Subgroups — C₅₃×#36606 #27244118

Order 13568.

2032 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2856	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2595	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2593	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2591	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2516	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2444	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2443	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2374	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2364	C₂	1	2	yes	maximal, complemented
19	C₅₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#123×C₅₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#121×C₅₃	C₂²	1	2	yes	—
32	C₂×#121×C₅₃	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×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×C₄²×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#400	C₂²	1	2	yes	—
44	C₅₃×#400	C₂²	1	2	yes	—
45	C₅₃×#400	C₂²	1	2	yes	—
46	C₅₃×#399	C₂²	1	2	yes	—
47	C₅₃×#398	C₂²	1	2	yes	—
48	C₅₃×#397	C₂²	1	2	yes	—
49	C₅₃×#397	C₂²	1	2	yes	—
50	C₅₃×#397	C₂²	1	2	yes	—
51	C₅₃×#394	C₂²	1	2	yes	—
52	C₅₃×#394	C₂²	1	2	yes	—
53	C₅₃×#394	C₂²	1	2	yes	—
54	C₅₃×#394	C₂²	1	2	yes	—
55	C₅₃×#391	C₂²	1	1	yes	characteristic
56	C₅₃×#391	C₂²	1	1	yes	characteristic
57	C₅₃×#391	C₂²	1	1	yes	characteristic
58	C₅₃×#390	C₂²	1	1	yes	characteristic
59	C₅₃×#390	C₂²	1	1	yes	characteristic
60	C₅₃×#390	C₂²	1	1	yes	characteristic
61	C₅₃×#390	C₂²	1	1	yes	characteristic
62	C₅₃×#390	C₂²	1	1	yes	characteristic
63	C₅₃×#390	C₂²	1	1	yes	characteristic
64	C₅₃×#390	C₂²	1	2	yes	—
65	C₅₃×#390	C₂²	1	2	yes	—
66	C₅₃×#389	C₂²	1	1	yes	characteristic
67	C₅₃×#389	C₂²	1	1	yes	characteristic
68	C₅₃×#389	C₂²	1	1	yes	characteristic
69	C₅₃×#388	C₂²	1	2	yes	—
70	C₅₃×#388	C₂²	1	2	yes	—
71	C₅₃×#388	C₂²	1	2	yes	—
72	C₅₃×#388	C₂²	1	2	yes	—
73	C₅₃×#388	C₂²	1	2	yes	—
74	C₅₃×#388	C₂²	1	2	yes	—
75	C₅₃×#388	C₂²	1	2	yes	—
76	C₅₃×#388	C₂²	1	2	yes	—
77	C₅₃×#388	C₂²	1	2	yes	—
78	C₅₃×#388	C₂²	1	2	yes	—
79	C₅₃×#388	C₂²	1	2	yes	—
80	C₅₃×#388	C₂²	1	2	yes	—
81	C₅₃×#388	C₂²	1	2	yes	—
82	C₅₃×#388	C₂²	1	2	yes	—
83	C₅₃×#387	C₂²	1	2	yes	—
84	C₅₃×#387	C₂²	1	2	yes	—
85	C₅₃×#387	C₂²	1	2	yes	—
86	C₅₃×#387	C₂²	1	2	yes	—
87	C₅₃×#387	C₂²	1	2	yes	—
88	C₅₃×#386	C₂²	1	2	yes	—
89	C₅₃×#386	C₂²	1	2	yes	—
90	C₅₃×#386	C₂²	1	2	yes	—
91	C₅₃×#386	C₂²	1	2	yes	—
92	C₅₃×#386	C₂²	1	2	yes	—
93	C₅₃×#386	C₂²	1	2	yes	—
94	C₅₃×#386	C₂²	1	2	yes	—
95	C₅₃×#386	C₂²	1	2	yes	—
96	C₅₃×#386	C₂²	1	2	yes	—
97	C₅₃×#385	C₂²	1	2	yes	—
98	C₅₃×#385	C₂²	1	2	yes	—
99	C₅₃×#384	C₂²	1	1	yes	characteristic
100	C₅₃×#382	C₂²	1	1	yes	characteristic
101	C₅₃×#382	C₂²	1	1	yes	characteristic
102	C₅₃×#381	C₂²	1	2	yes	—
103	C₅₃×#380	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
121	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	#127×C₅₃	—	4	2	no	—
