Subgroups — C₅₃×#18524 #27226036

Order 13568.

1716 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3109	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1629	C₂	1	4	yes	maximal, complemented
5	C₅₃×#1619	C₂	1	4	yes	maximal, complemented
6	C₅₃×#1555	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1490	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₅₃	—	2	2	no	—
9	C₂×AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
10	D₄²×C₅₃	—	2	2	no	—
11	D₄²×C₅₃	—	2	4	no	—
12	D₄²×C₅₃	C₂²	1	4	yes	—
13	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
14	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₅₃	—	2	2	no	—
16	C₂×#120×C₅₃	—	2	2	no	—
17	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
18	C₅₃×#496	—	2	2	no	—
19	C₅₃×#493	C₂²	1	2	yes	complemented
20	C₅₃×#492	C₂²	1	2	yes	complemented
21	C₅₃×#481	—	2	2	no	—
22	C₅₃×#476	C₂²	1	4	yes	complemented
23	C₅₃×#459	C₂²	1	4	yes	complemented
24	C₅₃×#447	—	2	2	no	—
25	C₅₃×#442	—	2	4	no	—
26	C₅₃×#432	C₂²	1	2	yes	complemented
27	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#331	C₂²	1	4	yes	complemented
29	C₅₃×D₄⋊C₈	C₂²	1	8	yes	complemented
30	C₂⁵×C₅₃	—	2	2	no	—
31	C₂×#41×C₅₃	—	2	1	no	—
32	C₂²×D₄×C₅₃	—	2	4	no	—
33	C₂²×D₄×C₅₃	—	2	8	no	—
34	C₂²×D₄×C₅₃	—	2	8	no	—
35	C₂²×D₄×C₅₃	—	2	2	no	—
36	C₂²×D₄×C₅₃	—	4	16	no	—
37	C₂²×D₄×C₅₃	D₄	1	2	yes	—
38	C₂²×D₄×C₅₃	D₄	1	2	yes	—
39	C₂³×C₄×C₅₃	—	2	2	no	—
40	AGL(1,ℤ/8)×C₅₃	—	4	8	no	—
41	C₂×SD₁₆×C₅₃	—	2	4	no	—
42	C₂×D₈×C₅₃	—	2	4	no	—
43	C₂×D₈×C₅₃	—	2	4	no	—
44	C₂×M₁₆×C₅₃	—	2	1	no	—
45	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
46	#127×C₅₃	—	2	2	no	—
47	#127×C₅₃	D₄	1	2	yes	—
48	#127×C₅₃	C₂³	1	2	yes	—
49	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
50	#124×C₅₃	—	2	1	no	—
51	#121×C₅₃	—	2	8	no	—
52	#121×C₅₃	—	2	8	no	—
53	#121×C₅₃	—	2	2	no	—
54	#120×C₅₃	—	2	8	no	—
55	#120×C₅₃	—	2	8	no	—
56	C₄×D₄×C₅₃	—	2	2	no	—
57	C₄×D₄×C₅₃	—	2	2	no	—
58	C₄×D₄×C₅₃	—	2	2	no	—
59	C₄×D₄×C₅₃	D₄	1	4	yes	—
60	C₄×D₄×C₅₃	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
64	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
65	#106×C₅₃	—	2	4	no	—
66	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
67	#102×C₅₃	—	2	4	no	—
68	#102×C₅₃	—	2	4	no	—
69	C₂²⋊C₈×C₅₃	—	2	2	no	—
70	#97×C₅₃	—	2	1	no	—
71	#97×C₅₃	—	2	2	no	—
72	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
73	C₂⁴×C₅₃	—	2	2	no	—
74	C₂⁴×C₅₃	—	2	8	no	—
75	C₂⁴×C₅₃	—	2	2	no	—
76	C₂⁴×C₅₃	—	4	16	no	—
77	C₂⁴×C₅₃	—	8	4	no	—
78	#41×C₅₃	—	4	4	no	—
79	C₂×Q₈×C₅₃	—	2	1	no	—
80	C₂×D₄×C₅₃	—	2	8	no	—
81	C₂×D₄×C₅₃	—	2	16	no	—
82	C₂×D₄×C₅₃	—	2	2	no	—
83	C₂×D₄×C₅₃	—	2	4	no	—
84	C₂×D₄×C₅₃	—	2	2	no	—
85	C₂×D₄×C₅₃	—	2	4	no	—
86	C₂×D₄×C₅₃	—	2	2	no	—
87	C₂×D₄×C₅₃	—	2	1	no	—
88	C₂×D₄×C₅₃	—	4	8	no	—
89	C₂×D₄×C₅₃	—	4	4	no	—
90	C₂×D₄×C₅₃	—	4	32	no	—
