Subgroups — C₅₃×#60626 #27268138

Order 13568.

2134 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3142	C₂	1	3	yes	maximal, complemented
4	C₅₃×#3138	C₂	1	3	yes	maximal, complemented
5	C₅₃×#3136	C₂	1	12	yes	maximal, complemented
6	C₅₃×#3135	C₂	1	3	yes	maximal, complemented
7	C₂×C₅₃×#490	C₂	1	3	yes	maximal, complemented
8	C₅₃×#2897	C₂	1	4	yes	maximal, complemented
9	C₅₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	—
11	C₂×#131×C₅₃	C₂²	1	2	yes	—
12	C₅₃×#557	—	2	2	no	—
13	C₅₃×#554	—	2	6	no	—
14	C₅₃×#550	—	2	2	no	—
15	D₄²×C₅₃	—	2	6	no	—
16	C₅₃×#544	C₂²	1	6	yes	complemented
17	C₅₃×#535	C₂²	1	6	yes	—
18	C₅₃×#533	C₂²	1	3	yes	complemented
19	C₅₃×#532	C₂²	1	3	yes	—
20	C₂×#127×C₅₃	C₂²	1	3	yes	—
21	C₂×#125×C₅₃	C₂²	1	3	yes	complemented
22	C₅₃×#520	C₂²	1	2	yes	—
23	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
25	C₅₃×#491	C₂²	1	3	yes	complemented
26	C₅₃×#490	C₂²	1	3	yes	complemented
27	C₅₃×#490	C₂²	1	12	yes	complemented
28	C₅₃×#490	C₂²	1	6	yes	complemented
29	C₅₃×#490	C₂²	1	3	yes	complemented
30	C₅₃×#489	C₂²	1	12	yes	complemented
31	C₅₃×#488	C₂²	1	12	yes	complemented
32	C₅₃×#486	C₂²	1	12	yes	complemented
33	C₅₃×#418	C₂²	1	12	yes	complemented
34	C₅₃×#417	C₂²	1	12	yes	complemented
35	C₅₃×#416	C₂²	1	12	yes	complemented
36	C₂×#102×C₅₃	C₂²	1	12	yes	complemented
37	C₅₃×#405	C₂²	1	6	yes	complemented
38	C₄×M₁₆×C₅₃	C₂²	1	3	yes	complemented
39	C₂×#97×C₅₃	C₂²	1	3	yes	complemented
40	H(5,𝔽₂)×C₅₃	—	2	16	no	—
41	C₂×#41×C₅₃	—	2	2	no	—
42	C₂×#41×C₅₃	C₂³	1	6	yes	—
43	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₅₃	—	2	6	no	—
45	C₂²×D₄×C₅₃	—	2	6	no	—
46	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
47	#131×C₅₃	—	2	8	no	—
48	C₂×M₁₆×C₅₃	C₂³	1	6	yes	—
49	C₂²×C₈×C₅₃	C₂³	1	6	yes	—
50	C₄⋊Q₈×C₅₃	—	2	6	no	—
51	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
52	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
53	#127×C₅₃	—	2	6	no	—
54	#127×C₅₃	C₂³	1	6	yes	—
55	#127×C₅₃	C₂³	1	3	yes	—
56	#125×C₅₃	—	2	6	no	—
57	#125×C₅₃	—	2	6	no	—
58	#125×C₅₃	C₂³	1	6	yes	—
59	#125×C₅₃	C₂³	1	3	yes	—
60	#125×C₅₃	C₂³	1	1	yes	characteristic
61	#124×C₅₃	C₂³	1	6	yes	—
62	C₂²⋊Q₈×C₅₃	—	2	12	no	—
63	C₂²⋊Q₈×C₅₃	—	2	6	no	—
64	#121×C₅₃	—	2	12	no	—
65	#121×C₅₃	—	2	6	no	—
66	#120×C₅₃	—	2	12	no	—
67	C₄×Q₈×C₅₃	—	2	6	no	—
68	C₄×Q₈×C₅₃	—	2	2	no	—
69	C₄×Q₈×C₅₃	D₄	1	2	yes	—
70	C₄×D₄×C₅₃	—	2	6	no	—
71	C₄×D₄×C₅₃	—	2	6	no	—
72	C₄×D₄×C₅₃	D₄	1	6	yes	—
73	#117×C₅₃	C₂³	1	6	yes	—
74	#117×C₅₃	C₂³	1	3	yes	—
75	C₂×C₄⋊C₄×C₅₃	—	2	6	no	—
76	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
