Subgroups — C₅₃×#34251 #27241763

Order 13568.

2834 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2353	C₂	1	4	yes	maximal, complemented
3	C₅₃×#2352	C₂	1	4	yes	maximal, complemented
4	C₅₃×#2343	C₂	1	4	yes	maximal, complemented
5	C₅₃×#2342	C₂	1	4	yes	maximal, complemented
6	C₅₃×#2318	C₂	1	4	yes	maximal, complemented
7	C₅₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2308	C₂	1	1	yes	maximal, characteristic
9	C₅₃×#2290	C₂	1	4	yes	maximal, complemented
10	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2273	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
16	C₅₃×#518	C₄	1	16	yes	complemented
17	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
19	C₂×#117×C₅₃	C₂²	1	2	yes	—
20	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
21	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
29	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
30	C₅₃×#388	C₂²	1	4	yes	complemented
31	C₅₃×#388	C₂²	1	4	yes	complemented
32	C₅₃×#388	C₂²	1	4	yes	complemented
33	C₅₃×#388	C₂²	1	4	yes	complemented
34	C₅₃×#387	C₂²	1	4	yes	complemented
35	C₅₃×#387	C₂²	1	4	yes	complemented
36	C₅₃×#387	C₂²	1	4	yes	complemented
37	C₅₃×#387	C₂²	1	4	yes	complemented
38	C₅₃×#386	C₂²	1	2	yes	—
39	C₅₃×#386	C₂²	1	2	yes	—
40	C₅₃×#386	C₂²	1	4	yes	—
41	C₅₃×#386	C₂²	1	4	yes	—
42	C₅₃×#386	C₂²	1	2	yes	—
43	C₅₃×#386	C₂²	1	2	yes	—
44	C₅₃×#385	C₂²	1	4	yes	—
45	C₅₃×#385	C₂²	1	4	yes	—
46	C₅₃×#385	C₂²	1	2	yes	complemented
47	C₅₃×#385	C₂²	1	2	yes	complemented
48	C₅₃×#385	C₂²	1	4	yes	complemented
49	C₅₃×#383	C₂²	1	4	yes	complemented
50	C₅₃×#382	C₂²	1	4	yes	complemented
51	C₅₃×#381	C₂²	1	2	yes	—
52	C₅₃×#381	C₂²	1	4	yes	complemented
53	C₅₃×#380	C₂²	1	4	yes	complemented
54	C₅₃×#380	C₂²	1	4	yes	complemented
55	C₅₃×#379	C₂²	1	2	yes	—
56	C₄×C₄⋊C₄×C₅₃	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
58	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
59	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
60	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
64	C₅₃×#376	C₂²	1	4	yes	complemented
65	C₂×#95×C₅₃	C₂²	1	2	yes	—
66	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
67	C₂×#95×C₅₃	C₂²	1	2	yes	complemented
68	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
69	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₅₃	—	2	4	no	—
71	C₂²×D₄×C₅₃	—	2	4	no	—
72	C₂²×D₄×C₅₃	C₂×C₄	1	8	yes	—
73	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₅₃	—	2	4	no	—
76	C₂³×C₄×C₅₃	—	4	4	no	—
77	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
89	C₄×D₄×C₅₃	C₂×C₄	1	32	yes	complemented
90	C₄×D₄×C₅₃	C₂×C₄	1	32	yes	complemented
91	#117×C₅₃	—	4	8	no	—
92	#117×C₅₃	C₂×C₄	1	16	yes	complemented
93	C₂×C₄⋊C₄×C₅₃	—	4	4	no	—
94	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
100	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
103	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	—
104	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	8	yes	—
105	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	16	yes	complemented
106	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
