Subgroups — C₅₃×#19133 #27226645

Order 13568.

770 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3100	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#1689	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1687	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1685	C₂	1	4	yes	maximal, complemented
7	C₅₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₅₃	—	2	1	no	—
10	C₂×#135×C₅₃	—	2	1	no	—
11	C₂²×M₁₆×C₅₃	—	2	1	no	—
12	C₅₃×#532	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
14	C₅₃×#495	—	2	1	no	—
15	C₅₃×#495	—	2	1	no	—
16	C₅₃×#494	C₂²	1	1	yes	characteristic, complemented
17	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
18	C₅₃×#492	C₂²	1	2	yes	complemented
19	C₅₃×#480	—	2	2	no	—
20	C₅₃×#474	C₂²	1	4	yes	—
21	C₅₃×#459	C₂²	1	4	yes	—
22	C₅₃×#447	—	2	2	no	—
23	C₄×D₈×C₅₃	—	2	4	no	—
24	C₅₃×#436	—	2	1	no	—
25	C₅₃×#436	—	2	1	no	—
26	C₅₃×#436	C₂²	1	2	yes	—
27	C₅₃×#436	C₂²	1	2	yes	—
28	C₅₃×#431	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
31	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#335	C₂²	1	2	yes	complemented
33	C₅₃×#334	C₂²	1	2	yes	complemented
34	C₅₃×#332	C₂²	1	4	yes	complemented
35	C₅₃×#331	C₂²	1	4	yes	complemented
36	C₂×#41×C₅₃	—	2	2	no	—
37	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₃	—	2	1	no	—
39	#135×C₅₃	—	4	4	no	—
40	#135×C₅₃	—	4	4	no	—
41	C₂×Q₁₆×C₅₃	—	2	1	no	—
42	C₂×Q₁₆×C₅₃	—	2	1	no	—
43	C₂×SD₁₆×C₅₃	—	2	2	no	—
44	C₂×SD₁₆×C₅₃	—	2	2	no	—
45	C₂×D₈×C₅₃	—	2	1	no	—
46	C₂×D₈×C₅₃	—	2	1	no	—
47	C₂×D₈×C₅₃	—	2	4	no	—
48	C₂×M₁₆×C₅₃	—	2	2	no	—
49	C₂×M₁₆×C₅₃	—	2	2	no	—
50	C₂×M₁₆×C₅₃	—	4	4	no	—
51	C₂²×C₈×C₅₃	—	2	1	no	—
52	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
55	#127×C₅₃	C₂³	1	2	yes	—
56	#124×C₅₃	—	2	2	no	—
57	#121×C₅₃	—	2	2	no	—
58	#121×C₅₃	—	2	2	no	—
59	C₄×D₄×C₅₃	—	2	1	no	—
60	C₄×D₄×C₅₃	—	2	1	no	—
61	C₄×D₄×C₅₃	—	2	2	no	—
62	C₄×D₄×C₅₃	—	2	2	no	—
63	C₄×D₄×C₅₃	D₄	1	2	yes	—
64	C₄×D₄×C₅₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
67	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
68	#107×C₅₃	—	2	4	no	—
69	C₄⋊C₈×C₅₃	—	2	1	no	—
70	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
71	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
72	#102×C₅₃	—	2	4	no	—
73	#102×C₅₃	—	2	4	no	—
74	C₂²⋊C₈×C₅₃	—	2	2	no	—
75	C₂²⋊C₈×C₅₃	—	2	2	no	—
76	C₂²⋊C₈×C₅₃	—	2	2	no	—
77	C₄×C₈×C₅₃	—	2	2	no	—
78	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂⁴×C₅₃	—	2	1	no	—
83	#41×C₅₃	—	4	4	no	—
84	#41×C₅₃	—	4	4	no	—
85	C₂×Q₈×C₅₃	—	2	2	no	—
86	C₂×D₄×C₅₃	—	2	1	no	—
87	C₂×D₄×C₅₃	—	2	2	no	—
88	C₂×D₄×C₅₃	—	2	2	no	—
89	C₂×D₄×C₅₃	—	2	2	no	—
90	C₂×D₄×C₅₃	—	4	2	no	—
91	C₂×D₄×C₅₃	—	4	2	no	—
