Subgroups — C₅₃×#60826 #27268338

Order 13568.

2026 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3500	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3223	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3222	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3216	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3215	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3044	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3043	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3011	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3009	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
18	C₂×#137×C₅₃	C₂²	1	2	yes	—
19	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
20	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
21	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
22	C₅₃×#557	—	2	2	no	—
23	C₅₃×#556	—	2	2	no	—
24	C₅₃×#552	—	2	4	no	—
25	C₅₃×#548	—	2	2	no	—
26	C₅₃×#546	—	2	4	no	—
27	C₅₃×#546	—	2	2	no	—
28	C₅₃×#541	C₂²	1	4	yes	complemented
29	C₅₃×#536	C₂²	1	2	yes	—
30	C₅₃×#536	C₂²	1	1	yes	characteristic
31	C₅₃×#536	C₂²	1	2	yes	—
32	C₅₃×#535	C₂²	1	2	yes	—
33	C₅₃×#535	C₂²	1	1	yes	characteristic
34	C₅₃×#533	C₂²	1	4	yes	complemented
35	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#532	C₂²	1	2	yes	—
37	C₅₃×#532	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#124×C₅₃	C₂²	1	2	yes	—
40	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#519	C₂²	1	2	yes	complemented
42	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#497	C₂²	1	2	yes	complemented
44	C₅₃×#497	C₂²	1	4	yes	complemented
45	C₅₃×#497	C₂²	1	2	yes	complemented
46	C₅₃×#497	C₂²	1	4	yes	complemented
47	C₅₃×#494	C₂²	1	2	yes	complemented
48	C₅₃×#492	C₂²	1	2	yes	complemented
49	C₅₃×#491	C₂²	1	2	yes	complemented
50	C₅₃×#490	C₂²	1	2	yes	complemented
51	C₅₃×#489	C₂²	1	2	yes	complemented
52	C₅₃×#489	C₂²	1	4	yes	complemented
53	C₅₃×#489	C₂²	1	2	yes	complemented
54	C₅₃×#488	C₂²	1	4	yes	complemented
55	C₅₃×#464	C₂²	1	8	yes	complemented
56	C₅₃×#464	C₂²	1	8	yes	complemented
57	C₅₃×#462	C₂²	1	8	yes	complemented
58	C₅₃×#460	C₂²	1	8	yes	complemented
59	C₅₃×#452	C₂²	1	8	yes	—
60	C₅₃×#452	C₂²	1	8	yes	complemented
61	C₅₃×#451	C₂²	1	8	yes	complemented
62	C₅₃×#450	C₂²	1	8	yes	—
63	C₅₃×#433	C₂²	1	4	yes	complemented
64	C₅₃×#432	C₂²	1	4	yes	complemented
65	C₅₃×#424	C₂²	1	2	yes	complemented
66	C₅₃×#419	C₂²	1	2	yes	complemented
67	C₅₃×#418	C₂²	1	2	yes	—
68	C₅₃×#416	C₂²	1	2	yes	—
69	C₅₃×#416	C₂²	1	2	yes	complemented
70	C₅₃×#408	C₂²	1	2	yes	—
71	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
73	2₋¹⁺⁴×C₅₃	—	4	4	no	—
74	H(5,𝔽₂)×C₅₃	—	4	4	no	—
75	C₂×#41×C₅₃	—	2	1	no	—
76	C₂×#41×C₅₃	—	2	2	no	—
77	C₂×#41×C₅₃	—	2	1	no	—
78	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
79	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
80	C₂×#41×C₅₃	C₂³	1	2	yes	—
