Subgroups — C₅₃×#36816 #27244328

Order 13568.

1800 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2852	C₂	1	2	yes	maximal, complemented
2	C₅₃×#2797	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2759	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2746	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2737	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2716	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2712	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2685	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2684	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2653	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2607	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2597	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2474	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2404	C₂	1	1	yes	maximal, characteristic
17	C₅₃×#2332	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#126×C₅₃	C₂²	1	2	yes	—
23	C₂×#124×C₅₃	C₂²	1	2	yes	—
24	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#401	C₂²	1	2	yes	complemented
32	C₅₃×#400	C₂²	1	2	yes	complemented
33	C₅₃×#399	C₂²	1	2	yes	—
34	C₅₃×#398	C₂²	1	2	yes	complemented
35	C₅₃×#397	C₂²	1	2	yes	—
36	C₅₃×#397	C₂²	1	2	yes	—
37	C₅₃×#397	C₂²	1	2	yes	—
38	C₅₃×#397	C₂²	1	2	yes	complemented
39	C₅₃×#397	C₂²	1	2	yes	complemented
40	C₅₃×#397	C₂²	1	2	yes	complemented
41	C₅₃×#396	C₂²	1	2	yes	—
42	C₅₃×#395	C₂²	1	2	yes	complemented
43	C₅₃×#394	C₂²	1	2	yes	—
44	C₅₃×#394	C₂²	1	2	yes	—
45	C₅₃×#394	C₂²	1	2	yes	—
46	C₅₃×#394	C₂²	1	2	yes	—
47	C₅₃×#394	C₂²	1	2	yes	—
48	C₅₃×#394	C₂²	1	2	yes	—
49	C₅₃×#393	C₂²	1	2	yes	—
50	C₅₃×#393	C₂²	1	2	yes	—
51	C₅₃×#393	C₂²	1	2	yes	—
52	C₅₃×#393	C₂²	1	2	yes	—
53	C₅₃×#393	C₂²	1	2	yes	complemented
54	C₅₃×#392	C₂²	1	2	yes	—
55	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#391	C₂²	1	2	yes	complemented
57	C₅₃×#391	C₂²	1	2	yes	complemented
58	C₅₃×#391	C₂²	1	2	yes	complemented
59	C₅₃×#391	C₂²	1	2	yes	complemented
60	C₅₃×#390	C₂²	1	2	yes	—
61	C₅₃×#390	C₂²	1	2	yes	—
62	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#388	C₂²	1	2	yes	—
64	C₅₃×#388	C₂²	1	2	yes	—
65	C₅₃×#388	C₂²	1	2	yes	—
66	C₅₃×#388	C₂²	1	2	yes	—
67	C₅₃×#388	C₂²	1	2	yes	—
68	C₅₃×#388	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×#388	C₂²	1	2	yes	—
74	C₅₃×#388	C₂²	1	2	yes	complemented
75	C₅₃×#388	C₂²	1	2	yes	complemented
76	C₅₃×#387	C₂²	1	2	yes	complemented
77	C₅₃×#387	C₂²	1	2	yes	complemented
78	C₅₃×#387	C₂²	1	2	yes	complemented
79	C₅₃×#387	C₂²	1	2	yes	complemented
80	C₅₃×#387	C₂²	1	2	yes	complemented
81	C₅₃×#387	C₂²	1	2	yes	complemented
82	C₅₃×#387	C₂²	1	2	yes	complemented
