Subgroups — C₂×C₅₃×#2375 #27241850

Order 13568.

4246 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#120×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2375	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅₃×#390	C₂	1	3	yes	maximal, complemented
4	C₂×C₅₃×#388	C₂	1	6	yes	maximal, complemented
5	C₂×C₅₃×#386	C₂	1	3	yes	maximal, complemented
6	C₂×C₅₃×#379	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₅₃	C₂²	1	3	yes	—
9	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
10	C₂×#120×C₅₃	C₄	1	16	yes	complemented
11	C₂×#120×C₅₃	C₂²	1	8	yes	—
12	C₂²×C₄⋊C₄×C₅₃	C₂²	1	3	yes	complemented
13	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	6	yes	—
14	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	6	yes	—
15	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	3	yes	—
16	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	3	yes	complemented
17	C₂²×C₄²×C₅₃	C₂²	1	3	yes	complemented
18	C₅₃×#390	C₂²	1	24	yes	complemented
19	C₅₃×#388	C₂²	1	48	yes	complemented
20	C₅₃×#386	C₂²	1	24	yes	complemented
21	C₅₃×#379	C₂²	1	16	yes	complemented
22	C₂×#95×C₅₃	C₂²	1	6	yes	complemented
23	C₂⁵×C₅₃	—	4	6	no	—
24	C₂⁵×C₅₃	—	4	6	no	—
25	C₂⁵×C₅₃	C₂×C₄	1	8	yes	complemented
26	C₂⁵×C₅₃	C₂³	1	3	yes	—
27	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
28	C₂⁵×C₅₃	C₂³	1	4	yes	—
29	C₂²×D₄×C₅₃	—	4	6	no	—
30	C₂²×D₄×C₅₃	—	4	6	no	—
31	C₂²×D₄×C₅₃	C₂×C₄	1	24	yes	—
32	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
33	C₂³×C₄×C₅₃	—	4	6	no	—
34	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
35	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
37	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
38	#120×C₅₃	C₂×C₄	1	64	yes	complemented
39	C₂×C₄⋊C₄×C₅₃	—	4	6	no	—
40	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
41	C₂×C₂²⋊C₄×C₅₃	—	4	12	no	—
42	C₂×C₂²⋊C₄×C₅₃	—	4	12	no	—
43	C₂×C₂²⋊C₄×C₅₃	—	4	6	no	—
44	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	24	yes	complemented
45	C₂×C₂²⋊C₄×C₅₃	C₂³	1	24	yes	—
46	C₂×C₂²⋊C₄×C₅₃	C₂³	1	24	yes	—
47	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
48	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	complemented
49	C₂×C₄²×C₅₃	—	4	6	no	—
50	C₂×C₄²×C₅₃	C₂³	1	12	yes	complemented
51	#95×C₅₃	C₂³	1	24	yes	complemented
52	C₂⁴×C₅₃	—	2	6	no	—
53	C₂⁴×C₅₃	—	2	12	no	—
54	C₂⁴×C₅₃	—	2	12	no	—
55	C₂⁴×C₅₃	—	2	6	no	—
56	C₂⁴×C₅₃	—	2	6	no	—
57	C₂⁴×C₅₃	—	2	6	no	—
58	C₂⁴×C₅₃	—	4	48	no	—
59	C₂⁴×C₅₃	—	4	12	no	—
60	C₂⁴×C₅₃	—	4	12	no	—
61	C₂⁴×C₅₃	—	4	48	no	—
62	C₂⁴×C₅₃	—	4	16	no	—