81	C₂×#41×C₅₃	C₂³	1	2	yes	—
82	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₅₃	—	2	1	no	—
84	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
85	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₅₃	—	2	2	no	—
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
91	#137×C₅₃	—	4	4	no	—
92	#137×C₅₃	—	4	4	no	—
93	C₂×Q₁₆×C₅₃	—	4	4	no	—
94	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
95	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
96	C₂×Q₁₆×C₅₃	C₂³	1	8	yes	—
97	C₂×SD₁₆×C₅₃	—	4	4	no	—
98	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
101	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
103	C₄⋊Q₈×C₅₃	—	2	2	no	—
104	C₄⋊Q₈×C₅₃	—	2	2	no	—
105	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
108	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
110	#127×C₅₃	C₂³	1	1	yes	characteristic
111	#127×C₅₃	C₂³	1	2	yes	—
112	#126×C₅₃	—	2	8	no	—
113	#125×C₅₃	—	2	8	no	—
114	#125×C₅₃	—	2	4	no	—
115	#125×C₅₃	C₂³	1	2	yes	—
116	#124×C₅₃	—	2	4	no	—
117	#124×C₅₃	—	2	2	no	—
118	#124×C₅₃	—	2	2	no	—
119	#124×C₅₃	C₂³	1	2	yes	—
120	#124×C₅₃	C₂³	1	1	yes	characteristic
121	#124×C₅₃	C₂³	1	2	yes	—
122	#124×C₅₃	C₂³	1	1	yes	characteristic
123	#124×C₅₃	C₂³	1	2	yes	—
124	#124×C₅₃	C₂³	1	2	yes	—
125	#123×C₅₃	—	2	2	no	—
126	#123×C₅₃	—	2	4	no	—
127	#123×C₅₃	—	2	4	no	—
128	C₂²⋊Q₈×C₅₃	—	2	2	no	—
129	C₂²⋊Q₈×C₅₃	—	2	4	no	—
130	C₂²⋊Q₈×C₅₃	—	2	2	no	—
131	C₂²⋊Q₈×C₅₃	—	2	4	no	—
132	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
133	#121×C₅₃	—	2	2	no	—
134	#121×C₅₃	—	2	4	no	—
135	#121×C₅₃	—	2	2	no	—
136	#121×C₅₃	—	2	4	no	—
137	#120×C₅₃	—	2	2	no	—
138	#120×C₅₃	—	2	4	no	—
139	C₄×Q₈×C₅₃	—	2	4	no	—
140	C₄×Q₈×C₅₃	—	2	4	no	—
141	C₄×Q₈×C₅₃	—	2	2	no	—
142	C₄×Q₈×C₅₃	D₄	1	2	yes	—
143	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
144	C₄×D₄×C₅₃	—	2	4	no	—
145	C₄×D₄×C₅₃	—	2	2	no	—
146	C₄×D₄×C₅₃	D₄	1	4	yes	—
147	C₄×D₄×C₅₃	D₄	1	2	yes	—
148	#117×C₅₃	—	2	4	no	—
149	#117×C₅₃	—	2	4	no	—
150	#117×C₅₃	C₂³	1	2	yes	—
151	#117×C₅₃	C₂³	1	1	yes	characteristic
152	#117×C₅₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
154	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
155	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
156	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
158	C₄⋊C₈×C₅₃	C₂³	1	8	yes	—
159	#103×C₅₃	C₂³	1	8	yes	—
160	#103×C₅₃	C₂³	1	4	yes	—
161	#103×C₅₃	C₂³	1	4	yes	—
162	#102×C₅₃	C₂³	1	8	yes	—
163	#102×C₅₃	C₂³	1	4	yes	—
164	#102×C₅₃	C₂³	1	4	yes	—
165	C₂²⋊C₈×C₅₃	C₂³	1	8	yes	—
166	#97×C₅₃	C₂³	1	2	yes	—
167	#97×C₅₃	C₂³	1	2	yes	—
168	#97×C₅₃	C₂³	1	2	yes	—
169	C₄×C₈×C₅₃	C₂³	1	2	yes	—
170	C₂⁴×C₅₃	—	2	2	no	—
171	C₂⁴×C₅₃	—	2	1	no	—
172	#41×C₅₃	—	2	4	no	—
173	#41×C₅₃	—	2	4	no	—
174	#41×C₅₃	—	2	4	no	—
175	#41×C₅₃	—	4	4	no	—
176	#41×C₅₃	—	4	4	no	—
177	#41×C₅₃	—	4	8	no	—
178	#41×C₅₃	—	4	4	no	—
179	#41×C₅₃	—	4	4	no	—
