Subgroups — C₅₃×#33470 #27240982

Order 13568.

632 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#510	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2957	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2180	C₂	1	8	yes	maximal, complemented
5	C₅₃×#2155	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2145	C₂	1	1	yes	maximal, characteristic
8	C₅₃×#2110	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
11	C₅₃×#568	—	2	1	no	—
12	C₅₃×#519	—	2	1	no	—
13	C₅₃×#510	C₄	1	4	yes	complemented
14	C₅₃×#510	C₂²	1	4	yes	—
15	C₂×Q₃₂×C₅₃	C₄	1	2	yes	complemented
16	C₂×SD₃₂×C₅₃	C₄	1	2	yes	complemented
17	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
18	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#444	C₂²	1	4	yes	—
20	C₅₃×#443	—	2	2	no	—
21	C₅₃×#441	C₂²	1	4	yes	complemented
22	C₄×Q₁₆×C₅₃	—	2	2	no	—
23	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#427	C₂²	1	1	yes	characteristic
25	C₅₃×#421	—	2	1	no	—
26	C₅₃×#419	—	2	1	no	—
27	C₅₃×#405	C₂²	1	1	yes	characteristic
28	C₅₃×#365	C₂²	1	4	yes	complemented
29	C₅₃×#362	C₂²	1	4	yes	complemented
30	C₅₃×#360	C₂²	1	4	yes	—
31	C₅₃×#347	C₂²	1	4	yes	complemented
32	C₂×#41×C₅₃	—	2	1	no	—
33	C₂²×Q₈×C₅₃	—	2	1	no	—
34	#135×C₅₃	—	2	1	no	—
35	#135×C₅₃	—	2	1	no	—
36	#135×C₅₃	C₂×C₄	1	2	yes	—
37	#135×C₅₃	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₅₃	—	2	1	no	—
39	C₂×Q₁₆×C₅₃	—	2	1	no	—
40	C₂×Q₁₆×C₅₃	—	2	1	no	—
41	C₂×Q₁₆×C₅₃	C₂×C₄	1	2	yes	—
42	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
43	C₂×Q₁₆×C₅₃	C₂×C₄	1	2	yes	—
44	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
45	C₂×SD₁₆×C₅₃	—	2	1	no	—
46	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
47	#131×C₅₃	—	2	4	no	—
48	#131×C₅₃	—	4	2	no	—
49	C₂×M₁₆×C₅₃	—	2	1	no	—
50	C₂×M₁₆×C₅₃	—	4	2	no	—
51	C₂×M₁₆×C₅₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
53	C₄×Q₈×C₅₃	—	2	4	no	—
54	C₄×Q₈×C₅₃	—	4	2	no	—
55	#117×C₅₃	—	2	1	no	—
56	#117×C₅₃	—	4	2	no	—
57	#117×C₅₃	D₄	1	1	yes	characteristic
58	Q₃₂×C₅₃	C₂×C₄	1	8	yes	—
59	SD₃₂×C₅₃	C₂×C₄	1	8	yes	—
60	M₃₂×C₅₃	—	2	1	no	—
61	M₃₂×C₅₃	C₂×C₄	1	2	yes	—
62	M₃₂×C₅₃	C₂³	1	2	yes	—
63	M₃₂×C₅₃	C₂³	1	2	yes	—
64	C₂×C₁₆×C₅₃	—	2	1	no	—
65	C₂×C₁₆×C₅₃	C₂×C₄	1	2	yes	—
66	#108×C₅₃	—	2	1	no	—
67	#108×C₅₃	C₂³	1	2	yes	—
68	#107×C₅₃	—	2	1	no	—
69	#106×C₅₃	C₂³	1	2	yes	—
70	#104×C₅₃	—	2	4	no	—
71	#103×C₅₃	—	2	4	no	—
72	#97×C₅₃	C₂³	1	2	yes	—
73	C₄×C₈×C₅₃	D₄	1	2	yes	—
74	#41×C₅₃	—	2	2	no	—
75	#41×C₅₃	—	2	2	no	—
76	#41×C₅₃	—	4	1	no	—
77	#41×C₅₃	—	4	1	no	—
78	C₂×Q₈×C₅₃	—	2	1	no	—
79	C₂×Q₈×C₅₃	—	2	2	no	—
80	C₂×Q₈×C₅₃	—	2	2	no	—
81	C₂×Q₈×C₅₃	—	2	2	no	—
82	C₂×Q₈×C₅₃	—	4	1	no	—
83	C₂×Q₈×C₅₃	—	4	1	no	—
84	C₂×Q₈×C₅₃	—	4	1	no	—
85	C₂×D₄×C₅₃	—	2	1	no	—
86	C₂×D₄×C₅₃	—	4	1	no	—
87	C₂²×C₄×C₅₃	—	4	1	no	—
88	C₂²×C₄×C₅₃	—	4	1	no	—
89	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
