Subgroups — C₅₃×#26923 #27234435

Order 13568.

782 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3081	C₂	1	2	yes	maximal, complemented
2	C₅₃×#2949	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2046	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2028	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2014	C₂	1	1	yes	maximal, characteristic
6	C₅₃×#1931	C₂	1	2	yes	maximal, complemented
7	C₅₃×#1922	C₂	1	2	yes	maximal, complemented
8	C₅₃×#1887	C₂	1	2	yes	maximal
9	C₅₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
11	C₅₃×#544	C₂²	1	1	yes	characteristic
12	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
13	C₅₃×#519	C₂²	1	1	yes	characteristic
14	C₅₃×#518	C₂²	1	2	yes	—
15	C₅₃×#478	—	2	2	no	—
16	C₅₃×#478	—	2	2	no	—
17	C₅₃×#476	—	2	2	no	—
18	C₅₃×#474	—	2	2	no	—
19	C₅₃×#440	—	2	2	no	—
20	C₅₃×#440	—	2	2	no	—
21	C₄×SD₁₆×C₅₃	—	2	2	no	—
22	C₄×SD₁₆×C₅₃	—	2	2	no	—
23	C₅₃×#428	C₂²	1	2	yes	—
24	C₅₃×#427	C₂²	1	2	yes	—
25	C₅₃×#424	C₂²	1	2	yes	—
26	C₅₃×#419	C₂²	1	2	yes	—
27	C₅₃×#418	C₂²	1	2	yes	—
28	C₅₃×#418	C₂²	1	2	yes	—
29	C₂×#102×C₅₃	C₂²	1	2	yes	—
30	C₂×#101×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#100×C₅₃	C₂²	1	2	yes	—
32	C₅₃×#405	C₂²	1	2	yes	—
33	C₅₃×#391	C₂²	1	1	yes	characteristic
34	C₅₃×#343	C₂²	1	1	yes	characteristic
35	C₅₃×#341	C₂²	1	2	yes	—
36	C₅₃×#339	C₂²	1	2	yes	—
37	C₅₃×#339	C₂²	1	2	yes	—
38	C₅₃×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₅₃	—	4	1	no	—
41	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
42	C₂×SD₁₆×C₅₃	—	2	2	no	—
43	C₂×SD₁₆×C₅₃	—	2	2	no	—
44	C₂×SD₁₆×C₅₃	—	2	4	no	—
45	C₂×SD₁₆×C₅₃	—	2	4	no	—
46	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
47	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₅₃	—	2	2	no	—
50	#127×C₅₃	—	2	4	no	—
51	#125×C₅₃	—	2	2	no	—
52	C₂²⋊Q₈×C₅₃	—	4	1	no	—
53	C₄×Q₈×C₅₃	—	2	2	no	—
54	C₄×Q₈×C₅₃	—	2	2	no	—
55	C₄×D₄×C₅₃	—	2	2	no	—
56	C₄×D₄×C₅₃	—	2	2	no	—
57	C₄×D₄×C₅₃	—	2	2	no	—
58	C₄×D₄×C₅₃	—	2	2	no	—
59	#117×C₅₃	—	4	1	no	—
60	#117×C₅₃	C₂³	1	2	yes	—
61	#117×C₅₃	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
64	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
65	#107×C₅₃	—	2	2	no	—
66	#107×C₅₃	D₄	1	2	yes	complemented
67	#107×C₅₃	D₄	1	2	yes	complemented
68	#106×C₅₃	—	2	2	no	—
69	#106×C₅₃	D₄	1	2	yes	complemented
70	#106×C₅₃	D₄	1	2	yes	complemented
71	C₄⋊C₈×C₅₃	—	2	2	no	—
72	C₄⋊C₈×C₅₃	—	2	2	no	—
73	#103×C₅₃	—	2	2	no	—
74	#103×C₅₃	—	2	2	no	—
75	#102×C₅₃	—	2	2	no	—
76	#102×C₅₃	—	2	2	no	—
77	#102×C₅₃	—	2	2	no	—
78	#102×C₅₃	—	2	2	no	—
79	#102×C₅₃	—	2	2	no	—
80	#102×C₅₃	—	2	2	no	—
81	#101×C₅₃	—	2	2	no	—
82	#100×C₅₃	—	2	4	no	—