77	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
78	#103×C₅₃	C₂³	1	12	yes	—
79	#103×C₅₃	C₂³	1	4	yes	—
80	#102×C₅₃	C₂³	1	12	yes	—
81	#102×C₅₃	C₂³	1	24	yes	—
82	#102×C₅₃	C₂³	1	12	yes	—
83	#97×C₅₃	C₂³	1	6	yes	—
84	#97×C₅₃	C₂³	1	1	yes	characteristic
85	#97×C₅₃	C₂³	1	3	yes	—
86	C₄×C₈×C₅₃	C₂³	1	6	yes	—
87	C₂⁴×C₅₃	—	2	6	no	—
88	#41×C₅₃	—	2	24	no	—
89	#41×C₅₃	—	4	8	no	—
90	#41×C₅₃	#41	1	8	yes	—
91	C₂×Q₈×C₅₃	—	2	6	no	—
92	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
94	C₂×D₄×C₅₃	—	2	6	no	—
95	C₂×D₄×C₅₃	—	2	6	no	—
96	C₂×D₄×C₅₃	—	2	6	no	—
97	C₂×D₄×C₅₃	—	2	12	no	—
98	C₂×D₄×C₅₃	—	2	24	no	—
99	C₂×D₄×C₅₃	—	4	24	no	—
100	C₂×D₄×C₅₃	—	8	12	no	—
101	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
102	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
103	C₂²×C₄×C₅₃	—	2	6	no	—
104	C₂²×C₄×C₅₃	—	2	6	no	—
105	C₂²×C₄×C₅₃	C₂×D₄	1	6	yes	—
106	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
107	M₁₆×C₅₃	—	2	12	no	—
108	C₂×C₈×C₅₃	—	2	12	no	—
109	C₂×C₈×C₅₃	C₂⁴	1	6	yes	—
110	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
111	C₄⋊C₄×C₅₃	—	2	6	no	—
112	C₄⋊C₄×C₅₃	—	2	12	no	—
113	C₄⋊C₄×C₅₃	—	2	6	no	—
114	C₄⋊C₄×C₅₃	—	2	2	no	—
115	C₄⋊C₄×C₅₃	—	2	2	no	—
116	C₄⋊C₄×C₅₃	—	2	6	no	—
117	C₄⋊C₄×C₅₃	C₂×D₄	1	6	yes	—
118	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
119	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
120	C₂²⋊C₄×C₅₃	—	2	6	no	—
121	C₂²⋊C₄×C₅₃	—	2	12	no	—
122	C₂²⋊C₄×C₅₃	C₂×D₄	1	6	yes	—
123	C₄²×C₅₃	—	2	6	no	—
124	C₄²×C₅₃	C₂×D₄	1	6	yes	—
125	C₄²×C₅₃	C₂⁴	1	3	yes	—
126	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
127	C₂³×C₅₃	—	2	6	no	—
128	C₂³×C₅₃	—	4	12	no	—
129	C₂³×C₅₃	—	8	12	no	—
130	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
131	Q₈×C₅₃	—	2	4	no	—
132	Q₈×C₅₃	—	8	6	no	—
133	Q₈×C₅₃	#124	1	4	yes	—
134	D₄×C₅₃	—	2	12	no	—
135	D₄×C₅₃	—	4	12	no	—
136	D₄×C₅₃	—	4	12	no	—
137	D₄×C₅₃	—	4	12	no	—
138	D₄×C₅₃	—	8	12	no	—
139	D₄×C₅₃	#124	1	12	yes	—
140	C₂×C₄×C₅₃	—	2	2	no	—
141	C₂×C₄×C₅₃	—	2	6	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	—	4	6	no	—
144	C₂×C₄×C₅₃	—	4	12	no	—
145	C₂×C₄×C₅₃	—	8	6	no	—
146	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
147	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
148	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
149	C₂×C₄×C₅₃	C₂×#41	1	12	yes	—
150	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
151	C₈×C₅₃	—	2	2	no	—
152	C₈×C₅₃	—	2	6	no	—
153	#60626	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂²×C₅₃	—	2	6	no	—
155	C₂²×C₅₃	—	4	12	no	—
