Subgroups — C₅₃×#21962 #27229474

Order 13568.

862 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2285	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2283	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1949	C₂	1	4	yes	maximal, complemented
5	C₅₃×#1948	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1947	C₂	1	2	yes	maximal, complemented
7	C₅₃×#1808	C₂	1	2	yes	maximal
8	C₅₃×#1807	C₂	1	2	yes	maximal
9	C₂³×C₈×C₅₃	C₂²	1	2	yes	—
10	C₂×#117×C₅₃	—	2	1	no	—
11	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×#107×C₅₃	C₂²	1	4	yes	—
13	C₂×#106×C₅₃	C₂²	1	4	yes	—
14	C₂×C₄⋊C₈×C₅₃	C₄	1	8	yes	complemented
15	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
18	C₅₃×#384	C₂²	1	2	yes	—
19	C₅₃×#383	—	2	1	no	—
20	C₅₃×#382	—	2	1	no	—
21	C₅₃×#382	C₂²	1	2	yes	—
22	C₅₃×#381	—	2	1	no	—
23	C₅₃×#380	—	2	1	no	—
24	C₅₃×#380	C₂²	1	1	yes	characteristic
25	C₅₃×#380	C₂²	1	1	yes	characteristic
26	C₅₃×#380	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₅₃	—	2	1	no	—
28	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₅₃	—	2	1	no	—
31	C₅₃×#376	—	2	1	no	—
32	C₅₃×#340	C₂²	1	4	yes	—
33	C₅₃×#340	C₂²	1	4	yes	—
34	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₅₃	—	4	4	no	—
38	C₂²×C₈×C₅₃	C₂×C₄	1	8	yes	—
39	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
41	#117×C₅₃	—	4	4	no	—
42	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
45	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
47	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
50	C₂×C₄²×C₅₃	—	2	2	no	—
51	C₂×C₄²×C₅₃	—	2	2	no	—
52	C₂×C₄²×C₅₃	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₃	Q₈	1	4	yes	—
56	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
58	#107×C₅₃	—	4	4	no	—
59	#106×C₅₃	—	4	4	no	—
60	C₄⋊C₈×C₅₃	C₂×C₄	1	4	yes	—
61	C₄⋊C₈×C₅₃	C₂×C₄	1	4	yes	—
62	C₄⋊C₈×C₅₃	C₂×C₄	1	8	yes	—
63	#95×C₅₃	—	2	1	no	—
64	#95×C₅₃	—	2	1	no	—
65	#95×C₅₃	—	2	2	no	—
66	#95×C₅₃	—	2	2	no	—
67	#95×C₅₃	—	2	2	no	—
68	#95×C₅₃	—	2	2	no	—
69	#95×C₅₃	—	2	2	no	—
70	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	—	2	2	no	—
72	C₂²×C₄×C₅₃	—	2	2	no	—
73	C₂²×C₄×C₅₃	—	2	4	no	—
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	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₅₃	C₄⋊C₄	1	4	yes	—
81	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
89	C₂×C₈×C₅₃	—	2	4	no	—
90	C₂×C₈×C₅₃	—	2	4	no	—
91	C₂×C₈×C₅₃	—	4	8	no	—
92	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₅₃	—	2	2	no	—
95	C₄⋊C₄×C₅₃	—	2	4	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	4	no	—
100	C₄⋊C₄×C₅₃	—	4	4	no	—
101	C₄⋊C₄×C₅₃	—	4	4	no	—
102	C₂²⋊C₄×C₅₃	—	4	2	no	—
103	C₂²⋊C₄×C₅₃	—	4	4	no	—
104	C₂²⋊C₄×C₅₃	—	4	2	no	—
105	C₄²×C₅₃	—	4	4	no	—
106	C₄²×C₅₃	—	4	4	no	—
107	C₄²×C₅₃	C₄⋊C₄	1	4	yes	—
108	C₄²×C₅₃	C₄⋊C₄	1	4	yes	—
109	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
110	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
111	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
112	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
113	C₂³×C₅₃	—	2	2	no	—
114	C₂³×C₅₃	—	2	2	no	—
115	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
