Subgroups — C₅₃×#22705 #27230217

Order 13568.

1054 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₅₃	C₂	1	2	yes	maximal
3	C₅₃×#1947	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1852	C₂	1	4	yes	maximal, complemented
5	C₅₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1808	C₂	1	2	yes	maximal, complemented
7	C₄×#107×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#340	C₂	1	2	yes	maximal, complemented
9	C₂³×C₈×C₅₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₅₃	—	2	2	no	—
11	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₅₃	C₂²	1	4	yes	—
13	C₈×D₄×C₅₃	C₄	1	8	yes	complemented
14	C₂×#107×C₅₃	C₂²	1	2	yes	—
15	C₂×#107×C₅₃	C₂²	1	4	yes	—
16	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#389	—	2	2	no	—
20	C₅₃×#385	—	2	4	no	—
21	C₅₃×#384	C₂²	1	2	yes	—
22	C₅₃×#380	C₂²	1	4	yes	—
23	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
24	C₅₃×#340	C₂²	1	4	yes	—
25	C₅₃×#340	C₂²	1	1	yes	characteristic
26	C₅₃×#340	C₂²	1	2	yes	—
27	C₅₃×#340	C₂²	1	1	yes	characteristic
28	C₅₃×#340	C₂²	1	2	yes	—
29	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅₃	—	2	4	no	—
31	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
32	C₂²×C₈×C₅₃	—	4	4	no	—
33	C₂²×C₈×C₅₃	C₂×C₄	1	8	yes	complemented
34	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
36	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
37	C₄×D₄×C₅₃	—	4	8	no	—
38	C₄×D₄×C₅₃	C₂×C₄	1	4	yes	—
39	C₄×D₄×C₅₃	Q₈	1	4	yes	—
40	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
44	C₂×C₄⋊C₄×C₅₃	—	4	4	no	—
45	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
47	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
49	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
51	C₂×C₄²×C₅₃	—	2	2	no	—
52	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
53	#107×C₅₃	—	2	4	no	—
54	#107×C₅₃	—	4	4	no	—
55	C₄⋊C₈×C₅₃	C₂×C₄	1	4	yes	complemented
56	C₂²⋊C₈×C₅₃	C₂×C₄	1	8	yes	complemented
57	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
58	#95×C₅₃	—	2	2	no	—
59	#95×C₅₃	—	2	4	no	—
60	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
61	C₂×D₄×C₅₃	C₄⋊C₄	1	4	yes	—
62	C₂×D₄×C₅₃	D₈	1	4	yes	—
63	C₂×D₄×C₅₃	Q₁₆	1	4	yes	—
64	C₂²×C₄×C₅₃	—	2	4	no	—
65	C₂²×C₄×C₅₃	—	2	4	no	—
66	C₂²×C₄×C₅₃	—	2	2	no	—
67	C₂²×C₄×C₅₃	—	2	2	no	—
68	C₂²×C₄×C₅₃	—	2	4	no	—
69	C₂²×C₄×C₅₃	—	4	8	no	—
70	C₂²×C₄×C₅₃	—	4	8	no	—
71	C₂²×C₄×C₅₃	—	8	4	no	—
72	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
73	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
77	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
78	C₂×C₈×C₅₃	—	2	2	no	—
79	C₂×C₈×C₅₃	—	2	4	no	—
80	C₂×C₈×C₅₃	—	2	2	no	—
81	C₂×C₈×C₅₃	—	4	8	no	—
82	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
83	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
84	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
85	C₄⋊C₄×C₅₃	—	2	2	no	—
86	C₄⋊C₄×C₅₃	—	2	2	no	—
87	C₄⋊C₄×C₅₃	—	2	4	no	—
88	C₄⋊C₄×C₅₃	—	2	2	no	—
89	C₄⋊C₄×C₅₃	—	2	4	no	—
