Subgroups — C₅₃×#34596 #27242108

Order 13568.

1760 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2665	C₂	1	2	yes	maximal, complemented
2	C₅₃×#2663	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2655	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2653	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2652	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2650	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2638	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2630	C₂	1	2	yes	maximal
9	C₅₃×#2401	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2398	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2392	C₂	1	1	yes	maximal, characteristic
15	C₄×C₂²⋊Q₈×C₅₃	C₂	1	2	yes	maximal, complemented
16	C₄×#123×C₅₃	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#123×C₅₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
27	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
29	C₅₃×#401	C₂²	1	2	yes	—
30	C₅₃×#400	C₂²	1	2	yes	—
31	C₅₃×#400	C₂²	1	2	yes	—
32	C₅₃×#400	C₂²	1	2	yes	—
33	C₅₃×#400	C₂²	1	1	yes	characteristic
34	C₅₃×#400	C₂²	1	2	yes	—
35	C₅₃×#400	C₂²	1	2	yes	—
36	C₅₃×#400	C₂²	1	2	yes	—
37	C₅₃×#399	C₂²	1	1	yes	characteristic
38	C₅₃×#398	C₂²	1	2	yes	—
39	C₅₃×#398	C₂²	1	2	yes	—
40	C₅₃×#398	C₂²	1	1	yes	characteristic
41	C₅₃×#398	C₂²	1	2	yes	—
42	C₅₃×#397	C₂²	1	2	yes	—
43	C₅₃×#397	C₂²	1	2	yes	—
44	C₅₃×#397	C₂²	1	2	yes	—
45	C₅₃×#397	C₂²	1	2	yes	—
46	C₅₃×#397	C₂²	1	1	yes	characteristic
47	C₅₃×#397	C₂²	1	2	yes	—
48	C₅₃×#397	C₂²	1	2	yes	—
49	C₅₃×#396	C₂²	1	2	yes	—
50	C₅₃×#396	C₂²	1	2	yes	—
51	C₅₃×#396	C₂²	1	2	yes	—
52	C₅₃×#395	C₂²	1	2	yes	—
53	C₅₃×#395	C₂²	1	1	yes	characteristic
54	C₅₃×#395	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	—
58	C₅₃×#394	C₂²	1	1	yes	characteristic
59	C₅₃×#394	C₂²	1	2	yes	—
60	C₅₃×#393	C₂²	1	2	yes	—
61	C₅₃×#393	C₂²	1	2	yes	—
62	C₅₃×#393	C₂²	1	1	yes	characteristic
63	C₅₃×#393	C₂²	1	2	yes	—
64	C₅₃×#392	C₂²	1	1	yes	characteristic
65	C₅₃×#391	C₂²	1	2	yes	—
66	C₅₃×#391	C₂²	1	2	yes	—
67	C₅₃×#389	C₂²	1	2	yes	—
68	C₅₃×#389	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	—
74	C₅₃×#387	C₂²	1	2	yes	—
75	C₅₃×#387	C₂²	1	2	yes	—
76	C₅₃×#387	C₂²	1	2	yes	—
77	C₅₃×#387	C₂²	1	2	yes	—
78	C₅₃×#387	C₂²	1	2	yes	—
79	C₅₃×#387	C₂²	1	2	yes	—
80	C₅₃×#387	C₂²	1	2	yes	—
81	C₅₃×#386	C₂²	1	2	yes	—
82	C₅₃×#385	C₂²	1	2	yes	—
83	C₅₃×#385	C₂²	1	2	yes	—