92	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₅₃	—	2	1	no	—
94	C₂²×C₄×C₅₃	—	2	2	no	—
95	C₂²×C₄×C₅₃	—	2	2	no	—
96	C₂²×C₄×C₅₃	—	4	2	no	—
97	C₂²×C₄×C₅₃	—	4	2	no	—
98	C₂²×C₄×C₅₃	—	4	2	no	—
99	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
102	Q₁₆×C₅₃	—	4	2	no	—
103	Q₁₆×C₅₃	—	4	2	no	—
104	SD₁₆×C₅₃	—	4	4	no	—
105	SD₁₆×C₅₃	—	4	4	no	—
106	D₈×C₅₃	—	4	2	no	—
107	D₈×C₅₃	—	4	8	no	—
108	D₈×C₅₃	—	4	2	no	—
109	M₁₆×C₅₃	—	4	4	no	—
110	M₁₆×C₅₃	—	4	4	no	—
111	C₂×C₈×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	—	2	4	no	—
113	C₂×C₈×C₅₃	—	2	2	no	—
114	C₂×C₈×C₅₃	—	4	2	no	—
115	C₂×C₈×C₅₃	D₈	1	4	yes	complemented
116	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₅₃	—	2	1	no	—
121	C₄⋊C₄×C₅₃	—	2	2	no	—
122	C₄⋊C₄×C₅₃	—	2	2	no	—
123	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₅₃	—	2	2	no	—
125	C₂²⋊C₄×C₅₃	—	2	2	no	—
126	C₂²⋊C₄×C₅₃	—	4	2	no	—
127	C₂²⋊C₄×C₅₃	—	4	2	no	—
128	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅₃	#41	1	1	yes	characteristic
131	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
132	C₂³×C₅₃	—	2	2	no	—
133	C₂³×C₅₃	—	4	2	no	—
134	C₂³×C₅₃	—	4	2	no	—
135	C₂³×C₅₃	—	4	2	no	—
136	C₂³×C₅₃	—	4	2	no	—
137	C₂³×C₅₃	#121	1	1	yes	characteristic
138	Q₈×C₅₃	—	4	2	no	—
139	Q₈×C₅₃	—	4	2	no	—
140	D₄×C₅₃	—	2	4	no	—
141	D₄×C₅₃	—	4	2	no	—
142	D₄×C₅₃	—	4	2	no	—
143	D₄×C₅₃	—	4	2	no	—
144	D₄×C₅₃	—	4	4	no	—
145	D₄×C₅₃	—	8	2	no	—
146	D₄×C₅₃	—	8	4	no	—
147	C₂×C₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	2	2	no	—
149	C₂×C₄×C₅₃	—	4	1	no	—
150	C₂×C₄×C₅₃	—	4	2	no	—
151	C₂×C₄×C₅₃	—	4	2	no	—
152	C₂×C₄×C₅₃	—	4	2	no	—
153	C₂×C₄×C₅₃	—	4	4	no	—
154	C₂×C₄×C₅₃	—	4	2	no	—
155	C₂×C₄×C₅₃	—	8	4	no	—
156	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂×D₈	1	2	yes	—
160	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
164	C₈×C₅₃	—	2	1	no	—
165	C₈×C₅₃	—	2	1	no	—
166	C₈×C₅₃	—	4	2	no	—
167	C₈×C₅₃	—	4	4	no	—
168	C₈×C₅₃	C₂×D₈	1	2	yes	—
169	C₈×C₅₃	C₂×D₈	1	2	yes	—
170	#19133	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₅₃	—	2	1	no	—
172	C₂²×C₅₃	—	2	1	no	—
173	C₂²×C₅₃	—	4	2	no	—
174	C₂²×C₅₃	—	4	2	no	—
175	C₂²×C₅₃	—	4	2	no	—
176	C₂²×C₅₃	—	8	4	no	—
177	C₂²×C₅₃	—	8	2	no	—
178	C₂²×C₅₃	—	8	2	no	—
179	C₂²×C₅₃	—	8	2	no	—
180	C₂²×C₅₃	#459	1	2	yes	—
181	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
182	C₄×C₅₃	—	2	1	no	—
183	C₄×C₅₃	—	2	1	no	—
184	C₄×C₅₃	—	2	1	no	—
185	C₄×C₅₃	—	4	2	no	—
186	C₄×C₅₃	—	8	2	no	—
187	C₄×C₅₃	#459	1	2	yes	—
188	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₄×C₅₃	#575	1	2	yes	—
191	#3147	C₂×C₅₃	1	1	yes	characteristic, complemented
192	#3100	C₂×C₅₃	1	2	yes	complemented
193	C₂×#436	C₂×C₅₃	1	1	yes	characteristic, complemented
194	#1689	C₂×C₅₃	1	2	yes	complemented
