Subgroups — C₅₃×#23720 #27231232

Order 13568.

744 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#137×C₅₃	C₂	1	2	yes	maximal
2	C₂×C₅₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2923	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2079	C₂	1	1	yes	maximal, characteristic
6	C₅₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₅₃×#2052	C₂	1	2	yes	maximal
8	C₅₃×#2047	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2020	C₂	1	1	yes	maximal, characteristic
10	C₅₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#101×C₅₃	C₂	1	2	yes	maximal, complemented
12	C₂×#137×C₅₃	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
14	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
16	C₅₃×#441	—	2	2	no	—
17	C₅₃×#441	—	2	2	no	—
18	C₅₃×#441	—	2	2	no	—
19	C₅₃×#440	—	2	2	no	—
20	C₄×Q₁₆×C₅₃	—	2	2	no	—
21	C₄×SD₁₆×C₅₃	—	2	2	no	—
22	C₅₃×#433	—	2	2	no	—
23	C₅₃×#432	—	2	2	no	—
24	C₂×#108×C₅₃	C₂²	1	2	yes	—
25	C₅₃×#428	C₂²	1	2	yes	—
26	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#424	C₂²	1	1	yes	characteristic
28	C₅₃×#424	C₂²	1	1	yes	characteristic
29	C₅₃×#419	C₂²	1	2	yes	—
30	C₅₃×#417	C₂²	1	2	yes	—
31	C₂×#103×C₅₃	C₂²	1	2	yes	—
32	C₂×#101×C₅₃	C₂²	1	2	yes	—
33	C₂×#101×C₅₃	C₂²	1	2	yes	—
34	C₅₃×#408	C₂²	1	1	yes	characteristic
35	C₅₃×#408	C₂²	1	1	yes	characteristic
36	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
37	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#343	C₂²	1	2	yes	—
40	C₅₃×#343	C₂²	1	2	yes	—
41	C₅₃×#341	C₂²	1	1	yes	characteristic
42	C₅₃×#341	C₂²	1	1	yes	characteristic
43	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
45	#137×C₅₃	—	2	4	no	—
46	#137×C₅₃	—	2	4	no	—
47	C₂×Q₁₆×C₅₃	—	2	2	no	—
48	C₂×Q₁₆×C₅₃	—	2	2	no	—
49	C₂×Q₁₆×C₅₃	—	2	4	no	—
50	C₂×SD₁₆×C₅₃	—	2	2	no	—
51	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
52	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₅₃	—	2	2	no	—
58	C₄×Q₈×C₅₃	—	2	2	no	—
59	C₄×Q₈×C₅₃	—	2	2	no	—
60	C₄×Q₈×C₅₃	—	2	2	no	—
61	C₄×Q₈×C₅₃	D₄	1	2	yes	—
62	C₄×D₄×C₅₃	—	2	2	no	—
63	C₄×D₄×C₅₃	D₄	1	2	yes	—
64	#117×C₅₃	—	2	1	no	—
65	#117×C₅₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₅₃	—	2	1	no	—
69	C₂×C₄²×C₅₃	—	2	2	no	—
70	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
71	#108×C₅₃	—	2	4	no	—
72	#107×C₅₃	—	2	2	no	—
73	#106×C₅₃	—	2	2	no	—
74	#106×C₅₃	—	2	2	no	—
75	C₄⋊C₈×C₅₃	—	2	2	no	—
76	C₄⋊C₈×C₅₃	—	2	2	no	—
77	#103×C₅₃	—	2	4	no	—
78	#103×C₅₃	—	2	2	no	—
79	#103×C₅₃	—	2	2	no	—
80	#103×C₅₃	—	2	2	no	—
81	#102×C₅₃	—	2	2	no	—
82	#101×C₅₃	—	2	4	no	—
83	#101×C₅₃	—	2	4	no	—
84	C₂²⋊C₈×C₅₃	—	2	2	no	—
85	C₂²⋊C₈×C₅₃	—	2	2	no	—
86	#97×C₅₃	—	2	1	no	—
87	#97×C₅₃	—	2	2	no	—
88	#97×C₅₃	D₄	1	2	yes	—
89	#97×C₅₃	D₄	1	2	yes	—
90	C₄×C₈×C₅₃	—	2	1	no	—
91	C₄×C₈×C₅₃	—	2	2	no	—
92	#41×C₅₃	—	2	2	no	—
93	#41×C₅₃	—	2	2	no	—
94	C₂×Q₈×C₅₃	—	2	2	no	—
95	C₂×Q₈×C₅₃	—	2	2	no	—
96	C₂×Q₈×C₅₃	—	2	2	no	—
97	C₂×Q₈×C₅₃	—	2	2	no	—
98	C₂×Q₈×C₅₃	—	2	2	no	—
99	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₅₃	#41	1	4	yes	—
101	C₂×D₄×C₅₃	—	2	1	no	—
102	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	—	2	2	no	—
104	C₂²×C₄×C₅₃	—	2	1	no	—
105	C₂²×C₄×C₅₃	—	2	2	no	—
106	C₂²×C₄×C₅₃	—	2	2	no	—
107	C₂²×C₄×C₅₃	#41	1	2	yes	—
108	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₅₃	—	2	8	no	—
110	Q₁₆×C₅₃	—	2	8	no	—
111	SD₁₆×C₅₃	—	2	8	no	—
112	M₁₆×C₅₃	—	2	2	no	—
