Subgroups — C₅₃×#20541 #27228053

Order 13568.

886 conjugacy classes of subgroups.

The subgroup lattice has 346 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	2	yes	maximal
2	C₅₃×#2296	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#1771	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1771	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1770	C₂	1	2	yes	maximal, complemented
6	C₈×C₄⋊C₄×C₅₃	C₂	1	2	yes	maximal, complemented
7	C₅₃×#1750	C₂	1	2	yes	maximal
8	C₅₃×#1749	C₂	1	1	yes	maximal, characteristic
9	C₄×C₂²⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
10	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
13	C₅₃×#433	C₄	1	16	yes	complemented
14	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
18	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×#97×C₅₃	C₂²	1	2	yes	—
21	C₂×#97×C₅₃	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
26	C₅₃×#389	C₄	1	2	yes	—
27	C₅₃×#389	C₄	1	2	yes	—
28	C₅₃×#385	C₄	1	4	yes	—
29	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
31	C₅₃×#336	C₂²	1	2	yes	—
32	C₅₃×#336	C₂²	1	2	yes	—
33	C₅₃×#336	C₂²	1	2	yes	—
34	C₅₃×#336	C₂²	1	2	yes	—
35	C₂³×C₄×C₅₃	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
41	#117×C₅₃	—	4	1	no	—
42	#117×C₅₃	—	4	1	no	—
43	#117×C₅₃	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₅₃	—	4	1	no	—
52	C₂×C₄²×C₅₃	—	4	1	no	—
53	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
57	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
58	C₄⋊C₈×C₅₃	C₂×C₄	1	8	yes	complemented
59	C₄⋊C₈×C₅₃	C₂×C₄	1	8	yes	complemented
60	C₂²⋊C₈×C₅₃	C₂×C₄	1	8	yes	—
61	C₂²⋊C₈×C₅₃	C₂×C₄	1	8	yes	—
62	#97×C₅₃	—	4	1	no	—
63	#97×C₅₃	—	4	1	no	—
64	#97×C₅₃	—	4	2	no	—
65	#97×C₅₃	C₂×C₄	1	8	yes	complemented
66	C₄×C₈×C₅₃	—	4	1	no	—
67	C₄×C₈×C₅₃	—	4	1	no	—
68	C₄×C₈×C₅₃	—	4	2	no	—
69	C₄×C₈×C₅₃	C₂×C₄	1	8	yes	complemented
70	#95×C₅₃	C₂×C₄	1	4	yes	—
71	#95×C₅₃	C₂×C₄	1	4	yes	—
72	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	—	2	1	no	—
74	C₂²×C₄×C₅₃	—	2	1	no	—
75	C₂²×C₄×C₅₃	—	2	2	no	—
76	C₂²×C₄×C₅₃	—	2	4	no	—
77	C₂²×C₄×C₅₃	—	4	2	no	—
78	C₂²×C₄×C₅₃	—	4	2	no	—
79	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₅₃	—	2	2	no	—
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	—	2	2	no	—
93	C₂×C₈×C₅₃	—	2	2	no	—
94	C₂×C₈×C₅₃	—	2	2	no	—
95	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
96	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
98	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
99	C₄⋊C₄×C₅₃	—	2	8	no	—
100	C₄⋊C₄×C₅₃	—	4	4	no	—
101	C₄⋊C₄×C₅₃	—	4	2	no	—
102	C₄⋊C₄×C₅₃	C₄²	1	4	yes	—
103	C₄⋊C₄×C₅₃	C₄²	1	4	yes	—
104	C₂²⋊C₄×C₅₃	—	4	2	no	—
105	C₂²⋊C₄×C₅₃	C₄²	1	8	yes	—
106	C₄²×C₅₃	—	2	1	no	—
107	C₄²×C₅₃	—	2	1	no	—
108	C₄²×C₅₃	—	2	2	no	—
109	C₄²×C₅₃	—	2	1	no	—
110	C₄²×C₅₃	—	2	1	no	—
111	C₄²×C₅₃	—	2	2	no	—
112	C₄²×C₅₃	—	4	2	no	—
113	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
114	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
115	C₂³×C₅₃	—	2	1	no	—
116	C₂³×C₅₃	—	2	1	no	—
117	C₂³×C₅₃	—	2	2	no	—
118	C₂³×C₅₃	—	2	2	no	—
119	C₂³×C₅₃	C₂×C₄²	1	2	yes	—
120	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
121	C₂×C₄×C₅₃	—	2	1	no	—
122	C₂×C₄×C₅₃	—	2	2	no	—
123	C₂×C₄×C₅₃	—	2	1	no	—
124	C₂×C₄×C₅₃	—	2	4	no	—
125	C₂×C₄×C₅₃	—	2	2	no	—
126	C₂×C₄×C₅₃	—	2	4	no	—
127	C₂×C₄×C₅₃	—	2	4	no	—
