Subgroups — C₄×#16810385 #27289272

Order 13568.

1182 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#88322	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810385	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×#88322	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₅₃	—	2	1	no	—
8	C₂×C₄×#88322	—	2	2	no	—
9	C₂×C₄×#88322	—	2	2	no	—
10	C₂×C₄×#88322	C₄	1	4	yes	complemented
11	C₄×C₄⋊Dic₅₃	—	2	2	no	—
12	C₄×C₄⋊Dic₅₃	C₄	1	4	yes	complemented
13	C₂×#13133124	—	2	1	no	—
14	#16810385	C₄	1	16	yes	direct product factor
15	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₅₃	—	2	1	no	—
17	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₅₃	—	2	2	no	—
19	C₄×C₄⋊C₄×C₅₃	C₄	1	4	yes	complemented
20	C₂×#95×C₅₃	—	2	1	no	—
21	C₂³×Dic₅₃	—	2	2	no	—
22	C₂²×#88322	—	2	2	no	—
23	C₂²×#88322	—	2	2	no	—
24	C₂²×#88322	—	2	4	no	—
25	C₂²×#88322	C₂×C₄	1	4	yes	—
26	C₂²×#88322	C₂×C₄	1	8	yes	—
27	C₂×C₄⋊Dic₅₃	—	2	2	no	—
28	C₂×C₄⋊Dic₅₃	—	2	4	no	—
29	C₂×C₄⋊Dic₅₃	C₂×C₄	1	8	yes	—
30	C₂×C₄⋊Dic₅₃	C₂×C₄	1	4	yes	—
31	C₂×C₄×Dic₅₃	—	2	4	no	—
32	C₂×C₄×Dic₅₃	—	4	2	no	—
33	C₂×C₄×Dic₅₃	—	4	2	no	—
34	C₄×#88322	—	2	8	no	—
35	#13133124	—	2	4	no	—
36	C₂³×C₄×C₅₃	—	2	2	no	—
37	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	8	yes	—
43	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₅₃	—	2	4	no	—
45	C₂×C₄²×C₅₃	—	4	2	no	—
46	C₂×C₄²×C₅₃	—	4	2	no	—
47	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₅₃	D₄	1	2	yes	—
51	C₂×C₄²×C₅₃	D₄	1	2	yes	—
52	C₂×C₄²×C₅₃	Q₈	1	2	yes	—
53	#95×C₅₃	—	2	4	no	—
54	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₅₃	—	2	4	no	—
56	C₂²×C₄×C₅₃	—	2	4	no	—
57	C₂²×C₄×C₅₃	—	2	8	no	—
58	C₂²×C₄×C₅₃	—	4	2	no	—
59	C₂²×C₄×C₅₃	—	4	2	no	—
60	C₂²×C₄×C₅₃	—	4	4	no	—
61	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₅₃	D₈	1	2	yes	—
68	C₂²×C₄×C₅₃	SD₁₆	1	2	yes	—
69	C₂²×C₄×C₅₃	SD₁₆	1	2	yes	—
70	C₂²×C₄×C₅₃	Q₁₆	1	2	yes	—
71	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	#41	1	4	yes	—
79	C₂²×Dic₅₃	—	2	4	no	—
80	C₂²×Dic₅₃	—	2	8	no	—
81	C₂²×Dic₅₃	—	4	2	no	—
82	C₂²×Dic₅₃	—	4	2	no	—
83	C₂²×Dic₅₃	—	4	4	no	—
84	C₄⋊C₄×C₅₃	—	2	4	no	—
85	C₄⋊C₄×C₅₃	—	2	8	no	—
86	C₄⋊C₄×C₅₃	C₄²	1	8	yes	complemented
87	C₄²×C₅₃	—	4	8	no	—
88	C₄²×C₅₃	C₄²	1	4	yes	—
89	C₄²×C₅₃	C₂²⋊C₄	1	4	yes	—
90	C₄²×C₅₃	C₄⋊C₄	1	4	yes	—
91	C₄²×C₅₃	C₄⋊C₄	1	4	yes	—
