Subgroups — C₅₃×#61849 #27269361

Order 13568.

1716 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3385	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3384	C₂	1	2	yes	maximal, complemented
5	Q₈×D₈×C₅₃	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3370	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3367	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3243	C₂	1	4	yes	maximal, complemented
10	C₅₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3118	C₂	1	4	yes	maximal, complemented
13	C₅₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic
15	C₅₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#563	—	2	2	no	—
17	C₅₃×#559	C₂²	1	2	yes	complemented
18	Q₈²×C₅₃	C₂²	1	2	yes	complemented
19	C₅₃×#556	—	2	1	no	—
20	C₅₃×#556	C₂²	1	2	yes	complemented
21	C₅₃×#554	—	2	1	no	—
22	C₅₃×#554	—	2	2	no	—
23	C₅₃×#554	C₂²	1	2	yes	—
24	C₅₃×#554	C₂²	1	4	yes	—
25	D₄×Q₈×C₅₃	—	2	1	no	—
26	D₄×Q₈×C₅₃	—	2	1	no	—
27	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
28	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
29	C₅₃×#544	C₂²	1	2	yes	—
30	C₅₃×#543	—	2	2	no	—
31	C₅₃×#542	—	2	2	no	—
32	C₅₃×#542	C₂²	1	4	yes	—
33	C₅₃×#536	—	2	2	no	—
34	C₅₃×#533	C₂²	1	1	yes	characteristic
35	C₅₃×#533	C₂²	1	1	yes	characteristic
36	C₅₃×#533	C₂²	1	1	yes	characteristic
37	C₅₃×#532	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
39	C₅₃×#518	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#501	C₂²	1	2	yes	complemented
42	C₅₃×#501	C₂²	1	4	yes	complemented
43	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#500	C₂²	1	4	yes	complemented
45	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#490	C₂²	1	2	yes	complemented
47	C₅₃×#489	C₂²	1	4	yes	complemented
48	C₅₃×#488	C₂²	1	4	yes	complemented
49	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#485	C₂²	1	4	yes	—
52	C₅₃×#484	C₂²	1	2	yes	—
53	C₅₃×#482	C₂²	1	4	yes	—
54	C₅₃×#480	C₂²	1	2	yes	—
55	C₅₃×#479	C₂²	1	4	yes	complemented
56	C₅₃×#479	C₂²	1	4	yes	complemented
57	C₅₃×#478	C₂²	1	4	yes	complemented
58	C₅₃×#477	C₂²	1	4	yes	complemented
59	C₅₃×#476	C₂²	1	4	yes	—
60	C₅₃×#476	C₂²	1	2	yes	complemented
61	C₅₃×#474	C₂²	1	2	yes	—
62	C₅₃×#474	C₂²	1	2	yes	—
63	C₅₃×#474	C₂²	1	4	yes	—
64	C₅₃×#474	C₂²	1	2	yes	complemented
65	C₅₃×#474	C₂²	1	4	yes	complemented
66	C₅₃×#463	C₂²	1	4	yes	—
67	C₅₃×#463	C₂²	1	4	yes	—
68	C₅₃×#461	C₂²	1	2	yes	—
69	C₅₃×#459	C₂²	1	2	yes	—
70	C₅₃×#450	C₂²	1	2	yes	—
71	C₅₃×#447	C₂²	1	2	yes	—
72	C₅₃×#446	C₂²	1	2	yes	complemented
73	C₅₃×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
75	C₅₃×#442	C₂²	1	4	yes	—
76	C₅₃×#440	C₂²	1	4	yes	—
77	C₅₃×#440	C₂²	1	4	yes	—
78	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
79	C₄×D₈×C₅₃	C₂²	1	2	yes	—
80	C₄×D₈×C₅₃	C₂²	1	2	yes	—
81	C₄×D₈×C₅₃	C₂²	1	4	yes	—
82	C₅₃×#433	C₂²	1	4	yes	—
83	C₅₃×#432	C₂²	1	1	yes	characteristic
84	C₅₃×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₅₃	—	2	1	no	—
86	C₂²×Q₈×C₅₃	—	2	2	no	—
87	C₂²×Q₈×C₅₃	—	2	2	no	—
88	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅₃	—	2	1	no	—