140	#124×C₅₃	—	2	4	no	—
141	#124×C₅₃	—	4	2	no	—
142	#123×C₅₃	—	2	8	no	—
143	C₂²⋊Q₈×C₅₃	—	2	4	no	—
144	#121×C₅₃	—	2	4	no	—
145	#121×C₅₃	—	2	4	no	—
146	#121×C₅₃	—	2	8	no	—
147	#121×C₅₃	—	4	4	no	—
148	C₄×Q₈×C₅₃	—	4	2	no	—
149	C₄×D₄×C₅₃	—	2	4	no	—
150	C₄×D₄×C₅₃	—	4	4	no	—
151	C₄×D₄×C₅₃	—	4	4	no	—
152	C₄×D₄×C₅₃	—	4	2	no	—
153	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
154	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
183	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
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×C₄²×C₅₃	—	2	4	no	—
198	C₂×C₄²×C₅₃	—	4	2	no	—
199	C₂×C₄²×C₅₃	—	4	2	no	—
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
215	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
216	#95×C₅₃	C₂³	1	1	yes	characteristic
217	#95×C₅₃	C₂³	1	1	yes	characteristic
218	#95×C₅₃	C₂³	1	1	yes	characteristic
219	#95×C₅₃	C₂³	1	1	yes	characteristic
220	#95×C₅₃	C₂³	1	1	yes	characteristic
221	#95×C₅₃	C₂³	1	1	yes	characteristic
222	#95×C₅₃	C₂³	1	1	yes	characteristic
223	#95×C₅₃	C₂³	1	1	yes	characteristic
224	#95×C₅₃	C₂³	1	2	yes	—
225	#95×C₅₃	C₂³	1	2	yes	—
226	#95×C₅₃	C₂³	1	2	yes	—
227	#95×C₅₃	C₂³	1	2	yes	—
228	#95×C₅₃	C₂³	1	2	yes	—
229	#95×C₅₃	C₂³	1	2	yes	—
230	#95×C₅₃	C₂³	1	2	yes	—
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	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
242	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
243	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₂×Q₈×C₅₃	—	2	2	no	—
245	C₂×Q₈×C₅₃	—	2	2	no	—
246	C₂×Q₈×C₅₃	—	2	2	no	—
247	C₂×D₄×C₅₃	—	2	4	no	—
248	C₂×D₄×C₅₃	—	2	4	no	—
249	C₂×D₄×C₅₃	—	2	4	no	—
250	C₂×D₄×C₅₃	—	2	4	no	—
251	C₂×D₄×C₅₃	—	2	4	no	—
252	C₂×D₄×C₅₃	—	2	4	no	—
253	C₂×D₄×C₅₃	—	2	2	no	—
254	C₂×D₄×C₅₃	—	2	2	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	2	no	—
257	C₂×D₄×C₅₃	—	2	4	no	—
258	C₂×D₄×C₅₃	—	2	4	no	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	4	2	no	—
262	C₂×D₄×C₅₃	—	4	2	no	—
263	C₂×D₄×C₅₃	—	4	2	no	—
264	C₂×D₄×C₅₃	—	4	2	no	—
265	C₂²×C₄×C₅₃	—	2	2	no	—
266	C₂²×C₄×C₅₃	—	2	2	no	—
267	C₂²×C₄×C₅₃	—	2	2	no	—
268	C₂²×C₄×C₅₃	—	2	2	no	—
269	C₂²×C₄×C₅₃	—	2	2	no	—
270	C₂²×C₄×C₅₃	—	2	2	no	—
271	C₂²×C₄×C₅₃	—	2	2	no	—
272	C₂²×C₄×C₅₃	—	2	2	no	—
273	C₂²×C₄×C₅₃	—	2	2	no	—
274	C₂²×C₄×C₅₃	—	2	2	no	—
275	C₂²×C₄×C₅₃	—	2	2	no	—
276	C₂²×C₄×C₅₃	—	2	2	no	—
277	C₂²×C₄×C₅₃	—	2	4	no	—
278	C₂²×C₄×C₅₃	—	2	4	no	—
279	C₂²×C₄×C₅₃	—	4	1	no	—
280	C₂²×C₄×C₅₃	—	4	1	no	—
281	C₂²×C₄×C₅₃	—	4	1	no	—
282	C₂²×C₄×C₅₃	—	4	1	no	—
283	C₂²×C₄×C₅₃	—	4	1	no	—
284	C₂²×C₄×C₅₃	—	4	1	no	—
285	C₂²×C₄×C₅₃	—	4	1	no	—
286	C₂²×C₄×C₅₃	—	4	2	no	—
287	C₂²×C₄×C₅₃	—	4	2	no	—
288	C₂²×C₄×C₅₃	—	4	2	no	—
289	C₂²×C₄×C₅₃	—	4	2	no	—
290	C₂²×C₄×C₅₃	#41	1	4	yes	—
291	C₂²×C₄×C₅₃	#41	1	4	yes	—
292	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₅₃	—	2	2	no	—
313	C₄⋊C₄×C₅₃	—	2	2	no	—
314	C₄⋊C₄×C₅₃	—	2	2	no	—
315	C₄⋊C₄×C₅₃	—	2	2	no	—
316	C₄⋊C₄×C₅₃	—	2	2	no	—