121	C₂×C₄²×C₅₃	—	4	4	no	—
122	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
124	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
125	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
126	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
127	#95×C₅₃	C₂³	1	4	yes	—
128	#95×C₅₃	C₂³	1	4	yes	—
129	#95×C₅₃	C₂³	1	4	yes	—
130	#95×C₅₃	C₂³	1	4	yes	—
131	#95×C₅₃	C₂³	1	4	yes	—
132	#95×C₅₃	C₂³	1	4	yes	—
133	#95×C₅₃	C₂³	1	4	yes	—
134	#95×C₅₃	C₂³	1	4	yes	—
135	#95×C₅₃	C₂³	1	4	yes	—
136	#95×C₅₃	C₂³	1	4	yes	—
137	#95×C₅₃	C₂³	1	4	yes	—
138	#95×C₅₃	C₂³	1	4	yes	—
139	C₂⁴×C₅₃	—	2	2	no	—
140	C₂⁴×C₅₃	—	2	2	no	—
141	C₂⁴×C₅₃	—	4	2	no	—
142	C₂⁴×C₅₃	—	4	2	no	—
143	C₂⁴×C₅₃	—	4	2	no	—
144	C₂⁴×C₅₃	—	4	2	no	—
145	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
146	C₂⁴×C₅₃	C₂²×C₄	1	4	yes	—
147	C₂⁴×C₅₃	#41	1	4	yes	—
148	C₂⁴×C₅₃	#41	1	4	yes	—
149	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
150	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
151	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
152	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
153	C₂×D₄×C₅₃	—	2	32	no	—
154	C₂×D₄×C₅₃	—	2	4	no	—
155	C₂×D₄×C₅₃	—	2	4	no	—
156	C₂×D₄×C₅₃	—	2	4	no	—
157	C₂×D₄×C₅₃	—	2	4	no	—
158	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
159	C₂×D₄×C₅₃	C₂²×C₄	1	8	yes	—
160	C₂²×C₄×C₅₃	—	2	2	no	—
161	C₂²×C₄×C₅₃	—	2	2	no	—
162	C₂²×C₄×C₅₃	—	2	2	no	—
163	C₂²×C₄×C₅₃	—	2	4	no	—
164	C₂²×C₄×C₅₃	—	2	4	no	—
165	C₂²×C₄×C₅₃	—	2	4	no	—
166	C₂²×C₄×C₅₃	—	2	4	no	—
167	C₂²×C₄×C₅₃	—	2	2	no	—
168	C₂²×C₄×C₅₃	—	2	2	no	—
169	C₂²×C₄×C₅₃	—	2	2	no	—
170	C₂²×C₄×C₅₃	—	2	4	no	—
171	C₂²×C₄×C₅₃	—	2	4	no	—
172	C₂²×C₄×C₅₃	—	2	4	no	—
173	C₂²×C₄×C₅₃	—	4	2	no	—
174	C₂²×C₄×C₅₃	—	4	2	no	—
175	C₂²×C₄×C₅₃	—	4	2	no	—
176	C₂²×C₄×C₅₃	—	4	4	no	—
177	C₂²×C₄×C₅₃	—	4	2	no	—
178	C₂²×C₄×C₅₃	—	4	2	no	—
179	C₂²×C₄×C₅₃	—	4	2	no	—
180	C₂²×C₄×C₅₃	—	4	2	no	—
181	C₂²×C₄×C₅₃	—	4	4	no	—
182	C₂²×C₄×C₅₃	—	4	2	no	—
183	C₂²×C₄×C₅₃	—	4	2	no	—
184	C₂²×C₄×C₅₃	—	4	2	no	—
185	C₂²×C₄×C₅₃	—	4	2	no	—
186	C₂²×C₄×C₅₃	—	4	2	no	—
187	C₂²×C₄×C₅₃	—	4	2	no	—
188	C₂²×C₄×C₅₃	—	4	16	no	—
189	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
191	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
192	C₂²×C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
193	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
202	C₄⋊C₄×C₅₃	—	2	8	no	—
203	C₄⋊C₄×C₅₃	—	4	4	no	—
204	C₄⋊C₄×C₅₃	—	4	4	no	—
205	C₄⋊C₄×C₅₃	—	4	4	no	—
206	C₄⋊C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
207	C₂²⋊C₄×C₅₃	—	2	4	no	—
208	C₂²⋊C₄×C₅₃	—	2	4	no	—
209	C₂²⋊C₄×C₅₃	—	2	4	no	—
210	C₂²⋊C₄×C₅₃	—	2	4	no	—
211	C₂²⋊C₄×C₅₃	—	2	4	no	—
212	C₂²⋊C₄×C₅₃	—	2	4	no	—
213	C₂²⋊C₄×C₅₃	—	2	8	no	—
214	C₂²⋊C₄×C₅₃	—	4	4	no	—
215	C₂²⋊C₄×C₅₃	—	4	4	no	—
216	C₂²⋊C₄×C₅₃	—	4	4	no	—
217	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
218	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
219	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
220	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
221	C₂²⋊C₄×C₅₃	C₂²×C₄	1	16	yes	complemented
222	C₄²×C₅₃	—	2	8	no	—
