Subgroups — D₅₃×#1706 #27371731

Order 13568.

1046 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#493×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#492×D₅₃	C₂	1	2	yes	maximal, complemented
4	#486×D₅₃	C₂	1	2	yes	maximal, complemented
5	#20274308	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274307	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274306	C₂	1	2	yes	maximal, complemented
8	#20274305	C₂	1	2	yes	maximal, complemented
9	#20274304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈²×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1706	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₅₃	—	2	4	no	—
13	C₂×D₈×D₅₃	—	2	2	no	—
14	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
15	#127×D₅₃	C₂²	1	2	yes	—
16	#16811028	C₂²	1	1	yes	characteristic, complemented
17	#16811027	—	2	2	no	—
18	#16811026	C₂²	1	2	yes	complemented
19	#16811000	C₂²	1	1	yes	characteristic
20	#16810999	C₂²	1	2	yes	—
21	#16810998	—	2	2	no	—
22	#16810997	C₂²	1	2	yes	complemented
23	#16810996	C₂²	1	2	yes	complemented
24	#16810995	C₂²	1	2	yes	complemented
25	#16810994	—	2	4	no	—
26	#16810971	C₂²	1	2	yes	complemented
27	#16810970	C₂²	1	2	yes	complemented
28	#16810969	C₂²	1	2	yes	complemented
29	#16810968	—	2	4	no	—
30	#107×D₅₃	—	2	2	no	—
31	#102×D₅₃	—	2	4	no	—
32	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
35	C₈×#88322	C₂²	1	1	yes	characteristic, complemented
36	C₈×#88322	C₂²	1	1	yes	characteristic, complemented
37	C₈×#88322	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#493	C₂²	1	1	yes	characteristic
40	C₅₃×#492	C₂²	1	2	yes	complemented
41	C₅₃×#486	C₂²	1	2	yes	complemented
42	C₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×Q₈×D₅₃	—	2	2	no	—
44	C₂×D₄×D₅₃	—	2	2	no	—
45	C₂×D₄×D₅₃	—	2	2	no	—
46	C₂×D₄×D₅₃	—	2	2	no	—
47	C₂×#11719913	—	2	4	no	—
48	C₂×#11719923	—	2	4	no	—
49	C₂×#11719924	—	2	4	no	—
50	SD₁₆×D₅₃	—	4	16	no	—
51	C₂×D₄₂₄	—	2	2	no	—
52	C₂×#11719922	—	2	4	no	—
53	D₈×D₅₃	—	4	8	no	—
54	C₂×C₈×D₅₃	D₄	1	2	yes	—
55	C₂×C₈×D₅₃	D₄	1	2	yes	—
56	C₂×C₈×D₅₃	D₄	1	2	yes	—
57	#13133217	C₂³	1	2	yes	—
58	#13133216	—	2	2	no	—
59	#13133216	—	2	2	no	—
60	#13133215	—	2	2	no	—
61	#13133214	C₂³	1	2	yes	—
62	#13133213	—	2	2	no	—
63	#13133213	—	2	2	no	—
64	#13133213	—	2	2	no	—
65	C₄⋊C₄×D₅₃	—	2	2	no	—
66	C₄⋊C₄×D₅₃	—	2	2	no	—
67	C₄²×D₅₃	C₂³	1	1	yes	characteristic
68	#13133151	—	2	2	no	—
69	#13133150	—	2	4	no	—
70	#13133139	—	2	4	no	—
71	#13133138	—	2	4	no	—
72	#13133137	—	2	4	no	—