113	M₁₆×C₅₃	—	2	2	no	—
114	M₁₆×C₅₃	—	2	2	no	—
115	M₁₆×C₅₃	—	2	2	no	—
116	M₁₆×C₅₃	—	2	2	no	—
117	M₁₆×C₅₃	#41	1	4	yes	—
118	C₂×C₈×C₅₃	—	2	2	no	—
119	C₂×C₈×C₅₃	—	2	2	no	—
120	C₂×C₈×C₅₃	—	2	2	no	—
121	C₂×C₈×C₅₃	—	2	1	no	—
122	C₂×C₈×C₅₃	—	2	1	no	—
123	C₂×C₈×C₅₃	—	2	2	no	—
124	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₅₃	—	2	2	no	—
127	C₄⋊C₄×C₅₃	—	2	2	no	—
128	C₄⋊C₄×C₅₃	—	2	2	no	—
129	C₄⋊C₄×C₅₃	—	4	2	no	—
130	C₄⋊C₄×C₅₃	—	4	2	no	—
131	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
132	C₂²⋊C₄×C₅₃	—	2	1	no	—
133	C₂²⋊C₄×C₅₃	—	2	2	no	—
134	C₄²×C₅₃	—	2	2	no	—
135	C₄²×C₅₃	—	2	1	no	—
136	C₄²×C₅₃	—	4	2	no	—
137	C₄²×C₅₃	—	4	2	no	—
138	C₄²×C₅₃	C₂×D₄	1	2	yes	—
139	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₅₃	—	2	1	no	—
142	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
143	Q₈×C₅₃	—	2	4	no	—
144	Q₈×C₅₃	—	2	4	no	—
145	Q₈×C₅₃	—	2	2	no	—
146	Q₈×C₅₃	—	4	2	no	—
147	Q₈×C₅₃	—	4	2	no	—
148	D₄×C₅₃	—	2	2	no	—
149	D₄×C₅₃	—	4	2	no	—
150	C₂×C₄×C₅₃	—	2	1	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	2	4	no	—
153	C₂×C₄×C₅₃	—	4	2	no	—
154	C₂×C₄×C₅₃	—	4	2	no	—
155	C₂×C₄×C₅₃	—	4	2	no	—
156	C₂×C₄×C₅₃	—	4	1	no	—
157	C₂×C₄×C₅₃	—	4	1	no	—
158	C₂×C₄×C₅₃	—	4	2	no	—
159	C₂×C₄×C₅₃	—	8	2	no	—
160	C₂×C₄×C₅₃	—	8	2	no	—
161	C₂×C₄×C₅₃	#121	1	2	yes	—
162	C₂×C₄×C₅₃	#121	1	2	yes	—
163	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
166	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
167	C₈×C₅₃	—	2	2	no	—
168	C₈×C₅₃	—	2	4	no	—
169	C₈×C₅₃	—	2	2	no	—
170	C₈×C₅₃	—	4	1	no	—
171	C₈×C₅₃	—	4	2	no	—
172	C₈×C₅₃	—	4	1	no	—
173	#23720	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₅₃	—	2	2	no	—
175	C₂²×C₅₃	—	4	1	no	—
176	C₂²×C₅₃	—	4	2	no	—
177	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
178	C₂²×C₅₃	#529	1	2	yes	—
179	C₄×C₅₃	—	2	2	no	—
180	C₄×C₅₃	—	2	2	no	—
181	C₄×C₅₃	—	4	1	no	—
182	C₄×C₅₃	—	4	4	no	—
183	C₄×C₅₃	—	4	2	no	—
184	C₄×C₅₃	—	8	2	no	—
185	C₄×C₅₃	#525	1	1	yes	characteristic
186	C₄×C₅₃	#525	1	2	yes	—
187	C₄×C₅₃	#532	1	1	yes	characteristic
188	C₄×#137	C₂×C₅₃	1	2	yes	—
189	C₂×#441	C₂×C₅₃	1	1	yes	characteristic, complemented
190	#2923	C₂×C₅₃	1	1	yes	characteristic
191	#2090	C₂×C₅₃	1	1	yes	characteristic, complemented
192	#2079	C₂×C₅₃	1	1	yes	characteristic
193	#2064	C₂×C₅₃	1	2	yes	complemented
194	#2052	C₂×C₅₃	1	2	yes	—
195	#2047	C₂×C₅₃	1	1	yes	characteristic, complemented
196	#2020	C₂×C₅₃	1	1	yes	characteristic
197	#1778	C₂×C₅₃	1	1	yes	characteristic, complemented
198	C₄×#101	C₂×C₅₃	1	2	yes	complemented
199	C₂×C₅₃	—	2	2	no	—
200	C₂×C₅₃	—	8	1	no	—
201	C₂×C₅₃	#2392	1	1	yes	characteristic
202	C₂×C₅₃	#3069	1	2	yes	—
203	C₂×#137	C₂²×C₅₃	1	2	yes	—
204	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
205	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
207	#441	—	2	2	no	—
208	#441	—	2	2	no	—
209	#441	—	2	2	no	—
210	#440	—	2	2	no	—
211	C₄×Q₁₆	—	2	2	no	—
212	C₄×SD₁₆	—	2	2	no	—
213	#433	—	2	2	no	—
214	#432	—	2	2	no	—
215	C₂×#108	C₂²×C₅₃	1	2	yes	—
216	#428	C₂²×C₅₃	1	2	yes	—
217	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
218	#424	C₂²×C₅₃	1	1	yes	characteristic
219	#424	C₂²×C₅₃	1	1	yes	characteristic
220	#419	C₂²×C₅₃	1	2	yes	—
221	#417	C₂²×C₅₃	1	2	yes	—
222	C₂×#103	C₂²×C₅₃	1	2	yes	—
223	C₂×#101	C₂²×C₅₃	1	2	yes	—
224	C₂×#101	C₂²×C₅₃	1	2	yes	—
225	#408	C₂²×C₅₃	1	1	yes	characteristic
