Subgroups — C₅₃×#61869 #27269381

Order 13568.

1644 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3503	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3383	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3381	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3374	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3372	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3363	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3359	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3242	C₂	1	4	yes	maximal, complemented
12	C₅₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3120	C₂	1	4	yes	maximal
15	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic
16	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic
17	C₅₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#564	—	2	2	no	—
19	Q₈²×C₅₃	C₂²	1	2	yes	—
20	C₅₃×#557	—	2	1	no	—
21	C₅₃×#557	—	2	1	no	—
22	C₅₃×#557	C₂²	1	2	yes	—
23	C₅₃×#557	C₂²	1	2	yes	—
24	C₅₃×#557	C₂²	1	2	yes	—
25	C₅₃×#557	C₂²	1	2	yes	—
26	C₅₃×#557	C₂²	1	2	yes	—
27	C₅₃×#554	—	2	2	no	—
28	C₅₃×#554	C₂²	1	2	yes	—
29	D₄×Q₈×C₅₃	—	2	2	no	—
30	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
31	C₅₃×#544	—	2	2	no	—
32	C₅₃×#544	C₂²	1	2	yes	—
33	C₅₃×#541	—	2	2	no	—
34	C₅₃×#541	—	2	2	no	—
35	C₅₃×#541	C₂²	1	4	yes	—
36	C₅₃×#533	—	2	1	no	—
37	C₅₃×#533	C₂²	1	1	yes	characteristic
38	C₅₃×#533	C₂²	1	1	yes	characteristic
39	C₅₃×#533	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₅₃	—	2	1	no	—
41	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#520	C₂²	1	2	yes	—
43	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#501	C₂²	1	4	yes	—
45	C₅₃×#500	C₂²	1	2	yes	—
46	C₅₃×#499	C₂²	1	4	yes	—
47	C₅₃×#498	C₂²	1	2	yes	—
48	C₅₃×#491	C₂²	1	4	yes	—
49	C₅₃×#487	C₂²	1	2	yes	—
50	C₅₃×#487	C₂²	1	2	yes	—
51	C₅₃×#487	C₂²	1	4	yes	—
52	C₅₃×#485	C₂²	1	2	yes	—
53	C₅₃×#485	C₂²	1	2	yes	—
54	C₅₃×#484	C₂²	1	4	yes	—
55	C₅₃×#483	C₂²	1	4	yes	—
56	C₅₃×#479	C₂²	1	4	yes	—
57	C₅₃×#479	C₂²	1	4	yes	—
58	C₅₃×#479	C₂²	1	4	yes	—
59	C₅₃×#478	C₂²	1	4	yes	—
60	C₅₃×#477	C₂²	1	2	yes	—
61	C₅₃×#477	C₂²	1	2	yes	—
62	C₅₃×#477	C₂²	1	4	yes	—
63	C₅₃×#475	C₂²	1	2	yes	—
64	C₅₃×#475	C₂²	1	2	yes	—
65	C₅₃×#475	C₂²	1	4	yes	—
66	C₅₃×#475	C₂²	1	1	yes	characteristic
67	C₅₃×#475	C₂²	1	1	yes	characteristic
68	C₅₃×#474	C₂²	1	1	yes	characteristic
69	C₅₃×#474	C₂²	1	1	yes	characteristic
70	C₅₃×#462	C₂²	1	1	yes	characteristic
71	C₅₃×#462	C₂²	1	1	yes	characteristic
72	C₅₃×#462	C₂²	1	4	yes	—
73	C₅₃×#461	C₂²	1	1	yes	characteristic
74	C₅₃×#461	C₂²	1	4	yes	—
75	C₅₃×#461	C₂²	1	1	yes	characteristic
76	C₅₃×#452	C₂²	1	2	yes	—
77	C₅₃×#452	C₂²	1	2	yes	—
78	C₅₃×#446	C₂²	1	2	yes	—
79	C₅₃×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₅₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₅₃	C₂²	1	2	yes	—
82	C₅₃×#441	C₂²	1	4	yes	—
83	C₅₃×#440	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
85	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