73	C₄×#88322	C₂³	1	1	yes	characteristic
74	C₄×#88322	C₂³	1	1	yes	characteristic
75	C₄×#88322	C₂³	1	1	yes	characteristic
76	C₈×Dic₅₃	D₄	1	2	yes	—
77	C₈×Dic₅₃	D₄	1	2	yes	—
78	C₈×Dic₅₃	D₄	1	2	yes	—
79	C₂×SD₁₆×C₅₃	—	2	4	no	—
80	C₂×D₈×C₅₃	—	2	2	no	—
81	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
82	#127×C₅₃	C₂³	1	2	yes	—
83	#107×C₅₃	—	2	2	no	—
84	#102×C₅₃	—	2	4	no	—
85	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
88	C₂³×D₅₃	—	4	2	no	—
89	C₂×Q₈×C₅₃	—	2	2	no	—
90	C₂×D₄×C₅₃	—	2	2	no	—
91	C₂×D₄×C₅₃	—	2	2	no	—
92	C₂×D₄×C₅₃	—	2	2	no	—
93	C₂×C₂²⋊D₅₃	—	4	2	no	—
94	C₂×C₂²⋊D₅₃	—	4	2	no	—
95	C₂×C₂²⋊D₅₃	—	4	2	no	—
96	Q₈×D₅₃	—	4	8	no	—
97	D₄×D₅₃	—	4	8	no	—
98	D₄×D₅₃	—	4	8	no	—
99	D₄×D₅₃	—	4	8	no	—
100	C₂×D₂₁₂	—	2	2	no	—
101	C₂×D₂₁₂	—	2	2	no	—
102	C₂×D₂₁₂	—	2	2	no	—
103	C₂×C₄×D₅₃	—	4	2	no	—
104	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂×Dic₁₀₆	—	2	2	no	—
108	C₂×Dic₁₀₆	—	4	2	no	—
109	SD₁₆×C₅₃	—	4	8	no	—
110	D₈×C₅₃	—	4	4	no	—
111	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
114	C₄⋊C₄×C₅₃	—	2	2	no	—
115	C₄⋊C₄×C₅₃	—	2	2	no	—
116	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
117	#11719924	—	4	8	no	—
118	#11719923	—	4	8	no	—
119	#11719922	—	4	8	no	—
120	C₄⋊Dic₅₃	—	2	2	no	—
121	C₄⋊Dic₅₃	—	2	2	no	—
122	#11719919	—	4	2	no	—
123	#11719919	—	4	2	no	—
124	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
125	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
127	C₂×#88322	C₂×D₄	1	2	yes	—
128	C₂×#88322	C₂×D₄	1	2	yes	—
129	C₂×#88322	C₂×D₄	1	2	yes	—
130	D₄₂₄	—	4	4	no	—
131	#11719913	—	4	8	no	—
132	C₈×D₅₃	—	2	4	no	—
133	C₈×D₅₃	D₈	1	8	yes	complemented
134	C₈×D₅₃	SD₁₆	1	8	yes	complemented
135	C₂³×C₅₃	—	4	2	no	—
136	C₂²×D₅₃	—	4	2	no	—
137	C₂²×D₅₃	—	8	4	no	—
138	C₂²×D₅₃	—	8	4	no	—
139	C₂²×D₅₃	—	8	4	no	—
140	C₂²×D₅₃	#127	1	1	yes	characteristic
141	Q₈×C₅₃	—	4	4	no	—
142	D₄×C₅₃	—	4	4	no	—
143	D₄×C₅₃	—	4	4	no	—
144	D₄×C₅₃	—	4	4	no	—
145	C₂×C₄×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
149	C₂²⋊D₅₃	—	8	4	no	—
150	C₂²⋊D₅₃	—	8	4	no	—
151	C₂²⋊D₅₃	—	8	4	no	—
152	C₂×Dic₅₃	—	4	2	no	—
153	C₂×Dic₅₃	#127	1	1	yes	characteristic
154	C₂×Dic₅₃	#127	1	1	yes	characteristic
155	C₂×Dic₅₃	#127	1	1	yes	characteristic
156	D₂₁₂	—	4	4	no	—
157	D₂₁₂	—	4	4	no	—
158	D₂₁₂	—	4	4	no	—
159	C₄×D₅₃	—	8	4	no	—
160	C₄×D₅₃	C₂×D₈	1	4	yes	—
161	C₄×D₅₃	C₂×SD₁₆	1	4	yes	—
162	C₄×D₅₃	#135	1	4	yes	—
163	Dic₁₀₆	—	4	4	no	—
164	Dic₁₀₆	—	8	4	no	—
165	C₈×C₅₃	—	2	2	no	—
166	C₈×C₅₃	C₂×D₈	1	4	yes	complemented