128	C₂×C₄×C₅₃	—	2	4	no	—
129	C₂×C₄×C₅₃	—	2	2	no	—
130	C₂×C₄×C₅₃	—	2	4	no	—
131	C₂×C₄×C₅₃	—	2	2	no	—
132	C₂×C₄×C₅₃	—	2	4	no	—
133	C₂×C₄×C₅₃	—	2	2	no	—
134	C₂×C₄×C₅₃	—	2	4	no	—
135	C₂×C₄×C₅₃	—	4	8	no	—
136	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
137	C₂×C₄×C₅₃	C₂×C₄²	1	4	yes	—
138	C₂×C₄×C₅₃	C₂×C₄²	1	4	yes	—
139	C₂×C₄×C₅₃	#131	1	4	yes	—
140	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
141	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
143	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
144	C₈×C₅₃	—	2	4	no	—
145	C₈×C₅₃	—	2	4	no	—
146	C₈×C₅₃	—	2	4	no	—
147	C₈×C₅₃	—	2	4	no	—
148	#20541	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂²×C₅₃	—	2	2	no	—
150	C₂²×C₅₃	—	2	2	no	—
151	C₂²×C₅₃	—	2	2	no	—
152	C₂²×C₅₃	—	4	2	no	—
153	C₂²×C₅₃	—	4	2	no	—
154	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
155	C₂²×C₅₃	#518	1	1	yes	characteristic
156	C₂²×C₅₃	#519	1	1	yes	characteristic
157	C₂²×C₅₃	C₂×#131	1	2	yes	—
158	C₂²×C₅₃	#568	1	2	yes	—
159	C₄×C₅₃	—	2	4	no	—
160	C₄×C₅₃	—	2	4	no	—
161	C₄×C₅₃	—	2	4	no	—
162	C₄×C₅₃	—	2	2	no	—
163	C₄×C₅₃	—	4	4	no	—
164	C₄×C₅₃	—	4	2	no	—
165	C₄×C₅₃	#520	1	2	yes	—
166	C₄×C₅₃	#520	1	2	yes	—
167	C₂×#433	C₂×C₅₃	1	2	yes	—
168	#2296	C₂×C₅₃	1	1	yes	characteristic
169	#1771	C₂×C₅₃	1	2	yes	complemented
170	#1771	C₂×C₅₃	1	2	yes	complemented
171	#1770	C₂×C₅₃	1	2	yes	complemented
172	C₈×C₄⋊C₄	C₂×C₅₃	1	2	yes	complemented
173	#1750	C₂×C₅₃	1	2	yes	—
174	#1749	C₂×C₅₃	1	1	yes	characteristic
175	C₄×C₂²⋊C₈	C₂×C₅₃	1	1	yes	characteristic
176	C₂×C₅₃	—	4	2	no	—
177	C₂×C₅₃	#2274	1	1	yes	characteristic
178	C₂×C₅₃	C₄×#131	1	1	yes	characteristic
179	C₂×C₅₃	#2875	1	1	yes	characteristic
180	C₂×C₅₃	#2976	1	2	yes	—
181	C₂×C₅₃	#2985	1	2	yes	—
182	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
183	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
184	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
185	#433	C₄×C₅₃	1	16	yes	complemented
186	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
188	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
189	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
190	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
191	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
192	C₂×#97	C₂²×C₅₃	1	2	yes	—
193	C₂×#97	C₂²×C₅₃	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
196	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	—
198	#389	C₄×C₅₃	1	2	yes	—
199	#389	C₄×C₅₃	1	2	yes	—
200	#385	C₄×C₅₃	1	4	yes	—
201	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
202	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
203	#336	C₂²×C₅₃	1	2	yes	—
204	#336	C₂²×C₅₃	1	2	yes	—
205	#336	C₂²×C₅₃	1	2	yes	—
206	#336	C₂²×C₅₃	1	2	yes	—
207	C₅₃	#20541	1	1	yes	characteristic, direct product factor, Sylow
208	C₂³×C₄	C₂×C₄×C₅₃	1	2	yes	—
209	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
211	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
213	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
214	#117	—	4	1	no	—
215	#117	—	4	1	no	—
216	#117	C₂×C₄×C₅₃	1	8	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
224	C₂×C₄²	—	4	1	no	—
225	C₂×C₄²	—	4	1	no	—
226	C₂×C₄²	C₂×C₄×C₅₃	1	2	yes	—
227	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
228	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
