Subgroups — C₄×M₃₂×D₅₃ #27536719

Order 13568.

918 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₅₃	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#13133157	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276308	C₂	1	2	yes	maximal, complemented
5	M₃₂×Dic₅₃	C₂	1	2	yes	maximal, complemented
6	C₄×#13133156	C₂	1	2	yes	maximal, complemented
7	#346×D₅₃	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
9	C₄×M₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₅₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₅₃	C₄	1	1	yes	characteristic
13	C₂×#13133157	C₂²	1	2	yes	—
14	C₂×#13133156	C₂²	1	4	yes	—
15	M₃₂×D₅₃	C₄	1	16	yes	direct product factor
16	C₂×C₁₆×D₅₃	C₂²	1	4	yes	—
17	C₂×C₄×#88322	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
20	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
21	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
22	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
23	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
28	#16810399	C₂²	1	2	yes	complemented
29	#16810398	C₂²	1	4	yes	complemented
30	C₄×#11719908	C₂²	1	2	yes	complemented
31	C₁₆×Dic₅₃	C₂²	1	4	yes	complemented
32	C₂×M₃₂×C₅₃	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₅₃×#346	C₂²	1	2	yes	complemented
35	C₄×C₁₆×C₅₃	C₂²	1	2	yes	complemented
36	C₂²×C₄×D₅₃	C₈	1	2	yes	—
37	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
39	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×D₅₃	C₈	1	8	yes	—
41	C₂×C₈×D₅₃	C₂×C₄	1	8	yes	—
42	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
50	C₂×C₄×Dic₅₃	C₈	1	2	yes	—
51	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₅₃	C₈	1	2	yes	—
53	C₄²×D₅₃	C₈	1	2	yes	—
54	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
58	#13133157	C₂×C₄	1	8	yes	complemented
59	#13133156	C₂×C₄	1	16	yes	complemented
60	C₂×#11719908	C₂³	1	4	yes	—
61	C₁₆×D₅₃	C₂×C₄	1	16	yes	complemented
62	C₄×#88322	C₂×C₄	1	1	yes	characteristic
63	C₄×#88322	C₂×C₄	1	1	yes	characteristic
64	C₄×#88322	C₂×C₄	1	1	yes	characteristic
65	C₄×#88322	C₂×C₄	1	1	yes	characteristic
66	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
73	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
77	M₃₂×C₅₃	C₂×C₄	1	8	yes	complemented
78	C₂×C₁₆×C₅₃	C₂³	1	4	yes	—
79	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂×C₈	1	2	yes	—
85	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₅₃	C₂×C₈	1	2	yes	—
87	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
88	C₂×C₄×D₅₃	—	2	8	no	—
89	C₂×C₄×D₅₃	C₄²	1	4	yes	—
90	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
92	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
93	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂×C₈	1	4	yes	—
96	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₅₃	C₂×C₈	1	4	yes	—
100	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
105	C₄²×C₅₃	C₂×C₈	1	2	yes	—
106	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
109	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
110	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