223	C₄²×C₅₃	—	4	4	no	—
224	C₄²×C₅₃	—	4	4	no	—
225	C₄²×C₅₃	—	4	4	no	—
226	C₄²×C₅₃	C₂²×C₄	1	16	yes	complemented
227	C₂³×C₅₃	—	2	2	no	—
228	C₂³×C₅₃	—	2	2	no	—
229	C₂³×C₅₃	—	2	2	no	—
230	C₂³×C₅₃	—	2	2	no	—
231	C₂³×C₅₃	—	2	2	no	—
232	C₂³×C₅₃	—	2	2	no	—
233	C₂³×C₅₃	—	2	2	no	—
234	C₂³×C₅₃	—	2	2	no	—
235	C₂³×C₅₃	—	2	4	no	—
236	C₂³×C₅₃	—	2	4	no	—
237	C₂³×C₅₃	—	2	8	no	—
238	C₂³×C₅₃	—	4	4	no	—
239	C₂³×C₅₃	—	4	8	no	—
240	C₂³×C₅₃	—	4	4	no	—
241	C₂³×C₅₃	—	4	8	no	—
242	C₂³×C₅₃	—	4	8	no	—
243	C₂³×C₅₃	—	8	2	no	—
244	C₂³×C₅₃	—	8	2	no	—
245	C₂³×C₅₃	—	8	4	no	—
246	C₂³×C₅₃	#117	1	16	yes	complemented
247	C₂³×C₅₃	C₂³×C₄	1	4	yes	—
248	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
249	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
250	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
251	C₂³×C₅₃	C₂×#41	1	2	yes	—
252	C₂³×C₅₃	C₂×#41	1	2	yes	—
253	C₂³×C₅₃	C₂×#41	1	2	yes	—
254	C₂³×C₅₃	C₂×#41	1	2	yes	—
255	C₂³×C₅₃	C₂×#41	1	2	yes	—
256	C₂³×C₅₃	C₂×#41	1	2	yes	—
257	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
258	D₄×C₅₃	—	2	16	no	—
259	D₄×C₅₃	—	2	16	no	—
260	C₂×C₄×C₅₃	—	2	8	no	—
261	C₂×C₄×C₅₃	—	2	8	no	—
262	C₂×C₄×C₅₃	—	2	2	no	—
263	C₂×C₄×C₅₃	—	2	2	no	—
264	C₂×C₄×C₅₃	—	2	2	no	—
265	C₂×C₄×C₅₃	—	2	2	no	—
266	C₂×C₄×C₅₃	—	2	4	no	—
267	C₂×C₄×C₅₃	—	2	4	no	—
268	C₂×C₄×C₅₃	—	2	4	no	—
269	C₂×C₄×C₅₃	—	2	4	no	—
270	C₂×C₄×C₅₃	—	2	2	no	—
271	C₂×C₄×C₅₃	—	2	2	no	—
272	C₂×C₄×C₅₃	—	2	2	no	—
273	C₂×C₄×C₅₃	—	2	4	no	—
274	C₂×C₄×C₅₃	—	2	4	no	—
275	C₂×C₄×C₅₃	—	2	2	no	—
276	C₂×C₄×C₅₃	—	2	2	no	—
277	C₂×C₄×C₅₃	—	2	4	no	—
278	C₂×C₄×C₅₃	—	2	4	no	—
279	C₂×C₄×C₅₃	—	2	4	no	—
280	C₂×C₄×C₅₃	—	2	4	no	—
281	C₂×C₄×C₅₃	—	2	4	no	—
282	C₂×C₄×C₅₃	—	2	4	no	—
283	C₂×C₄×C₅₃	—	4	8	no	—
284	C₂×C₄×C₅₃	—	4	8	no	—
285	C₂×C₄×C₅₃	—	4	16	no	—
286	C₂×C₄×C₅₃	—	4	8	no	—
287	C₂×C₄×C₅₃	—	4	8	no	—
288	C₂×C₄×C₅₃	—	4	8	no	—
289	C₂×C₄×C₅₃	—	4	4	no	—
290	C₂×C₄×C₅₃	—	8	2	no	—
291	C₂×C₄×C₅₃	—	8	2	no	—
292	C₂×C₄×C₅₃	—	8	4	no	—
293	C₂×C₄×C₅₃	C₂³×C₄	1	8	yes	—
294	C₂×C₄×C₅₃	C₂³×C₄	1	8	yes	—
295	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
297	#34251	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂²×C₅₃	—	2	4	no	—
299	C₂²×C₅₃	—	2	4	no	—
300	C₂²×C₅₃	—	2	4	no	—
301	C₂²×C₅₃	—	2	2	no	—
302	C₂²×C₅₃	—	2	2	no	—
303	C₂²×C₅₃	—	2	2	no	—
304	C₂²×C₅₃	—	2	2	no	—
305	C₂²×C₅₃	—	2	2	no	—
306	C₂²×C₅₃	—	2	2	no	—
307	C₂²×C₅₃	—	2	4	no	—
308	C₂²×C₅₃	—	2	4	no	—
309	C₂²×C₅₃	—	2	4	no	—
310	C₂²×C₅₃	—	2	4	no	—
311	C₂²×C₅₃	—	2	8	no	—
312	C₂²×C₅₃	—	4	16	no	—
313	C₂²×C₅₃	—	4	2	no	—
314	C₂²×C₅₃	—	4	2	no	—
315	C₂²×C₅₃	—	4	4	no	—
316	C₂²×C₅₃	—	8	8	no	—
317	C₂²×C₅₃	C₂×#117	1	4	yes	—
318	C₂²×C₅₃	C₂×#117	1	4	yes	—
319	C₂²×C₅₃	C₂×#117	1	4	yes	—
320	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
321	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
322	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
324	C₂²×C₅₃	#585	1	2	yes	—
325	C₄×C₅₃	—	2	4	no	—
326	C₄×C₅₃	—	2	8	no	—
327	C₄×C₅₃	—	2	8	no	—
328	C₄×C₅₃	—	2	4	no	—
329	C₄×C₅₃	—	4	2	no	—
330	C₄×C₅₃	—	4	2	no	—
331	C₄×C₅₃	—	4	2	no	—
332	C₄×C₅₃	—	4	4	no	—
333	C₄×C₅₃	—	4	4	no	—
334	C₂×#518	C₂×C₅₃	1	1	yes	characteristic
