Subgroups — C₅₃×#61264 #27268776

Order 13568.

1764 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3495	C₂	1	2	yes	maximal
2	C₅₃×#3349	C₂	1	4	yes	maximal, complemented
3	C₅₃×#3344	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3342	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3338	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3095	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2929	C₂	1	1	yes	maximal, characteristic
16	C₅₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₅₃×#556	C₂²	1	4	yes	—
22	C₅₃×#554	C₂²	1	4	yes	—
23	C₅₃×#552	—	2	4	no	—
24	C₅₃×#552	C₂²	1	4	yes	—
25	C₅₃×#552	C₂²	1	4	yes	—
26	C₅₃×#551	—	2	4	no	—
27	C₅₃×#544	C₂²	1	2	yes	—
28	C₅₃×#542	—	2	2	no	—
29	C₅₃×#541	—	2	2	no	—
30	C₅₃×#536	C₂²	1	2	yes	—
31	C₅₃×#533	—	2	2	no	—
32	C₅₃×#529	—	2	2	no	—
33	C₅₃×#525	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
35	C₅₃×#520	C₂²	1	2	yes	—
36	C₅₃×#519	C₂²	1	2	yes	—
37	C₂×#117×C₅₃	C₂²	1	2	yes	—
38	C₅₃×#501	C₂²	1	4	yes	complemented
39	C₅₃×#500	C₂²	1	2	yes	complemented
40	C₅₃×#499	C₂²	1	2	yes	complemented
41	C₅₃×#485	C₂²	1	4	yes	—
42	C₅₃×#485	C₂²	1	4	yes	—
43	C₅₃×#485	C₂²	1	4	yes	complemented
44	C₅₃×#485	C₂²	1	4	yes	complemented
45	C₅₃×#484	C₂²	1	4	yes	—
46	C₅₃×#484	C₂²	1	4	yes	complemented
47	C₅₃×#483	C₂²	1	4	yes	—
48	C₅₃×#483	C₂²	1	4	yes	complemented
49	C₅₃×#479	C₂²	1	4	yes	complemented
50	C₅₃×#479	C₂²	1	4	yes	complemented
51	C₅₃×#477	C₂²	1	4	yes	complemented
52	C₅₃×#475	C₂²	1	4	yes	complemented
53	C₅₃×#470	C₂²	1	4	yes	complemented
54	C₅₃×#467	C₂²	1	2	yes	—
55	C₅₃×#467	C₂²	1	2	yes	—
56	C₅₃×#467	C₂²	1	2	yes	—
57	C₅₃×#467	C₂²	1	2	yes	—
58	C₅₃×#467	C₂²	1	2	yes	complemented
59	C₅₃×#467	C₂²	1	2	yes	complemented
60	C₅₃×#441	C₂²	1	4	yes	complemented
61	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
62	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
63	C₅₃×#435	C₂²	1	2	yes	—
64	C₅₃×#435	C₂²	1	2	yes	—
65	C₈×D₄×C₅₃	C₂²	1	2	yes	—
66	C₈×D₄×C₅₃	C₂²	1	2	yes	—
67	C₅₃×#428	C₂²	1	2	yes	—
68	C₅₃×#428	C₂²	1	2	yes	—
69	C₅₃×#428	C₂²	1	4	yes	complemented
70	C₅₃×#427	C₂²	1	1	yes	characteristic
71	C₅₃×#427	C₂²	1	1	yes	characteristic
72	C₅₃×#427	C₂²	1	1	yes	characteristic
73	C₅₃×#427	C₂²	1	2	yes	—
74	C₅₃×#427	C₂²	1	1	yes	characteristic
75	C₅₃×#427	C₂²	1	2	yes	—
76	C₅₃×#427	C₂²	1	2	yes	complemented
77	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
78	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
79	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
80	C₂×#107×C₅₃	C₂²	1	2	yes	complemented
81	C₂×#106×C₅₃	C₂²	1	2	yes	—
82	C₅₃×#424	C₂²	1	1	yes	characteristic
83	C₅₃×#419	C₂²	1	2	yes	—
84	C₅₃×#419	C₂²	1	2	yes	—
85	C₂×#103×C₅₃	C₂²	1	2	yes	—
86	C₅₃×#408	C₂²	1	1	yes	characteristic
87	C₅₃×#407	C₂²	1	1	yes	characteristic
88	C₅₃×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂×Q₁₆×C₅₃	—	2	4	no	—
93	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
