Subgroups — C₅₃×#22438 #27229950

Order 13568.

1494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#442	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2339	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1971	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1877	C₂	1	4	yes	maximal, complemented
6	C₅₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1788	C₂	1	2	yes	maximal, complemented
8	C₅₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₅₃	C₂²	1	2	yes	—
10	C₂×#135×C₅₃	—	2	8	no	—
11	C₂×#135×C₅₃	C₄	1	8	yes	complemented
12	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
17	C₅₃×#442	—	2	8	no	—
18	C₂×#106×C₅₃	C₂²	1	2	yes	—
19	C₂×#103×C₅₃	C₂²	1	4	yes	—
20	C₂×#102×C₅₃	C₂²	1	4	yes	—
21	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×#97×C₅₃	C₂²	1	2	yes	—
23	C₅₃×#391	C₂²	1	4	yes	—
24	C₅₃×#386	—	2	4	no	—
25	C₅₃×#381	—	2	2	no	—
26	C₅₃×#380	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#95×C₅₃	—	2	2	no	—
29	C₅₃×#340	C₂²	1	2	yes	—
30	C₅₃×#336	C₂²	1	2	yes	—
31	C₂×#41×C₅₃	—	2	4	no	—
32	C₂×#41×C₅₃	—	2	8	no	—
33	C₂×#41×C₅₃	—	4	4	no	—
34	C₂×#41×C₅₃	C₂×C₄	1	8	yes	complemented
35	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
36	C₂²×D₄×C₅₃	—	2	2	no	—
37	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₅₃	—	2	2	no	—
39	C₂³×C₄×C₅₃	—	2	4	no	—
40	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
41	#135×C₅₃	—	2	32	no	—
42	C₂×Q₁₆×C₅₃	—	2	4	no	—
43	C₂×Q₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
44	C₂×SD₁₆×C₅₃	—	2	8	no	—
45	C₂×SD₁₆×C₅₃	C₂×C₄	1	8	yes	complemented
46	C₂×D₈×C₅₃	C₂×C₄	1	4	yes	—
47	C₂×D₈×C₅₃	D₄	1	8	yes	—
48	C₂²×C₈×C₅₃	—	2	4	no	—
49	C₂²×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₅₃	—	2	8	no	—
54	C₄×D₄×C₅₃	—	4	4	no	—
55	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
59	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
60	#106×C₅₃	—	2	4	no	—
61	#103×C₅₃	—	4	4	no	—
62	#102×C₅₃	—	2	8	no	—
63	C₂²⋊C₈×C₅₃	—	2	2	no	—
64	#97×C₅₃	—	2	4	no	—
65	#95×C₅₃	—	2	2	no	—
66	#95×C₅₃	—	2	4	no	—
67	#95×C₅₃	—	2	4	no	—
68	#95×C₅₃	D₄	1	2	yes	—
69	C₂⁴×C₅₃	—	2	2	no	—
70	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
71	#41×C₅₃	—	2	16	no	—
72	#41×C₅₃	—	4	8	no	—
73	#41×C₅₃	—	4	16	no	—
74	C₂×Q₈×C₅₃	—	2	2	no	—
75	C₂×Q₈×C₅₃	—	2	4	no	—
76	C₂×Q₈×C₅₃	—	2	4	no	—
77	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
78	C₂×D₄×C₅₃	—	2	8	no	—
79	C₂×D₄×C₅₃	—	2	2	no	—
80	C₂×D₄×C₅₃	—	2	4	no	—
81	C₂×D₄×C₅₃	—	4	8	no	—
82	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
83	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₅₃	—	2	2	no	—
85	C₂²×C₄×C₅₃	—	2	2	no	—
86	C₂²×C₄×C₅₃	—	2	2	no	—
87	C₂²×C₄×C₅₃	—	2	8	no	—
88	C₂²×C₄×C₅₃	—	2	4	no	—
89	C₂²×C₄×C₅₃	—	4	8	no	—