83	#97×C₅₃	—	2	2	no	—
84	C₄×C₈×C₅₃	—	2	2	no	—
85	#95×C₅₃	—	4	1	no	—
86	C₂⁴×C₅₃	—	2	2	no	—
87	C₂×Q₈×C₅₃	—	2	1	no	—
88	C₂×Q₈×C₅₃	—	2	2	no	—
89	C₂×Q₈×C₅₃	—	2	2	no	—
90	C₂×Q₈×C₅₃	—	4	1	no	—
91	C₂×Q₈×C₅₃	#41	1	2	yes	—
92	C₂×D₄×C₅₃	—	2	2	no	—
93	C₂×D₄×C₅₃	—	2	2	no	—
94	C₂×D₄×C₅₃	—	2	2	no	—
95	C₂×D₄×C₅₃	—	2	2	no	—
96	C₂×D₄×C₅₃	—	2	2	no	—
97	C₂×D₄×C₅₃	—	4	4	no	—
98	C₂×D₄×C₅₃	—	8	2	no	—
99	C₂×D₄×C₅₃	—	8	2	no	—
100	C₂×D₄×C₅₃	#41	1	4	yes	—
101	C₂²×C₄×C₅₃	—	2	1	no	—
102	C₂²×C₄×C₅₃	—	2	1	no	—
103	C₂²×C₄×C₅₃	—	2	1	no	—
104	C₂²×C₄×C₅₃	—	4	2	no	—
105	C₂²×C₄×C₅₃	—	4	2	no	—
106	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
107	SD₁₆×C₅₃	—	2	8	no	—
108	SD₁₆×C₅₃	—	2	8	no	—
109	M₁₆×C₅₃	—	2	2	no	—
110	M₁₆×C₅₃	—	2	2	no	—
111	M₁₆×C₅₃	—	2	2	no	—
112	M₁₆×C₅₃	—	2	2	no	—
113	C₂×C₈×C₅₃	—	2	2	no	—
114	C₂×C₈×C₅₃	—	2	2	no	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	—	2	2	no	—
117	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₅₃	—	2	2	no	—
120	C₄⋊C₄×C₅₃	—	4	1	no	—
121	C₄⋊C₄×C₅₃	—	4	1	no	—
122	C₄⋊C₄×C₅₃	—	4	1	no	—
123	C₄⋊C₄×C₅₃	—	4	2	no	—
124	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₅₃	—	2	2	no	—
129	C₂²⋊C₄×C₅₃	—	2	2	no	—
130	C₂²⋊C₄×C₅₃	—	4	2	no	—
131	C₂²⋊C₄×C₅₃	—	4	2	no	—
132	C₄²×C₅₃	—	2	2	no	—
133	C₄²×C₅₃	—	2	2	no	—
134	C₄²×C₅₃	—	2	2	no	—
135	C₄²×C₅₃	—	4	2	no	—
136	C₂³×C₅₃	—	2	4	no	—
137	C₂³×C₅₃	—	4	2	no	—
138	C₂³×C₅₃	—	4	2	no	—
139	C₂³×C₅₃	—	8	2	no	—
140	C₂³×C₅₃	—	8	2	no	—
141	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
142	Q₈×C₅₃	—	2	4	no	—
143	Q₈×C₅₃	—	4	2	no	—
144	Q₈×C₅₃	—	16	1	no	—
145	D₄×C₅₃	—	2	4	no	—
146	D₄×C₅₃	—	2	4	no	—
147	D₄×C₅₃	—	4	2	no	—
148	D₄×C₅₃	—	4	2	no	—
149	D₄×C₅₃	—	8	8	no	—
150	C₂×C₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	2	no	—
156	C₂×C₄×C₅₃	—	4	1	no	—
157	C₂×C₄×C₅₃	—	4	1	no	—
158	C₂×C₄×C₅₃	—	4	1	no	—
159	C₂×C₄×C₅₃	—	4	1	no	—
160	C₂×C₄×C₅₃	—	4	1	no	—
161	C₂×C₄×C₅₃	—	8	1	no	—
162	C₂×C₄×C₅₃	—	16	2	no	—
163	C₂×C₄×C₅₃	—	16	2	no	—
164	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
167	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
168	C₈×C₅₃	—	2	2	no	—
169	C₈×C₅₃	—	2	2	no	—
170	C₈×C₅₃	—	4	2	no	—
171	C₈×C₅₃	—	4	2	no	—
172	#26923	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₅₃	—	2	1	no	—
174	C₂²×C₅₃	—	2	1	no	—
175	C₂²×C₅₃	—	4	4	no	—
176	C₂²×C₅₃	—	8	4	no	—
177	C₂²×C₅₃	—	8	2	no	—
178	C₂²×C₅₃	—	8	2	no	—
179	C₂²×C₅₃	—	16	2	no	—
180	C₂²×C₅₃	#539	1	1	yes	characteristic
181	C₂²×C₅₃	D₄²	1	1	yes	characteristic
182	C₂²×C₅₃	#551	1	1	yes	characteristic
183	C₄×C₅₃	—	4	2	no	—
184	C₄×C₅₃	—	4	2	no	—
185	C₄×C₅₃	—	4	2	no	—
186	C₄×C₅₃	—	4	2	no	—
187	C₄×C₅₃	—	4	2	no	—