180	C₂×Q₈×C₅₃	—	2	2	no	—
181	C₂×Q₈×C₅₃	—	2	2	no	—
182	C₂×Q₈×C₅₃	—	2	2	no	—
183	C₂×Q₈×C₅₃	—	2	1	no	—
184	C₂×Q₈×C₅₃	—	2	4	no	—
185	C₂×Q₈×C₅₃	—	2	4	no	—
186	C₂×Q₈×C₅₃	—	2	4	no	—
187	C₂×Q₈×C₅₃	—	4	4	no	—
188	C₂×Q₈×C₅₃	—	4	4	no	—
189	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
191	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
192	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
193	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
194	C₂×D₄×C₅₃	—	2	2	no	—
195	C₂×D₄×C₅₃	—	2	1	no	—
196	C₂×D₄×C₅₃	—	2	2	no	—
197	C₂×D₄×C₅₃	—	2	1	no	—
198	C₂×D₄×C₅₃	—	2	2	no	—
199	C₂×D₄×C₅₃	—	2	1	no	—
200	C₂×D₄×C₅₃	—	2	4	no	—
201	C₂×D₄×C₅₃	—	2	2	no	—
202	C₂×D₄×C₅₃	—	2	4	no	—
203	C₂×D₄×C₅₃	—	4	4	no	—
204	C₂×D₄×C₅₃	—	4	8	no	—
205	C₂×D₄×C₅₃	—	4	4	no	—
206	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
209	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
210	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₅₃	—	2	2	no	—
212	C₂²×C₄×C₅₃	—	2	1	no	—
213	C₂²×C₄×C₅₃	—	2	2	no	—
214	C₂²×C₄×C₅₃	—	2	2	no	—
215	C₂²×C₄×C₅₃	—	2	1	no	—
216	C₂²×C₄×C₅₃	—	2	2	no	—
217	C₂²×C₄×C₅₃	—	2	1	no	—
218	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
222	Q₁₆×C₅₃	—	4	8	no	—
223	Q₁₆×C₅₃	—	4	4	no	—
224	Q₁₆×C₅₃	—	4	4	no	—
225	SD₁₆×C₅₃	—	4	8	no	—
226	SD₁₆×C₅₃	—	4	4	no	—
227	SD₁₆×C₅₃	—	4	4	no	—
228	M₁₆×C₅₃	—	2	4	no	—
229	C₂×C₈×C₅₃	—	2	4	no	—
230	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
231	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
232	C₄⋊C₄×C₅₃	—	2	4	no	—
233	C₄⋊C₄×C₅₃	—	2	4	no	—
234	C₄⋊C₄×C₅₃	—	2	2	no	—
235	C₄⋊C₄×C₅₃	—	2	8	no	—
236	C₄⋊C₄×C₅₃	—	2	4	no	—
237	C₄⋊C₄×C₅₃	—	2	2	no	—
238	C₄⋊C₄×C₅₃	—	2	4	no	—
239	C₄⋊C₄×C₅₃	—	2	8	no	—
240	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
242	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
243	C₂²⋊C₄×C₅₃	—	2	2	no	—
244	C₂²⋊C₄×C₅₃	—	2	8	no	—
245	C₂²⋊C₄×C₅₃	—	2	4	no	—
246	C₂²⋊C₄×C₅₃	—	2	2	no	—
247	C₂²⋊C₄×C₅₃	—	2	4	no	—
248	C₂²⋊C₄×C₅₃	—	2	4	no	—
249	C₂²⋊C₄×C₅₃	—	2	4	no	—
250	C₂²⋊C₄×C₅₃	—	2	2	no	—
251	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
252	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
253	C₄²×C₅₃	—	2	8	no	—
254	C₄²×C₅₃	—	2	2	no	—
255	C₄²×C₅₃	C₂×D₄	1	4	yes	—
256	C₄²×C₅₃	C₂×D₄	1	2	yes	—
257	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
259	C₄²×C₅₃	C₂⁴	1	2	yes	—
260	C₂³×C₅₃	—	2	1	no	—
261	C₂³×C₅₃	—	2	2	no	—
262	C₂³×C₅₃	—	2	1	no	—
263	C₂³×C₅₃	—	4	4	no	—
264	C₂³×C₅₃	—	4	2	no	—
265	C₂³×C₅₃	—	8	2	no	—
266	C₂³×C₅₃	—	8	4	no	—
267	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
268	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₅₃	—	2	2	no	—
270	Q₈×C₅₃	—	2	4	no	—
271	Q₈×C₅₃	—	2	4	no	—
272	Q₈×C₅₃	—	2	4	no	—
273	Q₈×C₅₃	—	2	2	no	—
274	Q₈×C₅₃	—	2	2	no	—
275	Q₈×C₅₃	—	4	4	no	—
276	Q₈×C₅₃	—	4	4	no	—
277	Q₈×C₅₃	—	4	4	no	—
278	Q₈×C₅₃	—	4	2	no	—
279	D₄×C₅₃	—	2	4	no	—