90	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
91	C₂×D₈×C₅₃	C₂³	1	2	yes	—
92	C₂×D₈×C₅₃	C₂³	1	2	yes	—
93	C₄⋊Q₈×C₅₃	—	2	4	no	—
94	C₄⋊Q₈×C₅₃	—	2	2	no	—
95	C₄⋊Q₈×C₅₃	—	2	2	no	—
96	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
97	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
101	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
103	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
105	#127×C₅₃	C₂³	1	1	yes	characteristic
106	#126×C₅₃	—	2	4	no	—
107	#126×C₅₃	—	2	4	no	—
108	#125×C₅₃	—	2	2	no	—
109	#125×C₅₃	—	2	1	no	—
110	#125×C₅₃	D₄	1	2	yes	—
111	#125×C₅₃	C₂³	1	4	yes	—
112	#125×C₅₃	C₂³	1	2	yes	—
113	#124×C₅₃	—	2	4	no	—
114	#124×C₅₃	—	2	1	no	—
115	#124×C₅₃	—	2	2	no	—
116	#124×C₅₃	C₂³	1	4	yes	—
117	#123×C₅₃	—	2	4	no	—
118	#123×C₅₃	—	2	4	no	—
119	C₂²⋊Q₈×C₅₃	—	2	2	no	—
120	C₂²⋊Q₈×C₅₃	—	2	4	no	—
121	C₂²⋊Q₈×C₅₃	—	2	2	no	—
122	C₂²⋊Q₈×C₅₃	—	2	4	no	—
123	C₂²⋊Q₈×C₅₃	—	2	4	no	—
124	C₂²⋊Q₈×C₅₃	—	2	4	no	—
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	—	2	4	no	—
131	C₂²⋊Q₈×C₅₃	—	2	1	no	—
132	C₂²⋊Q₈×C₅₃	—	2	1	no	—
133	C₂²⋊Q₈×C₅₃	—	2	1	no	—
134	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
135	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
136	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
137	#121×C₅₃	—	2	1	no	—
138	#121×C₅₃	C₂³	1	2	yes	—
139	C₄×Q₈×C₅₃	—	2	1	no	—
140	C₄×Q₈×C₅₃	—	2	1	no	—
141	C₄×Q₈×C₅₃	—	2	1	no	—
142	C₄×Q₈×C₅₃	—	2	2	no	—
143	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
144	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
145	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
147	C₄×D₄×C₅₃	—	2	2	no	—
148	C₄×D₄×C₅₃	—	2	2	no	—
149	C₄×D₄×C₅₃	—	2	2	no	—
150	C₄×D₄×C₅₃	—	2	1	no	—
151	C₄×D₄×C₅₃	—	2	1	no	—
152	C₄×D₄×C₅₃	—	2	1	no	—
153	C₄×D₄×C₅₃	C₂³	1	2	yes	—
154	C₄×D₄×C₅₃	C₂³	1	2	yes	—
155	C₄×D₄×C₅₃	C₂³	1	4	yes	—
156	C₄×D₄×C₅₃	C₂³	1	4	yes	—
157	C₄×D₄×C₅₃	C₂³	1	2	yes	—
158	C₄×D₄×C₅₃	C₂³	1	4	yes	—
159	#117×C₅₃	—	2	2	no	—
160	#117×C₅₃	—	2	1	no	—
161	#117×C₅₃	C₂³	1	2	yes	—
162	#117×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
164	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
167	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
168	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
169	#107×C₅₃	C₂³	1	4	yes	—
170	#107×C₅₃	C₂³	1	2	yes	—
171	#107×C₅₃	C₂³	1	4	yes	—
172	#107×C₅₃	C₂³	1	4	yes	—
173	#107×C₅₃	C₂³	1	2	yes	—
174	#106×C₅₃	C₂³	1	4	yes	—
175	#106×C₅₃	C₂³	1	4	yes	—
176	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
177	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
178	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
179	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
180	#103×C₅₃	C₂³	1	4	yes	—
181	#103×C₅₃	C₂³	1	4	yes	—
182	#103×C₅₃	C₂³	1	4	yes	—
183	#102×C₅₃	C₂³	1	2	yes	—
184	#102×C₅₃	C₂³	1	4	yes	—
185	#102×C₅₃	C₂³	1	2	yes	—
186	#102×C₅₃	C₂³	1	4	yes	—
187	#102×C₅₃	C₂³	1	2	yes	—
188	#102×C₅₃	C₂³	1	2	yes	—
189	#102×C₅₃	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
