Subgroups — SD₁₆×#41×C₅₃ #27268938

Order 13568.

2116 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3335	C₂	1	3	yes	maximal, complemented
8	C₅₃×#3298	C₂	1	3	yes	maximal, complemented
9	C₅₃×#3295	C₂	1	3	yes	maximal, complemented
10	D₄×SD₁₆×C₅₃	C₂	1	3	yes	maximal, complemented
11	C₅₃×#3167	C₂	1	3	yes	maximal, complemented
12	C₅₃×#3103	C₂	1	3	yes	maximal, complemented
13	C₅₃×#3101	C₂	1	3	yes	maximal, complemented
14	C₈×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×SD₁₆×C₅₃	C₂	1	3	yes	maximal, complemented
16	C₂²×#41×C₅₃	—	2	1	no	—
17	C₂²×SD₁₆×C₅₃	C₂²	1	3	yes	—
18	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₅₃×#557	—	2	1	no	—
20	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
21	C₅₃×#554	—	2	3	no	—
22	C₅₃×#554	C₂²	1	3	yes	complemented
23	C₅₃×#550	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
25	D₄×Q₈×C₅₃	C₂²	1	3	yes	complemented
26	C₅₃×#548	—	2	1	no	—
27	C₅₃×#547	C₂²	1	3	yes	—
28	C₅₃×#546	—	2	3	no	—
29	D₄²×C₅₃	C₂²	1	3	yes	—
30	C₅₃×#533	—	2	3	no	—
31	C₅₃×#533	C₂²	1	3	yes	complemented
32	C₅₃×#532	C₂²	1	3	yes	—
33	C₅₃×#525	—	2	3	no	—
34	C₄×#41×C₅₃	—	2	1	no	—
35	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₅₃	C₂²	1	3	yes	complemented
37	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	—
38	C₅₃×#498	C₂²	1	3	yes	complemented
39	C₅₃×#492	C₂²	1	3	yes	complemented
40	C₅₃×#487	C₂²	1	3	yes	complemented
41	C₅₃×#486	C₂²	1	3	yes	complemented
42	C₅₃×#483	C₂²	1	6	yes	complemented
43	C₅₃×#481	C₂²	1	6	yes	complemented
44	C₅₃×#476	C₂²	1	3	yes	—
45	C₅₃×#476	C₂²	1	3	yes	complemented
46	C₅₃×#475	C₂²	1	3	yes	complemented
47	C₅₃×#475	C₂²	1	3	yes	complemented
48	C₅₃×#465	C₂²	1	6	yes	complemented
49	C₅₃×#465	C₂²	1	6	yes	complemented
50	C₅₃×#461	C₂²	1	3	yes	—
51	C₅₃×#461	C₂²	1	3	yes	complemented
52	C₅₃×#460	C₂²	1	3	yes	complemented
53	C₅₃×#460	C₂²	1	3	yes	complemented
54	C₅₃×#450	C₂²	1	6	yes	—
55	C₅₃×#448	C₂²	1	6	yes	complemented
56	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
59	C₄×SD₁₆×C₅₃	C₂²	1	3	yes	—
60	C₄×SD₁₆×C₅₃	C₂²	1	3	yes	—
61	C₄×SD₁₆×C₅₃	C₂²	1	3	yes	—
62	C₄×SD₁₆×C₅₃	C₂²	1	3	yes	complemented
63	C₄×SD₁₆×C₅₃	C₂²	1	3	yes	complemented
64	C₄×SD₁₆×C₅₃	C₂²	1	3	yes	complemented
65	C₄×SD₁₆×C₅₃	C₂²	1	3	yes	complemented
66	C₄×SD₁₆×C₅₃	C₂²	1	6	yes	complemented
67	C₈×D₄×C₅₃	C₂²	1	3	yes	complemented
68	C₈×D₄×C₅₃	C₂²	1	3	yes	complemented
69	C₅₃×#431	C₂²	1	3	yes	complemented
70	C₂×#106×C₅₃	C₂²	1	3	yes	complemented
71	C₂×#103×C₅₃	C₂²	1	3	yes	complemented
72	C₂×#102×C₅₃	C₂²	1	3	yes	—
73	C₂×C₄×C₈×C₅₃	C₂²	1	3	yes	complemented
74	C₂×#41×C₅₃	—	2	1	no	—
75	C₂×#41×C₅₃	—	2	3	no	—
76	C₂×#41×C₅₃	—	2	3	no	—
77	C₂×#41×C₅₃	—	4	8	no	—
78	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₅₃	—	2	1	no	—
80	C₂²×Q₈×C₅₃	C₂³	1	3	yes	—
81	C₂²×D₄×C₅₃	—	2	3	no	—
82	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
83	C₂³×C₄×C₅₃	—	2	3	no	—
84	C₂×SD₁₆×C₅₃	—	2	12	no	—
85	C₂×SD₁₆×C₅₃	C₂³	1	3	yes	—
86	C₂×SD₁₆×C₅₃	C₂³	1	3	yes	—
87	C₂×SD₁₆×C₅₃	C₂³	1	3	yes	—
88	C₂×SD₁₆×C₅₃	C₂³	1	6	yes	—
89	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₅₃	C₂³	1	3	yes	—