280	D₄×C₅₃	—	2	2	no	—
281	D₄×C₅₃	—	2	4	no	—
282	D₄×C₅₃	—	2	2	no	—
283	D₄×C₅₃	—	2	2	no	—
284	D₄×C₅₃	—	4	4	no	—
285	D₄×C₅₃	—	4	4	no	—
286	D₄×C₅₃	—	4	4	no	—
287	D₄×C₅₃	—	4	2	no	—
288	D₄×C₅₃	—	4	2	no	—
289	D₄×C₅₃	—	4	2	no	—
290	D₄×C₅₃	—	8	4	no	—
291	D₄×C₅₃	—	8	2	no	—
292	C₂×C₄×C₅₃	—	2	4	no	—
293	C₂×C₄×C₅₃	—	2	1	no	—
294	C₂×C₄×C₅₃	—	2	2	no	—
295	C₂×C₄×C₅₃	—	2	1	no	—
296	C₂×C₄×C₅₃	—	2	4	no	—
297	C₂×C₄×C₅₃	—	2	4	no	—
298	C₂×C₄×C₅₃	—	4	2	no	—
299	C₂×C₄×C₅₃	—	4	4	no	—
300	C₂×C₄×C₅₃	—	4	4	no	—
301	C₂×C₄×C₅₃	—	4	4	no	—
302	C₂×C₄×C₅₃	—	4	4	no	—
303	C₂×C₄×C₅₃	—	4	4	no	—
304	C₂×C₄×C₅₃	—	4	2	no	—
305	C₂×C₄×C₅₃	—	4	2	no	—
306	C₂×C₄×C₅₃	—	4	2	no	—
307	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
310	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
313	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
314	C₈×C₅₃	—	2	4	no	—
315	C₈×C₅₃	—	2	4	no	—
316	#60826	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂²×C₅₃	—	2	2	no	—
318	C₂²×C₅₃	—	2	4	no	—
319	C₂²×C₅₃	—	2	2	no	—
320	C₂²×C₅₃	—	4	2	no	—
321	C₂²×C₅₃	—	4	4	no	—
322	C₂²×C₅₃	—	4	2	no	—
323	C₂²×C₅₃	—	4	1	no	—
324	C₂²×C₅₃	—	4	2	no	—
325	C₂²×C₅₃	—	4	1	no	—
326	C₂²×C₅₃	—	16	2	no	—
327	C₂²×C₅₃	—	16	4	no	—
328	C₂²×C₅₃	#535	1	2	yes	—
329	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
330	C₄×C₅₃	—	2	2	no	—
331	C₄×C₅₃	—	2	4	no	—
332	C₄×C₅₃	—	2	2	no	—
333	C₄×C₅₃	—	2	2	no	—
334	C₄×C₅₃	—	4	4	no	—
335	C₄×C₅₃	—	4	1	no	—
336	C₄×C₅₃	—	4	2	no	—
337	C₄×C₅₃	—	4	1	no	—
338	C₄×C₅₃	—	4	4	no	—
339	C₄×C₅₃	#535	1	2	yes	—
340	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
341	#3509	C₂×C₅₃	1	1	yes	characteristic, complemented
342	#3500	C₂×C₅₃	1	1	yes	characteristic
343	#3223	C₂×C₅₃	1	4	yes	complemented
344	#3222	C₂×C₅₃	1	4	yes	complemented
345	#3216	C₂×C₅₃	1	4	yes	complemented
346	#3215	C₂×C₅₃	1	4	yes	complemented
347	#3152	C₂×C₅₃	1	1	yes	characteristic, complemented
348	C₂×#497	C₂×C₅₃	1	1	yes	characteristic, complemented
349	#3140	C₂×C₅₃	1	1	yes	characteristic, complemented
350	#3135	C₂×C₅₃	1	1	yes	characteristic, complemented
351	#3044	C₂×C₅₃	1	2	yes	complemented
352	#3043	C₂×C₅₃	1	2	yes	complemented
353	#3011	C₂×C₅₃	1	2	yes	complemented
354	#3009	C₂×C₅₃	1	2	yes	complemented
355	#2923	C₂×C₅₃	1	1	yes	characteristic, complemented
356	C₂×C₅₃	—	2	2	no	—
357	C₂×C₅₃	—	4	2	no	—
358	C₂×C₅₃	—	8	1	no	—
359	C₂×C₅₃	—	8	2	no	—
360	C₂×C₅₃	—	8	1	no	—
361	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
362	C₂×C₅₃	#3586	1	2	yes	—
363	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
364	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
365	C₂×#137	C₂²×C₅₃	1	2	yes	—
366	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
367	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
368	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
369	#557	—	2	2	no	—
370	#556	—	2	2	no	—
371	#552	—	2	4	no	—
372	#548	—	2	2	no	—