86	C₄×Q₁₆×C₅₃	C₂²	1	4	yes	—
87	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
89	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
90	C₅₃×#433	C₂²	1	4	yes	—
91	C₅₃×#431	C₂²	1	1	yes	characteristic
92	C₅₃×#431	C₂²	1	1	yes	characteristic
93	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₅₃	—	2	2	no	—
95	C₂²×Q₈×C₅₃	—	2	1	no	—
96	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₅₃	—	2	2	no	—
101	C₄⋊Q₈×C₅₃	—	2	2	no	—
102	C₄⋊Q₈×C₅₃	—	2	4	no	—
103	C₄⋊Q₈×C₅₃	—	2	1	no	—
104	C₄⋊Q₈×C₅₃	—	2	1	no	—
105	C₄⋊Q₈×C₅₃	—	2	2	no	—
106	C₄⋊Q₈×C₅₃	—	2	2	no	—
107	C₄⋊Q₈×C₅₃	—	2	2	no	—
108	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
109	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
110	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
118	#126×C₅₃	—	2	4	no	—
119	#126×C₅₃	—	2	4	no	—
120	#125×C₅₃	—	2	2	no	—
121	#125×C₅₃	—	2	2	no	—
122	#125×C₅₃	—	2	2	no	—
123	#125×C₅₃	—	2	4	no	—
124	#125×C₅₃	—	2	4	no	—
125	#125×C₅₃	—	2	4	no	—
126	#125×C₅₃	—	2	4	no	—
127	#125×C₅₃	—	2	4	no	—
128	#125×C₅₃	—	2	4	no	—
129	#125×C₅₃	—	2	4	no	—
130	#125×C₅₃	—	2	1	no	—
131	#125×C₅₃	—	2	1	no	—
132	#125×C₅₃	D₄	1	2	yes	—
133	#125×C₅₃	C₂³	1	4	yes	—
134	#125×C₅₃	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₅₃	—	2	2	no	—
136	C₂²⋊Q₈×C₅₃	—	2	4	no	—
137	C₂²⋊Q₈×C₅₃	—	2	4	no	—
138	C₂²⋊Q₈×C₅₃	—	2	4	no	—
139	C₂²⋊Q₈×C₅₃	—	2	2	no	—
140	C₂²⋊Q₈×C₅₃	—	2	1	no	—
141	C₂²⋊Q₈×C₅₃	—	2	1	no	—
142	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
143	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
144	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₅₃	—	2	2	no	—
147	C₄×Q₈×C₅₃	—	2	2	no	—
148	C₄×Q₈×C₅₃	—	2	2	no	—
149	C₄×Q₈×C₅₃	—	2	1	no	—
150	C₄×Q₈×C₅₃	—	2	1	no	—
151	C₄×Q₈×C₅₃	—	2	2	no	—
152	C₄×Q₈×C₅₃	—	2	2	no	—
153	C₄×Q₈×C₅₃	—	2	2	no	—
154	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
159	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
162	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
163	C₄×D₄×C₅₃	—	2	4	no	—
164	C₄×D₄×C₅₃	—	2	1	no	—
165	C₄×D₄×C₅₃	—	2	1	no	—
166	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₅₃	C₂³	1	4	yes	—
169	#117×C₅₃	—	2	2	no	—
170	#117×C₅₃	—	2	1	no	—
171	#117×C₅₃	—	2	1	no	—
172	#117×C₅₃	—	2	1	no	—
173	#117×C₅₃	C₂³	1	1	yes	characteristic
174	#117×C₅₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
176	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
177	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₅₃	—	2	1	no	—
180	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
181	#107×C₅₃	C₂³	1	2	yes	—
182	#107×C₅₃	C₂³	1	2	yes	—
183	#107×C₅₃	C₂³	1	4	yes	—
184	#107×C₅₃	C₂³	1	4	yes	—
185	#106×C₅₃	C₂³	1	2	yes	—
186	#106×C₅₃	C₂³	1	2	yes	—
187	#106×C₅₃	C₂³	1	4	yes	—
188	#106×C₅₃	C₂³	1	4	yes	—
189	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
194	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
195	#103×C₅₃	C₂³	1	2	yes	—
196	#103×C₅₃	C₂³	1	2	yes	—
197	#103×C₅₃	C₂³	1	2	yes	—
