Subgroups — C₅₃×#36829 #27244341

Order 13568.

1462 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2855	C₂	1	2	yes	maximal
2	C₅₃×#2806	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2802	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2776	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2774	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2745	C₂	1	2	yes	maximal
7	C₅₃×#2738	C₂	1	2	yes	maximal
8	C₅₃×#2698	C₂	1	2	yes	maximal
9	C₅₃×#2689	C₂	1	2	yes	maximal
10	C₅₃×#2655	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2611	C₂	1	1	yes	maximal, characteristic
12	C₅₃×#2605	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2599	C₂	1	1	yes	maximal, characteristic
14	C₅₃×#2588	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2478	C₂	1	2	yes	maximal
17	C₅₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2296	C₂	1	1	yes	maximal, characteristic
20	C₂×#126×C₅₃	C₂²	1	2	yes	—
21	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#401	C₂²	1	2	yes	—
28	C₅₃×#400	C₂²	1	2	yes	—
29	C₅₃×#400	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	2	yes	—
34	C₅₃×#400	C₂²	1	2	yes	—
35	C₅₃×#400	C₂²	1	1	yes	characteristic
36	C₅₃×#399	C₂²	1	1	yes	characteristic
37	C₅₃×#398	C₂²	1	2	yes	—
38	C₅₃×#398	C₂²	1	2	yes	—
39	C₅₃×#398	C₂²	1	2	yes	—
40	C₅₃×#398	C₂²	1	2	yes	—
41	C₅₃×#398	C₂²	1	2	yes	—
42	C₅₃×#398	C₂²	1	2	yes	—
43	C₅₃×#398	C₂²	1	2	yes	—
44	C₅₃×#398	C₂²	1	1	yes	characteristic
45	C₅₃×#398	C₂²	1	1	yes	characteristic
46	C₅₃×#397	C₂²	1	1	yes	characteristic
47	C₅₃×#397	C₂²	1	2	yes	—
48	C₅₃×#397	C₂²	1	1	yes	characteristic
49	C₅₃×#397	C₂²	1	2	yes	—
50	C₅₃×#395	C₂²	1	2	yes	—
51	C₅₃×#395	C₂²	1	2	yes	—
52	C₅₃×#395	C₂²	1	2	yes	—
53	C₅₃×#395	C₂²	1	1	yes	characteristic
54	C₅₃×#393	C₂²	1	1	yes	characteristic
55	C₅₃×#391	C₂²	1	2	yes	—
56	C₅₃×#391	C₂²	1	2	yes	—
57	C₅₃×#391	C₂²	1	2	yes	—
58	C₅₃×#391	C₂²	1	2	yes	—
59	C₅₃×#391	C₂²	1	2	yes	—
60	C₅₃×#389	C₂²	1	2	yes	—
61	C₅₃×#389	C₂²	1	2	yes	—
62	C₅₃×#389	C₂²	1	2	yes	—
63	C₅₃×#389	C₂²	1	2	yes	—
64	C₅₃×#389	C₂²	1	2	yes	—
65	C₅₃×#389	C₂²	1	2	yes	—
66	C₅₃×#389	C₂²	1	2	yes	—
67	C₅₃×#389	C₂²	1	2	yes	—
68	C₅₃×#389	C₂²	1	2	yes	—
69	C₅₃×#389	C₂²	1	2	yes	—
70	C₅₃×#389	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×#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×#387	C₂²	1	2	yes	—
82	C₅₃×#387	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×#387	C₂²	1	2	yes	—
89	C₅₃×#387	C₂²	1	2	yes	—