373	#546	—	2	4	no	—
374	#546	—	2	2	no	—
375	#541	C₂²×C₅₃	1	4	yes	complemented
376	#536	C₂²×C₅₃	1	2	yes	—
377	#536	C₂²×C₅₃	1	1	yes	characteristic
378	#536	C₂²×C₅₃	1	2	yes	—
379	#535	C₂²×C₅₃	1	2	yes	—
380	#535	C₂²×C₅₃	1	1	yes	characteristic
381	#533	C₂²×C₅₃	1	4	yes	complemented
382	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
383	#532	C₂²×C₅₃	1	1	yes	characteristic
384	#532	C₂²×C₅₃	1	2	yes	—
385	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
386	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
387	C₂×#124	C₂²×C₅₃	1	2	yes	—
388	#519	C₂²×C₅₃	1	2	yes	complemented
389	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
390	#497	C₂²×C₅₃	1	4	yes	complemented
391	#497	C₂²×C₅₃	1	4	yes	complemented
392	#497	C₂²×C₅₃	1	2	yes	complemented
393	#497	C₂²×C₅₃	1	2	yes	complemented
394	#494	C₂²×C₅₃	1	2	yes	complemented
395	#492	C₂²×C₅₃	1	2	yes	complemented
396	#491	C₂²×C₅₃	1	2	yes	complemented
397	#490	C₂²×C₅₃	1	2	yes	complemented
398	#489	C₂²×C₅₃	1	2	yes	complemented
399	#489	C₂²×C₅₃	1	2	yes	complemented
400	#489	C₂²×C₅₃	1	4	yes	complemented
401	#488	C₂²×C₅₃	1	4	yes	complemented
402	#464	C₂²×C₅₃	1	8	yes	complemented
403	#464	C₂²×C₅₃	1	8	yes	complemented
404	#462	C₂²×C₅₃	1	8	yes	complemented
405	#460	C₂²×C₅₃	1	8	yes	complemented
406	#452	C₂²×C₅₃	1	8	yes	—
407	#452	C₂²×C₅₃	1	8	yes	complemented
408	#451	C₂²×C₅₃	1	8	yes	complemented
409	#450	C₂²×C₅₃	1	8	yes	—
410	#433	C₂²×C₅₃	1	4	yes	complemented
411	#432	C₂²×C₅₃	1	4	yes	complemented
412	#424	C₂²×C₅₃	1	2	yes	complemented
413	#419	C₂²×C₅₃	1	2	yes	complemented
414	#418	C₂²×C₅₃	1	2	yes	—
415	#416	C₂²×C₅₃	1	2	yes	—
416	#416	C₂²×C₅₃	1	2	yes	complemented
417	#408	C₂²×C₅₃	1	2	yes	—
418	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
419	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
420	C₅₃	#60826	1	1	yes	characteristic, direct product factor, Sylow
421	2₋¹⁺⁴	—	4	4	no	—
422	H(5,𝔽₂)	—	4	4	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	2	1	no	—
426	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
427	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
428	C₂×#41	C₂³×C₅₃	1	2	yes	—
429	C₂×#41	C₂³×C₅₃	1	2	yes	—
430	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
431	C₂²×Q₈	—	2	1	no	—
432	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
433	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
434	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
435	C₂²×D₄	—	2	2	no	—
436	C₂²×D₄	—	2	1	no	—
437	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
438	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
439	#137	—	4	4	no	—
440	#137	—	4	4	no	—
441	C₂×Q₁₆	—	4	4	no	—
442	C₂×Q₁₆	C₂³×C₅₃	1	8	yes	—
443	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
444	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
445	C₂×SD₁₆	—	4	4	no	—
446	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