84	C₅₃×#385	C₂²	1	2	yes	—
85	C₅₃×#381	C₂²	1	2	yes	—
86	C₅₃×#380	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
89	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
104	C₅₃×#376	C₂²	1	2	yes	—
105	C₅₃×#376	C₂²	1	1	yes	characteristic
106	C₄³×C₅₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
115	#123×C₅₃	—	2	8	no	—
116	C₂²⋊Q₈×C₅₃	—	2	8	no	—
117	C₄×Q₈×C₅₃	—	2	4	no	—
118	C₄×Q₈×C₅₃	—	4	4	no	—
119	C₄×D₄×C₅₃	—	2	4	no	—
120	C₄×D₄×C₅₃	—	2	8	no	—
121	C₄×D₄×C₅₃	—	4	4	no	—
122	#117×C₅₃	—	2	4	no	—
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₅₃	—	4	4	no	—
160	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
173	#95×C₅₃	C₂³	1	2	yes	—
174	#95×C₅₃	C₂³	1	2	yes	—
175	#95×C₅₃	C₂³	1	2	yes	—
176	#95×C₅₃	C₂³	1	2	yes	—
177	#95×C₅₃	C₂³	1	2	yes	—
178	#95×C₅₃	C₂³	1	2	yes	—
179	#95×C₅₃	C₂³	1	1	yes	characteristic
180	#95×C₅₃	C₂³	1	2	yes	—
181	#95×C₅₃	C₂³	1	1	yes	characteristic
182	#95×C₅₃	C₂³	1	2	yes	—
183	#95×C₅₃	C₂³	1	2	yes	—
184	#95×C₅₃	C₂³	1	2	yes	—
185	#95×C₅₃	C₂³	1	2	yes	—
186	#95×C₅₃	C₂³	1	2	yes	—
187	#95×C₅₃	C₂³	1	2	yes	—
188	#95×C₅₃	C₂³	1	2	yes	—
189	#95×C₅₃	C₂³	1	2	yes	—
190	#95×C₅₃	C₂³	1	2	yes	—
191	#95×C₅₃	C₂³	1	2	yes	—
192	#95×C₅₃	C₂³	1	2	yes	—
193	#95×C₅₃	C₂³	1	2	yes	—
194	#95×C₅₃	C₂³	1	2	yes	—
195	#95×C₅₃	C₂³	1	2	yes	—
196	#95×C₅₃	C₂³	1	2	yes	—
197	#95×C₅₃	C₂³	1	2	yes	—
198	#95×C₅₃	C₂³	1	2	yes	—
199	#95×C₅₃	C₂³	1	2	yes	—
200	#95×C₅₃	C₂³	1	1	yes	characteristic
201	#95×C₅₃	C₂³	1	1	yes	characteristic
202	#95×C₅₃	C₂³	1	2	yes	—
203	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
204	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₅₃	—	2	2	no	—
206	C₂×Q₈×C₅₃	—	2	4	no	—
207	C₂×Q₈×C₅₃	—	4	2	no	—
208	C₂×Q₈×C₅₃	—	4	2	no	—
209	C₂×Q₈×C₅₃	—	4	2	no	—
210	C₂×D₄×C₅₃	—	2	4	no	—
211	C₂×D₄×C₅₃	—	2	4	no	—
212	C₂×D₄×C₅₃	—	2	2	no	—
213	C₂×D₄×C₅₃	—	4	2	no	—
214	C₂×D₄×C₅₃	—	4	2	no	—
215	C₂²×C₄×C₅₃	—	2	2	no	—
216	C₂²×C₄×C₅₃	—	2	4	no	—
217	C₂²×C₄×C₅₃	—	2	4	no	—
218	C₂²×C₄×C₅₃	—	2	4	no	—
219	C₂²×C₄×C₅₃	—	2	2	no	—
220	C₂²×C₄×C₅₃	—	2	4	no	—
221	C₂²×C₄×C₅₃	—	2	2	no	—
222	C₂²×C₄×C₅₃	—	4	2	no	—
223	C₂²×C₄×C₅₃	—	4	2	no	—
224	C₂²×C₄×C₅₃	—	4	2	no	—
225	C₂²×C₄×C₅₃	—	4	2	no	—
226	C₂²×C₄×C₅₃	#41	1	8	yes	—
227	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₅₃	—	2	2	no	—
245	C₄⋊C₄×C₅₃	—	2	2	no	—
246	C₄⋊C₄×C₅₃	—	2	4	no	—
247	C₄⋊C₄×C₅₃	—	2	2	no	—
248	C₄⋊C₄×C₅₃	—	2	4	no	—
