Subgroups — C₂³×C₄×C₂²⋊D₅₃ #28290655

Order 13568.

19998 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₂²⋊D₅₃	C₂	1	56	yes	maximal, direct product factor
4	C₂³×#11719919	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₂²⋊Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×#11719921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₄×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁵×C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
10	C₂³×C₂²⋊D₅₃	C₄	1	32	yes	direct product factor
11	C₂³×C₂²⋊D₅₃	C₂²	1	28	yes	—
12	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
13	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
14	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×D₅₃	—	2	16	no	—
16	C₂³×C₄×D₅₃	C₂²	1	28	yes	complemented
17	C₂×C₄×C₂²⋊D₅₃	C₂²	1	448	yes	direct product factor
18	C₂²×#11719919	C₂²	1	28	yes	complemented
19	C₂²×C₂²⋊Dic₅₃	C₂²	1	28	yes	complemented
20	C₂²×#11719921	C₂²	1	28	yes	complemented
21	C₂²×C₄×Dic₅₃	C₂²	1	28	yes	complemented
22	C₂⁶×C₅₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₅₃	—	2	16	no	—
24	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₅₃	C₂²	1	28	yes	complemented
27	C₂⁴×D₅₃	—	2	8	no	—
28	C₂⁴×D₅₃	—	2	8	no	—
29	C₂⁴×D₅₃	C₂×C₄	1	16	yes	complemented
30	C₂⁴×D₅₃	C₂³	1	14	yes	—
31	C₂²×C₂²⋊D₅₃	C₂×C₄	1	448	yes	direct product factor
32	C₂²×C₂²⋊D₅₃	C₂³	1	112	yes	—
33	C₂³×Dic₅₃	—	2	8	no	—
34	C₂³×Dic₅₃	—	2	8	no	—
35	C₂³×Dic₅₃	C₂×C₄	1	16	yes	complemented
36	C₂³×Dic₅₃	C₂³	1	14	yes	—
37	C₂³×Dic₅₃	C₂³	1	14	yes	—
38	C₂³×Dic₅₃	C₂³	1	14	yes	—
39	C₂²×C₄×D₅₃	—	2	224	no	—
40	C₂²×C₄×D₅₃	C₂³	1	112	yes	complemented
41	C₄×C₂²⋊D₅₃	C₂³	1	512	yes	direct product factor
42	C₂×#11719919	C₂³	1	112	yes	complemented
43	C₂×C₂²⋊Dic₅₃	C₂³	1	112	yes	complemented
44	C₂×#11719921	C₂³	1	112	yes	complemented
45	C₂×C₄×Dic₅₃	C₂³	1	112	yes	complemented
46	C₂⁵×C₅₃	—	2	8	no	—
47	C₂⁵×C₅₃	—	2	8	no	—
48	C₂⁵×C₅₃	C₂×C₄	1	16	yes	complemented
49	C₂⁵×C₅₃	C₂³	1	14	yes	—
50	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₅₃	—	2	8	no	—
52	C₂³×C₄×C₅₃	—	2	224	no	—
53	C₂³×C₄×C₅₃	D₄	1	16	yes	complemented
54	C₂³×C₄×C₅₃	C₂³	1	14	yes	—
55	C₂³×C₄×C₅₃	C₂³	1	14	yes	—
56	C₂³×C₄×C₅₃	C₂³	1	112	yes	complemented
57	C₂⁴×C₅₃	—	2	128	no	—
58	C₂⁴×C₅₃	—	2	56	no	—
59	C₂⁴×C₅₃	—	2	56	no	—
60	C₂⁴×C₅₃	C₂²×C₄	1	8	yes	—
61	C₂⁴×C₅₃	C₂²×C₄	1	112	yes	complemented
62	C₂⁴×C₅₃	C₂×D₄	1	8	yes	—
63	C₂⁴×C₅₃	#41	1	8	yes	—