447	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
448	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
449	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
450	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
451	C₄⋊Q₈	—	2	2	no	—
452	C₄⋊Q₈	—	2	2	no	—
453	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
454	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
455	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
456	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
457	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
458	#127	C₂³×C₅₃	1	2	yes	—
459	#127	C₂³×C₅₃	1	1	yes	characteristic
460	#126	—	2	8	no	—
461	#125	—	2	8	no	—
462	#125	—	2	4	no	—
463	#125	C₂³×C₅₃	1	2	yes	—
464	#124	—	2	2	no	—
465	#124	—	2	4	no	—
466	#124	—	2	2	no	—
467	#124	C₂³×C₅₃	1	2	yes	—
468	#124	C₂³×C₅₃	1	1	yes	characteristic
469	#124	C₂³×C₅₃	1	2	yes	—
470	#124	C₂³×C₅₃	1	2	yes	—
471	#124	C₂³×C₅₃	1	2	yes	—
472	#124	C₂³×C₅₃	1	1	yes	characteristic
473	#123	—	2	4	no	—
474	#123	—	2	2	no	—
475	#123	—	2	4	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	4	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	4	no	—
480	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
481	#121	—	2	2	no	—
482	#121	—	2	4	no	—
483	#121	—	2	2	no	—
484	#121	—	2	4	no	—
485	#120	—	2	2	no	—
486	#120	—	2	4	no	—
487	C₄×Q₈	—	2	4	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	D₄×C₅₃	1	2	yes	—
491	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	D₄×C₅₃	1	4	yes	—
495	C₄×D₄	D₄×C₅₃	1	2	yes	—
496	#117	—	2	4	no	—
497	#117	—	2	4	no	—
498	#117	C₂³×C₅₃	1	2	yes	—
499	#117	C₂³×C₅₃	1	1	yes	characteristic
500	#117	C₂³×C₅₃	1	2	yes	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₂²⋊C₄	—	2	2	no	—
503	C₂×C₂²⋊C₄	—	2	4	no	—
504	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
506	C₄⋊C₈	C₂³×C₅₃	1	8	yes	—
507	#103	C₂³×C₅₃	1	4	yes	—
508	#103	C₂³×C₅₃	1	4	yes	—
509	#103	C₂³×C₅₃	1	8	yes	—
510	#102	C₂³×C₅₃	1	4	yes	—
511	#102	C₂³×C₅₃	1	4	yes	—
512	#102	C₂³×C₅₃	1	8	yes	—
513	C₂²⋊C₈	C₂³×C₅₃	1	8	yes	—
514	#97	C₂³×C₅₃	1	2	yes	—
515	#97	C₂³×C₅₃	1	2	yes	—
516	#97	C₂³×C₅₃	1	2	yes	—
517	C₄×C₈	C₂³×C₅₃	1	2	yes	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	1	no	—
520	#41	—	2	4	no	—
521	#41	—	2	4	no	—
522	#41	—	2	4	no	—
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	#41	—	4	8	no	—
526	#41	—	4	4	no	—
527	#41	—	4	4	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	4	no	—
535	C₂×Q₈	—	4	4	no	—
536	C₂×Q₈	—	4	4	no	—
537	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
538	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
539	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
540	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
541	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	—	4	8	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
