Subgroups — C₅₃×#17391 #27224903

Order 13568.

876 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#541	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#1473	C₂	1	4	yes	maximal
5	C₅₃×#1470	C₂	1	4	yes	maximal, complemented
6	C₅₃×#1461	C₂	1	2	yes	maximal, complemented
7	C₅₃×#1458	C₂	1	2	yes	maximal
8	C₅₃×#541	—	2	4	no	—
9	C₅₃×#541	—	2	4	no	—
10	C₂×C₄⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
11	C₂×#126×C₅₃	C₄	1	2	yes	—
12	C₂×#126×C₅₃	C₂²	1	2	yes	—
13	C₂×#125×C₅₃	C₄	1	1	yes	characteristic
14	C₂×#125×C₅₃	C₄	1	2	yes	—
15	C₂×#125×C₅₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
21	C₅₃×#446	—	2	4	no	—
22	C₈×Q₈×C₅₃	—	2	4	no	—
23	C₅₃×#432	C₂²	1	4	yes	—
24	C₅₃×#431	C₂²	1	2	yes	—
25	C₅₃×#431	C₂²	1	4	yes	—
26	C₅₃×#431	C₂²	1	2	yes	—
27	C₅₃×#324	C₂²	1	4	yes	—
28	C₅₃×#324	C₂²	1	8	yes	—
29	C₅₃×#323	C₂²	1	4	yes	—
30	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
33	C₄⋊Q₈×C₅₃	—	2	4	no	—
34	#126×C₅₃	—	2	8	no	—
35	#126×C₅₃	—	2	4	no	—
36	#126×C₅₃	—	2	4	no	—
37	#125×C₅₃	—	2	4	no	—
38	#125×C₅₃	—	2	8	no	—
39	#125×C₅₃	—	2	4	no	—
40	#125×C₅₃	—	2	4	no	—
41	C₂²⋊Q₈×C₅₃	—	2	4	no	—
42	C₂²⋊Q₈×C₅₃	—	2	4	no	—
43	C₄×Q₈×C₅₃	—	2	2	no	—
44	C₄×Q₈×C₅₃	—	2	2	no	—
45	C₄×Q₈×C₅₃	D₄	1	4	yes	—
46	C₄×Q₈×C₅₃	D₄	1	4	yes	—
47	#117×C₅₃	—	2	2	no	—
48	#117×C₅₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
69	C₄⋊C₈×C₅₃	—	2	2	no	—
70	C₄⋊C₈×C₅₃	—	2	4	no	—
71	C₄⋊C₈×C₅₃	—	2	2	no	—
72	C₄⋊C₈×C₅₃	—	2	4	no	—
73	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
74	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
75	#97×C₅₃	—	2	4	no	—
76	C₄×C₈×C₅₃	—	2	2	no	—
77	C₄×C₈×C₅₃	—	2	4	no	—
78	C₄×C₈×C₅₃	—	2	2	no	—
79	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
80	C₂×Q₈×C₅₃	—	2	2	no	—
81	C₂×Q₈×C₅₃	—	2	4	no	—
82	C₂×Q₈×C₅₃	—	2	4	no	—
83	C₂×Q₈×C₅₃	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₅₃	—	2	2	no	—
85	C₂²×C₄×C₅₃	—	2	4	no	—
86	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₅₃	—	2	4	no	—
97	C₂×C₈×C₅₃	—	2	4	no	—
98	C₄⋊C₄×C₅₃	—	2	2	no	—
99	C₄⋊C₄×C₅₃	—	2	2	no	—
100	C₄⋊C₄×C₅₃	—	2	4	no	—
101	C₄⋊C₄×C₅₃	—	2	4	no	—
102	C₄⋊C₄×C₅₃	—	2	4	no	—
103	C₄⋊C₄×C₅₃	—	2	4	no	—
104	C₄⋊C₄×C₅₃	—	2	4	no	—
105	C₄⋊C₄×C₅₃	—	2	4	no	—
106	C₄⋊C₄×C₅₃	—	2	1	no	—
107	C₄⋊C₄×C₅₃	—	2	1	no	—
108	C₄⋊C₄×C₅₃	—	2	2	no	—
109	C₄⋊C₄×C₅₃	—	2	2	no	—
110	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
111	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	8	yes	—
112	C₂²⋊C₄×C₅₃	—	2	2	no	—
113	C₂²⋊C₄×C₅₃	—	2	4	no	—
114	C₂²⋊C₄×C₅₃	—	2	4	no	—
115	C₂²⋊C₄×C₅₃	—	2	1	no	—
116	C₂²⋊C₄×C₅₃	—	2	1	no	—
117	C₄²×C₅₃	—	2	2	no	—
118	C₄²×C₅₃	—	2	4	no	—
119	C₄²×C₅₃	C₂×D₄	1	2	yes	—
120	C₄²×C₅₃	C₂×D₄	1	2	yes	—