335	#2353	C₂×C₅₃	1	4	yes	complemented
336	#2352	C₂×C₅₃	1	4	yes	complemented
337	#2343	C₂×C₅₃	1	4	yes	complemented
338	#2342	C₂×C₅₃	1	4	yes	complemented
339	#2318	C₂×C₅₃	1	4	yes	complemented
340	#2315	C₂×C₅₃	1	1	yes	characteristic, complemented
341	#2308	C₂×C₅₃	1	1	yes	characteristic
342	#2290	C₂×C₅₃	1	4	yes	complemented
343	C₂×#386	C₂×C₅₃	1	1	yes	characteristic
344	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
345	#2273	C₂×C₅₃	1	1	yes	characteristic, complemented
346	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
347	C₂×C₅₃	—	2	4	no	—
348	C₂×C₅₃	—	2	4	no	—
349	C₂×C₅₃	—	2	4	no	—
350	C₂×C₅₃	—	4	4	no	—
351	C₂×C₅₃	C₂²×#117	1	1	yes	characteristic
352	C₂×C₅₃	C₄×H(5,𝔽₂)	1	2	yes	—
353	C₂×C₅₃	#3490	1	1	yes	characteristic
354	C₂×C₅₃	#3491	1	1	yes	characteristic
355	C₂×C₅₃	#3505	1	2	yes	—
356	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
357	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
358	#518	C₄×C₅₃	1	16	yes	complemented
359	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
360	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
361	C₂×#117	C₂²×C₅₃	1	2	yes	—
362	C₂×#117	C₂²×C₅₃	1	4	yes	complemented
363	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
364	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
365	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
368	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
369	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
370	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
371	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
372	#388	C₂²×C₅₃	1	4	yes	complemented
373	#388	C₂²×C₅₃	1	4	yes	complemented
374	#388	C₂²×C₅₃	1	4	yes	complemented
375	#388	C₂²×C₅₃	1	4	yes	complemented
376	#387	C₂²×C₅₃	1	4	yes	complemented
377	#387	C₂²×C₅₃	1	4	yes	complemented
378	#387	C₂²×C₅₃	1	4	yes	complemented
379	#387	C₂²×C₅₃	1	4	yes	complemented
380	#386	C₂²×C₅₃	1	4	yes	—
381	#386	C₂²×C₅₃	1	2	yes	—
382	#386	C₂²×C₅₃	1	2	yes	—
383	#386	C₂²×C₅₃	1	2	yes	—
384	#386	C₂²×C₅₃	1	4	yes	—
385	#386	C₂²×C₅₃	1	2	yes	—
386	#385	C₂²×C₅₃	1	4	yes	—
387	#385	C₂²×C₅₃	1	4	yes	—
388	#385	C₂²×C₅₃	1	4	yes	complemented
389	#385	C₂²×C₅₃	1	2	yes	complemented
390	#385	C₂²×C₅₃	1	2	yes	complemented
391	#383	C₂²×C₅₃	1	4	yes	complemented
392	#382	C₂²×C₅₃	1	4	yes	complemented
393	#381	C₂²×C₅₃	1	2	yes	—
394	#381	C₂²×C₅₃	1	4	yes	complemented
395	#380	C₂²×C₅₃	1	4	yes	complemented
396	#380	C₂²×C₅₃	1	4	yes	complemented
397	#379	C₂²×C₅₃	1	2	yes	—
398	C₄×C₄⋊C₄	C₂²×C₅₃	1	4	yes	complemented
399	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
400	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
401	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
402	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
403	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
404	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
405	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
406	#376	C₂²×C₅₃	1	4	yes	complemented
407	C₂×#95	C₂²×C₅₃	1	2	yes	—
408	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