555	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
556	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
557	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
558	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
567	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
570	Q₁₆	—	4	8	no	—
571	Q₁₆	—	4	4	no	—
572	Q₁₆	—	4	4	no	—
573	SD₁₆	—	4	8	no	—
574	SD₁₆	—	4	4	no	—
575	SD₁₆	—	4	4	no	—
576	M₁₆	—	2	4	no	—
577	C₂×C₈	—	2	4	no	—
578	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
579	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
589	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
590	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
600	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
601	C₄²	—	2	8	no	—
602	C₄²	—	2	2	no	—
603	C₄²	C₂×D₄×C₅₃	1	4	yes	—
604	C₄²	C₂×D₄×C₅₃	1	2	yes	—
605	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
606	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
607	C₄²	C₂⁴×C₅₃	1	2	yes	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	4	4	no	—
612	C₂³	—	4	2	no	—
613	C₂³	—	8	2	no	—
614	C₂³	—	8	4	no	—
615	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
616	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
617	Q₈	—	2	2	no	—
618	Q₈	—	2	4	no	—
619	Q₈	—	2	4	no	—
620	Q₈	—	2	4	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	2	2	no	—
623	Q₈	—	4	4	no	—
624	Q₈	—	4	4	no	—
625	Q₈	—	4	4	no	—
626	Q₈	—	4	2	no	—
627	D₄	—	2	4	no	—
628	D₄	—	2	2	no	—
629	D₄	—	2	4	no	—
630	D₄	—	2	2	no	—
631	D₄	—	2	2	no	—
632	D₄	—	4	4	no	—
633	D₄	—	4	4	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	2	no	—
636	D₄	—	4	2	no	—
637	D₄	—	4	2	no	—
638	D₄	—	8	4	no	—
639	D₄	—	8	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
658	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
659	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
660	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
661	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
662	C₈	—	2	4	no	—
663	C₈	—	2	4	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	16	2	no	—
674	C₂²	—	16	4	no	—
675	C₂²	C₅₃×#535	1	2	yes	—
676	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	4	4	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	4	no	—
686	C₄	C₅₃×#535	1	2	yes	—
687	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
688	C₂	—	2	2	no	—
689	C₂	—	4	2	no	—
690	C₂	—	8	2	no	—
691	C₂	—	8	1	no	—
692	C₂	—	8	1	no	—
693	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
694	C₂	C₅₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3509	C₂	semidirect
3. C₅₃×#3223	C₂	semidirect
4. C₅₃×#3222	C₂	semidirect
5. C₅₃×#3216	C₂	semidirect
6. C₅₃×#3215	C₂	semidirect
7. C₅₃×#3152	C₂	semidirect
8. C₂×C₅₃×#497	C₂	semidirect
9. C₅₃×#3140	C₂	semidirect
10. C₅₃×#3135	C₂	semidirect
11. C₅₃×#3044	C₂	semidirect
12. C₅₃×#3043	C₂	semidirect