91	C₂²×C₈×C₅₃	C₂³	1	3	yes	—
92	C₄⋊Q₈×C₅₃	—	2	3	no	—
93	C₄⋊Q₈×C₅₃	—	2	3	no	—
94	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
95	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
96	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
97	#127×C₅₃	C₂³	1	3	yes	—
98	#125×C₅₃	—	2	3	no	—
99	#125×C₅₃	—	2	3	no	—
100	#125×C₅₃	—	2	3	no	—
101	#124×C₅₃	—	2	3	no	—
102	#123×C₅₃	—	2	6	no	—
103	C₂²⋊Q₈×C₅₃	—	2	3	no	—
104	C₂²⋊Q₈×C₅₃	—	2	3	no	—
105	C₂²⋊Q₈×C₅₃	—	2	6	no	—
106	C₂²⋊Q₈×C₅₃	—	2	6	no	—
107	C₂²⋊Q₈×C₅₃	—	2	3	no	—
108	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
109	#121×C₅₃	—	2	3	no	—
110	#121×C₅₃	—	2	3	no	—
111	#121×C₅₃	—	2	3	no	—
112	#121×C₅₃	C₂³	1	6	yes	—
113	#120×C₅₃	—	2	6	no	—
114	C₄×Q₈×C₅₃	—	2	3	no	—
115	C₄×Q₈×C₅₃	—	2	3	no	—
116	C₄×Q₈×C₅₃	—	2	3	no	—
117	C₄×Q₈×C₅₃	—	2	1	no	—
118	C₄×Q₈×C₅₃	—	2	1	no	—
119	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
122	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
123	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
124	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
125	C₄×D₄×C₅₃	—	2	3	no	—
126	C₄×D₄×C₅₃	—	2	3	no	—
127	C₄×D₄×C₅₃	—	2	3	no	—
128	C₄×D₄×C₅₃	—	2	3	no	—
129	C₄×D₄×C₅₃	—	2	3	no	—
130	C₄×D₄×C₅₃	D₄	1	3	yes	—
131	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₅₃	C₂³	1	3	yes	—
133	C₄×D₄×C₅₃	C₂³	1	3	yes	—
134	C₄×D₄×C₅₃	C₂³	1	3	yes	—
135	C₄×D₄×C₅₃	C₂³	1	3	yes	—
136	#117×C₅₃	—	2	3	no	—
137	#117×C₅₃	D₄	1	3	yes	—
138	C₂×C₄⋊C₄×C₅₃	—	2	3	no	—
139	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
140	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
141	C₂×C₂²⋊C₄×C₅₃	—	2	3	no	—
142	C₂×C₄²×C₅₃	—	2	3	no	—
143	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
144	#106×C₅₃	C₂³	1	3	yes	—
145	#106×C₅₃	C₂³	1	6	yes	—
146	#106×C₅₃	C₂³	1	1	yes	characteristic
147	#106×C₅₃	C₂³	1	3	yes	—
148	#106×C₅₃	C₂³	1	3	yes	—
149	C₄⋊C₈×C₅₃	C₂³	1	3	yes	—
150	C₄⋊C₈×C₅₃	C₂³	1	3	yes	—
151	#103×C₅₃	C₂³	1	3	yes	—
152	#103×C₅₃	C₂³	1	6	yes	—
153	#103×C₅₃	C₂³	1	1	yes	characteristic
154	#103×C₅₃	C₂³	1	3	yes	—
155	#103×C₅₃	C₂³	1	3	yes	—
156	#102×C₅₃	C₂³	1	3	yes	—
157	#102×C₅₃	C₂³	1	6	yes	—
158	#102×C₅₃	C₂³	1	1	yes	characteristic
159	#102×C₅₃	C₂³	1	3	yes	—
160	#102×C₅₃	C₂³	1	3	yes	—
161	C₂²⋊C₈×C₅₃	C₂³	1	6	yes	—
162	C₄×C₈×C₅₃	C₂³	1	3	yes	—
163	C₄×C₈×C₅₃	C₂³	1	3	yes	—
164	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄×C₈×C₅₃	C₂³	1	3	yes	—
166	C₂⁴×C₅₃	—	2	3	no	—
167	#41×C₅₃	—	4	4	no	—
168	#41×C₅₃	—	4	12	no	—
169	#41×C₅₃	—	4	12	no	—
170	#41×C₅₃	SD₁₆	1	8	yes	direct product factor
171	C₂×Q₈×C₅₃	—	2	3	no	—
172	C₂×Q₈×C₅₃	—	2	3	no	—
173	C₂×Q₈×C₅₃	—	2	3	no	—
174	C₂×Q₈×C₅₃	—	2	6	no	—
175	C₂×Q₈×C₅₃	—	4	3	no	—
176	C₂×Q₈×C₅₃	—	4	4	no	—
177	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
179	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
180	C₂×D₄×C₅₃	—	2	6	no	—
181	C₂×D₄×C₅₃	—	2	6	no	—
182	C₂×D₄×C₅₃	—	2	3	no	—
183	C₂×D₄×C₅₃	—	2	3	no	—
184	C₂×D₄×C₅₃	—	2	3	no	—
185	C₂×D₄×C₅₃	—	4	3	no	—
186	C₂×D₄×C₅₃	—	4	12	no	—