249	C₄⋊C₄×C₅₃	—	2	2	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	—	2	4	no	—
255	C₄⋊C₄×C₅₃	—	4	2	no	—
256	C₄⋊C₄×C₅₃	—	4	2	no	—
257	C₄⋊C₄×C₅₃	—	4	2	no	—
258	C₄⋊C₄×C₅₃	—	4	2	no	—
259	C₄⋊C₄×C₅₃	—	4	2	no	—
260	C₄⋊C₄×C₅₃	—	4	2	no	—
261	C₄⋊C₄×C₅₃	—	4	2	no	—
262	C₄⋊C₄×C₅₃	—	4	2	no	—
263	C₂²⋊C₄×C₅₃	—	2	4	no	—
264	C₂²⋊C₄×C₅₃	—	2	4	no	—
265	C₂²⋊C₄×C₅₃	—	2	4	no	—
266	C₂²⋊C₄×C₅₃	—	2	4	no	—
267	C₂²⋊C₄×C₅₃	—	2	2	no	—
268	C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂²⋊C₄×C₅₃	—	2	4	no	—
270	C₂²⋊C₄×C₅₃	—	2	4	no	—
271	C₂²⋊C₄×C₅₃	—	2	4	no	—
272	C₂²⋊C₄×C₅₃	—	2	4	no	—
273	C₂²⋊C₄×C₅₃	—	4	2	no	—
274	C₂²⋊C₄×C₅₃	—	4	2	no	—
275	C₂²⋊C₄×C₅₃	—	4	2	no	—
276	C₂²⋊C₄×C₅₃	—	4	2	no	—
277	C₂²⋊C₄×C₅₃	—	4	2	no	—
278	C₂²⋊C₄×C₅₃	—	4	2	no	—
279	C₂²⋊C₄×C₅₃	—	4	2	no	—
280	C₄²×C₅₃	—	2	2	no	—
281	C₄²×C₅₃	—	2	4	no	—
282	C₄²×C₅₃	—	2	4	no	—
283	C₄²×C₅₃	—	2	2	no	—
284	C₄²×C₅₃	—	2	4	no	—
285	C₄²×C₅₃	—	2	4	no	—
286	C₄²×C₅₃	—	2	2	no	—
287	C₄²×C₅₃	—	2	2	no	—
288	C₄²×C₅₃	—	2	2	no	—
289	C₄²×C₅₃	—	4	2	no	—
290	C₄²×C₅₃	—	4	2	no	—
291	C₄²×C₅₃	—	4	2	no	—
292	C₄²×C₅₃	#41	1	4	yes	—
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	2	no	—
298	C₂³×C₅₃	—	2	2	no	—
299	C₂³×C₅₃	—	2	1	no	—
300	C₂³×C₅₃	—	2	2	no	—
301	C₂³×C₅₃	—	2	1	no	—
302	C₂³×C₅₃	—	2	1	no	—
303	C₂³×C₅₃	—	2	2	no	—
304	C₂³×C₅₃	C₂×#41	1	4	yes	—
305	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
306	Q₈×C₅₃	—	4	4	no	—
307	Q₈×C₅₃	—	4	8	no	—
308	D₄×C₅₃	—	2	8	no	—
309	D₄×C₅₃	—	4	8	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	2	no	—
312	C₂×C₄×C₅₃	—	2	2	no	—
313	C₂×C₄×C₅₃	—	2	2	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	2	no	—
317	C₂×C₄×C₅₃	—	2	2	no	—
318	C₂×C₄×C₅₃	—	2	1	no	—
319	C₂×C₄×C₅₃	—	2	2	no	—
320	C₂×C₄×C₅₃	—	2	2	no	—
321	C₂×C₄×C₅₃	—	2	2	no	—
322	C₂×C₄×C₅₃	—	2	2	no	—
323	C₂×C₄×C₅₃	—	2	2	no	—
324	C₂×C₄×C₅₃	—	2	1	no	—
325	C₂×C₄×C₅₃	—	2	1	no	—
326	C₂×C₄×C₅₃	—	2	2	no	—
327	C₂×C₄×C₅₃	—	2	2	no	—
328	C₂×C₄×C₅₃	—	2	2	no	—
329	C₂×C₄×C₅₃	—	2	2	no	—
330	C₂×C₄×C₅₃	—	2	2	no	—
331	C₂×C₄×C₅₃	—	2	2	no	—
332	C₂×C₄×C₅₃	—	2	1	no	—
333	C₂×C₄×C₅₃	—	2	2	no	—
334	C₂×C₄×C₅₃	—	2	2	no	—
335	C₂×C₄×C₅₃	—	2	2	no	—
336	C₂×C₄×C₅₃	—	2	2	no	—
337	C₂×C₄×C₅₃	—	2	2	no	—
338	C₂×C₄×C₅₃	—	2	1	no	—
339	C₂×C₄×C₅₃	—	2	2	no	—
340	C₂×C₄×C₅₃	—	2	2	no	—
341	C₂×C₄×C₅₃	—	2	2	no	—
342	C₂×C₄×C₅₃	—	2	2	no	—
343	C₂×C₄×C₅₃	—	2	2	no	—
344	C₂×C₄×C₅₃	—	2	2	no	—
345	C₂×C₄×C₅₃	—	2	2	no	—
