Subgroups — C₅₃×#3563 #20272500

Order 6784.

912 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#564	C₂	1	2	yes	maximal, complemented
2	C₅₃×#563	C₂	1	2	yes	maximal, complemented
3	C₅₃×#557	C₂	1	2	yes	maximal, complemented
4	C₅₃×#554	C₂	1	2	yes	maximal, complemented
5	C₅₃×#552	C₂	1	4	yes	maximal, complemented
6	C₅₃×#552	C₂	1	2	yes	maximal, complemented
7	C₅₃×#552	C₂	1	2	yes	maximal, complemented
8	C₅₃×#544	C₂	1	2	yes	maximal, complemented
9	C₅₃×#544	C₂	1	2	yes	maximal, complemented
10	C₅₃×#541	C₂	1	2	yes	maximal, complemented
11	C₅₃×#541	C₂	1	4	yes	maximal, complemented
12	C₅₃×#539	C₂	1	2	yes	maximal
13	C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#529	C₂	1	1	yes	maximal, characteristic
15	C₂×#125×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₅₃	C₂²	1	4	yes	—
19	C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
20	C₄⋊Q₈×C₅₃	C₂²	1	4	yes	—
21	#126×C₅₃	C₂²	1	2	yes	—
22	#126×C₅₃	C₂²	1	4	yes	—
23	#126×C₅₃	C₂²	1	4	yes	—
24	#126×C₅₃	C₂²	1	4	yes	—
25	#126×C₅₃	C₂²	1	4	yes	—
26	#125×C₅₃	C₂²	1	2	yes	—
27	#125×C₅₃	C₂²	1	2	yes	—
28	#125×C₅₃	C₂²	1	2	yes	—
29	#125×C₅₃	C₂²	1	2	yes	—
30	#125×C₅₃	C₂²	1	1	yes	characteristic
31	#125×C₅₃	C₂²	1	2	yes	—
32	#125×C₅₃	C₂²	1	4	yes	—
33	#125×C₅₃	C₂²	1	4	yes	—
34	#125×C₅₃	C₂²	1	4	yes	—
35	#125×C₅₃	C₂²	1	4	yes	—
36	#125×C₅₃	C₂²	1	4	yes	—
37	#125×C₅₃	C₂²	1	4	yes	—
38	#125×C₅₃	C₂²	1	2	yes	—
39	#125×C₅₃	C₂²	1	4	yes	—
40	#125×C₅₃	C₂²	1	4	yes	—
41	#124×C₅₃	C₂²	1	1	yes	characteristic
42	#123×C₅₃	C₂²	1	2	yes	—
43	#123×C₅₃	C₂²	1	4	yes	—
44	#123×C₅₃	C₂²	1	4	yes	—
45	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
46	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
47	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
48	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
49	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
50	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
51	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
52	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
53	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
54	#121×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
56	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
57	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
58	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
59	C₄×Q₈×C₅₃	C₂²	1	4	yes	—
60	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
61	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
62	C₄×D₄×C₅₃	C₂²	1	2	yes	—
63	C₄×D₄×C₅₃	C₂²	1	4	yes	—
64	#117×C₅₃	C₂²	1	2	yes	—
65	#117×C₅₃	C₂²	1	2	yes	—
66	#117×C₅₃	C₂²	1	4	yes	—
67	#117×C₅₃	C₂²	1	4	yes	—
68	#117×C₅₃	C₂²	1	2	yes	—
69	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
70	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
71	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
74	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
76	C₂×Q₈×C₅₃	C₂³	1	4	yes	—
77	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
78	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
79	C₂×D₄×C₅₃	C₂³	1	2	yes	—
80	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
84	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
85	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
88	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
89	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
90	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
91	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
92	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
93	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
94	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
95	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
96	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
97	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
98	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
99	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
100	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
101	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
102	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
103	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
104	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
105	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
107	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
108	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
109	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
111	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
112	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
113	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
114	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
115	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
117	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
121	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₄²×C₅₃	C₂³	1	1	yes	characteristic
126	C₄²×C₅₃	C₂³	1	1	yes	characteristic
127	C₄²×C₅₃	C₂³	1	1	yes	characteristic