91	C₂×D₄×C₅₃	—	4	16	no	—
92	C₂×D₄×C₅₃	—	4	16	no	—
93	C₂×D₄×C₅₃	—	4	16	no	—
94	C₂×D₄×C₅₃	—	4	1	no	—
95	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₅₃	—	2	2	no	—
98	C₂²×C₄×C₅₃	—	2	4	no	—
99	C₂²×C₄×C₅₃	—	2	4	no	—
100	C₂²×C₄×C₅₃	—	4	8	no	—
101	C₂²×C₄×C₅₃	—	4	1	no	—
102	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
104	SD₁₆×C₅₃	—	4	8	no	—
105	D₈×C₅₃	—	4	8	no	—
106	D₈×C₅₃	—	4	8	no	—
107	M₁₆×C₅₃	—	2	4	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	—	2	4	no	—
110	C₄⋊C₄×C₅₃	—	2	2	no	—
111	C₄⋊C₄×C₅₃	—	2	2	no	—
112	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
113	C₂²⋊C₄×C₅₃	—	2	8	no	—
114	C₂²⋊C₄×C₅₃	—	2	4	no	—
115	C₂²⋊C₄×C₅₃	—	2	4	no	—
116	C₂²⋊C₄×C₅₃	—	4	2	no	—
117	C₄²×C₅₃	C₂×D₄	1	2	yes	—
118	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
120	C₂³×C₅₃	—	2	8	no	—
121	C₂³×C₅₃	—	2	4	no	—
122	C₂³×C₅₃	—	2	4	no	—
123	C₂³×C₅₃	—	4	4	no	—
124	C₂³×C₅₃	—	4	8	no	—
125	C₂³×C₅₃	—	4	32	no	—
126	C₂³×C₅₃	—	4	4	no	—
127	C₂³×C₅₃	—	4	4	no	—
128	C₂³×C₅₃	—	4	1	no	—
129	C₂³×C₅₃	—	8	8	no	—
130	C₂³×C₅₃	—	8	32	no	—
131	C₂³×C₅₃	#120	1	1	yes	characteristic
132	Q₈×C₅₃	—	4	2	no	—
133	D₄×C₅₃	—	2	8	no	—
134	D₄×C₅₃	—	2	4	no	—
135	D₄×C₅₃	—	4	4	no	—
136	D₄×C₅₃	—	4	8	no	—
137	D₄×C₅₃	—	4	2	no	—
138	D₄×C₅₃	—	4	32	no	—
139	D₄×C₅₃	—	4	8	no	—
140	D₄×C₅₃	—	4	4	no	—
141	D₄×C₅₃	—	8	2	no	—
142	D₄×C₅₃	—	8	2	no	—
143	D₄×C₅₃	AGL(1,ℤ/8)	1	8	yes	complemented
144	C₂×C₄×C₅₃	—	2	2	no	—
145	C₂×C₄×C₅₃	—	2	4	no	—
146	C₂×C₄×C₅₃	—	2	4	no	—
147	C₂×C₄×C₅₃	—	4	8	no	—
148	C₂×C₄×C₅₃	—	4	4	no	—
149	C₂×C₄×C₅₃	—	4	8	no	—
150	C₂×C₄×C₅₃	—	4	1	no	—
151	C₂×C₄×C₅₃	—	8	2	no	—
152	C₂×C₄×C₅₃	#120	1	2	yes	—
153	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
156	C₈×C₅₃	—	2	4	no	—
157	C₈×C₅₃	—	4	4	no	—
158	#18524	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₅₃	—	2	2	no	—
160	C₂²×C₅₃	—	2	8	no	—
161	C₂²×C₅₃	—	4	16	no	—
162	C₂²×C₅₃	—	4	4	no	—
163	C₂²×C₅₃	—	4	4	no	—
164	C₂²×C₅₃	—	4	8	no	—
165	C₂²×C₅₃	—	4	4	no	—
166	C₂²×C₅₃	—	8	8	no	—
167	C₂²×C₅₃	—	8	32	no	—
168	C₂²×C₅₃	—	8	2	no	—
169	C₂²×C₅₃	—	8	1	no	—
170	C₂²×C₅₃	#453	1	2	yes	—
171	C₂²×C₅₃	C₂×#120	1	1	yes	characteristic
172	C₄×C₅₃	—	2	2	no	—
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	—	2	1	no	—
175	C₄×C₅₃	—	4	4	no	—
176	C₄×C₅₃	—	8	1	no	—
177	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
178	C₂×D₄²	C₂×C₅₃	1	1	yes	characteristic, complemented
179	#3151	C₂×C₅₃	1	1	yes	characteristic, complemented
180	#3109	C₂×C₅₃	1	2	yes	complemented
181	#1629	C₂×C₅₃	1	4	yes	complemented
182	#1619	C₂×C₅₃	1	4	yes	complemented
183	#1555	C₂×C₅₃	1	1	yes	characteristic, complemented
184	#1490	C₂×C₅₃	1	2	yes	complemented
185	C₂×C₅₃	—	2	2	no	—
186	C₂×C₅₃	—	4	8	no	—
187	C₂×C₅₃	—	8	4	no	—
188	C₂×C₅₃	—	16	1	no	—
189	C₂×C₅₃	#3003	1	2	yes	—
190	C₂×C₅₃	C₂×#453	1	1	yes	characteristic