116	C₂³×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
117	C₂³×C₅₃	#137	1	2	yes	—
118	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
119	C₂×C₄×C₅₃	—	2	2	no	—
120	C₂×C₄×C₅₃	—	2	2	no	—
121	C₂×C₄×C₅₃	—	2	1	no	—
122	C₂×C₄×C₅₃	—	2	1	no	—
123	C₂×C₄×C₅₃	—	2	1	no	—
124	C₂×C₄×C₅₃	—	2	1	no	—
125	C₂×C₄×C₅₃	—	2	8	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	8	no	—
130	C₂×C₄×C₅₃	—	4	2	no	—
131	C₂×C₄×C₅₃	—	4	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	4	no	—
136	C₂×C₄×C₅₃	—	4	4	no	—
137	C₂×C₄×C₅₃	—	4	2	no	—
138	C₂×C₄×C₅₃	—	4	2	no	—
139	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₅₃	#135	1	4	yes	—
145	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
148	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
149	C₈×C₅₃	—	2	4	no	—
150	C₈×C₅₃	—	2	4	no	—
151	#21962	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂²×C₅₃	—	2	2	no	—
153	C₂²×C₅₃	—	2	2	no	—
154	C₂²×C₅₃	—	2	4	no	—
155	C₂²×C₅₃	—	2	4	no	—
156	C₂²×C₅₃	#428	1	4	yes	—
157	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
158	C₂²×C₅₃	#537	1	2	yes	—
159	C₂²×C₅₃	C₂×#135	1	2	yes	—
160	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂²×C₅₃	C₂×#137	1	1	yes	characteristic
162	C₄×C₅₃	—	2	2	no	—
163	C₄×C₅₃	—	2	2	no	—
164	C₄×C₅₃	—	2	2	no	—
165	C₄×C₅₃	—	2	2	no	—
166	C₄×C₅₃	—	8	2	no	—
167	C₄×C₅₃	—	8	4	no	—
168	C₄×C₅₃	—	8	2	no	—
169	C₄×C₅₃	#427	1	4	yes	—
170	C₄×C₅₃	#518	1	1	yes	characteristic
171	C₄×C₅₃	#519	1	1	yes	characteristic
172	C₄×C₅₃	#544	1	2	yes	—
173	C₂²×C₄⋊C₈	C₂×C₅₃	1	1	yes	characteristic
174	#2285	C₂×C₅₃	1	1	yes	characteristic
175	#2283	C₂×C₅₃	1	1	yes	characteristic
176	#1949	C₂×C₅₃	1	4	yes	complemented
177	#1948	C₂×C₅₃	1	2	yes	complemented
178	#1947	C₂×C₅₃	1	2	yes	complemented
179	#1808	C₂×C₅₃	1	2	yes	—
180	#1807	C₂×C₅₃	1	2	yes	—
181	C₂×C₅₃	—	2	4	no	—
182	C₂×C₅₃	#2316	1	1	yes	characteristic
183	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
184	C₂×C₅₃	C₂×#428	1	1	yes	characteristic
185	C₂×C₅₃	#3247	1	2	yes	—
186	C₂×C₅₃	#3248	1	2	yes	—
187	C₂³×C₈	C₂²×C₅₃	1	2	yes	—
188	C₂×#117	—	2	1	no	—
189	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
190	C₂×#107	C₂²×C₅₃	1	4	yes	—
191	C₂×#106	C₂²×C₅₃	1	4	yes	—
192	C₂×C₄⋊C₈	C₄×C₅₃	1	8	yes	complemented
193	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
196	#384	C₂²×C₅₃	1	2	yes	—
197	#383	—	2	1	no	—
198	#382	—	2	1	no	—
199	#382	C₂²×C₅₃	1	2	yes	—
200	#381	—	2	1	no	—
201	#380	—	2	1	no	—
202	#380	C₂²×C₅₃	1	1	yes	characteristic
203	#380	C₂²×C₅₃	1	2	yes	—
204	#380	C₂²×C₅₃	1	1	yes	characteristic
205	C₄×C₄⋊C₄	—	2	1	no	—
206	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
208	C₄×C₂²⋊C₄	—	2	1	no	—
209	#376	—	2	1	no	—
210	#340	C₂²×C₅₃	1	4	yes	—
211	#340	C₂²×C₅₃	1	4	yes	—
212	C₅₃	#21962	1	1	yes	characteristic, direct product factor, Sylow
213	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
216	C₂²×C₈	—	4	4	no	—
217	C₂²×C₈	C₂×C₄×C₅₃	1	8	yes	—
218	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
219	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
220	#117	—	4	4	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
224	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	C₂×C₄×C₅₃	1	4	yes	—
