Subgroups — D₅₃⋊#1747 #28318035

Order 13568.

930 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811586	C₂	1	2	yes	maximal
2	#20290437	C₂	1	4	yes	maximal, complemented
3	#20290436	C₂	1	4	yes	maximal, complemented
4	D₅₃⋊#338	C₂	1	1	yes	maximal, characteristic
5	#20290387	C₂	1	1	yes	maximal, characteristic
6	#20290385	C₂	1	2	yes	maximal
7	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂×#13133296	C₂²	1	2	yes	—
10	#16811586	C₄	1	4	yes	complemented
11	#16811586	C₄	1	4	yes	complemented
12	#16811586	C₂²	1	4	yes	—
13	#16811586	C₂²	1	4	yes	—
14	C₂×#13133271	C₄	1	4	yes	complemented
15	C₂×C₈×#6157	C₄	1	4	yes	complemented
16	#16811492	C₂²	1	4	yes	—
17	#16811491	C₂²	1	4	yes	—
18	#16811490	C₂²	1	8	yes	—
19	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
20	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
21	#117×D₅₃	C₂²	1	1	yes	characteristic
22	#16810581	C₄	1	1	yes	characteristic, complemented
23	#16810580	C₂²	1	2	yes	—
24	#16810579	C₄	1	1	yes	characteristic, complemented
25	#16810578	C₄	1	1	yes	characteristic, complemented
26	#16810577	C₂²	1	2	yes	—
27	#97×D₅₃	C₄	1	2	yes	complemented
28	C₄×C₈×D₅₃	C₄	1	2	yes	complemented
29	C₅₃×#405	C₄	1	1	yes	characteristic, complemented
30	C₂×#11719936	—	2	2	no	—
31	D₅₃⋊M₁₆	—	2	2	no	—
32	D₅₃⋊M₁₆	—	2	2	no	—
33	D₅₃⋊M₁₆	C₂×C₄	1	4	yes	—
34	D₅₃⋊M₁₆	C₂³	1	4	yes	—
35	C₂×#11719940	—	2	2	no	—
36	C₂×D₅₃⋊C₈	C₂×C₄	1	4	yes	—
37	#13133296	—	2	2	no	—
38	#13133296	—	2	2	no	—
39	#13133296	C₂×C₄	1	4	yes	—
40	#13133296	C₂³	1	4	yes	—
41	C₂×C₄⋊#6157	—	2	2	no	—
42	C₂×C₂²⋊#6157	—	2	2	no	—
43	C₂×C₄×#6157	C₂×C₄	1	4	yes	—
44	#13133271	C₂×C₄	1	8	yes	complemented
45	#13133271	C₂×C₄	1	8	yes	complemented
46	C₈×#6157	C₂×C₄	1	8	yes	complemented
47	C₈×#6157	C₂×C₄	1	8	yes	complemented
48	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
49	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
50	C₂×#11719912	C₂³	1	2	yes	—
51	M₁₆×D₅₃	—	2	2	no	—
52	M₁₆×D₅₃	—	2	2	no	—
53	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
55	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
59	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
60	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
63	#13133176	C₂×C₄	1	1	yes	characteristic
64	#13133175	—	2	1	no	—
65	#13133174	C₂³	1	2	yes	—
66	#13133173	—	2	1	no	—
67	C₄⋊C₄×D₅₃	—	2	1	no	—
68	C₂²⋊C₄×D₅₃	—	2	1	no	—
69	C₄²×D₅₃	C₂×C₄	1	2	yes	—
70	#13133128	C₂×C₄	1	2	yes	complemented
71	#13133127	C₂×C₄	1	2	yes	complemented
72	#13133127	C₂×C₄	1	2	yes	complemented
73	C₄×#88322	C₂×C₄	1	2	yes	complemented
74	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
75	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
76	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
