Subgroups — C₅₃×#23638 #27231150

Order 13568.

1126 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	C₂×C₅₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2280	C₂	1	2	yes	maximal
4	C₅₃×#2077	C₂	1	4	yes	maximal, complemented
5	C₅₃×#2076	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2075	C₂	1	2	yes	maximal, complemented
7	C₅₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1735	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×#117×C₅₃	C₂²	1	2	yes	—
13	C₂×#117×C₅₃	C₂²	1	2	yes	—
14	C₅₃×#427	—	2	4	no	—
15	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
18	C₂×C₂²⋊C₈×C₅₃	—	2	4	no	—
19	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
21	C₅₃×#381	—	2	2	no	—
22	C₅₃×#380	C₂²	1	4	yes	—
23	C₅₃×#380	C₂²	1	4	yes	—
24	C₅₃×#379	—	2	2	no	—
25	C₄×C₂²⋊C₄×C₅₃	—	2	4	no	—
26	C₅₃×#340	C₂²	1	2	yes	complemented
27	C₅₃×#340	C₂²	1	4	yes	complemented
28	C₅₃×#340	C₂²	1	4	yes	complemented
29	C₅₃×#340	C₂²	1	2	yes	complemented
30	C₂⁵×C₅₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₅₃	—	2	2	no	—
32	C₂³×C₄×C₅₃	—	2	2	no	—
33	C₂³×C₄×C₅₃	—	2	4	no	—
34	C₂³×C₄×C₅₃	—	2	4	no	—
35	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₅₃	D₄	1	2	yes	—
37	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₅₃	—	2	2	no	—
40	C₂²×C₈×C₅₃	—	2	4	no	—
41	C₂²×C₈×C₅₃	—	2	4	no	—
42	C₂²×C₈×C₅₃	D₄	1	4	yes	—
43	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
46	#117×C₅₃	—	2	4	no	—
47	#117×C₅₃	—	2	4	no	—
48	#117×C₅₃	—	2	4	no	—
49	#117×C₅₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
51	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
53	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
57	C₂×C₄²×C₅₃	—	2	2	no	—
58	C₂×C₄²×C₅₃	—	2	2	no	—
59	#107×C₅₃	—	2	2	no	—
60	#107×C₅₃	—	2	2	no	—
61	#106×C₅₃	—	2	4	no	—
62	C₂²⋊C₈×C₅₃	—	2	4	no	—
63	C₂²⋊C₈×C₅₃	—	2	4	no	—
64	#95×C₅₃	—	2	4	no	—
65	#95×C₅₃	—	2	4	no	—
66	C₂⁴×C₅₃	—	2	2	no	—
67	C₂⁴×C₅₃	—	2	4	no	—
68	C₂⁴×C₅₃	—	2	4	no	—
69	C₂⁴×C₅₃	—	4	2	no	—
70	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
71	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	—	2	2	no	—
73	C₂²×C₄×C₅₃	—	2	4	no	—
74	C₂²×C₄×C₅₃	—	2	4	no	—
75	C₂²×C₄×C₅₃	—	2	8	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	4	no	—
80	C₂²×C₄×C₅₃	—	2	2	no	—
81	C₂²×C₄×C₅₃	—	2	2	no	—
82	C₂²×C₄×C₅₃	—	2	4	no	—
83	C₂²×C₄×C₅₃	—	4	4	no	—
84	C₂²×C₄×C₅₃	—	4	4	no	—
85	C₂²×C₄×C₅₃	—	4	8	no	—
86	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	#41	1	2	yes	—
90	C₂²×C₄×C₅₃	#41	1	4	yes	—
91	C₂²×C₄×C₅₃	#41	1	4	yes	—
92	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₅₃	—	2	8	no	—
94	C₂×C₈×C₅₃	—	2	2	no	—
95	C₂×C₈×C₅₃	—	2	2	no	—
96	C₂×C₈×C₅₃	—	2	2	no	—
97	C₂×C₈×C₅₃	—	2	4	no	—
98	C₂×C₈×C₅₃	—	4	4	no	—
99	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
101	C₄⋊C₄×C₅₃	—	2	2	no	—
102	C₄⋊C₄×C₅₃	—	2	2	no	—
103	C₄⋊C₄×C₅₃	—	2	2	no	—
104	C₄⋊C₄×C₅₃	—	2	2	no	—
105	C₄⋊C₄×C₅₃	—	2	4	no	—
106	C₄⋊C₄×C₅₃	—	2	4	no	—
107	C₂²⋊C₄×C₅₃	—	4	8	no	—
108	C₂²⋊C₄×C₅₃	—	4	4	no	—
109	C₂²⋊C₄×C₅₃	—	4	4	no	—
110	C₂²⋊C₄×C₅₃	—	4	8	no	—
111	C₄²×C₅₃	—	4	4	no	—
112	C₄²×C₅₃	—	4	4	no	—
113	C₂³×C₅₃	—	2	2	no	—
114	C₂³×C₅₃	—	2	2	no	—
115	C₂³×C₅₃	—	2	8	no	—
116	C₂³×C₅₃	—	2	2	no	—
117	C₂³×C₅₃	—	2	4	no	—
118	C₂³×C₅₃	—	2	2	no	—
119	C₂³×C₅₃	—	2	4	no	—
120	C₂³×C₅₃	—	4	16	no	—
121	C₂³×C₅₃	—	4	4	no	—
122	C₂³×C₅₃	—	4	4	no	—
123	C₂³×C₅₃	#121	1	2	yes	—
124	C₂³×C₅₃	#123	1	4	yes	—
125	C₂³×C₅₃	#135	1	4	yes	—
126	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