167	C₈×C₅₃	C₂×SD₁₆	1	4	yes	complemented
168	#88322	—	2	2	no	—
169	#88322	C₂×D₈	1	4	yes	complemented
170	#88322	C₂×SD₁₆	1	4	yes	complemented
171	C₂×#1706	—	53	1	no	maximal, Sylow
172	C₂²×C₅₃	—	8	2	no	—
173	C₂²×C₅₃	—	8	2	no	—
174	C₂²×C₅₃	—	8	2	no	—
175	C₂²×C₅₃	C₂×#127	1	1	yes	characteristic
176	C₂×D₅₃	—	8	2	no	—
177	C₂×D₅₃	—	8	2	no	—
178	C₂×D₅₃	—	8	2	no	—
179	C₂×D₅₃	—	16	8	no	—
180	C₂×D₅₃	#492	1	2	yes	—
181	C₂×D₅₃	#493	1	2	yes	—
182	C₂×D₅₃	#495	1	2	yes	—
183	C₄×C₅₃	—	8	2	no	—
184	C₄×C₅₃	C₂²×D₈	1	2	yes	—
185	C₄×C₅₃	C₂²×SD₁₆	1	2	yes	—
186	C₄×C₅₃	C₂×#135	1	2	yes	—
187	Dic₅₃	—	8	2	no	—
188	Dic₅₃	#492	1	2	yes	—
189	Dic₅₃	#493	1	2	yes	—
190	Dic₅₃	#495	1	2	yes	—
191	C₂×#500	—	53	1	no	—
192	C₂×#493	—	53	1	no	—
193	C₂×#492	—	53	2	no	—
194	C₂×#486	—	53	2	no	—
195	#1706	—	53	1	no	—
196	#1706	—	53	1	no	—
197	#1706	—	53	2	no	—
198	#1706	—	53	2	no	—
199	#1706	—	53	1	no	—
200	#1706	D₅₃	1	1	yes	characteristic, direct product factor
201	C₂×C₈²	—	53	1	no	—
202	C₂×C₅₃	—	16	2	no	—
203	C₂×C₅₃	C₂×#492	1	1	yes	characteristic
204	C₂×C₅₃	C₂×#493	1	1	yes	characteristic
205	C₂×C₅₃	C₂×#495	1	1	yes	characteristic
206	D₅₃	—	16	2	no	—
207	D₅₃	#1706	1	4	yes	direct product factor
208	C₂²×SD₁₆	—	106	4	no	—
209	C₂²×D₈	—	106	2	no	—
210	C₂×C₄⋊Q₈	—	53	2	no	—
211	C₂×#127	—	53	2	no	—
212	#500	—	53	2	no	—
213	#500	—	53	1	no	—
214	#500	—	106	2	no	—
215	#500	C₂×D₅₃	1	1	yes	characteristic, complemented
216	#493	—	53	2	no	—
217	#493	—	53	1	no	—
218	#493	—	106	2	no	—
219	#493	C₂×D₅₃	1	1	yes	characteristic
220	#492	—	53	2	no	—
221	#492	—	53	2	no	—
222	#492	—	53	2	no	—
223	#492	—	106	4	no	—
224	#492	C₂×D₅₃	1	2	yes	complemented
225	#486	—	53	2	no	—
226	#486	—	53	2	no	—
227	#486	—	53	2	no	—
228	#486	—	106	4	no	—
229	#486	C₂×D₅₃	1	2	yes	complemented
230	C₂×#107	—	106	2	no	—
231	C₂×#102	—	106	4	no	—
232	C₂×C₄×C₈	—	53	1	no	—
233	C₂×C₄×C₈	—	53	1	no	—
234	C₂×C₄×C₈	—	53	1	no	—
235	C₈²	—	53	1	no	—
236	C₈²	—	53	1	no	—
237	C₈²	—	53	1	no	—
238	C₈²	C₂×D₅₃	1	1	yes	characteristic, complemented
239	C₅₃	C₂×#1706	1	1	yes	characteristic, complemented, Sylow
240	C₂²×Q₈	—	106	2	no	—
241	C₂²×D₄	—	106	2	no	—
242	C₂²×D₄	—	106	2	no	—
243	C₂²×D₄	—	106	2	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	106	4	no	—
246	C₂×SD₁₆	—	106	4	no	—
247	C₂×SD₁₆	—	106	4	no	—
248	C₂×SD₁₆	—	212	16	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	106	4	no	—
251	C₂×D₈	—	106	2	no	—
252	C₂×D₈	—	212	8	no	—
253	C₂²×C₈	—	53	2	no	—
254	C₂²×C₈	—	53	2	no	—
255	C₂²×C₈	—	53	2	no	—