192	#97×C₅₃	C₂³	1	4	yes	—
193	#97×C₅₃	C₂³	1	2	yes	—
194	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₅₃	C₂³	1	4	yes	—
197	C₂⁴×C₅₃	—	2	1	no	—
198	#41×C₅₃	—	8	2	no	—
199	C₂×Q₈×C₅₃	—	2	1	no	—
200	C₂×Q₈×C₅₃	—	2	1	no	—
201	C₂×Q₈×C₅₃	—	2	1	no	—
202	C₂×Q₈×C₅₃	—	2	4	no	—
203	C₂×Q₈×C₅₃	—	2	4	no	—
204	C₂×Q₈×C₅₃	—	2	1	no	—
205	C₂×Q₈×C₅₃	—	8	4	no	—
206	C₂×Q₈×C₅₃	—	8	4	no	—
207	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₅₃	—	2	4	no	—
211	C₂×D₄×C₅₃	—	2	2	no	—
212	C₂×D₄×C₅₃	—	2	1	no	—
213	C₂×D₄×C₅₃	—	2	1	no	—
214	C₂×D₄×C₅₃	—	2	1	no	—
215	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
216	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₃	—	2	1	no	—
218	C₂²×C₄×C₅₃	—	2	2	no	—
219	C₂²×C₄×C₅₃	—	2	2	no	—
220	C₂²×C₄×C₅₃	—	2	4	no	—
221	C₂²×C₄×C₅₃	—	2	4	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
223	C₂²×C₄×C₅₃	—	2	4	no	—
224	C₂²×C₄×C₅₃	—	8	2	no	—
225	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₅₃	—	2	8	no	—
229	D₈×C₅₃	—	2	4	no	—
230	D₈×C₅₃	—	2	4	no	—
231	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
232	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
233	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
234	C₄⋊C₄×C₅₃	—	2	2	no	—
235	C₄⋊C₄×C₅₃	—	2	1	no	—
236	C₄⋊C₄×C₅₃	—	2	4	no	—
237	C₄⋊C₄×C₅₃	—	2	4	no	—
238	C₄⋊C₄×C₅₃	—	2	4	no	—
239	C₄⋊C₄×C₅₃	—	2	1	no	—
240	C₄⋊C₄×C₅₃	—	2	1	no	—
241	C₄⋊C₄×C₅₃	—	2	1	no	—
242	C₄⋊C₄×C₅₃	—	2	1	no	—
243	C₄⋊C₄×C₅₃	—	2	1	no	—
244	C₄⋊C₄×C₅₃	—	2	2	no	—
245	C₄⋊C₄×C₅₃	—	2	1	no	—
246	C₄⋊C₄×C₅₃	—	2	2	no	—
247	C₄⋊C₄×C₅₃	—	2	4	no	—
248	C₄⋊C₄×C₅₃	—	2	4	no	—
249	C₄⋊C₄×C₅₃	—	2	2	no	—
250	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₅₃	—	2	2	no	—
262	C₂²⋊C₄×C₅₃	—	2	2	no	—
263	C₂²⋊C₄×C₅₃	—	2	2	no	—
264	C₂²⋊C₄×C₅₃	—	2	2	no	—
265	C₂²⋊C₄×C₅₃	—	2	4	no	—
266	C₂²⋊C₄×C₅₃	—	2	4	no	—
267	C₂²⋊C₄×C₅₃	—	2	4	no	—
268	C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂²⋊C₄×C₅₃	—	2	4	no	—
270	C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂²⋊C₄×C₅₃	—	2	4	no	—
272	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
273	C₄²×C₅₃	—	2	2	no	—
274	C₄²×C₅₃	—	2	4	no	—
275	C₄²×C₅₃	—	2	2	no	—
276	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₄²×C₅₃	C₂⁴	1	4	yes	—
280	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
281	C₂³×C₅₃	—	2	4	no	—
282	C₂³×C₅₃	—	2	2	no	—
283	C₂³×C₅₃	—	2	2	no	—
284	C₂³×C₅₃	—	8	1	no	—
285	C₂³×C₅₃	—	8	1	no	—
286	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₅₃	—	2	4	no	—
288	Q₈×C₅₃	—	2	4	no	—
289	Q₈×C₅₃	—	4	2	no	—
290	Q₈×C₅₃	—	4	2	no	—
291	Q₈×C₅₃	—	4	2	no	—
292	Q₈×C₅₃	—	8	1	no	—
293	Q₈×C₅₃	—	8	4	no	—
294	Q₈×C₅₃	—	8	4	no	—
295	Q₈×C₅₃	—	8	1	no	—
296	D₄×C₅₃	—	2	4	no	—
297	D₄×C₅₃	—	2	2	no	—
298	D₄×C₅₃	—	2	2	no	—
299	D₄×C₅₃	—	2	2	no	—
300	D₄×C₅₃	—	4	2	no	—
301	D₄×C₅₃	—	8	1	no	—
302	D₄×C₅₃	—	8	2	no	—
303	D₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
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	2	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	2	2	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	2	no	—
