Subgroups — C₄×#121×C₅₃ #20271237

Order 6784.

824 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₅₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#388	C₂	1	2	yes	maximal, complemented
8	C₅₃×#386	C₂	1	2	yes	maximal, complemented
9	C₅₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊C₄×C₅₃	C₂	1	2	yes	maximal, complemented
12	C₂²×D₄×C₅₃	C₂²	1	2	yes	—
13	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₅₃	C₂²	1	2	yes	—
16	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
18	#121×C₅₃	C₄	1	8	yes	direct product factor
19	C₄×D₄×C₅₃	—	2	4	no	—
20	C₄×D₄×C₅₃	—	2	8	no	—
21	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₂×C₄²×C₅₃	—	2	4	no	—
31	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₅₃	C₂²	1	2	yes	—
35	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
36	#95×C₅₃	C₂²	1	2	yes	—
37	#95×C₅₃	C₂²	1	2	yes	—
38	#95×C₅₃	C₂²	1	2	yes	—
39	C₂⁴×C₅₃	C₂³	1	2	yes	—
40	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
41	C₂×D₄×C₅₃	—	2	4	no	—
42	C₂×D₄×C₅₃	—	2	4	no	—
43	C₂×D₄×C₅₃	—	2	2	no	—
44	C₂×D₄×C₅₃	—	2	2	no	—
45	C₂×D₄×C₅₃	C₂×C₄	1	8	yes	complemented
46	C₂×D₄×C₅₃	C₂×C₄	1	4	yes	complemented
47	C₂²×C₄×C₅₃	—	2	2	no	—
48	C₂²×C₄×C₅₃	—	2	2	no	—
49	C₂²×C₄×C₅₃	—	2	2	no	—
50	C₂²×C₄×C₅₃	—	2	2	no	—
51	C₂²×C₄×C₅₃	—	2	2	no	—
52	C₂²×C₄×C₅₃	—	2	2	no	—
53	C₂²×C₄×C₅₃	—	2	2	no	—
54	C₂²×C₄×C₅₃	—	2	4	no	—
55	C₂²×C₄×C₅₃	—	2	4	no	—
56	C₂²×C₄×C₅₃	—	2	4	no	—
57	C₂²×C₄×C₅₃	C₂×C₄	1	4	yes	complemented
58	C₂²×C₄×C₅₃	D₄	1	4	yes	complemented
59	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
60	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
61	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
63	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₅₃	—	2	4	no	—
69	C₄⋊C₄×C₅₃	—	2	2	no	—
70	C₄⋊C₄×C₅₃	—	2	2	no	—
71	C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	complemented
72	C₂²⋊C₄×C₅₃	—	2	4	no	—
73	C₂²⋊C₄×C₅₃	—	2	4	no	—
74	C₂²⋊C₄×C₅₃	—	2	4	no	—
75	C₂²⋊C₄×C₅₃	—	2	4	no	—
76	C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
77	C₄²×C₅₃	—	2	2	no	—
78	C₄²×C₅₃	—	2	2	no	—
79	C₄²×C₅₃	—	2	2	no	—
80	C₄²×C₅₃	—	2	4	no	—
81	C₄²×C₅₃	D₄	1	4	yes	complemented
82	C₂³×C₅₃	—	2	1	no	—
83	C₂³×C₅₃	—	2	1	no	—
84	C₂³×C₅₃	—	2	1	no	—
85	C₂³×C₅₃	—	2	1	no	—
86	C₂³×C₅₃	—	2	2	no	—
87	C₂³×C₅₃	—	2	2	no	—
88	C₂³×C₅₃	—	2	2	no	—
89	C₂³×C₅₃	—	2	2	no	—
90	C₂³×C₅₃	—	2	2	no	—
91	C₂³×C₅₃	—	2	2	no	—
92	C₂³×C₅₃	C₂²×C₄	1	4	yes	—
93	C₂³×C₅₃	C₂²×C₄	1	2	yes	—
94	C₂³×C₅₃	C₂×D₄	1	2	yes	—
95	C₂³×C₅₃	#41	1	2	yes	—
96	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
97	D₄×C₅₃	—	2	16	no	—
98	D₄×C₅₃	—	2	8	no	—
99	C₂×C₄×C₅₃	—	2	8	no	—
100	C₂×C₄×C₅₃	—	2	1	no	—
101	C₂×C₄×C₅₃	—	2	1	no	—
102	C₂×C₄×C₅₃	—	2	1	no	—
103	C₂×C₄×C₅₃	—	2	2	no	—
104	C₂×C₄×C₅₃	—	2	1	no	—
105	C₂×C₄×C₅₃	—	2	1	no	—
106	C₂×C₄×C₅₃	—	2	1	no	—
107	C₂×C₄×C₅₃	—	2	1	no	—
108	C₂×C₄×C₅₃	—	2	1	no	—
109	C₂×C₄×C₅₃	—	2	2	no	—
110	C₂×C₄×C₅₃	—	2	8	no	—
111	C₂×C₄×C₅₃	—	2	8	no	—