64	C₂⁴×C₅₃	C₂⁴	1	28	yes	—
65	C₂⁴×C₅₃	C₂⁴	1	7	yes	—
66	C₂³×D₅₃	—	2	128	no	—
67	C₂³×D₅₃	—	2	56	no	—
68	C₂³×D₅₃	—	2	56	no	—
69	C₂³×D₅₃	C₂²×C₄	1	112	yes	complemented
70	C₂³×D₅₃	C₂⁴	1	28	yes	—
71	C₂²×C₄×C₅₃	—	2	56	no	—
72	C₂²×C₄×C₅₃	—	2	448	no	—
73	C₂²×C₄×C₅₃	C₂×D₄	1	112	yes	complemented
74	C₂²×C₄×C₅₃	C₂⁴	1	28	yes	—
75	C₂²×C₄×C₅₃	C₂⁴	1	28	yes	—
76	C₂²×C₄×C₅₃	C₂⁴	1	64	yes	complemented
77	C₂×C₂²⋊D₅₃	C₂²×C₄	1	896	yes	direct product factor
78	C₂×C₂²⋊D₅₃	C₂⁴	1	64	yes	—
79	C₂²×Dic₅₃	—	2	56	no	—
80	C₂²×Dic₅₃	—	2	56	no	—
81	C₂²×Dic₅₃	C₂²×C₄	1	112	yes	complemented
82	C₂²×Dic₅₃	C₂⁴	1	28	yes	—
83	C₂²×Dic₅₃	C₂⁴	1	28	yes	—
84	C₂²×Dic₅₃	C₂⁴	1	28	yes	—
85	C₂×C₄×D₅₃	—	2	448	no	—
86	C₂×C₄×D₅₃	C₂⁴	1	64	yes	complemented
87	C₂²⋊Dic₅₃	C₂⁴	1	64	yes	complemented
88	#11719921	C₂⁴	1	64	yes	complemented
89	#11719919	C₂⁴	1	64	yes	complemented
90	C₄×Dic₅₃	C₂⁴	1	64	yes	complemented
91	C₂³×C₅₃	—	2	448	no	—
92	C₂³×C₅₃	—	2	56	no	—
93	C₂³×C₅₃	—	2	56	no	—
94	C₂³×C₅₃	C₄×D₄	1	64	yes	complemented
95	C₂³×C₅₃	C₂³×C₄	1	28	yes	—
96	C₂³×C₅₃	C₂³×C₄	1	112	yes	complemented
97	C₂³×C₅₃	C₂²×D₄	1	28	yes	—
98	C₂³×C₅₃	C₂×#41	1	28	yes	—
99	C₂³×C₅₃	C₂⁵	1	8	yes	—
100	C₂³×C₅₃	C₂⁵	1	7	yes	—
101	C₂²×D₅₃	—	2	448	no	—
102	C₂²×D₅₃	—	2	56	no	—
103	C₂²×D₅₃	—	2	56	no	—
104	C₂²×D₅₃	C₂³×C₄	1	112	yes	complemented
105	C₂²×D₅₃	C₂⁵	1	8	yes	—
106	C₂×C₄×C₅₃	—	2	56	no	—
107	C₂×C₄×C₅₃	—	2	128	no	—
108	C₂×C₄×C₅₃	C₂²×D₄	1	112	yes	complemented
109	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
110	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
111	C₂²⋊D₅₃	C₂³×C₄	1	256	yes	direct product factor
112	C₂×Dic₅₃	—	2	56	no	—
113	C₂×Dic₅₃	—	2	56	no	—
114	C₂×Dic₅₃	C₂³×C₄	1	112	yes	complemented
115	C₂×Dic₅₃	C₂⁵	1	8	yes	—
116	C₂×Dic₅₃	C₂⁵	1	8	yes	—
117	C₂×Dic₅₃	C₂⁵	1	8	yes	—
118	C₄×D₅₃	—	2	128	no	—
119	C₂³×C₄×D₄	—	53	1	no	maximal, Sylow
120	C₂²×C₅₃	—	2	8	no	—
121	C₂²×C₅₃	—	2	8	no	—
122	C₂²×C₅₃	—	2	224	no	—
123	C₂²×C₅₃	C₂×C₄×D₄	1	112	yes	complemented
124	C₂²×C₅₃	C₂⁴×C₄	1	14	yes	—
125	C₂²×C₅₃	C₂⁴×C₄	1	16	yes	complemented
126	C₂²×C₅₃	C₂³×D₄	1	14	yes	—
127	C₂²×C₅₃	C₂²×#41	1	14	yes	—
128	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
129	C₂×D₅₃	—	2	8	no	—
130	C₂×D₅₃	—	2	8	no	—
131	C₂×D₅₃	—	2	224	no	—
132	C₂×D₅₃	C₂⁴×C₄	1	16	yes	complemented
133	C₄×C₅₃	—	2	8	no	—
134	C₄×C₅₃	C₂³×D₄	1	16	yes	complemented
135	Dic₅₃	—	2	8	no	—
136	Dic₅₃	—	2	8	no	—
137	Dic₅₃	C₂⁴×C₄	1	16	yes	complemented
138	C₂⁴×D₄	—	53	1	no	—