187	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
188	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
189	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₅₃	—	2	3	no	—
191	C₂²×C₄×C₅₃	—	2	3	no	—
192	C₂²×C₄×C₅₃	—	2	3	no	—
193	C₂²×C₄×C₅₃	—	2	3	no	—
194	C₂²×C₄×C₅₃	—	2	3	no	—
195	C₂²×C₄×C₅₃	—	2	1	no	—
196	C₂²×C₄×C₅₃	—	2	3	no	—
197	C₂²×C₄×C₅₃	—	4	12	no	—
198	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
199	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
200	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
201	SD₁₆×C₅₃	—	2	6	no	—
202	SD₁₆×C₅₃	—	2	6	no	—
203	SD₁₆×C₅₃	—	2	6	no	—
204	SD₁₆×C₅₃	—	4	6	no	—
205	SD₁₆×C₅₃	#41	1	4	yes	direct product factor
206	C₂×C₈×C₅₃	—	2	6	no	—
207	C₂×C₈×C₅₃	—	4	3	no	—
208	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
209	C₂×C₈×C₅₃	C₂⁴	1	3	yes	—
210	C₂×C₈×C₅₃	C₂⁴	1	3	yes	—
211	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₅₃	—	2	1	no	—
213	C₄⋊C₄×C₅₃	—	2	3	no	—
214	C₄⋊C₄×C₅₃	—	2	3	no	—
215	C₄⋊C₄×C₅₃	—	2	3	no	—
216	C₄⋊C₄×C₅₃	—	2	3	no	—
217	C₄⋊C₄×C₅₃	—	2	3	no	—
218	C₄⋊C₄×C₅₃	—	2	3	no	—
219	C₄⋊C₄×C₅₃	—	2	3	no	—
220	C₄⋊C₄×C₅₃	—	2	3	no	—
221	C₄⋊C₄×C₅₃	—	2	3	no	—
222	C₄⋊C₄×C₅₃	—	2	6	no	—
223	C₄⋊C₄×C₅₃	C₂×D₄	1	3	yes	—
224	C₄⋊C₄×C₅₃	C₂×D₄	1	3	yes	—
225	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
227	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
229	C₂²⋊C₄×C₅₃	—	2	6	no	—
230	C₂²⋊C₄×C₅₃	—	2	1	no	—
231	C₂²⋊C₄×C₅₃	—	2	3	no	—
232	C₂²⋊C₄×C₅₃	—	2	3	no	—
233	C₂²⋊C₄×C₅₃	—	2	3	no	—
234	C₂²⋊C₄×C₅₃	—	2	6	no	—
235	C₂²⋊C₄×C₅₃	C₂×D₄	1	6	yes	—
236	C₄²×C₅₃	—	2	3	no	—
237	C₄²×C₅₃	—	2	3	no	—
238	C₄²×C₅₃	—	2	1	no	—
239	C₄²×C₅₃	—	2	3	no	—
240	C₄²×C₅₃	C₂×D₄	1	3	yes	—
241	C₄²×C₅₃	C₂×D₄	1	3	yes	—
242	C₄²×C₅₃	C₂⁴	1	3	yes	—
243	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₂³×C₅₃	—	2	1	no	—
245	C₂³×C₅₃	—	2	3	no	—
246	C₂³×C₅₃	—	4	6	no	—
247	C₂³×C₅₃	—	4	6	no	—
248	C₂³×C₅₃	—	8	3	no	—
249	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
250	Q₈×C₅₃	—	2	1	no	—
251	Q₈×C₅₃	—	2	3	no	—
252	Q₈×C₅₃	—	2	3	no	—
253	Q₈×C₅₃	—	4	6	no	—
254	Q₈×C₅₃	—	4	6	no	—
255	Q₈×C₅₃	—	8	3	no	—
256	Q₈×C₅₃	C₂×SD₁₆	1	4	yes	complemented
257	Q₈×C₅₃	C₂×#41	1	2	yes	complemented
258	D₄×C₅₃	—	2	3	no	—
259	D₄×C₅₃	—	2	1	no	—
260	D₄×C₅₃	—	2	3	no	—
261	D₄×C₅₃	—	4	6	no	—
262	D₄×C₅₃	—	4	12	no	—
263	D₄×C₅₃	—	4	6	no	—
264	D₄×C₅₃	—	8	3	no	—
265	D₄×C₅₃	C₂×SD₁₆	1	12	yes	complemented
266	D₄×C₅₃	C₂×#41	1	2	yes	—
267	C₂×C₄×C₅₃	—	2	1	no	—
268	C₂×C₄×C₅₃	—	2	3	no	—
269	C₂×C₄×C₅₃	—	2	3	no	—
270	C₂×C₄×C₅₃	—	2	1	no	—
271	C₂×C₄×C₅₃	—	2	3	no	—
272	C₂×C₄×C₅₃	—	2	1	no	—
273	C₂×C₄×C₅₃	—	2	3	no	—
274	C₂×C₄×C₅₃	—	2	3	no	—
275	C₂×C₄×C₅₃	—	4	3	no	—
276	C₂×C₄×C₅₃	—	4	6	no	—
277	C₂×C₄×C₅₃	—	4	6	no	—
278	C₂×C₄×C₅₃	—	4	2	no	—
279	C₂×C₄×C₅₃	—	4	6	no	—
280	C₂×C₄×C₅₃	—	4	6	no	—
281	C₂×C₄×C₅₃	—	4	6	no	—
282	C₂×C₄×C₅₃	—	8	3	no	—
283	C₂×C₄×C₅₃	C₂×SD₁₆	1	12	yes	complemented
284	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
286	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
287	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