198	#103×C₅₃	C₂³	1	2	yes	—
199	#103×C₅₃	C₂³	1	4	yes	—
200	#103×C₅₃	C₂³	1	4	yes	—
201	#103×C₅₃	C₂³	1	4	yes	—
202	#103×C₅₃	C₂³	1	4	yes	—
203	#103×C₅₃	C₂³	1	2	yes	—
204	#103×C₅₃	C₂³	1	2	yes	—
205	#102×C₅₃	C₂³	1	2	yes	—
206	#102×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
209	#97×C₅₃	C₂³	1	4	yes	—
210	C₄×C₈×C₅₃	C₂³	1	2	yes	—
211	C₄×C₈×C₅₃	C₂³	1	4	yes	—
212	C₄×C₈×C₅₃	C₂³	1	2	yes	—
213	#41×C₅₃	—	2	2	no	—
214	#41×C₅₃	—	2	2	no	—
215	C₂×Q₈×C₅₃	—	2	1	no	—
216	C₂×Q₈×C₅₃	—	2	1	no	—
217	C₂×Q₈×C₅₃	—	2	2	no	—
218	C₂×Q₈×C₅₃	—	2	2	no	—
219	C₂×Q₈×C₅₃	—	2	4	no	—
220	C₂×Q₈×C₅₃	—	8	2	no	—
221	C₂×Q₈×C₅₃	—	8	4	no	—
222	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
227	C₂×D₄×C₅₃	—	2	1	no	—
228	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₅₃	—	2	1	no	—
230	C₂²×C₄×C₅₃	—	2	2	no	—
231	C₂²×C₄×C₅₃	—	2	1	no	—
232	C₂²×C₄×C₅₃	—	2	1	no	—
233	C₂²×C₄×C₅₃	—	2	4	no	—
234	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
237	Q₁₆×C₅₃	—	2	4	no	—
238	Q₁₆×C₅₃	—	2	4	no	—
239	SD₁₆×C₅₃	—	2	4	no	—
240	SD₁₆×C₅₃	—	2	4	no	—
241	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
245	C₄⋊C₄×C₅₃	—	2	2	no	—
246	C₄⋊C₄×C₅₃	—	2	2	no	—
247	C₄⋊C₄×C₅₃	—	2	4	no	—
248	C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₄⋊C₄×C₅₃	—	2	4	no	—
250	C₄⋊C₄×C₅₃	—	2	1	no	—
251	C₄⋊C₄×C₅₃	—	2	1	no	—
252	C₄⋊C₄×C₅₃	—	2	1	no	—
253	C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₄⋊C₄×C₅₃	—	2	1	no	—
258	C₄⋊C₄×C₅₃	—	2	4	no	—
259	C₄⋊C₄×C₅₃	—	2	4	no	—
260	C₄⋊C₄×C₅₃	—	2	2	no	—
261	C₄⋊C₄×C₅₃	—	2	2	no	—
262	C₄⋊C₄×C₅₃	—	2	4	no	—
263	C₄⋊C₄×C₅₃	—	2	4	no	—
264	C₄⋊C₄×C₅₃	—	2	4	no	—
265	C₄⋊C₄×C₅₃	—	2	4	no	—
266	C₄⋊C₄×C₅₃	—	2	2	no	—
267	C₄⋊C₄×C₅₃	—	2	2	no	—
268	C₄⋊C₄×C₅₃	—	2	4	no	—
269	C₄⋊C₄×C₅₃	—	2	4	no	—
270	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
271	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
275	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
279	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
281	C₂²⋊C₄×C₅₃	—	2	2	no	—
282	C₂²⋊C₄×C₅₃	—	2	2	no	—
283	C₂²⋊C₄×C₅₃	—	2	1	no	—
284	C₂²⋊C₄×C₅₃	—	2	4	no	—
285	C₂²⋊C₄×C₅₃	—	2	1	no	—
286	C₂²⋊C₄×C₅₃	—	2	1	no	—
287	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
288	C₄²×C₅₃	—	2	1	no	—
289	C₄²×C₅₃	—	2	1	no	—
290	C₄²×C₅₃	—	2	1	no	—
291	C₄²×C₅₃	—	2	4	no	—
292	C₄²×C₅₃	—	2	2	no	—
293	C₄²×C₅₃	—	2	2	no	—
294	C₄²×C₅₃	—	2	4	no	—
295	C₄²×C₅₃	—	2	4	no	—
296	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
299	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
300	C₄²×C₅₃	C₂⁴	1	4	yes	—
301	C₂³×C₅₃	—	2	1	no	—
302	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₅₃	—	2	4	no	—
304	Q₈×C₅₃	—	2	4	no	—
305	Q₈×C₅₃	—	2	1	no	—
306	Q₈×C₅₃	—	2	2	no	—
307	Q₈×C₅₃	—	2	2	no	—
308	Q₈×C₅₃	—	2	2	no	—
309	Q₈×C₅₃	—	2	2	no	—
310	Q₈×C₅₃	—	4	2	no	—
311	Q₈×C₅₃	—	4	4	no	—
312	Q₈×C₅₃	—	4	2	no	—
313	Q₈×C₅₃	—	8	2	no	—
314	Q₈×C₅₃	—	8	4	no	—
315	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
316	D₄×C₅₃	—	2	4	no	—
317	D₄×C₅₃	—	2	1	no	—