112	C₂×C₄×C₅₃	—	2	2	no	—
113	C₂×C₄×C₅₃	—	2	2	no	—
114	C₂×C₄×C₅₃	—	2	2	no	—
115	C₂×C₄×C₅₃	—	2	2	no	—
116	C₂×C₄×C₅₃	—	2	2	no	—
117	C₂×C₄×C₅₃	—	2	2	no	—
118	C₂×C₄×C₅₃	—	4	8	no	—
119	C₂×C₄×C₅₃	C₂²×C₄	1	2	yes	—
120	C₂×C₄×C₅₃	C₂²×C₄	1	4	yes	—
121	C₂×C₄×C₅₃	C₂²×C₄	1	2	yes	—
122	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
123	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
124	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
125	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
126	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
127	C₂×C₄×C₅₃	#41	1	2	yes	—
128	C₂×C₄×C₅₃	#41	1	2	yes	—
129	C₂×C₄×C₅₃	#41	1	2	yes	—
130	C₂²×C₅₃	—	2	2	no	—
131	C₂²×C₅₃	—	2	2	no	—
132	C₂²×C₅₃	—	2	2	no	—
133	C₂²×C₅₃	—	2	2	no	—
134	C₂²×C₅₃	—	2	2	no	—
135	C₂²×C₅₃	—	2	2	no	—
136	C₂²×C₅₃	—	2	4	no	—
137	C₂²×C₅₃	—	2	4	no	—
138	C₂²×C₅₃	—	2	4	no	—
139	C₂²×C₅₃	—	4	2	no	—
140	C₂²×C₅₃	—	4	2	no	—
141	C₂²×C₅₃	—	4	2	no	—
142	C₂²×C₅₃	—	4	2	no	—
143	C₂²×C₅₃	C₄×D₄	1	4	yes	complemented
144	C₂²×C₅₃	C₂³×C₄	1	1	yes	characteristic
145	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
146	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
147	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
148	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
149	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
150	C₂²×C₅₃	C₂×#41	1	1	yes	characteristic
151	C₄×C₅₃	—	2	2	no	—
152	C₄×C₅₃	—	2	4	no	—
153	C₄×C₅₃	—	2	2	no	—
154	C₄×C₅₃	—	2	2	no	—
155	C₄×C₅₃	—	2	2	no	—
156	C₄×C₅₃	—	4	2	no	—
157	C₄×C₅₃	—	4	2	no	—
158	C₄×C₅₃	C₄×D₄	1	4	yes	complemented
159	C₄×C₅₃	#121	1	4	yes	direct product factor
160	C₄×#121	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂×C₅₃	—	2	4	no	—
162	C₂×C₅₃	—	4	4	no	—
163	C₂×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
164	C₂×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
165	C₂×C₅₃	C₄×#41	1	1	yes	characteristic
166	C₂×C₅₃	C₂×#121	1	1	yes	characteristic
167	C₂×C₅₃	#525	1	1	yes	characteristic
168	C₂×C₅₃	#529	1	1	yes	characteristic
169	C₂×C₅₃	#532	1	1	yes	characteristic
170	C₂×#121	C₂×C₅₃	1	1	yes	characteristic
171	C₂×C₄×D₄	C₂×C₅₃	1	2	yes	complemented
172	C₂×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
173	C₂²×C₄²	C₂×C₅₃	1	1	yes	characteristic, complemented
174	#390	C₂×C₅₃	1	1	yes	characteristic, complemented
175	#389	C₂×C₅₃	1	1	yes	characteristic, complemented
176	#388	C₂×C₅₃	1	2	yes	complemented
177	#386	C₂×C₅₃	1	2	yes	complemented
178	#380	C₂×C₅₃	1	1	yes	characteristic, complemented
179	C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊C₄	C₂×C₅₃	1	2	yes	complemented
181	C₅₃	C₄×#121	1	1	yes	characteristic, direct product factor, Sylow
182	C₂²×D₄	C₂²×C₅₃	1	2	yes	—
183	C₂²×D₄	C₂²×C₅₃	1	1	yes	characteristic
184	C₂³×C₄	C₂²×C₅₃	1	2	yes	—
185	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
186	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
187	C₂³×C₄	C₂²×C₅₃	1	1	yes	characteristic