409	C₂×#95	C₂²×C₅₃	1	2	yes	complemented
410	C₅₃	#34251	1	1	yes	characteristic, direct product factor, Sylow
411	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
412	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
413	C₂²×D₄	—	2	4	no	—
414	C₂²×D₄	—	2	4	no	—
415	C₂²×D₄	C₂×C₄×C₅₃	1	8	yes	—
416	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
417	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
418	C₂³×C₄	—	2	4	no	—
419	C₂³×C₄	—	4	4	no	—
420	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
422	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
423	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
425	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
428	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
430	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
431	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
432	C₄×D₄	C₂×C₄×C₅₃	1	32	yes	complemented
433	C₄×D₄	C₂×C₄×C₅₃	1	32	yes	complemented
434	#117	—	4	8	no	—
435	#117	C₂×C₄×C₅₃	1	16	yes	complemented
436	C₂×C₄⋊C₄	—	4	4	no	—
437	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
438	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
442	C₂×C₂²⋊C₄	—	2	4	no	—
443	C₂×C₂²⋊C₄	—	2	4	no	—
444	C₂×C₂²⋊C₄	—	2	4	no	—
445	C₂×C₂²⋊C₄	—	4	4	no	—
446	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	—
447	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	8	yes	—
448	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	16	yes	complemented
449	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
464	C₂×C₄²	—	4	4	no	—
465	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
466	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
467	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
468	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
469	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
470	#95	C₂³×C₅₃	1	4	yes	—
471	#95	C₂³×C₅₃	1	4	yes	—
472	#95	C₂³×C₅₃	1	4	yes	—
473	#95	C₂³×C₅₃	1	4	yes	—
474	#95	C₂³×C₅₃	1	4	yes	—
475	#95	C₂³×C₅₃	1	4	yes	—
476	#95	C₂³×C₅₃	1	4	yes	—
477	#95	C₂³×C₅₃	1	4	yes	—
478	#95	C₂³×C₅₃	1	4	yes	—
479	#95	C₂³×C₅₃	1	4	yes	—
480	#95	C₂³×C₅₃	1	4	yes	—
481	#95	C₂³×C₅₃	1	4	yes	—
482	C₂⁴	—	2	2	no	—
483	C₂⁴	—	2	2	no	—
484	C₂⁴	—	4	2	no	—
485	C₂⁴	—	4	2	no	—
486	C₂⁴	—	4	2	no	—
487	C₂⁴	—	4	2	no	—
488	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
489	C₂⁴	C₂²×C₄×C₅₃	1	4	yes	—
490	C₂⁴	#41×C₅₃	1	4	yes	—
491	C₂⁴	#41×C₅₃	1	4	yes	—
492	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
493	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
494	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
495	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
496	C₂×D₄	—	2	32	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
502	C₂×D₄	C₂²×C₄×C₅₃	1	8	yes	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	4	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	16	no	—
532	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
533	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
534	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