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	4	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	4	no	—
326	C₄⋊C₄×C₅₃	—	2	2	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	#41	1	4	yes	—
332	C₂²⋊C₄×C₅₃	—	2	4	no	—
333	C₂²⋊C₄×C₅₃	—	2	4	no	—
334	C₂²⋊C₄×C₅₃	—	2	4	no	—
335	C₂²⋊C₄×C₅₃	—	2	4	no	—
336	C₂²⋊C₄×C₅₃	—	2	4	no	—
337	C₂²⋊C₄×C₅₃	—	2	4	no	—
338	C₂²⋊C₄×C₅₃	—	2	4	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	—	4	2	no	—
345	C₂²⋊C₄×C₅₃	—	4	2	no	—
346	C₂²⋊C₄×C₅₃	—	4	2	no	—
347	C₂²⋊C₄×C₅₃	—	4	2	no	—
348	C₂²⋊C₄×C₅₃	—	4	2	no	—
349	C₂²⋊C₄×C₅₃	—	4	2	no	—
350	C₂²⋊C₄×C₅₃	—	4	2	no	—
351	C₂²⋊C₄×C₅₃	—	4	2	no	—
352	C₂²⋊C₄×C₅₃	—	4	2	no	—
353	C₂²⋊C₄×C₅₃	—	4	2	no	—
354	C₄²×C₅₃	—	2	2	no	—
355	C₄²×C₅₃	—	2	2	no	—
356	C₄²×C₅₃	—	2	2	no	—
357	C₄²×C₅₃	—	2	2	no	—
358	C₄²×C₅₃	—	2	2	no	—
359	C₄²×C₅₃	—	2	2	no	—
360	C₄²×C₅₃	—	2	2	no	—
361	C₄²×C₅₃	—	4	1	no	—
362	C₄²×C₅₃	—	4	1	no	—
363	C₄²×C₅₃	—	4	1	no	—
364	C₄²×C₅₃	—	4	1	no	—
365	C₄²×C₅₃	—	4	2	no	—
366	C₄²×C₅₃	—	4	2	no	—
367	C₄²×C₅₃	—	4	2	no	—
368	C₄²×C₅₃	—	4	2	no	—
369	C₄²×C₅₃	#41	1	4	yes	—
370	C₂³×C₅₃	—	2	1	no	—
371	C₂³×C₅₃	—	2	1	no	—
372	C₂³×C₅₃	—	2	1	no	—
373	C₂³×C₅₃	—	2	1	no	—
374	C₂³×C₅₃	—	2	2	no	—
375	C₂³×C₅₃	—	2	2	no	—
376	C₂³×C₅₃	—	2	2	no	—
377	C₂³×C₅₃	—	2	2	no	—
378	C₂³×C₅₃	—	2	2	no	—
379	C₂³×C₅₃	—	2	2	no	—
380	C₂³×C₅₃	—	2	2	no	—
381	C₂³×C₅₃	—	2	2	no	—
382	C₂³×C₅₃	—	2	2	no	—
383	C₂³×C₅₃	—	2	2	no	—
384	C₂³×C₅₃	—	2	2	no	—
385	C₂³×C₅₃	—	2	2	no	—
386	C₂³×C₅₃	—	2	2	no	—
387	C₂³×C₅₃	—	2	2	no	—
388	C₂³×C₅₃	C₂×#41	1	2	yes	—
389	C₂³×C₅₃	C₂×#41	1	2	yes	—
390	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
391	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
392	Q₈×C₅₃	—	4	4	no	—
393	D₄×C₅₃	—	4	8	no	—
394	D₄×C₅₃	—	4	8	no	—
395	D₄×C₅₃	—	4	4	no	—
396	D₄×C₅₃	—	4	4	no	—
397	D₄×C₅₃	—	8	4	no	—
398	D₄×C₅₃	—	8	4	no	—
399	C₂×C₄×C₅₃	—	2	8	no	—
400	C₂×C₄×C₅₃	—	2	1	no	—
401	C₂×C₄×C₅₃	—	2	1	no	—
402	C₂×C₄×C₅₃	—	2	1	no	—
403	C₂×C₄×C₅₃	—	2	1	no	—
404	C₂×C₄×C₅₃	—	2	1	no	—
405	C₂×C₄×C₅₃	—	2	1	no	—
406	C₂×C₄×C₅₃	—	2	1	no	—
407	C₂×C₄×C₅₃	—	2	1	no	—
408	C₂×C₄×C₅₃	—	2	1	no	—
409	C₂×C₄×C₅₃	—	2	1	no	—
410	C₂×C₄×C₅₃	—	2	1	no	—
411	C₂×C₄×C₅₃	—	2	1	no	—
412	C₂×C₄×C₅₃	—	2	1	no	—
413	C₂×C₄×C₅₃	—	2	1	no	—
414	C₂×C₄×C₅₃	—	2	1	no	—
415	C₂×C₄×C₅₃	—	2	1	no	—
416	C₂×C₄×C₅₃	—	2	8	no	—
417	C₂×C₄×C₅₃	—	2	1	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	1	no	—
422	C₂×C₄×C₅₃	—	2	1	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	2	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	1	no	—
436	C₂×C₄×C₅₃	—	2	1	no	—
437	C₂×C₄×C₅₃	—	2	1	no	—
438	C₂×C₄×C₅₃	—	2	1	no	—
439	C₂×C₄×C₅₃	—	2	2	no	—
440	C₂×C₄×C₅₃	—	2	2	no	—
441	C₂×C₄×C₅₃	—	2	2	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	2	no	—
446	C₂×C₄×C₅₃	—	2	1	no	—
447	C₂×C₄×C₅₃	—	2	1	no	—
448	C₂×C₄×C₅₃	—	2	1	no	—
449	C₂×C₄×C₅₃	—	2	2	no	—
450	C₂×C₄×C₅₃	—	4	4	no	—
451	C₂×C₄×C₅₃	—	4	4	no	—