13. C₅₃×#3011	C₂	semidirect
14. C₅₃×#3009	C₂	semidirect
15. C₅₃×#2923	C₂	semidirect
19. C₂×#137×C₅₃	C₂²	semidirect
20. C₂²×Q₁₆×C₅₃	C₂²	semidirect
28. C₅₃×#541	C₂²	semidirect
34. C₅₃×#533	C₂²	semidirect
35. C₅₃×#533	C₂²	semidirect
38. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
41. C₅₃×#519	C₂²	semidirect
43. C₅₃×#497	C₂²	semidirect
44. C₅₃×#497	C₂²	semidirect
45. C₅₃×#497	C₂²	semidirect
46. C₅₃×#497	C₂²	semidirect
47. C₅₃×#494	C₂²	semidirect
48. C₅₃×#492	C₂²	semidirect
49. C₅₃×#491	C₂²	semidirect
50. C₅₃×#490	C₂²	semidirect
51. C₅₃×#489	C₂²	semidirect
52. C₅₃×#489	C₂²	semidirect
53. C₅₃×#489	C₂²	semidirect
54. C₅₃×#488	C₂²	semidirect
55. C₅₃×#464	C₂²	semidirect
56. C₅₃×#464	C₂²	semidirect
57. C₅₃×#462	C₂²	semidirect
58. C₅₃×#460	C₂²	semidirect
60. C₅₃×#452	C₂²	semidirect
61. C₅₃×#451	C₂²	semidirect
63. C₅₃×#433	C₂²	semidirect
64. C₅₃×#432	C₂²	semidirect
65. C₅₃×#424	C₂²	semidirect
66. C₅₃×#419	C₂²	semidirect
69. C₅₃×#416	C₂²	semidirect
71. C₄×M₁₆×C₅₃	C₂²	semidirect
72. C₂×#97×C₅₃	C₂²	semidirect
316. #60826	C₅₃	direct (N × H)
341. #3509	C₂×C₅₃	semidirect
343. #3223	C₂×C₅₃	semidirect
344. #3222	C₂×C₅₃	semidirect
345. #3216	C₂×C₅₃	semidirect
346. #3215	C₂×C₅₃	semidirect
347. #3152	C₂×C₅₃	semidirect
348. C₂×#497	C₂×C₅₃	semidirect
349. #3140	C₂×C₅₃	semidirect
350. #3135	C₂×C₅₃	semidirect
351. #3044	C₂×C₅₃	semidirect
352. #3043	C₂×C₅₃	semidirect
353. #3011	C₂×C₅₃	semidirect
354. #3009	C₂×C₅₃	semidirect
355. #2923	C₂×C₅₃	semidirect
366. C₂×#137	C₂²×C₅₃	semidirect
367. C₂²×Q₁₆	C₂²×C₅₃	semidirect
375. #541	C₂²×C₅₃	semidirect
381. #533	C₂²×C₅₃	semidirect
382. #533	C₂²×C₅₃	semidirect
385. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
388. #519	C₂²×C₅₃	semidirect
390. #497	C₂²×C₅₃	semidirect
391. #497	C₂²×C₅₃	semidirect
392. #497	C₂²×C₅₃	semidirect
393. #497	C₂²×C₅₃	semidirect
394. #494	C₂²×C₅₃	semidirect
395. #492	C₂²×C₅₃	semidirect
396. #491	C₂²×C₅₃	semidirect
397. #490	C₂²×C₅₃	semidirect
398. #489	C₂²×C₅₃	semidirect
399. #489	C₂²×C₅₃	semidirect
400. #489	C₂²×C₅₃	semidirect
401. #488	C₂²×C₅₃	semidirect
402. #464	C₂²×C₅₃	semidirect
403. #464	C₂²×C₅₃	semidirect
404. #462	C₂²×C₅₃	semidirect
405. #460	C₂²×C₅₃	semidirect
407. #452	C₂²×C₅₃	semidirect
408. #451	C₂²×C₅₃	semidirect
410. #433	C₂²×C₅₃	semidirect
411. #432	C₂²×C₅₃	semidirect
412. #424	C₂²×C₅₃	semidirect
413. #419	C₂²×C₅₃	semidirect
416. #416	C₂²×C₅₃	semidirect
418. C₄×M₁₆	C₂²×C₅₃	semidirect
419. C₂×#97	C₂²×C₅₃	semidirect
420. C₅₃	#60826	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3509	2
C₅₃×#3500	2
C₅₃×#3223	2
C₅₃×#3222	2
C₅₃×#3216	2
C₅₃×#3215	2
C₅₃×#3152	2
C₂×C₅₃×#497	2
C₅₃×#3140	2
C₅₃×#3135	2
C₅₃×#3044	2
C₅₃×#3043	2
C₅₃×#3011	2
C₅₃×#3009	2
C₅₃×#2923	2
#60826	53

Subgroups — C53×#60826 #27268338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60826 #27268338