94	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
95	#131×C₅₃	—	2	4	no	—
96	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
98	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₅₃	—	2	4	no	—
100	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₃	—	2	2	no	—
108	C₄⋊Q₈×C₅₃	—	2	2	no	—
109	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
110	#126×C₅₃	—	2	4	no	—
111	#126×C₅₃	—	2	4	no	—
112	#126×C₅₃	—	2	4	no	—
113	#126×C₅₃	—	2	4	no	—
114	#125×C₅₃	—	2	2	no	—
115	#125×C₅₃	—	2	4	no	—
116	#125×C₅₃	—	2	4	no	—
117	#125×C₅₃	—	2	4	no	—
118	#125×C₅₃	C₂³	1	4	yes	—
119	#124×C₅₃	—	2	2	no	—
120	#124×C₅₃	—	2	4	no	—
121	#123×C₅₃	—	2	4	no	—
122	#123×C₅₃	—	2	4	no	—
123	#123×C₅₃	—	2	4	no	—
124	#123×C₅₃	D₄	1	2	yes	—
125	C₂²⋊Q₈×C₅₃	—	2	4	no	—
126	C₂²⋊Q₈×C₅₃	—	2	4	no	—
127	C₂²⋊Q₈×C₅₃	—	2	4	no	—
128	C₂²⋊Q₈×C₅₃	—	2	2	no	—
129	C₂²⋊Q₈×C₅₃	—	2	2	no	—
130	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
131	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
132	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
134	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
136	#121×C₅₃	D₄	1	1	yes	characteristic
137	#121×C₅₃	D₄	1	1	yes	characteristic
138	#120×C₅₃	D₄	1	2	yes	—
139	C₄×Q₈×C₅₃	—	2	2	no	—
140	C₄×Q₈×C₅₃	—	2	2	no	—
141	C₄×Q₈×C₅₃	—	2	4	no	—
142	C₄×Q₈×C₅₃	—	2	2	no	—
143	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
144	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
145	C₄×D₄×C₅₃	—	2	2	no	—
146	C₄×D₄×C₅₃	—	2	4	no	—
147	C₄×D₄×C₅₃	—	2	4	no	—
148	C₄×D₄×C₅₃	C₂³	1	2	yes	—
149	C₄×D₄×C₅₃	C₂³	1	2	yes	—
150	#117×C₅₃	—	2	4	no	—
151	#117×C₅₃	—	2	4	no	—
152	#117×C₅₃	—	2	4	no	—
153	#117×C₅₃	—	2	2	no	—
154	#117×C₅₃	—	2	2	no	—
155	#117×C₅₃	C₂³	1	2	yes	—
156	#117×C₅₃	C₂³	1	2	yes	—
157	#117×C₅₃	C₂³	1	4	yes	—
158	#117×C₅₃	C₂³	1	2	yes	—
159	#117×C₅₃	C₂³	1	2	yes	—
160	#117×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
167	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
168	C₂×C₄²×C₅₃	—	2	2	no	—
169	#107×C₅₃	C₂³	1	4	yes	—
170	#107×C₅₃	C₂³	1	4	yes	—
171	#107×C₅₃	C₂³	1	2	yes	—
172	#107×C₅₃	C₂³	1	1	yes	characteristic
173	#107×C₅₃	C₂³	1	2	yes	—
174	#107×C₅₃	C₂³	1	1	yes	characteristic
175	#107×C₅₃	C₂³	1	2	yes	—
176	#107×C₅₃	C₂³	1	1	yes	characteristic
177	#107×C₅₃	C₂³	1	1	yes	characteristic
178	#107×C₅₃	C₂³	1	2	yes	—
179	#106×C₅₃	C₂³	1	4	yes	—
180	#106×C₅₃	C₂³	1	4	yes	—
181	#106×C₅₃	C₂³	1	2	yes	—
182	#106×C₅₃	C₂³	1	2	yes	—
183	#106×C₅₃	C₂³	1	2	yes	—
184	#106×C₅₃	C₂³	1	2	yes	—
185	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
186	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
187	#103×C₅₃	C₂³	1	4	yes	—
188	#103×C₅₃	C₂³	1	4	yes	—
189	#103×C₅₃	C₂³	1	4	yes	—
190	#103×C₅₃	C₂³	1	4	yes	—
191	#103×C₅₃	C₂³	1	4	yes	—
192	#103×C₅₃	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
197	#97×C₅₃	C₂³	1	2	yes	—
198	C₄×C₈×C₅₃	C₂³	1	2	yes	—
199	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
200	#41×C₅₃	—	2	2	no	—
201	#41×C₅₃	—	2	2	no	—