288	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
290	C₈×C₅₃	—	2	3	no	—
291	C₈×C₅₃	—	2	1	no	—
292	C₈×C₅₃	—	2	3	no	—
293	C₈×C₅₃	C₂×#41	1	2	yes	complemented
294	SD₁₆×#41	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂²×C₅₃	—	2	3	no	—
296	C₂²×C₅₃	—	2	3	no	—
297	C₂²×C₅₃	—	2	2	no	—
298	C₂²×C₅₃	—	4	1	no	—
299	C₂²×C₅₃	—	4	1	no	—
300	C₂²×C₅₃	—	4	3	no	—
301	C₂²×C₅₃	—	4	3	no	—
302	C₂²×C₅₃	—	4	3	no	—
303	C₂²×C₅₃	—	8	12	no	—
304	C₂²×C₅₃	C₂²×SD₁₆	1	6	yes	—
305	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
306	C₄×C₅₃	—	2	1	no	—
307	C₄×C₅₃	—	2	3	no	—
308	C₄×C₅₃	—	2	3	no	—
309	C₄×C₅₃	—	2	2	no	—
310	C₄×C₅₃	—	4	1	no	—
311	C₄×C₅₃	—	4	3	no	—
312	C₄×C₅₃	—	4	3	no	—
313	C₄×C₅₃	—	4	1	no	—
314	C₄×C₅₃	—	4	3	no	—
315	C₄×C₅₃	C₂²×SD₁₆	1	2	yes	—
316	C₄×C₅₃	C₂²×SD₁₆	1	6	yes	—
317	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
318	C₄×C₅₃	#585	1	1	yes	characteristic
319	Q₈×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
320	D₄×#41	C₂×C₅₃	1	1	yes	characteristic
321	#3392	C₂×C₅₃	1	1	yes	characteristic, complemented
322	Q₈×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
323	#3362	C₂×C₅₃	1	1	yes	characteristic, complemented
324	#3359	C₂×C₅₃	1	1	yes	characteristic, complemented
325	#3335	C₂×C₅₃	1	3	yes	complemented
326	#3298	C₂×C₅₃	1	3	yes	complemented
327	#3295	C₂×C₅₃	1	3	yes	complemented
328	D₄×SD₁₆	C₂×C₅₃	1	3	yes	complemented
329	#3167	C₂×C₅₃	1	3	yes	complemented
330	#3103	C₂×C₅₃	1	3	yes	complemented
331	#3101	C₂×C₅₃	1	3	yes	complemented
332	C₈×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
333	C₂×C₄×SD₁₆	C₂×C₅₃	1	3	yes	complemented
334	C₂×C₅₃	—	2	6	no	—
335	C₂×C₅₃	—	4	2	no	—
336	C₂×C₅₃	—	8	3	no	—
337	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
338	C₂×C₅₃	C₂³×SD₁₆	1	1	yes	characteristic
339	C₂×C₅₃	#3584	1	1	yes	characteristic
340	C₂²×#41	—	2	1	no	—
341	C₂²×SD₁₆	C₂²×C₅₃	1	3	yes	—
342	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
343	#557	—	2	1	no	—
344	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
345	#554	—	2	3	no	—
346	#554	C₂²×C₅₃	1	3	yes	complemented
347	#550	C₂²×C₅₃	1	1	yes	characteristic
348	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
349	D₄×Q₈	C₂²×C₅₃	1	3	yes	complemented
350	#548	—	2	1	no	—
351	#547	C₂²×C₅₃	1	3	yes	—
352	#546	—	2	3	no	—
353	D₄²	C₂²×C₅₃	1	3	yes	—
354	#533	—	2	3	no	—
355	#533	C₂²×C₅₃	1	3	yes	complemented
356	#532	C₂²×C₅₃	1	3	yes	—
357	#525	—	2	3	no	—
358	C₄×#41	—	2	1	no	—
359	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₅₃	1	3	yes	complemented
361	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	—
362	#498	C₂²×C₅₃	1	3	yes	complemented
363	#492	C₂²×C₅₃	1	3	yes	complemented
364	#487	C₂²×C₅₃	1	3	yes	complemented
365	#486	C₂²×C₅₃	1	3	yes	complemented
366	#483	C₂²×C₅₃	1	6	yes	complemented
367	#481	C₂²×C₅₃	1	6	yes	complemented
368	#476	C₂²×C₅₃	1	3	yes	—
369	#476	C₂²×C₅₃	1	3	yes	complemented
370	#475	C₂²×C₅₃	1	3	yes	complemented
371	#475	C₂²×C₅₃	1	3	yes	complemented
372	#465	C₂²×C₅₃	1	6	yes	complemented
373	#465	C₂²×C₅₃	1	6	yes	complemented
374	#461	C₂²×C₅₃	1	3	yes	—
