Subgroups — C₂×#20276532 #27537239

Order 13568.

806 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11719908	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20276532	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16810441	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810402	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₆×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
11	C₂²×#11719908	—	2	4	no	—
12	C₂²×#11719908	C₂²	1	1	yes	characteristic
13	C₂²×#11719908	C₂²	1	1	yes	characteristic
14	C₂²×#11719908	C₂²	1	4	yes	complemented
15	C₂×C₁₆×D₅₃	—	2	4	no	—
16	C₂×C₁₆×D₅₃	C₂²	1	4	yes	complemented
17	C₈×C₂²⋊D₅₃	C₄	1	4	yes	—
18	C₈×C₂²⋊D₅₃	C₂²	1	4	yes	—
19	C₂×#13133146	C₄	1	1	yes	characteristic
20	C₂×C₂²⋊#88322	C₄	1	1	yes	characteristic
21	C₂×#13133129	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
23	#16810441	C₂²	1	4	yes	complemented
24	#16810402	C₂²	1	4	yes	complemented
25	C₁₆×Dic₅₃	C₂²	1	4	yes	complemented
26	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
29	C₅₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
30	C₂²×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
31	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
33	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×D₅₃	—	2	2	no	—
35	C₂×C₈×D₅₃	—	2	2	no	—
36	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₅₃	C₂³	1	2	yes	—
38	C₄×C₂²⋊D₅₃	C₈	1	4	yes	—
39	C₄×C₂²⋊D₅₃	C₂×C₄	1	4	yes	—
40	C₂×#11719919	C₈	1	1	yes	characteristic
41	C₂×C₂²⋊Dic₅₃	C₈	1	1	yes	characteristic
42	C₂×#11719921	C₈	1	1	yes	characteristic
43	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×#11719908	—	2	2	no	—
45	C₂×#11719908	—	2	8	no	—
46	C₂×#11719908	D₄	1	4	yes	complemented
47	C₂×#11719908	C₂³	1	2	yes	—
48	C₂×#11719908	C₂³	1	2	yes	—
49	C₁₆×D₅₃	—	2	8	no	—
50	#13133146	C₂×C₄	1	4	yes	—
51	C₂²⋊#88322	C₂×C₄	1	4	yes	—
52	#13133129	C₂×C₄	1	4	yes	—
53	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
54	C₈×Dic₅₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₅₃	—	2	2	no	—
57	C₂²×C₈×C₅₃	—	2	2	no	—
58	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
62	C₂×C₁₆×C₅₃	—	2	2	no	—
63	C₂×C₁₆×C₅₃	—	2	2	no	—
64	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
65	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
66	C₂⁴×C₅₃	C₂×C₈	1	1	yes	characteristic
67	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	—	2	2	no	—
69	C₂²×C₄×C₅₃	—	2	2	no	—
70	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂×C₈	1	2	yes	—
72	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊D₅₃	C₁₆	1	8	yes	complemented
75	C₂×C₂²⋊D₅₃	C₂×C₈	1	4	yes	—
76	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
77	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
78	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
79	C₂×C₄×D₅₃	—	2	2	no	—
80	C₂×C₄×D₅₃	—	2	2	no	—
81	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
82	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
83	C₂×C₈×C₅₃	—	2	2	no	—
84	C₂×C₈×C₅₃	—	2	4	no	—
85	C₂×C₈×C₅₃	—	2	2	no	—