78	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
79	#97×C₅₃	C₂×C₄	1	2	yes	complemented
80	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
81	C₂³×D₅₃	#41	1	1	yes	characteristic
82	C₂²×#6157	—	2	4	no	—
83	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×Dic₅₃	#41	1	1	yes	characteristic
85	C₂×C₄×D₅₃	—	2	2	no	—
86	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
88	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
90	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
91	C₂×C₄×D₅₃	#41	1	2	yes	—
92	C₂×C₄×D₅₃	#41	1	2	yes	—
93	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
94	C₂²⋊#6157	—	2	4	no	—
95	C₂²⋊#6157	—	2	4	no	—
96	#11719940	—	2	4	no	—
97	#11719940	—	2	4	no	—
98	C₂×#88324	—	2	4	no	—
99	C₄⋊#6157	—	2	4	no	—
100	C₄⋊#6157	—	2	4	no	—
101	C₄×#6157	—	2	4	no	—
102	C₄×#6157	C₂²×C₄	1	8	yes	—
103	#11719936	—	2	4	no	—
104	#11719936	—	2	4	no	—
105	D₅₃⋊C₈	—	2	4	no	—
106	D₅₃⋊C₈	C₂²×C₄	1	8	yes	—
107	M₁₆×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	C₄²	1	2	yes	—
109	C₂×C₈×C₅₃	C₄²	1	2	yes	—
110	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₅₃	—	2	1	no	—
114	C₂²⋊C₄×C₅₃	—	2	1	no	—
115	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
116	C₂²⋊Dic₅₃	—	2	1	no	—
117	#11719921	—	2	2	no	—
118	C₄⋊Dic₅₃	—	2	1	no	—
119	#11719919	—	2	2	no	—
120	C₄×Dic₅₃	—	2	2	no	—
121	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
122	#11719917	—	2	2	no	—
123	C₂×#88322	C₄²	1	2	yes	—
124	C₂×#88322	C₄²	1	2	yes	—
125	C₂×#88322	C₂²×C₄	1	2	yes	—
126	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
127	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
128	#11719912	—	2	4	no	—
129	C₈×D₅₃	—	2	2	no	—
130	C₈×D₅₃	—	2	2	no	—
131	C₈×D₅₃	C₄²	1	1	yes	characteristic
132	C₈×D₅₃	C₄²	1	1	yes	characteristic
133	C₈×D₅₃	C₄²	1	2	yes	—
134	C₈×D₅₃	C₄²	1	2	yes	—
135	C₈×D₅₃	C₄²	1	1	yes	characteristic
136	C₈×D₅₃	C₄²	1	1	yes	characteristic
137	C₈×D₅₃	C₂²×C₄	1	2	yes	—
138	C₈×D₅₃	C₂²×C₄	1	2	yes	—
139	C₈×D₅₃	C₂²×C₄	1	2	yes	—
140	C₈×D₅₃	C₂²×C₄	1	2	yes	—
141	C₂³×C₅₃	#117	1	1	yes	characteristic
142	C₂²×D₅₃	—	4	2	no	—
143	C₂²×D₅₃	#117	1	2	yes	—
144	C₂²×D₅₃	#117	1	1	yes	characteristic
145	C₂²×D₅₃	#117	1	2	yes	—
146	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
147	C₂×#6157	—	2	8	no	—
148	C₂×#6157	—	4	8	no	—
149	C₂×C₄×C₅₃	—	2	2	no	—
150	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₅₃	#117	1	2	yes	—
152	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×Dic₅₃	—	2	2	no	—
155	C₂×Dic₅₃	#117	1	2	yes	—
156	C₂×Dic₅₃	#117	1	2	yes	—
157	C₂×Dic₅₃	#117	1	1	yes	characteristic
158	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
159	C₄×D₅₃	—	4	4	no	—