202	C₂×Q₈×C₅₃	—	2	2	no	—
203	C₂×Q₈×C₅₃	—	2	4	no	—
204	C₂×Q₈×C₅₃	—	2	4	no	—
205	C₂×Q₈×C₅₃	—	2	4	no	—
206	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
208	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
209	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
211	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₅₃	—	2	2	no	—
213	C₂²×C₄×C₅₃	—	2	2	no	—
214	C₂²×C₄×C₅₃	—	2	2	no	—
215	C₂²×C₄×C₅₃	—	2	2	no	—
216	C₂²×C₄×C₅₃	—	2	2	no	—
217	C₂²×C₄×C₅₃	—	2	2	no	—
218	C₂²×C₄×C₅₃	—	2	4	no	—
219	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
226	Q₁₆×C₅₃	—	2	4	no	—
227	Q₁₆×C₅₃	—	2	4	no	—
228	M₁₆×C₅₃	—	2	2	no	—
229	M₁₆×C₅₃	—	2	2	no	—
230	M₁₆×C₅₃	—	2	4	no	—
231	C₂×C₈×C₅₃	—	2	2	no	—
232	C₂×C₈×C₅₃	—	2	2	no	—
233	C₂×C₈×C₅₃	—	2	2	no	—
234	C₂×C₈×C₅₃	—	2	2	no	—
235	C₂×C₈×C₅₃	—	2	2	no	—
236	C₂×C₈×C₅₃	—	2	4	no	—
237	C₂×C₈×C₅₃	#41	1	4	yes	—
238	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
241	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₅₃	—	2	4	no	—
245	C₄⋊C₄×C₅₃	—	2	4	no	—
246	C₄⋊C₄×C₅₃	—	2	2	no	—
247	C₄⋊C₄×C₅₃	—	2	2	no	—
248	C₄⋊C₄×C₅₃	—	2	2	no	—
249	C₄⋊C₄×C₅₃	—	2	4	no	—
250	C₄⋊C₄×C₅₃	—	2	4	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	—	2	4	no	—
255	C₄⋊C₄×C₅₃	—	2	4	no	—
256	C₄⋊C₄×C₅₃	—	2	4	no	—
257	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₅₃	—	2	2	no	—
267	C₂²⋊C₄×C₅₃	—	2	2	no	—
268	C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂²⋊C₄×C₅₃	—	2	4	no	—
271	C₂²⋊C₄×C₅₃	—	2	4	no	—
272	C₂²⋊C₄×C₅₃	—	2	4	no	—
273	C₂²⋊C₄×C₅₃	—	2	4	no	—
274	C₂²⋊C₄×C₅₃	—	2	4	no	—
275	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
278	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
280	C₄²×C₅₃	—	2	2	no	—
281	C₄²×C₅₃	—	2	2	no	—
282	C₄²×C₅₃	—	2	2	no	—
283	C₄²×C₅₃	—	2	2	no	—
284	C₄²×C₅₃	—	2	4	no	—
285	C₄²×C₅₃	—	2	4	no	—
286	C₄²×C₅₃	—	2	4	no	—
287	C₄²×C₅₃	C₂⁴	1	2	yes	—
288	C₂³×C₅₃	—	2	2	no	—
289	C₂³×C₅₃	—	2	2	no	—
290	C₂³×C₅₃	—	4	1	no	—
291	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
292	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₅₃	—	2	2	no	—
296	Q₈×C₅₃	—	2	4	no	—
297	Q₈×C₅₃	—	2	4	no	—
298	Q₈×C₅₃	—	4	4	no	—
299	Q₈×C₅₃	—	8	4	no	—
300	D₄×C₅₃	—	2	4	no	—
301	D₄×C₅₃	—	2	4	no	—
302	D₄×C₅₃	—	2	2	no	—
303	D₄×C₅₃	—	4	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	2	2	no	—
310	C₂×C₄×C₅₃	—	2	1	no	—
311	C₂×C₄×C₅₃	—	2	1	no	—
312	C₂×C₄×C₅₃	—	2	2	no	—
313	C₂×C₄×C₅₃	—	2	2	no	—
314	C₂×C₄×C₅₃	—	2	4	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	4	no	—
317	C₂×C₄×C₅₃	—	2	2	no	—
318	C₂×C₄×C₅₃	—	2	2	no	—
319	C₂×C₄×C₅₃	—	4	4	no	—
320	C₂×C₄×C₅₃	—	4	4	no	—
321	C₂×C₄×C₅₃	—	8	4	no	—
322	C₂×C₄×C₅₃	—	8	2	no	—
323	C₂×C₄×C₅₃	—	8	2	no	—
324	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
331	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
332	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
333	C₈×C₅₃	—	2	1	no	—
334	C₈×C₅₃	—	2	1	no	—
335	C₈×C₅₃	—	2	2	no	—