83	C₅₃×#386	C₂²	1	2	yes	—
84	C₅₃×#386	C₂²	1	2	yes	—
85	C₅₃×#386	C₂²	1	2	yes	—
86	C₅₃×#386	C₂²	1	2	yes	—
87	C₅₃×#386	C₂²	1	1	yes	characteristic
88	C₅₃×#386	C₂²	1	1	yes	characteristic
89	C₅₃×#386	C₂²	1	2	yes	—
90	C₅₃×#386	C₂²	1	2	yes	complemented
91	C₅₃×#385	C₂²	1	2	yes	complemented
92	C₅₃×#385	C₂²	1	2	yes	complemented
93	C₅₃×#385	C₂²	1	2	yes	complemented
94	C₅₃×#385	C₂²	1	2	yes	complemented
95	C₅₃×#383	C₂²	1	2	yes	complemented
96	C₅₃×#381	C₂²	1	2	yes	—
97	C₅₃×#381	C₂²	1	1	yes	characteristic
98	C₅₃×#380	C₂²	1	2	yes	—
99	C₅₃×#379	C₂²	1	2	yes	—
100	C₅₃×#379	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
108	C₂×#41×C₅₃	—	2	4	no	—
109	C₂×#41×C₅₃	—	4	2	no	—
110	C₂×#41×C₅₃	—	4	2	no	—
111	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₅₃	—	4	2	no	—
125	#126×C₅₃	—	4	4	no	—
126	#124×C₅₃	—	4	4	no	—
127	#124×C₅₃	—	4	2	no	—
128	C₂²⋊Q₈×C₅₃	—	2	4	no	—
129	#120×C₅₃	—	4	2	no	—
130	#120×C₅₃	—	4	2	no	—
131	#117×C₅₃	—	4	2	no	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
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	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₅₃	—	4	2	no	—
173	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
201	#95×C₅₃	C₂³	1	2	yes	—
202	#95×C₅₃	C₂³	1	2	yes	—
203	#95×C₅₃	C₂³	1	2	yes	—
204	#95×C₅₃	C₂³	1	2	yes	—
205	#95×C₅₃	C₂³	1	2	yes	—
206	#95×C₅₃	C₂³	1	2	yes	—
207	C₂⁴×C₅₃	—	2	2	no	—
208	C₂⁴×C₅₃	—	4	2	no	—
209	C₂⁴×C₅₃	—	4	1	no	—
210	C₂⁴×C₅₃	—	4	1	no	—
211	C₂⁴×C₅₃	—	4	2	no	—
212	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
213	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
216	#41×C₅₃	—	4	16	no	—
217	C₂×Q₈×C₅₃	—	2	2	no	—
218	C₂×Q₈×C₅₃	—	2	2	no	—
219	C₂×Q₈×C₅₃	—	2	2	no	—
220	C₂×Q₈×C₅₃	—	4	1	no	—
221	C₂×Q₈×C₅₃	—	4	1	no	—
222	C₂×Q₈×C₅₃	—	4	2	no	—
223	C₂×Q₈×C₅₃	—	4	1	no	—
224	C₂×Q₈×C₅₃	—	4	2	no	—
225	C₂×Q₈×C₅₃	—	4	2	no	—
226	C₂×D₄×C₅₃	—	2	2	no	—
227	C₂×D₄×C₅₃	—	2	2	no	—
228	C₂×D₄×C₅₃	—	2	2	no	—
229	C₂×D₄×C₅₃	—	2	2	no	—
230	C₂×D₄×C₅₃	—	2	4	no	—
231	C₂×D₄×C₅₃	—	2	2	no	—
232	C₂×D₄×C₅₃	—	2	2	no	—
233	C₂×D₄×C₅₃	—	4	1	no	—
234	C₂×D₄×C₅₃	—	4	1	no	—
235	C₂×D₄×C₅₃	—	4	1	no	—
236	C₂×D₄×C₅₃	—	4	2	no	—
237	C₂×D₄×C₅₃	—	4	2	no	—
238	C₂×D₄×C₅₃	—	4	2	no	—
239	C₂×D₄×C₅₃	—	4	2	no	—
240	C₂×D₄×C₅₃	—	4	2	no	—
241	C₂²×C₄×C₅₃	—	2	2	no	—
242	C₂²×C₄×C₅₃	—	2	2	no	—
243	C₂²×C₄×C₅₃	—	2	2	no	—
244	C₂²×C₄×C₅₃	—	2	2	no	—
245	C₂²×C₄×C₅₃	—	2	2	no	—
246	C₂²×C₄×C₅₃	—	4	2	no	—
247	C₂²×C₄×C₅₃	—	4	2	no	—
248	C₂²×C₄×C₅₃	—	4	2	no	—
249	C₂²×C₄×C₅₃	—	4	1	no	—
250	C₂²×C₄×C₅₃	—	4	1	no	—
251	C₂²×C₄×C₅₃	—	4	1	no	—
252	C₂²×C₄×C₅₃	—	4	1	no	—
253	C₂²×C₄×C₅₃	—	4	2	no	—
254	C₂²×C₄×C₅₃	#41	1	4	yes	—
255	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
