Subgroups — #27536730

Order 13568.

826 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133156	C₂	1	1	yes	maximal, characteristic
2	C₂×M₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20276314	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276313	C₂	1	2	yes	maximal, complemented
6	#20276312	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276311	C₂	1	1	yes	maximal, characteristic, complemented
8	#20276310	C₂	1	2	yes	maximal, complemented
9	#20276308	C₂	1	2	yes	maximal, complemented
10	C₄×#13133156	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
14	#117×D₅₃	C₄	1	1	yes	characteristic
15	C₂×#13133157	C₂²	1	1	yes	characteristic
16	C₂×#13133156	C₄	1	8	yes	complemented
17	C₂×#13133156	C₂²	1	2	yes	—
18	C₂×#13133156	C₂²	1	1	yes	characteristic
19	C₂×#13133156	C₂²	1	1	yes	characteristic
20	C₂×#13133156	C₂²	1	1	yes	characteristic
21	C₂×#13133156	C₂²	1	1	yes	characteristic
22	M₃₂×D₅₃	C₄	1	8	yes	complemented
23	C₂²×#11719908	C₂²	1	1	yes	characteristic
24	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
25	#16810581	C₄	1	1	yes	characteristic
26	#16810580	C₄	1	2	yes	—
27	#16810579	C₄	1	1	yes	characteristic
28	#16810578	C₂²	1	1	yes	characteristic
29	#16810577	C₂²	1	2	yes	—
30	#97×D₅₃	C₄	1	2	yes	—
31	C₄×C₈×D₅₃	C₂²	1	2	yes	—
32	#16810399	C₂²	1	2	yes	complemented
33	#16810398	C₂²	1	2	yes	complemented
34	#16810398	C₂²	1	2	yes	complemented
35	C₄×#11719908	C₂²	1	2	yes	complemented
36	C₁₆×Dic₅₃	C₂²	1	2	yes	complemented
37	C₁₆×Dic₅₃	C₂²	1	2	yes	complemented
38	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#405	C₂²	1	1	yes	characteristic
41	C₅₃×#346	C₂²	1	2	yes	complemented
42	C₄×C₁₆×C₅₃	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
45	C₂×#11719912	C₂×C₄	1	2	yes	—
46	M₁₆×D₅₃	C₈	1	8	yes	—
47	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
49	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
50	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
55	#13133176	C₂×C₄	1	1	yes	characteristic
56	#13133175	C₈	1	2	yes	—
57	#13133174	C₂×C₄	1	2	yes	—
58	#13133173	C₈	1	2	yes	—
59	C₄⋊C₄×D₅₃	C₈	1	2	yes	—
60	C₂²⋊C₄×D₅₃	C₈	1	2	yes	—
61	C₄²×D₅₃	C₂×C₄	1	2	yes	—
62	#13133157	C₂×C₄	1	4	yes	complemented
63	#13133156	C₂×C₄	1	8	yes	—
64	#13133156	C₂×C₄	1	4	yes	—
65	#13133156	C₂×C₄	1	4	yes	—
66	#13133156	C₂×C₄	1	4	yes	complemented
67	#13133156	C₂×C₄	1	4	yes	complemented
68	C₂×#11719908	C₂×C₄	1	4	yes	complemented
69	C₂×#11719908	C₂³	1	2	yes	—
70	C₂×#11719908	C₂³	1	1	yes	characteristic
71	C₂×#11719908	C₂³	1	1	yes	characteristic
72	C₁₆×D₅₃	C₂×C₄	1	8	yes	complemented
73	#13133128	C₂×C₄	1	2	yes	—
74	#13133127	C₂×C₄	1	2	yes	—
75	#13133127	C₂×C₄	1	2	yes	—
76	C₄×#88322	C₂×C₄	1	2	yes	—
77	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
78	C₈×Dic₅₃	C₂³	1	2	yes	—
79	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
81	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
82	M₃₂×C₅₃	C₂×C₄	1	4	yes	complemented
83	C₂×C₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
84	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
87	#97×C₅₃	C₂×C₄	1	2	yes	—
88	C₄×C₈×C₅₃	C₂³	1	2	yes	—