160	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
161	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
162	C₄×D₅₃	#117	1	2	yes	—
163	C₄×D₅₃	#117	1	2	yes	—
164	C₄×D₅₃	#117	1	1	yes	characteristic
165	C₄×D₅₃	#117	1	1	yes	characteristic
166	C₄×D₅₃	#117	1	2	yes	—
167	C₄×D₅₃	#117	1	2	yes	—
168	C₄×D₅₃	C₂³×C₄	1	2	yes	—
169	C₄×D₅₃	C₂×#41	1	2	yes	—
170	#88324	—	2	8	no	—
171	C₈×C₅₃	—	2	2	no	—
172	C₈×C₅₃	C₂×C₄²	1	2	yes	—
173	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
174	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
175	#88322	—	2	2	no	—
176	#88322	C₂×C₄²	1	1	yes	characteristic
177	#88322	C₂×C₄²	1	2	yes	—
178	#88322	C₂×C₄²	1	1	yes	characteristic
179	C₂×#1747	—	53	1	no	maximal, Sylow
180	C₂²×C₅₃	—	4	1	no	—
181	C₂²×C₅₃	#376	1	2	yes	—
182	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
183	C₂×D₅₃	—	2	2	no	—
184	C₂×D₅₃	—	2	4	no	—
185	C₂×D₅₃	—	4	2	no	—
186	C₂×D₅₃	—	4	1	no	—
187	C₂×D₅₃	#376	1	1	yes	characteristic
188	C₂×D₅₃	#376	1	1	yes	characteristic
189	C₂×D₅₃	C₂×#117	1	2	yes	—
190	#6157	—	4	8	no	—
191	C₄×C₅₃	—	4	2	no	—
192	C₄×C₅₃	#376	1	2	yes	—
193	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
194	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
195	Dic₅₃	—	4	2	no	—
196	Dic₅₃	#376	1	1	yes	characteristic
197	Dic₅₃	#376	1	1	yes	characteristic
198	Dic₅₃	C₂×#117	1	2	yes	—
199	C₂×#405	—	53	2	no	—
200	C₂×#405	—	53	1	no	—
201	#1747	—	53	4	no	—
202	#1747	—	53	4	no	—
203	C₂×#338	—	53	1	no	—
204	C₂×H(3,ℤ/4)	—	53	2	no	—
205	C₂×H(3,ℤ/4)	—	53	1	no	—
206	C₂×C₅₃	—	2	1	no	—
207	C₂×C₅₃	—	2	2	no	—
208	C₂×C₅₃	C₂×#376	1	1	yes	characteristic
209	D₅₃	—	2	2	no	—
210	D₅₃	—	2	1	no	—
211	D₅₃	#1747	1	2	yes	complemented
212	C₂²×M₁₆	—	53	2	no	—
213	C₂²×M₁₆	—	53	1	no	—
214	C₂³×C₈	—	53	1	no	—
215	C₂×#117	—	53	2	no	—
216	C₂×#117	—	53	1	no	—
217	#405	—	53	4	no	—
218	#405	—	53	4	no	—
219	#405	—	53	4	no	—
220	#405	—	53	4	no	—
221	#405	—	53	1	no	—
222	#405	—	53	1	no	—
223	#405	—	53	1	no	—
224	#405	—	53	2	no	—
225	#405	—	53	2	no	—
226	#405	#6157	1	1	yes	characteristic, complemented
227	C₂×#97	—	53	4	no	—
228	C₂×#97	—	53	2	no	—
229	C₂×C₄×C₈	—	53	4	no	—
230	C₂×C₄×C₈	—	53	2	no	—
231	#338	—	53	4	no	—
232	H(3,ℤ/4)	—	53	8	no	—
233	H(3,ℤ/4)	—	53	4	no	—
234	C₅₃	C₂×#1747	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₄	—	53	1	no	—
236	C₂×M₁₆	—	53	4	no	—
237	C₂×M₁₆	—	53	4	no	—
238	C₂×M₁₆	—	53	1	no	—
239	C₂×M₁₆	—	53	2	no	—
240	C₂×M₁₆	—	106	2	no	—
241	C₂×M₁₆	—	106	2	no	—
242	C₂×M₁₆	—	106	2	no	—
243	C₂×M₁₆	—	106	2	no	—
244	C₂×M₁₆	—	106	2	no	—
245	C₂×M₁₆	—	106	2	no	—
246	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
247	C₂²×C₈	—	53	1	no	—
248	C₂²×C₈	—	53	2	no	—
249	C₂²×C₈	—	53	2	no	—
250	C₂²×C₈	—	53	2	no	—
251	C₂²×C₈	—	53	2	no	—