156	C₂²×C₅₃	—	4	6	no	—
157	C₂²×C₅₃	—	16	12	no	—
158	C₂²×C₅₃	C₂×#124	1	6	yes	—
159	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
160	C₄×C₅₃	—	2	2	no	—
161	C₄×C₅₃	—	2	6	no	—
162	C₄×C₅₃	—	4	6	no	—
163	C₄×C₅₃	—	4	2	no	—
164	C₄×C₅₃	—	4	2	no	—
165	C₄×C₅₃	C₂×#124	1	6	yes	—
166	C₄×C₅₃	C₂²×#41	1	2	yes	—
167	#3504	C₂×C₅₃	1	1	yes	characteristic, complemented
168	#3498	C₂×C₅₃	1	1	yes	characteristic
169	#3142	C₂×C₅₃	1	3	yes	complemented
170	#3138	C₂×C₅₃	1	3	yes	complemented
171	#3136	C₂×C₅₃	1	12	yes	complemented
172	#3135	C₂×C₅₃	1	3	yes	complemented
173	C₂×#490	C₂×C₅₃	1	3	yes	complemented
174	#2897	C₂×C₅₃	1	4	yes	complemented
175	#2875	C₂×C₅₃	1	1	yes	characteristic, complemented
176	C₂×C₅₃	—	2	6	no	—
177	C₂×C₅₃	—	8	6	no	—
178	C₂×C₅₃	C₂²×#124	1	1	yes	characteristic
179	C₂×C₅₃	#3585	1	2	yes	—
180	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	—
181	C₂×#131	C₂²×C₅₃	1	2	yes	—
182	#557	—	2	2	no	—
183	#554	—	2	6	no	—
184	#550	—	2	2	no	—
185	D₄²	—	2	6	no	—
186	#544	C₂²×C₅₃	1	6	yes	complemented
187	#535	C₂²×C₅₃	1	6	yes	—
188	#533	C₂²×C₅₃	1	3	yes	complemented
189	#532	C₂²×C₅₃	1	3	yes	—
190	C₂×#127	C₂²×C₅₃	1	3	yes	—
191	C₂×#125	C₂²×C₅₃	1	3	yes	complemented
192	#520	C₂²×C₅₃	1	2	yes	—
193	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
194	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
195	#491	C₂²×C₅₃	1	3	yes	complemented
196	#490	C₂²×C₅₃	1	3	yes	complemented
197	#490	C₂²×C₅₃	1	12	yes	complemented
198	#490	C₂²×C₅₃	1	6	yes	complemented
199	#490	C₂²×C₅₃	1	3	yes	complemented
200	#489	C₂²×C₅₃	1	12	yes	complemented
201	#488	C₂²×C₅₃	1	12	yes	complemented
202	#486	C₂²×C₅₃	1	12	yes	complemented
203	#418	C₂²×C₅₃	1	12	yes	complemented
204	#417	C₂²×C₅₃	1	12	yes	complemented
205	#416	C₂²×C₅₃	1	12	yes	complemented
206	C₂×#102	C₂²×C₅₃	1	12	yes	complemented
207	#405	C₂²×C₅₃	1	6	yes	complemented
208	C₄×M₁₆	C₂²×C₅₃	1	3	yes	complemented
209	C₂×#97	C₂²×C₅₃	1	3	yes	complemented
210	C₅₃	#60626	1	1	yes	characteristic, direct product factor, Sylow
211	H(5,𝔽₂)	—	2	16	no	—
212	C₂×#41	—	2	2	no	—
213	C₂×#41	C₂³×C₅₃	1	6	yes	—
214	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
215	C₂²×D₄	—	2	6	no	—
216	C₂²×D₄	—	2	6	no	—
217	C₂²×D₄	C₂³×C₅₃	1	6	yes	—
218	#131	—	2	8	no	—
219	C₂×M₁₆	C₂³×C₅₃	1	6	yes	—
220	C₂²×C₈	C₂³×C₅₃	1	6	yes	—
221	C₄⋊Q₈	—	2	6	no	—
222	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
223	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
224	#127	—	2	6	no	—
225	#127	C₂³×C₅₃	1	3	yes	—
226	#127	C₂³×C₅₃	1	6	yes	—
227	#125	—	2	6	no	—
228	#125	—	2	6	no	—
