	no	—
705	#121	—	4	2	no	—
706	#120	—	2	8	no	—
707	C₄×Q₈	—	4	2	no	—
708	C₄×D₄	—	2	4	no	—
709	C₄×D₄	—	2	4	no	—
710	C₄×D₄	—	2	4	no	—
711	C₂×C₄⋊C₄	—	4	2	no	—
712	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
730	C₂×C₂²⋊C₄	—	2	8	no	—
731	C₂×C₂²⋊C₄	—	4	4	no	—
732	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
764	C₂×C₄²	—	4	2	no	—
765	C₂×C₄²	—	4	2	no	—
766	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
775	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
777	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
781	#95	C₂³×C₅₃	1	1	yes	characteristic
782	#95	C₂³×C₅₃	1	1	yes	characteristic
783	#95	C₂³×C₅₃	1	1	yes	characteristic
784	#95	C₂³×C₅₃	1	1	yes	characteristic
785	#95	C₂³×C₅₃	1	1	yes	characteristic
786	#95	C₂³×C₅₃	1	1	yes	characteristic
787	#95	C₂³×C₅₃	1	2	yes	—
788	#95	C₂³×C₅₃	1	2	yes	—
789	#95	C₂³×C₅₃	1	2	yes	—
790	#95	C₂³×C₅₃	1	2	yes	—
791	#95	C₂³×C₅₃	1	2	yes	—
792	#95	C₂³×C₅₃	1	2	yes	—
793	#95	C₂³×C₅₃	1	2	yes	—
794	#95	C₂³×C₅₃	1	2	yes	—
795	#95	C₂³×C₅₃	1	2	yes	—
796	#95	C₂³×C₅₃	1	2	yes	—
797	#95	C₂³×C₅₃	1	2	yes	—
798	#95	C₂³×C₅₃	1	2	yes	—
799	#95	C₂³×C₅₃	1	2	yes	—
800	C₂⁴	—	2	4	no	—
801	C₂⁴	—	2	4	no	—
802	C₂⁴	—	2	4	no	—
803	C₂⁴	—	4	2	no	—
804	C₂⁴	—	4	2	no	—
805	C₂⁴	—	4	2	no	—
806	C₂⁴	—	4	2	no	—
807	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
808	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
809	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
810	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
811	C₂×Q₈	—	2	2	no	—
812	C₂×Q₈	—	2	2	no	—
813	C₂×Q₈	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	16	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	#41×C₅₃	1	4	yes	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	#41×C₅₃	1	4	yes	—
853	C₂²×C₄	#41×C₅₃	1	4	yes	—
854	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	4	2	no	—
884	C₄⋊C₄	—	4	2	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	—	4	2	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₄⋊C₄	—	4	2	no	—
890	C₄⋊C₄	—	4	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	2	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	4	1	no	—
932	C₄²	—	4	1	no	—
933	C₄²	—	4	1	no	—
934	C₄²	—	4	1	no	—
935	C₄²	—	4	2	no	—
936	C₄²	—	4	2	no	—
937	C₄²	—	4	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	4	8	no	—
963	C₂³	—	4	8	no	—
964	C₂³	—	4	8	no	—
965	C₂³	—	8	4	no	—
966	C₂³	—	8	4	no	—
967	C₂³	—	8	4	no	—
968	C₂³	—	8	4	no	—
969	C₂³	C₂×#41×C₅₃	1	2	yes	—
970	C₂³	C₂×#41×C₅₃	1	2	yes	—
971	C₂³	C₂×#41×C₅₃	1	2	yes	—
972	C₂³	C₂×#41×C₅₃	1	2	yes	—
973	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
974	Q₈	—	4	4	no	—
975	D₄	—	2	8	no	—
976	D₄	—	4	8	no	—
977	D₄	—	4	4	no	—
978	D₄	—	4	4	no	—
979	D₄	—	8	4	no	—
980	D₄	—	8	4	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	8	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	8	4	no	—
1037	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1038	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1039	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1040	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1041	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1042	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1043	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1044	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	8	16	no	—