191	C₂³×D₄	—	2	2	no	—
192	C₂×AGL(1,ℤ/8)	—	2	2	no	—
193	D₄²	—	2	2	no	—
194	D₄²	—	2	4	no	—
195	D₄²	C₂²×C₅₃	1	4	yes	—
196	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
197	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
198	C₂×#121	—	2	2	no	—
199	C₂×#120	—	2	2	no	—
200	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
201	#496	—	2	2	no	—
202	#493	C₂²×C₅₃	1	2	yes	complemented
203	#492	C₂²×C₅₃	1	2	yes	complemented
204	#481	—	2	2	no	—
205	#476	C₂²×C₅₃	1	4	yes	complemented
206	#459	C₂²×C₅₃	1	4	yes	complemented
207	#447	—	2	2	no	—
208	#442	—	2	4	no	—
209	#432	C₂²×C₅₃	1	2	yes	complemented
210	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
211	#331	C₂²×C₅₃	1	4	yes	complemented
212	D₄⋊C₈	C₂²×C₅₃	1	8	yes	complemented
213	C₅₃	#18524	1	1	yes	characteristic, direct product factor, Sylow
214	C₂⁵	—	2	2	no	—
215	C₂×#41	—	2	1	no	—
216	C₂²×D₄	—	2	4	no	—
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	2	8	no	—
219	C₂²×D₄	—	2	2	no	—
220	C₂²×D₄	—	4	16	no	—
221	C₂²×D₄	D₄×C₅₃	1	2	yes	—
222	C₂²×D₄	D₄×C₅₃	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	AGL(1,ℤ/8)	—	4	8	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×D₈	—	2	4	no	—
227	C₂×D₈	—	2	4	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
230	#127	—	2	2	no	—
231	#127	D₄×C₅₃	1	2	yes	—
232	#127	C₂³×C₅₃	1	2	yes	—
233	#127	C₂³×C₅₃	1	1	yes	characteristic, complemented
234	#124	—	2	1	no	—
235	#121	—	2	8	no	—
236	#121	—	2	8	no	—
237	#121	—	2	2	no	—
238	#120	—	2	8	no	—
239	#120	—	2	8	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	D₄×C₅₃	1	4	yes	—
244	C₄×D₄	C₂³×C₅₃	1	4	yes	—
245	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
249	#106	—	2	4	no	—
250	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
251	#102	—	2	4	no	—
252	#102	—	2	4	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	#97	—	2	1	no	—
255	#97	—	2	2	no	—
256	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
257	C₂⁴	—	2	2	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	2	2	no	—
260	C₂⁴	—	4	16	no	—
261	C₂⁴	—	8	4	no	—
262	#41	—	4	4	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	32	no	—
275	C₂×D₄	—	4	16	no	—
276	C₂×D₄	—	4	16	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
280	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
288	SD₁₆	—	4	8	no	—
289	D₈	—	4	8	no	—
290	D₈	—	4	8	no	—
291	M₁₆	—	2	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
297	C₂²⋊C₄	—	2	8	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	C₂×D₄×C₅₃	1	2	yes	—
302	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
303	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
304	C₂³	—	2	8	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	8	no	—
309	C₂³	—	4	32	no	—
310	C₂³	—	4	4	no	—
311	C₂³	—	4	4	no	—