226	#408	C₂²×C₅₃	1	1	yes	characteristic
227	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
228	C₄×M₁₆	C₂²×C₅₃	1	2	yes	—
229	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
230	#343	C₂²×C₅₃	1	2	yes	—
231	#343	C₂²×C₅₃	1	2	yes	—
232	#341	C₂²×C₅₃	1	1	yes	characteristic
233	#341	C₂²×C₅₃	1	1	yes	characteristic
234	C₅₃	#23720	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
237	#137	—	2	4	no	—
238	#137	—	2	4	no	—
239	C₂×Q₁₆	—	2	2	no	—
240	C₂×Q₁₆	—	2	4	no	—
241	C₂×Q₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
244	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
245	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
246	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	D₄×C₅₃	1	2	yes	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	D₄×C₅₃	1	2	yes	—
256	#117	—	2	1	no	—
257	#117	C₂³×C₅₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
263	#108	—	2	4	no	—
264	#107	—	2	2	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	2	4	no	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#102	—	2	2	no	—
274	#101	—	2	4	no	—
275	#101	—	2	4	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	#97	—	2	1	no	—
279	#97	—	2	2	no	—
280	#97	D₄×C₅₃	1	2	yes	—
281	#97	D₄×C₅₃	1	2	yes	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
292	C₂×Q₈	#41×C₅₃	1	4	yes	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	#41×C₅₃	1	2	yes	—
300	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
301	Q₁₆	—	2	8	no	—
302	Q₁₆	—	2	8	no	—
303	SD₁₆	—	2	8	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	#41×C₅₃	1	4	yes	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
317	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂×D₄×C₅₃	1	2	yes	—
331	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
333	C₂³	—	2	1	no	—
334	C₂³	C₂×#41×C₅₃	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	2	4	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	#121×C₅₃	1	2	yes	—
354	C₂×C₄	#121×C₅₃	1	2	yes	—
355	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
358	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
359	C₈	—	2	2	no	—
360	C₈	—	2	4	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	C₂×#121×C₅₃	1	1	yes	characteristic
369	C₂²	C₅₃×#529	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	4	no	—
375	C₄	—	8	2	no	—
376	C₄	C₅₃×#525	1	1	yes	characteristic
377	C₄	C₅₃×#525	1	2	yes	—
378	C₄	C₅₃×#532	1	1	yes	characteristic
379	C₂	—	2	2	no	—
380	C₂	—	8	1	no	—
381	C₂	C₅₃×#2392	1	1	yes	characteristic
382	C₂	C₅₃×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×#41×C₅₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#441	C₂	semidirect
4. C₅₃×#2090	C₂	semidirect
6. C₅₃×#2064	C₂	semidirect
8. C₅₃×#2047	C₂	semidirect
10. C₅₃×#1778	C₂	semidirect
11. C₄×#101×C₅₃	C₂	semidirect
173. #23720	C₅₃	direct (N × H)
189. C₂×#441	C₂×C₅₃	semidirect
191. #2090	C₂×C₅₃	semidirect
193. #2064	C₂×C₅₃	semidirect
195. #2047	C₂×C₅₃	semidirect
197. #1778	C₂×C₅₃	semidirect
198. C₄×#101	C₂×C₅₃	semidirect
234. C₅₃	#23720	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#137×C₅₃	2
C₂×C₅₃×#441	2
C₅₃×#2923	2
C₅₃×#2090	2
C₅₃×#2079	2
C₅₃×#2064	2
C₅₃×#2052	2
C₅₃×#2047	2
C₅₃×#2020	2
C₅₃×#1778	2
C₄×#101×C₅₃	2
#23720	53

Subgroups — C53×#23720 #27231232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#23720 #27231232