452	C₂×C₄×C₅₃	—	4	4	no	—
453	C₂×C₄×C₅₃	—	4	4	no	—
454	C₂×C₄×C₅₃	—	4	4	no	—
455	C₂×C₄×C₅₃	—	8	4	no	—
456	C₂×C₄×C₅₃	—	8	4	no	—
457	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
458	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
459	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
460	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
461	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
462	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
463	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
464	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
465	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
466	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
467	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
468	#36606	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
469	C₂²×C₅₃	—	2	2	no	—
470	C₂²×C₅₃	—	2	2	no	—
471	C₂²×C₅₃	—	2	2	no	—
472	C₂²×C₅₃	—	2	2	no	—
473	C₂²×C₅₃	—	2	2	no	—
474	C₂²×C₅₃	—	2	2	no	—
475	C₂²×C₅₃	—	4	2	no	—
476	C₂²×C₅₃	—	4	2	no	—
477	C₂²×C₅₃	—	4	2	no	—
478	C₂²×C₅₃	—	4	2	no	—
479	C₂²×C₅₃	—	4	2	no	—
480	C₂²×C₅₃	—	4	2	no	—
481	C₂²×C₅₃	—	4	2	no	—
482	C₂²×C₅₃	—	4	2	no	—
483	C₂²×C₅₃	—	4	2	no	—
484	C₂²×C₅₃	—	4	2	no	—
485	C₂²×C₅₃	—	4	2	no	—
486	C₂²×C₅₃	—	4	2	no	—
487	C₂²×C₅₃	—	4	2	no	—
488	C₂²×C₅₃	—	4	2	no	—
489	C₂²×C₅₃	#559	1	4	yes	—
490	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
491	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
492	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
493	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
494	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂²×C₅₃	#585	1	1	yes	characteristic
497	C₄×C₅₃	—	2	2	no	—
498	C₄×C₅₃	—	2	2	no	—
499	C₄×C₅₃	—	2	2	no	—
500	C₄×C₅₃	—	2	2	no	—
501	C₄×C₅₃	—	2	2	no	—
502	C₄×C₅₃	—	2	2	no	—
503	C₄×C₅₃	—	2	2	no	—
504	C₄×C₅₃	—	2	2	no	—
505	C₄×C₅₃	—	4	2	no	—
506	C₄×C₅₃	—	4	2	no	—
507	C₄×C₅₃	—	4	2	no	—
508	C₄×C₅₃	—	4	2	no	—
509	C₄×C₅₃	—	4	1	no	—
510	C₄×C₅₃	—	4	2	no	—
511	C₄×C₅₃	—	4	1	no	—
512	C₄×C₅₃	—	4	1	no	—
513	C₄×C₅₃	—	4	1	no	—
514	C₄×C₅₃	—	4	1	no	—
515	C₄×C₅₃	—	4	2	no	—
516	C₄×C₅₃	#553	1	4	yes	—
517	#2856	C₂×C₅₃	1	1	yes	characteristic
518	#2850	C₂×C₅₃	1	1	yes	characteristic, complemented
519	#2850	C₂×C₅₃	1	1	yes	characteristic, complemented
520	#2595	C₂×C₅₃	1	2	yes	complemented
521	#2593	C₂×C₅₃	1	2	yes	complemented
522	#2591	C₂×C₅₃	1	2	yes	complemented
523	#2570	C₂×C₅₃	1	1	yes	characteristic, complemented
524	#2544	C₂×C₅₃	1	1	yes	characteristic, complemented
525	#2516	C₂×C₅₃	1	2	yes	complemented
526	#2513	C₂×C₅₃	1	1	yes	characteristic, complemented
527	#2511	C₂×C₅₃	1	1	yes	characteristic, complemented
528	#2448	C₂×C₅₃	1	1	yes	characteristic, complemented
529	#2445	C₂×C₅₃	1	1	yes	characteristic, complemented
530	#2444	C₂×C₅₃	1	2	yes	complemented
531	#2443	C₂×C₅₃	1	2	yes	complemented
532	#2374	C₂×C₅₃	1	2	yes	complemented