312	C₂×C₄×C₅₃	—	4	1	no	—
313	C₂×C₄×C₅₃	—	4	4	no	—
314	C₂×C₄×C₅₃	—	4	4	no	—
315	C₂×C₄×C₅₃	—	8	4	no	—
316	C₂×C₄×C₅₃	—	8	2	no	—
317	C₂×C₄×C₅₃	—	8	4	no	—
318	C₂×C₄×C₅₃	—	8	4	no	—
319	C₂×C₄×C₅₃	—	8	1	no	—
320	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
327	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
328	C₈×C₅₃	—	2	2	no	—
329	C₈×C₅₃	—	2	2	no	—
330	C₈×C₅₃	—	2	4	no	—
331	#61849	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂²×C₅₃	—	2	1	no	—
333	C₂²×C₅₃	—	2	1	no	—
334	C₂²×C₅₃	—	2	4	no	—
335	C₂²×C₅₃	—	2	1	no	—
336	C₂²×C₅₃	—	4	2	no	—
337	C₂²×C₅₃	—	4	2	no	—
338	C₂²×C₅₃	—	4	2	no	—
339	C₂²×C₅₃	—	4	2	no	—
340	C₂²×C₅₃	—	4	2	no	—
341	C₂²×C₅₃	—	8	4	no	—
342	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₅₃	—	2	1	no	—
344	C₄×C₅₃	—	2	1	no	—
345	C₄×C₅₃	—	2	4	no	—
346	C₄×C₅₃	—	2	1	no	—
347	C₄×C₅₃	—	2	1	no	—
348	C₄×C₅₃	—	2	4	no	—
349	C₄×C₅₃	—	4	2	no	—
350	C₄×C₅₃	—	4	2	no	—
351	C₄×C₅₃	—	4	2	no	—
352	C₄×C₅₃	—	4	2	no	—
353	C₄×C₅₃	—	4	2	no	—
354	C₄×C₅₃	—	4	2	no	—
355	C₄×C₅₃	#576	1	2	yes	—
356	C₄×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
357	#3550	C₂×C₅₃	1	1	yes	characteristic, complemented
358	#3501	C₂×C₅₃	1	1	yes	characteristic, complemented
359	#3385	C₂×C₅₃	1	4	yes	complemented
360	#3384	C₂×C₅₃	1	2	yes	complemented
361	Q₈×D₈	C₂×C₅₃	1	2	yes	complemented
362	#3370	C₂×C₅₃	1	4	yes	complemented
363	#3367	C₂×C₅₃	1	2	yes	complemented
364	#3360	C₂×C₅₃	1	2	yes	complemented
365	#3243	C₂×C₅₃	1	4	yes	complemented
366	#3235	C₂×C₅₃	1	1	yes	characteristic, complemented
367	#3231	C₂×C₅₃	1	1	yes	characteristic, complemented
368	#3118	C₂×C₅₃	1	4	yes	complemented
369	#3110	C₂×C₅₃	1	1	yes	characteristic, complemented
370	#3100	C₂×C₅₃	1	1	yes	characteristic
371	#2985	C₂×C₅₃	1	1	yes	characteristic, complemented
372	C₂×C₅₃	—	4	1	no	—
373	C₂×C₅₃	—	4	4	no	—
374	C₂×C₅₃	—	8	2	no	—
375	C₂×C₅₃	#3486	1	1	yes	characteristic
376	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
377	C₂×C₅₃	#3586	1	1	yes	characteristic
378	#563	—	2	2	no	—
379	#559	C₂²×C₅₃	1	2	yes	complemented
380	Q₈²	C₂²×C₅₃	1	2	yes	complemented
381	#556	—	2	1	no	—
382	#556	C₂²×C₅₃	1	2	yes	complemented
383	#554	—	2	1	no	—
384	#554	—	2	2	no	—
385	#554	C₂²×C₅₃	1	2	yes	—
386	#554	C₂²×C₅₃	1	4	yes	—
387	D₄×Q₈	—	2	1	no	—
388	D₄×Q₈	—	2	1	no	—
389	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
390	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
391	#544	C₂²×C₅₃	1	2	yes	—
392	#543	—	2	2	no	—
393	#542	—	2	2	no	—
394	#542	C₂²×C₅₃	1	4	yes	—
395	#536	—	2	2	no	—
396	#533	C₂²×C₅₃	1	1	yes	characteristic
397	#533	C₂²×C₅₃	1	1	yes	characteristic
398	#533	C₂²×C₅₃	1	1	yes	characteristic
399	#532	C₂²×C₅₃	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	—	2	2	no	—
401	#518	C₂²×C₅₃	1	2	yes	—
402	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
403	#501	C₂²×C₅₃	1	4	yes	complemented
404	#501	C₂²×C₅₃	1	2	yes	complemented
405	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
406	#500	C₂²×C₅₃	1	4	yes	complemented