346	C₂×C₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	2	2	no	—
350	C₂×C₄×C₅₃	—	4	8	no	—
351	C₂×C₄×C₅₃	—	4	8	no	—
352	C₂×C₄×C₅₃	—	4	8	no	—
353	C₂×C₄×C₅₃	—	4	4	no	—
354	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
355	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
356	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
357	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
358	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
359	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
361	#34596	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂²×C₅₃	—	2	4	no	—
363	C₂²×C₅₃	—	2	4	no	—
364	C₂²×C₅₃	—	2	4	no	—
365	C₂²×C₅₃	—	4	2	no	—
366	C₂²×C₅₃	—	4	2	no	—
367	C₂²×C₅₃	—	4	2	no	—
368	C₂²×C₅₃	—	4	2	no	—
369	C₂²×C₅₃	—	4	1	no	—
370	C₂²×C₅₃	—	4	1	no	—
371	C₂²×C₅₃	—	4	1	no	—
372	C₂²×C₅₃	—	4	2	no	—
373	C₂²×C₅₃	—	4	2	no	—
374	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₅₃	C₂²×#41	1	2	yes	—
376	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₅₃	#585	1	2	yes	—
379	C₄×C₅₃	—	2	2	no	—
380	C₄×C₅₃	—	2	2	no	—
381	C₄×C₅₃	—	2	4	no	—
382	C₄×C₅₃	—	2	4	no	—
383	C₄×C₅₃	—	4	1	no	—
384	C₄×C₅₃	—	4	2	no	—
385	C₄×C₅₃	—	4	2	no	—
386	C₄×C₅₃	—	4	1	no	—
387	C₄×C₅₃	—	4	1	no	—
388	C₄×C₅₃	—	4	2	no	—
389	C₄×C₅₃	—	4	2	no	—
390	C₄×C₅₃	—	4	2	no	—
391	C₄×C₅₃	—	4	2	no	—
392	C₄×C₅₃	—	4	2	no	—
393	C₄×C₅₃	—	4	2	no	—
394	C₄×C₅₃	—	4	2	no	—
395	C₄×C₅₃	#542	1	4	yes	—
396	#2665	C₂×C₅₃	1	2	yes	complemented
397	#2663	C₂×C₅₃	1	2	yes	complemented
398	#2655	C₂×C₅₃	1	2	yes	complemented
399	#2653	C₂×C₅₃	1	2	yes	complemented
400	#2652	C₂×C₅₃	1	2	yes	complemented
401	#2650	C₂×C₅₃	1	2	yes	complemented
402	#2638	C₂×C₅₃	1	2	yes	complemented
403	#2630	C₂×C₅₃	1	2	yes	—
404	#2401	C₂×C₅₃	1	2	yes	complemented
405	#2399	C₂×C₅₃	1	1	yes	characteristic, complemented
406	#2398	C₂×C₅₃	1	1	yes	characteristic, complemented
407	#2398	C₂×C₅₃	1	2	yes	complemented
408	#2396	C₂×C₅₃	1	1	yes	characteristic, complemented
409	#2392	C₂×C₅₃	1	1	yes	characteristic
410	C₄×C₂²⋊Q₈	C₂×C₅₃	1	2	yes	complemented
411	C₄×#123	C₂×C₅₃	1	2	yes	complemented
412	#2298	C₂×C₅₃	1	1	yes	characteristic, complemented
413	#2295	C₂×C₅₃	1	1	yes	characteristic, complemented
414	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
415	C₂×C₅₃	—	4	4	no	—
416	C₂×C₅₃	—	8	1	no	—
417	C₂×C₅₃	#3444	1	1	yes	characteristic
418	C₂×C₅₃	C₂×#542	1	1	yes	characteristic