111	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
112	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
113	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×#88322	C₄²	1	4	yes	—
116	C₂×#88322	C₂×C₈	1	4	yes	—
117	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
118	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
119	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
120	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₅₃	C₄²	1	4	yes	—
122	C₈×D₅₃	C₄²	1	4	yes	—
123	C₈×D₅₃	C₂×C₈	1	4	yes	—
124	C₈×D₅₃	C₂×C₈	1	4	yes	—
125	C₈×D₅₃	C₂×C₈	1	4	yes	—
126	C₈×D₅₃	C₂×C₈	1	4	yes	—
127	C₈×D₅₃	C₂²×C₄	1	4	yes	—
128	C₈×D₅₃	C₂²×C₄	1	4	yes	—
129	C₁₆×C₅₃	C₂²×C₄	1	8	yes	complemented
130	#11719908	C₂²×C₄	1	8	yes	complemented
131	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
132	C₂²×D₅₃	—	2	4	no	—
133	C₂²×D₅₃	C₄×C₈	1	4	yes	—
134	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
135	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
136	C₂×C₄×C₅₃	—	2	4	no	—
137	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×Dic₅₃	—	2	4	no	—
144	C₂×Dic₅₃	C₄×C₈	1	4	yes	—
145	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
146	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
148	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
149	C₄×D₅₃	—	2	4	no	—
150	C₄×D₅₃	—	2	4	no	—
151	C₄×D₅₃	—	2	4	no	—
152	C₄×D₅₃	C₄×C₈	1	4	yes	—
153	C₄×D₅₃	C₄×C₈	1	4	yes	—
154	C₄×D₅₃	M₃₂	1	8	yes	direct product factor
155	C₄×D₅₃	C₂×C₄²	1	2	yes	—
156	C₄×D₅₃	C₂×C₄²	1	2	yes	—
157	C₄×D₅₃	C₂²×C₈	1	2	yes	—
158	C₄×D₅₃	C₂²×C₈	1	2	yes	—
159	C₈×C₅₃	C₂×C₄²	1	2	yes	—
160	C₈×C₅₃	C₂²×C₈	1	2	yes	—
161	C₈×C₅₃	C₂²×C₈	1	2	yes	—
162	C₈×C₅₃	C₂³×C₄	1	2	yes	—
163	#88322	C₂×C₄²	1	2	yes	—
164	#88322	C₂×C₄²	1	2	yes	—
165	#88322	C₂²×C₈	1	2	yes	—
166	#88322	C₂²×C₈	1	2	yes	—
167	C₂×C₄×M₃₂	—	53	1	no	maximal, Sylow
168	C₂²×C₅₃	—	2	2	no	—
169	C₂²×C₅₃	C₂×C₄×C₈	1	2	yes	—
170	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
171	C₂×D₅₃	—	2	2	no	—
172	C₂×D₅₃	—	2	8	no	—
173	C₂×D₅₃	C₂×C₄×C₈	1	2	yes	—
174	C₂×D₅₃	C₂×C₄×C₈	1	2	yes	—
175	C₂×D₅₃	C₂×M₃₂	1	4	yes	—
176	C₄×C₅₃	—	2	2	no	—
177	C₄×C₅₃	C₂×C₄×C₈	1	2	yes	—
178	C₄×C₅₃	C₂×M₃₂	1	4	yes	complemented
179	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
180	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
181	Dic₅₃	—	2	2	no	—
182	Dic₅₃	C₂×C₄×C₈	1	2	yes	—
183	Dic₅₃	C₂×C₄×C₈	1	2	yes	—
184	Dic₅₃	C₂×M₃₂	1	4	yes	complemented
185	C₂²×M₃₂	—	53	2	no	—
186	C₂²×C₄×C₈	—	53	1	no	—
187	C₄×M₃₂	—	53	2	no	—
188	C₄×M₃₂	—	53	1	no	—
189	C₄×M₃₂	—	53	2	no	—
190	C₄×M₃₂	—	53	2	no	—
191	C₄×M₃₂	D₅₃	1	1	yes	characteristic, direct product factor
192	C₂×#346	—	53	2	no	—
193	C₂×C₄×C₁₆	—	53	2	no	—
194	C₂×C₅₃	—	2	2	no	—
195	C₂×C₅₃	C₂²×C₄×C₈	1	1	yes	characteristic
196	C₂×C₅₃	C₂²×M₃₂	1	2	yes	—
197	D₅₃	—	2	2	no	—
198	D₅₃	C₄×M₃₂	1	4	yes	direct product factor
199	C₂³×C₈	—	53	1	no	—
200	C₂³×C₈	—	53	1	no	—
201	C₂²×C₄²	—	53	1	no	—
202	C₂×M₃₂	—	53	2	no	—
203	C₂×M₃₂	—	53	16	no	—
204	C₂×M₃₂	—	53	4	no	—
205	C₂×M₃₂	C₂×D₅₃	1	2	yes	—
206	C₂²×C₁₆	—	53	4	no	—
207	C₂×C₄×C₈	—	53	1	no	—
