Subgroups — C₅₃×#21369 #27228881

Order 13568.

826 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#433	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2314	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2274	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1949	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1948	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1854	C₂	1	2	yes	maximal
7	C₅₃×#1853	C₂	1	2	yes	maximal
8	C₅₃×#1776	C₂	1	2	yes	maximal, complemented
9	C₄×#106×C₅₃	C₂	1	2	yes	maximal, complemented
10	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
13	C₅₃×#433	C₄	1	8	yes	complemented
14	C₂×#107×C₅₃	C₂²	1	2	yes	—
15	C₂×#106×C₅₃	C₂²	1	2	yes	—
16	C₂×#106×C₅₃	C₂²	1	2	yes	—
17	C₂×#106×C₅₃	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
20	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₅₃×#388	—	2	2	no	—
23	C₅₃×#387	—	2	2	no	—
24	C₅₃×#384	C₂²	1	1	yes	characteristic
25	C₅₃×#382	C₂²	1	1	yes	characteristic
26	C₅₃×#380	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₅₃	—	2	2	no	—
28	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₅₃	—	2	2	no	—
32	C₅₃×#340	C₂²	1	2	yes	—
33	C₅₃×#340	C₂²	1	2	yes	—
34	C₅₃×#340	C₂²	1	2	yes	—
35	C₅₃×#340	C₂²	1	2	yes	—
36	C₂³×C₄×C₅₃	—	2	1	no	—
37	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
40	#117×C₅₃	—	2	4	no	—
41	#117×C₅₃	C₂×C₄	1	4	yes	—
42	#117×C₅₃	Q₈	1	4	yes	—
43	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
51	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
54	C₂×C₄²×C₅₃	—	2	1	no	—
55	C₂×C₄²×C₅₃	—	2	2	no	—
56	C₂×C₄²×C₅₃	—	2	2	no	—
57	C₂×C₄²×C₅₃	—	2	2	no	—
58	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
60	#107×C₅₃	—	2	4	no	—
61	#106×C₅₃	—	2	4	no	—
62	#106×C₅₃	—	2	4	no	—
63	#106×C₅₃	—	2	4	no	—
64	C₄⋊C₈×C₅₃	C₂×C₄	1	8	yes	complemented
65	C₂²⋊C₈×C₅₃	C₂×C₄	1	8	yes	—
66	#97×C₅₃	C₂×C₄	1	4	yes	complemented
67	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
68	#95×C₅₃	—	2	2	no	—
69	#95×C₅₃	—	2	2	no	—
70	#95×C₅₃	—	2	2	no	—
71	#95×C₅₃	—	2	2	no	—
72	#95×C₅₃	—	2	2	no	—
73	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	—	2	2	no	—
75	C₂²×C₄×C₅₃	—	2	2	no	—
76	C₂²×C₄×C₅₃	—	2	2	no	—
77	C₂²×C₄×C₅₃	—	2	2	no	—
78	C₂²×C₄×C₅₃	—	2	4	no	—
79	C₂²×C₄×C₅₃	—	2	2	no	—
80	C₂²×C₄×C₅₃	—	2	2	no	—
81	C₂²×C₄×C₅₃	—	8	2	no	—
82	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₅₃	—	2	2	no	—
89	C₂×C₈×C₅₃	—	2	2	no	—
90	C₂×C₈×C₅₃	—	2	2	no	—
91	C₂×C₈×C₅₃	—	2	2	no	—
92	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₅₃	—	2	4	no	—
95	C₄⋊C₄×C₅₃	—	2	2	no	—
96	C₄⋊C₄×C₅₃	—	2	2	no	—
97	C₄⋊C₄×C₅₃	—	2	2	no	—
98	C₄⋊C₄×C₅₃	—	2	2	no	—
99	C₄⋊C₄×C₅₃	—	2	2	no	—
100	C₄⋊C₄×C₅₃	—	2	2	no	—
101	C₄⋊C₄×C₅₃	—	8	2	no	—
102	C₄⋊C₄×C₅₃	C₄⋊C₄	1	8	yes	—
103	C₄⋊C₄×C₅₃	#41	1	4	yes	—
104	C₄⋊C₄×C₅₃	#41	1	4	yes	—
105	C₂²⋊C₄×C₅₃	—	2	4	no	—
106	C₂²⋊C₄×C₅₃	—	8	2	no	—
107	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	8	yes	—
108	C₄²×C₅₃	—	2	4	no	—
109	C₄²×C₅₃	—	8	2	no	—
110	C₄²×C₅₃	—	8	2	no	—
111	C₄²×C₅₃	—	8	2	no	—
112	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
113	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
114	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