63	C₂⁴×C₅₃	C₂²×C₄	1	12	yes	—
64	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
65	C₂⁴×C₅₃	C₂²×C₄	1	16	yes	complemented
66	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
67	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
68	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
69	C₂×D₄×C₅₃	—	4	48	no	—
70	C₂×D₄×C₅₃	—	4	12	no	—
71	C₂×D₄×C₅₃	—	4	12	no	—
72	C₂×D₄×C₅₃	C₂²×C₄	1	48	yes	—
73	C₂²×C₄×C₅₃	—	2	6	no	—
74	C₂²×C₄×C₅₃	—	2	6	no	—
75	C₂²×C₄×C₅₃	—	2	12	no	—
76	C₂²×C₄×C₅₃	—	2	12	no	—
77	C₂²×C₄×C₅₃	—	2	12	no	—
78	C₂²×C₄×C₅₃	—	2	12	no	—
79	C₂²×C₄×C₅₃	—	4	12	no	—
80	C₂²×C₄×C₅₃	—	4	16	no	—
81	C₂²×C₄×C₅₃	C₂²×C₄	1	12	yes	—
82	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
83	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
84	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
85	C₄⋊C₄×C₅₃	—	4	12	no	—
86	C₂²⋊C₄×C₅₃	—	4	24	no	—
87	C₂²⋊C₄×C₅₃	—	4	24	no	—
88	C₂²⋊C₄×C₅₃	—	4	12	no	—
89	C₂²⋊C₄×C₅₃	C₂²×C₄	1	48	yes	complemented
90	C₄²×C₅₃	—	4	12	no	—
91	C₂³×C₅₃	—	2	24	no	—
92	C₂³×C₅₃	—	2	24	no	—
93	C₂³×C₅₃	—	2	48	no	—
94	C₂³×C₅₃	—	2	6	no	—
95	C₂³×C₅₃	—	2	6	no	—
96	C₂³×C₅₃	—	2	6	no	—
97	C₂³×C₅₃	—	2	6	no	—
98	C₂³×C₅₃	—	2	12	no	—
99	C₂³×C₅₃	—	2	12	no	—
100	C₂³×C₅₃	—	4	48	no	—
101	C₂³×C₅₃	—	4	128	no	—
102	C₂³×C₅₃	—	4	48	no	—
103	C₂³×C₅₃	—	4	16	no	—
104	C₂³×C₅₃	—	4	12	no	—
105	C₂³×C₅₃	—	4	12	no	—
106	C₂³×C₅₃	—	4	24	no	—
107	C₂³×C₅₃	—	4	4	no	—
108	C₂³×C₅₃	—	4	12	no	—
109	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
110	C₂³×C₅₃	C₂³×C₄	1	12	yes	—
111	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
112	C₂³×C₅₃	H(5,𝔽₂)	1	6	yes	—
113	C₂³×C₅₃	H(5,𝔽₂)	1	6	yes	—
114	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
115	D₄×C₅₃	—	4	48	no	—
116	C₂×C₄×C₅₃	—	2	24	no	—
117	C₂×C₄×C₅₃	—	2	6	no	—
118	C₂×C₄×C₅₃	—	2	6	no	—
119	C₂×C₄×C₅₃	—	2	12	no	—
120	C₂×C₄×C₅₃	—	2	12	no	—
121	C₂×C₄×C₅₃	—	2	12	no	—
122	C₂×C₄×C₅₃	—	2	12	no	—
123	C₂×C₄×C₅₃	—	4	16	no	—
124	C₂×C₄×C₅₃	—	4	24	no	—
125	C₂×C₄×C₅₃	—	4	8	no	—
126	C₂×C₄×C₅₃	C₂³×C₄	1	12	yes	—
127	C₂×#2375	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂²×C₅₃	—	2	12	no	—
129	C₂²×C₅₃	—	2	12	no	—
130	C₂²×C₅₃	—	2	24	no	—
131	C₂²×C₅₃	—	4	64	no	—
132	C₂²×C₅₃	—	4	16	no	—
133	C₂²×C₅₃	—	4	48	no	—
134	C₂²×C₅₃	—	4	6	no	—
135	C₂²×C₅₃	—	4	12	no	—
136	C₂²×C₅₃	—	4	6	no	—
137	C₂²×C₅₃	—	4	2	no	—
138	C₂²×C₅₃	—	4	6	no	—
139	C₂²×C₅₃	#518	1	12	yes	—
140	C₂²×C₅₃	#560	1	12	yes	—
141	C₂²×C₅₃	H(3,𝔽₄)	1	4	yes	—
142	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
143	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	3	yes	—
