Subgroups — C₅₃×#17827 #27225339

Order 13568.

610 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2925	C₂	1	2	yes	maximal
3	C₅₃×#1572	C₂	1	4	yes	maximal, complemented
4	C₅₃×#1571	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1568	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1564	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
10	C₈×Q₈×C₅₃	C₄	1	1	yes	characteristic
11	C₈×Q₈×C₅₃	C₄	1	1	yes	characteristic
12	C₈×D₄×C₅₃	C₄	1	1	yes	characteristic
13	C₈×D₄×C₅₃	C₄	1	2	yes	—
14	C₈×D₄×C₅₃	C₄	1	1	yes	characteristic
15	C₈×D₄×C₅₃	C₄	1	2	yes	—
16	C₅₃×#433	—	2	4	no	—
17	C₅₃×#432	C₂²	1	4	yes	—
18	C₅₃×#431	C₂²	1	4	yes	—
19	C₅₃×#431	C₂²	1	1	yes	characteristic
20	C₅₃×#431	C₂²	1	2	yes	—
21	C₅₃×#423	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
23	C₅₃×#408	—	2	2	no	—
24	C₅₃×#405	—	2	2	no	—
25	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#335	C₂²	1	4	yes	—
28	C₅₃×#335	C₂²	1	4	yes	—
29	C₅₃×#334	C₂²	1	1	yes	characteristic
30	C₅₃×#334	C₂²	1	1	yes	characteristic
31	C₅₃×#334	C₂²	1	2	yes	—
32	C₅₃×#334	C₂²	1	2	yes	—
33	C₅₃×#334	C₂²	1	2	yes	—
34	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₅₃	—	2	2	no	—
36	C₂²×C₈×C₅₃	—	2	2	no	—
37	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
41	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
42	C₄×Q₈×C₅₃	Q₈	1	1	yes	characteristic
43	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
44	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
45	C₄×D₄×C₅₃	Q₈	1	1	yes	characteristic
46	C₄×D₄×C₅₃	Q₈	1	2	yes	—
47	#117×C₅₃	D₄	1	1	yes	characteristic
48	#117×C₅₃	D₄	1	2	yes	—
49	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
51	C₄⋊C₈×C₅₃	—	2	2	no	—
52	C₄⋊C₈×C₅₃	—	2	2	no	—
53	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
54	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
55	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
56	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
57	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
58	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
59	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
60	C₂²⋊C₈×C₅₃	—	2	4	no	—
61	C₂²⋊C₈×C₅₃	—	2	4	no	—
62	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
64	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
65	#97×C₅₃	—	2	4	no	—
66	C₄×C₈×C₅₃	—	2	4	no	—
67	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₅₃	C₂³	1	2	yes	—
74	#41×C₅₃	—	2	4	no	—
75	C₂×Q₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂×D₄×C₅₃	C₄⋊C₄	1	2	yes	—
77	C₂×D₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
84	M₁₆×C₅₃	—	4	4	no	—
85	C₂×C₈×C₅₃	—	2	2	no	—
86	C₂×C₈×C₅₃	—	2	4	no	—
87	C₂×C₈×C₅₃	—	2	2	no	—
88	C₂×C₈×C₅₃	—	2	4	no	—
89	C₂×C₈×C₅₃	—	2	2	no	—
90	C₂×C₈×C₅₃	—	4	1	no	—
91	C₂×C₈×C₅₃	—	4	2	no	—
92	C₂×C₈×C₅₃	—	4	4	no	—
93	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
100	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
102	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
104	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
105	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
106	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
107	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₅₃	C₂×D₄	1	2	yes	—
109	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
111	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
113	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
114	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
115	Q₈×C₅₃	—	2	2	no	—
116	D₄×C₅₃	—	2	4	no	—
117	D₄×C₅₃	—	2	2	no	—
118	C₂×C₄×C₅₃	—	2	1	no	—
119	C₂×C₄×C₅₃	—	2	2	no	—
120	C₂×C₄×C₅₃	—	2	1	no	—
121	C₂×C₄×C₅₃	—	2	2	no	—
122	C₂×C₄×C₅₃	—	2	4	no	—
123	C₂×C₄×C₅₃	—	4	1	no	—
124	C₂×C₄×C₅₃	—	4	2	no	—
125	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	#135	1	4	yes	—