270	C₄⋊C₄×C₅₃	—	2	4	no	—
271	C₄⋊C₄×C₅₃	—	2	2	no	—
272	C₄⋊C₄×C₅₃	—	2	4	no	—
273	C₄⋊C₄×C₅₃	—	4	2	no	—
274	C₄⋊C₄×C₅₃	—	4	2	no	—
275	C₄⋊C₄×C₅₃	—	4	2	no	—
276	C₄⋊C₄×C₅₃	—	4	2	no	—
277	C₄⋊C₄×C₅₃	—	4	2	no	—
278	C₄⋊C₄×C₅₃	—	4	2	no	—
279	C₄⋊C₄×C₅₃	—	4	2	no	—
280	C₄⋊C₄×C₅₃	—	4	2	no	—
281	C₄⋊C₄×C₅₃	—	4	2	no	—
282	C₂²⋊C₄×C₅₃	—	2	4	no	—
283	C₂²⋊C₄×C₅₃	—	2	4	no	—
284	C₂²⋊C₄×C₅₃	—	2	4	no	—
285	C₂²⋊C₄×C₅₃	—	2	4	no	—
286	C₂²⋊C₄×C₅₃	—	2	4	no	—
287	C₂²⋊C₄×C₅₃	—	2	4	no	—
288	C₂²⋊C₄×C₅₃	—	4	2	no	—
289	C₂²⋊C₄×C₅₃	—	4	2	no	—
290	C₂²⋊C₄×C₅₃	—	4	2	no	—
291	C₂²⋊C₄×C₅₃	—	4	2	no	—
292	C₂²⋊C₄×C₅₃	—	4	2	no	—
293	C₂²⋊C₄×C₅₃	—	4	2	no	—
294	C₂²⋊C₄×C₅₃	—	4	2	no	—
295	C₂²⋊C₄×C₅₃	—	4	2	no	—
296	C₂²⋊C₄×C₅₃	—	4	2	no	—
297	C₂²⋊C₄×C₅₃	—	4	2	no	—
298	C₂²⋊C₄×C₅₃	—	4	2	no	—
299	C₂²⋊C₄×C₅₃	—	4	2	no	—
300	C₂²⋊C₄×C₅₃	—	4	2	no	—
301	C₂²⋊C₄×C₅₃	—	4	2	no	—
302	C₂²⋊C₄×C₅₃	—	4	1	no	—
303	C₂²⋊C₄×C₅₃	—	4	1	no	—
304	C₂²⋊C₄×C₅₃	—	4	2	no	—
305	C₂²⋊C₄×C₅₃	—	4	2	no	—
306	C₂²⋊C₄×C₅₃	—	4	2	no	—
307	C₂²⋊C₄×C₅₃	—	4	2	no	—
308	C₂²⋊C₄×C₅₃	—	4	2	no	—
309	C₄²×C₅₃	—	2	4	no	—
310	C₄²×C₅₃	—	4	1	no	—
311	C₄²×C₅₃	—	4	1	no	—
312	C₄²×C₅₃	—	4	2	no	—
313	C₄²×C₅₃	—	4	1	no	—
314	C₄²×C₅₃	—	4	1	no	—
315	C₄²×C₅₃	—	4	1	no	—
316	C₄²×C₅₃	—	4	2	no	—
317	C₄²×C₅₃	—	4	1	no	—
318	C₂³×C₅₃	—	2	1	no	—
319	C₂³×C₅₃	—	2	1	no	—
320	C₂³×C₅₃	—	2	1	no	—
321	C₂³×C₅₃	—	2	1	no	—
322	C₂³×C₅₃	—	2	2	no	—
323	C₂³×C₅₃	—	2	2	no	—
324	C₂³×C₅₃	—	2	2	no	—
325	C₂³×C₅₃	—	2	2	no	—
326	C₂³×C₅₃	—	2	1	no	—
327	C₂³×C₅₃	—	2	2	no	—
328	C₂³×C₅₃	—	2	1	no	—
329	C₂³×C₅₃	—	2	1	no	—
330	C₂³×C₅₃	—	2	2	no	—
331	C₂³×C₅₃	—	2	2	no	—
332	C₂³×C₅₃	—	2	2	no	—
333	C₂³×C₅₃	—	2	2	no	—
334	C₂³×C₅₃	—	2	2	no	—
335	C₂³×C₅₃	—	2	2	no	—
336	C₂³×C₅₃	—	2	2	no	—
337	C₂³×C₅₃	—	2	2	no	—
338	C₂³×C₅₃	—	4	4	no	—
339	C₂³×C₅₃	—	8	2	no	—
340	C₂³×C₅₃	—	8	2	no	—
341	C₂³×C₅₃	—	8	4	no	—
342	C₂³×C₅₃	—	8	4	no	—
343	C₂³×C₅₃	C₂×#41	1	2	yes	—
344	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
345	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
346	Q₈×C₅₃	—	4	4	no	—
347	Q₈×C₅₃	—	8	2	no	—
348	Q₈×C₅₃	—	8	4	no	—
349	D₄×C₅₃	—	4	4	no	—
350	D₄×C₅₃	—	4	4	no	—
351	D₄×C₅₃	—	4	4	no	—
352	D₄×C₅₃	—	8	4	no	—
353	D₄×C₅₃	—	8	4	no	—
354	C₂×C₄×C₅₃	—	2	8	no	—
355	C₂×C₄×C₅₃	—	2	1	no	—
356	C₂×C₄×C₅₃	—	2	1	no	—
357	C₂×C₄×C₅₃	—	2	1	no	—
358	C₂×C₄×C₅₃	—	2	1	no	—
359	C₂×C₄×C₅₃	—	2	1	no	—
360	C₂×C₄×C₅₃	—	2	1	no	—
361	C₂×C₄×C₅₃	—	2	1	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	1	no	—
366	C₂×C₄×C₅₃	—	2	1	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	2	no	—
375	C₂×C₄×C₅₃	—	2	2	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	2	2	no	—
385	C₂×C₄×C₅₃	—	2	2	no	—
386	C₂×C₄×C₅₃	—	2	2	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	2	2	no	—