90	C₅₃×#387	C₂²	1	2	yes	—
91	C₅₃×#385	C₂²	1	2	yes	—
92	C₅₃×#385	C₂²	1	2	yes	—
93	C₅₃×#385	C₂²	1	2	yes	—
94	C₅₃×#385	C₂²	1	2	yes	—
95	C₅₃×#383	C₂²	1	2	yes	—
96	C₅₃×#383	C₂²	1	1	yes	characteristic
97	C₅₃×#382	C₂²	1	2	yes	—
98	C₅₃×#381	C₂²	1	2	yes	—
99	C₅₃×#381	C₂²	1	2	yes	—
100	C₅₃×#380	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₅₃	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	C₅₃×#376	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
111	#126×C₅₃	—	4	4	no	—
112	#125×C₅₃	—	2	4	no	—
113	C₂²⋊Q₈×C₅₃	—	4	4	no	—
114	C₄×Q₈×C₅₃	—	2	4	no	—
115	#117×C₅₃	—	2	4	no	—
116	#117×C₅₃	—	4	2	no	—
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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×C₄²×C₅₃	—	4	2	no	—
153	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
164	#95×C₅₃	C₂³	1	1	yes	characteristic
165	#95×C₅₃	C₂³	1	1	yes	characteristic
166	#95×C₅₃	C₂³	1	2	yes	—
167	#95×C₅₃	C₂³	1	2	yes	—
168	#95×C₅₃	C₂³	1	2	yes	—
169	#95×C₅₃	C₂³	1	2	yes	—
170	#95×C₅₃	C₂³	1	2	yes	—
171	#95×C₅₃	C₂³	1	2	yes	—
172	#95×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
180	#95×C₅₃	C₂³	1	2	yes	—
181	#95×C₅₃	C₂³	1	2	yes	—
182	#95×C₅₃	C₂³	1	2	yes	—
183	#95×C₅₃	C₂³	1	2	yes	—
184	#95×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₅₃	—	2	2	no	—
203	C₂×Q₈×C₅₃	—	2	4	no	—
204	C₂×Q₈×C₅₃	—	4	2	no	—
205	C₂×Q₈×C₅₃	—	4	2	no	—
206	C₂×Q₈×C₅₃	—	4	2	no	—
207	C₂²×C₄×C₅₃	—	2	2	no	—
208	C₂²×C₄×C₅₃	—	2	2	no	—
209	C₂²×C₄×C₅₃	—	2	2	no	—
210	C₂²×C₄×C₅₃	—	2	4	no	—
211	C₂²×C₄×C₅₃	—	2	4	no	—
212	C₂²×C₄×C₅₃	—	4	2	no	—
213	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
231	C₄⋊C₄×C₅₃	—	2	2	no	—
232	C₄⋊C₄×C₅₃	—	2	2	no	—
233	C₄⋊C₄×C₅₃	—	2	4	no	—
234	C₄⋊C₄×C₅₃	—	2	2	no	—
235	C₄⋊C₄×C₅₃	—	2	4	no	—
236	C₄⋊C₄×C₅₃	—	2	4	no	—
237	C₄⋊C₄×C₅₃	—	2	2	no	—
238	C₄⋊C₄×C₅₃	—	2	2	no	—
239	C₄⋊C₄×C₅₃	—	2	4	no	—
240	C₄⋊C₄×C₅₃	—	2	4	no	—
241	C₄⋊C₄×C₅₃	—	2	4	no	—
242	C₄⋊C₄×C₅₃	—	2	4	no	—
243	C₄⋊C₄×C₅₃	—	2	4	no	—
244	C₄⋊C₄×C₅₃	—	4	2	no	—
245	C₄⋊C₄×C₅₃	—	4	2	no	—
246	C₄⋊C₄×C₅₃	—	4	2	no	—
247	C₄⋊C₄×C₅₃	—	4	2	no	—
248	C₄⋊C₄×C₅₃	—	4	2	no	—
249	C₄⋊C₄×C₅₃	—	4	2	no	—
250	C₄⋊C₄×C₅₃	—	4	2	no	—
251	C₄⋊C₄×C₅₃	—	4	2	no	—
252	C₄⋊C₄×C₅₃	—	4	2	no	—
253	C₄⋊C₄×C₅₃	—	4	2	no	—
254	C₄⋊C₄×C₅₃	—	4	2	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	C₂²⋊C₄×C₅₃	—	2	4	no	—
260	C₂²⋊C₄×C₅₃	—	2	4	no	—
261	C₂²⋊C₄×C₅₃	—	2	4	no	—
262	C₂²⋊C₄×C₅₃	—	2	2	no	—
263	C₂²⋊C₄×C₅₃	—	2	2	no	—
264	C₂²⋊C₄×C₅₃	—	4	2	no	—