375	#461	C₂²×C₅₃	1	3	yes	complemented
376	#460	C₂²×C₅₃	1	3	yes	complemented
377	#460	C₂²×C₅₃	1	3	yes	complemented
378	#450	C₂²×C₅₃	1	6	yes	—
379	#448	C₂²×C₅₃	1	6	yes	complemented
380	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
381	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
382	C₄×SD₁₆	C₂²×C₅₃	1	3	yes	—
383	C₄×SD₁₆	C₂²×C₅₃	1	3	yes	—
384	C₄×SD₁₆	C₂²×C₅₃	1	3	yes	—
385	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
386	C₄×SD₁₆	C₂²×C₅₃	1	3	yes	complemented
387	C₄×SD₁₆	C₂²×C₅₃	1	6	yes	complemented
388	C₄×SD₁₆	C₂²×C₅₃	1	3	yes	complemented
389	C₄×SD₁₆	C₂²×C₅₃	1	3	yes	complemented
390	C₄×SD₁₆	C₂²×C₅₃	1	3	yes	complemented
391	C₈×D₄	C₂²×C₅₃	1	3	yes	complemented
392	C₈×D₄	C₂²×C₅₃	1	3	yes	complemented
393	#431	C₂²×C₅₃	1	3	yes	complemented
394	C₂×#106	C₂²×C₅₃	1	3	yes	complemented
395	C₂×#103	C₂²×C₅₃	1	3	yes	complemented
396	C₂×#102	C₂²×C₅₃	1	3	yes	—
397	C₂×C₄×C₈	C₂²×C₅₃	1	3	yes	complemented
398	C₅₃	SD₁₆×#41	1	1	yes	characteristic, direct product factor, Sylow
399	C₂×#41	—	2	1	no	—
400	C₂×#41	—	2	3	no	—
401	C₂×#41	—	2	3	no	—
402	C₂×#41	—	4	8	no	—
403	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×Q₈	C₂³×C₅₃	1	3	yes	—
406	C₂²×D₄	—	2	3	no	—
407	C₂²×D₄	C₂³×C₅₃	1	3	yes	—
408	C₂³×C₄	—	2	3	no	—
409	C₂×SD₁₆	—	2	12	no	—
410	C₂×SD₁₆	C₂³×C₅₃	1	3	yes	—
411	C₂×SD₁₆	C₂³×C₅₃	1	3	yes	—
412	C₂×SD₁₆	C₂³×C₅₃	1	3	yes	—
413	C₂×SD₁₆	C₂³×C₅₃	1	6	yes	—
414	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₅₃	1	3	yes	—
416	C₂²×C₈	C₂³×C₅₃	1	3	yes	—
417	C₄⋊Q₈	—	2	3	no	—
418	C₄⋊Q₈	—	2	3	no	—
419	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
420	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
421	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
422	#127	C₂³×C₅₃	1	3	yes	—
423	#125	—	2	3	no	—
424	#125	—	2	3	no	—
425	#125	—	2	3	no	—
426	#124	—	2	3	no	—
427	#123	—	2	6	no	—
428	C₂²⋊Q₈	—	2	3	no	—
429	C₂²⋊Q₈	—	2	3	no	—
430	C₂²⋊Q₈	—	2	3	no	—
431	C₂²⋊Q₈	—	2	6	no	—
432	C₂²⋊Q₈	—	2	6	no	—
433	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
434	#121	—	2	3	no	—
435	#121	—	2	3	no	—
436	#121	—	2	3	no	—
437	#121	C₂³×C₅₃	1	6	yes	—
438	#120	—	2	6	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×Q₈	—	2	1	no	—
441	C₄×Q₈	—	2	3	no	—
442	C₄×Q₈	—	2	3	no	—
443	C₄×Q₈	—	2	3	no	—
444	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
445	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
446	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
447	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
448	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
449	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
450	C₄×D₄	—	2	3	no	—
451	C₄×D₄	—	2	3	no	—
452	C₄×D₄	—	2	3	no	—
453	C₄×D₄	—	2	3	no	—
454	C₄×D₄	—	2	3	no	—
455	C₄×D₄	D₄×C₅₃	1	3	yes	—
456	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
457	C₄×D₄	C₂³×C₅₃	1	3	yes	—
458	C₄×D₄	C₂³×C₅₃	1	3	yes	—
459	C₄×D₄	C₂³×C₅₃	1	3	yes	—
460	C₄×D₄	C₂³×C₅₃	1	3	yes	—
461	#117	—	2	3	no	—
462	#117	D₄×C₅₃	1	3	yes	—
463	C₂×C₄⋊C₄	—	2	3	no	—
464	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