144	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	3	yes	—
145	C₄×C₅₃	—	2	12	no	—
146	C₄×C₅₃	—	4	12	no	—
147	C₄×C₅₃	—	4	4	no	—
148	C₂²×#120	C₂×C₅₃	1	1	yes	characteristic
149	#2375	C₂×C₅₃	1	16	yes	direct product factor
150	C₂×#390	C₂×C₅₃	1	3	yes	complemented
151	C₂×#388	C₂×C₅₃	1	6	yes	complemented
152	C₂×#386	C₂×C₅₃	1	3	yes	complemented
153	C₂×#379	C₂×C₅₃	1	2	yes	complemented
154	C₂×C₅₃	—	4	4	no	—
155	C₂×C₅₃	—	4	12	no	—
156	C₂×C₅₃	#2375	1	8	yes	direct product factor
157	C₂×C₅₃	C₂×#518	1	3	yes	—
158	C₂×C₅₃	C₂×#560	1	3	yes	—
159	C₂×C₅₃	C₂×H(3,𝔽₄)	1	1	yes	characteristic
160	C₂⁶	C₂²×C₅₃	1	1	yes	characteristic
161	C₂³×D₄	C₂²×C₅₃	1	3	yes	—
162	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
163	C₂×#120	C₄×C₅₃	1	16	yes	complemented
164	C₂×#120	C₂²×C₅₃	1	8	yes	—
165	C₂²×C₄⋊C₄	C₂²×C₅₃	1	3	yes	complemented
166	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	6	yes	—
167	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	6	yes	—
168	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	3	yes	—
169	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	3	yes	complemented
170	C₂²×C₄²	C₂²×C₅₃	1	3	yes	complemented
171	#390	C₂²×C₅₃	1	24	yes	complemented
172	#388	C₂²×C₅₃	1	48	yes	complemented
173	#386	C₂²×C₅₃	1	24	yes	complemented
174	#379	C₂²×C₅₃	1	16	yes	complemented
175	C₂×#95	C₂²×C₅₃	1	6	yes	complemented
176	C₅₃	C₂×#2375	1	1	yes	characteristic, direct product factor, Sylow
177	C₂⁵	—	4	6	no	—
178	C₂⁵	—	4	6	no	—
179	C₂⁵	C₂×C₄×C₅₃	1	8	yes	complemented
180	C₂⁵	C₂³×C₅₃	1	3	yes	—
181	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
182	C₂⁵	C₂³×C₅₃	1	4	yes	—
183	C₂²×D₄	—	4	6	no	—
184	C₂²×D₄	—	4	6	no	—
185	C₂²×D₄	C₂×C₄×C₅₃	1	24	yes	—
186	C₂²×D₄	C₂³×C₅₃	1	12	yes	—
187	C₂³×C₄	—	4	6	no	—
188	C₂³×C₄	C₂³×C₅₃	1	6	yes	—
189	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
190	C₂³×C₄	C₂³×C₅₃	1	3	yes	—
191	C₂³×C₄	C₂³×C₅₃	1	4	yes	complemented
192	#120	C₂×C₄×C₅₃	1	64	yes	complemented
193	C₂×C₄⋊C₄	—	4	6	no	—
194	C₂×C₄⋊C₄	C₂³×C₅₃	1	12	yes	complemented
195	C₂×C₂²⋊C₄	—	4	12	no	—
196	C₂×C₂²⋊C₄	—	4	12	no	—
197	C₂×C₂²⋊C₄	—	4	6	no	—
198	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	24	yes	complemented
199	C₂×C₂²⋊C₄	C₂³×C₅₃	1	24	yes	—
200	C₂×C₂²⋊C₄	C₂³×C₅₃	1	24	yes	—
201	C₂×C₂²⋊C₄	C₂³×C₅₃	1	12	yes	—
202	C₂×C₂²⋊C₄	C₂³×C₅₃	1	12	yes	complemented
203	C₂×C₄²	—	4	6	no	—
204	C₂×C₄²	C₂³×C₅₃	1	12	yes	complemented
205	#95	C₂³×C₅₃	1	24	yes	complemented
206	C₂⁴	—	2	6	no	—
207	C₂⁴	—	2	12	no	—
208	C₂⁴	—	2	12	no	—
209	C₂⁴	—	2	6	no	—