389	C₂×C₄×C₅₃	—	2	2	no	—
390	C₂×C₄×C₅₃	—	2	2	no	—
391	C₂×C₄×C₅₃	—	2	2	no	—
392	C₂×C₄×C₅₃	—	2	2	no	—
393	C₂×C₄×C₅₃	—	2	2	no	—
394	C₂×C₄×C₅₃	—	2	2	no	—
395	C₂×C₄×C₅₃	—	2	2	no	—
396	C₂×C₄×C₅₃	—	2	2	no	—
397	C₂×C₄×C₅₃	—	4	4	no	—
398	C₂×C₄×C₅₃	—	4	4	no	—
399	C₂×C₄×C₅₃	—	4	8	no	—
400	C₂×C₄×C₅₃	—	8	2	no	—
401	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
402	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
403	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
404	#36816	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂²×C₅₃	—	2	2	no	—
406	C₂²×C₅₃	—	2	2	no	—
407	C₂²×C₅₃	—	2	2	no	—
408	C₂²×C₅₃	—	2	2	no	—
409	C₂²×C₅₃	—	2	4	no	—
410	C₂²×C₅₃	—	4	1	no	—
411	C₂²×C₅₃	—	4	1	no	—
412	C₂²×C₅₃	—	4	2	no	—
413	C₂²×C₅₃	—	4	2	no	—
414	C₂²×C₅₃	—	4	2	no	—
415	C₂²×C₅₃	—	4	1	no	—
416	C₂²×C₅₃	—	4	2	no	—
417	C₂²×C₅₃	—	4	1	no	—
418	C₂²×C₅₃	—	4	2	no	—
419	C₂²×C₅₃	—	4	1	no	—
420	C₂²×C₅₃	—	4	2	no	—
421	C₂²×C₅₃	—	4	2	no	—
422	C₂²×C₅₃	—	4	2	no	—
423	C₂²×C₅₃	—	4	2	no	—
424	C₂²×C₅₃	—	4	2	no	—
425	C₂²×C₅₃	—	4	2	no	—
426	C₂²×C₅₃	—	4	2	no	—
427	C₂²×C₅₃	—	8	8	no	—
428	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₅₃	#585	1	2	yes	—
432	C₂²×C₅₃	#585	1	2	yes	—
433	C₄×C₅₃	—	2	2	no	—
434	C₄×C₅₃	—	2	2	no	—
435	C₄×C₅₃	—	2	2	no	—
436	C₄×C₅₃	—	4	2	no	—
437	C₄×C₅₃	—	4	1	no	—
438	C₄×C₅₃	—	4	2	no	—
439	C₄×C₅₃	—	4	2	no	—
440	C₄×C₅₃	—	4	2	no	—
441	C₄×C₅₃	—	4	2	no	—
442	C₄×C₅₃	—	4	2	no	—
443	C₄×C₅₃	—	4	2	no	—
444	C₄×C₅₃	—	4	2	no	—
445	C₄×C₅₃	—	4	2	no	—
446	C₄×C₅₃	—	4	2	no	—
447	C₄×C₅₃	—	4	2	no	—
448	#2852	C₂×C₅₃	1	2	yes	complemented
449	#2797	C₂×C₅₃	1	2	yes	complemented
450	#2759	C₂×C₅₃	1	2	yes	complemented
451	#2746	C₂×C₅₃	1	2	yes	complemented
452	#2737	C₂×C₅₃	1	2	yes	complemented
453	#2716	C₂×C₅₃	1	2	yes	complemented
454	#2712	C₂×C₅₃	1	2	yes	complemented
455	#2685	C₂×C₅₃	1	2	yes	complemented
456	#2684	C₂×C₅₃	1	2	yes	complemented
457	#2653	C₂×C₅₃	1	2	yes	complemented
458	#2607	C₂×C₅₃	1	1	yes	characteristic, complemented
459	#2597	C₂×C₅₃	1	2	yes	complemented
460	#2561	C₂×C₅₃	1	1	yes	characteristic, complemented
461	#2474	C₂×C₅₃	1	2	yes	complemented
462	#2432	C₂×C₅₃	1	1	yes	characteristic, complemented
463	#2404	C₂×C₅₃	1	1	yes	characteristic
464	#2332	C₂×C₅₃	1	1	yes	characteristic, complemented
465	#2312	C₂×C₅₃	1	1	yes	characteristic, complemented
466	#2297	C₂×C₅₃	1	1	yes	characteristic, complemented
467	C₂×C₅₃	—	4	2	no	—
468	C₂×C₅₃	—	4	2	no	—
469	C₂×C₅₃	—	8	1	no	—
470	C₂×C₅₃	—	8	2	no	—
471	C₂×C₅₃	#3455	1	1	yes	characteristic
472	C₂×C₅₃	#3490	1	1	yes	characteristic
473	C₂×C₅₃	#3510	1	1	yes	characteristic
474	C₂×C₅₃	#3540	1	2	yes	—
475	C₂×C₅₃	#3560	1	2	yes	—