195	#1687	C₂×C₅₃	1	2	yes	complemented
196	#1685	C₂×C₅₃	1	4	yes	complemented
197	#1564	C₂×C₅₃	1	1	yes	characteristic, complemented
198	#1540	C₂×C₅₃	1	2	yes	complemented
199	C₂×C₅₃	—	2	2	no	—
200	C₂×C₅₃	—	8	2	no	—
201	C₂×C₅₃	—	16	2	no	—
202	C₂×C₅₃	C₂×#459	1	1	yes	characteristic
203	C₂×C₅₃	#3054	1	1	yes	characteristic
204	C₂×C₅₃	#3067	1	1	yes	characteristic
205	C₂×#135	—	2	1	no	—
206	C₂×#135	—	2	1	no	—
207	C₂²×M₁₆	—	2	1	no	—
208	#532	C₂²×C₅₃	1	2	yes	—
209	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
210	#495	—	2	1	no	—
211	#495	—	2	1	no	—
212	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
213	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
214	#492	C₂²×C₅₃	1	2	yes	complemented
215	#480	—	2	2	no	—
216	#474	C₂²×C₅₃	1	4	yes	—
217	#459	C₂²×C₅₃	1	4	yes	—
218	#447	—	2	2	no	—
219	C₄×D₈	—	2	4	no	—
220	#436	—	2	1	no	—
221	#436	—	2	1	no	—
222	#436	C₂²×C₅₃	1	2	yes	—
223	#436	C₂²×C₅₃	1	2	yes	—
224	#431	C₂²×C₅₃	1	2	yes	—
225	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	—	2	1	no	—
227	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
228	#335	C₂²×C₅₃	1	2	yes	complemented
229	#334	C₂²×C₅₃	1	2	yes	complemented
230	#332	C₂²×C₅₃	1	4	yes	complemented
231	#331	C₂²×C₅₃	1	4	yes	complemented
232	C₅₃	#19133	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#41	—	2	2	no	—
234	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
235	C₂³×C₄	—	2	1	no	—
236	#135	—	4	4	no	—
237	#135	—	4	4	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×D₈	—	2	4	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	4	4	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	D₄×C₅₃	1	1	yes	characteristic
250	C₂²×C₈	D₄×C₅₃	1	1	yes	characteristic
251	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
252	#127	C₂³×C₅₃	1	2	yes	—
253	#124	—	2	2	no	—
254	#121	—	2	2	no	—
255	#121	—	2	2	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	D₄×C₅₃	1	2	yes	—
261	C₄×D₄	C₂³×C₅₃	1	2	yes	—
262	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
265	#107	—	2	4	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
268	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
269	#102	—	2	4	no	—
270	#102	—	2	4	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	C₄×C₈	D₄×C₅₃	1	1	yes	characteristic
276	C₄×C₈	D₄×C₅₃	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
279	C₂⁴	—	2	1	no	—
280	#41	—	4	4	no	—
281	#41	—	4	4	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
298	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	4	2	no	—
301	SD₁₆	—	4	4	no	—
302	SD₁₆	—	4	4	no	—
303	D₈	—	4	2	no	—
304	D₈	—	4	8	no	—
305	D₈	—	4	2	no	—
306	M₁₆	—	4	4	no	—