89	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₄²	1	4	yes	—
93	C₂×C₄×D₅₃	C₂×C₈	1	4	yes	—
94	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂×C₈	1	4	yes	—
97	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
99	M₁₆×C₅₃	C₂×C₈	1	4	yes	—
100	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₅₃	C₂×C₈	1	2	yes	—
106	C₂²⋊C₄×C₅₃	C₂×C₈	1	2	yes	—
107	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
108	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
109	#11719921	C₂×C₈	1	4	yes	—
110	C₄⋊Dic₅₃	C₂×C₈	1	2	yes	—
111	#11719919	C₂×C₈	1	4	yes	—
112	C₄×Dic₅₃	C₂×C₈	1	4	yes	—
113	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
114	#11719917	C₂×C₈	1	4	yes	—
115	C₂×#88322	C₄²	1	4	yes	—
116	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
117	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
118	C₂×#88322	C₂²×C₄	1	2	yes	—
119	#11719912	C₂×C₈	1	8	yes	—
120	C₈×D₅₃	C₄²	1	4	yes	—
121	C₈×D₅₃	C₄²	1	4	yes	—
122	C₈×D₅₃	C₂×C₈	1	8	yes	—
123	C₈×D₅₃	C₂²×C₄	1	2	yes	—
124	C₈×D₅₃	C₂²×C₄	1	2	yes	—
125	C₈×D₅₃	C₂²×C₄	1	2	yes	—
126	C₈×D₅₃	C₂²×C₄	1	2	yes	—
127	C₁₆×C₅₃	C₂²×C₄	1	2	yes	—
128	C₁₆×C₅₃	C₂²×C₄	1	2	yes	—
129	C₁₆×C₅₃	C₂²×C₄	1	4	yes	—
130	#11719908	C₂²×C₄	1	4	yes	—
131	#11719908	C₂²×C₄	1	2	yes	—
132	#11719908	C₂²×C₄	1	2	yes	—
133	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₅₃	—	4	2	no	—
135	C₂²×D₅₃	C₄×C₈	1	4	yes	—
136	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
137	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₅₃	C₂²×C₈	1	4	yes	—
140	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×Dic₅₃	C₄×C₈	1	4	yes	—
144	C₂×Dic₅₃	C₂²×C₈	1	4	yes	—
145	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
147	C₄×D₅₃	—	4	4	no	—
148	C₄×D₅₃	C₄×C₈	1	4	yes	—
149	C₄×D₅₃	C₄×C₈	1	4	yes	—
150	C₄×D₅₃	C₂×C₄²	1	2	yes	—
151	C₄×D₅₃	C₂×C₄²	1	2	yes	—
152	C₄×D₅₃	C₂²×C₈	1	2	yes	—
153	C₄×D₅₃	C₂²×C₈	1	2	yes	—
154	C₈×C₅₃	C₂×C₄²	1	2	yes	—
155	C₈×C₅₃	C₂²×C₈	1	4	yes	—
156	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
157	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
158	#88322	C₂×C₄²	1	2	yes	—
159	#88322	C₂×C₄²	1	2	yes	—
160	#88322	C₂²×C₈	1	4	yes	—
161	#33324	—	53	1	no	maximal, Sylow
162	C₂²×C₅₃	—	2	2	no	—
163	C₂²×C₅₃	C₂×C₄×C₈	1	2	yes	—
164	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
165	C₂×D₅₃	—	2	2	no	—
166	C₂×D₅₃	—	2	2	no	—
167	C₂×D₅₃	—	4	4	no	—
168	C₂×D₅₃	C₂×C₄×C₈	1	2	yes	—
169	C₂×D₅₃	C₂×C₄×C₈	1	2	yes	—
170	C₄×C₅₃	—	2	4	no	—
171	C₄×C₅₃	C₂×C₄×C₈	1	2	yes	—
172	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
173	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
174	Dic₅₃	—	2	4	no	—
175	Dic₅₃	C₂×C₄×C₈	1	2	yes	—
176	Dic₅₃	C₂×C₄×C₈	1	2	yes	—
177	C₂²×M₃₂	—	53	1	no	—
178	C₂²×M₃₂	—	53	1	no	—
179	C₂×#405	—	53	1	no	—
180	#2108	—	53	1	no	—
181	#2108	—	53	1	no	—
182	#2108	—	53	1	no	—
183	#2108	—	53	2	no	—
184	#2108	—	53	2	no	—
185	#2108	D₅₃	1	1	yes	characteristic, complemented
186	C₄×M₃₂	—	53	2	no	—
187	C₄×M₃₂	—	53	2	no	—
188	C₂×C₅₃	—	2	2	no	—
189	C₂×C₅₃	C₂²×C₄×C₈	1	1	yes	characteristic
190	C₂×C₅₃	#3407	1	2	yes	—
191	D₅₃	—	2	2	no	—
192	D₅₃	—	2	2	no	—