256	C₄⋊Q₈	—	53	2	no	—
257	C₄⋊Q₈	—	106	2	no	—
258	C₄⋊Q₈	—	106	2	no	—
259	C₄⋊Q₈	—	106	2	no	—
260	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
261	#127	—	53	2	no	—
262	#127	—	106	2	no	—
263	#127	—	106	2	no	—
264	#127	—	106	2	no	—
265	#127	C₂²×D₅₃	1	2	yes	—
266	C₂×C₄⋊C₄	—	106	2	no	—
267	C₂×C₄⋊C₄	—	106	2	no	—
268	C₂×C₄²	—	53	1	no	—
269	#107	—	2	2	no	—
270	#107	—	106	4	no	—
271	#107	—	106	2	no	—
272	#102	—	2	4	no	—
273	#102	—	106	4	no	—
274	#102	—	106	4	no	—
275	#102	—	106	4	no	—
276	C₄×C₈	—	53	2	no	—
277	C₄×C₈	—	53	2	no	—
278	C₄×C₈	—	53	2	no	—
279	C₄×C₈	—	53	1	no	—
280	C₄×C₈	—	53	1	no	—
281	C₄×C₈	—	53	1	no	—
282	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
283	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
285	C₂⁴	—	212	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	106	2	no	—
288	C₂×Q₈	—	212	2	no	—
289	C₂×Q₈	—	212	8	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	106	2	no	—
294	C₂×D₄	—	106	2	no	—
295	C₂×D₄	—	106	2	no	—
296	C₂×D₄	—	212	8	no	—
297	C₂×D₄	—	212	8	no	—
298	C₂×D₄	—	212	8	no	—
299	C₂×D₄	—	212	2	no	—
300	C₂×D₄	—	212	2	no	—
301	C₂×D₄	—	212	2	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	212	2	no	—
306	SD₁₆	—	4	8	no	—
307	SD₁₆	—	212	8	no	—
308	SD₁₆	—	212	8	no	—
309	SD₁₆	—	212	8	no	—
310	D₈	—	4	4	no	—
311	D₈	—	212	8	no	—
312	D₈	—	212	4	no	—
313	C₂×C₈	—	53	2	no	—
314	C₂×C₈	—	53	2	no	—
315	C₂×C₈	—	53	8	no	—
316	C₂×C₈	—	53	8	no	—
317	C₂×C₈	—	53	2	no	—
318	C₂×C₈	—	106	4	no	—
319	C₂×C₈	D₄×D₅₃	1	2	yes	—
320	C₂×C₈	D₄×D₅₃	1	2	yes	—
321	C₂×C₈	D₄×D₅₃	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	106	2	no	—
325	C₄⋊C₄	—	106	2	no	—
326	C₄⋊C₄	—	212	2	no	—
327	C₄⋊C₄	—	212	2	no	—
328	C₄²	—	53	1	no	—
329	C₄²	—	53	1	no	—
330	C₄²	—	53	1	no	—
331	C₄²	C₂³×D₅₃	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	53	1	no	—
334	C₂³	—	424	4	no	—
335	C₂³	—	424	4	no	—
336	C₂³	—	424	4	no	—
337	C₂³	—	212	2	no	—
338	Q₈	—	4	4	no	—
339	Q₈	—	424	4	no	—
340	Q₈	—	212	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	424	4	no	—
345	D₄	—	424	4	no	—
346	D₄	—	424	4	no	—
347	D₄	—	212	4	no	—
348	D₄	—	212	4	no	—
349	D₄	—	212	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	53	1	no	—
352	C₂×C₄	—	53	1	no	—
353	C₂×C₄	—	53	1	no	—
354	C₂×C₄	—	53	4	no	—
355	C₂×C₄	—	53	4	no	—
356	C₂×C₄	—	53	4	no	—
357	C₂×C₄	—	424	4	no	—
358	C₂×C₄	—	212	2	no	—
359	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
360	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