265	C₂²⋊C₄×C₅₃	—	4	2	no	—
266	C₄²×C₅₃	—	2	2	no	—
267	C₄²×C₅₃	—	2	4	no	—
268	C₄²×C₅₃	—	4	1	no	—
269	C₄²×C₅₃	—	4	2	no	—
270	C₄²×C₅₃	—	4	1	no	—
271	C₄²×C₅₃	—	4	2	no	—
272	C₄²×C₅₃	—	4	2	no	—
273	C₄²×C₅₃	—	4	1	no	—
274	C₄²×C₅₃	—	4	1	no	—
275	C₄²×C₅₃	—	4	2	no	—
276	C₄²×C₅₃	#41	1	4	yes	—
277	C₂³×C₅₃	—	2	1	no	—
278	C₂³×C₅₃	—	2	1	no	—
279	C₂³×C₅₃	—	2	2	no	—
280	C₂³×C₅₃	—	2	2	no	—
281	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
282	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
283	Q₈×C₅₃	—	4	4	no	—
284	Q₈×C₅₃	—	8	4	no	—
285	C₂×C₄×C₅₃	—	2	8	no	—
286	C₂×C₄×C₅₃	—	2	1	no	—
287	C₂×C₄×C₅₃	—	2	2	no	—
288	C₂×C₄×C₅₃	—	2	1	no	—
289	C₂×C₄×C₅₃	—	2	1	no	—
290	C₂×C₄×C₅₃	—	2	1	no	—
291	C₂×C₄×C₅₃	—	2	2	no	—
292	C₂×C₄×C₅₃	—	2	2	no	—
293	C₂×C₄×C₅₃	—	2	2	no	—
294	C₂×C₄×C₅₃	—	2	2	no	—
295	C₂×C₄×C₅₃	—	2	1	no	—
296	C₂×C₄×C₅₃	—	2	1	no	—
297	C₂×C₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	2	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	2	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	2	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	2	2	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	2	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	2	no	—
325	C₂×C₄×C₅₃	—	2	2	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	—	4	8	no	—
332	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
333	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
334	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
335	C₂×C₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
336	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
337	#36829	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂²×C₅₃	—	2	2	no	—
339	C₂²×C₅₃	—	2	4	no	—
340	C₂²×C₅₃	—	4	1	no	—
341	C₂²×C₅₃	—	4	1	no	—
342	C₂²×C₅₃	—	4	2	no	—
343	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
344	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
347	C₂²×C₅₃	#585	1	2	yes	—
348	C₄×C₅₃	—	2	2	no	—
349	C₄×C₅₃	—	2	2	no	—
350	C₄×C₅₃	—	2	2	no	—
351	C₄×C₅₃	—	2	2	no	—
352	C₄×C₅₃	—	2	4	no	—
353	C₄×C₅₃	—	4	1	no	—
354	C₄×C₅₃	—	4	2	no	—
355	C₄×C₅₃	—	4	2	no	—
356	C₄×C₅₃	—	4	2	no	—
357	C₄×C₅₃	—	4	2	no	—
358	C₄×C₅₃	—	4	1	no	—
359	C₄×C₅₃	—	4	2	no	—
360	C₄×C₅₃	—	4	2	no	—
361	C₄×C₅₃	—	4	2	no	—
362	C₄×C₅₃	—	4	2	no	—
363	C₄×C₅₃	—	4	2	no	—
364	C₄×C₅₃	—	4	2	no	—
365	C₄×C₅₃	—	4	2	no	—
366	#2855	C₂×C₅₃	1	2	yes	—
367	#2806	C₂×C₅₃	1	2	yes	complemented
368	#2802	C₂×C₅₃	1	2	yes	complemented