208	C₂×C₄×C₈	—	53	1	no	—
209	C₂×C₄×C₈	—	53	1	no	—
210	C₂×C₄×C₈	—	53	1	no	—
211	C₂×C₄×C₈	—	53	1	no	—
212	C₂×C₄×C₈	—	53	1	no	—
213	C₂×C₄×C₈	—	53	1	no	—
214	C₂×C₄×C₈	—	53	1	no	—
215	C₂×C₄×C₈	—	53	1	no	—
216	C₂×C₄×C₈	—	53	1	no	—
217	C₂×C₄×C₈	—	53	1	no	—
218	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
219	#346	—	53	4	no	—
220	#346	—	53	2	no	—
221	#346	C₂×D₅₃	1	2	yes	complemented
222	C₄×C₁₆	—	53	4	no	—
223	C₄×C₁₆	—	53	2	no	—
224	C₄×C₁₆	C₂×D₅₃	1	2	yes	complemented
225	C₅₃	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₄	—	53	1	no	—
227	C₂³×C₄	—	53	2	no	—
228	C₂²×C₈	—	53	1	no	—
229	C₂²×C₈	—	53	1	no	—
230	C₂²×C₈	—	53	1	no	—
231	C₂²×C₈	—	53	1	no	—
232	C₂²×C₈	—	53	1	no	—
233	C₂²×C₈	—	53	1	no	—
234	C₂²×C₈	—	53	1	no	—
235	C₂²×C₈	—	53	1	no	—
236	C₂²×C₈	—	53	8	no	—
237	C₂²×C₈	—	53	1	no	—
238	C₂²×C₈	—	53	1	no	—
239	C₂²×C₈	—	53	8	no	—
240	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
241	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
242	C₂×C₄²	—	53	1	no	—
243	C₂×C₄²	—	53	2	no	—
244	C₂×C₄²	—	53	1	no	—
245	C₂×C₄²	—	53	1	no	—
246	C₂×C₄²	—	53	1	no	—
247	C₂×C₄²	—	53	1	no	—
248	C₂×C₄²	—	53	2	no	—
249	C₂×C₄²	—	53	2	no	—
250	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
251	M₃₂	—	53	8	no	—
252	M₃₂	—	53	16	no	—
253	M₃₂	C₄×D₅₃	1	8	yes	direct product factor
254	C₂×C₁₆	—	53	4	no	—
255	C₂×C₁₆	—	53	16	no	—
256	C₂×C₁₆	C₂²×D₅₃	1	4	yes	—
257	C₄×C₈	—	53	1	no	—
258	C₄×C₈	—	53	1	no	—
259	C₄×C₈	—	53	1	no	—
260	C₄×C₈	—	53	1	no	—
261	C₄×C₈	—	53	1	no	—
262	C₄×C₈	—	53	1	no	—
263	C₄×C₈	—	53	1	no	—
264	C₄×C₈	—	53	1	no	—
265	C₄×C₈	—	53	1	no	—
266	C₄×C₈	—	53	1	no	—
267	C₄×C₈	—	53	1	no	—
268	C₄×C₈	—	53	1	no	—
269	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
270	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
271	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
272	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
273	C₂⁴	—	53	1	no	—
274	C₂²×C₄	—	53	1	no	—
275	C₂²×C₄	—	53	4	no	—
276	C₂²×C₄	—	53	2	no	—
277	C₂²×C₄	—	53	1	no	—
278	C₂²×C₄	—	53	1	no	—
279	C₂²×C₄	—	53	4	no	—
280	C₂²×C₄	—	53	1	no	—
281	C₂²×C₄	—	53	1	no	—
282	C₂²×C₄	—	53	2	no	—
283	C₂²×C₄	—	53	2	no	—
284	C₂²×C₄	—	53	2	no	—
285	C₂²×C₄	—	53	2	no	—
286	C₂²×C₄	—	106	8	no	—
287	C₂²×C₄	C₈×D₅₃	1	2	yes	—
288	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
289	C₂×C₈	—	53	4	no	—
290	C₂×C₈	—	53	4	no	—
291	C₂×C₈	—	53	1	no	—
292	C₂×C₈	—	53	1	no	—
293	C₂×C₈	—	53	1	no	—
294	C₂×C₈	—	53	1	no	—
295	C₂×C₈	—	53	4	no	—
296	C₂×C₈	—	53	4	no	—
297	C₂×C₈	—	53	4	no	—
298	C₂×C₈	—	53	4	no	—
299	C₂×C₈	—	53	4	no	—
300	C₂×C₈	—	53	4	no	—
301	C₂×C₈	—	53	4	no	—
302	C₂×C₈	—	53	4	no	—
303	C₂×C₈	C₈×D₅₃	1	4	yes	—
304	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
305	C₂×C₈	C₂×C₄×D₅₃	1	4	yes	—
306	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
308	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
309	C₄²	—	53	2	no	—
310	C₄²	—	53	2	no	—
311	C₄²	—	53	2	no	—
312	C₄²	—	53	2	no	—
313	C₄²	—	53	2	no	—
314	C₄²	—	53	1	no	—
315	C₄²	—	53	1	no	—
316	C₄²	C₈×D₅₃	1	2	yes	—
317	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