476	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
477	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
478	C₂×#126	C₂²×C₅₃	1	2	yes	—
479	C₂×#124	C₂²×C₅₃	1	2	yes	—
480	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
481	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
482	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
483	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
484	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
485	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
486	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
487	#401	C₂²×C₅₃	1	2	yes	complemented
488	#400	C₂²×C₅₃	1	2	yes	complemented
489	#399	C₂²×C₅₃	1	2	yes	—
490	#398	C₂²×C₅₃	1	2	yes	complemented
491	#397	C₂²×C₅₃	1	2	yes	—
492	#397	C₂²×C₅₃	1	2	yes	—
493	#397	C₂²×C₅₃	1	2	yes	—
494	#397	C₂²×C₅₃	1	2	yes	complemented
495	#397	C₂²×C₅₃	1	2	yes	complemented
496	#397	C₂²×C₅₃	1	2	yes	complemented
497	#396	C₂²×C₅₃	1	2	yes	—
498	#395	C₂²×C₅₃	1	2	yes	complemented
499	#394	C₂²×C₅₃	1	2	yes	—
500	#394	C₂²×C₅₃	1	2	yes	—
501	#394	C₂²×C₅₃	1	2	yes	—
502	#394	C₂²×C₅₃	1	2	yes	—
503	#394	C₂²×C₅₃	1	2	yes	—
504	#394	C₂²×C₅₃	1	2	yes	—
505	#393	C₂²×C₅₃	1	2	yes	—
506	#393	C₂²×C₅₃	1	2	yes	—
507	#393	C₂²×C₅₃	1	2	yes	—
508	#393	C₂²×C₅₃	1	2	yes	—
509	#393	C₂²×C₅₃	1	2	yes	complemented
510	#392	C₂²×C₅₃	1	2	yes	—
511	#391	C₂²×C₅₃	1	2	yes	complemented
512	#391	C₂²×C₅₃	1	2	yes	complemented
513	#391	C₂²×C₅₃	1	2	yes	complemented
514	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
515	#391	C₂²×C₅₃	1	2	yes	complemented
516	#390	C₂²×C₅₃	1	2	yes	—
517	#390	C₂²×C₅₃	1	2	yes	—
518	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
519	#388	C₂²×C₅₃	1	2	yes	—
520	#388	C₂²×C₅₃	1	2	yes	—
521	#388	C₂²×C₅₃	1	2	yes	—
522	#388	C₂²×C₅₃	1	2	yes	—
523	#388	C₂²×C₅₃	1	2	yes	—
524	#388	C₂²×C₅₃	1	2	yes	—
525	#388	C₂²×C₅₃	1	2	yes	—
526	#388	C₂²×C₅₃	1	2	yes	—
527	#388	C₂²×C₅₃	1	2	yes	—
528	#388	C₂²×C₅₃	1	2	yes	—
529	#388	C₂²×C₅₃	1	2	yes	—
530	#388	C₂²×C₅₃	1	2	yes	complemented
531	#388	C₂²×C₅₃	1	2	yes	complemented
532	#387	C₂²×C₅₃	1	2	yes	complemented
533	#387	C₂²×C₅₃	1	2	yes	complemented
534	#387	C₂²×C₅₃	1	2	yes	complemented
535	#387	C₂²×C₅₃	1	2	yes	complemented
536	#387	C₂²×C₅₃	1	2	yes	complemented
537	#387	C₂²×C₅₃	1	2	yes	complemented
538	#387	C₂²×C₅₃	1	2	yes	complemented
539	#386	C₂²×C₅₃	1	2	yes	—
540	#386	C₂²×C₅₃	1	2	yes	—
541	#386	C₂²×C₅₃	1	2	yes	—
542	#386	C₂²×C₅₃	1	2	yes	—
543	#386	C₂²×C₅₃	1	1	yes	characteristic
544	#386	C₂²×C₅₃	1	1	yes	characteristic
545	#386	C₂²×C₅₃	1	2	yes	—
546	#386	C₂²×C₅₃	1	2	yes	complemented
547	#385	C₂²×C₅₃	1	2	yes	complemented
548	#385	C₂²×C₅₃	1	2	yes	complemented