419	C₂×C₅₃	#3455	1	1	yes	characteristic
420	C₂×C₅₃	#3459	1	2	yes	—
421	C₂×C₅₃	#3461	1	2	yes	—
422	C₂×#123	C₂²×C₅₃	1	2	yes	—
423	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
424	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
426	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
429	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
430	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
431	#401	C₂²×C₅₃	1	2	yes	—
432	#400	C₂²×C₅₃	1	2	yes	—
433	#400	C₂²×C₅₃	1	2	yes	—
434	#400	C₂²×C₅₃	1	2	yes	—
435	#400	C₂²×C₅₃	1	1	yes	characteristic
436	#400	C₂²×C₅₃	1	2	yes	—
437	#400	C₂²×C₅₃	1	2	yes	—
438	#400	C₂²×C₅₃	1	2	yes	—
439	#399	C₂²×C₅₃	1	1	yes	characteristic
440	#398	C₂²×C₅₃	1	2	yes	—
441	#398	C₂²×C₅₃	1	2	yes	—
442	#398	C₂²×C₅₃	1	1	yes	characteristic
443	#398	C₂²×C₅₃	1	2	yes	—
444	#397	C₂²×C₅₃	1	2	yes	—
445	#397	C₂²×C₅₃	1	2	yes	—
446	#397	C₂²×C₅₃	1	2	yes	—
447	#397	C₂²×C₅₃	1	2	yes	—
448	#397	C₂²×C₅₃	1	1	yes	characteristic
449	#397	C₂²×C₅₃	1	2	yes	—
450	#397	C₂²×C₅₃	1	2	yes	—
451	#396	C₂²×C₅₃	1	2	yes	—
452	#396	C₂²×C₅₃	1	2	yes	—
453	#396	C₂²×C₅₃	1	2	yes	—
454	#395	C₂²×C₅₃	1	2	yes	—
455	#395	C₂²×C₅₃	1	1	yes	characteristic
456	#395	C₂²×C₅₃	1	2	yes	—
457	#394	C₂²×C₅₃	1	2	yes	—
458	#394	C₂²×C₅₃	1	2	yes	—
459	#394	C₂²×C₅₃	1	2	yes	—
460	#394	C₂²×C₅₃	1	1	yes	characteristic
461	#394	C₂²×C₅₃	1	2	yes	—
462	#393	C₂²×C₅₃	1	2	yes	—
463	#393	C₂²×C₅₃	1	2	yes	—
464	#393	C₂²×C₅₃	1	1	yes	characteristic
465	#393	C₂²×C₅₃	1	2	yes	—
466	#392	C₂²×C₅₃	1	1	yes	characteristic
467	#391	C₂²×C₅₃	1	2	yes	—
468	#391	C₂²×C₅₃	1	2	yes	—
469	#389	C₂²×C₅₃	1	2	yes	—
470	#389	C₂²×C₅₃	1	2	yes	—
471	#388	C₂²×C₅₃	1	2	yes	—
472	#388	C₂²×C₅₃	1	2	yes	—
473	#388	C₂²×C₅₃	1	2	yes	—
474	#388	C₂²×C₅₃	1	2	yes	—
475	#387	C₂²×C₅₃	1	2	yes	—
476	#387	C₂²×C₅₃	1	2	yes	—
477	#387	C₂²×C₅₃	1	2	yes	—
478	#387	C₂²×C₅₃	1	2	yes	—
479	#387	C₂²×C₅₃	1	2	yes	—
480	#387	C₂²×C₅₃	1	2	yes	—
481	#387	C₂²×C₅₃	1	2	yes	—
482	#387	C₂²×C₅₃	1	2	yes	—
483	#386	C₂²×C₅₃	1	2	yes	—
484	#385	C₂²×C₅₃	1	2	yes	—
485	#385	C₂²×C₅₃	1	2	yes	—
486	#385	C₂²×C₅₃	1	2	yes	—
487	#381	C₂²×C₅₃	1	2	yes	—
488	#380	C₂²×C₅₃	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
490	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
497	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
506	#376	C₂²×C₅₃	1	1	yes	characteristic
507	#376	C₂²×C₅₃	1	2	yes	—