115	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
116	C₂³×C₅₃	—	2	1	no	—
117	C₂³×C₅₃	—	2	1	no	—
118	C₂³×C₅₃	—	2	2	no	—
119	C₂³×C₅₃	—	2	2	no	—
120	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
122	C₂×C₄×C₅₃	—	2	1	no	—
123	C₂×C₄×C₅₃	—	2	1	no	—
124	C₂×C₄×C₅₃	—	2	2	no	—
125	C₂×C₄×C₅₃	—	2	2	no	—
126	C₂×C₄×C₅₃	—	2	2	no	—
127	C₂×C₄×C₅₃	—	2	2	no	—
128	C₂×C₄×C₅₃	—	2	4	no	—
129	C₂×C₄×C₅₃	—	2	4	no	—
130	C₂×C₄×C₅₃	—	2	4	no	—
131	C₂×C₄×C₅₃	—	2	4	no	—
132	C₂×C₄×C₅₃	—	4	2	no	—
133	C₂×C₄×C₅₃	—	4	2	no	—
134	C₂×C₄×C₅₃	—	4	2	no	—
135	C₂×C₄×C₅₃	—	4	2	no	—
136	C₂×C₄×C₅₃	—	4	2	no	—
137	C₂×C₄×C₅₃	—	4	2	no	—
138	C₂×C₄×C₅₃	—	4	2	no	—
139	C₂×C₄×C₅₃	—	4	2	no	—
140	C₂×C₄×C₅₃	—	4	2	no	—
141	C₂×C₄×C₅₃	—	4	2	no	—
142	C₂×C₄×C₅₃	—	8	4	no	—
143	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
146	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
149	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
150	C₈×C₅₃	—	2	4	no	—
151	C₈×C₅₃	—	2	4	no	—
152	#21369	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂²×C₅₃	—	2	4	no	—
154	C₂²×C₅₃	—	2	2	no	—
155	C₂²×C₅₃	—	4	1	no	—
156	C₂²×C₅₃	—	4	2	no	—
157	C₂²×C₅₃	—	4	1	no	—
158	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₅₃	#525	1	1	yes	characteristic
160	C₂²×C₅₃	#525	1	1	yes	characteristic
161	C₂²×C₅₃	#577	1	2	yes	—
162	C₂²×C₅₃	#577	1	2	yes	—
163	C₄×C₅₃	—	2	4	no	—
164	C₄×C₅₃	—	2	4	no	—
165	C₄×C₅₃	—	2	2	no	—
166	C₄×C₅₃	—	4	4	no	—
167	C₄×C₅₃	—	4	4	no	—
168	C₄×C₅₃	—	8	2	no	—
169	C₄×C₅₃	—	8	2	no	—
170	C₄×C₅₃	C₄×#41	1	2	yes	—
171	C₄×C₅₃	#533	1	2	yes	—
172	C₂×#433	C₂×C₅₃	1	1	yes	characteristic
173	#2314	C₂×C₅₃	1	1	yes	characteristic
174	#2274	C₂×C₅₃	1	1	yes	characteristic
175	#1949	C₂×C₅₃	1	2	yes	complemented
176	#1948	C₂×C₅₃	1	2	yes	complemented
177	#1854	C₂×C₅₃	1	2	yes	—
178	#1853	C₂×C₅₃	1	2	yes	—
179	#1776	C₂×C₅₃	1	2	yes	complemented
180	C₄×#106	C₂×C₅₃	1	2	yes	complemented
181	C₂×C₅₃	—	4	2	no	—
182	C₂×C₅₃	#2296	1	1	yes	characteristic
183	C₂×C₅₃	#2912	1	2	yes	—
184	C₂×C₅₃	#3123	1	1	yes	characteristic
185	C₂×C₅₃	#3125	1	2	yes	—
186	C₂×C₅₃	#3126	1	1	yes	characteristic
187	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
188	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
189	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
190	#433	C₄×C₅₃	1	8	yes	complemented
191	C₂×#107	C₂²×C₅₃	1	2	yes	—
192	C₂×#106	C₂²×C₅₃	1	2	yes	—
193	C₂×#106	C₂²×C₅₃	1	2	yes	—
194	C₂×#106	C₂²×C₅₃	1	2	yes	—
195	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
197	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
199	#388	—	2	2	no	—
200	#387	—	2	2	no	—
201	#384	C₂²×C₅₃	1	1	yes	characteristic
202	#382	C₂²×C₅₃	1	1	yes	characteristic
203	#380	C₂²×C₅₃	1	2	yes	—
204	C₄×C₄⋊C₄	—	2	2	no	—
205	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
206	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
208	C₄×C₂²⋊C₄	—	2	2	no	—
209	#340	C₂²×C₅₃	1	2	yes	—
210	#340	C₂²×C₅₃	1	2	yes	—
211	#340	C₂²×C₅₃	1	2	yes	—
212	#340	C₂²×C₅₃	1	2	yes	—
213	C₅₃	#21369	1	1	yes	characteristic, direct product factor, Sylow
214	C₂³×C₄	—	2	1	no	—
215	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