549	#385	C₂²×C₅₃	1	2	yes	complemented
550	#385	C₂²×C₅₃	1	2	yes	complemented
551	#383	C₂²×C₅₃	1	2	yes	complemented
552	#381	C₂²×C₅₃	1	2	yes	—
553	#381	C₂²×C₅₃	1	1	yes	characteristic
554	#380	C₂²×C₅₃	1	2	yes	—
555	#379	C₂²×C₅₃	1	2	yes	—
556	#379	C₂²×C₅₃	1	2	yes	—
557	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
558	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
561	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
562	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
563	C₅₃	#36816	1	1	yes	characteristic, direct product factor, Sylow
564	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
565	C₂×#41	—	2	4	no	—
566	C₂×#41	—	4	2	no	—
567	C₂×#41	—	4	2	no	—
568	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
569	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
570	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
571	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
575	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
576	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
580	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
581	C₄⋊Q₈	—	4	2	no	—
582	#126	—	4	4	no	—
583	#124	—	4	4	no	—
584	#124	—	4	2	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	#120	—	4	2	no	—
587	#120	—	4	2	no	—
588	#117	—	4	2	no	—
589	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
601	C₂×C₂²⋊C₄	—	2	4	no	—
602	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
629	C₂×C₄²	—	4	2	no	—
630	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
631	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
634	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
639	#95	C₂³×C₅₃	1	2	yes	—
640	#95	C₂³×C₅₃	1	2	yes	—
641	#95	C₂³×C₅₃	1	2	yes	—
642	#95	C₂³×C₅₃	1	2	yes	—
643	#95	C₂³×C₅₃	1	2	yes	—
644	#95	C₂³×C₅₃	1	2	yes	—
645	#95	C₂³×C₅₃	1	2	yes	—
646	#95	C₂³×C₅₃	1	2	yes	—
647	#95	C₂³×C₅₃	1	2	yes	—
648	#95	C₂³×C₅₃	1	2	yes	—
649	#95	C₂³×C₅₃	1	2	yes	—
650	#95	C₂³×C₅₃	1	2	yes	—
651	#95	C₂³×C₅₃	1	2	yes	—
652	#95	C₂³×C₅₃	1	2	yes	—
653	#95	C₂³×C₅₃	1	2	yes	—
654	#95	C₂³×C₅₃	1	2	yes	—
655	#95	C₂³×C₅₃	1	2	yes	—
656	#95	C₂³×C₅₃	1	2	yes	—
657	#95	C₂³×C₅₃	1	2	yes	—
658	#95	C₂³×C₅₃	1	2	yes	—
659	#95	C₂³×C₅₃	1	2	yes	—
660	#95	C₂³×C₅₃	1	2	yes	—
661	#95	C₂³×C₅₃	1	2	yes	—
662	#95	C₂³×C₅₃	1	2	yes	—
663	#95	C₂³×C₅₃	1	2	yes	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	4	2	no	—
666	C₂⁴	—	4	1	no	—
667	C₂⁴	—	4	1	no	—
668	C₂⁴	—	4	2	no	—
669	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
670	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
672	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