369	#2776	C₂×C₅₃	1	2	yes	complemented
370	#2774	C₂×C₅₃	1	2	yes	complemented
371	#2745	C₂×C₅₃	1	2	yes	—
372	#2738	C₂×C₅₃	1	2	yes	—
373	#2698	C₂×C₅₃	1	2	yes	—
374	#2689	C₂×C₅₃	1	2	yes	—
375	#2655	C₂×C₅₃	1	2	yes	complemented
376	#2611	C₂×C₅₃	1	1	yes	characteristic
377	#2605	C₂×C₅₃	1	1	yes	characteristic, complemented
378	#2599	C₂×C₅₃	1	1	yes	characteristic
379	#2588	C₂×C₅₃	1	2	yes	complemented
380	#2584	C₂×C₅₃	1	1	yes	characteristic, complemented
381	#2478	C₂×C₅₃	1	2	yes	—
382	#2336	C₂×C₅₃	1	1	yes	characteristic, complemented
383	#2320	C₂×C₅₃	1	1	yes	characteristic, complemented
384	#2296	C₂×C₅₃	1	1	yes	characteristic
385	C₂×C₅₃	—	4	2	no	—
386	C₂×C₅₃	#3455	1	1	yes	characteristic
387	C₂×C₅₃	#3492	1	1	yes	characteristic
388	C₂×C₅₃	#3509	1	1	yes	characteristic
389	C₂×C₅₃	#3535	1	2	yes	—
390	C₂×C₅₃	#3555	1	2	yes	—
391	C₂×#126	C₂²×C₅₃	1	2	yes	—
392	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
393	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
394	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
395	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
396	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
398	#401	C₂²×C₅₃	1	2	yes	—
399	#400	C₂²×C₅₃	1	2	yes	—
400	#400	C₂²×C₅₃	1	2	yes	—
401	#400	C₂²×C₅₃	1	2	yes	—
402	#400	C₂²×C₅₃	1	1	yes	characteristic
403	#400	C₂²×C₅₃	1	2	yes	—
404	#400	C₂²×C₅₃	1	2	yes	—
405	#400	C₂²×C₅₃	1	2	yes	—
406	#400	C₂²×C₅₃	1	2	yes	—
407	#399	C₂²×C₅₃	1	1	yes	characteristic
408	#398	C₂²×C₅₃	1	2	yes	—
409	#398	C₂²×C₅₃	1	2	yes	—
410	#398	C₂²×C₅₃	1	1	yes	characteristic
411	#398	C₂²×C₅₃	1	1	yes	characteristic
412	#398	C₂²×C₅₃	1	2	yes	—
413	#398	C₂²×C₅₃	1	2	yes	—
414	#398	C₂²×C₅₃	1	2	yes	—
415	#398	C₂²×C₅₃	1	2	yes	—
416	#398	C₂²×C₅₃	1	2	yes	—
417	#397	C₂²×C₅₃	1	1	yes	characteristic
418	#397	C₂²×C₅₃	1	1	yes	characteristic
419	#397	C₂²×C₅₃	1	2	yes	—
420	#397	C₂²×C₅₃	1	2	yes	—
421	#395	C₂²×C₅₃	1	2	yes	—
422	#395	C₂²×C₅₃	1	2	yes	—
423	#395	C₂²×C₅₃	1	1	yes	characteristic
424	#395	C₂²×C₅₃	1	2	yes	—
425	#393	C₂²×C₅₃	1	1	yes	characteristic
426	#391	C₂²×C₅₃	1	2	yes	—
427	#391	C₂²×C₅₃	1	2	yes	—
428	#391	C₂²×C₅₃	1	2	yes	—
429	#391	C₂²×C₅₃	1	2	yes	—
430	#391	C₂²×C₅₃	1	2	yes	—
431	#389	C₂²×C₅₃	1	2	yes	—
432	#389	C₂²×C₅₃	1	2	yes	—
433	#389	C₂²×C₅₃	1	2	yes	—
434	#389	C₂²×C₅₃	1	2	yes	—
435	#389	C₂²×C₅₃	1	2	yes	—
436	#389	C₂²×C₅₃	1	2	yes	—
437	#389	C₂²×C₅₃	1	2	yes	—
438	#389	C₂²×C₅₃	1	2	yes	—