318	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
319	C₁₆	—	53	8	no	—
320	C₁₆	C₂×C₄×D₅₃	1	8	yes	complemented
321	C₂³	—	53	1	no	—
322	C₂³	—	53	4	no	—
323	C₂³	—	53	1	no	—
324	C₂³	—	106	4	no	—
325	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	53	4	no	—
328	C₂×C₄	—	53	2	no	—
329	C₂×C₄	—	53	1	no	—
330	C₂×C₄	—	53	1	no	—
331	C₂×C₄	—	53	8	no	—
332	C₂×C₄	—	53	2	no	—
333	C₂×C₄	—	53	2	no	—
334	C₂×C₄	—	53	4	no	—
335	C₂×C₄	—	53	4	no	—
336	C₂×C₄	—	53	2	no	—
337	C₂×C₄	—	53	2	no	—
338	C₂×C₄	—	53	2	no	—
339	C₂×C₄	—	106	4	no	—
340	C₂×C₄	—	106	4	no	—
341	C₂×C₄	—	106	4	no	—
342	C₂×C₄	—	106	4	no	—
343	C₂×C₄	C₄²×D₅₃	1	2	yes	—
344	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
348	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
349	C₈	—	53	2	no	—
350	C₈	—	53	2	no	—
351	C₈	—	53	2	no	—
352	C₈	—	53	2	no	—
353	C₈	C₄²×D₅₃	1	2	yes	—
354	C₈	C₂×C₈×D₅₃	1	2	yes	—
355	C₈	C₂×C₈×D₅₃	1	2	yes	—
356	C₈	C₂²×C₄×D₅₃	1	2	yes	—
357	C₂²	—	2	2	no	—
358	C₂²	—	53	4	no	—
359	C₂²	—	53	2	no	—
360	C₂²	—	53	2	no	—
361	C₂²	—	106	8	no	—
362	C₂²	—	106	2	no	—
363	C₂²	C₄×C₈×D₅₃	1	2	yes	—
364	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	53	4	no	—
367	C₄	—	53	2	no	—
368	C₄	—	53	2	no	—
369	C₄	—	106	2	no	—
370	C₄	C₄×C₈×D₅₃	1	2	yes	—
371	C₄	M₃₂×D₅₃	1	4	yes	direct product factor
372	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
373	C₄	C₂²×C₈×D₅₃	1	1	yes	characteristic
374	C₂	—	2	2	no	—
375	C₂	—	53	4	no	—
376	C₂	—	106	2	no	—
377	C₂	C₂×C₄×C₈×D₅₃	1	1	yes	characteristic
378	C₂	C₂×M₃₂×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂²×D₅₃
commutator	C₂×C₅₃	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₄×M₃₂×C₅₃	C₂
socle	C₂²×C₅₃	C₂³×C₈
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₄×M₃₂	D₅₃
hypocenter	C₅₃	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. C₄×#13133157	C₂	semidirect
4. #20276308	C₂	semidirect
5. M₃₂×Dic₅₃	C₂	semidirect
6. C₄×#13133156	C₂	semidirect
7. #346×D₅₃	C₂	semidirect
8. C₄×C₁₆×D₅₃	C₂	semidirect
9. C₄×M₃₂×C₅₃	C₂	semidirect
15. M₃₂×D₅₃	C₄	direct (N × H)
28. #16810399	C₂²	semidirect
29. #16810398	C₂²	semidirect
30. C₄×#11719908	C₂²	semidirect
31. C₁₆×Dic₅₃	C₂²	semidirect
34. C₅₃×#346	C₂²	semidirect
35. C₄×C₁₆×C₅₃	C₂²	semidirect
58. #13133157	C₂×C₄	semidirect
59. #13133156	C₂×C₄	semidirect
61. C₁₆×D₅₃	C₂×C₄	semidirect
77. M₃₂×C₅₃	C₂×C₄	semidirect
129. C₁₆×C₅₃	C₂²×C₄	semidirect
130. #11719908	C₂²×C₄	semidirect
154. C₄×D₅₃	M₃₂	direct (N × H)
178. C₄×C₅₃	C₂×M₃₂	semidirect
184. Dic₅₃	C₂×M₃₂	semidirect
191. C₄×M₃₂	D₅₃	direct (N × H)
198. D₅₃	C₄×M₃₂	direct (N × H)
221. #346	C₂×D₅₃	semidirect
224. C₄×C₁₆	C₂×D₅₃	semidirect
225. C₅₃	C₂×C₄×M₃₂	semidirect
253. M₃₂	C₄×D₅₃	direct (N × H)
320. C₁₆	C₂×C₄×D₅₃	semidirect
371. C₄	M₃₂×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
C₂×M₃₂×D₅₃	2
C₂×C₄×C₈×D₅₃	2
C₄×#13133157	2
#20276308	2
M₃₂×Dic₅₃	2
C₄×#13133156	2
#346×D₅₃	2
C₄×C₁₆×D₅₃	2
C₄×M₃₂×C₅₃	2
C₂×C₄×M₃₂	53

Subgroups — C4×M32×D53 #27536719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×M₃₂×D₅₃ #27536719