508	C₄³	C₂²×C₅₃	1	1	yes	characteristic
509	C₅₃	#34596	1	1	yes	characteristic, direct product factor, Sylow
510	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
511	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
514	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
516	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
517	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
518	#123	—	2	8	no	—
519	C₂²⋊Q₈	—	2	8	no	—
520	C₄×Q₈	—	2	4	no	—
521	C₄×Q₈	—	4	4	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	4	4	no	—
525	#117	—	2	4	no	—
526	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
562	C₂×C₄²	—	4	4	no	—
563	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
575	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
576	#95	C₂³×C₅₃	1	2	yes	—
577	#95	C₂³×C₅₃	1	2	yes	—
578	#95	C₂³×C₅₃	1	2	yes	—
579	#95	C₂³×C₅₃	1	2	yes	—
580	#95	C₂³×C₅₃	1	2	yes	—
581	#95	C₂³×C₅₃	1	2	yes	—
582	#95	C₂³×C₅₃	1	1	yes	characteristic
583	#95	C₂³×C₅₃	1	2	yes	—
584	#95	C₂³×C₅₃	1	1	yes	characteristic
585	#95	C₂³×C₅₃	1	2	yes	—
586	#95	C₂³×C₅₃	1	2	yes	—
587	#95	C₂³×C₅₃	1	2	yes	—
588	#95	C₂³×C₅₃	1	2	yes	—
589	#95	C₂³×C₅₃	1	2	yes	—
590	#95	C₂³×C₅₃	1	2	yes	—
591	#95	C₂³×C₅₃	1	2	yes	—
592	#95	C₂³×C₅₃	1	2	yes	—
593	#95	C₂³×C₅₃	1	2	yes	—
594	#95	C₂³×C₅₃	1	2	yes	—
595	#95	C₂³×C₅₃	1	2	yes	—
596	#95	C₂³×C₅₃	1	2	yes	—
597	#95	C₂³×C₅₃	1	2	yes	—
598	#95	C₂³×C₅₃	1	2	yes	—
599	#95	C₂³×C₅₃	1	2	yes	—
600	#95	C₂³×C₅₃	1	2	yes	—
601	#95	C₂³×C₅₃	1	2	yes	—
602	#95	C₂³×C₅₃	1	2	yes	—
603	#95	C₂³×C₅₃	1	1	yes	characteristic
604	#95	C₂³×C₅₃	1	1	yes	characteristic
605	#95	C₂³×C₅₃	1	2	yes	—
606	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
607	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	#41×C₅₃	1	8	yes	—
630	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	—	4	2	no	—
695	C₄²	#41×C₅₃	1	4	yes	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	2	no	—
707	C₂³	C₂×#41×C₅₃	1	4	yes	—
708	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
709	Q₈	—	4	4	no	—
710	Q₈	—	4	8	no	—
711	D₄	—	2	8	no	—
712	D₄	—	4	8	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	8	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
758	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
759	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
760	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