92	C₄⋊Dic₅₃	—	2	4	no	—
93	C₄⋊Dic₅₃	—	2	8	no	—
94	C₄⋊Dic₅₃	C₄²	1	8	yes	complemented
95	C₄×Dic₅₃	—	4	8	no	—
96	C₂×#88322	—	2	4	no	—
97	C₂×#88322	—	2	4	no	—
98	C₂×#88322	—	2	8	no	—
99	C₂×#88322	—	2	8	no	—
100	C₂×#88322	C₄²	1	8	yes	complemented
101	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂³×C₅₃	C₄×D₄	1	4	yes	—
105	C₂³×C₅₃	C₂×D₈	1	1	yes	characteristic
106	C₂³×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
107	C₂³×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
108	C₂³×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
109	C₂³×C₅₃	#135	1	4	yes	—
110	C₂×C₄×C₅₃	—	2	4	no	—
111	C₂×C₄×C₅₃	—	2	4	no	—
112	C₂×C₄×C₅₃	—	2	4	no	—
113	C₂×C₄×C₅₃	—	2	8	no	—
114	C₂×C₄×C₅₃	—	4	4	no	—
115	C₂×C₄×C₅₃	—	4	4	no	—
116	C₂×C₄×C₅₃	—	4	8	no	—
117	C₂×C₄×C₅₃	—	4	8	no	—
118	C₂×C₄×C₅₃	#95	1	4	yes	—
119	C₂×C₄×C₅₃	#95	1	4	yes	—
120	C₂×C₄×C₅₃	#102	1	4	yes	—
121	C₂×C₄×C₅₃	#102	1	4	yes	—
122	C₂×C₄×C₅₃	#103	1	4	yes	—
123	C₂×C₄×C₅₃	#103	1	4	yes	—
124	C₂×C₄×C₅₃	#106	1	4	yes	—
125	C₂×C₄×C₅₃	#107	1	4	yes	—
126	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
127	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
129	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
130	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	#117	1	2	yes	—
134	C₂×C₄×C₅₃	#117	1	2	yes	—
135	C₂×C₄×C₅₃	#117	1	2	yes	—
136	C₂×C₄×C₅₃	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₅₃	C₄×D₄	1	4	yes	—
138	C₂×C₄×C₅₃	C₄×Q₈	1	4	yes	—
139	C₂×Dic₅₃	—	2	8	no	—
140	C₂×Dic₅₃	—	4	4	no	—
141	C₂×Dic₅₃	—	4	4	no	—
142	C₂×Dic₅₃	—	4	8	no	—
143	C₂×Dic₅₃	—	4	8	no	—
144	#88322	—	2	8	no	—
145	C₄×#340	—	53	1	no	maximal, Sylow
146	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
147	C₂²×C₅₃	C₄×C₂²⋊C₄	1	2	yes	—
148	C₂²×C₅₃	C₄×C₂²⋊C₄	1	2	yes	—
149	C₂²×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
150	C₂²×C₅₃	C₂×#102	1	1	yes	characteristic
151	C₂²×C₅₃	C₂×#102	1	1	yes	characteristic
152	C₂²×C₅₃	C₂×#103	1	1	yes	characteristic
153	C₂²×C₅₃	C₂×#103	1	1	yes	characteristic
154	C₂²×C₅₃	#416	1	2	yes	—
155	C₂²×C₅₃	#416	1	2	yes	—
156	C₂²×C₅₃	C₂×#106	1	1	yes	characteristic
157	C₂²×C₅₃	C₂×#107	1	1	yes	characteristic
158	C₂²×C₅₃	#427	1	2	yes	—
159	C₂²×C₅₃	C₄×D₈	1	4	yes	—
160	C₂²×C₅₃	C₄×SD₁₆	1	4	yes	—
161	C₂²×C₅₃	C₄×SD₁₆	1	4	yes	—
162	C₂²×C₅₃	C₄×Q₁₆	1	4	yes	—