533	#2367	C₂×C₅₃	1	1	yes	characteristic, complemented
534	#2364	C₂×C₅₃	1	2	yes	complemented
535	#2357	C₂×C₅₃	1	1	yes	characteristic, complemented
536	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
537	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
538	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
539	C₂×C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
540	C₂×C₅₃	—	2	4	no	—
541	C₂×C₅₃	—	8	2	no	—
542	C₂×C₅₃	—	8	2	no	—
543	C₂×C₅₃	#3444	1	1	yes	characteristic
544	C₂×C₅₃	C₂×#553	1	1	yes	characteristic
545	C₂×C₅₃	C₂×#559	1	1	yes	characteristic
546	C₂×C₅₃	#3480	1	1	yes	characteristic
547	C₂×C₅₃	#3494	1	1	yes	characteristic
548	C₂×C₅₃	#3505	1	1	yes	characteristic
549	C₂×C₅₃	#3519	1	1	yes	characteristic
550	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
551	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
552	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
553	C₂×#123	C₂²×C₅₃	1	2	yes	—
554	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
555	C₂×#121	C₂²×C₅₃	1	2	yes	—
556	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
557	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
558	C₂×#121	C₂²×C₅₃	1	2	yes	—
559	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
560	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
562	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
563	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
564	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
565	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
566	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
567	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
568	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
569	#400	C₂²×C₅₃	1	2	yes	—
570	#400	C₂²×C₅₃	1	2	yes	—
571	#400	C₂²×C₅₃	1	2	yes	—
572	#399	C₂²×C₅₃	1	2	yes	—
573	#398	C₂²×C₅₃	1	2	yes	—
574	#397	C₂²×C₅₃	1	2	yes	—
575	#397	C₂²×C₅₃	1	2	yes	—
576	#397	C₂²×C₅₃	1	2	yes	—
577	#394	C₂²×C₅₃	1	2	yes	—
578	#394	C₂²×C₅₃	1	2	yes	—
579	#394	C₂²×C₅₃	1	2	yes	—
580	#394	C₂²×C₅₃	1	2	yes	—
581	#391	C₂²×C₅₃	1	1	yes	characteristic
582	#391	C₂²×C₅₃	1	1	yes	characteristic
583	#391	C₂²×C₅₃	1	1	yes	characteristic
584	#390	C₂²×C₅₃	1	2	yes	—
585	#390	C₂²×C₅₃	1	1	yes	characteristic
586	#390	C₂²×C₅₃	1	1	yes	characteristic
587	#390	C₂²×C₅₃	1	2	yes	—
588	#390	C₂²×C₅₃	1	1	yes	characteristic
589	#390	C₂²×C₅₃	1	1	yes	characteristic
590	#390	C₂²×C₅₃	1	1	yes	characteristic
591	#390	C₂²×C₅₃	1	1	yes	characteristic
592	#389	C₂²×C₅₃	1	1	yes	characteristic
593	#389	C₂²×C₅₃	1	1	yes	characteristic
594	#389	C₂²×C₅₃	1	1	yes	characteristic
595	#388	C₂²×C₅₃	1	2	yes	—
596	#388	C₂²×C₅₃	1	2	yes	—
597	#388	C₂²×C₅₃	1	2	yes	—
598	#388	C₂²×C₅₃	1	2	yes	—
599	#388	C₂²×C₅₃	1	2	yes	—
600	#388	C₂²×C₅₃	1	2	yes	—
601	#388	C₂²×C₅₃	1	2	yes	—
602	#388	C₂²×C₅₃	1	2	yes	—
603	#388	C₂²×C₅₃	1	2	yes	—
604	#388	C₂²×C₅₃	1	2	yes	—