90	Q₁₆×C₅₃	—	2	2	no	—
91	Q₁₆×C₅₃	—	2	2	no	—
92	Q₁₆×C₅₃	—	2	1	no	—
93	Q₁₆×C₅₃	—	2	2	no	—
94	Q₁₆×C₅₃	C₂²×C₄	1	4	yes	—
95	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
96	SD₁₆×C₅₃	—	2	2	no	—
97	SD₁₆×C₅₃	—	2	2	no	—
98	D₈×C₅₃	—	2	1	no	—
99	D₈×C₅₃	C₂²×C₄	1	2	yes	—
100	M₁₆×C₅₃	—	2	1	no	—
101	M₁₆×C₅₃	—	2	1	no	—
102	M₁₆×C₅₃	—	2	2	no	—
103	M₁₆×C₅₃	—	4	4	no	—
104	M₁₆×C₅₃	—	4	1	no	—
105	C₂×C₈×C₅₃	—	4	4	no	—
106	C₂×C₈×C₅₃	—	4	1	no	—
107	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
112	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₅₃	—	2	1	no	—
115	C₄⋊C₄×C₅₃	—	2	2	no	—
116	C₄⋊C₄×C₅₃	—	4	4	no	—
117	C₂²⋊C₄×C₅₃	—	2	1	no	—
118	C₂²⋊C₄×C₅₃	—	4	1	no	—
119	C₄²×C₅₃	—	4	4	no	—
120	C₄²×C₅₃	—	4	1	no	—
121	C₄²×C₅₃	C₂×D₄	1	2	yes	—
122	C₁₆×C₅₃	—	2	2	no	—
123	C₁₆×C₅₃	C₂²×C₄	1	4	yes	—
124	C₂³×C₅₃	—	4	1	no	—
125	C₂³×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
126	Q₈×C₅₃	—	2	4	no	—
127	Q₈×C₅₃	—	2	2	no	—
128	Q₈×C₅₃	—	4	2	no	—
129	Q₈×C₅₃	—	4	2	no	—
130	Q₈×C₅₃	—	4	2	no	—
131	Q₈×C₅₃	—	4	1	no	—
132	D₄×C₅₃	—	2	2	no	—
133	D₄×C₅₃	—	4	2	no	—
134	D₄×C₅₃	—	4	2	no	—
135	D₄×C₅₃	—	4	1	no	—
136	C₂×C₄×C₅₃	—	2	2	no	—
137	C₂×C₄×C₅₃	—	4	2	no	—
138	C₂×C₄×C₅₃	—	4	1	no	—
139	C₂×C₄×C₅₃	—	4	2	no	—
140	C₂×C₄×C₅₃	—	4	2	no	—
141	C₂×C₄×C₅₃	—	4	2	no	—
142	C₂×C₄×C₅₃	—	4	2	no	—
143	C₂×C₄×C₅₃	—	4	2	no	—
144	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₅₃	—	2	2	no	—
151	C₈×C₅₃	—	4	2	no	—
152	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
153	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
154	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
155	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
156	#33470	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂²×C₅₃	—	4	1	no	—
158	C₂²×C₅₃	—	4	2	no	—
159	C₂²×C₅₃	—	16	1	no	—
160	C₂²×C₅₃	#442	1	1	yes	characteristic
161	C₂²×C₅₃	#442	1	1	yes	characteristic
162	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₄×C₅₃	—	4	2	no	—
164	C₄×C₅₃	—	4	2	no	—
165	C₄×C₅₃	—	4	4	no	—
166	C₄×C₅₃	—	8	2	no	—
167	C₄×C₅₃	#442	1	1	yes	characteristic
168	C₄×C₅₃	#442	1	1	yes	characteristic
169	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×#510	C₂×C₅₃	1	1	yes	characteristic
172	#2957	C₂×C₅₃	1	1	yes	characteristic
173	#2950	C₂×C₅₃	1	1	yes	characteristic, complemented
174	#2180	C₂×C₅₃	1	8	yes	complemented
175	#2155	C₂×C₅₃	1	1	yes	characteristic, complemented
176	C₂×#362	C₂×C₅₃	1	1	yes	characteristic, complemented
177	#2145	C₂×C₅₃	1	1	yes	characteristic
178	#2110	C₂×C₅₃	1	1	yes	characteristic, complemented
179	C₂×C₅₃	—	2	1	no	—
180	C₂×C₅₃	—	2	1	no	—
181	C₂×C₅₃	—	2	1	no	—
182	C₂×C₅₃	—	8	2	no	—
183	C₂×C₅₃	C₂×#442	1	1	yes	characteristic
184	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
185	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
186	#568	—	2	1	no	—
187	#519	—	2	1	no	—