252	C₂²×C₈	—	53	1	no	—
253	C₂²×C₈	—	53	1	no	—
254	C₂²×C₈	—	53	1	no	—
255	C₂²×C₈	—	53	1	no	—
256	C₂²×C₈	—	53	4	no	—
257	C₂²×C₈	—	53	2	no	—
258	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
259	#117	—	53	4	no	—
260	#117	—	53	4	no	—
261	#117	—	53	1	no	—
262	#117	—	53	2	no	—
263	#117	—	106	1	no	—
264	#117	—	106	1	no	—
265	#117	—	106	2	no	—
266	#117	—	106	2	no	—
267	#117	C₂×#6157	1	1	yes	characteristic
268	C₂×C₄⋊C₄	—	106	1	no	—
269	C₂×C₄⋊C₄	—	106	2	no	—
270	C₂×C₂²⋊C₄	—	106	1	no	—
271	C₂×C₂²⋊C₄	—	106	2	no	—
272	C₂×C₄²	—	53	4	no	—
273	C₂×C₄²	—	53	2	no	—
274	#97	—	53	8	no	—
275	#97	—	53	8	no	—
276	#97	—	53	2	no	—
277	#97	—	53	2	no	—
278	#97	—	53	2	no	—
279	#97	C₂×#6157	1	2	yes	complemented
280	C₄×C₈	—	53	8	no	—
281	C₄×C₈	—	53	8	no	—
282	C₄×C₈	—	53	2	no	—
283	C₄×C₈	—	53	2	no	—
284	C₄×C₈	—	53	2	no	—
285	C₄×C₈	C₂×#6157	1	2	yes	complemented
286	C₂⁴	—	53	1	no	—
287	C₂²×C₄	—	53	1	no	—
288	C₂²×C₄	—	53	2	no	—
289	C₂²×C₄	—	53	2	no	—
290	C₂²×C₄	—	53	2	no	—
291	C₂²×C₄	—	53	1	no	—
292	C₂²×C₄	—	53	1	no	—
293	C₂²×C₄	—	53	2	no	—
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	1	no	—
296	C₂²×C₄	—	106	2	no	—
297	C₂²×C₄	—	106	4	no	—
298	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
299	M₁₆	—	2	2	no	—
300	M₁₆	—	106	4	no	—
301	M₁₆	—	106	4	no	—
302	M₁₆	—	106	4	no	—
303	M₁₆	—	106	4	no	—
304	M₁₆	—	106	4	no	—
305	M₁₆	—	106	2	no	—
306	C₂×C₈	—	53	2	no	—
307	C₂×C₈	—	53	2	no	—
308	C₂×C₈	—	53	1	no	—
309	C₂×C₈	—	53	1	no	—
310	C₂×C₈	—	53	2	no	—
311	C₂×C₈	—	53	2	no	—
312	C₂×C₈	—	53	2	no	—
313	C₂×C₈	—	53	2	no	—
314	C₂×C₈	—	53	1	no	—
315	C₂×C₈	—	53	1	no	—
316	C₂×C₈	—	53	2	no	—
317	C₂×C₈	—	53	2	no	—
318	C₂×C₈	—	53	1	no	—
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	53	8	no	—
321	C₂×C₈	—	53	2	no	—
322	C₂×C₈	—	106	2	no	—
323	C₂×C₈	—	106	2	no	—
324	C₂×C₈	—	106	4	no	—
325	C₂×C₈	—	106	4	no	—
326	C₂×C₈	C₄×#6157	1	2	yes	—
327	C₂×C₈	C₄×#6157	1	2	yes	—
328	C₂×C₈	C₂²×#6157	1	2	yes	—
329	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
330	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	106	2	no	—
333	C₄⋊C₄	—	106	4	no	—
334	C₄⋊C₄	—	106	4	no	—
335	C₄⋊C₄	—	106	1	no	—
336	C₂²⋊C₄	—	2	1	no	—
337	C₂²⋊C₄	—	106	2	no	—
338	C₂²⋊C₄	—	106	4	no	—
339	C₂²⋊C₄	—	106	4	no	—
340	C₂²⋊C₄	—	106	1	no	—
341	C₄²	—	53	8	no	—
342	C₄²	—	53	2	no	—
343	C₄²	—	106	2	no	—
344	C₄²	—	106	4	no	—
345	C₄²	C₂²×#6157	1	2	yes	—
346	C₂³	—	53	2	no	—
347	C₂³	—	53	1	no	—
348	C₂³	—	53	2	no	—
349	C₂³	—	53	1	no	—
350	C₂³	—	212	2	no	—
351	C₂³	#13133296	1	1	yes	characteristic
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	53	2	no	—
354	C₂×C₄	—	53	2	no	—
355	C₂×C₄	—	53	1	no	—
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	53	2	no	—