188	#121	C₄×C₅₃	1	8	yes	direct product factor
189	C₄×D₄	—	2	8	no	—
190	C₄×D₄	—	2	4	no	—
191	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
192	C₂×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
193	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
195	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
196	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
197	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
198	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
199	C₂×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
200	C₂×C₄²	—	2	4	no	—
201	C₂×C₄²	C₂²×C₅₃	1	2	yes	—
202	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic
203	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic
204	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic
205	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic
206	#95	C₂²×C₅₃	1	2	yes	—
207	#95	C₂²×C₅₃	1	2	yes	—
208	#95	C₂²×C₅₃	1	2	yes	—
209	C₂⁴	C₂³×C₅₃	1	2	yes	—
210	C₂⁴	C₂³×C₅₃	1	1	yes	characteristic
211	C₂×D₄	—	2	4	no	—
212	C₂×D₄	—	2	4	no	—
213	C₂×D₄	—	2	2	no	—
214	C₂×D₄	—	2	2	no	—
215	C₂×D₄	C₂×C₄×C₅₃	1	8	yes	complemented
216	C₂×D₄	C₂×C₄×C₅₃	1	4	yes	complemented
217	C₂²×C₄	—	2	2	no	—
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	C₂×C₄×C₅₃	1	4	yes	complemented
228	C₂²×C₄	D₄×C₅₃	1	4	yes	complemented
229	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
230	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
231	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
232	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
233	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
234	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
235	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
236	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
237	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
238	C₄⋊C₄	—	2	4	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	C₂×C₄×C₅₃	1	4	yes	complemented
242	C₂²⋊C₄	—	2	4	no	—
243	C₂²⋊C₄	—	2	4	no	—
244	C₂²⋊C₄	—	2	4	no	—
245	C₂²⋊C₄	—	2	4	no	—
246	C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
247	C₄²	—	2	2	no	—
248	C₄²	—	2	2	no	—
249	C₄²	—	2	2	no	—
250	C₄²	—	2	4	no	—
251	C₄²	D₄×C₅₃	1	4	yes	complemented
252	C₂³	—	2	1	no	—
253	C₂³	—	2	1	no	—
254	C₂³	—	2	1	no	—
255	C₂³	—	2	1	no	—
256	C₂³	—	2	2	no	—
257	C₂³	—	2	2	no	—
258	C₂³	—	2	2	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	2	no	—
262	C₂³	C₂²×C₄×C₅₃	1	4	yes	—
263	C₂³	C₂²×C₄×C₅₃	1	2	yes	—
264	C₂³	C₂×D₄×C₅₃	1	2	yes	—
265	C₂³	#41×C₅₃	1	2	yes	—
266	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
267	D₄	—	2	16	no	—
268	D₄	—	2	8	no	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	4	8	no	—
289	C₂×C₄	C₂²×C₄×C₅₃	1	2	yes	—
290	C₂×C₄	C₂²×C₄×C₅₃	1	4	yes	—
291	C₂×C₄	C₂²×C₄×C₅₃	1	2	yes	—
292	C₂×C₄	C₂×D₄×C₅₃	1	2	yes	—
293	C₂×C₄	C₂×D₄×C₅₃	1	2	yes	—
294	C₂×C₄	C₂×D₄×C₅₃	1	2	yes	—
295	C₂×C₄	C₂×D₄×C₅₃	1	2	yes	—