231	C₄⋊C₈	C₂×C₄×C₅₃	1	8	yes	complemented
232	C₄⋊C₈	C₂×C₄×C₅₃	1	8	yes	complemented
233	C₂²⋊C₈	C₂×C₄×C₅₃	1	8	yes	—
234	C₂²⋊C₈	C₂×C₄×C₅₃	1	8	yes	—
235	#97	—	4	1	no	—
236	#97	—	4	1	no	—
237	#97	—	4	2	no	—
238	#97	C₂×C₄×C₅₃	1	8	yes	complemented
239	C₄×C₈	—	4	1	no	—
240	C₄×C₈	—	4	1	no	—
241	C₄×C₈	—	4	2	no	—
242	C₄×C₈	C₂×C₄×C₅₃	1	8	yes	complemented
243	#95	C₂×C₄×C₅₃	1	4	yes	—
244	#95	C₂×C₄×C₅₃	1	4	yes	—
245	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
254	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
258	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
259	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
269	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
270	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
271	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	4	2	no	—
274	C₄⋊C₄	—	4	4	no	—
275	C₄⋊C₄	C₄²×C₅₃	1	4	yes	—
276	C₄⋊C₄	C₄²×C₅₃	1	4	yes	—
277	C₂²⋊C₄	—	4	2	no	—
278	C₂²⋊C₄	C₄²×C₅₃	1	8	yes	—
279	C₄²	—	2	1	no	—
280	C₄²	—	2	1	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	4	2	no	—
286	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
287	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	C₂×C₄²×C₅₃	1	2	yes	—
293	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	C₂×C₄²×C₅₃	1	4	yes	—
310	C₂×C₄	C₂×C₄²×C₅₃	1	4	yes	—
311	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
312	C₂×C₄	#131×C₅₃	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
314	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
315	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
316	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
317	C₈	—	2	4	no	—
318	C₈	—	2	4	no	—
319	C₈	—	2	4	no	—
320	C₈	—	2	4	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	C₂²×C₄²×C₅₃	1	1	yes	characteristic
327	C₂²	C₅₃×#518	1	1	yes	characteristic
328	C₂²	C₅₃×#519	1	1	yes	characteristic
329	C₂²	C₂×#131×C₅₃	1	2	yes	—
330	C₂²	C₅₃×#568	1	2	yes	—
331	C₄	—	2	4	no	—
332	C₄	—	2	2	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	4	2	no	—
336	C₄	—	4	4	no	—
337	C₄	C₅₃×#520	1	2	yes	—
338	C₄	C₅₃×#520	1	2	yes	—
339	C₂	—	4	2	no	—
340	C₂	C₅₃×#2274	1	1	yes	characteristic
341	C₂	C₄×#131×C₅₃	1	1	yes	characteristic
342	C₂	C₅₃×#2875	1	1	yes	characteristic
343	C₂	C₅₃×#2976	1	2	yes	—
344	C₂	C₅₃×#2985	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂⁴×C₅₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₃×#1771	C₂	semidirect
4. C₅₃×#1771	C₂	semidirect
5. C₅₃×#1770	C₂	semidirect
6. C₈×C₄⋊C₄×C₅₃	C₂	semidirect
13. C₅₃×#433	C₄	semidirect
58. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
59. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
65. #97×C₅₃	C₂×C₄	semidirect
69. C₄×C₈×C₅₃	C₂×C₄	semidirect
148. #20541	C₅₃	direct (N × H)
169. #1771	C₂×C₅₃	semidirect
170. #1771	C₂×C₅₃	semidirect
171. #1770	C₂×C₅₃	semidirect
172. C₈×C₄⋊C₄	C₂×C₅₃	semidirect
185. #433	C₄×C₅₃	semidirect
207. C₅₃	#20541	direct (N × H)
231. C₄⋊C₈	C₂×C₄×C₅₃	semidirect
232. C₄⋊C₈	C₂×C₄×C₅₃	semidirect
238. #97	C₂×C₄×C₅₃	semidirect
242. 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×#2296	2
C₅₃×#1771	2
C₅₃×#1770	2
C₈×C₄⋊C₄×C₅₃	2
C₅₃×#1750	2
C₅₃×#1749	2
C₄×C₂²⋊C₈×C₅₃	2
#20541	53

Subgroups — C53×#20541 #27228053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#20541 #27228053