163	C₄×C₅₃	—	2	4	no	—
164	C₄×C₅₃	—	4	8	no	—
165	C₄×C₅₃	#340	1	8	yes	complemented
166	C₄×C₅₃	C₄³	1	1	yes	characteristic
167	C₄×C₅₃	#376	1	1	yes	characteristic
168	C₄×C₅₃	C₄×C₂²⋊C₄	1	2	yes	—
169	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
170	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
171	Dic₅₃	—	4	8	no	—
172	C₂²×C₄×C₈	—	53	1	no	—
173	C₂×C₄×C₄⋊C₄	—	53	1	no	—
174	C₂×C₄×C₄⋊C₄	D₅₃	1	1	yes	characteristic
175	C₂×#340	—	53	4	no	—
176	C₂×C₅₃	C₄×#95	1	1	yes	characteristic
177	C₂×C₅₃	C₂×#340	1	1	yes	characteristic
178	C₂×C₅₃	#1735	1	1	yes	characteristic
179	C₂×C₅₃	C₄×#102	1	2	yes	—
180	C₂×C₅₃	C₄×#102	1	2	yes	—
181	C₂×C₅₃	C₄×#103	1	2	yes	—
182	C₂×C₅₃	C₄×#103	1	2	yes	—
183	C₂×C₅₃	C₄×#106	1	2	yes	—
184	C₂×C₅₃	C₄×#107	1	2	yes	—
185	C₂³×C₈	—	53	2	no	—
186	C₂²×C₄⋊C₄	—	53	2	no	—
187	C₂²×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
188	C₂²×C₄²	—	2	1	no	—
189	C₂²×C₄²	—	106	1	no	—
190	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
191	C₂×C₄×C₈	—	53	4	no	—
192	C₂×C₄×C₈	—	106	2	no	—
193	C₂×C₄×C₈	—	106	2	no	—
194	C₄×C₄⋊C₄	—	2	2	no	—
195	C₄×C₄⋊C₄	—	53	4	no	—
196	C₄×C₄⋊C₄	—	106	2	no	—
197	C₄×C₄⋊C₄	Dic₅₃	1	4	yes	complemented
198	C₂×#95	—	2	1	no	—
199	C₂×#95	—	106	1	no	—
200	#340	—	53	16	no	—
201	C₅₃	C₄×#340	1	1	yes	characteristic, complemented, Sylow
202	C₂³×C₄	—	2	2	no	—
203	C₂³×C₄	—	106	2	no	—
204	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
205	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
206	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
207	C₂²×C₈	—	53	8	no	—
208	C₂²×C₈	—	53	4	no	—
209	C₂²×C₈	—	106	2	no	—
210	C₂²×C₈	—	106	4	no	—
211	C₂²×C₈	—	106	2	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	53	8	no	—
215	C₂×C₄⋊C₄	—	53	4	no	—
216	C₂×C₄⋊C₄	—	106	2	no	—
217	C₂×C₄⋊C₄	—	106	4	no	—
218	C₂×C₄⋊C₄	C₄×D₅₃	1	8	yes	—
219	C₂×C₄⋊C₄	C₂×Dic₅₃	1	4	yes	—
220	C₂×C₄²	—	2	4	no	—
221	C₂×C₄²	—	4	2	no	—
222	C₂×C₄²	—	4	2	no	—
223	C₂×C₄²	—	106	4	no	—
224	C₂×C₄²	—	212	2	no	—
225	C₂×C₄²	—	212	2	no	—
226	C₂×C₄²	Dic₁₀₆	1	2	yes	—
227	C₂×C₄²	C₄×D₅₃	1	2	yes	—
228	C₂×C₄²	C₄×D₅₃	1	2	yes	—
229	C₂×C₄²	D₂₁₂	1	2	yes	—
230	C₂×C₄²	C₂×Dic₅₃	1	2	yes	—
231	C₂×C₄²	C₂²⋊D₅₃	1	2	yes	—
232	C₄×C₈	—	106	8	no	—
233	#95	—	2	4	no	—
234	#95	—	106	4	no	—
235	C₂⁴	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	8	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	—	106	4	no	—