605	#388	C₂²×C₅₃	1	2	yes	—
606	#388	C₂²×C₅₃	1	2	yes	—
607	#388	C₂²×C₅₃	1	2	yes	—
608	#388	C₂²×C₅₃	1	2	yes	—
609	#387	C₂²×C₅₃	1	2	yes	—
610	#387	C₂²×C₅₃	1	2	yes	—
611	#387	C₂²×C₅₃	1	2	yes	—
612	#387	C₂²×C₅₃	1	2	yes	—
613	#387	C₂²×C₅₃	1	2	yes	—
614	#386	C₂²×C₅₃	1	2	yes	—
615	#386	C₂²×C₅₃	1	2	yes	—
616	#386	C₂²×C₅₃	1	2	yes	—
617	#386	C₂²×C₅₃	1	2	yes	—
618	#386	C₂²×C₅₃	1	2	yes	—
619	#386	C₂²×C₅₃	1	2	yes	—
620	#386	C₂²×C₅₃	1	2	yes	—
621	#386	C₂²×C₅₃	1	2	yes	—
622	#386	C₂²×C₅₃	1	2	yes	—
623	#385	C₂²×C₅₃	1	2	yes	—
624	#385	C₂²×C₅₃	1	2	yes	—
625	#384	C₂²×C₅₃	1	1	yes	characteristic
626	#382	C₂²×C₅₃	1	1	yes	characteristic
627	#382	C₂²×C₅₃	1	1	yes	characteristic
628	#381	C₂²×C₅₃	1	2	yes	—
629	#380	C₂²×C₅₃	1	1	yes	characteristic
630	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
631	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
632	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
633	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
634	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
635	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
637	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
638	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
640	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
641	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
642	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
643	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
644	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
646	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
647	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
648	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
649	C₅₃	#36606	1	1	yes	characteristic, direct product factor, Sylow
650	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
652	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
653	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
654	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
656	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
657	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
658	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
659	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
661	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
662	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
664	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
665	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
666	#127	—	4	2	no	—
667	#124	—	2	4	no	—
668	#124	—	4	2	no	—
669	#123	—	2	8	no	—
670	C₂²⋊Q₈	—	2	4	no	—
671	#121	—	2	4	no	—
672	#121	—	2	4	no	—
673	#121	—	2	8	no	—
674	#121	—	4	4	no	—
675	C₄×Q₈	—	4	2	no	—
676	C₄×D₄	—	2	4	no	—
677	C₄×D₄	—	4	2	no	—
678	C₄×D₄	—	4	4	no	—
679	C₄×D₄	—	4	4	no	—
680	C₂×C₄⋊C₄	—	2	4	no	—
681	C₂×C₄⋊C₄	—	2	4	no	—
682	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
724	C₂×C₄²	—	2	4	no	—