358	C₂×C₄	—	53	2	no	—
359	C₂×C₄	—	53	2	no	—
360	C₂×C₄	—	53	2	no	—
361	C₂×C₄	—	53	1	no	—
362	C₂×C₄	—	53	1	no	—
363	C₂×C₄	—	53	2	no	—
364	C₂×C₄	—	53	1	no	—
365	C₂×C₄	—	53	1	no	—
366	C₂×C₄	—	53	2	no	—
367	C₂×C₄	—	106	8	no	—
368	C₂×C₄	—	106	2	no	—
369	C₂×C₄	—	212	4	no	—
370	C₂×C₄	—	212	8	no	—
371	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
372	C₂×C₄	#13133296	1	1	yes	characteristic
373	C₂×C₄	#13133296	1	2	yes	—
374	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	53	1	no	—
377	C₈	—	53	1	no	—
378	C₈	—	53	2	no	—
379	C₈	—	106	8	no	—
380	C₈	—	106	2	no	—
381	C₈	C₂×C₄×#6157	1	2	yes	—
382	C₈	C₂×C₄×#6157	1	1	yes	characteristic
383	C₈	C₂×C₄×#6157	1	1	yes	characteristic
384	C₂²	—	4	1	no	—
385	C₂²	—	53	1	no	—
386	C₂²	—	53	2	no	—
387	C₂²	—	53	1	no	—
388	C₂²	—	106	2	no	—
389	C₂²	—	106	4	no	—
390	C₂²	—	212	1	no	—
391	C₂²	—	212	2	no	—
392	C₂²	#16811559	1	2	yes	—
393	C₂²	C₂×#13133296	1	1	yes	characteristic
394	C₄	—	4	2	no	—
395	C₄	—	53	2	no	—
396	C₄	—	53	1	no	—
397	C₄	—	53	1	no	—
398	C₄	—	212	2	no	—
399	C₄	—	212	8	no	—
400	C₄	#16811559	1	2	yes	—
401	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
402	C₄	C₂×#13133296	1	1	yes	characteristic
403	C₂	—	2	1	no	—
404	C₂	—	2	2	no	—
405	C₂	—	53	2	no	—
406	C₂	—	106	2	no	—
407	C₂	—	106	1	no	—
408	C₂	C₂×#16811559	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×C₄×#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₅₃×#405	C₄
socle	C₂×C₅₃	C₂×#376
prime radical	C₂³×D₅₃	#41
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	C₂×#1747
LCS	G ▷ C₄×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #20290437	C₂	semidirect
3. #20290436	C₂	semidirect
10. #16811586	C₄	semidirect
11. #16811586	C₄	semidirect
14. C₂×#13133271	C₄	semidirect
15. C₂×C₈×#6157	C₄	semidirect
22. #16810581	C₄	semidirect
24. #16810579	C₄	semidirect
25. #16810578	C₄	semidirect
27. #97×D₅₃	C₄	semidirect
28. C₄×C₈×D₅₃	C₄	semidirect
29. C₅₃×#405	C₄	semidirect
44. #13133271	C₂×C₄	semidirect
45. #13133271	C₂×C₄	semidirect
46. C₈×#6157	C₂×C₄	semidirect
47. C₈×#6157	C₂×C₄	semidirect
70. #13133128	C₂×C₄	semidirect
71. #13133127	C₂×C₄	semidirect
72. #13133127	C₂×C₄	semidirect
73. C₄×#88322	C₂×C₄	semidirect
74. C₈×Dic₅₃	C₂×C₄	semidirect
75. C₈×Dic₅₃	C₂×C₄	semidirect
79. #97×C₅₃	C₂×C₄	semidirect
80. C₄×C₈×C₅₃	C₂×C₄	semidirect
211. D₅₃	#1747	semidirect
226. #405	#6157	semidirect
234. C₅₃	C₂×#1747	semidirect
279. #97	C₂×#6157	semidirect
285. C₄×C₈	C₂×#6157	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811586	2
#20290437	2
#20290436	2
D₅₃⋊#338	2
#20290387	2
#20290385	2
#405×D₅₃	2
C₂×#1747	53

Subgroups — D53⋊#1747 #28318035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃⋊#1747 #28318035