243	C₂²×C₄	—	106	8	no	—
244	C₂²×C₄	—	212	2	no	—
245	C₂²×C₄	—	212	2	no	—
246	C₂²×C₄	—	212	4	no	—
247	C₂²×C₄	#11719919	1	2	yes	—
248	C₂²×C₄	#11719919	1	2	yes	—
249	C₂²×C₄	#11719921	1	2	yes	—
250	C₂²×C₄	#11719921	1	2	yes	—
251	C₂²×C₄	#11719922	1	2	yes	—
252	C₂²×C₄	#11719923	1	2	yes	—
253	C₂²×C₄	#11719924	1	2	yes	—
254	C₂²×C₄	#11719925	1	2	yes	—
255	C₂²×C₄	C₂²⋊Dic₅₃	1	2	yes	—
256	C₂²×C₄	C₂²⋊Dic₅₃	1	2	yes	—
257	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	—
261	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
262	C₂²×C₄	#11719945	1	4	yes	—
263	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
265	C₂×C₈	—	53	8	no	—
266	C₂×C₈	—	106	4	no	—
267	C₂×C₈	—	106	4	no	—
268	C₂×C₈	—	106	8	no	—
269	C₂×C₈	—	106	8	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	8	no	—
272	C₄⋊C₄	—	53	8	no	—
273	C₄⋊C₄	—	106	4	no	—
274	C₄⋊C₄	—	106	8	no	—
275	C₄⋊C₄	C₄×Dic₅₃	1	8	yes	complemented
276	C₄²	—	4	8	no	—
277	C₄²	—	212	8	no	—
278	C₄²	C₄×Dic₅₃	1	4	yes	—
279	C₄²	#11719919	1	4	yes	—
280	C₄²	C₄⋊Dic₅₃	1	4	yes	—
281	C₄²	#11719921	1	4	yes	—
282	C₂³	C₂×#11719921	1	1	yes	characteristic
283	C₂³	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
284	C₂³	C₂×#11719919	1	1	yes	characteristic
285	C₂³	C₄×C₂²⋊D₅₃	1	4	yes	—
286	C₂³	C₂×#11719922	1	1	yes	characteristic
287	C₂³	C₂×#11719924	1	1	yes	characteristic
288	C₂³	C₂×#11719923	1	1	yes	characteristic
289	C₂³	C₂×#11719925	1	1	yes	characteristic
290	C₂³	#13133237	1	4	yes	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	8	no	—
298	C₂×C₄	—	4	8	no	—
299	C₂×C₄	—	106	8	no	—
300	C₂×C₄	—	212	4	no	—
301	C₂×C₄	—	212	4	no	—
302	C₂×C₄	—	212	8	no	—
303	C₂×C₄	—	212	8	no	—
304	C₂×C₄	#13133124	1	4	yes	—
305	C₂×C₄	#13133124	1	4	yes	—
306	C₂×C₄	#13133137	1	4	yes	—
307	C₂×C₄	#13133138	1	4	yes	—
308	C₂×C₄	#13133140	1	4	yes	—
309	C₂×C₄	#13133141	1	4	yes	—
310	C₂×C₄	#13133148	1	4	yes	—
311	C₂×C₄	#13133150	1	4	yes	—
312	C₂×C₄	C₄²×D₅₃	1	2	yes	—
313	C₂×C₄	C₄²×D₅₃	1	2	yes	—
314	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
315	C₂×C₄	C₂×C₄×Dic₅₃	1	2	yes	—
316	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
317	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
318	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