229	#125	C₂³×C₅₃	1	3	yes	—
230	#125	C₂³×C₅₃	1	6	yes	—
231	#125	C₂³×C₅₃	1	1	yes	characteristic
232	#124	C₂³×C₅₃	1	6	yes	—
233	C₂²⋊Q₈	—	2	6	no	—
234	C₂²⋊Q₈	—	2	12	no	—
235	#121	—	2	6	no	—
236	#121	—	2	12	no	—
237	#120	—	2	12	no	—
238	C₄×Q₈	—	2	2	no	—
239	C₄×Q₈	—	2	6	no	—
240	C₄×Q₈	D₄×C₅₃	1	2	yes	—
241	C₄×D₄	—	2	6	no	—
242	C₄×D₄	—	2	6	no	—
243	C₄×D₄	D₄×C₅₃	1	6	yes	—
244	#117	C₂³×C₅₃	1	6	yes	—
245	#117	C₂³×C₅₃	1	3	yes	—
246	C₂×C₄⋊C₄	—	2	6	no	—
247	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
248	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
249	#103	C₂³×C₅₃	1	4	yes	—
250	#103	C₂³×C₅₃	1	12	yes	—
251	#102	C₂³×C₅₃	1	12	yes	—
252	#102	C₂³×C₅₃	1	24	yes	—
253	#102	C₂³×C₅₃	1	12	yes	—
254	#97	C₂³×C₅₃	1	1	yes	characteristic
255	#97	C₂³×C₅₃	1	3	yes	—
256	#97	C₂³×C₅₃	1	6	yes	—
257	C₄×C₈	C₂³×C₅₃	1	6	yes	—
258	C₂⁴	—	2	6	no	—
259	#41	—	2	24	no	—
260	#41	—	4	8	no	—
261	#41	#41×C₅₃	1	8	yes	—
262	C₂×Q₈	—	2	6	no	—
263	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
264	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
265	C₂×D₄	—	2	6	no	—
266	C₂×D₄	—	2	6	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	2	12	no	—
269	C₂×D₄	—	2	24	no	—
270	C₂×D₄	—	4	24	no	—
271	C₂×D₄	—	8	12	no	—
272	C₂×D₄	C₂×D₄×C₅₃	1	3	yes	—
273	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
274	C₂²×C₄	—	2	6	no	—
275	C₂²×C₄	—	2	6	no	—
276	C₂²×C₄	C₂×D₄×C₅₃	1	6	yes	—
277	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
278	M₁₆	—	2	12	no	—
279	C₂×C₈	—	2	12	no	—
280	C₂×C₈	C₂⁴×C₅₃	1	6	yes	—
281	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
282	C₄⋊C₄	—	2	6	no	—
283	C₄⋊C₄	—	2	12	no	—
284	C₄⋊C₄	—	2	6	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	6	no	—
288	C₄⋊C₄	C₂×D₄×C₅₃	1	6	yes	—
289	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
290	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
291	C₂²⋊C₄	—	2	6	no	—
292	C₂²⋊C₄	—	2	12	no	—
293	C₂²⋊C₄	C₂×D₄×C₅₃	1	6	yes	—
294	C₄²	—	2	6	no	—
295	C₄²	C₂×D₄×C₅₃	1	6	yes	—
296	C₄²	C₂⁴×C₅₃	1	3	yes	—
297	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
298	C₂³	—	2	6	no	—
299	C₂³	—	4	12	no	—
300	C₂³	—	8	12	no	—
301	C₂³	C₂²×D₄×C₅₃	1	3	yes	—
302	Q₈	—	2	4	no	—
303	Q₈	—	8	6	no	—
304	Q₈	#124×C₅₃	1	4	yes	—
305	D₄	—	2	12	no	—
306	D₄	—	4	12	no	—
307	D₄	—	4	12	no	—
308	D₄	—	4	12	no	—
309	D₄	—	8	12	no	—
310	D₄	#124×C₅₃	1	12	yes	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	6	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	6	no	—
315	C₂×C₄	—	4	12	no	—
316	C₂×C₄	—	8	6	no	—