193	C₂²×M₁₆	—	53	1	no	—
194	C₂³×C₈	—	53	1	no	—
195	C₂×#117	—	53	1	no	—
196	C₂×M₃₂	—	53	1	no	—
197	C₂×M₃₂	—	53	8	no	—
198	C₂×M₃₂	—	53	8	no	—
199	C₂×M₃₂	—	53	1	no	—
200	C₂×M₃₂	—	53	2	no	—
201	C₂×M₃₂	—	53	1	no	—
202	C₂×M₃₂	—	53	1	no	—
203	C₂×M₃₂	—	53	1	no	—
204	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
205	C₂²×C₁₆	—	53	1	no	—
206	C₂²×C₁₆	—	53	2	no	—
207	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
208	#405	—	53	1	no	—
209	#405	—	53	1	no	—
210	#405	—	53	1	no	—
211	#405	—	53	2	no	—
212	#405	—	53	2	no	—
213	#405	C₂×D₅₃	1	1	yes	characteristic
214	C₂×#97	—	53	2	no	—
215	C₂×C₄×C₈	—	53	2	no	—
216	#346	—	53	2	no	—
217	#346	—	53	2	no	—
218	#346	—	53	2	no	—
219	#346	C₂×D₅₃	1	2	yes	complemented
220	C₄×C₁₆	—	53	2	no	—
221	C₄×C₁₆	—	53	2	no	—
222	C₄×C₁₆	—	53	2	no	—
223	C₄×C₁₆	C₂×D₅₃	1	2	yes	complemented
224	C₅₃	#33324	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₄	—	53	1	no	—
226	C₂×M₁₆	—	53	1	no	—
227	C₂×M₁₆	—	53	8	no	—
228	C₂×M₁₆	—	53	2	no	—
229	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
230	C₂²×C₈	—	53	1	no	—
231	C₂²×C₈	—	53	1	no	—
232	C₂²×C₈	—	53	1	no	—
233	C₂²×C₈	—	53	4	no	—
234	C₂²×C₈	—	53	4	no	—
235	C₂²×C₈	—	53	2	no	—
236	C₂²×C₈	—	53	1	no	—
237	C₂²×C₈	—	53	1	no	—
238	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
239	#117	—	53	1	no	—
240	#117	—	53	2	no	—
241	#117	—	53	2	no	—
242	#117	—	53	2	no	—
243	#117	C₄×D₅₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	53	2	no	—
245	C₂×C₂²⋊C₄	—	53	2	no	—
246	C₂×C₄²	—	53	2	no	—
247	M₃₂	—	53	4	no	—
248	M₃₂	—	53	8	no	—
249	M₃₂	—	53	4	no	—
250	M₃₂	—	53	4	no	—
251	M₃₂	—	53	4	no	—
252	M₃₂	—	53	4	no	—
253	M₃₂	C₄×D₅₃	1	4	yes	complemented
254	C₂×C₁₆	—	53	4	no	—
255	C₂×C₁₆	—	53	1	no	—
256	C₂×C₁₆	—	53	2	no	—
257	C₂×C₁₆	—	53	1	no	—
258	C₂×C₁₆	—	53	8	no	—
259	C₂×C₁₆	C₄×D₅₃	1	4	yes	complemented
260	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
261	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
262	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
263	#97	—	53	2	no	—
264	#97	—	53	2	no	—
265	#97	—	53	2	no	—
266	#97	C₄×D₅₃	1	2	yes	—
267	C₄×C₈	—	53	2	no	—
268	C₄×C₈	—	53	2	no	—
269	C₄×C₈	—	53	2	no	—
270	C₄×C₈	C₂²×D₅₃	1	2	yes	—
271	C₂⁴	—	53	1	no	—
272	C₂²×C₄	—	53	1	no	—
273	C₂²×C₄	—	53	4	no	—
274	C₂²×C₄	—	53	1	no	—
275	C₂²×C₄	—	53	1	no	—
276	C₂²×C₄	—	53	4	no	—
277	C₂²×C₄	—	53	1	no	—
278	C₂²×C₄	—	53	1	no	—
279	C₂²×C₄	—	53	4	no	—
280	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
281	M₁₆	—	53	4	no	—
282	M₁₆	—	53	8	no	—
283	M₁₆	C₈×D₅₃	1	4	yes	—
284	C₂×C₈	—	53	4	no	—
285	C₂×C₈	—	53	1	no	—
286	C₂×C₈	—	53	2	no	—
287	C₂×C₈	—	53	1	no	—
288	C₂×C₈	—	53	4	no	—
289	C₂×C₈	—	53	4	no	—
290	C₂×C₈	—	53	8	no	—
291	C₂×C₈	—	53	2	no	—
292	C₂×C₈	—	53	2	no	—
293	C₂×C₈	—	53	2	no	—
294	C₂×C₈	—	53	2	no	—
295	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
296	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
297	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
298	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
299	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
300	C₄⋊C₄	—	53	4	no	—