127	C₂×C₄×C₅₃	—	2	2	no	—
128	C₂×C₄×C₅₃	—	2	4	no	—
129	C₂×C₄×C₅₃	—	4	4	no	—
130	C₂×C₄×C₅₃	—	4	2	no	—
131	C₂×C₄×C₅₃	—	4	2	no	—
132	C₂×C₄×C₅₃	—	4	4	no	—
133	C₂×C₄×C₅₃	—	4	8	no	—
134	C₂×C₄×C₅₃	—	4	2	no	—
135	C₂×C₄×C₅₃	—	4	2	no	—
136	C₂×C₄×C₅₃	—	4	4	no	—
137	C₂×C₄×C₅₃	—	4	4	no	—
138	C₂×C₄×C₅₃	—	4	4	no	—
139	C₂×C₄×C₅₃	—	4	4	no	—
140	C₂×C₄×C₅₃	—	4	4	no	—
141	C₂×C₄×C₅₃	#121	1	2	yes	—
142	C₂×C₄×C₅₃	#123	1	4	yes	—
143	C₂×C₄×C₅₃	#123	1	4	yes	—
144	C₂×C₄×C₅₃	#124	1	4	yes	—
145	C₂×C₄×C₅₃	#126	1	8	yes	—
146	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
148	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
149	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
150	C₈×C₅₃	—	2	2	no	—
151	C₈×C₅₃	—	2	2	no	—
152	C₈×C₅₃	—	4	2	no	—
153	#23638	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂²×C₅₃	—	2	8	no	—
155	C₂²×C₅₃	—	2	2	no	—
156	C₂²×C₅₃	—	2	2	no	—
157	C₂²×C₅₃	—	2	8	no	—
158	C₂²×C₅₃	—	2	4	no	—
159	C₂²×C₅₃	—	4	16	no	—
160	C₂²×C₅₃	—	4	4	no	—
161	C₂²×C₅₃	—	4	2	no	—
162	C₂²×C₅₃	—	4	2	no	—
163	C₂²×C₅₃	#397	1	4	yes	—
164	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
165	C₂²×C₅₃	C₂×#123	1	2	yes	—
166	C₂²×C₅₃	C₂×#135	1	2	yes	—
167	C₂²×C₅₃	#575	1	2	yes	—
168	C₄×C₅₃	—	4	2	no	—
169	C₄×C₅₃	—	8	4	no	—
170	C₄×C₅₃	—	8	2	no	—
171	C₄×C₅₃	—	8	2	no	—
172	C₄×C₅₃	#397	1	4	yes	—
173	C₄×C₅₃	C₂×#123	1	1	yes	characteristic
174	C₄×C₅₃	C₂×#124	1	1	yes	characteristic
175	C₄×C₅₃	C₂×#126	1	2	yes	—
176	C₂×#427	C₂×C₅₃	1	1	yes	characteristic, complemented
177	C₂²×C₂²⋊C₈	C₂×C₅₃	1	1	yes	characteristic
178	#2280	C₂×C₅₃	1	2	yes	—
179	#2077	C₂×C₅₃	1	4	yes	complemented
180	#2076	C₂×C₅₃	1	2	yes	complemented
181	#2075	C₂×C₅₃	1	2	yes	complemented
182	#1735	C₂×C₅₃	1	2	yes	complemented
183	#1735	C₂×C₅₃	1	1	yes	characteristic, complemented
184	C₂×C₅₃	—	2	4	no	—
185	C₂×C₅₃	—	4	4	no	—
186	C₂×C₅₃	C₂×#397	1	1	yes	characteristic
187	C₂×C₅₃	#3050	1	1	yes	characteristic
188	C₂×C₅₃	#3054	1	1	yes	characteristic
189	C₂×C₅₃	#3091	1	4	yes	—
190	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
191	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
192	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
193	C₂×#117	C₂²×C₅₃	1	2	yes	—
194	C₂×#117	C₂²×C₅₃	1	2	yes	—
195	#427	—	2	4	no	—
196	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
197	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
198	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
199	C₂×C₂²⋊C₈	—	2	4	no	—
200	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
202	#381	—	2	2	no	—
203	#380	C₂²×C₅₃	1	4	yes	—
204	#380	C₂²×C₅₃	1	4	yes	—
205	#379	—	2	2	no	—
206	C₄×C₂²⋊C₄	—	2	4	no	—
207	#340	C₂²×C₅₃	1	2	yes	complemented
208	#340	C₂²×C₅₃	1	4	yes	complemented
209	#340	C₂²×C₅₃	1	4	yes	complemented
210	#340	C₂²×C₅₃	1	2	yes	complemented
211	C₅₃	#23638	1	1	yes	characteristic, direct product factor, Sylow
212	C₂⁵	D₄×C₅₃	1	1	yes	characteristic
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	D₄×C₅₃	1	2	yes	—
218	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
220	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	D₄×C₅₃	1	4	yes	—
225	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
226	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
228	#117	—	2	4	no	—
229	#117	—	2	4	no	—
230	#117	—	2	4	no	—
231	#117	—	2	4	no	—
232	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
233	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	4	no	—