139	C₂⁵×C₄	—	53	1	no	—
140	C₂⁵×C₄	D₅₃	1	1	yes	characteristic, complemented
141	C₂²×C₄×D₄	—	53	56	no	—
142	C₂³×C₄⋊C₄	—	53	1	no	—
143	C₂³×C₂²⋊C₄	—	53	1	no	—
144	C₂³×C₂²⋊C₄	—	53	1	no	—
145	C₂³×C₄²	—	53	1	no	—
146	C₂×C₅₃	—	2	16	no	—
147	C₂×C₅₃	C₂²×C₄×D₄	1	28	yes	complemented
148	C₂×C₅₃	C₂⁵×C₄	1	1	yes	characteristic
149	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
150	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
151	D₅₃	—	2	16	no	—
152	C₂⁶	—	53	1	no	—
153	C₂⁶	C₂×D₅₃	1	1	yes	characteristic
154	C₂³×D₄	—	53	32	no	—
155	C₂³×D₄	—	53	28	no	—
156	C₂⁴×C₄	—	2	16	no	—
157	C₂⁴×C₄	—	53	1	no	—
158	C₂⁴×C₄	—	53	1	no	—
159	C₂⁴×C₄	—	53	1	no	—
160	C₂⁴×C₄	—	53	28	no	—
161	C₂⁴×C₄	—	106	16	no	—
162	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic
163	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic
164	C₂⁴×C₄	C₂×D₅₃	1	28	yes	complemented
165	C₂×C₄×D₄	—	53	448	no	—
166	C₂²×C₄⋊C₄	—	53	28	no	—
167	C₂²×C₂²⋊C₄	—	53	28	no	—
168	C₂²×C₂²⋊C₄	—	53	28	no	—
169	C₂²×C₄²	—	53	28	no	—
170	C₅₃	C₂³×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
171	C₂⁵	—	2	8	no	—
172	C₂⁵	—	2	8	no	—
173	C₂⁵	—	53	16	no	—
174	C₂⁵	—	53	14	no	—
175	C₂⁵	—	106	8	no	—
176	C₂⁵	—	106	8	no	—
177	C₂⁵	C₄×D₅₃	1	16	yes	complemented
178	C₂⁵	C₂²×D₅₃	1	14	yes	—
179	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
180	C₂²×D₄	—	53	448	no	—
181	C₂²×D₄	—	53	112	no	—
182	C₂³×C₄	—	2	8	no	—
183	C₂³×C₄	—	2	224	no	—
184	C₂³×C₄	—	53	16	no	—
185	C₂³×C₄	—	53	14	no	—
186	C₂³×C₄	—	53	14	no	—
187	C₂³×C₄	—	53	14	no	—
188	C₂³×C₄	—	53	112	no	—
189	C₂³×C₄	—	106	8	no	—
190	C₂³×C₄	—	106	8	no	—
191	C₂³×C₄	—	106	224	no	—
192	C₂³×C₄	C₂²⋊D₅₃	1	16	yes	direct product factor
193	C₂³×C₄	C₂²×D₅₃	1	14	yes	—
194	C₂³×C₄	C₂²×D₅₃	1	14	yes	—
195	C₂³×C₄	C₂²×D₅₃	1	112	yes	complemented
196	C₄×D₄	—	53	512	no	—
197	C₂×C₄⋊C₄	—	53	112	no	—
198	C₂×C₂²⋊C₄	—	53	112	no	—
199	C₂×C₂²⋊C₄	—	53	112	no	—
200	C₂×C₄²	—	53	112	no	—
201	C₂⁴	—	2	128	no	—
202	C₂⁴	—	2	56	no	—
203	C₂⁴	—	2	56	no	—
204	C₂⁴	—	53	112	no	—
205	C₂⁴	—	53	28	no	—
206	C₂⁴	—	106	128	no	—
207	C₂⁴	—	106	56	no	—
208	C₂⁴	—	106	56	no	—
209	C₂⁴	C₂×C₄×D₅₃	1	8	yes	—
210	C₂⁴	C₂×C₄×D₅₃	1	112	yes	complemented
211	C₂⁴	#11719945	1	8	yes	—
212	C₂⁴	C₂×C₂²⋊D₅₃	1	8	yes	—
213	C₂⁴	C₂³×D₅₃	1	28	yes	—
214	C₂⁴	C₂³×D₅₃	1	7	yes	—
215	C₂×D₄	—	53	896	no	—
216	C₂×D₄	—	53	64	no	—
217	C₂²×C₄	—	2	56	no	—
218	C₂²×C₄	—	2	448	no	—
219	C₂²×C₄	—	53	112	no	—