465	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
466	C₂×C₂²⋊C₄	—	2	3	no	—
467	C₂×C₄²	—	2	3	no	—
468	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
469	#106	C₂³×C₅₃	1	1	yes	characteristic
470	#106	C₂³×C₅₃	1	3	yes	—
471	#106	C₂³×C₅₃	1	3	yes	—
472	#106	C₂³×C₅₃	1	3	yes	—
473	#106	C₂³×C₅₃	1	6	yes	—
474	C₄⋊C₈	C₂³×C₅₃	1	3	yes	—
475	C₄⋊C₈	C₂³×C₅₃	1	3	yes	—
476	#103	C₂³×C₅₃	1	1	yes	characteristic
477	#103	C₂³×C₅₃	1	3	yes	—
478	#103	C₂³×C₅₃	1	3	yes	—
479	#103	C₂³×C₅₃	1	3	yes	—
480	#103	C₂³×C₅₃	1	6	yes	—
481	#102	C₂³×C₅₃	1	1	yes	characteristic
482	#102	C₂³×C₅₃	1	3	yes	—
483	#102	C₂³×C₅₃	1	3	yes	—
484	#102	C₂³×C₅₃	1	3	yes	—
485	#102	C₂³×C₅₃	1	6	yes	—
486	C₂²⋊C₈	C₂³×C₅₃	1	6	yes	—
487	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
488	C₄×C₈	C₂³×C₅₃	1	3	yes	—
489	C₄×C₈	C₂³×C₅₃	1	3	yes	—
490	C₄×C₈	C₂³×C₅₃	1	3	yes	—
491	C₂⁴	—	2	3	no	—
492	#41	—	4	4	no	—
493	#41	—	4	12	no	—
494	#41	—	4	12	no	—
495	#41	SD₁₆×C₅₃	1	8	yes	direct product factor
496	C₂×Q₈	—	2	3	no	—
497	C₂×Q₈	—	2	3	no	—
498	C₂×Q₈	—	2	3	no	—
499	C₂×Q₈	—	2	6	no	—
500	C₂×Q₈	—	4	3	no	—
501	C₂×Q₈	—	4	4	no	—
502	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
503	C₂×Q₈	C₂⁴×C₅₃	1	3	yes	—
504	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
505	C₂×D₄	—	2	6	no	—
506	C₂×D₄	—	2	6	no	—
507	C₂×D₄	—	2	3	no	—
508	C₂×D₄	—	2	3	no	—
509	C₂×D₄	—	2	3	no	—
510	C₂×D₄	—	4	3	no	—
511	C₂×D₄	—	4	12	no	—
512	C₂×D₄	C₂×D₄×C₅₃	1	3	yes	—
513	C₂×D₄	C₂⁴×C₅₃	1	3	yes	—
514	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
515	C₂²×C₄	—	2	3	no	—
516	C₂²×C₄	—	2	3	no	—
517	C₂²×C₄	—	2	3	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	3	no	—
520	C₂²×C₄	—	2	3	no	—
521	C₂²×C₄	—	2	3	no	—
522	C₂²×C₄	—	4	12	no	—
523	C₂²×C₄	C₂×D₄×C₅₃	1	3	yes	—
524	C₂²×C₄	C₂×D₄×C₅₃	1	3	yes	—
525	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
526	SD₁₆	—	2	6	no	—
527	SD₁₆	—	2	6	no	—
528	SD₁₆	—	2	6	no	—
529	SD₁₆	—	4	6	no	—
530	SD₁₆	#41×C₅₃	1	4	yes	direct product factor
531	C₂×C₈	—	2	6	no	—
532	C₂×C₈	—	4	3	no	—
533	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
534	C₂×C₈	C₂⁴×C₅₃	1	3	yes	—
535	C₂×C₈	C₂⁴×C₅₃	1	3	yes	—
536	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	3	no	—
539	C₄⋊C₄	—	2	3	no	—
540	C₄⋊C₄	—	2	3	no	—
541	C₄⋊C₄	—	2	3	no	—
542	C₄⋊C₄	—	2	3	no	—
543	C₄⋊C₄	—	2	3	no	—
544	C₄⋊C₄	—	2	3	no	—
545	C₄⋊C₄	—	2	3	no	—
546	C₄⋊C₄	—	2	3	no	—
547	C₄⋊C₄	—	2	6	no	—
548	C₄⋊C₄	C₂×D₄×C₅₃	1	3	yes	—
549	C₄⋊C₄	C₂×D₄×C₅₃	1	3	yes	—
550	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
551	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
552	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
553	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
554	C₂²⋊C₄	—	2	6	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	3	no	—
557	C₂²⋊C₄	—	2	3	no	—
558	C₂²⋊C₄	—	2	3	no	—
559	C₂²⋊C₄	—	2	6	no	—
560	C₂²⋊C₄	C₂×D₄×C₅₃	1	6	yes	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	3	no	—
563	C₄²	—	2	3	no	—
564	C₄²	—	2	3	no	—
565	C₄²	C₂×D₄×C₅₃	1	3	yes	—
566	C₄²	C₂×D₄×C₅₃	1	3	yes	—