188	#510	C₄×C₅₃	1	4	yes	complemented
189	#510	C₂²×C₅₃	1	4	yes	—
190	C₂×Q₃₂	C₄×C₅₃	1	2	yes	complemented
191	C₂×SD₃₂	C₄×C₅₃	1	2	yes	complemented
192	C₂×M₃₂	C₂²×C₅₃	1	1	yes	characteristic
193	C₂×M₃₂	C₂²×C₅₃	1	1	yes	characteristic
194	#444	C₂²×C₅₃	1	4	yes	—
195	#443	—	2	2	no	—
196	#441	C₂²×C₅₃	1	4	yes	complemented
197	C₄×Q₁₆	—	2	2	no	—
198	C₂×#108	C₂²×C₅₃	1	1	yes	characteristic
199	#427	C₂²×C₅₃	1	1	yes	characteristic
200	#421	—	2	1	no	—
201	#419	—	2	1	no	—
202	#405	C₂²×C₅₃	1	1	yes	characteristic
203	#365	C₂²×C₅₃	1	4	yes	complemented
204	#362	C₂²×C₅₃	1	4	yes	complemented
205	#360	C₂²×C₅₃	1	4	yes	—
206	#347	C₂²×C₅₃	1	4	yes	complemented
207	C₅₃	#33470	1	1	yes	characteristic, direct product factor, Sylow
208	C₂×#41	—	2	1	no	—
209	C₂²×Q₈	—	2	1	no	—
210	#135	—	2	1	no	—
211	#135	—	2	1	no	—
212	#135	C₂×C₄×C₅₃	1	2	yes	—
213	#135	C₂³×C₅₃	1	2	yes	—
214	C₂×Q₁₆	—	2	1	no	—
215	C₂×Q₁₆	—	2	1	no	—
216	C₂×Q₁₆	—	2	1	no	—
217	C₂×Q₁₆	C₂×C₄×C₅₃	1	2	yes	—
218	C₂×Q₁₆	C₂×C₄×C₅₃	1	2	yes	—
219	C₂×Q₁₆	C₂×C₄×C₅₃	1	1	yes	characteristic
220	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
221	C₂×SD₁₆	—	2	1	no	—
222	C₂×D₈	C₂×C₄×C₅₃	1	1	yes	characteristic
223	#131	—	2	4	no	—
224	#131	—	4	2	no	—
225	C₂×M₁₆	—	2	1	no	—
226	C₂×M₁₆	—	4	2	no	—
227	C₂×M₁₆	D₄×C₅₃	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
229	C₄×Q₈	—	2	4	no	—
230	C₄×Q₈	—	4	2	no	—
231	#117	—	2	1	no	—
232	#117	—	4	2	no	—
233	#117	D₄×C₅₃	1	1	yes	characteristic
234	Q₃₂	C₂×C₄×C₅₃	1	8	yes	—
235	SD₃₂	C₂×C₄×C₅₃	1	8	yes	—
236	M₃₂	—	2	1	no	—
237	M₃₂	C₂×C₄×C₅₃	1	2	yes	—
238	M₃₂	C₂³×C₅₃	1	2	yes	—
239	M₃₂	C₂³×C₅₃	1	2	yes	—
240	C₂×C₁₆	—	2	1	no	—
241	C₂×C₁₆	C₂×C₄×C₅₃	1	2	yes	—
242	#108	—	2	1	no	—
243	#108	C₂³×C₅₃	1	2	yes	—
244	#107	—	2	1	no	—
245	#106	C₂³×C₅₃	1	2	yes	—
246	#104	—	2	4	no	—
247	#103	—	2	4	no	—
248	#97	C₂³×C₅₃	1	2	yes	—
249	C₄×C₈	D₄×C₅₃	1	2	yes	—
250	#41	—	2	2	no	—
251	#41	—	2	2	no	—
252	#41	—	4	1	no	—
253	#41	—	4	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	4	1	no	—
259	C₂×Q₈	—	4	1	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
266	Q₁₆	—	2	2	no	—
267	Q₁₆	—	2	2	no	—
268	Q₁₆	—	2	1	no	—
269	Q₁₆	—	2	2	no	—
270	Q₁₆	C₂²×C₄×C₅₃	1	4	yes	—
271	Q₁₆	C₂²×C₄×C₅₃	1	2	yes	—
272	SD₁₆	—	2	2	no	—
273	SD₁₆	—	2	2	no	—
274	D₈	—	2	1	no	—
275	D₈	C₂²×C₄×C₅₃	1	2	yes	—
276	M₁₆	—	2	1	no	—
277	M₁₆	—	2	1	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	4	4	no	—
280	M₁₆	—	4	1	no	—
281	C₂×C₈	—	4	4	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	C₂²×C₄×C₅₃	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₄×C₅₃	1	1	yes	characteristic
285	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
286	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
287	C₂×C₈	#41×C₅₃	1	1	yes	characteristic
288	C₂×C₈	#41×C₅₃	1	1	yes	characteristic
289	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	4	1	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	4	1	no	—