761	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
762	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
763	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	1	no	—
776	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₅₃	1	2	yes	—
778	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
779	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
780	C₂²	C₅₃×#585	1	2	yes	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	4	no	—
784	C₄	—	2	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	2	no	—
797	C₄	C₅₃×#542	1	4	yes	—
798	C₂	—	4	4	no	—
799	C₂	—	8	1	no	—
800	C₂	C₅₃×#3444	1	1	yes	characteristic
801	C₂	C₂×C₅₃×#542	1	1	yes	characteristic
802	C₂	C₅₃×#3455	1	1	yes	characteristic
803	C₂	C₅₃×#3459	1	2	yes	—
804	C₂	C₅₃×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₅₃×#392	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#2665	C₂	semidirect
2. C₅₃×#2663	C₂	semidirect
3. C₅₃×#2655	C₂	semidirect
4. C₅₃×#2653	C₂	semidirect
5. C₅₃×#2652	C₂	semidirect
6. C₅₃×#2650	C₂	semidirect
7. C₅₃×#2638	C₂	semidirect
9. C₅₃×#2401	C₂	semidirect
10. C₅₃×#2399	C₂	semidirect
11. C₅₃×#2398	C₂	semidirect
12. C₅₃×#2398	C₂	semidirect
13. C₅₃×#2396	C₂	semidirect
15. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
16. C₄×#123×C₅₃	C₂	semidirect
17. C₅₃×#2298	C₂	semidirect
18. C₅₃×#2295	C₂	semidirect
19. C₄²×D₄×C₅₃	C₂	semidirect
361. #34596	C₅₃	direct (N × H)
396. #2665	C₂×C₅₃	semidirect
397. #2663	C₂×C₅₃	semidirect
398. #2655	C₂×C₅₃	semidirect
399. #2653	C₂×C₅₃	semidirect
400. #2652	C₂×C₅₃	semidirect
401. #2650	C₂×C₅₃	semidirect
402. #2638	C₂×C₅₃	semidirect
404. #2401	C₂×C₅₃	semidirect
405. #2399	C₂×C₅₃	semidirect
406. #2398	C₂×C₅₃	semidirect
407. #2398	C₂×C₅₃	semidirect
408. #2396	C₂×C₅₃	semidirect
410. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
411. C₄×#123	C₂×C₅₃	semidirect
412. #2298	C₂×C₅₃	semidirect
413. #2295	C₂×C₅₃	semidirect
414. C₄²×D₄	C₂×C₅₃	semidirect
509. C₅₃	#34596	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×#2665	2
C₅₃×#2663	2
C₅₃×#2655	2
C₅₃×#2653	2
C₅₃×#2652	2
C₅₃×#2650	2
C₅₃×#2638	2
C₅₃×#2630	2
C₅₃×#2401	2
C₅₃×#2399	2
C₅₃×#2398	2
C₅₃×#2396	2
C₅₃×#2392	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#123×C₅₃	2
C₅₃×#2298	2
C₅₃×#2295	2
C₄²×D₄×C₅₃	2
#34596	53

Subgroups — C53×#34596 #27242108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34596 #27242108