86	C₂×C₈×C₅₃	—	2	2	no	—
87	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₅₃	#41	1	2	yes	—
91	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
92	C₂²⋊Dic₅₃	C₂×C₈	1	4	yes	—
93	#11719921	C₂×C₈	1	4	yes	—
94	#11719919	C₂×C₈	1	4	yes	—
95	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
96	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
97	C₂×#88322	—	2	2	no	—
98	C₂×#88322	—	2	2	no	—
99	C₂×#88322	C₂²×C₄	1	2	yes	—
100	C₂×#88322	C₂²×C₄	1	2	yes	—
101	C₈×D₅₃	—	2	4	no	—
102	C₈×D₅₃	—	2	2	no	—
103	C₈×D₅₃	—	2	2	no	—
104	C₁₆×C₅₃	—	2	2	no	—
105	C₁₆×C₅₃	—	2	2	no	—
106	#11719908	—	2	2	no	—
107	#11719908	C₂×D₄	1	4	yes	complemented
108	C₂³×C₅₃	—	2	2	no	—
109	C₂³×C₅₃	—	2	2	no	—
110	C₂³×C₅₃	C₂×C₁₆	1	4	yes	complemented
111	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
112	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
113	C₂²×D₅₃	—	2	2	no	—
114	C₂²×D₅₃	—	2	2	no	—
115	C₂²×D₅₃	C₂×C₁₆	1	4	yes	complemented
116	C₂²×D₅₃	C₂²×C₈	1	2	yes	—
117	C₂×C₄×C₅₃	—	2	2	no	—
118	C₂×C₄×C₅₃	—	2	2	no	—
119	C₂×C₄×C₅₃	—	2	2	no	—
120	C₂×C₄×C₅₃	—	2	4	no	—
121	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
123	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
124	C₂×C₄×C₅₃	#131	1	2	yes	—
125	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
126	C₂²⋊D₅₃	C₂×C₁₆	1	16	yes	complemented
127	C₂×Dic₅₃	—	2	2	no	—
128	C₂×Dic₅₃	—	2	2	no	—
129	C₂×Dic₅₃	C₂×C₁₆	1	4	yes	complemented
130	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
131	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
132	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
133	C₄×D₅₃	—	2	2	no	—
134	C₄×D₅₃	—	2	2	no	—
135	C₄×D₅₃	—	2	4	no	—
136	C₈×C₅₃	—	2	2	no	—
137	C₈×C₅₃	C₄×D₄	1	2	yes	—
138	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
139	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
140	#88322	—	2	2	no	—
141	#88322	—	2	2	no	—
142	C₂×D₄×C₁₆	—	53	1	no	maximal, Sylow
143	C₂²×C₅₃	—	2	2	no	—
144	C₂²×C₅₃	—	2	2	no	—
145	C₂²×C₅₃	—	2	8	no	—
146	C₂²×C₅₃	C₈×D₄	1	2	yes	—
147	C₂²×C₅₃	C₂²×C₁₆	1	2	yes	—
148	C₂²×C₅₃	C₂²×C₁₆	1	4	yes	complemented
149	C₂²×C₅₃	#504	1	2	yes	—
150	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
151	C₂×D₅₃	—	2	2	no	—
152	C₂×D₅₃	—	2	2	no	—
153	C₂×D₅₃	—	2	8	no	—
154	C₂×D₅₃	C₂²×C₁₆	1	4	yes	complemented
155	C₄×C₅₃	—	2	2	no	—
156	C₄×C₅₃	C₈×D₄	1	2	yes	—
157	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
158	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
159	Dic₅₃	—	2	2	no	—
160	Dic₅₃	—	2	2	no	—
161	Dic₅₃	C₂²×C₁₆	1	4	yes	complemented
162	C₂³×C₁₆	—	53	1	no	—
163	C₂³×C₁₆	—	53	1	no	—
164	C₂×C₈×D₄	—	53	1	no	—
165	D₄×C₁₆	—	53	8	no	—
166	C₂×C₄⋊C₁₆	—	53	1	no	—
167	C₂×C₂²⋊C₁₆	—	53	1	no	—
168	C₂×C₂²⋊C₁₆	D₅₃	1	1	yes	characteristic, complemented
169	C₂×C₄×C₁₆	—	53	1	no	—
170	C₂×C₅₃	—	2	4	no	—
171	C₂×C₅₃	D₄×C₁₆	1	4	yes	complemented
172	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
173	C₂×C₅₃	C₂³×C₁₆	1	1	yes	characteristic
174	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
175	D₅₃	—	2	4	no	—