673	#41	—	4	16	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	4	1	no	—
678	C₂×Q₈	—	4	1	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	#41×C₅₃	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	4	1	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	1	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	1	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	1	no	—
771	C₄²	—	4	1	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	1	no	—
774	C₄²	—	4	2	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	4	no	—
796	C₂³	—	8	2	no	—
797	C₂³	—	8	2	no	—
798	C₂³	—	8	4	no	—
799	C₂³	—	8	4	no	—
800	C₂³	C₂×#41×C₅₃	1	2	yes	—
801	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
802	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
803	Q₈	—	4	4	no	—
804	Q₈	—	8	2	no	—
805	Q₈	—	8	4	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	8	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
859	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
860	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
885	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
886	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
887	C₂²	C₅₃×#585	1	2	yes	—
888	C₂²	C₅₃×#585	1	2	yes	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₂	—	4	2	no	—
905	C₂	—	4	2	no	—
906	C₂	—	8	2	no	—
907	C₂	—	8	1	no	—
908	C₂	C₅₃×#3455	1	1	yes	characteristic
909	C₂	C₅₃×#3490	1	1	yes	characteristic
910	C₂	C₅₃×#3510	1	1	yes	characteristic
911	C₂	C₅₃×#3540	1	2	yes	—
912	C₂	C₅₃×#3560	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2404	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×#2852	C₂	semidirect
2. C₅₃×#2797	C₂	semidirect
3. C₅₃×#2759	C₂	semidirect
4. C₅₃×#2746	C₂	semidirect
5. C₅₃×#2737	C₂	semidirect
6. C₅₃×#2716	C₂	semidirect
7. C₅₃×#2712	C₂	semidirect
8. C₅₃×#2685	C₂	semidirect
9. C₅₃×#2684	C₂	semidirect
10. C₅₃×#2653	C₂	semidirect
11. C₅₃×#2607	C₂	semidirect
12. C₅₃×#2597	C₂	semidirect
13. C₅₃×#2561	C₂	semidirect
14. C₅₃×#2474	C₂	semidirect
15. C₅₃×#2432	C₂	semidirect
17. C₅₃×#2332	C₂	semidirect
18. C₅₃×#2312	C₂	semidirect
19. C₅₃×#2297	C₂	semidirect
21. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
24. C₂×#124×C₅₃	C₂²	semidirect
28. C₂×#117×C₅₃	C₂²	semidirect
30. C₂²×C₄²×C₅₃	C₂²	semidirect
31. C₅₃×#401	C₂²	semidirect
32. C₅₃×#400	C₂²	semidirect
34. C₅₃×#398	C₂²	semidirect
38. C₅₃×#397	C₂²	semidirect
39. C₅₃×#397	C₂²	semidirect
40. C₅₃×#397	C₂²	semidirect
42. C₅₃×#395	C₂²	semidirect
53. C₅₃×#393	C₂²	semidirect
55. C₅₃×#391	C₂²	semidirect
56. C₅₃×#391	C₂²	semidirect
57. C₅₃×#391	C₂²	semidirect
58. C₅₃×#391	C₂²	semidirect
59. C₅₃×#391	C₂²	semidirect
62. C₅₃×#390	C₂²	semidirect