336	C₈×C₅₃	—	2	2	no	—
337	C₈×C₅₃	C₂×#41	1	2	yes	—
338	C₈×C₅₃	C₂×#41	1	2	yes	—
339	#61264	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂²×C₅₃	—	2	1	no	—
341	C₂²×C₅₃	—	2	1	no	—
342	C₂²×C₅₃	—	2	1	no	—
343	C₂²×C₅₃	—	2	1	no	—
344	C₂²×C₅₃	—	2	2	no	—
345	C₂²×C₅₃	—	2	1	no	—
346	C₂²×C₅₃	—	2	1	no	—
347	C₂²×C₅₃	—	2	2	no	—
348	C₂²×C₅₃	—	2	2	no	—
349	C₂²×C₅₃	—	2	1	no	—
350	C₂²×C₅₃	—	4	4	no	—
351	C₂²×C₅₃	#547	1	2	yes	—
352	C₂²×C₅₃	#578	1	2	yes	—
353	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
354	C₄×C₅₃	—	2	2	no	—
355	C₄×C₅₃	—	2	1	no	—
356	C₄×C₅₃	—	2	1	no	—
357	C₄×C₅₃	—	2	2	no	—
358	C₄×C₅₃	—	2	2	no	—
359	C₄×C₅₃	—	4	2	no	—
360	C₄×C₅₃	—	4	4	no	—
361	C₄×C₅₃	—	4	2	no	—
362	C₄×C₅₃	—	4	4	no	—
363	C₄×C₅₃	—	4	2	no	—
364	C₄×C₅₃	—	4	2	no	—
365	C₄×C₅₃	#547	1	2	yes	—
366	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
367	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	#3495	C₂×C₅₃	1	2	yes	—
369	#3349	C₂×C₅₃	1	4	yes	complemented
370	#3344	C₂×C₅₃	1	4	yes	complemented
371	#3342	C₂×C₅₃	1	2	yes	complemented
372	#3338	C₂×C₅₃	1	2	yes	complemented
373	#3336	C₂×C₅₃	1	2	yes	complemented
374	#3336	C₂×C₅₃	1	2	yes	complemented
375	#3164	C₂×C₅₃	1	1	yes	characteristic, complemented
376	#3097	C₂×C₅₃	1	2	yes	complemented
377	#3095	C₂×C₅₃	1	2	yes	complemented
378	#3082	C₂×C₅₃	1	2	yes	complemented
379	#3059	C₂×C₅₃	1	1	yes	characteristic, complemented
380	C₂×#467	C₂×C₅₃	1	1	yes	characteristic, complemented
381	#2950	C₂×C₅₃	1	1	yes	characteristic, complemented
382	#2929	C₂×C₅₃	1	1	yes	characteristic
383	#2913	C₂×C₅₃	1	1	yes	characteristic, complemented
384	C₂×#427	C₂×C₅₃	1	1	yes	characteristic, complemented
385	C₂×C₅₃	—	2	2	no	—
386	C₂×C₅₃	—	2	2	no	—
387	C₂×C₅₃	—	4	2	no	—
388	C₂×C₅₃	—	4	1	no	—
389	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
390	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
391	C₂×C₅₃	#3584	1	1	yes	characteristic
392	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
393	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
394	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
395	#556	C₂²×C₅₃	1	4	yes	—
396	#554	C₂²×C₅₃	1	4	yes	—
397	#552	—	2	4	no	—
398	#552	C₂²×C₅₃	1	4	yes	—
399	#552	C₂²×C₅₃	1	4	yes	—
400	#551	—	2	4	no	—
401	#544	C₂²×C₅₃	1	2	yes	—
402	#542	—	2	2	no	—
403	#541	—	2	2	no	—
404	#536	C₂²×C₅₃	1	2	yes	—
405	#533	—	2	2	no	—
406	#529	—	2	2	no	—
407	#525	C₂²×C₅₃	1	1	yes	characteristic
408	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
409	#520	C₂²×C₅₃	1	2	yes	—
410	#519	C₂²×C₅₃	1	2	yes	—
411	C₂×#117	C₂²×C₅₃	1	2	yes	—
412	#501	C₂²×C₅₃	1	4	yes	complemented
413	#500	C₂²×C₅₃	1	2	yes	complemented
414	#499	C₂²×C₅₃	1	2	yes	complemented
415	#485	C₂²×C₅₃	1	4	yes	—
416	#485	C₂²×C₅₃	1	4	yes	—
417	#485	C₂²×C₅₃	1	4	yes	complemented
418	#485	C₂²×C₅₃	1	4	yes	complemented
419	#484	C₂²×C₅₃	1	4	yes	—
420	#484	C₂²×C₅₃	1	4	yes	complemented
421	#483	C₂²×C₅₃	1	4	yes	—
422	#483	C₂²×C₅₃	1	4	yes	complemented