407	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
408	#490	C₂²×C₅₃	1	2	yes	complemented
409	#489	C₂²×C₅₃	1	4	yes	complemented
410	#488	C₂²×C₅₃	1	4	yes	complemented
411	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
412	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
413	#485	C₂²×C₅₃	1	4	yes	—
414	#484	C₂²×C₅₃	1	2	yes	—
415	#482	C₂²×C₅₃	1	4	yes	—
416	#480	C₂²×C₅₃	1	2	yes	—
417	#479	C₂²×C₅₃	1	4	yes	complemented
418	#479	C₂²×C₅₃	1	4	yes	complemented
419	#478	C₂²×C₅₃	1	4	yes	complemented
420	#477	C₂²×C₅₃	1	4	yes	complemented
421	#476	C₂²×C₅₃	1	4	yes	—
422	#476	C₂²×C₅₃	1	2	yes	complemented
423	#474	C₂²×C₅₃	1	2	yes	—
424	#474	C₂²×C₅₃	1	2	yes	—
425	#474	C₂²×C₅₃	1	4	yes	—
426	#474	C₂²×C₅₃	1	2	yes	complemented
427	#474	C₂²×C₅₃	1	4	yes	complemented
428	#463	C₂²×C₅₃	1	4	yes	—
429	#463	C₂²×C₅₃	1	4	yes	—
430	#461	C₂²×C₅₃	1	2	yes	—
431	#459	C₂²×C₅₃	1	2	yes	—
432	#450	C₂²×C₅₃	1	2	yes	—
433	#447	C₂²×C₅₃	1	2	yes	—
434	#446	C₂²×C₅₃	1	2	yes	complemented
435	#446	C₂²×C₅₃	1	4	yes	complemented
436	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
437	#442	C₂²×C₅₃	1	4	yes	—
438	#440	C₂²×C₅₃	1	4	yes	—
439	#440	C₂²×C₅₃	1	4	yes	—
440	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
441	C₄×D₈	C₂²×C₅₃	1	2	yes	—
442	C₄×D₈	C₂²×C₅₃	1	2	yes	—
443	C₄×D₈	C₂²×C₅₃	1	4	yes	—
444	#433	C₂²×C₅₃	1	4	yes	—
445	#432	C₂²×C₅₃	1	1	yes	characteristic
446	#431	C₂²×C₅₃	1	1	yes	characteristic
447	C₅₃	#61849	1	1	yes	characteristic, direct product factor, Sylow
448	C₂×#41	—	2	1	no	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×Q₈	—	2	2	no	—
451	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
452	C₂³×C₄	—	2	1	no	—
453	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
454	C₂×D₈	C₂³×C₅₃	1	2	yes	—
455	C₂×D₈	C₂³×C₅₃	1	2	yes	—
456	C₄⋊Q₈	—	2	4	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
460	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
461	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
467	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
468	#127	C₂³×C₅₃	1	1	yes	characteristic
469	#126	—	2	4	no	—
470	#126	—	2	4	no	—
471	#125	—	2	2	no	—
472	#125	—	2	1	no	—
473	#125	D₄×C₅₃	1	2	yes	—
474	#125	C₂³×C₅₃	1	2	yes	—
475	#125	C₂³×C₅₃	1	4	yes	—
476	#124	—	2	2	no	—
477	#124	—	2	4	no	—
478	#124	—	2	1	no	—
479	#124	C₂³×C₅₃	1	4	yes	—
480	#123	—	2	4	no	—
481	#123	—	2	4	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	—	2	4	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
498	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
499	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
500	#121	—	2	1	no	—
501	#121	C₂³×C₅₃	1	2	yes	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	—	2	1	no	—
506	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
507	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
508	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
509	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	C₂³×C₅₃	1	2	yes	—
517	C₄×D₄	C₂³×C₅₃	1	2	yes	—
518	C₄×D₄	C₂³×C₅₃	1	4	yes	—