217	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
218	#117	—	2	4	no	—
219	#117	C₂×C₄×C₅₃	1	4	yes	—
220	#117	Q₈×C₅₃	1	4	yes	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
238	#107	—	2	4	no	—
239	#106	—	2	4	no	—
240	#106	—	2	4	no	—
241	#106	—	2	4	no	—
242	C₄⋊C₈	C₂×C₄×C₅₃	1	8	yes	complemented
243	C₂²⋊C₈	C₂×C₄×C₅₃	1	8	yes	—
244	#97	C₂×C₄×C₅₃	1	4	yes	complemented
245	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	complemented
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	8	2	no	—
260	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
264	C₂²×C₄	C₂×Q₈×C₅₃	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
271	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	8	2	no	—
280	C₄⋊C₄	C₄⋊C₄×C₅₃	1	8	yes	—
281	C₄⋊C₄	#41×C₅₃	1	4	yes	—
282	C₄⋊C₄	#41×C₅₃	1	4	yes	—
283	C₂²⋊C₄	—	2	4	no	—
284	C₂²⋊C₄	—	8	2	no	—
285	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	8	yes	—
286	C₄²	—	2	4	no	—
287	C₄²	—	8	2	no	—
288	C₄²	—	8	2	no	—
289	C₄²	—	8	2	no	—
290	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
291	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
292	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
293	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
299	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	8	4	no	—
321	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	4	yes	—
322	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	4	yes	—
323	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
324	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
326	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
327	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
328	C₈	—	2	4	no	—
329	C₈	—	2	4	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
336	C₂²	C₅₃×#525	1	1	yes	characteristic
337	C₂²	C₅₃×#525	1	1	yes	characteristic
338	C₂²	C₅₃×#577	1	2	yes	—
339	C₂²	C₅₃×#577	1	2	yes	—
340	C₄	—	2	2	no	—
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	8	2	no	—
346	C₄	—	8	2	no	—
347	C₄	C₄×#41×C₅₃	1	2	yes	—
348	C₄	C₅₃×#533	1	2	yes	—
349	C₂	—	4	2	no	—
350	C₂	C₅₃×#2296	1	1	yes	characteristic
351	C₂	C₅₃×#2912	1	2	yes	—
352	C₂	C₅₃×#3123	1	1	yes	characteristic
353	C₂	C₅₃×#3125	1	2	yes	—
354	C₂	C₅₃×#3126	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂⁴×C₅₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₃×#1949	C₂	semidirect
5. C₅₃×#1948	C₂	semidirect
8. C₅₃×#1776	C₂	semidirect
9. C₄×#106×C₅₃	C₂	semidirect
13. C₅₃×#433	C₄	semidirect
64. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
66. #97×C₅₃	C₂×C₄	semidirect
67. C₄×C₈×C₅₃	C₂×C₄	semidirect
152. #21369	C₅₃	direct (N × H)
175. #1949	C₂×C₅₃	semidirect
176. #1948	C₂×C₅₃	semidirect
179. #1776	C₂×C₅₃	semidirect
180. C₄×#106	C₂×C₅₃	semidirect
190. #433	C₄×C₅₃	semidirect
213. C₅₃	#21369	direct (N × H)
242. C₄⋊C₈	C₂×C₄×C₅₃	semidirect
244. #97	C₂×C₄×C₅₃	semidirect
245. C₄×C₈	C₂×C₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#433	2
C₅₃×#2314	2
C₅₃×#2274	2
C₅₃×#1949	2
C₅₃×#1948	2
C₅₃×#1854	2
C₅₃×#1853	2
C₅₃×#1776	2
C₄×#106×C₅₃	2
#21369	53

Subgroups — C53×#21369 #27228881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#21369 #27228881