90	C₂²×C₄×C₅₃	—	4	8	no	—
91	C₂²×C₄×C₅₃	—	4	8	no	—
92	C₂²×C₄×C₅₃	—	8	4	no	—
93	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	#41	1	2	yes	—
97	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₅₃	—	2	8	no	—
99	SD₁₆×C₅₃	—	2	16	no	—
100	D₈×C₅₃	C₂²⋊C₄	1	16	yes	complemented
101	C₂×C₈×C₅₃	—	2	2	no	—
102	C₂×C₈×C₅₃	—	2	8	no	—
103	C₂×C₈×C₅₃	—	2	2	no	—
104	C₂×C₈×C₅₃	—	2	2	no	—
105	C₂×C₈×C₅₃	—	2	2	no	—
106	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₅₃	C₂×D₄	1	4	yes	—
109	C₄⋊C₄×C₅₃	—	2	4	no	—
110	C₄⋊C₄×C₅₃	—	2	4	no	—
111	C₂²⋊C₄×C₅₃	—	4	2	no	—
112	C₂²⋊C₄×C₅₃	—	4	8	no	—
113	C₂²⋊C₄×C₅₃	—	8	2	no	—
114	C₄²×C₅₃	—	2	2	no	—
115	C₄²×C₅₃	—	2	2	no	—
116	C₂³×C₅₃	—	2	4	no	—
117	C₂³×C₅₃	—	2	2	no	—
118	C₂³×C₅₃	—	2	8	no	—
119	C₂³×C₅₃	—	2	2	no	—
120	C₂³×C₅₃	—	2	2	no	—
121	C₂³×C₅₃	—	4	4	no	—
122	C₂³×C₅₃	—	4	2	no	—
123	C₂³×C₅₃	—	4	2	no	—
124	C₂³×C₅₃	C₄×D₄	1	2	yes	—
125	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₅₃	—	2	4	no	—
127	Q₈×C₅₃	—	2	4	no	—
128	Q₈×C₅₃	—	4	4	no	—
129	D₄×C₅₃	—	2	4	no	—
130	D₄×C₅₃	—	2	8	no	—
131	D₄×C₅₃	—	4	16	no	—
132	D₄×C₅₃	C₂×C₂²⋊C₄	1	8	yes	—
133	C₂×C₄×C₅₃	—	2	2	no	—
134	C₂×C₄×C₅₃	—	2	2	no	—
135	C₂×C₄×C₅₃	—	2	2	no	—
136	C₂×C₄×C₅₃	—	2	4	no	—
137	C₂×C₄×C₅₃	—	2	4	no	—
138	C₂×C₄×C₅₃	—	2	4	no	—
139	C₂×C₄×C₅₃	—	2	4	no	—
140	C₂×C₄×C₅₃	—	2	4	no	—
141	C₂×C₄×C₅₃	—	4	16	no	—
142	C₂×C₄×C₅₃	—	4	4	no	—
143	C₂×C₄×C₅₃	—	4	4	no	—
144	C₂×C₄×C₅₃	—	4	4	no	—
145	C₂×C₄×C₅₃	—	4	4	no	—
146	C₂×C₄×C₅₃	—	8	16	no	—
147	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
152	C₈×C₅₃	—	2	2	no	—
153	C₈×C₅₃	—	4	2	no	—
154	C₈×C₅₃	C₂×C₂²⋊C₄	1	4	yes	—
155	#22438	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂²×C₅₃	—	2	2	no	—
157	C₂²×C₅₃	—	2	8	no	—
158	C₂²×C₅₃	—	2	2	no	—
159	C₂²×C₅₃	—	2	2	no	—
160	C₂²×C₅₃	—	4	4	no	—
161	C₂²×C₅₃	—	4	4	no	—
162	C₂²×C₅₃	—	4	8	no	—
163	C₂²×C₅₃	—	4	4	no	—
164	C₂²×C₅₃	—	4	8	no	—
165	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₅₃	D₄²	1	2	yes	—
167	C₂²×C₅₃	#575	1	2	yes	—
168	C₂²×C₅₃	#577	1	2	yes	—
169	C₄×C₅₃	—	2	2	no	—
170	C₄×C₅₃	—	4	4	no	—
171	C₄×C₅₃	—	4	4	no	—
172	C₄×C₅₃	—	8	4	no	—
173	C₄×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
174	C₄×C₅₃	#518	1	1	yes	characteristic
175	C₄×C₅₃	#546	1	2	yes	—
176	C₂²×#135	C₂×C₅₃	1	1	yes	characteristic
177	C₂×#442	C₂×C₅₃	1	2	yes	complemented
178	#2339	C₂×C₅₃	1	2	yes	complemented
179	#1971	C₂×C₅₃	1	2	yes	complemented
180	#1877	C₂×C₅₃	1	4	yes	complemented
181	#1807	C₂×C₅₃	1	1	yes	characteristic, complemented
182	#1788	C₂×C₅₃	1	2	yes	complemented
183	#1752	C₂×C₅₃	1	1	yes	characteristic, complemented
184	C₂×C₅₃	—	4	2	no	—
185	C₂×C₅₃	—	4	8	no	—
186	C₂×C₅₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₅₃	#2943	1	1	yes	characteristic