90	C₄⋊C₄×C₅₃	—	4	8	no	—
91	C₄⋊C₄×C₅₃	—	4	4	no	—
92	C₄⋊C₄×C₅₃	—	8	2	no	—
93	C₄⋊C₄×C₅₃	C₄⋊C₄	1	4	yes	—
94	C₄⋊C₄×C₅₃	#41	1	4	yes	—
95	C₂²⋊C₄×C₅₃	—	4	8	no	—
96	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	8	yes	—
97	C₄²×C₅₃	—	4	4	no	—
98	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
99	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
100	C₂³×C₅₃	—	2	4	no	—
101	C₂³×C₅₃	—	2	4	no	—
102	C₂³×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
103	C₂³×C₅₃	C₂×D₈	1	4	yes	—
104	C₂³×C₅₃	C₂×Q₁₆	1	4	yes	—
105	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
106	D₄×C₅₃	#107	1	16	yes	complemented
107	C₂×C₄×C₅₃	—	2	4	no	—
108	C₂×C₄×C₅₃	—	2	2	no	—
109	C₂×C₄×C₅₃	—	2	4	no	—
110	C₂×C₄×C₅₃	—	2	4	no	—
111	C₂×C₄×C₅₃	—	2	8	no	—
112	C₂×C₄×C₅₃	—	2	4	no	—
113	C₂×C₄×C₅₃	—	4	2	no	—
114	C₂×C₄×C₅₃	—	4	2	no	—
115	C₂×C₄×C₅₃	—	4	4	no	—
116	C₂×C₄×C₅₃	—	4	2	no	—
117	C₂×C₄×C₅₃	—	4	4	no	—
118	C₂×C₄×C₅₃	—	4	2	no	—
119	C₂×C₄×C₅₃	—	4	2	no	—
120	C₂×C₄×C₅₃	—	4	4	no	—
121	C₂×C₄×C₅₃	—	8	16	no	—
122	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
123	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
126	C₂×C₄×C₅₃	C₂×Q₁₆	1	2	yes	—
127	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
128	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
129	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
130	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
131	C₈×C₅₃	—	2	2	no	—
132	C₈×C₅₃	—	2	2	no	—
133	C₈×C₅₃	—	2	4	no	—
134	#22705	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂²×C₅₃	—	2	4	no	—
136	C₂²×C₅₃	—	2	4	no	—
137	C₂²×C₅₃	—	2	8	no	—
138	C₂²×C₅₃	—	2	8	no	—
139	C₂²×C₅₃	C₂×#107	1	8	yes	—
140	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
141	C₂²×C₅₃	#546	1	2	yes	—
142	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
143	C₂²×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
144	C₂²×C₅₃	#577	1	2	yes	—
145	C₄×C₅₃	—	2	4	no	—
146	C₄×C₅₃	—	2	2	no	—
147	C₄×C₅₃	—	4	4	no	—
148	C₄×C₅₃	—	8	2	no	—
149	C₄×C₅₃	—	8	4	no	—
150	C₄×C₅₃	C₂×#107	1	4	yes	—
151	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
152	C₄×C₅₃	#518	1	1	yes	characteristic
153	C₄×C₅₃	#554	1	2	yes	—
154	C₂×C₈×D₄	C₂×C₅₃	1	1	yes	characteristic
155	D₄×C₄⋊C₄	C₂×C₅₃	1	2	yes	—
156	#1947	C₂×C₅₃	1	2	yes	complemented
157	#1852	C₂×C₅₃	1	4	yes	complemented
158	#1834	C₂×C₅₃	1	1	yes	characteristic, complemented
159	#1808	C₂×C₅₃	1	2	yes	complemented
160	C₄×#107	C₂×C₅₃	1	1	yes	characteristic, complemented
161	C₂×#340	C₂×C₅₃	1	2	yes	complemented
162	C₂×C₅₃	—	2	8	no	—
163	C₂×C₅₃	#2349	1	1	yes	characteristic
164	C₂×C₅₃	C₂²×#107	1	1	yes	characteristic
165	C₂×C₅₃	#2912	1	1	yes	characteristic
166	C₂×C₅₃	#3294	1	2	yes	—
167	C₂×C₅₃	#3299	1	2	yes	—
168	C₂³×C₈	C₂²×C₅₃	1	2	yes	—
169	C₂×C₄×D₄	—	2	2	no	—
170	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
171	C₂²×C₄⋊C₄	C₂²×C₅₃	1	4	yes	—
172	C₈×D₄	C₄×C₅₃	1	8	yes	complemented
173	C₂×#107	C₂²×C₅₃	1	2	yes	—