423	#479	C₂²×C₅₃	1	4	yes	complemented
424	#479	C₂²×C₅₃	1	4	yes	complemented
425	#477	C₂²×C₅₃	1	4	yes	complemented
426	#475	C₂²×C₅₃	1	4	yes	complemented
427	#470	C₂²×C₅₃	1	4	yes	complemented
428	#467	C₂²×C₅₃	1	2	yes	—
429	#467	C₂²×C₅₃	1	2	yes	—
430	#467	C₂²×C₅₃	1	2	yes	—
431	#467	C₂²×C₅₃	1	2	yes	—
432	#467	C₂²×C₅₃	1	2	yes	complemented
433	#467	C₂²×C₅₃	1	2	yes	complemented
434	#441	C₂²×C₅₃	1	4	yes	complemented
435	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
436	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
437	#435	C₂²×C₅₃	1	2	yes	—
438	#435	C₂²×C₅₃	1	2	yes	—
439	C₈×D₄	C₂²×C₅₃	1	2	yes	—
440	C₈×D₄	C₂²×C₅₃	1	2	yes	—
441	#428	C₂²×C₅₃	1	2	yes	—
442	#428	C₂²×C₅₃	1	2	yes	—
443	#428	C₂²×C₅₃	1	4	yes	complemented
444	#427	C₂²×C₅₃	1	1	yes	characteristic
445	#427	C₂²×C₅₃	1	2	yes	—
446	#427	C₂²×C₅₃	1	1	yes	characteristic
447	#427	C₂²×C₅₃	1	2	yes	—
448	#427	C₂²×C₅₃	1	1	yes	characteristic
449	#427	C₂²×C₅₃	1	1	yes	characteristic
450	#427	C₂²×C₅₃	1	2	yes	complemented
451	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
452	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
453	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
454	C₂×#107	C₂²×C₅₃	1	2	yes	complemented
455	C₂×#106	C₂²×C₅₃	1	2	yes	—
456	#424	C₂²×C₅₃	1	1	yes	characteristic
457	#419	C₂²×C₅₃	1	2	yes	—
458	#419	C₂²×C₅₃	1	2	yes	—
459	C₂×#103	C₂²×C₅₃	1	2	yes	—
460	#408	C₂²×C₅₃	1	1	yes	characteristic
461	#407	C₂²×C₅₃	1	1	yes	characteristic
462	#405	C₂²×C₅₃	1	1	yes	characteristic
463	C₅₃	#61264	1	1	yes	characteristic, direct product factor, Sylow
464	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
466	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
467	C₂×Q₁₆	—	2	4	no	—
468	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
469	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
470	#131	—	2	4	no	—
471	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
472	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
473	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
474	C₂²×C₈	—	2	4	no	—
475	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
481	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#126	—	2	4	no	—
488	#126	—	2	4	no	—
489	#125	—	2	2	no	—
490	#125	—	2	4	no	—
491	#125	—	2	4	no	—
492	#125	—	2	4	no	—
493	#125	C₂³×C₅₃	1	4	yes	—
494	#124	—	2	2	no	—
495	#124	—	2	4	no	—
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	D₄×C₅₃	1	2	yes	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
506	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
507	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
508	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
509	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
510	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
511	#121	D₄×C₅₃	1	1	yes	characteristic
512	#121	D₄×C₅₃	1	1	yes	characteristic
513	#120	D₄×C₅₃	1	2	yes	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	4	no	—