312	C₂³	—	4	1	no	—
313	C₂³	—	8	8	no	—
314	C₂³	—	8	32	no	—
315	C₂³	#120×C₅₃	1	1	yes	characteristic
316	Q₈	—	4	2	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	4	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	8	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	32	no	—
323	D₄	—	4	8	no	—
324	D₄	—	4	4	no	—
325	D₄	—	8	2	no	—
326	D₄	—	8	2	no	—
327	D₄	AGL(1,ℤ/8)×C₅₃	1	8	yes	complemented
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
337	C₂×C₄	#120×C₅₃	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
340	C₈	—	2	4	no	—
341	C₈	—	4	4	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	4	16	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	8	8	no	—
350	C₂²	—	8	32	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	1	no	—
353	C₂²	C₅₃×#453	1	2	yes	—
354	C₂²	C₂×#120×C₅₃	1	1	yes	characteristic
355	C₄	—	2	2	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	4	no	—
359	C₄	—	8	1	no	—
360	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
361	C₂	—	2	2	no	—
362	C₂	—	4	8	no	—
363	C₂	—	8	4	no	—
364	C₂	—	16	1	no	—
365	C₂	C₅₃×#3003	1	2	yes	—
366	C₂	C₂×C₅₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
LCS	G ▷ C₄² ▷ C₂² ▷ 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
1. C₂×D₄²×C₅₃	C₂	semidirect
2. C₅₃×#3151	C₂	semidirect
3. C₅₃×#3109	C₂	semidirect
4. C₅₃×#1629	C₂	semidirect
5. C₅₃×#1619	C₂	semidirect
6. C₅₃×#1555	C₂	semidirect
7. C₅₃×#1490	C₂	semidirect
13. C₅₃×#532	C₂²	semidirect
19. C₅₃×#493	C₂²	semidirect
20. C₅₃×#492	C₂²	semidirect
22. C₅₃×#476	C₂²	semidirect
23. C₅₃×#459	C₂²	semidirect
26. C₅₃×#432	C₂²	semidirect
27. C₄×M₁₆×C₅₃	C₂²	semidirect
28. C₅₃×#331	C₂²	semidirect
29. C₅₃×D₄⋊C₈	C₂²	semidirect
45. C₄⋊Q₈×C₅₃	C₂³	semidirect
49. #127×C₅₃	C₂³	semidirect
66. C₄⋊C₈×C₅₃	C₂³	semidirect
72. C₄×C₈×C₅₃	C₂³	semidirect
143. D₄×C₅₃	AGL(1,ℤ/8)	semidirect
158. #18524	C₅₃	direct (N × H)
178. C₂×D₄²	C₂×C₅₃	semidirect
179. #3151	C₂×C₅₃	semidirect
180. #3109	C₂×C₅₃	semidirect
181. #1629	C₂×C₅₃	semidirect
182. #1619	C₂×C₅₃	semidirect
183. #1555	C₂×C₅₃	semidirect
184. #1490	C₂×C₅₃	semidirect
196. #532	C₂²×C₅₃	semidirect
202. #493	C₂²×C₅₃	semidirect
203. #492	C₂²×C₅₃	semidirect
205. #476	C₂²×C₅₃	semidirect
206. #459	C₂²×C₅₃	semidirect
209. #432	C₂²×C₅₃	semidirect
210. C₄×M₁₆	C₂²×C₅₃	semidirect
211. #331	C₂²×C₅₃	semidirect
212. D₄⋊C₈	C₂²×C₅₃	semidirect
213. C₅₃	#18524	direct (N × H)
229. C₄⋊Q₈	C₂³×C₅₃	semidirect
233. #127	C₂³×C₅₃	semidirect
250. C₄⋊C₈	C₂³×C₅₃	semidirect
256. C₄×C₈	C₂³×C₅₃	semidirect
327. D₄	AGL(1,ℤ/8)×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₅₃	2
C₅₃×#3151	2
C₅₃×#3109	2
C₅₃×#1629	2
C₅₃×#1619	2
C₅₃×#1555	2
C₅₃×#1490	2
#18524	53

Subgroups — C53×#18524 #27226036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#18524 #27226036