188	C₂×C₅₃	#2952	1	1	yes	characteristic
189	C₂×C₅₃	#3267	1	4	yes	—
190	C₂²×#41	C₂²×C₅₃	1	2	yes	—
191	C₂×#135	—	2	8	no	—
192	C₂×#135	C₄×C₅₃	1	8	yes	complemented
193	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
194	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
195	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
198	#442	—	2	8	no	—
199	C₂×#106	C₂²×C₅₃	1	2	yes	—
200	C₂×#103	C₂²×C₅₃	1	4	yes	—
201	C₂×#102	C₂²×C₅₃	1	4	yes	—
202	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
203	C₂×#97	C₂²×C₅₃	1	2	yes	—
204	#391	C₂²×C₅₃	1	4	yes	—
205	#386	—	2	4	no	—
206	#381	—	2	2	no	—
207	#380	C₂²×C₅₃	1	2	yes	—
208	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
209	C₂×#95	—	2	2	no	—
210	#340	C₂²×C₅₃	1	2	yes	—
211	#336	C₂²×C₅₃	1	2	yes	—
212	C₅₃	#22438	1	1	yes	characteristic, direct product factor, Sylow
213	C₂×#41	—	2	4	no	—
214	C₂×#41	—	2	8	no	—
215	C₂×#41	—	4	4	no	—
216	C₂×#41	C₂×C₄×C₅₃	1	8	yes	complemented
217	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
223	#135	—	2	32	no	—
224	C₂×Q₁₆	—	2	4	no	—
225	C₂×Q₁₆	C₂×C₄×C₅₃	1	4	yes	complemented
226	C₂×SD₁₆	—	2	8	no	—
227	C₂×SD₁₆	C₂×C₄×C₅₃	1	8	yes	complemented
228	C₂×D₈	C₂×C₄×C₅₃	1	4	yes	—
229	C₂×D₈	D₄×C₅₃	1	8	yes	—
230	C₂²×C₈	—	2	4	no	—
231	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	complemented
232	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
233	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
235	C₄×D₄	—	2	8	no	—
236	C₄×D₄	—	4	4	no	—
237	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
238	C₂×C₂²⋊C₄	—	2	4	no	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
241	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
242	#106	—	2	4	no	—
243	#103	—	4	4	no	—
244	#102	—	2	8	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	#97	—	2	4	no	—
247	#95	—	2	2	no	—
248	#95	—	2	4	no	—
249	#95	—	2	4	no	—
250	#95	D₄×C₅₃	1	2	yes	—
251	C₂⁴	—	2	2	no	—
252	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
253	#41	—	2	16	no	—
254	#41	—	4	8	no	—
255	#41	—	4	16	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
260	C₂×D₄	—	2	8	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	4	8	no	—
264	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
265	C₂×D₄	C₂×D₄×C₅₃	1	8	yes	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	—	8	4	no	—
275	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
277	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
278	C₂²×C₄	#41×C₅₃	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
280	Q₁₆	—	2	8	no	—
281	SD₁₆	—	2	16	no	—
282	D₈	C₂²⋊C₄×C₅₃	1	16	yes	complemented
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
289	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