188	C₄×C₅₃	—	4	2	no	—
189	C₄×C₅₃	—	8	1	no	—
190	C₄×C₅₃	#525	1	2	yes	—
191	C₄×C₅₃	#548	1	2	yes	—
192	#3081	C₂×C₅₃	1	2	yes	complemented
193	#2949	C₂×C₅₃	1	2	yes	complemented
194	#2046	C₂×C₅₃	1	2	yes	complemented
195	#2028	C₂×C₅₃	1	1	yes	characteristic, complemented
196	#2014	C₂×C₅₃	1	1	yes	characteristic
197	#1931	C₂×C₅₃	1	2	yes	complemented
198	#1922	C₂×C₅₃	1	2	yes	complemented
199	#1887	C₂×C₅₃	1	2	yes	—
200	#1857	C₂×C₅₃	1	1	yes	characteristic, complemented
201	C₂×C₅₃	—	2	1	no	—
202	C₂×C₅₃	—	2	1	no	—
203	C₂×C₅₃	—	8	4	no	—
204	C₂×C₅₃	#2463	1	1	yes	characteristic
205	C₂×C₅₃	#3288	1	1	yes	characteristic
206	C₂×C₅₃	#3291	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
208	#544	C₂²×C₅₃	1	1	yes	characteristic
209	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
210	#519	C₂²×C₅₃	1	1	yes	characteristic
211	#518	C₂²×C₅₃	1	2	yes	—
212	#478	—	2	2	no	—
213	#478	—	2	2	no	—
214	#476	—	2	2	no	—
215	#474	—	2	2	no	—
216	#440	—	2	2	no	—
217	#440	—	2	2	no	—
218	C₄×SD₁₆	—	2	2	no	—
219	C₄×SD₁₆	—	2	2	no	—
220	#428	C₂²×C₅₃	1	2	yes	—
221	#427	C₂²×C₅₃	1	2	yes	—
222	#424	C₂²×C₅₃	1	2	yes	—
223	#419	C₂²×C₅₃	1	2	yes	—
224	#418	C₂²×C₅₃	1	2	yes	—
225	#418	C₂²×C₅₃	1	2	yes	—
226	C₂×#102	C₂²×C₅₃	1	2	yes	—
227	C₂×#101	C₂²×C₅₃	1	1	yes	characteristic
228	C₂×#100	C₂²×C₅₃	1	2	yes	—
229	#405	C₂²×C₅₃	1	2	yes	—
230	#391	C₂²×C₅₃	1	1	yes	characteristic
231	#343	C₂²×C₅₃	1	1	yes	characteristic
232	#341	C₂²×C₅₃	1	2	yes	—
233	#339	C₂²×C₅₃	1	2	yes	—
234	#339	C₂²×C₅₃	1	2	yes	—
235	#336	C₂²×C₅₃	1	1	yes	characteristic
236	C₅₃	#26923	1	1	yes	characteristic, direct product factor, Sylow
237	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
238	C₂²×D₄	—	4	1	no	—
239	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
240	C₂×SD₁₆	—	2	4	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
245	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
246	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
247	C₄⋊Q₈	—	2	2	no	—
248	#127	—	2	4	no	—
249	#125	—	2	2	no	—
250	C₂²⋊Q₈	—	4	1	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	#117	—	4	1	no	—
258	#117	C₂³×C₅₃	1	2	yes	—
259	#117	C₂³×C₅₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	4	2	no	—
262	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
263	#107	—	2	2	no	—
264	#107	D₄×C₅₃	1	2	yes	complemented
265	#107	D₄×C₅₃	1	2	yes	complemented
266	#106	—	2	2	no	—
267	#106	D₄×C₅₃	1	2	yes	complemented
268	#106	D₄×C₅₃	1	2	yes	complemented
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#102	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#101	—	2	2	no	—