439	#389	C₂²×C₅₃	1	2	yes	—
440	#389	C₂²×C₅₃	1	2	yes	—
441	#389	C₂²×C₅₃	1	2	yes	—
442	#388	C₂²×C₅₃	1	2	yes	—
443	#388	C₂²×C₅₃	1	2	yes	—
444	#388	C₂²×C₅₃	1	2	yes	—
445	#387	C₂²×C₅₃	1	2	yes	—
446	#387	C₂²×C₅₃	1	2	yes	—
447	#387	C₂²×C₅₃	1	2	yes	—
448	#387	C₂²×C₅₃	1	2	yes	—
449	#387	C₂²×C₅₃	1	2	yes	—
450	#387	C₂²×C₅₃	1	2	yes	—
451	#387	C₂²×C₅₃	1	2	yes	—
452	#387	C₂²×C₅₃	1	2	yes	—
453	#387	C₂²×C₅₃	1	2	yes	—
454	#387	C₂²×C₅₃	1	2	yes	—
455	#387	C₂²×C₅₃	1	2	yes	—
456	#387	C₂²×C₅₃	1	2	yes	—
457	#387	C₂²×C₅₃	1	2	yes	—
458	#387	C₂²×C₅₃	1	2	yes	—
459	#387	C₂²×C₅₃	1	2	yes	—
460	#387	C₂²×C₅₃	1	2	yes	—
461	#387	C₂²×C₅₃	1	2	yes	—
462	#385	C₂²×C₅₃	1	2	yes	—
463	#385	C₂²×C₅₃	1	2	yes	—
464	#385	C₂²×C₅₃	1	2	yes	—
465	#385	C₂²×C₅₃	1	2	yes	—
466	#383	C₂²×C₅₃	1	2	yes	—
467	#383	C₂²×C₅₃	1	1	yes	characteristic
468	#382	C₂²×C₅₃	1	2	yes	—
469	#381	C₂²×C₅₃	1	2	yes	—
470	#381	C₂²×C₅₃	1	2	yes	—
471	#380	C₂²×C₅₃	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
477	#376	C₂²×C₅₃	1	1	yes	characteristic
478	C₅₃	#36829	1	1	yes	characteristic, direct product factor, Sylow
479	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
483	#126	—	4	4	no	—
484	#125	—	2	4	no	—
485	C₂²⋊Q₈	—	4	4	no	—
486	C₄×Q₈	—	2	4	no	—
487	#117	—	2	4	no	—
488	#117	—	4	2	no	—
489	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
524	C₂×C₄²	—	4	2	no	—
525	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
531	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
536	#95	C₂³×C₅₃	1	1	yes	characteristic
537	#95	C₂³×C₅₃	1	1	yes	characteristic
538	#95	C₂³×C₅₃	1	2	yes	—
539	#95	C₂³×C₅₃	1	2	yes	—
540	#95	C₂³×C₅₃	1	2	yes	—
541	#95	C₂³×C₅₃	1	2	yes	—
542	#95	C₂³×C₅₃	1	2	yes	—
543	#95	C₂³×C₅₃	1	2	yes	—
544	#95	C₂³×C₅₃	1	2	yes	—
545	#95	C₂³×C₅₃	1	2	yes	—
546	#95	C₂³×C₅₃	1	2	yes	—
547	#95	C₂³×C₅₃	1	2	yes	—
548	#95	C₂³×C₅₃	1	2	yes	—
549	#95	C₂³×C₅₃	1	2	yes	—
550	#95	C₂³×C₅₃	1	2	yes	—
551	#95	C₂³×C₅₃	1	2	yes	—
552	#95	C₂³×C₅₃	1	2	yes	—
553	#95	C₂³×C₅₃	1	2	yes	—
554	#95	C₂³×C₅₃	1	2	yes	—
555	#95	C₂³×C₅₃	1	2	yes	—
556	#95	C₂³×C₅₃	1	1	yes	characteristic
557	#95	C₂³×C₅₃	1	2	yes	—
558	#95	C₂³×C₅₃	1	2	yes	—
559	#95	C₂³×C₅₃	1	2	yes	—
560	#95	C₂³×C₅₃	1	1	yes	characteristic
561	#95	C₂³×C₅₃	1	2	yes	—
562	#95	C₂³×C₅₃	1	2	yes	—
563	#95	C₂³×C₅₃	1	2	yes	—
564	#95	C₂³×C₅₃	1	2	yes	—
565	#95	C₂³×C₅₃	1	2	yes	—
566	#95	C₂³×C₅₃	1	2	yes	—
567	#95	C₂³×C₅₃	1	2	yes	—
568	#95	C₂³×C₅₃	1	2	yes	—
569	#95	C₂³×C₅₃	1	2	yes	—
570	#95	C₂³×C₅₃	1	2	yes	—