121	C₄²×C₅₃	C₂×D₄	1	4	yes	—
122	C₄²×C₅₃	C₂×D₄	1	4	yes	—
123	C₂³×C₅₃	—	2	1	no	—
124	C₂³×C₅₃	—	2	2	no	—
125	C₂³×C₅₃	—	4	1	no	—
126	C₂³×C₅₃	—	4	1	no	—
127	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
128	Q₈×C₅₃	—	2	8	no	—
129	Q₈×C₅₃	—	4	4	no	—
130	C₂×C₄×C₅₃	—	2	4	no	—
131	C₂×C₄×C₅₃	—	2	1	no	—
132	C₂×C₄×C₅₃	—	2	2	no	—
133	C₂×C₄×C₅₃	—	2	1	no	—
134	C₂×C₄×C₅₃	—	2	2	no	—
135	C₂×C₄×C₅₃	—	2	1	no	—
136	C₂×C₄×C₅₃	—	2	2	no	—
137	C₂×C₄×C₅₃	—	2	4	no	—
138	C₂×C₄×C₅₃	—	4	1	no	—
139	C₂×C₄×C₅₃	—	4	2	no	—
140	C₂×C₄×C₅₃	—	4	1	no	—
141	C₂×C₄×C₅₃	—	4	4	no	—
142	C₂×C₄×C₅₃	—	4	1	no	—
143	C₂×C₄×C₅₃	—	4	2	no	—
144	C₂×C₄×C₅₃	—	4	1	no	—
145	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	4	yes	—
146	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	4	yes	—
148	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₅₃	#131	1	4	yes	—
150	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₅₃	—	4	4	no	—
153	C₈×C₅₃	—	4	4	no	—
154	#17391	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₅₃	—	2	1	no	—
156	C₂²×C₅₃	—	2	1	no	—
157	C₂²×C₅₃	—	4	1	no	—
158	C₂²×C₅₃	—	4	1	no	—
159	C₂²×C₅₃	—	4	1	no	—
160	C₂²×C₅₃	—	8	2	no	—
161	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₅₃	C₂×#131	1	2	yes	—
163	C₄×C₅₃	—	2	4	no	—
164	C₄×C₅₃	—	2	1	no	—
165	C₄×C₅₃	—	2	1	no	—
166	C₄×C₅₃	—	2	2	no	—
167	C₄×C₅₃	—	2	4	no	—
168	C₄×C₅₃	—	4	1	no	—
169	C₄×C₅₃	—	4	2	no	—
170	C₄×C₅₃	—	4	1	no	—
171	C₄×C₅₃	—	4	2	no	—
172	C₄×C₅₃	—	4	1	no	—
173	C₄×C₅₃	#408	1	4	yes	—
174	C₂×#541	C₂×C₅₃	1	1	yes	characteristic
175	#2983	C₂×C₅₃	1	1	yes	characteristic, complemented
176	#2982	C₂×C₅₃	1	1	yes	characteristic, complemented
177	#1473	C₂×C₅₃	1	4	yes	—
178	#1470	C₂×C₅₃	1	4	yes	complemented
179	#1461	C₂×C₅₃	1	2	yes	complemented
180	#1458	C₂×C₅₃	1	2	yes	—
181	C₂×C₅₃	—	2	2	no	—
182	C₂×C₅₃	—	8	1	no	—
183	C₂×C₅₃	C₂×#408	1	1	yes	characteristic
184	C₂×C₅₃	#2884	1	1	yes	characteristic
185	C₂×C₅₃	#2889	1	1	yes	characteristic
186	#541	—	2	4	no	—
187	#541	—	2	4	no	—
188	C₂×C₄⋊Q₈	C₄×C₅₃	1	1	yes	characteristic
189	C₂×#126	C₄×C₅₃	1	2	yes	—
190	C₂×#126	C₂²×C₅₃	1	2	yes	—
191	C₂×#125	C₄×C₅₃	1	1	yes	characteristic
192	C₂×#125	C₄×C₅₃	1	2	yes	—
193	C₂×#125	C₂²×C₅₃	1	2	yes	—
194	C₂×C₂²⋊Q₈	C₄×C₅₃	1	1	yes	characteristic
195	C₂×C₂²⋊Q₈	C₄×C₅₃	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
198	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
199	#446	—	2	4	no	—
200	C₈×Q₈	—	2	4	no	—
201	#432	C₂²×C₅₃	1	4	yes	—
202	#431	C₂²×C₅₃	1	2	yes	—
203	#431	C₂²×C₅₃	1	4	yes	—
204	#431	C₂²×C₅₃	1	2	yes	—
205	#324	C₂²×C₅₃	1	4	yes	—
206	#324	C₂²×C₅₃	1	8	yes	—
207	#323	C₂²×C₅₃	1	4	yes	—
208	C₅₃	#17391	1	1	yes	characteristic, direct product factor, Sylow