280	#100	—	2	4	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	#95	—	4	1	no	—
284	C₂⁴	—	2	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	#41×C₅₃	1	2	yes	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂×D₄	#41×C₅₃	1	4	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
305	SD₁₆	—	2	8	no	—
306	SD₁₆	—	2	8	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	M₁₆	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
316	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
323	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
324	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
325	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
340	Q₈	—	2	4	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	16	1	no	—
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	8	8	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	—	16	2	no	—
362	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
363	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
364	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
365	C₂×C₄	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	4	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	16	2	no	—
377	C₂²	C₅₃×#539	1	1	yes	characteristic
378	C₂²	D₄²×C₅₃	1	1	yes	characteristic
379	C₂²	C₅₃×#551	1	1	yes	characteristic
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	1	no	—
387	C₄	C₅₃×#525	1	2	yes	—
388	C₄	C₅₃×#548	1	2	yes	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	8	4	no	—
392	C₂	C₅₃×#2463	1	1	yes	characteristic
393	C₂	C₅₃×#3288	1	1	yes	characteristic
394	C₂	C₅₃×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×#127×C₅₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3081	C₂	semidirect
2. C₅₃×#2949	C₂	semidirect
3. C₅₃×#2046	C₂	semidirect
4. C₅₃×#2028	C₂	semidirect
6. C₅₃×#1931	C₂	semidirect
7. C₅₃×#1922	C₂	semidirect
9. C₅₃×#1857	C₂	semidirect
66. #107×C₅₃	D₄	semidirect
67. #107×C₅₃	D₄	semidirect
69. #106×C₅₃	D₄	semidirect
70. #106×C₅₃	D₄	semidirect
172. #26923	C₅₃	direct (N × H)
192. #3081	C₂×C₅₃	semidirect
193. #2949	C₂×C₅₃	semidirect
194. #2046	C₂×C₅₃	semidirect
195. #2028	C₂×C₅₃	semidirect
197. #1931	C₂×C₅₃	semidirect
198. #1922	C₂×C₅₃	semidirect
200. #1857	C₂×C₅₃	semidirect
236. C₅₃	#26923	direct (N × H)
264. #107	D₄×C₅₃	semidirect
265. #107	D₄×C₅₃	semidirect
267. #106	D₄×C₅₃	semidirect
268. #106	D₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3081	2
C₅₃×#2949	2
C₅₃×#2046	2
C₅₃×#2028	2
C₅₃×#2014	2
C₅₃×#1931	2
C₅₃×#1922	2
C₅₃×#1887	2
C₅₃×#1857	2
#26923	53

Subgroups — C53×#26923 #27234435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#26923 #27234435