174	C₂×#107	C₂²×C₅₃	1	4	yes	—
175	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
176	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
178	#389	—	2	2	no	—
179	#385	—	2	4	no	—
180	#384	C₂²×C₅₃	1	2	yes	—
181	#380	C₂²×C₅₃	1	4	yes	—
182	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
183	#340	C₂²×C₅₃	1	1	yes	characteristic
184	#340	C₂²×C₅₃	1	2	yes	—
185	#340	C₂²×C₅₃	1	2	yes	—
186	#340	C₂²×C₅₃	1	4	yes	—
187	#340	C₂²×C₅₃	1	1	yes	characteristic
188	C₅₃	#22705	1	1	yes	characteristic, direct product factor, Sylow
189	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
190	C₂³×C₄	—	2	4	no	—
191	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
192	C₂²×C₈	—	4	4	no	—
193	C₂²×C₈	C₂×C₄×C₅₃	1	8	yes	complemented
194	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
195	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
196	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
197	C₄×D₄	—	4	8	no	—
198	C₄×D₄	C₂×C₄×C₅₃	1	4	yes	—
199	C₄×D₄	Q₈×C₅₃	1	4	yes	—
200	C₂×C₄⋊C₄	—	2	8	no	—
201	C₂×C₄⋊C₄	—	2	4	no	—
202	C₂×C₄⋊C₄	—	2	2	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	4	4	no	—
205	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
207	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
208	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
209	C₂×C₂²⋊C₄	—	2	4	no	—
210	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
211	C₂×C₄²	—	2	2	no	—
212	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
213	#107	—	2	4	no	—
214	#107	—	4	4	no	—
215	C₄⋊C₈	C₂×C₄×C₅₃	1	4	yes	complemented
216	C₂²⋊C₈	C₂×C₄×C₅₃	1	8	yes	complemented
217	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	complemented
218	#95	—	2	2	no	—
219	#95	—	2	4	no	—
220	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
221	C₂×D₄	C₄⋊C₄×C₅₃	1	4	yes	—
222	C₂×D₄	D₈×C₅₃	1	4	yes	—
223	C₂×D₄	Q₁₆×C₅₃	1	4	yes	—
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	4	8	no	—
230	C₂²×C₄	—	4	8	no	—
231	C₂²×C₄	—	8	4	no	—
232	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
233	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
235	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
236	C₂²×C₄	C₂×Q₈×C₅₃	1	4	yes	—
237	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	—	2	4	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	4	8	no	—
242	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
243	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
244	C₂×C₈	C₂²×C₄×C₅₃	1	4	yes	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	2	2	no	—
247	C₄⋊C₄	—	2	4	no	—
248	C₄⋊C₄	—	2	2	no	—
249	C₄⋊C₄	—	2	4	no	—
250	C₄⋊C₄	—	4	8	no	—
251	C₄⋊C₄	—	4	4	no	—
252	C₄⋊C₄	—	8	2	no	—
253	C₄⋊C₄	C₄⋊C₄×C₅₃	1	4	yes	—
254	C₄⋊C₄	#41×C₅₃	1	4	yes	—
255	C₂²⋊C₄	—	4	8	no	—
256	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	8	yes	—
257	C₄²	—	4	4	no	—
258	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
259	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