128	C₄²×C₅₃	C₂³	1	1	yes	characteristic
129	C₄²×C₅₃	C₂³	1	4	yes	—
130	C₄²×C₅₃	C₂³	1	4	yes	—
131	C₄²×C₅₃	C₂³	1	2	yes	—
132	C₄²×C₅₃	C₂³	1	4	yes	—
133	C₄²×C₅₃	C₂³	1	4	yes	—
134	C₂³×C₅₃	C₂⁴	1	2	yes	—
135	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
136	Q₈×C₅₃	—	2	4	no	—
137	Q₈×C₅₃	—	4	4	no	—
138	Q₈×C₅₃	—	4	1	no	—
139	Q₈×C₅₃	—	4	2	no	—
140	D₄×C₅₃	—	2	4	no	—
141	D₄×C₅₃	—	4	1	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	—	2	4	no	—
144	C₂×C₄×C₅₃	—	2	2	no	—
145	C₂×C₄×C₅₃	—	2	4	no	—
146	C₂×C₄×C₅₃	—	4	2	no	—
147	C₂×C₄×C₅₃	—	4	4	no	—
148	C₂×C₄×C₅₃	—	4	1	no	—
149	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
150	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
153	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
157	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
158	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
160	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
161	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
162	C₂²×C₅₃	—	2	1	no	—
163	C₂²×C₅₃	—	2	1	no	—
164	C₂²×C₅₃	—	2	2	no	—
165	C₂²×C₅₃	—	2	2	no	—
166	C₂²×C₅₃	—	2	2	no	—
167	C₂²×C₅₃	2₋¹⁺⁴	1	2	yes	—
168	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
169	C₄×C₅₃	—	2	1	no	—
170	C₄×C₅₃	—	2	1	no	—
171	C₄×C₅₃	—	2	4	no	—
172	C₄×C₅₃	—	2	1	no	—
173	C₄×C₅₃	—	2	2	no	—
174	C₄×C₅₃	—	2	2	no	—
175	C₄×C₅₃	—	2	4	no	—
176	C₄×C₅₃	—	2	4	no	—
177	C₄×C₅₃	—	2	1	no	—
178	C₄×C₅₃	—	2	4	no	—
179	C₄×C₅₃	—	2	1	no	—
180	C₄×C₅₃	—	2	2	no	—
181	C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
182	#3563	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₅₃	—	2	2	no	—
184	C₂×C₅₃	—	4	2	no	—
185	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×C₅₃	#585	1	1	yes	characteristic
188	#564	C₂×C₅₃	1	2	yes	complemented
189	#563	C₂×C₅₃	1	2	yes	complemented
190	#557	C₂×C₅₃	1	2	yes	complemented
191	#554	C₂×C₅₃	1	2	yes	complemented
192	#552	C₂×C₅₃	1	4	yes	complemented
193	#552	C₂×C₅₃	1	2	yes	complemented
194	#552	C₂×C₅₃	1	2	yes	complemented
195	#544	C₂×C₅₃	1	2	yes	complemented
196	#544	C₂×C₅₃	1	2	yes	complemented
197	#541	C₂×C₅₃	1	2	yes	complemented
198	#541	C₂×C₅₃	1	4	yes	complemented
199	#539	C₂×C₅₃	1	2	yes	—
200	#533	C₂×C₅₃	1	1	yes	characteristic, complemented
201	#529	C₂×C₅₃	1	1	yes	characteristic
202	C₂×#125	C₂×C₅₃	1	1	yes	characteristic, complemented
203	C₅₃	#3563	1	1	yes	characteristic, direct product factor, Sylow
204	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
205	C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
206	C₄⋊Q₈	C₂²×C₅₃	1	4	yes	—
207	C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
208	C₄⋊Q₈	C₂²×C₅₃	1	4	yes	—
209	#126	C₂²×C₅₃	1	2	yes	—
210	#126	C₂²×C₅₃	1	4	yes	—
211	#126	C₂²×C₅₃	1	4	yes	—
212	#126	C₂²×C₅₃	1	4	yes	—
213	#126	C₂²×C₅₃	1	4	yes	—
214	#125	C₂²×C₅₃	1	2	yes	—
215	#125	C₂²×C₅₃	1	2	yes	—
216	#125	C₂²×C₅₃	1	2	yes	—
217	#125	C₂²×C₅₃	1	2	yes	—
218	#125	C₂²×C₅₃	1	1	yes	characteristic
219	#125	C₂²×C₅₃	1	2	yes	—
220	#125	C₂²×C₅₃	1	4	yes	—
221	#125	C₂²×C₅₃	1	4	yes	—
222	#125	C₂²×C₅₃	1	4	yes	—
223	#125	C₂²×C₅₃	1	4	yes	—
224	#125	C₂²×C₅₃	1	4	yes	—
225	#125	C₂²×C₅₃	1	4	yes	—
226	#125	C₂²×C₅₃	1	2	yes	—
227	#125	C₂²×C₅₃	1	4	yes	—
228	#125	C₂²×C₅₃	1	4	yes	—
229	#124	C₂²×C₅₃	1	1	yes	characteristic
230	#123	C₂²×C₅₃	1	2	yes	—
231	#123	C₂²×C₅₃	1	4	yes	—
232	#123	C₂²×C₅₃	1	4	yes	—
233	C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
234	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
235	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
236	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
237	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
238	C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
239	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
240	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
241	C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
242	#121	C₂²×C₅₃	1	1	yes	characteristic
243	C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
244	C₄×Q₈	C₂²×C₅₃	1	2	yes	—
245	C₄×Q₈	C₂²×C₅₃	1	2	yes	—
246	C₄×Q₈	C₂²×C₅₃	1	4	yes	—
247	C₄×Q₈	C₂²×C₅₃	1	2	yes	—
248	C₄×Q₈	C₂²×C₅₃	1	2	yes	—
249	C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
250	C₄×D₄	C₂²×C₅₃	1	2	yes	—
251	C₄×D₄	C₂²×C₅₃	1	4	yes	—
252	#117	C₂²×C₅₃	1	2	yes	—
253	#117	C₂²×C₅₃	1	2	yes	—
254	#117	C₂²×C₅₃	1	4	yes	—
255	#117	C₂²×C₅₃	1	2	yes	—
256	#117	C₂²×C₅₃	1	4	yes	—
257	C₂×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
262	C₂×C₄²	C₂²×C₅₃	1	1	yes	characteristic
263	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
264	C₂×Q₈	C₂³×C₅₃	1	4	yes	—
265	C₂×Q₈	C₂³×C₅₃	1	2	yes	—
266	C₂×Q₈	C₂³×C₅₃	1	1	yes	characteristic
267	C₂×D₄	C₂³×C₅₃	1	2	yes	—
268	C₂×D₄	C₂³×C₅₃	1	1	yes	characteristic
269	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
270	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
271	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
272	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
273	C₂²×C₄	C₂³×C₅₃	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₅₃	1	2	yes	—