210	C₂⁴	—	2	6	no	—
211	C₂⁴	—	2	6	no	—
212	C₂⁴	—	4	48	no	—
213	C₂⁴	—	4	12	no	—
214	C₂⁴	—	4	12	no	—
215	C₂⁴	—	4	48	no	—
216	C₂⁴	—	4	16	no	—
217	C₂⁴	C₂²×C₄×C₅₃	1	12	yes	—
218	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
219	C₂⁴	C₂²×C₄×C₅₃	1	16	yes	complemented
220	C₂⁴	C₂⁴×C₅₃	1	6	yes	—
221	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
222	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
223	C₂×D₄	—	4	48	no	—
224	C₂×D₄	—	4	12	no	—
225	C₂×D₄	—	4	12	no	—
226	C₂×D₄	C₂²×C₄×C₅₃	1	48	yes	—
227	C₂²×C₄	—	2	6	no	—
228	C₂²×C₄	—	2	6	no	—
229	C₂²×C₄	—	2	12	no	—
230	C₂²×C₄	—	2	12	no	—
231	C₂²×C₄	—	2	12	no	—
232	C₂²×C₄	—	2	12	no	—
233	C₂²×C₄	—	4	12	no	—
234	C₂²×C₄	—	4	16	no	—
235	C₂²×C₄	C₂²×C₄×C₅₃	1	12	yes	—
236	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
237	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
238	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
239	C₄⋊C₄	—	4	12	no	—
240	C₂²⋊C₄	—	4	24	no	—
241	C₂²⋊C₄	—	4	24	no	—
242	C₂²⋊C₄	—	4	12	no	—
243	C₂²⋊C₄	C₂²×C₄×C₅₃	1	48	yes	complemented
244	C₄²	—	4	12	no	—
245	C₂³	—	2	24	no	—
246	C₂³	—	2	24	no	—
247	C₂³	—	2	48	no	—
248	C₂³	—	2	6	no	—
249	C₂³	—	2	12	no	—
250	C₂³	—	2	12	no	—
251	C₂³	—	2	6	no	—
252	C₂³	—	2	6	no	—
253	C₂³	—	2	6	no	—
254	C₂³	—	4	48	no	—
255	C₂³	—	4	48	no	—
256	C₂³	—	4	16	no	—
257	C₂³	—	4	128	no	—
258	C₂³	—	4	12	no	—
259	C₂³	—	4	12	no	—
260	C₂³	—	4	24	no	—
261	C₂³	—	4	4	no	—
262	C₂³	—	4	12	no	—
263	C₂³	C₂³×C₄×C₅₃	1	12	yes	—
264	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
265	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
266	C₂³	H(5,𝔽₂)×C₅₃	1	6	yes	—
267	C₂³	H(5,𝔽₂)×C₅₃	1	6	yes	—
268	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
269	D₄	—	4	48	no	—
270	C₂×C₄	—	2	24	no	—
271	C₂×C₄	—	2	6	no	—
272	C₂×C₄	—	2	6	no	—
273	C₂×C₄	—	2	12	no	—
274	C₂×C₄	—	2	12	no	—
275	C₂×C₄	—	2	12	no	—
276	C₂×C₄	—	2	12	no	—
277	C₂×C₄	—	4	16	no	—
278	C₂×C₄	—	4	24	no	—
279	C₂×C₄	—	4	8	no	—
280	C₂×C₄	C₂³×C₄×C₅₃	1	12	yes	—
281	C₂²	—	2	12	no	—
282	C₂²	—	2	12	no	—
283	C₂²	—	2	24	no	—
284	C₂²	—	4	64	no	—
285	C₂²	—	4	6	no	—
286	C₂²	—	4	12	no	—
287	C₂²	—	4	6	no	—
288	C₂²	—	4	2	no	—
289	C₂²	—	4	6	no	—
290	C₂²	—	4	48	no	—
291	C₂²	—	4	16	no	—
292	C₂²	C₅₃×#518	1	12	yes	—
293	C₂²	C₅₃×#560	1	12	yes	—
294	C₂²	C₅₃×H(3,𝔽₄)	1	4	yes	—
295	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
296	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	3	yes	—
297	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	3	yes	—
298	C₄	—	2	12	no	—
299	C₄	—	4	12	no	—