318	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
319	C₂×C₄×C₅₃	—	2	4	no	—
320	C₂×C₄×C₅₃	—	2	1	no	—
321	C₂×C₄×C₅₃	—	2	2	no	—
322	C₂×C₄×C₅₃	—	2	2	no	—
323	C₂×C₄×C₅₃	—	2	1	no	—
324	C₂×C₄×C₅₃	—	2	1	no	—
325	C₂×C₄×C₅₃	—	2	4	no	—
326	C₂×C₄×C₅₃	—	2	1	no	—
327	C₂×C₄×C₅₃	—	2	1	no	—
328	C₂×C₄×C₅₃	—	2	2	no	—
329	C₂×C₄×C₅₃	—	2	2	no	—
330	C₂×C₄×C₅₃	—	2	2	no	—
331	C₂×C₄×C₅₃	—	2	2	no	—
332	C₂×C₄×C₅₃	—	4	2	no	—
333	C₂×C₄×C₅₃	—	4	2	no	—
334	C₂×C₄×C₅₃	—	8	4	no	—
335	C₂×C₄×C₅₃	—	8	2	no	—
336	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
341	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
344	C₈×C₅₃	—	2	2	no	—
345	C₈×C₅₃	—	2	2	no	—
346	C₈×C₅₃	—	2	2	no	—
347	C₈×C₅₃	—	2	2	no	—
348	#61869	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂²×C₅₃	—	2	1	no	—
350	C₂²×C₅₃	—	2	2	no	—
351	C₂²×C₅₃	—	2	1	no	—
352	C₂²×C₅₃	—	2	1	no	—
353	C₂²×C₅₃	—	4	1	no	—
354	C₂²×C₅₃	—	4	1	no	—
355	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₅₃	—	2	1	no	—
357	C₄×C₅₃	—	2	2	no	—
358	C₄×C₅₃	—	2	1	no	—
359	C₄×C₅₃	—	2	4	no	—
360	C₄×C₅₃	—	2	1	no	—
361	C₄×C₅₃	—	2	4	no	—
362	C₄×C₅₃	—	4	2	no	—
363	C₄×C₅₃	—	4	2	no	—
364	C₄×C₅₃	—	4	1	no	—
365	C₄×C₅₃	—	4	4	no	—
366	C₄×C₅₃	—	4	2	no	—
367	C₄×C₅₃	—	4	1	no	—
368	C₄×C₅₃	—	4	2	no	—
369	C₄×C₅₃	#577	1	2	yes	—
370	C₄×C₅₃	#578	1	2	yes	—
371	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
372	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
373	#3556	C₂×C₅₃	1	1	yes	characteristic, complemented
374	#3503	C₂×C₅₃	1	1	yes	characteristic
375	#3387	C₂×C₅₃	1	2	yes	complemented
376	#3386	C₂×C₅₃	1	2	yes	complemented
377	#3383	C₂×C₅₃	1	2	yes	complemented
378	#3381	C₂×C₅₃	1	2	yes	complemented
379	#3374	C₂×C₅₃	1	2	yes	complemented
380	#3372	C₂×C₅₃	1	2	yes	complemented
381	#3363	C₂×C₅₃	1	2	yes	complemented
382	#3359	C₂×C₅₃	1	2	yes	complemented
383	#3242	C₂×C₅₃	1	4	yes	complemented
384	#3230	C₂×C₅₃	1	1	yes	characteristic, complemented
385	#3229	C₂×C₅₃	1	1	yes	characteristic, complemented
386	#3120	C₂×C₅₃	1	4	yes	—
387	#3107	C₂×C₅₃	1	1	yes	characteristic
388	#3107	C₂×C₅₃	1	1	yes	characteristic
389	#2986	C₂×C₅₃	1	1	yes	characteristic, complemented
390	C₂×C₅₃	—	4	1	no	—
391	C₂×C₅₃	—	4	2	no	—
392	C₂×C₅₃	#3486	1	1	yes	characteristic
393	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
394	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
395	#564	—	2	2	no	—
396	Q₈²	C₂²×C₅₃	1	2	yes	—
397	#557	—	2	1	no	—
398	#557	—	2	1	no	—
399	#557	C₂²×C₅₃	1	2	yes	—
400	#557	C₂²×C₅₃	1	2	yes	—
401	#557	C₂²×C₅₃	1	2	yes	—
402	#557	C₂²×C₅₃	1	2	yes	—
403	#557	C₂²×C₅₃	1	2	yes	—
404	#554	—	2	2	no	—
405	#554	C₂²×C₅₃	1	2	yes	—
406	D₄×Q₈	—	2	2	no	—
407	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
408	#544	—	2	2	no	—
409	#544	C₂²×C₅₃	1	2	yes	—
410	#541	—	2	2	no	—
411	#541	—	2	2	no	—
412	#541	C₂²×C₅₃	1	4	yes	—
413	#533	—	2	1	no	—
414	#533	C₂²×C₅₃	1	1	yes	characteristic
415	#533	C₂²×C₅₃	1	1	yes	characteristic