319	C₂×C₄	#13133174	1	2	yes	—
320	C₂×C₄	#13133174	1	2	yes	—
321	C₂×C₄	#13133176	1	2	yes	—
322	C₂×C₄	C₄×C₂²⋊D₅₃	1	4	yes	—
323	C₂×C₄	C₄×D₂₁₂	1	4	yes	—
324	C₂×C₄	C₄×Dic₁₀₆	1	4	yes	—
325	C₈	—	106	8	no	—
326	C₂²	C₂×#13133124	1	1	yes	characteristic
327	C₂²	C₄×C₂²⋊Dic₅₃	1	2	yes	—
328	C₂²	C₄×#11719921	1	2	yes	—
329	C₂²	C₄×#11719919	1	2	yes	—
330	C₂²	C₂×#13133137	1	1	yes	characteristic
331	C₂²	C₂×#13133138	1	1	yes	characteristic
332	C₂²	C₂×#13133140	1	1	yes	characteristic
333	C₂²	C₂×#13133141	1	1	yes	characteristic
334	C₂²	#16810617	1	2	yes	—
335	C₂²	#16810619	1	2	yes	—
336	C₂²	C₂×#13133148	1	1	yes	characteristic
337	C₂²	C₂×#13133150	1	1	yes	characteristic
338	C₂²	#16810659	1	2	yes	—
339	C₂²	C₄×#11719922	1	4	yes	—
340	C₂²	C₄×#11719923	1	4	yes	—
341	C₂²	C₄×#11719924	1	4	yes	—
342	C₂²	C₄×#11719925	1	4	yes	—
343	C₄	—	2	4	no	—
344	C₄	—	4	8	no	—
345	C₄	—	212	8	no	—
346	C₄	#16810385	1	8	yes	direct product factor
347	C₄	C₄²×Dic₅₃	1	1	yes	characteristic
348	C₄	#16810469	1	1	yes	characteristic
349	C₄	C₄×#11719921	1	2	yes	—
350	C₄	C₄×C₄⋊Dic₅₃	1	2	yes	—
351	C₄	C₄×#11719919	1	2	yes	—
352	C₂	C₄×#13133124	1	1	yes	characteristic
353	C₂	C₂×#16810385	1	1	yes	characteristic
354	C₂	#20274431	1	1	yes	characteristic
355	C₂	C₄×#13133138	1	2	yes	—
356	C₂	C₄×#13133137	1	2	yes	—
357	C₂	C₄×#13133141	1	2	yes	—
358	C₂	C₄×#13133140	1	2	yes	—
359	C₂	C₄×#13133148	1	2	yes	—
360	C₂	C₄×#13133150	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₅₃
commutator	C₄×C₅₃	C₄³
Frattini	C₂³×C₄	C₂²×D₅₃
Fitting	C₂×C₄×C₄⋊C₄×C₅₃	C₂
socle, prime radical	C₂⁴×C₅₃	C₂×D₄
cosocle	C₂³×C₄×C₅₃	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₅₃
hypocenter	C₅₃	C₄×#340
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×#88322	C₄	semidirect
12. C₄×C₄⋊Dic₅₃	C₄	semidirect
14. #16810385	C₄	direct (N × H)
19. C₄×C₄⋊C₄×C₅₃	C₄	semidirect
86. C₄⋊C₄×C₅₃	C₄²	semidirect
94. C₄⋊Dic₅₃	C₄²	semidirect
100. C₂×#88322	C₄²	semidirect
165. C₄×C₅₃	#340	semidirect
197. C₄×C₄⋊C₄	Dic₅₃	semidirect
201. C₅₃	C₄×#340	semidirect
275. C₄⋊C₄	C₄×Dic₅₃	semidirect
346. C₄	#16810385	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×#88322	2
C₂×C₄×C₄⋊Dic₅₃	2
C₂×#16810385	2
C₂×C₄×C₄⋊C₄×C₅₃	2
C₄×#340	53

Subgroups — C4×#16810385 #27289272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16810385 #27289272