725	C₂×C₄²	—	4	2	no	—
726	C₂×C₄²	—	4	2	no	—
727	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
735	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
736	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
737	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
738	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
743	#95	C₂³×C₅₃	1	1	yes	characteristic
744	#95	C₂³×C₅₃	1	1	yes	characteristic
745	#95	C₂³×C₅₃	1	1	yes	characteristic
746	#95	C₂³×C₅₃	1	1	yes	characteristic
747	#95	C₂³×C₅₃	1	1	yes	characteristic
748	#95	C₂³×C₅₃	1	1	yes	characteristic
749	#95	C₂³×C₅₃	1	1	yes	characteristic
750	#95	C₂³×C₅₃	1	1	yes	characteristic
751	#95	C₂³×C₅₃	1	2	yes	—
752	#95	C₂³×C₅₃	1	2	yes	—
753	#95	C₂³×C₅₃	1	2	yes	—
754	#95	C₂³×C₅₃	1	2	yes	—
755	#95	C₂³×C₅₃	1	2	yes	—
756	#95	C₂³×C₅₃	1	2	yes	—
757	#95	C₂³×C₅₃	1	2	yes	—
758	#95	C₂³×C₅₃	1	2	yes	—
759	#95	C₂³×C₅₃	1	2	yes	—
760	#95	C₂³×C₅₃	1	2	yes	—
761	#95	C₂³×C₅₃	1	2	yes	—
762	#95	C₂³×C₅₃	1	2	yes	—
763	#95	C₂³×C₅₃	1	2	yes	—
764	#95	C₂³×C₅₃	1	2	yes	—
765	#95	C₂³×C₅₃	1	2	yes	—
766	#95	C₂³×C₅₃	1	2	yes	—
767	#95	C₂³×C₅₃	1	2	yes	—
768	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
769	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
770	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	4	no	—
785	C₂×D₄	—	2	4	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	—	4	1	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	#41×C₅₃	1	4	yes	—
818	C₂²×C₄	#41×C₅₃	1	4	yes	—
819	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	#41×C₅₃	1	4	yes	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	4	1	no	—
889	C₄²	—	4	1	no	—
890	C₄²	—	4	1	no	—
891	C₄²	—	4	1	no	—
892	C₄²	—	4	2	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	2	no	—
895	C₄²	—	4	2	no	—
896	C₄²	#41×C₅₃	1	4	yes	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	C₂×#41×C₅₃	1	2	yes	—
916	C₂³	C₂×#41×C₅₃	1	2	yes	—
917	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
918	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
919	Q₈	—	4	4	no	—
920	D₄	—	4	8	no	—
921	D₄	—	4	8	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	8	4	no	—
925	D₄	—	8	4	no	—
926	C₂×C₄	—	2	8	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	8	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	8	4	no	—
983	C₂×C₄	—	8	4	no	—
984	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
985	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
986	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
987	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
988	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
989	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
990	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
991	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
992	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
993	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