232	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
234	C₂×C₄²	Q₈×C₅₃	1	4	yes	—
235	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
237	#107	—	4	4	no	—
238	#106	—	4	4	no	—
239	C₄⋊C₈	C₂×C₄×C₅₃	1	4	yes	—
240	C₄⋊C₈	C₂×C₄×C₅₃	1	4	yes	—
241	C₄⋊C₈	C₂×C₄×C₅₃	1	8	yes	—
242	#95	—	2	1	no	—
243	#95	—	2	1	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	C₄⋊C₄×C₅₃	1	4	yes	—
259	C₂²×C₄	C₄⋊C₄×C₅₃	1	4	yes	—
260	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×Q₈×C₅₃	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	4	8	no	—
271	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
272	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	4	4	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₄²	—	4	4	no	—
285	C₄²	—	4	4	no	—
286	C₄²	C₄⋊C₄×C₅₃	1	4	yes	—
287	C₄²	C₄⋊C₄×C₅₃	1	4	yes	—
288	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
289	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
290	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
291	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
295	C₂³	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
296	C₂³	#137×C₅₃	1	2	yes	—
297	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	4	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	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
319	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
320	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
321	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
322	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
323	C₂×C₄	#135×C₅₃	1	4	yes	—
324	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
326	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
327	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
328	C₈	—	2	4	no	—
329	C₈	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	C₅₃×#428	1	4	yes	—
335	C₂²	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
336	C₂²	C₅₃×#537	1	2	yes	—
337	C₂²	C₂×#135×C₅₃	1	2	yes	—
338	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
339	C₂²	C₂×#137×C₅₃	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	8	2	no	—
345	C₄	—	8	4	no	—
346	C₄	—	8	2	no	—
347	C₄	C₅₃×#427	1	4	yes	—
348	C₄	C₅₃×#518	1	1	yes	characteristic
349	C₄	C₅₃×#519	1	1	yes	characteristic
350	C₄	C₅₃×#544	1	2	yes	—
351	C₂	—	2	4	no	—
352	C₂	C₅₃×#2316	1	1	yes	characteristic
353	C₂	C₂×C₅₃×#427	1	1	yes	characteristic
354	C₂	C₂×C₅₃×#428	1	1	yes	characteristic
355	C₂	C₅₃×#3247	1	2	yes	—
356	C₂	C₅₃×#3248	1	2	yes	—

	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 ◁ C₂²×C₄²×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
6. C₅₃×#1947	C₂	semidirect
14. C₂×C₄⋊C₈×C₅₃	C₄	semidirect
151. #21962	C₅₃	direct (N × H)
176. #1949	C₂×C₅₃	semidirect
177. #1948	C₂×C₅₃	semidirect
178. #1947	C₂×C₅₃	semidirect
192. C₂×C₄⋊C₈	C₄×C₅₃	semidirect
212. C₅₃	#21962	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₅₃	2
C₅₃×#2285	2
C₅₃×#2283	2
C₅₃×#1949	2
C₅₃×#1948	2
C₅₃×#1947	2
C₅₃×#1808	2
C₅₃×#1807	2
#21962	53

Subgroups — C53×#21962 #27229474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#21962 #27229474