416	#533	C₂²×C₅₃	1	1	yes	characteristic
417	C₂×C₄⋊Q₈	—	2	1	no	—
418	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
419	#520	C₂²×C₅₃	1	2	yes	—
420	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
421	#501	C₂²×C₅₃	1	4	yes	—
422	#500	C₂²×C₅₃	1	2	yes	—
423	#499	C₂²×C₅₃	1	4	yes	—
424	#498	C₂²×C₅₃	1	2	yes	—
425	#491	C₂²×C₅₃	1	4	yes	—
426	#487	C₂²×C₅₃	1	4	yes	—
427	#487	C₂²×C₅₃	1	2	yes	—
428	#487	C₂²×C₅₃	1	2	yes	—
429	#485	C₂²×C₅₃	1	2	yes	—
430	#485	C₂²×C₅₃	1	2	yes	—
431	#484	C₂²×C₅₃	1	4	yes	—
432	#483	C₂²×C₅₃	1	4	yes	—
433	#479	C₂²×C₅₃	1	4	yes	—
434	#479	C₂²×C₅₃	1	4	yes	—
435	#479	C₂²×C₅₃	1	4	yes	—
436	#478	C₂²×C₅₃	1	4	yes	—
437	#477	C₂²×C₅₃	1	2	yes	—
438	#477	C₂²×C₅₃	1	4	yes	—
439	#477	C₂²×C₅₃	1	2	yes	—
440	#475	C₂²×C₅₃	1	2	yes	—
441	#475	C₂²×C₅₃	1	4	yes	—
442	#475	C₂²×C₅₃	1	1	yes	characteristic
443	#475	C₂²×C₅₃	1	1	yes	characteristic
444	#475	C₂²×C₅₃	1	2	yes	—
445	#474	C₂²×C₅₃	1	1	yes	characteristic
446	#474	C₂²×C₅₃	1	1	yes	characteristic
447	#462	C₂²×C₅₃	1	1	yes	characteristic
448	#462	C₂²×C₅₃	1	1	yes	characteristic
449	#462	C₂²×C₅₃	1	4	yes	—
450	#461	C₂²×C₅₃	1	1	yes	characteristic
451	#461	C₂²×C₅₃	1	4	yes	—
452	#461	C₂²×C₅₃	1	1	yes	characteristic
453	#452	C₂²×C₅₃	1	2	yes	—
454	#452	C₂²×C₅₃	1	2	yes	—
455	#446	C₂²×C₅₃	1	2	yes	—
456	#446	C₂²×C₅₃	1	2	yes	—
457	C₈×Q₈	C₂²×C₅₃	1	2	yes	—
458	C₈×Q₈	C₂²×C₅₃	1	2	yes	—
459	#441	C₂²×C₅₃	1	4	yes	—
460	#440	C₂²×C₅₃	1	4	yes	—
461	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
462	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
463	C₄×Q₁₆	C₂²×C₅₃	1	4	yes	—
464	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
465	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
466	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
467	#433	C₂²×C₅₃	1	4	yes	—
468	#431	C₂²×C₅₃	1	1	yes	characteristic
469	#431	C₂²×C₅₃	1	1	yes	characteristic
470	C₅₃	#61869	1	1	yes	characteristic, direct product factor, Sylow
471	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
472	C₂²×Q₈	—	2	2	no	—
473	C₂²×Q₈	—	2	1	no	—
474	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
475	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
476	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
477	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	4	no	—
484	C₄⋊Q₈	—	2	1	no	—
485	C₄⋊Q₈	—	2	1	no	—
486	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
487	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
492	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
493	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
496	#126	—	2	4	no	—
497	#126	—	2	4	no	—
498	#125	—	2	2	no	—
499	#125	—	2	2	no	—
500	#125	—	2	2	no	—
501	#125	—	2	4	no	—
502	#125	—	2	4	no	—
503	#125	—	2	4	no	—
504	#125	—	2	4	no	—
505	#125	—	2	4	no	—
506	#125	—	2	4	no	—
507	#125	—	2	4	no	—
508	#125	—	2	1	no	—
509	#125	—	2	1	no	—
510	#125	D₄×C₅₃	1	2	yes	—
511	#125	C₂³×C₅₃	1	4	yes	—
512	#125	C₂³×C₅₃	1	4	yes	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	1	no	—