567	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
568	C₄²	C₂⁴×C₅₃	1	3	yes	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	3	no	—
571	C₂³	—	4	6	no	—
572	C₂³	—	4	6	no	—
573	C₂³	—	8	3	no	—
574	C₂³	C₂²×D₄×C₅₃	1	3	yes	—
575	Q₈	—	2	1	no	—
576	Q₈	—	2	3	no	—
577	Q₈	—	2	3	no	—
578	Q₈	—	4	6	no	—
579	Q₈	—	4	6	no	—
580	Q₈	—	8	3	no	—
581	Q₈	C₂×SD₁₆×C₅₃	1	4	yes	complemented
582	Q₈	C₂×#41×C₅₃	1	2	yes	complemented
583	D₄	—	2	3	no	—
584	D₄	—	2	1	no	—
585	D₄	—	2	3	no	—
586	D₄	—	4	6	no	—
587	D₄	—	4	12	no	—
588	D₄	—	4	6	no	—
589	D₄	—	8	3	no	—
590	D₄	C₂×SD₁₆×C₅₃	1	12	yes	complemented
591	D₄	C₂×#41×C₅₃	1	2	yes	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	3	no	—
594	C₂×C₄	—	2	3	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	3	no	—
597	C₂×C₄	—	2	3	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	3	no	—
600	C₂×C₄	—	4	3	no	—
601	C₂×C₄	—	4	6	no	—
602	C₂×C₄	—	4	6	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	6	no	—
605	C₂×C₄	—	4	6	no	—
606	C₂×C₄	—	4	6	no	—
607	C₂×C₄	—	8	3	no	—
608	C₂×C₄	C₂×SD₁₆×C₅₃	1	12	yes	complemented
609	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₅₃	1	3	yes	—
611	C₂×C₄	C₂²×D₄×C₅₃	1	3	yes	—
612	C₂×C₄	C₂²×D₄×C₅₃	1	3	yes	—
613	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
614	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
615	C₈	—	2	3	no	—
616	C₈	—	2	1	no	—
617	C₈	—	2	3	no	—
618	C₈	C₂×#41×C₅₃	1	2	yes	complemented
619	C₂²	—	2	3	no	—
620	C₂²	—	2	3	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	3	no	—
625	C₂²	—	4	3	no	—
626	C₂²	—	4	3	no	—
627	C₂²	—	8	12	no	—
628	C₂²	C₂²×SD₁₆×C₅₃	1	6	yes	—
629	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
630	C₄	—	2	3	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	3	no	—
634	C₄	—	4	3	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	3	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	3	no	—
639	C₄	C₂²×SD₁₆×C₅₃	1	2	yes	—
640	C₄	C₂²×SD₁₆×C₅₃	1	6	yes	—
641	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
642	C₄	C₅₃×#585	1	1	yes	characteristic
643	C₂	—	2	6	no	—
644	C₂	—	4	2	no	—
645	C₂	—	8	3	no	—
646	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
647	C₂	C₂³×SD₁₆×C₅₃	1	1	yes	characteristic
648	C₂	C₅₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. Q₈×#41×C₅₃	C₂	semidirect
3. C₅₃×#3392	C₂	semidirect
4. Q₈×SD₁₆×C₅₃	C₂	semidirect
5. C₅₃×#3362	C₂	semidirect
6. C₅₃×#3359	C₂	semidirect
7. C₅₃×#3335	C₂	semidirect
8. C₅₃×#3298	C₂	semidirect
9. C₅₃×#3295	C₂	semidirect
10. D₄×SD₁₆×C₅₃	C₂	semidirect
11. C₅₃×#3167	C₂	semidirect
12. C₅₃×#3103	C₂	semidirect
13. C₅₃×#3101	C₂	semidirect
14. C₈×#41×C₅₃	C₂	semidirect
15. C₂×C₄×SD₁₆×C₅₃	C₂	semidirect
18. Q₈²×C₅₃	C₂²	semidirect
20. C₅₃×#557	C₂²	semidirect
22. C₅₃×#554	C₂²	semidirect
25. D₄×Q₈×C₅₃	C₂²	semidirect
31. C₅₃×#533	C₂²	semidirect
36. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
38. C₅₃×#498	C₂²	semidirect
39. C₅₃×#492	C₂²	semidirect
40. C₅₃×#487	C₂²	semidirect
41. C₅₃×#486	C₂²	semidirect
42. C₅₃×#483	C₂²	semidirect
43. C₅₃×#481	C₂²	semidirect