519	C₄×D₄	C₂³×C₅₃	1	4	yes	—
520	C₄×D₄	C₂³×C₅₃	1	2	yes	—
521	C₄×D₄	C₂³×C₅₃	1	4	yes	—
522	#117	—	2	1	no	—
523	#117	—	2	2	no	—
524	#117	C₂³×C₅₃	1	2	yes	—
525	#117	C₂³×C₅₃	1	2	yes	—
526	C₂×C₄⋊C₄	—	2	4	no	—
527	C₂×C₄⋊C₄	—	2	2	no	—
528	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
532	#107	C₂³×C₅₃	1	4	yes	—
533	#107	C₂³×C₅₃	1	2	yes	—
534	#107	C₂³×C₅₃	1	2	yes	—
535	#107	C₂³×C₅₃	1	4	yes	—
536	#107	C₂³×C₅₃	1	4	yes	—
537	#106	C₂³×C₅₃	1	4	yes	—
538	#106	C₂³×C₅₃	1	4	yes	—
539	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
540	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
541	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
542	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
543	#103	C₂³×C₅₃	1	4	yes	—
544	#103	C₂³×C₅₃	1	4	yes	—
545	#103	C₂³×C₅₃	1	4	yes	—
546	#102	C₂³×C₅₃	1	2	yes	—
547	#102	C₂³×C₅₃	1	2	yes	—
548	#102	C₂³×C₅₃	1	4	yes	—
549	#102	C₂³×C₅₃	1	2	yes	—
550	#102	C₂³×C₅₃	1	2	yes	—
551	#102	C₂³×C₅₃	1	4	yes	—
552	#102	C₂³×C₅₃	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
555	#97	C₂³×C₅₃	1	2	yes	—
556	#97	C₂³×C₅₃	1	4	yes	—
557	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₅₃	1	4	yes	—
560	C₂⁴	—	2	1	no	—
561	#41	—	8	2	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	8	4	no	—
569	C₂×Q₈	—	8	4	no	—
570	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
571	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
572	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
579	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	8	2	no	—
588	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
591	SD₁₆	—	2	8	no	—
592	D₈	—	2	4	no	—
593	D₈	—	2	4	no	—
594	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
595	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
596	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
615	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
616	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
619	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
641	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
642	C₄²	C₂⁴×C₅₃	1	4	yes	—
643	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
644	C₂³	—	2	4	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	8	1	no	—
648	C₂³	—	8	1	no	—
649	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
650	Q₈	—	2	4	no	—
651	Q₈	—	2	4	no	—
652	Q₈	—	4	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	8	1	no	—
656	Q₈	—	8	4	no	—
657	Q₈	—	8	4	no	—
658	Q₈	—	8	1	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	8	1	no	—
665	D₄	—	8	2	no	—
666	D₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	—	8	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
686	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
689	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
690	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	2	no	—
693	C₈	—	2	4	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	4	no	—
704	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	4	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	C₅₃×#576	1	2	yes	—