297	C₄²	C₂×D₄×C₅₃	1	2	yes	—
298	C₁₆	—	2	2	no	—
299	C₁₆	C₂²×C₄×C₅₃	1	4	yes	—
300	C₂³	—	4	1	no	—
301	C₂³	AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
302	Q₈	—	2	2	no	—
303	Q₈	—	2	4	no	—
304	Q₈	—	4	2	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	4	2	no	—
307	Q₈	—	4	1	no	—
308	D₄	—	2	2	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	2	no	—
311	D₄	—	4	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	C₄×D₄×C₅₃	1	1	yes	characteristic
321	C₂×C₄	C₄×D₄×C₅₃	1	1	yes	characteristic
322	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
323	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
324	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
326	C₈	—	2	2	no	—
327	C₈	—	4	2	no	—
328	C₈	C₄×D₄×C₅₃	1	1	yes	characteristic
329	C₈	C₄×D₄×C₅₃	1	1	yes	characteristic
330	C₈	C₂³×C₄×C₅₃	1	1	yes	characteristic
331	C₈	C₂×#41×C₅₃	1	1	yes	characteristic
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	16	1	no	—
335	C₂²	C₅₃×#442	1	1	yes	characteristic
336	C₂²	C₅₃×#442	1	1	yes	characteristic
337	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
338	C₄	—	4	2	no	—
339	C₄	—	4	2	no	—
340	C₄	—	4	4	no	—
341	C₄	—	8	2	no	—
342	C₄	C₅₃×#442	1	1	yes	characteristic
343	C₄	C₅₃×#442	1	1	yes	characteristic
344	C₄	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
345	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
346	C₂	—	2	1	no	—
347	C₂	—	2	1	no	—
348	C₂	—	2	1	no	—
349	C₂	—	8	2	no	—
350	C₂	C₂×C₅₃×#442	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₃	C₂×#442
commutator	C₈	C₂³×C₄×C₅₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₅₃
prime radical	C₂×#135×C₅₃	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₃ ◁ C₂²×C₄×C₅₃ ◁ C₅₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₃×#2950	C₂	semidirect
4. C₅₃×#2180	C₂	semidirect
5. C₅₃×#2155	C₂	semidirect
6. C₂×C₅₃×#362	C₂	semidirect
8. C₅₃×#2110	C₂	semidirect
13. C₅₃×#510	C₄	semidirect
15. C₂×Q₃₂×C₅₃	C₄	semidirect
16. C₂×SD₃₂×C₅₃	C₄	semidirect
21. C₅₃×#441	C₂²	semidirect
28. C₅₃×#365	C₂²	semidirect
29. C₅₃×#362	C₂²	semidirect
31. C₅₃×#347	C₂²	semidirect
156. #33470	C₅₃	direct (N × H)
173. #2950	C₂×C₅₃	semidirect
174. #2180	C₂×C₅₃	semidirect
175. #2155	C₂×C₅₃	semidirect
176. C₂×#362	C₂×C₅₃	semidirect
178. #2110	C₂×C₅₃	semidirect
188. #510	C₄×C₅₃	semidirect
190. C₂×Q₃₂	C₄×C₅₃	semidirect
191. C₂×SD₃₂	C₄×C₅₃	semidirect
196. #441	C₂²×C₅₃	semidirect
203. #365	C₂²×C₅₃	semidirect
204. #362	C₂²×C₅₃	semidirect
206. #347	C₂²×C₅₃	semidirect
207. C₅₃	#33470	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×#510	2
C₅₃×#2957	2
C₅₃×#2950	2
C₅₃×#2180	2
C₅₃×#2155	2
C₂×C₅₃×#362	2
C₅₃×#2145	2
C₅₃×#2110	2
#33470	53

Subgroups — C53×#33470 #27240982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#33470 #27240982