45. C₅₃×#476	C₂²	semidirect
46. C₅₃×#475	C₂²	semidirect
47. C₅₃×#475	C₂²	semidirect
48. C₅₃×#465	C₂²	semidirect
49. C₅₃×#465	C₂²	semidirect
51. C₅₃×#461	C₂²	semidirect
52. C₅₃×#460	C₂²	semidirect
53. C₅₃×#460	C₂²	semidirect
55. C₅₃×#448	C₂²	semidirect
56. C₈×Q₈×C₅₃	C₂²	semidirect
57. C₈×Q₈×C₅₃	C₂²	semidirect
62. C₄×SD₁₆×C₅₃	C₂²	semidirect
63. C₄×SD₁₆×C₅₃	C₂²	semidirect
64. C₄×SD₁₆×C₅₃	C₂²	semidirect
65. C₄×SD₁₆×C₅₃	C₂²	semidirect
66. C₄×SD₁₆×C₅₃	C₂²	semidirect
67. C₈×D₄×C₅₃	C₂²	semidirect
68. C₈×D₄×C₅₃	C₂²	semidirect
69. C₅₃×#431	C₂²	semidirect
70. C₂×#106×C₅₃	C₂²	semidirect
71. C₂×#103×C₅₃	C₂²	semidirect
73. C₂×C₄×C₈×C₅₃	C₂²	semidirect
170. #41×C₅₃	SD₁₆	direct (N × H)
205. SD₁₆×C₅₃	#41	direct (N × H)
256. Q₈×C₅₃	C₂×SD₁₆	semidirect
257. Q₈×C₅₃	C₂×#41	semidirect
265. D₄×C₅₃	C₂×SD₁₆	semidirect
283. C₂×C₄×C₅₃	C₂×SD₁₆	semidirect
293. C₈×C₅₃	C₂×#41	semidirect
294. SD₁₆×#41	C₅₃	direct (N × H)
319. Q₈×#41	C₂×C₅₃	semidirect
321. #3392	C₂×C₅₃	semidirect
322. Q₈×SD₁₆	C₂×C₅₃	semidirect
323. #3362	C₂×C₅₃	semidirect
324. #3359	C₂×C₅₃	semidirect
325. #3335	C₂×C₅₃	semidirect
326. #3298	C₂×C₅₃	semidirect
327. #3295	C₂×C₅₃	semidirect
328. D₄×SD₁₆	C₂×C₅₃	semidirect
329. #3167	C₂×C₅₃	semidirect
330. #3103	C₂×C₅₃	semidirect
331. #3101	C₂×C₅₃	semidirect
332. C₈×#41	C₂×C₅₃	semidirect
333. C₂×C₄×SD₁₆	C₂×C₅₃	semidirect
342. Q₈²	C₂²×C₅₃	semidirect
344. #557	C₂²×C₅₃	semidirect
346. #554	C₂²×C₅₃	semidirect
349. D₄×Q₈	C₂²×C₅₃	semidirect
355. #533	C₂²×C₅₃	semidirect
360. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
362. #498	C₂²×C₅₃	semidirect
363. #492	C₂²×C₅₃	semidirect
364. #487	C₂²×C₅₃	semidirect
365. #486	C₂²×C₅₃	semidirect
366. #483	C₂²×C₅₃	semidirect
367. #481	C₂²×C₅₃	semidirect
369. #476	C₂²×C₅₃	semidirect
370. #475	C₂²×C₅₃	semidirect
371. #475	C₂²×C₅₃	semidirect
372. #465	C₂²×C₅₃	semidirect
373. #465	C₂²×C₅₃	semidirect
375. #461	C₂²×C₅₃	semidirect
376. #460	C₂²×C₅₃	semidirect
377. #460	C₂²×C₅₃	semidirect
379. #448	C₂²×C₅₃	semidirect
380. C₈×Q₈	C₂²×C₅₃	semidirect
381. C₈×Q₈	C₂²×C₅₃	semidirect
386. C₄×SD₁₆	C₂²×C₅₃	semidirect
387. C₄×SD₁₆	C₂²×C₅₃	semidirect
388. C₄×SD₁₆	C₂²×C₅₃	semidirect
389. C₄×SD₁₆	C₂²×C₅₃	semidirect
390. C₄×SD₁₆	C₂²×C₅₃	semidirect
391. C₈×D₄	C₂²×C₅₃	semidirect
392. C₈×D₄	C₂²×C₅₃	semidirect
393. #431	C₂²×C₅₃	semidirect
394. C₂×#106	C₂²×C₅₃	semidirect
395. C₂×#103	C₂²×C₅₃	semidirect
397. C₂×C₄×C₈	C₂²×C₅₃	semidirect
398. C₅₃	SD₁₆×#41	direct (N × H)
495. #41	SD₁₆×C₅₃	direct (N × H)
530. SD₁₆	#41×C₅₃	direct (N × H)
581. Q₈	C₂×SD₁₆×C₅₃	semidirect
582. Q₈	C₂×#41×C₅₃	semidirect
590. D₄	C₂×SD₁₆×C₅₃	semidirect
608. C₂×C₄	C₂×SD₁₆×C₅₃	semidirect
618. C₈	C₂×#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41×C₅₃	2
D₄×#41×C₅₃	2
C₅₃×#3392	2
Q₈×SD₁₆×C₅₃	2
C₅₃×#3362	2
C₅₃×#3359	2
C₅₃×#3335	2
C₅₃×#3298	2
C₅₃×#3295	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3167	2
C₅₃×#3103	2
C₅₃×#3101	2
C₈×#41×C₅₃	2
C₂×C₄×SD₁₆×C₅₃	2
SD₁₆×#41	53

Subgroups — SD16×#41×C53 #27268938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×#41×C₅₃ #27268938