300	C₄	—	4	4	no	—
301	C₂	—	4	12	no	—
302	C₂	—	4	4	no	—
303	C₂	C₅₃×#2375	1	8	yes	direct product factor
304	C₂	C₂×C₅₃×#518	1	3	yes	—
305	C₂	C₂×C₅₃×#560	1	3	yes	—
306	C₂	C₂×C₅₃×H(3,𝔽₄)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂²×#120×C₅₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2375	C₂	direct (N × H)
3. C₂×C₅₃×#390	C₂	semidirect
4. C₂×C₅₃×#388	C₂	semidirect
5. C₂×C₅₃×#386	C₂	semidirect
6. C₂×C₅₃×#379	C₂	semidirect
9. C₂⁴×C₄×C₅₃	C₂²	semidirect
10. C₂×#120×C₅₃	C₄	semidirect
12. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
16. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
17. C₂²×C₄²×C₅₃	C₂²	semidirect
18. C₅₃×#390	C₂²	semidirect
19. C₅₃×#388	C₂²	semidirect
20. C₅₃×#386	C₂²	semidirect
21. C₅₃×#379	C₂²	semidirect
22. C₂×#95×C₅₃	C₂²	semidirect
25. C₂⁵×C₅₃	C₂×C₄	semidirect
37. C₂³×C₄×C₅₃	C₂³	semidirect
38. #120×C₅₃	C₂×C₄	semidirect
40. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
44. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
48. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
50. C₂×C₄²×C₅₃	C₂³	semidirect
51. #95×C₅₃	C₂³	semidirect
65. C₂⁴×C₅₃	C₂²×C₄	semidirect
89. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
127. C₂×#2375	C₅₃	direct (N × H)
149. #2375	C₂×C₅₃	direct (N × H)
150. C₂×#390	C₂×C₅₃	semidirect
151. C₂×#388	C₂×C₅₃	semidirect
152. C₂×#386	C₂×C₅₃	semidirect
153. C₂×#379	C₂×C₅₃	semidirect
156. C₂×C₅₃	#2375	direct (N × H)
162. C₂⁴×C₄	C₂²×C₅₃	semidirect
163. C₂×#120	C₄×C₅₃	semidirect
165. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
169. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
170. C₂²×C₄²	C₂²×C₅₃	semidirect
171. #390	C₂²×C₅₃	semidirect
172. #388	C₂²×C₅₃	semidirect
173. #386	C₂²×C₅₃	semidirect
174. #379	C₂²×C₅₃	semidirect
175. C₂×#95	C₂²×C₅₃	semidirect
176. C₅₃	C₂×#2375	direct (N × H)
179. C₂⁵	C₂×C₄×C₅₃	semidirect
191. C₂³×C₄	C₂³×C₅₃	semidirect
192. #120	C₂×C₄×C₅₃	semidirect
194. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
198. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
202. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
204. C₂×C₄²	C₂³×C₅₃	semidirect
205. #95	C₂³×C₅₃	semidirect
219. C₂⁴	C₂²×C₄×C₅₃	semidirect
243. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
303. C₂	C₅₃×#2375	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×#120×C₅₃	2
C₅₃×#2375	2
C₂×C₅₃×#390	2
C₂×C₅₃×#388	2
C₂×C₅₃×#386	2
C₂×C₅₃×#379	2
C₂×#2375	53

Subgroups — C2×C53×#2375 #27241850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2375 #27241850