176	C₂³×C₈	—	53	1	no	—
177	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
178	C₂×C₄×D₄	—	53	1	no	—
179	C₂²×C₁₆	—	53	1	no	—
180	C₂²×C₁₆	—	53	4	no	—
181	C₂²×C₁₆	—	53	1	no	—
182	C₂²×C₁₆	—	53	4	no	—
183	C₂²×C₁₆	—	106	4	no	—
184	C₂²×C₁₆	—	106	4	no	—
185	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
186	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
187	C₈×D₄	—	53	4	no	—
188	C₈×D₄	—	53	4	no	—
189	C₂×C₄⋊C₈	—	53	1	no	—
190	C₂×C₂²⋊C₈	—	53	1	no	—
191	C₂×C₂²⋊C₈	—	53	1	no	—
192	C₂×C₄×C₈	—	53	1	no	—
193	C₄⋊C₁₆	—	53	4	no	—
194	C₂²⋊C₁₆	—	53	4	no	—
195	C₂²⋊C₁₆	C₂×D₅₃	1	4	yes	complemented
196	C₄×C₁₆	—	53	4	no	—
197	C₅₃	C₂×D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
198	C₂²×D₄	—	53	1	no	—
199	C₂³×C₄	—	53	1	no	—
200	C₂³×C₄	C₄×D₅₃	1	1	yes	characteristic
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	—	2	2	no	—
203	C₂²×C₈	—	53	1	no	—
204	C₂²×C₈	—	53	1	no	—
205	C₂²×C₈	—	53	2	no	—
206	C₂²×C₈	—	53	2	no	—
207	C₂²×C₈	—	106	2	no	—
208	C₂²×C₈	—	106	2	no	—
209	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
210	C₂²×C₈	C₄×D₅₃	1	2	yes	—
211	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
212	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
213	C₄×D₄	—	53	4	no	—
214	C₄×D₄	—	53	4	no	—
215	C₂×C₄⋊C₄	—	53	1	no	—
216	C₂×C₂²⋊C₄	—	53	1	no	—
217	C₂×C₂²⋊C₄	—	53	1	no	—
218	C₂×C₄²	—	53	1	no	—
219	C₂×C₁₆	—	2	2	no	—
220	C₂×C₁₆	—	2	2	no	—
221	C₂×C₁₆	—	53	4	no	—
222	C₂×C₁₆	—	53	2	no	—
223	C₂×C₁₆	—	53	2	no	—
224	C₂×C₁₆	—	106	8	no	—
225	C₂×C₁₆	—	106	8	no	—
226	C₂×C₁₆	—	106	2	no	—
227	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
228	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
229	C₄⋊C₈	—	53	4	no	—
230	C₂²⋊C₈	—	53	4	no	—
231	C₂²⋊C₈	—	53	4	no	—
232	C₄×C₈	—	53	2	no	—
233	C₄×C₈	—	53	2	no	—
234	C₂⁴	—	53	1	no	—
235	C₂⁴	C₈×D₅₃	1	1	yes	characteristic
236	C₂×D₄	—	53	8	no	—
237	C₂×D₄	—	53	4	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	53	1	no	—
241	C₂²×C₄	—	53	1	no	—
242	C₂²×C₄	—	53	1	no	—
243	C₂²×C₄	—	53	2	no	—
244	C₂²×C₄	—	53	2	no	—
245	C₂²×C₄	—	106	2	no	—
246	C₂²×C₄	—	106	2	no	—
247	C₂²×C₄	C₈×D₅₃	1	1	yes	characteristic
248	C₂²×C₄	C₈×D₅₃	1	2	yes	—
249	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
250	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	53	2	no	—
256	C₂×C₈	—	53	2	no	—
257	C₂×C₈	—	106	2	no	—
258	C₂×C₈	—	106	2	no	—
259	C₂×C₈	—	106	4	no	—
260	C₂×C₈	—	106	2	no	—
261	C₂×C₈	—	106	2	no	—
262	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
263	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
264	C₂×C₈	D₄×D₅₃	1	2	yes	—
265	C₂×C₈	#11719947	1	2	yes	—
266	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
267	C₄⋊C₄	—	53	4	no	—
268	C₂²⋊C₄	—	53	4	no	—
269	C₂²⋊C₄	—	53	4	no	—
270	C₄²	—	53	2	no	—
271	C₄²	—	53	2	no	—
272	C₁₆	—	2	2	no	—
273	C₁₆	—	2	2	no	—
274	C₁₆	—	53	4	no	—
275	C₁₆	—	106	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	53	4	no	—
279	C₂³	—	53	2	no	—
280	C₂³	—	106	2	no	—
281	C₂³	—	106	2	no	—
282	C₂³	C₁₆×D₅₃	1	4	yes	complemented
283	C₂³	C₂×C₈×D₅₃	1	2	yes	—