515	C₂²⋊Q₈	—	2	1	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
521	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
522	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
523	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	—	2	1	no	—
532	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
533	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
534	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
535	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
536	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
537	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
538	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
539	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
540	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
545	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
546	C₄×D₄	C₂³×C₅₃	1	4	yes	—
547	#117	—	2	1	no	—
548	#117	—	2	1	no	—
549	#117	—	2	2	no	—
550	#117	—	2	1	no	—
551	#117	C₂³×C₅₃	1	1	yes	characteristic
552	#117	C₂³×C₅₃	1	2	yes	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
559	#107	C₂³×C₅₃	1	2	yes	—
560	#107	C₂³×C₅₃	1	2	yes	—
561	#107	C₂³×C₅₃	1	4	yes	—
562	#107	C₂³×C₅₃	1	4	yes	—
563	#106	C₂³×C₅₃	1	2	yes	—
564	#106	C₂³×C₅₃	1	4	yes	—
565	#106	C₂³×C₅₃	1	2	yes	—
566	#106	C₂³×C₅₃	1	4	yes	—
567	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
568	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
569	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
570	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
571	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
572	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
573	#103	C₂³×C₅₃	1	2	yes	—
574	#103	C₂³×C₅₃	1	4	yes	—
575	#103	C₂³×C₅₃	1	2	yes	—
576	#103	C₂³×C₅₃	1	2	yes	—
577	#103	C₂³×C₅₃	1	2	yes	—
578	#103	C₂³×C₅₃	1	2	yes	—
579	#103	C₂³×C₅₃	1	4	yes	—
580	#103	C₂³×C₅₃	1	2	yes	—
581	#103	C₂³×C₅₃	1	4	yes	—
582	#103	C₂³×C₅₃	1	4	yes	—
583	#102	C₂³×C₅₃	1	2	yes	—
584	#102	C₂³×C₅₃	1	2	yes	—
585	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
586	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
587	#97	C₂³×C₅₃	1	4	yes	—
588	C₄×C₈	C₂³×C₅₃	1	2	yes	—
589	C₄×C₈	C₂³×C₅₃	1	2	yes	—
590	C₄×C₈	C₂³×C₅₃	1	4	yes	—
591	#41	—	2	2	no	—
592	#41	—	2	2	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	8	2	no	—
599	C₂×Q₈	—	8	4	no	—
600	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
601	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
602	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
603	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
604	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
615	Q₁₆	—	2	4	no	—
616	Q₁₆	—	2	4	no	—
617	SD₁₆	—	2	4	no	—
618	SD₁₆	—	2	4	no	—
619	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
620	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
621	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