571	#95	C₂³×C₅₃	1	2	yes	—
572	#95	C₂³×C₅₃	1	2	yes	—
573	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	—	4	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	4	1	no	—
641	C₄²	—	4	1	no	—
642	C₄²	—	4	2	no	—
643	C₄²	—	4	1	no	—
644	C₄²	—	4	1	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	2	no	—
648	C₄²	#41×C₅₃	1	4	yes	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
654	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
655	Q₈	—	4	4	no	—
656	Q₈	—	8	4	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
705	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
706	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
707	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
708	C₂×C₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
715	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
716	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
717	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
718	C₂²	C₅₃×#585	1	2	yes	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	4	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₂	—	4	2	no	—
738	C₂	C₅₃×#3455	1	1	yes	characteristic
739	C₂	C₅₃×#3492	1	1	yes	characteristic
740	C₂	C₅₃×#3509	1	1	yes	characteristic
741	C₂	C₅₃×#3535	1	2	yes	—
742	C₂	C₅₃×#3555	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂⁴×C₅₃	C₂⁴
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×#2806	C₂	semidirect
3. C₅₃×#2802	C₂	semidirect
4. C₅₃×#2776	C₂	semidirect
5. C₅₃×#2774	C₂	semidirect
10. C₅₃×#2655	C₂	semidirect
12. C₅₃×#2605	C₂	semidirect
14. C₅₃×#2588	C₂	semidirect
15. C₅₃×#2584	C₂	semidirect
17. C₅₃×#2336	C₂	semidirect
18. C₅₃×#2320	C₂	semidirect
337. #36829	C₅₃	direct (N × H)
367. #2806	C₂×C₅₃	semidirect
368. #2802	C₂×C₅₃	semidirect
369. #2776	C₂×C₅₃	semidirect
370. #2774	C₂×C₅₃	semidirect
375. #2655	C₂×C₅₃	semidirect
377. #2605	C₂×C₅₃	semidirect
379. #2588	C₂×C₅₃	semidirect
380. #2584	C₂×C₅₃	semidirect
382. #2336	C₂×C₅₃	semidirect
383. #2320	C₂×C₅₃	semidirect
478. C₅₃	#36829	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×#2855	2
C₅₃×#2806	2
C₅₃×#2802	2
C₅₃×#2776	2
C₅₃×#2774	2
C₅₃×#2745	2
C₅₃×#2738	2
C₅₃×#2698	2
C₅₃×#2689	2
C₅₃×#2655	2
C₅₃×#2611	2
C₅₃×#2605	2
C₅₃×#2599	2
C₅₃×#2588	2
C₅₃×#2584	2
C₅₃×#2478	2
C₅₃×#2336	2
C₅₃×#2320	2
C₅₃×#2296	2
#36829	53

Subgroups — C53×#36829 #27244341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36829 #27244341