290	C₂×C₈	C₂×D₄×C₅₃	1	4	yes	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	4	2	no	—
294	C₂²⋊C₄	—	4	8	no	—
295	C₂²⋊C₄	—	8	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	4	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	C₄×D₄×C₅₃	1	2	yes	—
307	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
308	Q₈	—	2	4	no	—
309	Q₈	—	2	4	no	—
310	Q₈	—	4	4	no	—
311	D₄	—	2	4	no	—
312	D₄	—	2	8	no	—
313	D₄	—	4	16	no	—
314	D₄	C₂×C₂²⋊C₄×C₅₃	1	8	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	8	16	no	—
329	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
330	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
332	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
333	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₂×C₂²⋊C₄×C₅₃	1	4	yes	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	8	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	8	no	—
346	C₂²	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
347	C₂²	D₄²×C₅₃	1	2	yes	—
348	C₂²	C₅₃×#575	1	2	yes	—
349	C₂²	C₅₃×#577	1	2	yes	—
350	C₄	—	2	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	4	no	—
353	C₄	—	8	4	no	—
354	C₄	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
355	C₄	C₅₃×#518	1	1	yes	characteristic
356	C₄	C₅₃×#546	1	2	yes	—
357	C₂	—	4	2	no	—
358	C₂	—	4	8	no	—
359	C₂	D₄×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
360	C₂	C₅₃×#2943	1	1	yes	characteristic
361	C₂	C₅₃×#2952	1	1	yes	characteristic
362	C₂	C₅₃×#3267	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂²×#135×C₅₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₄×C₂²⋊C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#442	C₂	semidirect
3. C₅₃×#2339	C₂	semidirect
4. C₅₃×#1971	C₂	semidirect
5. C₅₃×#1877	C₂	semidirect
6. C₅₃×#1807	C₂	semidirect
7. C₅₃×#1788	C₂	semidirect
8. C₅₃×#1752	C₂	semidirect
11. C₂×#135×C₅₃	C₄	semidirect
34. C₂×#41×C₅₃	C₂×C₄	semidirect
43. C₂×Q₁₆×C₅₃	C₂×C₄	semidirect
45. C₂×SD₁₆×C₅₃	C₂×C₄	semidirect
49. C₂²×C₈×C₅₃	C₂×C₄	semidirect
100. D₈×C₅₃	C₂²⋊C₄	semidirect
155. #22438	C₅₃	direct (N × H)
177. C₂×#442	C₂×C₅₃	semidirect
178. #2339	C₂×C₅₃	semidirect
179. #1971	C₂×C₅₃	semidirect
180. #1877	C₂×C₅₃	semidirect
181. #1807	C₂×C₅₃	semidirect
182. #1788	C₂×C₅₃	semidirect
183. #1752	C₂×C₅₃	semidirect
192. C₂×#135	C₄×C₅₃	semidirect
212. C₅₃	#22438	direct (N × H)
216. C₂×#41	C₂×C₄×C₅₃	semidirect
225. C₂×Q₁₆	C₂×C₄×C₅₃	semidirect
227. C₂×SD₁₆	C₂×C₄×C₅₃	semidirect
231. C₂²×C₈	C₂×C₄×C₅₃	semidirect
282. D₈	C₂²⋊C₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₅₃	2
C₂×C₅₃×#442	2
C₅₃×#2339	2
C₅₃×#1971	2
C₅₃×#1877	2
C₅₃×#1807	2
C₅₃×#1788	2
C₅₃×#1752	2
#22438	53

Subgroups — C53×#22438 #27229950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22438 #27229950