622	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
653	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
654	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
657	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
658	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
666	C₄²	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	4	no	—
674	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
676	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
677	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
678	C₄²	C₂⁴×C₅₃	1	4	yes	—
679	C₂³	—	2	1	no	—
680	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
681	Q₈	—	2	4	no	—
682	Q₈	—	2	4	no	—
683	Q₈	—	2	1	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	4	2	no	—
689	Q₈	—	4	4	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	2	no	—
692	Q₈	—	8	4	no	—
693	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
694	D₄	—	2	4	no	—
695	D₄	—	2	1	no	—
696	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
715	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
717	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
721	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
722	C₈	—	2	2	no	—
723	C₈	—	2	2	no	—
724	C₈	—	2	2	no	—
725	C₈	—	2	2	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	4	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	C₅₃×#577	1	2	yes	—
747	C₄	C₅₃×#578	1	2	yes	—
748	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
749	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
750	C₂	—	4	1	no	—
751	C₂	—	4	2	no	—
752	C₂	C₅₃×#3486	1	1	yes	characteristic
753	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
754	C₂	C₂×C₅₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂×#41×C₅₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3556	C₂	semidirect
3. C₅₃×#3387	C₂	semidirect
4. C₅₃×#3386	C₂	semidirect
5. C₅₃×#3383	C₂	semidirect
6. C₅₃×#3381	C₂	semidirect
7. C₅₃×#3374	C₂	semidirect
8. C₅₃×#3372	C₂	semidirect
9. C₅₃×#3363	C₂	semidirect
10. C₅₃×#3359	C₂	semidirect
11. C₅₃×#3242	C₂	semidirect
12. C₅₃×#3230	C₂	semidirect
13. C₅₃×#3229	C₂	semidirect
17. C₅₃×#2986	C₂	semidirect
348. #61869	C₅₃	direct (N × H)
373. #3556	C₂×C₅₃	semidirect
375. #3387	C₂×C₅₃	semidirect
376. #3386	C₂×C₅₃	semidirect
377. #3383	C₂×C₅₃	semidirect
378. #3381	C₂×C₅₃	semidirect
379. #3374	C₂×C₅₃	semidirect
380. #3372	C₂×C₅₃	semidirect
381. #3363	C₂×C₅₃	semidirect
382. #3359	C₂×C₅₃	semidirect
383. #3242	C₂×C₅₃	semidirect
384. #3230	C₂×C₅₃	semidirect
385. #3229	C₂×C₅₃	semidirect
389. #2986	C₂×C₅₃	semidirect
470. C₅₃	#61869	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×#3556	2
C₅₃×#3503	2
C₅₃×#3387	2
C₅₃×#3386	2
C₅₃×#3383	2
C₅₃×#3381	2
C₅₃×#3374	2
C₅₃×#3372	2
C₅₃×#3363	2
C₅₃×#3359	2
C₅₃×#3242	2
C₅₃×#3230	2
C₅₃×#3229	2
C₅₃×#3120	2
C₅₃×#3107	2
C₅₃×#2986	2
#61869	53

Subgroups — C53×#61869 #27269381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61869 #27269381