209	C₂²×Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
210	C₂²×Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
211	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
212	C₄⋊Q₈	—	2	4	no	—
213	#126	—	2	8	no	—
214	#126	—	2	4	no	—
215	#126	—	2	4	no	—
216	#125	—	2	4	no	—
217	#125	—	2	8	no	—
218	#125	—	2	4	no	—
219	#125	—	2	4	no	—
220	C₂²⋊Q₈	—	2	4	no	—
221	C₂²⋊Q₈	—	2	4	no	—
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	—	2	2	no	—
224	C₄×Q₈	D₄×C₅₃	1	4	yes	—
225	C₄×Q₈	D₄×C₅₃	1	4	yes	—
226	#117	—	2	2	no	—
227	#117	—	2	2	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₅₃	1	2	yes	—
246	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	4	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
253	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
254	#97	—	2	4	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	—	2	4	no	—
257	C₄×C₈	—	2	2	no	—
258	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	C₂²⋊C₄×C₅₃	1	4	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	4	yes	—
290	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	8	yes	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	4	no	—
298	C₄²	C₂×D₄×C₅₃	1	2	yes	—
299	C₄²	C₂×D₄×C₅₃	1	2	yes	—
300	C₄²	C₂×D₄×C₅₃	1	4	yes	—
301	C₄²	C₂×D₄×C₅₃	1	4	yes	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	Q₈	—	4	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
328	C₂×C₄	#131×C₅₃	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
331	C₈	—	4	4	no	—
332	C₈	—	4	4	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	8	2	no	—
339	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
340	C₂²	C₂×#131×C₅₃	1	2	yes	—
341	C₄	—	2	4	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	4	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	2	no	—
350	C₄	—	4	1	no	—
351	C₄	C₅₃×#408	1	4	yes	—
352	C₂	—	2	2	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂×C₅₃×#408	1	1	yes	characteristic
355	C₂	C₅₃×#2884	1	1	yes	characteristic
356	C₂	C₅₃×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂⁴×C₅₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂×C₄×Q₈×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2983	C₂	semidirect
3. C₅₃×#2982	C₂	semidirect
5. C₅₃×#1470	C₂	semidirect
6. C₅₃×#1461	C₂	semidirect
154. #17391	C₅₃	direct (N × H)
175. #2983	C₂×C₅₃	semidirect
176. #2982	C₂×C₅₃	semidirect
178. #1470	C₂×C₅₃	semidirect
179. #1461	C₂×C₅₃	semidirect
208. C₅₃	#17391	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×C₅₃×#541	2
C₅₃×#2983	2
C₅₃×#2982	2
C₅₃×#1473	2
C₅₃×#1470	2
C₅₃×#1461	2
C₅₃×#1458	2
#17391	53

Subgroups — C53×#17391 #27224903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#17391 #27224903