132	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
135	C₈×C₅₃	—	2	1	no	—
136	C₈×C₅₃	—	2	2	no	—
137	C₈×C₅₃	—	2	1	no	—
138	C₈×C₅₃	—	2	1	no	—
139	C₈×C₅₃	—	2	2	no	—
140	C₈×C₅₃	—	4	2	no	—
141	C₈×C₅₃	—	4	2	no	—
142	C₈×C₅₃	—	4	4	no	—
143	C₈×C₅₃	#131	1	2	yes	—
144	#17827	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂²×C₅₃	—	2	1	no	—
146	C₂²×C₅₃	—	2	1	no	—
147	C₂²×C₅₃	—	2	2	no	—
148	C₂²×C₅₃	—	2	2	no	—
149	C₂²×C₅₃	—	2	2	no	—
150	C₂²×C₅₃	#427	1	2	yes	—
151	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
152	C₄×C₅₃	—	2	1	no	—
153	C₄×C₅₃	—	2	2	no	—
154	C₄×C₅₃	—	2	2	no	—
155	C₄×C₅₃	—	2	1	no	—
156	C₄×C₅₃	—	2	1	no	—
157	C₄×C₅₃	—	2	2	no	—
158	C₄×C₅₃	#427	1	2	yes	—
159	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
160	C₄×C₅₃	#568	1	1	yes	characteristic
161	C₄×C₅₃	C₂×#135	1	2	yes	—
162	C₈×#41	C₂×C₅₃	1	1	yes	characteristic
163	#2925	C₂×C₅₃	1	2	yes	—
164	#1572	C₂×C₅₃	1	4	yes	complemented
165	#1571	C₂×C₅₃	1	2	yes	complemented
166	#1568	C₂×C₅₃	1	2	yes	complemented
167	#1566	C₂×C₅₃	1	1	yes	characteristic, complemented
168	#1564	C₂×C₅₃	1	2	yes	complemented
169	C₂×#334	C₂×C₅₃	1	1	yes	characteristic, complemented
170	C₂×C₅₃	—	2	2	no	—
171	C₂×C₅₃	—	4	2	no	—
172	C₂×C₅₃	#2906	1	1	yes	characteristic
173	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
174	C₂×C₅₃	#2916	1	1	yes	characteristic
175	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
176	C₈×Q₈	C₄×C₅₃	1	1	yes	characteristic
177	C₈×Q₈	C₄×C₅₃	1	1	yes	characteristic
178	C₈×D₄	C₄×C₅₃	1	1	yes	characteristic
179	C₈×D₄	C₄×C₅₃	1	2	yes	—
180	C₈×D₄	C₄×C₅₃	1	1	yes	characteristic
181	C₈×D₄	C₄×C₅₃	1	2	yes	—
182	#433	—	2	4	no	—
183	#432	C₂²×C₅₃	1	4	yes	—
184	#431	C₂²×C₅₃	1	4	yes	—
185	#431	C₂²×C₅₃	1	1	yes	characteristic
186	#431	C₂²×C₅₃	1	2	yes	—
187	#423	C₂²×C₅₃	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
189	#408	—	2	2	no	—
190	#405	—	2	2	no	—
191	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	—
193	#335	C₂²×C₅₃	1	4	yes	—
194	#335	C₂²×C₅₃	1	4	yes	—
195	#334	C₂²×C₅₃	1	1	yes	characteristic
196	#334	C₂²×C₅₃	1	1	yes	characteristic
197	#334	C₂²×C₅₃	1	2	yes	—
198	#334	C₂²×C₅₃	1	2	yes	—
199	#334	C₂²×C₅₃	1	2	yes	—
200	C₅₃	#17827	1	1	yes	characteristic, direct product factor, Sylow
201	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
202	C₂×M₁₆	—	2	2	no	—
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
205	C₂²×C₈	C₂×C₄×C₅₃	1	2	yes	—
206	C₂²×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
207	C₂²×C₈	C₂×C₄×C₅₃	1	2	yes	—
208	C₄×Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
209	C₄×Q₈	Q₈×C₅₃	1	1	yes	characteristic
210	C₄×D₄	C₂×C₄×C₅₃	1	2	yes	—
211	C₄×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
212	C₄×D₄	Q₈×C₅₃	1	2	yes	—
213	C₄×D₄	Q₈×C₅₃	1	1	yes	characteristic
214	#117	D₄×C₅₃	1	1	yes	characteristic
215	#117	D₄×C₅₃	1	2	yes	—
216	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
218	C₄⋊C₈	—	2	2	no	—
219	C₄⋊C₈	—	2	2	no	—
220	C₄⋊C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
221	C₄⋊C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
222	C₄⋊C₈	C₂×C₄×C₅₃	1	2	yes	—
223	C₄⋊C₈	C₂×C₄×C₅₃	1	2	yes	—
224	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
225	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
226	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
227	C₂²⋊C₈	—	2	4	no	—
228	C₂²⋊C₈	—	2	4	no	—
229	C₂²⋊C₈	C₂×C₄×C₅₃	1	2	yes	—
230	C₂²⋊C₈	C₂×C₄×C₅₃	1	2	yes	—
231	C₂²⋊C₈	C₂×C₄×C₅₃	1	2	yes	—
232	#97	—	2	4	no	—
233	C₄×C₈	—	2	4	no	—
234	C₄×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
235	C₄×C₈	C₂×C₄×C₅₃	1	2	yes	—
236	C₄×C₈	C₂×C₄×C₅₃	1	1	yes	characteristic
237	C₄×C₈	C₂×C₄×C₅₃	1	2	yes	—
238	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
239	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