220	C₂²×C₄	—	53	28	no	—
221	C₂²×C₄	—	53	28	no	—
222	C₂²×C₄	—	53	28	no	—
223	C₂²×C₄	—	53	64	no	—
224	C₂²×C₄	—	106	56	no	—
225	C₂²×C₄	—	106	56	no	—
226	C₂²×C₄	—	106	448	no	—
227	C₂²×C₄	C₂×C₂²⋊D₅₃	1	112	yes	direct product factor
228	C₂²×C₄	C₂³×D₅₃	1	28	yes	—
229	C₂²×C₄	C₂³×D₅₃	1	28	yes	—
230	C₂²×C₄	C₂³×D₅₃	1	64	yes	complemented
231	C₄⋊C₄	—	53	64	no	—
232	C₂²⋊C₄	—	53	64	no	—
233	C₂²⋊C₄	—	53	64	no	—
234	C₄²	—	53	64	no	—
235	C₂³	—	2	448	no	—
236	C₂³	—	2	56	no	—
237	C₂³	—	2	56	no	—
238	C₂³	—	53	112	no	—
239	C₂³	—	53	8	no	—
240	C₂³	—	106	448	no	—
241	C₂³	—	106	56	no	—
242	C₂³	—	106	56	no	—
243	C₂³	C₄×C₂²⋊D₅₃	1	64	yes	direct product factor
244	C₂³	C₂²×C₄×D₅₃	1	28	yes	—
245	C₂³	C₂²×C₄×D₅₃	1	112	yes	complemented
246	C₂³	C₂²×C₂²⋊D₅₃	1	28	yes	—
247	C₂³	C₂×#11719945	1	28	yes	—
248	C₂³	C₂⁴×D₅₃	1	8	yes	—
249	C₂³	C₂⁴×D₅₃	1	7	yes	—
250	D₄	—	53	256	no	—
251	C₂×C₄	—	2	56	no	—
252	C₂×C₄	—	2	128	no	—
253	C₂×C₄	—	53	112	no	—
254	C₂×C₄	—	53	8	no	—
255	C₂×C₄	—	53	8	no	—
256	C₂×C₄	—	53	8	no	—
257	C₂×C₄	—	106	56	no	—
258	C₂×C₄	—	106	56	no	—
259	C₂×C₄	—	106	128	no	—
260	C₂×C₄	C₂²×C₂²⋊D₅₃	1	112	yes	direct product factor
261	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
262	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
263	C₂²	—	2	224	no	—
264	C₂²	—	2	8	no	—
265	C₂²	—	2	8	no	—
266	C₂²	—	53	16	no	—
267	C₂²	—	106	224	no	—
268	C₂²	—	106	8	no	—
269	C₂²	—	106	8	no	—
270	C₂²	C₂×C₄×C₂²⋊D₅₃	1	112	yes	direct product factor
271	C₂²	C₂³×C₄×D₅₃	1	14	yes	—
272	C₂²	C₂³×C₄×D₅₃	1	16	yes	complemented
273	C₂²	C₂³×C₂²⋊D₅₃	1	14	yes	—
274	C₂²	C₂²×#11719945	1	14	yes	—
275	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
276	C₄	—	2	8	no	—
277	C₄	—	53	16	no	—
278	C₄	—	106	8	no	—
279	C₄	—	106	8	no	—
280	C₄	C₂³×C₂²⋊D₅₃	1	16	yes	direct product factor
281	C₂	—	2	16	no	—
282	C₂	—	106	16	no	—
283	C₂	C₂²×C₄×C₂²⋊D₅₃	1	28	yes	direct product factor
284	C₂	C₂⁴×C₄×D₅₃	1	1	yes	characteristic
285	C₂	C₂⁴×C₂²⋊D₅₃	1	1	yes	characteristic
286	C₂	C₂³×#11719945	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₄	C₂×D₅₃
commutator	C₂×C₅₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂⁵×C₄×C₅₃	C₂
socle	C₂⁵×C₅₃	C₂³
prime radical	C₂⁴×C₂²⋊D₅₃	C₂
cosocle	C₂²×C₅₃	C₂⁶
hypercenter	C₂⁵×C₄	D₅₃
hypocenter	C₅₃	C₂³×C₄×D₄
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴×C₄ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₄×D₅₃	C₂	semidirect
3. C₂²×C₄×C₂²⋊D₅₃	C₂	direct (N × H)