238	C₂×C₂²⋊C₄	—	2	4	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	#107	—	2	2	no	—
242	#107	—	2	2	no	—
243	#106	—	2	4	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	C₂²⋊C₈	—	2	4	no	—
246	#95	—	2	4	no	—
247	#95	—	2	4	no	—
248	C₂⁴	—	2	2	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	4	2	no	—
252	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
253	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	—	4	8	no	—
268	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
271	C₂²×C₄	#41×C₅₃	1	2	yes	—
272	C₂²×C₄	#41×C₅₃	1	4	yes	—
273	C₂²×C₄	#41×C₅₃	1	4	yes	—
274	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₂²⋊C₄	—	4	8	no	—
290	C₂²⋊C₄	—	4	4	no	—
291	C₂²⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	4	8	no	—
293	C₄²	—	4	4	no	—
294	C₄²	—	4	4	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	8	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	4	16	no	—
303	C₂³	—	4	4	no	—
304	C₂³	—	4	4	no	—
305	C₂³	#121×C₅₃	1	2	yes	—
306	C₂³	#123×C₅₃	1	4	yes	—
307	C₂³	#135×C₅₃	1	4	yes	—
308	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	#121×C₅₃	1	2	yes	—
324	C₂×C₄	#123×C₅₃	1	4	yes	—
325	C₂×C₄	#123×C₅₃	1	4	yes	—
326	C₂×C₄	#124×C₅₃	1	4	yes	—
327	C₂×C₄	#126×C₅₃	1	8	yes	—
328	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
330	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
331	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	—	2	2	no	—
334	C₈	—	4	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	4	16	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	2	no	—
344	C₂²	C₅₃×#397	1	4	yes	—
345	C₂²	C₂×#121×C₅₃	1	1	yes	characteristic
346	C₂²	C₂×#123×C₅₃	1	2	yes	—
347	C₂²	C₂×#135×C₅₃	1	2	yes	—
348	C₂²	C₅₃×#575	1	2	yes	—
349	C₄	—	4	2	no	—
350	C₄	—	8	2	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	4	no	—
353	C₄	C₅₃×#397	1	4	yes	—
354	C₄	C₂×#123×C₅₃	1	1	yes	characteristic
355	C₄	C₂×#124×C₅₃	1	1	yes	characteristic
356	C₄	C₂×#126×C₅₃	1	2	yes	—
357	C₂	—	2	4	no	—
358	C₂	—	4	4	no	—
359	C₂	C₂×C₅₃×#397	1	1	yes	characteristic
360	C₂	C₅₃×#3050	1	1	yes	characteristic
361	C₂	C₅₃×#3054	1	1	yes	characteristic
362	C₂	C₅₃×#3091	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₂²×D₄
prime radical	C₂⁵×C₅₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ C₂⁴×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#427	C₂	semidirect
4. C₅₃×#2077	C₂	semidirect
5. C₅₃×#2076	C₂	semidirect
6. C₅₃×#2075	C₂	semidirect
7. C₅₃×#1735	C₂	semidirect
8. C₅₃×#1735	C₂	semidirect
15. C₂×#107×C₅₃	C₂²	semidirect
16. C₂×#107×C₅₃	C₂²	semidirect
17. C₂×#106×C₅₃	C₂²	semidirect
26. C₅₃×#340	C₂²	semidirect
27. C₅₃×#340	C₂²	semidirect
28. C₅₃×#340	C₂²	semidirect
29. C₅₃×#340	C₂²	semidirect
153. #23638	C₅₃	direct (N × H)
176. C₂×#427	C₂×C₅₃	semidirect
179. #2077	C₂×C₅₃	semidirect
180. #2076	C₂×C₅₃	semidirect
181. #2075	C₂×C₅₃	semidirect
182. #1735	C₂×C₅₃	semidirect
183. #1735	C₂×C₅₃	semidirect
196. C₂×#107	C₂²×C₅₃	semidirect
197. C₂×#107	C₂²×C₅₃	semidirect
198. C₂×#106	C₂²×C₅₃	semidirect
207. #340	C₂²×C₅₃	semidirect
208. #340	C₂²×C₅₃	semidirect
209. #340	C₂²×C₅₃	semidirect
210. #340	C₂²×C₅₃	semidirect
211. C₅₃	#23638	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#427	2
C₂²×C₂²⋊C₈×C₅₃	2
C₅₃×#2280	2
C₅₃×#2077	2
C₅₃×#2076	2
C₅₃×#2075	2
C₅₃×#1735	2
#23638	53

Subgroups — C53×#23638 #27231150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#23638 #27231150