240	C₄×C₈	C₂³×C₅₃	1	2	yes	—
241	#41	—	2	4	no	—
242	C₂×Q₈	C₄⋊C₄×C₅₃	1	1	yes	characteristic
243	C₂×D₄	C₄⋊C₄×C₅₃	1	2	yes	—
244	C₂×D₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
247	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
248	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
249	C₂²×C₄	C₂×Q₈×C₅₃	1	2	yes	—
250	C₂²×C₄	C₂×Q₈×C₅₃	1	1	yes	characteristic
251	M₁₆	—	4	4	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	4	1	no	—
258	C₂×C₈	—	4	2	no	—
259	C₂×C₈	—	4	4	no	—
260	C₂×C₈	C₂²×C₄×C₅₃	1	1	yes	characteristic
261	C₂×C₈	C₂²×C₄×C₅₃	1	1	yes	characteristic
262	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
263	C₂×C₈	C₂²×C₄×C₅₃	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
265	C₂×C₈	C₂²×C₄×C₅₃	1	1	yes	characteristic
266	C₄⋊C₄	C₄⋊C₄×C₅₃	1	2	yes	—
267	C₄⋊C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
268	C₄⋊C₄	C₄⋊C₄×C₅₃	1	2	yes	—
269	C₄⋊C₄	C₄⋊C₄×C₅₃	1	1	yes	characteristic
270	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	2	yes	—
271	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	2	yes	—
272	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	2	yes	—
273	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
274	C₄²	C₂²×C₄×C₅₃	1	1	yes	characteristic
275	C₄²	C₂×D₄×C₅₃	1	2	yes	—
276	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
277	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
278	C₄²	C₂×Q₈×C₅₃	1	1	yes	characteristic
279	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
280	C₂³	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
281	C₂³	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
282	Q₈	—	2	2	no	—
283	D₄	—	2	4	no	—
284	D₄	—	2	2	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
293	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
294	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
295	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
296	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
297	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	1	yes	characteristic
298	C₂×C₄	#135×C₅₃	1	4	yes	—
299	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
300	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
301	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
302	C₈	—	2	1	no	—
303	C₈	—	2	2	no	—
304	C₈	—	2	1	no	—
305	C₈	—	2	1	no	—
306	C₈	—	2	2	no	—
307	C₈	—	4	2	no	—
308	C₈	—	4	2	no	—
309	C₈	—	4	4	no	—
310	C₈	#131×C₅₃	1	2	yes	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	C₅₃×#427	1	2	yes	—
317	C₂²	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
318	C₄	—	2	1	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	2	1	no	—
322	C₄	—	2	1	no	—
323	C₄	—	2	2	no	—
324	C₄	C₅₃×#427	1	2	yes	—
325	C₄	C₂×#131×C₅₃	1	1	yes	characteristic
326	C₄	C₅₃×#568	1	1	yes	characteristic
327	C₄	C₂×#135×C₅₃	1	2	yes	—
328	C₂	—	2	2	no	—
329	C₂	—	4	2	no	—
330	C₂	C₅₃×#2906	1	1	yes	characteristic
331	C₂	C₂×C₅₃×#427	1	1	yes	characteristic
332	C₂	C₅₃×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₄²	C₂⁴×C₅₃
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₅₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₃×#1572	C₂	semidirect
4. C₅₃×#1571	C₂	semidirect
5. C₅₃×#1568	C₂	semidirect
6. C₅₃×#1566	C₂	semidirect
7. C₅₃×#1564	C₂	semidirect
8. C₂×C₅₃×#334	C₂	semidirect
144. #17827	C₅₃	direct (N × H)
164. #1572	C₂×C₅₃	semidirect
165. #1571	C₂×C₅₃	semidirect
166. #1568	C₂×C₅₃	semidirect
167. #1566	C₂×C₅₃	semidirect
168. #1564	C₂×C₅₃	semidirect
169. C₂×#334	C₂×C₅₃	semidirect
200. C₅₃	#17827	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#41×C₅₃	2
C₅₃×#2925	2
C₅₃×#1572	2
C₅₃×#1571	2
C₅₃×#1568	2
C₅₃×#1566	2
C₅₃×#1564	2
C₂×C₅₃×#334	2
#17827	53

Subgroups — C53×#17827 #27225339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#17827 #27225339