718	C₄	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
719	C₂	—	4	1	no	—
720	C₂	—	4	4	no	—
721	C₂	—	8	2	no	—
722	C₂	C₅₃×#3486	1	1	yes	characteristic
723	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
724	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3100	C₂
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×#3550	C₂	semidirect
2. C₅₃×#3501	C₂	semidirect
3. C₅₃×#3385	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. Q₈×D₈×C₅₃	C₂	semidirect
6. C₅₃×#3370	C₂	semidirect
7. C₅₃×#3367	C₂	semidirect
8. C₅₃×#3360	C₂	semidirect
9. C₅₃×#3243	C₂	semidirect
10. C₅₃×#3235	C₂	semidirect
11. C₅₃×#3231	C₂	semidirect
12. C₅₃×#3118	C₂	semidirect
13. C₅₃×#3110	C₂	semidirect
15. C₅₃×#2985	C₂	semidirect
17. C₅₃×#559	C₂²	semidirect
18. Q₈²×C₅₃	C₂²	semidirect
20. C₅₃×#556	C₂²	semidirect
28. D₄×Q₈×C₅₃	C₂²	semidirect
41. C₅₃×#501	C₂²	semidirect
42. C₅₃×#501	C₂²	semidirect
43. C₅₃×#500	C₂²	semidirect
44. C₅₃×#500	C₂²	semidirect
45. C₅₃×#498	C₂²	semidirect
46. C₅₃×#490	C₂²	semidirect
47. C₅₃×#489	C₂²	semidirect
48. C₅₃×#488	C₂²	semidirect
49. C₅₃×#487	C₂²	semidirect
50. C₅₃×#487	C₂²	semidirect
55. C₅₃×#479	C₂²	semidirect
56. C₅₃×#479	C₂²	semidirect
57. C₅₃×#478	C₂²	semidirect
58. C₅₃×#477	C₂²	semidirect
60. C₅₃×#476	C₂²	semidirect
64. C₅₃×#474	C₂²	semidirect
65. C₅₃×#474	C₂²	semidirect
72. C₅₃×#446	C₂²	semidirect
73. C₅₃×#446	C₂²	semidirect
74. C₈×Q₈×C₅₃	C₂²	semidirect
331. #61849	C₅₃	direct (N × H)
357. #3550	C₂×C₅₃	semidirect
358. #3501	C₂×C₅₃	semidirect
359. #3385	C₂×C₅₃	semidirect
360. #3384	C₂×C₅₃	semidirect
361. Q₈×D₈	C₂×C₅₃	semidirect
362. #3370	C₂×C₅₃	semidirect
363. #3367	C₂×C₅₃	semidirect
364. #3360	C₂×C₅₃	semidirect
365. #3243	C₂×C₅₃	semidirect
366. #3235	C₂×C₅₃	semidirect
367. #3231	C₂×C₅₃	semidirect
368. #3118	C₂×C₅₃	semidirect
369. #3110	C₂×C₅₃	semidirect
371. #2985	C₂×C₅₃	semidirect
379. #559	C₂²×C₅₃	semidirect
380. Q₈²	C₂²×C₅₃	semidirect
382. #556	C₂²×C₅₃	semidirect
390. D₄×Q₈	C₂²×C₅₃	semidirect
403. #501	C₂²×C₅₃	semidirect
404. #501	C₂²×C₅₃	semidirect
405. #500	C₂²×C₅₃	semidirect
406. #500	C₂²×C₅₃	semidirect
407. #498	C₂²×C₅₃	semidirect
408. #490	C₂²×C₅₃	semidirect
409. #489	C₂²×C₅₃	semidirect
410. #488	C₂²×C₅₃	semidirect
411. #487	C₂²×C₅₃	semidirect
412. #487	C₂²×C₅₃	semidirect
417. #479	C₂²×C₅₃	semidirect
418. #479	C₂²×C₅₃	semidirect
419. #478	C₂²×C₅₃	semidirect
420. #477	C₂²×C₅₃	semidirect
422. #476	C₂²×C₅₃	semidirect
426. #474	C₂²×C₅₃	semidirect
427. #474	C₂²×C₅₃	semidirect
434. #446	C₂²×C₅₃	semidirect
435. #446	C₂²×C₅₃	semidirect
436. C₈×Q₈	C₂²×C₅₃	semidirect
447. C₅₃	#61849	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×#3550	2
C₅₃×#3501	2
C₅₃×#3385	2
C₅₃×#3384	2
Q₈×D₈×C₅₃	2
C₅₃×#3370	2
C₅₃×#3367	2
C₅₃×#3360	2
C₅₃×#3243	2
C₅₃×#3235	2
C₅₃×#3231	2
C₅₃×#3118	2
C₅₃×#3110	2
C₅₃×#3100	2
C₅₃×#2985	2
#61849	53

Subgroups — C53×#61849 #27269361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61849 #27269361