518	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
519	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	C₂³×C₅₃	1	2	yes	—
524	C₄×D₄	C₂³×C₅₃	1	2	yes	—
525	#117	—	2	2	no	—
526	#117	—	2	2	no	—
527	#117	—	2	4	no	—
528	#117	—	2	4	no	—
529	#117	—	2	4	no	—
530	#117	C₂³×C₅₃	1	2	yes	—
531	#117	C₂³×C₅₃	1	2	yes	—
532	#117	C₂³×C₅₃	1	2	yes	—
533	#117	C₂³×C₅₃	1	2	yes	—
534	#117	C₂³×C₅₃	1	4	yes	—
535	#117	C₂³×C₅₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	C₂×C₂²⋊C₄	—	2	2	no	—
543	C₂×C₄²	—	2	2	no	—
544	#107	C₂³×C₅₃	1	1	yes	characteristic
545	#107	C₂³×C₅₃	1	2	yes	—
546	#107	C₂³×C₅₃	1	1	yes	characteristic
547	#107	C₂³×C₅₃	1	1	yes	characteristic
548	#107	C₂³×C₅₃	1	1	yes	characteristic
549	#107	C₂³×C₅₃	1	2	yes	—
550	#107	C₂³×C₅₃	1	2	yes	—
551	#107	C₂³×C₅₃	1	2	yes	—
552	#107	C₂³×C₅₃	1	4	yes	—
553	#107	C₂³×C₅₃	1	4	yes	—
554	#106	C₂³×C₅₃	1	2	yes	—
555	#106	C₂³×C₅₃	1	2	yes	—
556	#106	C₂³×C₅₃	1	2	yes	—
557	#106	C₂³×C₅₃	1	2	yes	—
558	#106	C₂³×C₅₃	1	4	yes	—
559	#106	C₂³×C₅₃	1	4	yes	—
560	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
561	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
562	#103	C₂³×C₅₃	1	4	yes	—
563	#103	C₂³×C₅₃	1	4	yes	—
564	#103	C₂³×C₅₃	1	4	yes	—
565	#103	C₂³×C₅₃	1	4	yes	—
566	#103	C₂³×C₅₃	1	4	yes	—
567	#103	C₂³×C₅₃	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
571	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
572	#97	C₂³×C₅₃	1	2	yes	—
573	C₄×C₈	C₂³×C₅₃	1	2	yes	—
574	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
582	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
583	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
585	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
601	Q₁₆	—	2	4	no	—
602	Q₁₆	—	2	4	no	—
603	M₁₆	—	2	2	no	—
604	M₁₆	—	2	2	no	—
605	M₁₆	—	2	4	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	#41×C₅₃	1	4	yes	—
613	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
614	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
640	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
651	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	C₂⁴×C₅₃	1	2	yes	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	4	1	no	—
666	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
667	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
668	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
669	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
670	Q₈	—	2	2	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	4	4	no	—
674	Q₈	—	8	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
705	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
706	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
707	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
708	C₈	—	2	1	no	—
709	C₈	—	2	1	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	C₂×#41×C₅₃	1	2	yes	—
713	C₈	C₂×#41×C₅₃	1	2	yes	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	4	4	no	—