317	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
318	C₂×C₄	C₂²×D₄×C₅₃	1	6	yes	—
319	C₂×C₄	C₂²×D₄×C₅₃	1	3	yes	—
320	C₂×C₄	C₂×#41×C₅₃	1	12	yes	—
321	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	6	no	—
324	C₂²	—	2	6	no	—
325	C₂²	—	4	12	no	—
326	C₂²	—	4	6	no	—
327	C₂²	—	16	12	no	—
328	C₂²	C₂×#124×C₅₃	1	6	yes	—
329	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	6	no	—
332	C₄	—	4	6	no	—
333	C₄	—	4	2	no	—
334	C₄	—	4	2	no	—
335	C₄	C₂×#124×C₅₃	1	6	yes	—
336	C₄	C₂²×#41×C₅₃	1	2	yes	—
337	C₂	—	2	6	no	—
338	C₂	—	8	6	no	—
339	C₂	C₂²×#124×C₅₃	1	1	yes	characteristic
340	C₂	C₅₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3504	C₂	semidirect
3. C₅₃×#3142	C₂	semidirect
4. C₅₃×#3138	C₂	semidirect
5. C₅₃×#3136	C₂	semidirect
6. C₅₃×#3135	C₂	semidirect
7. C₂×C₅₃×#490	C₂	semidirect
8. C₅₃×#2897	C₂	semidirect
9. C₅₃×#2875	C₂	semidirect
16. C₅₃×#544	C₂²	semidirect
18. C₅₃×#533	C₂²	semidirect
21. C₂×#125×C₅₃	C₂²	semidirect
24. C₅₃×#491	C₂²	semidirect
25. C₅₃×#491	C₂²	semidirect
26. C₅₃×#490	C₂²	semidirect
27. C₅₃×#490	C₂²	semidirect
28. C₅₃×#490	C₂²	semidirect
29. C₅₃×#490	C₂²	semidirect
30. C₅₃×#489	C₂²	semidirect
31. C₅₃×#488	C₂²	semidirect
32. C₅₃×#486	C₂²	semidirect
33. C₅₃×#418	C₂²	semidirect
34. C₅₃×#417	C₂²	semidirect
35. C₅₃×#416	C₂²	semidirect
36. C₂×#102×C₅₃	C₂²	semidirect
37. C₅₃×#405	C₂²	semidirect
38. C₄×M₁₆×C₅₃	C₂²	semidirect
39. C₂×#97×C₅₃	C₂²	semidirect
153. #60626	C₅₃	direct (N × H)
167. #3504	C₂×C₅₃	semidirect
169. #3142	C₂×C₅₃	semidirect
170. #3138	C₂×C₅₃	semidirect
171. #3136	C₂×C₅₃	semidirect
172. #3135	C₂×C₅₃	semidirect
173. C₂×#490	C₂×C₅₃	semidirect
174. #2897	C₂×C₅₃	semidirect
175. #2875	C₂×C₅₃	semidirect
186. #544	C₂²×C₅₃	semidirect
188. #533	C₂²×C₅₃	semidirect
191. C₂×#125	C₂²×C₅₃	semidirect
194. #491	C₂²×C₅₃	semidirect
195. #491	C₂²×C₅₃	semidirect
196. #490	C₂²×C₅₃	semidirect
197. #490	C₂²×C₅₃	semidirect
198. #490	C₂²×C₅₃	semidirect
199. #490	C₂²×C₅₃	semidirect
200. #489	C₂²×C₅₃	semidirect
201. #488	C₂²×C₅₃	semidirect
202. #486	C₂²×C₅₃	semidirect
203. #418	C₂²×C₅₃	semidirect
204. #417	C₂²×C₅₃	semidirect
205. #416	C₂²×C₅₃	semidirect
206. C₂×#102	C₂²×C₅₃	semidirect
207. #405	C₂²×C₅₃	semidirect
208. C₄×M₁₆	C₂²×C₅₃	semidirect
209. C₂×#97	C₂²×C₅₃	semidirect
210. C₅₃	#60626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3504	2
C₅₃×#3498	2
C₅₃×#3142	2
C₅₃×#3138	2
C₅₃×#3136	2
C₅₃×#3135	2
C₂×C₅₃×#490	2
C₅₃×#2897	2
C₅₃×#2875	2
#60626	53

Subgroups — C53×#60626 #27268138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60626 #27268138