74. C₅₃×#388	C₂²	semidirect
75. C₅₃×#388	C₂²	semidirect
76. C₅₃×#387	C₂²	semidirect
77. C₅₃×#387	C₂²	semidirect
78. C₅₃×#387	C₂²	semidirect
79. C₅₃×#387	C₂²	semidirect
80. C₅₃×#387	C₂²	semidirect
81. C₅₃×#387	C₂²	semidirect
82. C₅₃×#387	C₂²	semidirect
90. C₅₃×#386	C₂²	semidirect
91. C₅₃×#385	C₂²	semidirect
92. C₅₃×#385	C₂²	semidirect
93. C₅₃×#385	C₂²	semidirect
94. C₅₃×#385	C₂²	semidirect
95. C₅₃×#383	C₂²	semidirect
101. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
404. #36816	C₅₃	direct (N × H)
448. #2852	C₂×C₅₃	semidirect
449. #2797	C₂×C₅₃	semidirect
450. #2759	C₂×C₅₃	semidirect
451. #2746	C₂×C₅₃	semidirect
452. #2737	C₂×C₅₃	semidirect
453. #2716	C₂×C₅₃	semidirect
454. #2712	C₂×C₅₃	semidirect
455. #2685	C₂×C₅₃	semidirect
456. #2684	C₂×C₅₃	semidirect
457. #2653	C₂×C₅₃	semidirect
458. #2607	C₂×C₅₃	semidirect
459. #2597	C₂×C₅₃	semidirect
460. #2561	C₂×C₅₃	semidirect
461. #2474	C₂×C₅₃	semidirect
462. #2432	C₂×C₅₃	semidirect
464. #2332	C₂×C₅₃	semidirect
465. #2312	C₂×C₅₃	semidirect
466. #2297	C₂×C₅₃	semidirect
477. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
480. C₂×#124	C₂²×C₅₃	semidirect
484. C₂×#117	C₂²×C₅₃	semidirect
486. C₂²×C₄²	C₂²×C₅₃	semidirect
487. #401	C₂²×C₅₃	semidirect
488. #400	C₂²×C₅₃	semidirect
490. #398	C₂²×C₅₃	semidirect
494. #397	C₂²×C₅₃	semidirect
495. #397	C₂²×C₅₃	semidirect
496. #397	C₂²×C₅₃	semidirect
498. #395	C₂²×C₅₃	semidirect
509. #393	C₂²×C₅₃	semidirect
511. #391	C₂²×C₅₃	semidirect
512. #391	C₂²×C₅₃	semidirect
513. #391	C₂²×C₅₃	semidirect
514. #391	C₂²×C₅₃	semidirect
515. #391	C₂²×C₅₃	semidirect
518. #390	C₂²×C₅₃	semidirect
530. #388	C₂²×C₅₃	semidirect
531. #388	C₂²×C₅₃	semidirect
532. #387	C₂²×C₅₃	semidirect
533. #387	C₂²×C₅₃	semidirect
534. #387	C₂²×C₅₃	semidirect
535. #387	C₂²×C₅₃	semidirect
536. #387	C₂²×C₅₃	semidirect
537. #387	C₂²×C₅₃	semidirect
538. #387	C₂²×C₅₃	semidirect
546. #386	C₂²×C₅₃	semidirect
547. #385	C₂²×C₅₃	semidirect
548. #385	C₂²×C₅₃	semidirect
549. #385	C₂²×C₅₃	semidirect
550. #385	C₂²×C₅₃	semidirect
551. #383	C₂²×C₅₃	semidirect
557. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
561. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
562. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
563. C₅₃	#36816	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×#2852	2
C₅₃×#2797	2
C₅₃×#2759	2
C₅₃×#2746	2
C₅₃×#2737	2
C₅₃×#2716	2
C₅₃×#2712	2
C₅₃×#2685	2
C₅₃×#2684	2
C₅₃×#2653	2
C₅₃×#2607	2
C₅₃×#2597	2
C₅₃×#2561	2
C₅₃×#2474	2
C₅₃×#2432	2
C₅₃×#2404	2
C₅₃×#2332	2
C₅₃×#2312	2
C₅₃×#2297	2
#36816	53

Subgroups — C53×#36816 #27244328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36816 #27244328