535	C₂²×C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
536	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
540	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
545	C₄⋊C₄	—	2	8	no	—
546	C₄⋊C₄	—	4	4	no	—
547	C₄⋊C₄	—	4	4	no	—
548	C₄⋊C₄	—	4	4	no	—
549	C₄⋊C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	8	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₅₃	1	16	yes	complemented
565	C₄²	—	2	8	no	—
566	C₄²	—	4	4	no	—
567	C₄²	—	4	4	no	—
568	C₄²	—	4	4	no	—
569	C₄²	C₂²×C₄×C₅₃	1	16	yes	complemented
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	8	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	8	no	—
585	C₂³	—	4	8	no	—
586	C₂³	—	8	2	no	—
587	C₂³	—	8	2	no	—
588	C₂³	—	8	4	no	—
589	C₂³	#117×C₅₃	1	16	yes	complemented
590	C₂³	C₂³×C₄×C₅₃	1	4	yes	—
591	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
592	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
593	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
594	C₂³	C₂×#41×C₅₃	1	2	yes	—
595	C₂³	C₂×#41×C₅₃	1	2	yes	—
596	C₂³	C₂×#41×C₅₃	1	2	yes	—
597	C₂³	C₂×#41×C₅₃	1	2	yes	—
598	C₂³	C₂×#41×C₅₃	1	2	yes	—
599	C₂³	C₂×#41×C₅₃	1	2	yes	—
600	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
601	D₄	—	2	16	no	—
602	D₄	—	2	16	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	4	8	no	—
628	C₂×C₄	—	4	16	no	—
629	C₂×C₄	—	4	8	no	—
630	C₂×C₄	—	4	8	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	—	4	4	no	—
633	C₂×C₄	—	8	2	no	—
634	C₂×C₄	—	8	2	no	—
635	C₂×C₄	—	8	4	no	—
636	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₅₃	1	8	yes	—
638	C₂×C₄	C₂³×C₄×C₅₃	1	8	yes	—
639	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	8	no	—
654	C₂²	—	4	16	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	8	8	no	—
659	C₂²	C₂×#117×C₅₃	1	4	yes	—
660	C₂²	C₂×#117×C₅₃	1	4	yes	—
661	C₂²	C₂×#117×C₅₃	1	4	yes	—
662	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
663	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
664	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
665	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
666	C₂²	C₅₃×#585	1	2	yes	—
667	C₄	—	2	4	no	—
668	C₄	—	2	4	no	—
669	C₄	—	2	8	no	—
670	C₄	—	2	8	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	4	no	—
675	C₄	—	4	4	no	—
676	C₂	—	2	4	no	—
677	C₂	—	2	4	no	—
678	C₂	—	2	4	no	—
679	C₂	—	4	4	no	—
680	C₂	C₂²×#117×C₅₃	1	1	yes	characteristic
681	C₂	C₄×H(5,𝔽₂)×C₅₃	1	2	yes	—
682	C₂	C₅₃×#3490	1	1	yes	characteristic
683	C₂	C₅₃×#3491	1	1	yes	characteristic
684	C₂	C₅₃×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂³×D₄×C₅₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2353	C₂	semidirect
3. C₅₃×#2352	C₂	semidirect
4. C₅₃×#2343	C₂	semidirect
5. C₅₃×#2342	C₂	semidirect
6. C₅₃×#2318	C₂	semidirect
7. C₅₃×#2315	C₂	semidirect
9. C₅₃×#2290	C₂	semidirect
11. C₂×C₅₃×#385	C₂	semidirect
12. C₅₃×#2273	C₂	semidirect
13. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
16. C₅₃×#518	C₄	semidirect
20. C₂×#117×C₅₃	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
29. C₂²×C₄²×C₅₃	C₂²	semidirect
30. C₅₃×#388	C₂²	semidirect