296	C₂×C₄	C₂×D₄×C₅₃	1	2	yes	—
297	C₂×C₄	#41×C₅₃	1	2	yes	—
298	C₂×C₄	#41×C₅₃	1	2	yes	—
299	C₂×C₄	#41×C₅₃	1	2	yes	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	4	2	no	—
310	C₂²	—	4	2	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	2	no	—
313	C₂²	C₄×D₄×C₅₃	1	4	yes	complemented
314	C₂²	C₂³×C₄×C₅₃	1	1	yes	characteristic
315	C₂²	C₂²×D₄×C₅₃	1	1	yes	characteristic
316	C₂²	C₂²×D₄×C₅₃	1	1	yes	characteristic
317	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
318	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
319	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
320	C₂²	C₂×#41×C₅₃	1	1	yes	characteristic
321	C₄	—	2	2	no	—
322	C₄	—	2	4	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	2	no	—
328	C₄	C₄×D₄×C₅₃	1	4	yes	complemented
329	C₄	#121×C₅₃	1	4	yes	direct product factor
330	C₂	—	2	4	no	—
331	C₂	—	4	4	no	—
332	C₂	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
333	C₂	C₂×C₄×D₄×C₅₃	1	1	yes	characteristic
334	C₂	C₄×#41×C₅₃	1	1	yes	characteristic
335	C₂	C₂×#121×C₅₃	1	1	yes	characteristic
336	C₂	C₅₃×#525	1	1	yes	characteristic
337	C₂	C₅₃×#529	1	1	yes	characteristic
338	C₂	C₅₃×#532	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×C₅₃	C₂	semidirect
3. C₂×C₄×D₄×C₅₃	C₂	semidirect
4. C₂²×C₄²×C₅₃	C₂	semidirect
5. C₅₃×#390	C₂	semidirect
6. C₅₃×#389	C₂	semidirect
7. C₅₃×#388	C₂	semidirect
8. C₅₃×#386	C₂	semidirect
9. C₅₃×#380	C₂	semidirect
10. C₄×C₄⋊C₄×C₅₃	C₂	semidirect
11. C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
18. #121×C₅₃	C₄	direct (N × H)
45. C₂×D₄×C₅₃	C₂×C₄	semidirect
46. C₂×D₄×C₅₃	C₂×C₄	semidirect
57. C₂²×C₄×C₅₃	C₂×C₄	semidirect
58. C₂²×C₄×C₅₃	D₄	semidirect
71. C₄⋊C₄×C₅₃	C₂×C₄	semidirect
76. C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
81. C₄²×C₅₃	D₄	semidirect
143. C₂²×C₅₃	C₄×D₄	semidirect
158. C₄×C₅₃	C₄×D₄	semidirect
159. C₄×C₅₃	#121	direct (N × H)
160. C₄×#121	C₅₃	direct (N × H)
171. C₂×C₄×D₄	C₂×C₅₃	semidirect
172. C₂×C₄×D₄	C₂×C₅₃	semidirect
173. C₂²×C₄²	C₂×C₅₃	semidirect
174. #390	C₂×C₅₃	semidirect
175. #389	C₂×C₅₃	semidirect
176. #388	C₂×C₅₃	semidirect
177. #386	C₂×C₅₃	semidirect
178. #380	C₂×C₅₃	semidirect
179. C₄×C₄⋊C₄	C₂×C₅₃	semidirect
180. C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
181. C₅₃	C₄×#121	direct (N × H)
188. #121	C₄×C₅₃	direct (N × H)
215. C₂×D₄	C₂×C₄×C₅₃	semidirect
216. C₂×D₄	C₂×C₄×C₅₃	semidirect
227. C₂²×C₄	C₂×C₄×C₅₃	semidirect
228. C₂²×C₄	D₄×C₅₃	semidirect
241. C₄⋊C₄	C₂×C₄×C₅₃	semidirect
246. C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
251. C₄²	D₄×C₅₃	semidirect
313. C₂²	C₄×D₄×C₅₃	semidirect
328. C₄	C₄×D₄×C₅₃	semidirect
329. C₄	#121×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#121×C₅₃	2
C₂×C₄×D₄×C₅₃	2
C₂²×C₄²×C₅₃	2
C₅₃×#390	2
C₅₃×#389	2
C₅₃×#388	2
C₅₃×#386	2
C₅₃×#380	2
C₄×C₄⋊C₄×C₅₃	2
C₄×C₂²⋊C₄×C₅₃	2
C₄×#121	53

Subgroups — C4×#121×C53 #20271237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#121×C₅₃ #20271237