260	C₂³	—	2	4	no	—
261	C₂³	—	2	4	no	—
262	C₂³	C₂×C₄⋊C₄×C₅₃	1	4	yes	—
263	C₂³	C₂×D₈×C₅₃	1	4	yes	—
264	C₂³	C₂×Q₁₆×C₅₃	1	4	yes	—
265	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
266	D₄	#107×C₅₃	1	16	yes	complemented
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	2	4	no	—
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	4	4	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	—	4	4	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	8	16	no	—
282	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
283	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	4	yes	—
284	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
285	C₂×C₄	C₂×D₈×C₅₃	1	2	yes	—
286	C₂×C₄	C₂×Q₁₆×C₅₃	1	2	yes	—
287	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
288	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
289	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
290	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
291	C₈	—	2	2	no	—
292	C₈	—	2	2	no	—
293	C₈	—	2	4	no	—
294	C₂²	—	2	8	no	—
295	C₂²	—	2	8	no	—
296	C₂²	—	2	4	no	—
297	C₂²	—	2	4	no	—
298	C₂²	C₂×#107×C₅₃	1	8	yes	—
299	C₂²	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
300	C₂²	C₅₃×#546	1	2	yes	—
301	C₂²	C₂²×D₈×C₅₃	1	1	yes	characteristic
302	C₂²	C₂²×Q₁₆×C₅₃	1	1	yes	characteristic
303	C₂²	C₅₃×#577	1	2	yes	—
304	C₄	—	2	4	no	—
305	C₄	—	2	2	no	—
306	C₄	—	4	4	no	—
307	C₄	—	8	4	no	—
308	C₄	—	8	2	no	—
309	C₄	C₂×#107×C₅₃	1	4	yes	—
310	C₄	C₄×#41×C₅₃	1	1	yes	characteristic
311	C₄	C₅₃×#518	1	1	yes	characteristic
312	C₄	C₅₃×#554	1	2	yes	—
313	C₂	—	2	8	no	—
314	C₂	C₅₃×#2349	1	1	yes	characteristic
315	C₂	C₂²×#107×C₅₃	1	1	yes	characteristic
316	C₂	C₅₃×#2912	1	1	yes	characteristic
317	C₂	C₅₃×#3294	1	2	yes	—
318	C₂	C₅₃×#3299	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	C₂²×D₄×C₅₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₃×#1947	C₂	semidirect
4. C₅₃×#1852	C₂	semidirect
5. C₅₃×#1834	C₂	semidirect
6. C₅₃×#1808	C₂	semidirect
7. C₄×#107×C₅₃	C₂	semidirect
8. C₂×C₅₃×#340	C₂	semidirect
13. C₈×D₄×C₅₃	C₄	semidirect
33. C₂²×C₈×C₅₃	C₂×C₄	semidirect
55. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
56. C₂²⋊C₈×C₅₃	C₂×C₄	semidirect
57. C₄×C₈×C₅₃	C₂×C₄	semidirect
106. D₄×C₅₃	#107	semidirect
134. #22705	C₅₃	direct (N × H)
156. #1947	C₂×C₅₃	semidirect
157. #1852	C₂×C₅₃	semidirect
158. #1834	C₂×C₅₃	semidirect
159. #1808	C₂×C₅₃	semidirect
160. C₄×#107	C₂×C₅₃	semidirect
161. C₂×#340	C₂×C₅₃	semidirect
172. C₈×D₄	C₄×C₅₃	semidirect
188. C₅₃	#22705	direct (N × H)
193. C₂²×C₈	C₂×C₄×C₅₃	semidirect
215. C₄⋊C₈	C₂×C₄×C₅₃	semidirect
216. C₂²⋊C₈	C₂×C₄×C₅₃	semidirect
217. C₄×C₈	C₂×C₄×C₅₃	semidirect
266. D₄	#107×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₅₃	2
D₄×C₄⋊C₄×C₅₃	2
C₅₃×#1947	2
C₅₃×#1852	2
C₅₃×#1834	2
C₅₃×#1808	2
C₄×#107×C₅₃	2
C₂×C₅₃×#340	2
#22705	53

Subgroups — C53×#22705 #27230217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22705 #27230217