301	C₄⋊C₄	—	53	2	no	—
302	C₄⋊C₄	C₈×D₅₃	1	2	yes	—
303	C₂²⋊C₄	—	53	2	no	—
304	C₂²⋊C₄	—	53	4	no	—
305	C₂²⋊C₄	C₈×D₅₃	1	2	yes	—
306	C₄²	—	53	4	no	—
307	C₄²	—	53	2	no	—
308	C₄²	C₂×C₄×D₅₃	1	2	yes	—
309	C₁₆	—	53	2	no	—
310	C₁₆	—	53	2	no	—
311	C₁₆	—	53	4	no	—
312	C₁₆	C₂×C₄×D₅₃	1	4	yes	—
313	C₁₆	C₂×C₄×D₅₃	1	2	yes	—
314	C₁₆	C₂×C₄×D₅₃	1	2	yes	—
315	C₂³	—	53	1	no	—
316	C₂³	—	53	1	no	—
317	C₂³	—	53	4	no	—
318	C₂³	—	212	2	no	—
319	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
320	C₂×C₄	—	53	4	no	—
321	C₂×C₄	—	53	1	no	—
322	C₂×C₄	—	53	1	no	—
323	C₂×C₄	—	53	2	no	—
324	C₂×C₄	—	53	2	no	—
325	C₂×C₄	—	53	4	no	—
326	C₂×C₄	—	53	4	no	—
327	C₂×C₄	—	53	2	no	—
328	C₂×C₄	—	53	2	no	—
329	C₂×C₄	—	53	4	no	—
330	C₂×C₄	—	212	4	no	—
331	C₂×C₄	C₄²×D₅₃	1	2	yes	—
332	C₂×C₄	C₂×C₈×D₅₃	1	4	yes	—
333	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
335	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
336	C₈	—	53	2	no	—
337	C₈	—	53	2	no	—
338	C₈	—	53	4	no	—
339	C₈	C₄²×D₅₃	1	2	yes	—
340	C₈	C₂×C₈×D₅₃	1	4	yes	—
341	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
342	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
343	C₂²	—	2	2	no	—
344	C₂²	—	53	2	no	—
345	C₂²	—	53	2	no	—
346	C₂²	—	106	2	no	—
347	C₂²	—	106	2	no	—
348	C₂²	—	212	4	no	—
349	C₂²	C₄×C₈×D₅₃	1	2	yes	—
350	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	53	2	no	—
353	C₄	—	53	2	no	—
354	C₄	—	106	4	no	—
355	C₄	C₄×C₈×D₅₃	1	2	yes	—
356	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
357	C₄	C₂²×C₈×D₅₃	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	106	2	no	—
360	C₂	—	106	2	no	—
361	C₂	C₂×C₄×C₈×D₅₃	1	1	yes	characteristic
362	C₂	#20287816	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₃
commutator	C₂×C₅₃	C₂²×C₄×C₈
Fitting	C₅₃×#2108	C₂
socle	C₂²×C₅₃	C₂³×C₈
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2108	D₅₃
hypocenter	C₅₃	#33324
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #2108

Complements

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

N	H ≅ G/N	type
4. #20276314	C₂	semidirect
5. #20276313	C₂	semidirect
6. #20276312	C₂	semidirect
7. #20276311	C₂	semidirect
8. #20276310	C₂	semidirect
9. #20276308	C₂	semidirect
10. C₄×#13133156	C₂	semidirect
11. C₅₃×#2108	C₂	semidirect
16. C₂×#13133156	C₄	semidirect
22. M₃₂×D₅₃	C₄	semidirect
32. #16810399	C₂²	semidirect
33. #16810398	C₂²	semidirect
34. #16810398	C₂²	semidirect
35. C₄×#11719908	C₂²	semidirect
36. C₁₆×Dic₅₃	C₂²	semidirect
37. C₁₆×Dic₅₃	C₂²	semidirect
41. C₅₃×#346	C₂²	semidirect
42. C₄×C₁₆×C₅₃	C₂²	semidirect
62. #13133157	C₂×C₄	semidirect
66. #13133156	C₂×C₄	semidirect
67. #13133156	C₂×C₄	semidirect
68. C₂×#11719908	C₂×C₄	semidirect
72. C₁₆×D₅₃	C₂×C₄	semidirect
82. M₃₂×C₅₃	C₂×C₄	semidirect
83. C₂×C₁₆×C₅₃	C₂×C₄	semidirect
185. #2108	D₅₃	semidirect
219. #346	C₂×D₅₃	semidirect
223. C₄×C₁₆	C₂×D₅₃	semidirect
224. C₅₃	#33324	semidirect
253. M₃₂	C₄×D₅₃	semidirect
259. C₂×C₁₆	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133156	2
C₂×M₃₂×D₅₃	2
#405×D₅₃	2
#20276314	2
#20276313	2
#20276312	2
#20276311	2
#20276310	2
#20276308	2
C₄×#13133156	2
C₅₃×#2108	2
#33324	53