307	M₁₆	—	4	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	D₈×C₅₃	1	4	yes	complemented
313	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
327	C₄²	#41×C₅₃	1	1	yes	characteristic
328	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	#121×C₅₃	1	1	yes	characteristic
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	D₄	—	2	4	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	4	no	—
342	D₄	—	8	2	no	—
343	D₄	—	8	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
354	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
355	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
356	C₂×C₄	C₂×D₈×C₅₃	1	2	yes	—
357	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
358	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
360	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	4	no	—
365	C₈	C₂×D₈×C₅₃	1	2	yes	—
366	C₈	C₂×D₈×C₅₃	1	2	yes	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	C₅₃×#459	1	2	yes	—
377	C₂²	C₂×#121×C₅₃	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	2	no	—
383	C₄	C₅₃×#459	1	2	yes	—
384	C₄	C₂²×D₈×C₅₃	1	1	yes	characteristic
385	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
386	C₄	C₅₃×#575	1	2	yes	—
387	C₂	—	2	2	no	—
388	C₂	—	8	2	no	—
389	C₂	—	16	2	no	—
390	C₂	C₂×C₅₃×#459	1	1	yes	characteristic
391	C₂	C₅₃×#3054	1	1	yes	characteristic
392	C₂	C₅₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
socle	C₂²×C₅₃	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3147	C₂	semidirect
2. C₅₃×#3100	C₂	semidirect
3. C₂×C₅₃×#436	C₂	semidirect
4. C₅₃×#1689	C₂	semidirect
5. C₅₃×#1687	C₂	semidirect
6. C₅₃×#1685	C₂	semidirect
7. C₅₃×#1564	C₂	semidirect
8. C₅₃×#1540	C₂	semidirect
16. C₅₃×#494	C₂²	semidirect
17. C₅₃×#493	C₂²	semidirect
18. C₅₃×#492	C₂²	semidirect
32. C₅₃×#335	C₂²	semidirect
33. C₅₃×#334	C₂²	semidirect
34. C₅₃×#332	C₂²	semidirect
35. C₅₃×#331	C₂²	semidirect
115. C₂×C₈×C₅₃	D₈	semidirect
170. #19133	C₅₃	direct (N × H)
191. #3147	C₂×C₅₃	semidirect
192. #3100	C₂×C₅₃	semidirect
193. C₂×#436	C₂×C₅₃	semidirect
194. #1689	C₂×C₅₃	semidirect
195. #1687	C₂×C₅₃	semidirect
196. #1685	C₂×C₅₃	semidirect
197. #1564	C₂×C₅₃	semidirect
198. #1540	C₂×C₅₃	semidirect
212. #494	C₂²×C₅₃	semidirect
213. #493	C₂²×C₅₃	semidirect
214. #492	C₂²×C₅₃	semidirect
228. #335	C₂²×C₅₃	semidirect
229. #334	C₂²×C₅₃	semidirect
230. #332	C₂²×C₅₃	semidirect
231. #331	C₂²×C₅₃	semidirect
232. C₅₃	#19133	direct (N × H)
312. C₂×C₈	D₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3147	2
C₅₃×#3100	2
C₂×C₅₃×#436	2
C₅₃×#1689	2
C₅₃×#1687	2
C₅₃×#1685	2
C₅₃×#1564	2
C₅₃×#1540	2
#19133	53

Subgroups — C53×#19133 #27226645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#19133 #27226645