4. C₂³×#11719919	C₂	semidirect
5. C₂³×C₂²⋊Dic₅₃	C₂	semidirect
6. C₂³×#11719921	C₂	semidirect
7. C₂³×C₄×Dic₅₃	C₂	semidirect
8. C₂⁵×C₄×C₅₃	C₂	semidirect
10. C₂³×C₂²⋊D₅₃	C₄	direct (N × H)
16. C₂³×C₄×D₅₃	C₂²	semidirect
17. C₂×C₄×C₂²⋊D₅₃	C₂²	direct (N × H)
18. C₂²×#11719919	C₂²	semidirect
19. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
20. C₂²×#11719921	C₂²	semidirect
21. C₂²×C₄×Dic₅₃	C₂²	semidirect
26. C₂⁴×C₄×C₅₃	C₂²	semidirect
29. C₂⁴×D₅₃	C₂×C₄	semidirect
31. C₂²×C₂²⋊D₅₃	C₂×C₄	direct (N × H)
35. C₂³×Dic₅₃	C₂×C₄	semidirect
40. C₂²×C₄×D₅₃	C₂³	semidirect
41. C₄×C₂²⋊D₅₃	C₂³	direct (N × H)
42. C₂×#11719919	C₂³	semidirect
43. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
44. C₂×#11719921	C₂³	semidirect
45. C₂×C₄×Dic₅₃	C₂³	semidirect
48. C₂⁵×C₅₃	C₂×C₄	semidirect
53. C₂³×C₄×C₅₃	D₄	semidirect
56. C₂³×C₄×C₅₃	C₂³	semidirect
61. C₂⁴×C₅₃	C₂²×C₄	semidirect
69. C₂³×D₅₃	C₂²×C₄	semidirect
73. C₂²×C₄×C₅₃	C₂×D₄	semidirect
76. C₂²×C₄×C₅₃	C₂⁴	semidirect
77. C₂×C₂²⋊D₅₃	C₂²×C₄	direct (N × H)
81. C₂²×Dic₅₃	C₂²×C₄	semidirect
86. C₂×C₄×D₅₃	C₂⁴	semidirect
87. C₂²⋊Dic₅₃	C₂⁴	semidirect
88. #11719921	C₂⁴	semidirect
89. #11719919	C₂⁴	semidirect
90. C₄×Dic₅₃	C₂⁴	semidirect
94. C₂³×C₅₃	C₄×D₄	semidirect
96. C₂³×C₅₃	C₂³×C₄	semidirect
104. C₂²×D₅₃	C₂³×C₄	semidirect
108. C₂×C₄×C₅₃	C₂²×D₄	semidirect
111. C₂²⋊D₅₃	C₂³×C₄	direct (N × H)
114. C₂×Dic₅₃	C₂³×C₄	semidirect
123. C₂²×C₅₃	C₂×C₄×D₄	semidirect
125. C₂²×C₅₃	C₂⁴×C₄	semidirect
132. C₂×D₅₃	C₂⁴×C₄	semidirect
134. C₄×C₅₃	C₂³×D₄	semidirect
137. Dic₅₃	C₂⁴×C₄	semidirect
140. C₂⁵×C₄	D₅₃	semidirect
147. C₂×C₅₃	C₂²×C₄×D₄	semidirect
164. C₂⁴×C₄	C₂×D₅₃	semidirect
170. C₅₃	C₂³×C₄×D₄	semidirect
177. C₂⁵	C₄×D₅₃	semidirect
192. C₂³×C₄	C₂²⋊D₅₃	direct (N × H)
195. C₂³×C₄	C₂²×D₅₃	semidirect
210. C₂⁴	C₂×C₄×D₅₃	semidirect
227. C₂²×C₄	C₂×C₂²⋊D₅₃	direct (N × H)
230. C₂²×C₄	C₂³×D₅₃	semidirect
243. C₂³	C₄×C₂²⋊D₅₃	direct (N × H)
245. C₂³	C₂²×C₄×D₅₃	semidirect
260. C₂×C₄	C₂²×C₂²⋊D₅₃	direct (N × H)
270. C₂²	C₂×C₄×C₂²⋊D₅₃	direct (N × H)
272. C₂²	C₂³×C₄×D₅₃	semidirect
280. C₄	C₂³×C₂²⋊D₅₃	direct (N × H)
283. C₂	C₂²×C₄×C₂²⋊D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₂²⋊D₅₃	2
C₂⁴×C₄×D₅₃	2
C₂²×C₄×C₂²⋊D₅₃	2
C₂³×#11719919	2
C₂³×C₂²⋊Dic₅₃	2
C₂³×#11719921	2
C₂³×C₄×Dic₅₃	2
C₂⁵×C₄×C₅₃	2
C₂³×C₄×D₄	53

Subgroups — C23×C4×C22⋊D53 #28290655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×C₂²⋊D₅₃ #28290655