1073	C₂²	C₅₃×#529	1	4	yes	—
1074	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1075	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1076	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1077	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1078	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1079	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1080	C₂²	C₅₃×#585	1	1	yes	characteristic
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	C₅₃×#538	1	4	yes	—
1100	C₂	—	2	4	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	8	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
1105	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
1106	C₂	C₅₃×#3460	1	1	yes	characteristic
1107	C₂	C₅₃×#3505	1	1	yes	characteristic
1108	C₂	C₅₃×#3508	1	1	yes	characteristic
1109	C₂	C₅₃×#3514	1	1	yes	characteristic
1110	C₂	C₅₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2408	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2861	C₂	semidirect
2. C₅₃×#2860	C₂	semidirect
3. C₅₃×#2854	C₂	semidirect
4. C₅₃×#2850	C₂	semidirect
5. C₅₃×#2651	C₂	semidirect
6. C₅₃×#2648	C₂	semidirect
7. C₅₃×#2593	C₂	semidirect
8. C₅₃×#2554	C₂	semidirect
9. C₅₃×#2513	C₂	semidirect
10. C₅₃×#2490	C₂	semidirect
11. C₅₃×#2480	C₂	semidirect
12. C₅₃×#2448	C₂	semidirect
13. C₅₃×#2442	C₂	semidirect
14. C₅₃×#2435	C₂	semidirect
15. C₅₃×#2426	C₂	semidirect
16. C₅₃×#2418	C₂	semidirect
17. C₅₃×#2417	C₂	semidirect
19. C₅₃×#2321	C₂	semidirect
20. C₅₃×#2312	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
22. C₂×C₅₃×#390	C₂	semidirect
23. C₄²×D₄×C₅₃	C₂	semidirect
25. C₂×#126×C₅₃	C₂²	semidirect
26. C₂×#125×C₅₃	C₂²	semidirect
29. C₂×#123×C₅₃	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
35. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
43. C₂²×C₄²×C₅₃	C₂²	semidirect
44. C₅₃×#400	C₂²	semidirect
45. C₅₃×#399	C₂²	semidirect
46. C₅₃×#398	C₂²	semidirect
47. C₅₃×#398	C₂²	semidirect
48. C₅₃×#397	C₂²	semidirect
49. C₅₃×#397	C₂²	semidirect
50. C₅₃×#397	C₂²	semidirect
51. C₅₃×#397	C₂²	semidirect
52. C₅₃×#396	C₂²	semidirect
53. C₅₃×#396	C₂²	semidirect
57. C₅₃×#394	C₂²	semidirect
58. C₅₃×#394	C₂²	semidirect
60. C₅₃×#391	C₂²	semidirect
61. C₅₃×#391	C₂²	semidirect
72. C₅₃×#390	C₂²	semidirect
73. C₅₃×#390	C₂²	semidirect
74. C₅₃×#389	C₂²	semidirect
75. C₅₃×#389	C₂²	semidirect
76. C₅₃×#389	C₂²	semidirect
77. C₅₃×#389	C₂²	semidirect
78. C₅₃×#388	C₂²	semidirect
79. C₅₃×#388	C₂²	semidirect
80. C₅₃×#388	C₂²	semidirect
81. C₅₃×#388	C₂²	semidirect
82. C₅₃×#388	C₂²	semidirect
83. C₅₃×#388	C₂²	semidirect
84. C₅₃×#388	C₂²	semidirect
85. C₅₃×#388	C₂²	semidirect
86. C₅₃×#388	C₂²	semidirect
87. C₅₃×#388	C₂²	semidirect
88. C₅₃×#388	C₂²	semidirect
89. C₅₃×#388	C₂²	semidirect
90. C₅₃×#388	C₂²	semidirect
91. C₅₃×#388	C₂²	semidirect
92. C₅₃×#388	C₂²	semidirect
93. C₅₃×#388	C₂²	semidirect
94. C₅₃×#388	C₂²	semidirect
95. C₅₃×#387	C₂²	semidirect
97. C₅₃×#386	C₂²	semidirect
98. C₅₃×#386	C₂²	semidirect
99. C₅₃×#386	C₂²	semidirect
102. C₅₃×#382	C₂²	semidirect
106. C₅₃×#380	C₂²	semidirect
110. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
111. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
112. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
113. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
114. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
122. C₄³×C₅₃	C₂²	semidirect
489. #35025	C₅₃	direct (N × H)
545. #2861	C₂×C₅₃	semidirect
546. #2860	C₂×C₅₃	semidirect
547. #2854	C₂×C₅₃	semidirect
548. #2850	C₂×C₅₃	semidirect
549. #2651	C₂×C₅₃	semidirect
550. #2648	C₂×C₅₃	semidirect
551. #2593	C₂×C₅₃	semidirect
552. #2554	C₂×C₅₃	semidirect
553. #2513	C₂×C₅₃	semidirect
554. #2490	C₂×C₅₃	semidirect
555. #2480	C₂×C₅₃	semidirect
556. #2448	C₂×C₅₃	semidirect
557. #2442	C₂×C₅₃	semidirect
558. #2435	C₂×C₅₃	semidirect
559. #2426	C₂×C₅₃	semidirect
560. #2418	C₂×C₅₃	semidirect
561. #2417	C₂×C₅₃	semidirect
563. #2321	C₂×C₅₃	semidirect
564. #2312	C₂×C₅₃	semidirect
565. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
566. C₂×#390	C₂×C₅₃	semidirect
567. C₄²×D₄	C₂×C₅₃	semidirect
580. C₂×#126	C₂²×C₅₃	semidirect
581. C₂×#125	C₂²×C₅₃	semidirect
584. C₂×#123	C₂²×C₅₃	semidirect
586. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
590. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
598. C₂²×C₄²	C₂²×C₅₃	semidirect
599. #400	C₂²×C₅₃	semidirect
600. #399	C₂²×C₅₃	semidirect
601. #398	C₂²×C₅₃	semidirect
602. #398	C₂²×C₅₃	semidirect
603. #397	C₂²×C₅₃	semidirect
604. #397	C₂²×C₅₃	semidirect
605. #397	C₂²×C₅₃	semidirect
606. #397	C₂²×C₅₃	semidirect
607. #396	C₂²×C₅₃	semidirect
608. #396	C₂²×C₅₃	semidirect
612. #394	C₂²×C₅₃	semidirect
613. #394	C₂²×C₅₃	semidirect
615. #391	C₂²×C₅₃	semidirect
616. #391	C₂²×C₅₃	semidirect
627. #390	C₂²×C₅₃	semidirect
628. #390	C₂²×C₅₃	semidirect
629. #389	C₂²×C₅₃	semidirect
630. #389	C₂²×C₅₃	semidirect
631. #389	C₂²×C₅₃	semidirect
632. #389	C₂²×C₅₃	semidirect
633. #388	C₂²×C₅₃	semidirect
634. #388	C₂²×C₅₃	semidirect
635. #388	C₂²×C₅₃	semidirect
636. #388	C₂²×C₅₃	semidirect
637. #388	C₂²×C₅₃	semidirect
638. #388	C₂²×C₅₃	semidirect
639. #388	C₂²×C₅₃	semidirect
640. #388	C₂²×C₅₃	semidirect
641. #388	C₂²×C₅₃	semidirect
642. #388	C₂²×C₅₃	semidirect
643. #388	C₂²×C₅₃	semidirect
644. #388	C₂²×C₅₃	semidirect
645. #388	C₂²×C₅₃	semidirect
646. #388	C₂²×C₅₃	semidirect
647. #388	C₂²×C₅₃	semidirect
648. #388	C₂²×C₅₃	semidirect
649. #388	C₂²×C₅₃	semidirect
650. #387	C₂²×C₅₃	semidirect
652. #386	C₂²×C₅₃	semidirect
653. #386	C₂²×C₅₃	semidirect
654. #386	C₂²×C₅₃	semidirect
657. #382	C₂²×C₅₃	semidirect
661. #380	C₂²×C₅₃	semidirect
665. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
666. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
667. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
668. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
669. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
674. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
675. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
676. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
677. C₄³	C₂²×C₅₃	semidirect
678. C₅₃	#35025	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2861	2
C₅₃×#2860	2
C₅₃×#2854	2
C₅₃×#2850	2
C₅₃×#2651	2
C₅₃×#2648	2
C₅₃×#2593	2
C₅₃×#2554	2
C₅₃×#2513	2
C₅₃×#2490	2
C₅₃×#2480	2
C₅₃×#2448	2
C₅₃×#2442	2
C₅₃×#2435	2
C₅₃×#2426	2
C₅₃×#2418	2
C₅₃×#2417	2
C₅₃×#2408	2
C₅₃×#2321	2
C₅₃×#2312	2
C₄×C₂²⋊Q₈×C₅₃	2
C₂×C₅₃×#390	2
C₄²×D₄×C₅₃	2
#35025	53

Subgroups — C53×#35025 #27242537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35025 #27242537