275	C₂²×C₄	C₂³×C₅₃	1	4	yes	—
276	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
277	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
278	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
279	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
280	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
281	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
282	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
283	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
284	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
285	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
286	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
287	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
288	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
289	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
290	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
291	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
292	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
293	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
294	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
295	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
296	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
297	C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
298	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
299	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
300	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
301	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
302	C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
303	C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
304	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
305	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
306	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
307	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
308	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
309	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
310	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
311	C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
312	C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
313	C₄²	C₂³×C₅₃	1	1	yes	characteristic
314	C₄²	C₂³×C₅₃	1	1	yes	characteristic
315	C₄²	C₂³×C₅₃	1	1	yes	characteristic
316	C₄²	C₂³×C₅₃	1	1	yes	characteristic
317	C₄²	C₂³×C₅₃	1	4	yes	—
318	C₄²	C₂³×C₅₃	1	4	yes	—
319	C₄²	C₂³×C₅₃	1	2	yes	—
320	C₄²	C₂³×C₅₃	1	4	yes	—
321	C₄²	C₂³×C₅₃	1	4	yes	—
322	C₂³	C₂⁴×C₅₃	1	2	yes	—
323	C₂³	C₂⁴×C₅₃	1	1	yes	characteristic
324	Q₈	—	2	4	no	—
325	Q₈	—	4	4	no	—
326	Q₈	—	4	1	no	—
327	Q₈	—	4	2	no	—
328	D₄	—	2	4	no	—
329	D₄	—	4	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
338	C₂×C₄	C₂⁴×C₅₃	1	4	yes	—
339	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
340	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
341	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
342	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
343	C₂×C₄	C₂⁴×C₅₃	1	2	yes	—
344	C₂×C₄	C₂⁴×C₅₃	1	4	yes	—
345	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
346	C₂×C₄	C₂⁴×C₅₃	1	4	yes	—
347	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
348	C₂×C₄	C₂⁴×C₅₃	1	4	yes	—
349	C₂×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	2₋¹⁺⁴×C₅₃	1	2	yes	—
356	C₂²	C₂⁵×C₅₃	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	4	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	4	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	2	no	—
369	C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
370	C₂	—	2	2	no	—
371	C₂	—	4	2	no	—
372	C₂	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
373	C₂	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
374	C₂	C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₅₃
prime radical	#121×C₅₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#564	C₂	semidirect
2. C₅₃×#563	C₂	semidirect
3. C₅₃×#557	C₂	semidirect
4. C₅₃×#554	C₂	semidirect
5. C₅₃×#552	C₂	semidirect
6. C₅₃×#552	C₂	semidirect
7. C₅₃×#552	C₂	semidirect
8. C₅₃×#544	C₂	semidirect
9. C₅₃×#544	C₂	semidirect
10. C₅₃×#541	C₂	semidirect
11. C₅₃×#541	C₂	semidirect
13. C₅₃×#533	C₂	semidirect
15. C₂×#125×C₅₃	C₂	semidirect
182. #3563	C₅₃	direct (N × H)
188. #564	C₂×C₅₃	semidirect
189. #563	C₂×C₅₃	semidirect
190. #557	C₂×C₅₃	semidirect
191. #554	C₂×C₅₃	semidirect
192. #552	C₂×C₅₃	semidirect
193. #552	C₂×C₅₃	semidirect
194. #552	C₂×C₅₃	semidirect
195. #544	C₂×C₅₃	semidirect
196. #544	C₂×C₅₃	semidirect
197. #541	C₂×C₅₃	semidirect
198. #541	C₂×C₅₃	semidirect
200. #533	C₂×C₅₃	semidirect
202. C₂×#125	C₂×C₅₃	semidirect
203. C₅₃	#3563	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×#564	2
C₅₃×#563	2
C₅₃×#557	2
C₅₃×#554	2
C₅₃×#552	2
C₅₃×#544	2
C₅₃×#541	2
C₅₃×#539	2
C₅₃×#533	2
C₅₃×#529	2
C₂×#125×C₅₃	2
#3563	53

Subgroups — C53×#3563 #20272500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#3563 #20272500