725	C₂²	C₅₃×#547	1	2	yes	—
726	C₂²	C₅₃×#578	1	2	yes	—
727	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	4	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	2	no	—
739	C₄	C₅₃×#547	1	2	yes	—
740	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
741	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
747	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
748	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#3349	C₂	semidirect
3. C₅₃×#3344	C₂	semidirect
4. C₅₃×#3342	C₂	semidirect
5. C₅₃×#3338	C₂	semidirect
6. C₅₃×#3336	C₂	semidirect
7. C₅₃×#3336	C₂	semidirect
8. C₅₃×#3164	C₂	semidirect
9. C₅₃×#3097	C₂	semidirect
10. C₅₃×#3095	C₂	semidirect
11. C₅₃×#3082	C₂	semidirect
12. C₅₃×#3059	C₂	semidirect
13. C₂×C₅₃×#467	C₂	semidirect
14. C₅₃×#2950	C₂	semidirect
16. C₅₃×#2913	C₂	semidirect
17. C₂×C₅₃×#427	C₂	semidirect
38. C₅₃×#501	C₂²	semidirect
39. C₅₃×#500	C₂²	semidirect
40. C₅₃×#499	C₂²	semidirect
43. C₅₃×#485	C₂²	semidirect
44. C₅₃×#485	C₂²	semidirect
46. C₅₃×#484	C₂²	semidirect
48. C₅₃×#483	C₂²	semidirect
49. C₅₃×#479	C₂²	semidirect
50. C₅₃×#479	C₂²	semidirect
51. C₅₃×#477	C₂²	semidirect
52. C₅₃×#475	C₂²	semidirect
53. C₅₃×#470	C₂²	semidirect
58. C₅₃×#467	C₂²	semidirect
59. C₅₃×#467	C₂²	semidirect
60. C₅₃×#441	C₂²	semidirect
61. C₄×Q₁₆×C₅₃	C₂²	semidirect
62. C₄×Q₁₆×C₅₃	C₂²	semidirect
69. C₅₃×#428	C₂²	semidirect
76. C₅₃×#427	C₂²	semidirect
80. C₂×#107×C₅₃	C₂²	semidirect
339. #61264	C₅₃	direct (N × H)
369. #3349	C₂×C₅₃	semidirect
370. #3344	C₂×C₅₃	semidirect
371. #3342	C₂×C₅₃	semidirect
372. #3338	C₂×C₅₃	semidirect
373. #3336	C₂×C₅₃	semidirect
374. #3336	C₂×C₅₃	semidirect
375. #3164	C₂×C₅₃	semidirect
376. #3097	C₂×C₅₃	semidirect
377. #3095	C₂×C₅₃	semidirect
378. #3082	C₂×C₅₃	semidirect
379. #3059	C₂×C₅₃	semidirect
380. C₂×#467	C₂×C₅₃	semidirect
381. #2950	C₂×C₅₃	semidirect
383. #2913	C₂×C₅₃	semidirect
384. C₂×#427	C₂×C₅₃	semidirect
412. #501	C₂²×C₅₃	semidirect
413. #500	C₂²×C₅₃	semidirect
414. #499	C₂²×C₅₃	semidirect
417. #485	C₂²×C₅₃	semidirect
418. #485	C₂²×C₅₃	semidirect
420. #484	C₂²×C₅₃	semidirect
422. #483	C₂²×C₅₃	semidirect
423. #479	C₂²×C₅₃	semidirect
424. #479	C₂²×C₅₃	semidirect
425. #477	C₂²×C₅₃	semidirect
426. #475	C₂²×C₅₃	semidirect
427. #470	C₂²×C₅₃	semidirect
432. #467	C₂²×C₅₃	semidirect
433. #467	C₂²×C₅₃	semidirect
434. #441	C₂²×C₅₃	semidirect
435. C₄×Q₁₆	C₂²×C₅₃	semidirect
436. C₄×Q₁₆	C₂²×C₅₃	semidirect
443. #428	C₂²×C₅₃	semidirect
450. #427	C₂²×C₅₃	semidirect
454. C₂×#107	C₂²×C₅₃	semidirect
463. C₅₃	#61264	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×#3495	2
C₅₃×#3349	2
C₅₃×#3344	2
C₅₃×#3342	2
C₅₃×#3338	2
C₅₃×#3336	2
C₅₃×#3164	2
C₅₃×#3097	2
C₅₃×#3095	2
C₅₃×#3082	2
C₅₃×#3059	2
C₂×C₅₃×#467	2
C₅₃×#2950	2
C₅₃×#2929	2
C₅₃×#2913	2
C₂×C₅₃×#427	2
#61264	53

Subgroups — C53×#61264 #27268776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61264 #27268776