284	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
285	D₄	—	53	16	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	53	4	no	—
291	C₂×C₄	—	53	2	no	—
292	C₂×C₄	—	53	2	no	—
293	C₂×C₄	—	53	2	no	—
294	C₂×C₄	—	106	2	no	—
295	C₂×C₄	—	106	2	no	—
296	C₂×C₄	—	106	2	no	—
297	C₂×C₄	—	106	2	no	—
298	C₂×C₄	—	106	4	no	—
299	C₂×C₄	#13133177	1	2	yes	—
300	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
301	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
302	C₂×C₄	#13133225	1	2	yes	—
303	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
304	C₈	—	2	2	no	—
305	C₈	—	106	2	no	—
306	C₈	—	106	2	no	—
307	C₈	#13133177	1	2	yes	—
308	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
309	C₈	C₂×#11719947	1	1	yes	characteristic
310	C₂²	—	2	8	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	53	4	no	—
314	C₂²	—	106	8	no	—
315	C₂²	—	106	2	no	—
316	C₂²	—	106	2	no	—
317	C₂²	#16810686	1	2	yes	—
318	C₂²	C₂×C₁₆×D₅₃	1	2	yes	—
319	C₂²	C₂×C₁₆×D₅₃	1	4	yes	complemented
320	C₂²	#16811041	1	2	yes	—
321	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
322	C₄	—	2	2	no	—
323	C₄	—	53	4	no	—
324	C₄	—	106	2	no	—
325	C₄	—	106	2	no	—
326	C₄	#16810686	1	2	yes	—
327	C₄	C₂×#13133177	1	1	yes	characteristic
328	C₄	C₂×#13133225	1	1	yes	characteristic
329	C₂	—	2	4	no	—
330	C₂	—	106	4	no	—
331	C₂	#20276532	1	4	yes	direct product factor
332	C₂	C₂×#16810686	1	1	yes	characteristic
333	C₂	C₂²×C₁₆×D₅₃	1	1	yes	characteristic
334	C₂	C₂×#16811041	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₅₃
commutator	C₂×C₅₃	C₂³×C₁₆
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₂×C₅₃×C₂²⋊C₁₆	C₂
socle	C₂³×C₅₃	C₂²×C₈
prime radical	C₂²×C₂²⋊D₅₃	C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₅₃
hypocenter	C₅₃	C₂×D₄×C₁₆
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂³×#11719908	C₂	semidirect
2. C₂²×C₁₆×D₅₃	C₂	semidirect
4. #20276532	C₂	direct (N × H)
5. C₂×#16810441	C₂	semidirect
6. C₂×#16810402	C₂	semidirect
7. C₂×C₁₆×Dic₅₃	C₂	semidirect
8. C₂×C₅₃×C₂²⋊C₁₆	C₂	semidirect
14. C₂²×#11719908	C₂²	semidirect
16. C₂×C₁₆×D₅₃	C₂²	semidirect
23. #16810441	C₂²	semidirect
24. #16810402	C₂²	semidirect
25. C₁₆×Dic₅₃	C₂²	semidirect
29. C₅₃×C₂²⋊C₁₆	C₂²	semidirect
46. C₂×#11719908	D₄	semidirect
74. C₂×C₂²⋊D₅₃	C₁₆	semidirect
107. #11719908	C₂×D₄	semidirect
110. C₂³×C₅₃	C₂×C₁₆	semidirect
115. C₂²×D₅₃	C₂×C₁₆	semidirect
126. C₂²⋊D₅₃	C₂×C₁₆	semidirect
129. C₂×Dic₅₃	C₂×C₁₆	semidirect
148. C₂²×C₅₃	C₂²×C₁₆	semidirect
154. C₂×D₅₃	C₂²×C₁₆	semidirect
161. Dic₅₃	C₂²×C₁₆	semidirect
168. C₂×C₂²⋊C₁₆	D₅₃	semidirect
171. C₂×C₅₃	D₄×C₁₆	semidirect
195. C₂²⋊C₁₆	C₂×D₅₃	semidirect
197. C₅₃	C₂×D₄×C₁₆	semidirect
282. C₂³	C₁₆×D₅₃	semidirect
319. C₂²	C₂×C₁₆×D₅₃	semidirect
331. C₂	#20276532	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11719908	2
C₂²×C₁₆×D₅₃	2
C₂×C₈×C₂²⋊D₅₃	2
#20276532	2
C₂×#16810441	2
C₂×#16810402	2
C₂×C₁₆×Dic₅₃	2
C₂×C₅₃×C₂²⋊C₁₆	2
C₂×D₄×C₁₆	53

Subgroups — C2×#20276532 #27537239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20276532 #27537239