361	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	53	4	no	—
364	C₈	—	53	4	no	—
365	C₈	—	106	2	no	—
366	C₈	D₈×D₅₃	1	4	yes	complemented
367	C₈	SD₁₆×D₅₃	1	4	yes	complemented
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	53	2	no	—
372	C₂²	—	53	2	no	—
373	C₂²	—	53	2	no	—
374	C₂²	—	848	8	no	—
375	C₂²	—	424	2	no	—
376	C₂²	—	424	2	no	—
377	C₂²	—	424	2	no	—
378	C₂²	#127×D₅₃	1	1	yes	characteristic
379	C₄	—	8	2	no	—
380	C₄	—	53	2	no	—
381	C₄	—	53	2	no	—
382	C₄	—	53	2	no	—
383	C₄	—	424	2	no	—
384	C₄	C₂×D₈×D₅₃	1	2	yes	—
385	C₄	C₂×SD₁₆×D₅₃	1	2	yes	—
386	C₄	#135×D₅₃	1	2	yes	—
387	C₂	—	16	2	no	—
388	C₂	—	53	4	no	—
389	C₂	—	848	2	no	—
390	C₂	#492×D₅₃	1	1	yes	characteristic
391	C₂	#493×D₅₃	1	1	yes	characteristic
392	C₂	#495×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1706	C₂
socle	C₂²×C₅₃	C₂×#127
prime radical	#493×D₅₃	C₂
hypercenter	#1706	D₅₃
hypocenter	C₅₃	C₂×#1706
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1706

Complements

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

N	H ≅ G/N	type
1. #500×D₅₃	C₂	semidirect
3. #492×D₅₃	C₂	semidirect
4. #486×D₅₃	C₂	semidirect
5. #20274308	C₂	semidirect
6. #20274307	C₂	semidirect
7. #20274306	C₂	semidirect
8. #20274305	C₂	semidirect
9. #20274304	C₂	semidirect
10. C₈²×D₅₃	C₂	semidirect
11. C₅₃×#1706	C₂	semidirect
16. #16811028	C₂²	semidirect
18. #16811026	C₂²	semidirect
22. #16810997	C₂²	semidirect
23. #16810996	C₂²	semidirect
24. #16810995	C₂²	semidirect
26. #16810971	C₂²	semidirect
27. #16810970	C₂²	semidirect
28. #16810969	C₂²	semidirect
35. C₈×#88322	C₂²	semidirect
36. C₈×#88322	C₂²	semidirect
37. C₈×#88322	C₂²	semidirect
38. C₅₃×#500	C₂²	semidirect
40. C₅₃×#492	C₂²	semidirect
41. C₅₃×#486	C₂²	semidirect
42. C₈²×C₅₃	C₂²	semidirect
133. C₈×D₅₃	D₈	semidirect
134. C₈×D₅₃	SD₁₆	semidirect
166. C₈×C₅₃	C₂×D₈	semidirect
167. C₈×C₅₃	C₂×SD₁₆	semidirect
169. #88322	C₂×D₈	semidirect
170. #88322	C₂×SD₁₆	semidirect
200. #1706	D₅₃	direct (N × H)
207. D₅₃	#1706	direct (N × H)
215. #500	C₂×D₅₃	semidirect
224. #492	C₂×D₅₃	semidirect
229. #486	C₂×D₅₃	semidirect
238. C₈²	C₂×D₅₃	semidirect
239. C₅₃	C₂×#1706	semidirect
366. C₈	D₈×D₅₃	semidirect
367. C₈	SD₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#500×D₅₃	2
#493×D₅₃	2
#492×D₅₃	2
#486×D₅₃	2
#20274308	2
#20274307	2
#20274306	2
#20274305	2
#20274304	2
C₈²×D₅₃	2
C₅₃×#1706	2
C₂×#1706	53

Subgroups — D53×#1706 #27371731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1706 #27371731