31. C₅₃×#388	C₂²	semidirect
32. C₅₃×#388	C₂²	semidirect
33. C₅₃×#388	C₂²	semidirect
34. C₅₃×#387	C₂²	semidirect
35. C₅₃×#387	C₂²	semidirect
36. C₅₃×#387	C₂²	semidirect
37. C₅₃×#387	C₂²	semidirect
46. C₅₃×#385	C₂²	semidirect
47. C₅₃×#385	C₂²	semidirect
48. C₅₃×#385	C₂²	semidirect
49. C₅₃×#383	C₂²	semidirect
50. C₅₃×#382	C₂²	semidirect
52. C₅₃×#381	C₂²	semidirect
53. C₅₃×#380	C₂²	semidirect
54. C₅₃×#380	C₂²	semidirect
56. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
59. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
64. C₅₃×#376	C₂²	semidirect
66. C₂×#95×C₅₃	C₂²	semidirect
67. C₂×#95×C₅₃	C₂²	semidirect
89. C₄×D₄×C₅₃	C₂×C₄	semidirect
90. C₄×D₄×C₅₃	C₂×C₄	semidirect
92. #117×C₅₃	C₂×C₄	semidirect
105. C₂×C₂²⋊C₄×C₅₃	C₂×C₄	semidirect
192. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
206. C₄⋊C₄×C₅₃	C₂²×C₄	semidirect
221. C₂²⋊C₄×C₅₃	C₂²×C₄	semidirect
226. C₄²×C₅₃	C₂²×C₄	semidirect
246. C₂³×C₅₃	#117	semidirect
297. #34251	C₅₃	direct (N × H)
335. #2353	C₂×C₅₃	semidirect
336. #2352	C₂×C₅₃	semidirect
337. #2343	C₂×C₅₃	semidirect
338. #2342	C₂×C₅₃	semidirect
339. #2318	C₂×C₅₃	semidirect
340. #2315	C₂×C₅₃	semidirect
342. #2290	C₂×C₅₃	semidirect
344. C₂×#385	C₂×C₅₃	semidirect
345. #2273	C₂×C₅₃	semidirect
346. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
358. #518	C₄×C₅₃	semidirect
362. C₂×#117	C₂²×C₅₃	semidirect
363. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
371. C₂²×C₄²	C₂²×C₅₃	semidirect
372. #388	C₂²×C₅₃	semidirect
373. #388	C₂²×C₅₃	semidirect
374. #388	C₂²×C₅₃	semidirect
375. #388	C₂²×C₅₃	semidirect
376. #387	C₂²×C₅₃	semidirect
377. #387	C₂²×C₅₃	semidirect
378. #387	C₂²×C₅₃	semidirect
379. #387	C₂²×C₅₃	semidirect
388. #385	C₂²×C₅₃	semidirect
389. #385	C₂²×C₅₃	semidirect
390. #385	C₂²×C₅₃	semidirect
391. #383	C₂²×C₅₃	semidirect
392. #382	C₂²×C₅₃	semidirect
394. #381	C₂²×C₅₃	semidirect
395. #380	C₂²×C₅₃	semidirect
396. #380	C₂²×C₅₃	semidirect
398. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
401. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
402. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
403. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
404. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
405. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
406. #376	C₂²×C₅₃	semidirect
408. C₂×#95	C₂²×C₅₃	semidirect
409. C₂×#95	C₂²×C₅₃	semidirect
410. C₅₃	#34251	direct (N × H)
432. C₄×D₄	C₂×C₄×C₅₃	semidirect
433. C₄×D₄	C₂×C₄×C₅₃	semidirect
435. #117	C₂×C₄×C₅₃	semidirect
448. C₂×C₂²⋊C₄	C₂×C₄×C₅₃	semidirect
535. C₂²×C₄	C₂²×C₄×C₅₃	semidirect
549. C₄⋊C₄	C₂²×C₄×C₅₃	semidirect
564. C₂²⋊C₄	C₂²×C₄×C₅₃	semidirect
569. C₄²	C₂²×C₄×C₅₃	semidirect
589. C₂³	#117×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#518	2
C₅₃×#2353	2
C₅₃×#2352	2
C₅₃×#2343	2
C₅₃×#2342	2
C₅₃×#2318	2
C₅₃×#2315	2
C₅₃×#2308	2
C₅₃×#2290	2
C₂×C₅₃×#386	2
C₂×C₅₃×#385	2
C₅₃×#2273	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#34251	53

Subgroups — C53×#34251 #27241763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34251 #27241763