994	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	C₅₃×#559	1	4	yes	—
1016	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1017	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1018	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1019	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1020	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1021	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1022	C₂²	C₅₃×#585	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	2	no	—
1042	C₄	C₅₃×#553	1	4	yes	—
1043	C₂	—	2	4	no	—
1044	C₂	—	8	2	no	—
1045	C₂	—	8	2	no	—
1046	C₂	C₅₃×#3444	1	1	yes	characteristic
1047	C₂	C₂×C₅₃×#553	1	1	yes	characteristic
1048	C₂	C₂×C₅₃×#559	1	1	yes	characteristic
1049	C₂	C₅₃×#3480	1	1	yes	characteristic
1050	C₂	C₅₃×#3494	1	1	yes	characteristic
1051	C₂	C₅₃×#3505	1	1	yes	characteristic
1052	C₂	C₅₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2856	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
2. C₅₃×#2850	C₂	semidirect
3. C₅₃×#2850	C₂	semidirect
4. C₅₃×#2595	C₂	semidirect
5. C₅₃×#2593	C₂	semidirect
6. C₅₃×#2591	C₂	semidirect
7. C₅₃×#2570	C₂	semidirect
8. C₅₃×#2544	C₂	semidirect
9. C₅₃×#2516	C₂	semidirect
10. C₅₃×#2513	C₂	semidirect
11. C₅₃×#2511	C₂	semidirect
12. C₅₃×#2448	C₂	semidirect
13. C₅₃×#2445	C₂	semidirect
14. C₅₃×#2444	C₂	semidirect
15. C₅₃×#2443	C₂	semidirect
16. C₅₃×#2374	C₂	semidirect
17. C₅₃×#2367	C₂	semidirect
18. C₅₃×#2364	C₂	semidirect
19. C₅₃×#2357	C₂	semidirect
20. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
21. C₄×#121×C₅₃	C₂	semidirect
22. C₄×#121×C₅₃	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₅₃	C₂	semidirect
468. #36606	C₅₃	direct (N × H)
518. #2850	C₂×C₅₃	semidirect
519. #2850	C₂×C₅₃	semidirect
520. #2595	C₂×C₅₃	semidirect
521. #2593	C₂×C₅₃	semidirect
522. #2591	C₂×C₅₃	semidirect
523. #2570	C₂×C₅₃	semidirect
524. #2544	C₂×C₅₃	semidirect
525. #2516	C₂×C₅₃	semidirect
526. #2513	C₂×C₅₃	semidirect
527. #2511	C₂×C₅₃	semidirect
528. #2448	C₂×C₅₃	semidirect
529. #2445	C₂×C₅₃	semidirect
530. #2444	C₂×C₅₃	semidirect
531. #2443	C₂×C₅₃	semidirect
532. #2374	C₂×C₅₃	semidirect
533. #2367	C₂×C₅₃	semidirect
534. #2364	C₂×C₅₃	semidirect
535. #2357	C₂×C₅₃	semidirect
536. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
537. C₄×#121	C₂×C₅₃	semidirect
538. C₄×#121	C₂×C₅₃	semidirect
539. C₂×C₄×C₄⋊C₄	C₂×C₅₃	semidirect
649. C₅₃	#36606	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×#2856	2
C₅₃×#2850	2
C₅₃×#2595	2
C₅₃×#2593	2
C₅₃×#2591	2
C₅₃×#2570	2
C₅₃×#2544	2
C₅₃×#2516	2
C₅₃×#2513	2
C₅₃×#2511	2
C₅₃×#2448	2
C₅₃×#2445	2
C₅₃×#2444	2
C₅₃×#2443	2
C₅₃×#2374	2
C₅₃×#2367	2
C₅₃×#2364	2
C₅₃×#2357	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#121×C₅₃	2
C₂×C₄×C₄⋊C₄×C₅₃	2
#36606	53

Subgroups — C53×#36606 #27244118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36606 #27244118